**Notes on Numerical Fluid Mechanics and Multidisciplinary Design 146**

Nikolaus A. Adams · Wolfgang Schröder · Rolf Radespiel · Oskar J. Haidn · Thomas Sattelmayer · Christian Stemmer · Bernhard Weigand Editors

Future Space-Transport-System Components under High Thermal and Mechanical Loads

Results from the DFG Collaborative Research Center TRR40

## Notes on Numerical Fluid Mechanics and Multidisciplinary Design

Volume 146

## Founding Editor

Ernst Heinrich Hirschel, Zorneding, Germany

## Series Editor

Wolfgang Schröder, Aerodynamisches Institut, RWTH Aachen, Aachen, Germany

## Editorial Board

Bendiks Jan Boersma, Delft University of Technology, Delft, The Netherlands

Kozo Fujii, Institute of Space & Astronautical Science (ISAS), Sagamihara, Kanagawa, Japan

Werner Haase, Hohenbrunn, Germany

Michael A. Leschziner, Department of Aeronautics, Imperial College, London, UK

Jacques Periaux, Paris, France

Sergio Pirozzoli, Department of Mechanical and Aerospace Engineering, University of Rome 'La Sapienza', Roma, Italy

Arthur Rizzi, Department of Aeronautics, KTH Royal Institute of Technology, Stockholm, Sweden

Bernard Roux, Ecole Supérieure d'Ingénieurs de Marseille, Marseille CX 20, France

Yurii I. Shokin, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

## Managing Editor

Esther Mäteling, RWTH Aachen University, Aachen, Germany

Notes on Numerical Fluid Mechanics and Multidisciplinary Design publishes state-of-art methods (including high performance methods) for numerical fluid mechanics, numerical simulation and multidisciplinary design optimization. The series includes proceedings of specialized conferences and workshops, as well as relevant project reports and monographs.

More information about this series at http://www.springer.com/series/4629

Nikolaus A. Adams • Wolfgang Schröder • Rolf Radespiel • Oskar J. Haidn • Thomas Sattelmayer • Christian Stemmer • Bernhard Weigand Editors

# Future Space-Transport-System Components under High Thermal and Mechanical Loads

Results from the DFG Collaborative Research Center TRR40

Editors Nikolaus A. Adams LS für Aerodynamik & Strömungsmechanik Technische Universität München Munich, Bayern, Germany

Rolf Radespiel Institut für Strömungsmechanik Technische Universität Braunschweig Braunschweig, Germany

Thomas Sattelmayer Technische Universität München Munich, Bayern, Germany

Bernhard Weigand Institut für Thermodynamik der Luftund Raumfahrt University of Stuttgart Stuttgart, Baden-Württemberg, Germany Wolfgang Schröder LS für Strömungslehre und Aerodynamisches Institut RWTH Aachen University Aachen, Nordrhein-Westfalen, Germany

Oskar J. Haidn Technische Universität München Munich, Bayern, Germany

Christian Stemmer LS für Aerodynamik & Strömungsmechanik Technische Universität München Munich, Bayern, Germany

ISSN 1612-2909 ISSN 1860-0824 (electronic) Notes on Numerical Fluid Mechanics and Multidisciplinary Design ISBN 978-3-030-53846-0 ISBN 978-3-030-53847-7 (eBook) https://doi.org/10.1007/978-3-030-53847-7

© The Editor(s) (if applicable) and The Author(s) 2021. This book is an open access publication.

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## Preface

This book summarizes major achievements of the Collaborative Research Center Transregio 40 (TRR40) funded from July 2008 to June 2020 by the German Research Foundation (Deutsche Forschungsgemeinschaft DFG).

The TRR40 was the first DFG collaborative research center with teams from five universities (RWTH Aachen, Technical University Braunschweig, Technical University München, University of Armed Forces München and University of Stuttgart) in cooperation with the German Aerospace Center (DLR institutes in Braunschweig, Göttingen, Köln, Stuttgart and Lampoldshausen), and the industrial partner ArianeGroup in Ottobrunn, jointly working on fundamental space-transportation-system research. The key objectives of the SFB TRR40 were to increase the level of understanding of dominating phenomena in the propulsion systems of liquid propellant rocket engines and their integration into the transportation system, to improve current technologies, develop new solutions, and to prepare the scientific basis for future space transportation.

Throughout the three four-year funding periods, the program pursued five research focus areas to cover all aspects of thrust chamber assemblies: structural cooling, aft-body flows, combustion chamber, nozzle and thrust chamber assembly. Cross-sectional education activities for doctoral students such as graduate schools, modeling workshops and research summer programs, aiming at education and cooperation, supplemented the project-driven research activities. The overall scientific achievements enable new technologies with significant gains in efficiency and reliability of future propulsion systems and as such contribute to maintain the capability for an independent European access to space.

The members of the executive board endorse that the wealth of scientific and technological achievements constitutes a proof of excellence of the TRR40 collaborative research. The particular TRR40 structure facilitates the connection between fundamental research at universities and research institutions with technology development at industry and can be envisioned as a role-model for establishing future strategic research and development funding schemes in astronautics, following existing successful nation-wide programs in aeronautics.

Garching, Germany March 2020

Nikolaus A. Adams Speaker SFB TRR40

## Contents

#### Contents ix

## **Collaborative Research for Future Space Transportation Systems**

**Oskar J. Haidn, Nikolaus A. Adams, Rolf Radespiel, Thomas Sattelmayer, Wolfgang Schröder, Christian Stemmer, and Bernhard Weigand**

**Abstract** This chapter book summarizes the major achievements of the five topical focus areas, Structural Cooling, Aft-Body Flows, Combustion Chamber, Thrust Nozzle, and Thrust-Chamber Assembly of the Collaborative Research Center (Sonderforschungsbereich) Transregio 40. Obviously, only sample highlights of each of the more than twenty individual projects can be given here and thus the interested reader is invited to read their reports which again are only a summary of the entire achievements and much more information can be found in the referenced publications. The structural cooling focus area included results from experimental as well as numerical research on transpiration cooling of thrust chamber structures as well as film cooling supersonic nozzles. The topics of the aft-body flow group reached from studies of classical flow separation to interaction of rocket plumes with nozzle structures for sub-, trans-, and supersonic conditions both experimentally and numerically. Combustion instabilities, boundary layer heat transfer, injection, mixing and combustion under real gas conditions and in particular the investigation of the impact of trans-critical conditions on propellant jet disintegration and the behavior under trans-critical conditions were the subjects dealt with in the combustion chamber focus area. The thrust nozzle group worked on thermal barrier coatings and life prediction methods, investigated cooling channel flows and paid special attention to the clarification and description of fluid-structure-interaction phenomena I nozzle flows. The main emphasis of the focal area thrust-chamber assembly was combustion and heat

O. J. Haidn (B) · N. A. Adams · T. Sattelmayer · C. Stemmer

Technical University of Munich, Boltzmannstr. 15, 85748 Garching, Germany e-mail<EMAIL_ADDRESS>
R. Radespiel Technical University of Braunschweig, Hermann-Blenk-Str. 37, 38108 Braunschweig, Germany

W. Schröder RWTH Aachen University, Wüllnerstraße 5a, 52062 Aachen, Germany

B. Weigand University of Stuttgart, Pfaffenwaldring 31, 70550 Stuttgart, Germany

© The Author(s) 2021

N. A. Adams et al. (eds.), *Future Space-Transport-System Components under High Thermal and Mechanical Loads*, Notes on Numerical Fluid Mechanics and Multidisciplinary Design 146, https://doi.org/10.1007/978-3-030-53847-7\_1

transfer investigated in various model combustors, on dual-bell nozzle phenomena and on the definition and design of three demonstrations for which the individual projects have contributed according to their research field.

## **1 Introduction**

Independent access to space has since years been a prerequisite of European policy which required highly reliable and efficient propulsion technologies. In order to remain competitive, Germany, the key developer of combustion devices for liquid propellant rocket engines, initiated a research program more than a decade ago dedicated to increase the theoretical and technological knowledge base of future space-propulsion systems named:

#### **Technological Foundations for the Design of Thermally and Mechanically Highly Loaded Components of Future Space Transportation Systems**

The different topics tackled within were based on an assessment of the state-of-the-art of space-propulsion systems. The general findings were: First, the lack of comprehensive fundamental knowledge about design-driving phenomena which required expensive and time-consuming testing at sub- and full scale level of components and systems for any new development. Second, existing engineering design tools base on empirical relations which in order to compensate their uncertainties necessitate sufficient safety factors and result in experience-based posterior optimization procedures. Although the literature provides a lot of information about the different design driving phenomena, the degree of uncertainty and lack of detailed understanding of propellant injection, atomization and mixing, ignition, combustion and its instability, heat transfer and cooling and nozzle flows which define the complexity of liquid propellant rocket engines still exists [1–6]. At this point in time, more than 12 years after the start of the research program, the European space sector is faced with the challenge of *New Space*, where instead of mainly government-sponsored companies which develop and operate launch vehicles an ever increasing number of private start-ups are pushing aggressively into the market. Therefore, the need for new, knowledge-based methods and tools for component design and manufacturing techniques of propulsion technologies which have to be low-cost but still have to meet the requirements of reliability and performance has become even more challenging.

It doesn't surprise that limited resources within SFB TRR40 did not allow to tackle every aspect of cryogenic liquid-propellant thrust chambers in detail. Nevertheless, all major phenomena like propellant injection and mixing including trans-critical phase change thermodynamics, combustion and combustion instability, heat transfer and cooling in thrust chamber processes and nozzles, material and material failure description have been investigated both numerically and experimentally. The strong interdisciplinary character of the program required an appropriate topical structure to identify commonalities and missing links and to coordinate interaction and collaboration between the individual research projects within the following research areas:

In each of the three four year funding phases, the program has been focused on different aspects. In the first phase, the main emphasis was put on explorative research aiming at fundamental modeling, development of critical methods and tools and analyses of innovative concepts. The second phase has seen application-focused modeling activities and efforts towards consolidation of technologies, tools and innovations. The final funding phase, the majority of the projects aimed at the establishment of an integrated simulation environment, demonstration of technologies and on hardware demonstration. Hence, the TRR40 collaborative research center was a well-balanced program between fundamental and application oriented research.

## **2 Research Area A: Structural Cooling**

Effective cooling is essential for combustion chambers to keep wall temperatures below material limits. Therefore, the focus of this research area was on foundations and methods for thrust chamber and nozzle-extension cooling. One possible method to sustain such loads are actively cooled ceramic porous structures and combinations of film, transpiration and regenerative cooling. In addition to these subsonic cooling methods, film cooling of rocket nozzles at supersonic conditions were studied both experimentally and numerically. Furthermore, the impact of pressure pulsations on heat transfer and damping performance of resonators was investigated. The general aim of Research Area A was to contribute with models, tools and data to the design or design solutions of the structures for the demonstrator engines defined within Research Area K.

## *2.1 Transpiration Cooled Ceramic Structures*

Utilizing the beneficial properties of highly-conductive ceramics, such a combination could lead to a very effective cooling system for rocket combustion chambers. Multiscale modeling of transpiration cooling and in particular an appropriate description of the phenomena at the interface between the porous material and the hot gas flow with special emphasis on the coupling conditions has been at the focal point of project A1 (see König et al. in this volume). Interface conditions were designed to couple a hot gas flow, subsonic in a combustion chamber or supersonic in a nozzle, with a porous

**Fig. 1** Temperature distributions for a combined (transpiration, convective, film) cooling concept of a rocket combustion chamber throat area using the developed numerical framework with coupled domains. Relative changes in coolant pressure and temperature to regenerative cooled design (bottom right - Wp - transpiration cooled region, WS - film cooled region)

wall [7] and, more generally, the coupling of two hyperbolic systems in conservation form [8]. Material properties and manufacturing techniques yielded inhomogeneous coolant injection and thus these coupling conditions had to be modified accordingly. Since the modification does not model the interaction of the different scales resulting from the pore size at the surface and the transport of the flow, a more sophisticated approach has been developed based on up-scaling techniques [9]. The idea is to first solve a zeroth-order problem, e.g, a two-domain approach where the hot gas domain and the porous medium were solved alternately using the aforementioned coupling conditions. This information was used to solve cell problems on a micro-scale at the material interface between the hot gas and the porous medium. From the solution of the cell problem, effective coefficients were determined and incorporated into the boundary conditions. Finally, the hot gas flow was solved again using the effective boundary conditions to update the zeroth-order solution. Model reduction strategies have been employed to accelerate solving the numerous cell problems [10]. Figure 1 gives an overview of the flow states in the subsonic and supersonic region of a combustion chamber together with some modeling results.

Parallel to the modeling approach, project A5 (see Peichl et al. in this volume) aimed at the development of lightweight ceramic fiber composites due to their intrinsic favorable thermo-physical properties [11, 12]. The detailed experimental data enable the validation of novel numerical modelling approaches in close cooperation with project A1 including material specific flow conditions [8, 10]. Therefrom, numerical frameworks have been developed to support potential engineering designs in collaboration with project K2 (see Génin et al. in this volume) for rocket applications in combination with classical film and regenerative cooling [10]. All the results were transferred to the design of a Sub-scale Validation Experiment (SVE) with parameters close to applications to be investigated under pressurized hot gas conditions. Figure 2 shows on its left side exit velocities measured with a Pitot probe about 1 mm from the surface and on its right side surface temperatures from a simulation.

**Fig. 2** Measured exit velocities (left) Simulated surface temperatures (right)

**Fig. 3** Correlation of cooling efficiencies gained from experiments with different coolant gases (He, Ar, N2, CO2), different injection slot heights (s1 = 0.46mm, s2 = 0.41mm, s3 = 0.56mm) and different hot gas stagnation conditions (C1: p0 = 30 bar, T0 = 3660 K, C2: p0 = 40 bar, T0 = 3685 K, C3: p0 = 50 bar, T0 = 3730 K), over correlation factor ξ as developed by project A2, enhanced by the ratio of the heat capacities, red curve represents the newly derived correlation

## *2.2 Supersonic Film Cooling*

Project A2 (see Ludescher and Olivier in this volume) aimed at the experimental investigation of supersonic film cooling of a nozzle. Appropriate flow conditions have been provided by a detonation based short-duration facility and validated intensively [13]. A detailed parametric study revealed the impact of different coolant mass fluxes, injection slot heights, hot-gas stagnation conditions and coolant gases on the film cooling efficiency [14]. Based on this data, a new film cooling correlation was developed, see Fig. 3, which can be used as a preliminary design tool for real rocket nozzles. Investigations of the film cooling efficiency in the extension of a dual-bell nozzle indicated that a sharp-edge inflection geometry results in an improved efficiency downstream.

**Fig. 4** Snapshot of film-cooling flow field: Vortices colored by the temperature (blue – cold, red – hot), and mass fraction of the cool helium (yellow: 1, blue: zero) on the lower wall and the outlet plane. Flow from lower left

In parallel, project A4 (see Peter and Kloker in this volume), developed a framework to enable high-order direct numerical simulations of film cooling by tangential blowing through a backward-facing step to scrutinize the fundamental thermo-fluid dynamical physics of the cooling/mixing process. A cold laminar supersonic helium flow is fed at various blowing ratios by varying the coolant density into the hot, turbulent flow at Mach 3.3. The cooling effectiveness showed the expected better performance for higher density and thus mass flow rates, also because the laminar/turbulent transition of the film is delayed due to smaller turbulent structures; see Fig. 4 (blowing ratio of one) where transition to turbulence sets in downstream of the step (above the yellow colored wall). Initially, 2D structures (blue) appear near the step that undergo 3D deformation yielding turbulence with structures much finer than the ones in the oncoming hot-gas boundary layer (along the red-colored plane). Injecting a constant mass flow rate is more effective with a smaller slot height; and the coolant Mach number has no significant influence on the flow mixing, as well as the lip thickness. Cooling the wall upstream of the blowing leads to a significantly higher shear and thus to a stronger turbulence production in the free shear layer downstream of the step. Close to the injection slot, the cooling effectiveness therefore shows a reduction compared to an adiabatic upstream wall. Hence, the wall temperature of the oncoming boundary-layer needs to be incorporated for any comprehensive scaling formula used for designing the film cooling. Results of comparisons of tangential to wall-normal helium blowing can be found in [15, 16].

## *2.3 Damping Performance of Resonators*

Within project A3 (see van Buren and Polifke in this volume) an efficient numerical framework to assess resonator performance has been developed which combines

**Fig. 5** Local thermal diffusivity over the channel width for increasing Prandtl numbers (left to right). Laminar flows: blue and orange. Turbulent flow: yellow and purple

CFD with a form of supervised machine learning. The acoustic impedance of a resonator was estimated over a wide range of frequencies from time-series data generated in the presence of broad-band excitation. One interesting result was that for a given mean temperature, its spatial distribution within the resonator cavity will influence eigenfrequencies and effective damping of the resonator. The investigation of two fundamental configurations of heat transfer in an oscillating flow revealed that, first, acoustic pulsations enhance the wall-normal heat transfer and, second, if an oscillating resonator flow is characterized by thin hydrodynamic and thermal boundary layers, longitudinal heat transfer increases drastically [17]. Figure 5 physically interprets this finding: Turbulence increases the thermal penetration depth from the wall into the channel (non-dimensional width −1 ≤ η ≤ 1). Thus, a wider effective cross-sectional area contributes to the longitudinal thermal diffusivity κ*e*/ωω*x* 2.

## **3 Research Area B: Aft-Body Flows**

Turbulent aft-body flows of modern rockets exhibit complex aerodynamic interactions that can lead to significant buffet loads. Furthermore, thermal interactions also can be significant, as aft-body heating is caused by the combined effects of radiation and turbulent transport within a complex flow field. The design of future rocket transport vehicles therefore calls for a thorough understanding of fundamental flow phenomena at the aft-body and its sensitivities with respect to the non-dimensional flow parameters of the outer flow and the propulsive jet.

## *3.1 Nozzle Flow Separation Studies*

Project B6 (see Bolgar et al. in this volume) has contributed to the research area by providing fundamental experimental analyses in transonic and supersonic flow regimes. The experimental set up consisted of generic 2D representations of rocket aft-body flows in a tri-sonic wind tunnel. Sophisticated measurement techniques **Fig. 6** Correlation of wall pressure fluctuations at x/h = 7 and the vertical velocity component downstream of a backward-facing step at Ma<sup>∞</sup> = 0.8

comprised a range of advanced PIV approaches, PSP, and unsteady wall pressure measurements [18, 19]. Typical research findings for the dynamical flow behavior are shown in Fig. 6.

## *3.2 Interaction of Rocket Plume and External Flow*

The projects B4 and B1 (see Barklage and Radespiel and Kirchheck et al. in this volume) both dealt with research into the interactions of a propulsive jet in sub-, trans-, and supersonic outer flows. Axisymmetric aft-bodies with TIC and Dual-Bell contour nozzles were investigated in a unique propulsion simulation facility with a supersonic heated air co-flow and Helium jet flows in order to achieve representative velocity ratios were the main objective of project B4 [20]. The aerodynamic integration of

**Fig. 7** Pressure signal at the nozzle wall (left) and hysteresis behavior of the separation position inside the nozzle as calculated by LES

Dual Bell nozzles turned out as a particular challenge, as it employs two adaptive design points of operation, the sea-level and altitude modes. The research comprised measurements as well as RANS and LES [21]. Sensitivity studies revealed important effects of nozzle Reynolds number and the aft-body geometry on the transition behavior between the two operation modes. An unstable nozzle operation occurs for certain combinations of these parameters. This features an alternating switching between the two modes leading to high pressure fluctuations in the nozzle, as shown in Fig. 7. As a result, we now have indicators of this unstable mechanism and a parameter space where it occurs. Critical is the interaction with the external-flow shear layer. It was observed that for a reattaching outer flow along the nozzle fairing, unstable nozzle operation occurs while for a non-reattaching flow it does not.

Project B1 entirely focused on the experimental characterization of unsteady aerodynamic and thermal loads at the axisymmetric rocket base along the subsonic to transonic flight trajectory. For simulating the interactions of the hot propulsive jet, a completely new Hot Plume Testing Facility (HPTF) was established in the Vertical Wind Tunnel Cologne (VMK) which duplicated important hot-plume similarity parameters. Gaseous hydrogen and oxygen are fed into the combustion chamber inside the wind tunnel model, see Fig. 8. Unsteady aft-body flow phenomena are identified through high-frequency sensing at the model surface and optical flow-field measurement techniques. Pressure and temperature sensors are used to quantify pressure fluctuations and hot gas entrainment of the recirculating base flow. Non-intrusive optical measurements include high-speed Schlieren Imaging, PIV, and infrared thermography. Access to the measured data is provided by spectral analysis and modal decomposition methods, revealing the characteristic motions of the flow field, which are connected to dominating aerodynamic aft-body loads [24, 25].

**Fig. 8** PIV measurement during hot plume interaction test in the VMK

## *3.3 Modeling of Buffeting*

Interaction of mechanical and thermal loads on the nozzle structure were key objectives of projects B3 and B5 (see Loosen et al. and Schumann et al. in this volume, respectively). While B3 concentrated its effort on provision of fundamental knowledge on the origin of buffet loads acting on the nozzle, B5 focused on the flow physics of hot plumes and thermal loads. The B3 team employed high-fidelity scale-resolving simulations and developed flow control means to reduce dynamic loads. Therefore, a large number of configurations including planar geometries, wind-tunnel models with support struts, and axisymmetric flight configurations were analyzed at transonic and supersonic free-stream Mach numbers [22, 23]. The time-resolved numerical simulations of the flow fields were performed with a zonal RANS and LES approach. Extraction of dynamic flow modes yielded understanding of the complex interaction and superposition of periodic and quasi-stochastic flow phenomena responsible for buffet. Figure 9 displays the simulation concept, where RANS equations are solved for the boundary layers attached to the rocket forebody, while aft-body wake flows are represented by LES.

**Fig. 9** Instantaneous Mach number and pressure coefficient distribution around a generic configuration representing the flow physics of Ariane 5

The team of project B5 focused on the flow physics of hot plumes and hot walls using numerical simulation [26, 27]. For this purpose, the flow solver was coupled to a thermal structure solver to obtain realistic wall temperature distributions. Scaleresolving hybrid RANS-LES show a surprisingly strong impact of hot plume and hot walls on the aft-body flow. The reattachment of the turbulent shear layer is significantly delayed if a hot plume is present while the temperature in the recirculation region at the base of the launcher is increased. This affects the static pressure distribution along the nozzle fairing and the dynamic loads. While the forces acting on the nozzle structure are very similar for cold and hot plumes assuming cold walls, they change by around 20% due to the hot-wall impact. Figure 10 displays the heated turbulent structures at the base of the launcher as they re-attach to the nozzle fairing and interact with the hot plume.

## **4 Research Area C: Combustion Chamber**

The five projects of Research Area C mainly focused on reacting flows in thrust chambers of liquid-propellant rocket engines (LREs) since they have to operate reliably under extreme conditions, i.e. exceptionally high thermal, mechanical and vibrational loads. This is particularly true for the combustion chamber liner. Near the injector head, oxidizer may get in contact with the hot wall and high temperatures and pressures in combination with near sonic velocities and thin boundary layers imply extreme heat loads further downstream. The projects covered studies of propellant injection, turbulent mixing, combustion and heat release, gas-side heat transfer and thermo-acoustic stability. In addition, several novel simulation tools for these processes have been developed, which have significantly advanced the state-of-the-art in LRE modelling.

**Fig. 10** Free shear layer enclosing the recirculation region of the generic rocket base and the hot plume at transonic flow conditions in VMK

## *4.1 Dynamic Processes in Trans-Critical Jets*

Project C4 (see Föll et al. in this volume) provided a framework to perform jet disintegration experiments under well-defined conditions, in order to gain a better understanding of the physics at high pressures. This provides the starting point enabling the validation of the different thermodynamic models employed in other projects of the research area. Figure 11 schematically shows the different high-pressure disintegration regimes that were obtained by varying the injection temperature across the critical temperature of the fuel (i.e., 0.8 < *Tinj* /*Tc* < 1.2). As can be seen, the jet morphology varies drastically across the disintegration regimes and requires the development of accurate thermodynamic models capable of describing both non-equilibrium phase transitions and multi-component mixing processes in dense gases [28].

After the phenomenological classification of the disintegration regimes, the experimental activities were mainly focused on the acquisition of quantitative data to characterize the mixing process in high pressure super-critical jets. For this purpose, the applicability of Laser Induced Thermo Acoustics (LITA) was extended to high pressure turbulent jets. The LITA data show that the adiabatic mixing assumption, commonly employed in many solvers, loses its validity even at Reynolds numbers as high as 105, in presence of large temperature and concentration gradients. This required the development of more accurate models for the description of diffusive transport on the mixing process. The numerical and theoretical activities focused on the implementation and assessment of thermodynamic and phase transition models and aimed at providing an accurate description of the mixing process in trans-critical jets. For that purpose, a novel numerical framework based on a high order discontinu-

**Fig. 11** Schematic overview of the different disintegration regimes with increasing injection temperature

ous Galerkin approximation was developed by extending the open-source large eddy simulation code FLEXI to the multi-phase regime. High-order accuracy in combination with local refinement and robust shock-capturing allows high resolution of the multi-scale phenomena around the critical point. Real-gas effects are handled accurately and efficiently by means of adaptive tabulation techniques. The numerical modelling of the jet-mixing process turned out to be a difficult process that strongly depends on the numerical diffusion of the numerical simulation also. Therefore, a central aspect was to study different approaches to assess, which models adhere best to the experimental findings. The knowledge about the consistency between experimental data, thermodynamic theory and the prediction provides a prerequisite for the correct calculation of such processes in the framework of thrust-chamber flow computations.

## *4.2 Injection, Mixing and Combustion Under Real-Gas Conditions*

For the numerical investigation of injection, mixing and combustion under LRE conditions, a CFD tool has been developed within project C1 (see Traxinger et al. in this volume) which employs the open-source toolbox OpenFOAM [29]. The particular focus was on the thermodynamics of combustion modelling under high-pressure conditions (Fig. 12). For the accurate representation, a fully consistent framework based on a cubic equation of state was devised considering real-gas and phase separation effects [30]. Several combustion models have been implemented ranging from tabulated combustion models for real-gas and non-adiabatic conditions up to transported PDF approaches [31]. Applying this framework, different LES investigations have been conducted: For inert and reacting cases, detailed thermodynamic studies [30–32] showed the occurrence of single-phase instabilities. Under LRE-like conditions, this phase separation processes can be attributed to mixing, i.e., to the

**Fig. 12** Critical point and real gas effects on non-adiabatic reacting flow

thermodynamic behaviour of the multi-component system. For the investigation of the combustion process in LREs and the reliable prediction of wall-heat fluxes, a numerical simulations [33] of a multi-element combustion chamber has been conducted. The comparison with experimental data showed good agreement and wallmodeled LES together with a non-adiabatic tabulated combustion model has been deduced as a promising candidate for accurate, reliable and efficient numerical simulations. Thereby, heat losses and associated influences on the reaction kinetics can be considered. In conclusion, the developed CFD code is well-suited for the numerical investigation and reliable prediction of the injection and combustion process under LRE conditions.

## *4.3 Boundary Layer Heat Transfer Modelling*

The aim of project C6 (see Olmeda et al. in this volume) was to model wall heat transfer in LREs with high accuracy and to investigate the influence of wall films on cooling. OpenFoam [29] has been used to carry out the combustion simulations. Flamelet tables have been generated in a pre-processing phase taking into account the influence of non-adiabatic sources and turbulent fluctuations since the conventional adiabatic models are not able to capture the recombination phenomena in proximity of the cooled chamber walls. Large-Eddy Simulations with and without film cooling have been performed, achieving good agreement for the wall heat flux with the experimental data [34]. The heat flux is decreased by the cooling film, the full mixing of fuel and oxidizer is reached in the same position in the axial direction as for the

**Fig. 13** Temperature field at cross sections x=10, 20, 40, 80mm. Top: without film. Bottom: with film

non-cooled case. The injected film increases the chamber pressure after the inlet with respect to the non-cooled setup. The cooling film causes a drop of the flame thickness perpendicularly to the film direction. The cooling effect of the film ceases to be effective after half the length of the combustion chamber (Fig. 13).

The code CATUM [35] has been used to analyze the effect of wall roughness on the velocity and temperature fields, which causes an enhancement of the heat transfer at the wall. Different roughness models have been implemented and tested. The results have shown good agreement with the DNS data available [36], particularly considering the low transitionally rough regime.

## *4.4 Combustion Stability of Rocket Engines*

Projects C3 and C7 (see Chemnitz and Sattelmayer and Armbruster et al. in this volume, respectively) were focused on combustion instabilities. While C3 aimed at the numerical assessment of the stability of the reacting flow focusing on efficient models suitable for industrial design processes, C7 concentrated on establishing a data base on forced and intrinsic instabilities in a LOX/GH2 model rocket engine. To fulfill the demand for a lean tool, a hybrid approach relying on the linearized Euler Equations (LEE) was chosen. A quasi one-dimensional flow was used as reference state for the perturbation analysis to avoid the computationally cost-intensive resolution of the large number of diffusion flames typically present in combustion chambers of larger engines. As the combustor acoustics may be severely influenced by other thrust chamber components, these were included as well via frequency dependent boundary conditions. An approach to quantify the flame feedback from Flame Transfer Functions (FTF) obtained from single-flame simulations using source terms was

**Fig. 14** Numerical assessment of thermo-acoustic stability of LREs

later enlarged and combined with chamber acoustics to replace the LEE calculations in time domain by an eigenvalue analysis in frequency space [37, 38]. The approach was validated using the stability data from the C7 project.

Additionally, a procedure for calculating mean flow fields that are fully consistent with the Euler Equations has been introduced. Based on this approach, the impact of the diffusion flame structures in the chamber flow (see Fig. 14: Principles) on the acoustics has been studied [39]. The acoustic mode and the oscillation frequencies have been found to be insensitive to radial stratification. The associated damping rates changed stronger due to their dependence on the entropy and vorticity modes. The results were used for the adaption of the FTF calculation method. To further validate the single flame simulations, an efficient method for the calculation of OH\* radiation has been developed (see Fig. 14: Validation). For the acoustic characterization of the virtual thrust chamber demonstrators, the mean-flow calculation procedure was extended to account for the respective chamber geometry (see Fig. 14: Methodology). Based on previous studies on the impact of dampers on rocket engine acoustics [40], the relation between mode split and absorber characteristics was identified [41]. This allows to specify constraints for the absorber characteristics that can be used to design a damping device without explicitly re-evaluating the chamber acoustics.

The hot-fire tests were conducted at the P8 test bench. One combustor, BKD, runs with the cryogenic propellants LOX/H2 injected through 42 shear-coaxial injectors and operates at supercritical pressures for oxygen. Gröning was able to prove that self-excited combustion instabilities of the 1 T mode in the BKD are driven by injection-coupling through acoustic eigenmodes in the LOX injector [42]. This type of coupling mechanism is rather common for cryogenic rocket engines with coaxial injectors [2]. A water-cooled measurement ring including a small sapphire window was designed and installed in BKD. Simultaneous high-speed imaging of OH\* and also blue radiation (BR) was conducted with 60,000 FPS. Mean flame images for the operating condition of *pcc* ≈ 80 bar and ROF 5.3 are shown in Fig. 15. The thin shear layer originating from the injector exit is rapidly spreading along the reaction

**Fig. 15** Time-averaged OH\* image (left) and blue radiation image (middle), and reconstructed DMD mode at the injector resonance frequency (right). All images are in false colour

zone in downstream direction, as can be seen in the OH\* image (left) and in the BR image (middle) as well. The path of the LOX jet is visible in the BR image only.

The flame dynamics were investigated by Dynamic Mode Decomposition (DMD). The influence of the 1 L resonance in the LOX injector on the LOX jet is visualized on the right side in Fig. 15. Standing waves in the injectors lead to periodic variation of the injected LOX mass flow rate, producing wavy structures on the surface of the dense LOX jet. The symmetrical character of the LOX jet pulsation is consistent with a periodic variation in the rate of injection [43, 44]. Therefore, the LOX jet dynamics found in the experiments is in agreement with the LOX injector coupling mechanism hypothesized by Gröning [42]. Since such detailed flame visualization has not been achieved previously under representative conditions, this data will be of high value for the future validation of numerical simulations and predictive tools.

## **5 Research Area D: Thrust Nozzle**

Thrust nozzles are a highly critical and extremely loaded propulsion component of any space transportation system. Designed for the enormous thrust forces in the axial direction, they have to withstand radially, and temporally fluctuating loads as well. Moreover, the nozzles very often are the major means for thrust vector control. Due to its nominal load, the thrust nozzle is designed as a thin-wall structure. For primary propulsion systems, it consists of actively cooled metallic material more or less exclusively. The nozzle flow is determined by the flow state at the outlet of the combustion chamber which defines the outlet conditions and the downstream boundary conditions at the nozzle exit. The latter vary along the ascent trajectory and strongly interact with the unsteady base flow, i.e., the flow field near the aft face of the main body of the rocket. Especially during engine start-up and the early ascent phase, the internal nozzle flow is dominated by shock induced unsteady separations which result in pronounced fluctuating asymmetric radial pressure loads, so-called side loads, and local peaks in the heat load distribution. These local and tempo-

**Fig. 16** Fatigue Segment developed for Cyclic Life Determination

ral inhomogeneities which interact with the nozzle structure are the key drivers for thrust-nozzle design and thus were in the focus of Research Area D. The six projects of research area D dealt with the physical fundamentals and modeling of the mechanical and thermal fluid-structure interaction in the thrust nozzle. New concepts and methods were developed to master those fluid-structure interactions. The following discussion covers only an excerpt of the findings. A more thorough analysis of the results is given in the contribution of each project.

## *5.1 Thermal Barrier Coatings and Component Life Prediction*

Methods and models for nozzle lifetime prediction and measures to extend the overall lifetime of rocket engines were developed by considering the impact of thermal and mechanical loads. The tools comprising the thermo-mechanical material modelling, e.g., for metallic alloy and CMC material, and the fluid-structure interaction derived in project D3 (see Barfusz et al. in this volume) were validated on the basis of the sub-scale combustion chamber experiments performed in project D9 (see Hötte et al. in this volume). There, a fatigue segment, see Fig. 16, was placed sufficiently downstream in a GOX/GCH4 combustion chamber with rectangular cross section to guarantee fully developed hot gas conditions and as such allow for a proper determination of the cyclic life of such structures. The fatigue segment housed an actively cooled fatigue specimen made of CuCr1Zr and was equipped with an extensive measurement technique. The specimen was loaded cyclically and inspected regularly for deformations, roughness, and leakages.  The results showed that the height of the deformation profile increased nearly linearly with the number of load cycles until the cooling channel structure failed due to the so-called doghouse effect, see Fig. 17.

**Fig. 17** Comparison with experimental observations - deformed geometry and damage contour after 47 cycles obtained from simulation (top) and cut view of the fatigue experiment after 48 cycles showing a macroscopic crack in the center cooling channel (bottom)

While the slope of this deformation profile strongly depended on the thermal loads, i.e., temperature level and temperature gradients, the critical deformation which occurs in case of failure was not affected. For lifetime prediction, the temperature determined from the conjugate heat transfer (CHT) served as input for a series of quasi-static mechanical analyses, in which a newly developed visco-plastic damage model was utilized [45, 46]. During the numerical analysis of the deformation process, it was found that the damage initially spread diagonally from the cooling channel corner to the hot gas wall and eventually merged into a macroscopic failure zone. The comparison with the experiment, which is shown in Fig. 17, revealed that the number of cycles until failure, the position of maximum deformation and degradation, and the final failure mode, i.e., the doghouse effect, were accurately predicted by the simulation. To protect the copper liners of liquid-fuel rocket combustion chambers against the doghouse effect, a new metallic coating system was developed in project D2 (see Fiedler et al. in this volume), consisting of a NiCuCrAl bond-coat and a Rene 80 top-coat, and applied with high velocity oxyfuel spray (HVOF). The coatings were tested in laser-cycling experiments to investigate their performance under large heat-fluxes and thermo-shock loading. FEM simulations were used to identify critical loads for coating failure to develop guidelines for coating design [47, 48]. Delamination, buckling, and diffusion pores can be avoided by following these new guidelines for coating design, vertical cracks, see Fig. 18, however, are inevitable for any coatings in the combustion chamber. The cracks can be tolerated in rocket-engine application as they close at high temperature and are not expected to propagate into the substrate.

**Fig. 18** Vertical crack in a thermal barrier coating

## *5.2 Cooling Channel Flows*

The heat transfer through cooling ducts was investigated in projects D4 (see Kaller et al. in this volume) and project D9 (see Hötte et al. in this volume) experimentally and numerically. Based on the reference experiment [49], the flow field in the thermal entrance region of a straight high aspect-ratio water-cooling duct with an aspect ratio AR = 4.3, a Reynolds number of Re*<sup>b</sup>* = 1.1 × 10<sup>5</sup> and an average Nusselt number of Nu = 371 was investigated by LES and RANS simulations. The validation of the LES with DNS data and the good agreement between numerical LES and experimental PIV results for velocity and Reynolds stress profiles are reported in [50]. Figure 19 depicts the temperature and secondary flow development along the heated domain in the lower duct quarter. The secondary flow increases the mixing of hot and cold fluid. The overall temperature increase is relatively moderate. The comparison of the RANS and LES data shows the deviation to increase with rising flow complexity.

## *5.3 Fluid Structure Interaction*

Thermo-mechanical loads caused by high-enthalpy flows in conjunction with constraints on the movement of the structure lead to undesirable localized deformation and buckling phenomena. Experimental studies of the heat transfer under super-

**Fig. 19** Corner vortices, temperature profile development and accompanying secondary-flow change represented by the lower wall-normal velocity. The figure shows the lower duct quarter at streamwise positions of 50, 200, and 600mm (from left to right). In the bottom row, the left half of each picture shows v and the right the v-change with respect to the adiabatic case

sonic conditions including thermally-induced deformations and their interaction with the flow field were conducted in project D6 (see Daub et al. in this volume). The fluid-structure interaction (FSI) experiments were performed in a very hightemperature environment such that massive deformations with and without plastic behavior occurred [51]. The additional numerical flow analysis was part of a coupled fluid-structure interaction simulation conducted in project D10 (see Martin et al. in this volume). The FSI modeling was carried out by an iterative staggered scheme. For the mechanical structural computation, a thermodynamic consistent elasto-viscoplastic material model with thermal expansion for large deformations was developed and implemented into a user material subroutine in Abaqus. Figure 20 emphasizes the detached bow chock, the evident deformation of the panel, and the drastic temperature increase on the deformed surface.

## **6 Research Area K: Thrust-Chamber Assembly**

The major task of this research area with the topics combustion and heat transfer, Dual-Bell nozzle flows and thrust-chamber demonstrators was on maturing and transfer of innovative concepts, solution methods and design tools towards industrial application.

Projects K1 (see Perakis and Haidn in this volume) and C5 (see Seitz et al. in this volume) were dedicated to establish a broad base of experimental data applying different model combustors operating with gaseous as well as liquid propellants. They developed and applied different numerical models capable to predict typical

**Fig. 20** Numerical fluid-structure interaction analysis of the buckling phenomenon

processes in rocket engines using this data base with sufficient accuracy. Project K2 (see Génin et al. in this volume) aimed at providing both an experimental data base as well as numerical tools for sub-scale dual bell nozzles operating in cold and hot-gas mode. Project K4 (see Eiringhaus et al. in this volume) led by the industrial partner ArianeGroup, defined three virtual thrust-chamber demonstrators that reflected all main characteristics of current European upper and main stage engines. Additionally, they incorporated advanced features like e.g. transpiration cooling, dual-bell nozzle extensions or heat-transfer enhancement methods for expander-cycle engines. Thereby, these virtual demonstrators included all topics addressed by the different projects within TRR 40 in a sensible way. They are used as numerical test beds under realistic operating conditions and thus cover an area which is not accessible via experimental means within TRR 40. Furthermore, the system competence accumulated within the research area and its actors contributed substantially to recommendations and refined requirements for experiment design, orientation and in particular relevant boundary and operating conditions for numerous projects of other research areas.

## *6.1 Combustion and Heat Transfer*

Detailed knowledge about the effect of injector fluid dynamics and geometry variations on axial wall heat loads distribution and in particular performance are essential for the design of the cooling system, i.e. cooling channel geometry, the necessity for additional cooling methods such as film or transpiration cooling or thermal barrier coatings. For the new propellant combination oxygen/methane, a broad data base has been established for a wide range of combustion chamber pressures, propellant mixture ratios with different combustor applications having 1, 5 and 7 injector ele-

**Fig. 21** Near-injector flame of a gas/gas (left) and gas/liquid (right) CH4/O2 Combustor

**Fig. 22** Instantaneous temperature distribution for the PennState model combustor using iDDES

ments [52, 53]. Recently, the facility, a single injector combustor and the 7-injector element combustor were modified to allow for operation with liquid oxygen, too. Figure 21 shows the distinct differences of the near-injector regions of the singleinjector flame for the cases of liquid and gaseous oxygen supply. Due to the much denser oxygen, the velocity ratio of these two cases with a mixture ratio of 2.6 and a combustion pressure of 20 bar, was 1.1 and 25.5, respectively. While the flame of the gas/gas case seems to expand at an almost constant angle, the flame of the liquid/gas case converges first but at a downstream position of one LOX jet diameter expands rather quickly. This is an effect which can be attributed to the very high momentum of the co-flowing methane.

A considerable effort has been made towards the development and validation of predictive tools which are sufficiently accurate but still require an acceptable numerical effort. The main emphasis was laid on models for chemical kinetics and turbulence, and in particular turbulence/chemistry interaction [54, 55]. One frequently simulated test case was the PennState preburner combustor [56], see Fig. 22, which has been simulated with a newly developed hybrid finite volume/transported PDF (TPDF) method. This revealed that near the faceplate a non-equilibrium chemistry approach is favorable [57]. A comparison of measured and simulated wall pressure and heat-flux distributions applying an adiabatic and a non-adiabatic flamelet approach revealed that although the overall trend of axial heat release was captured by both methods, the absolute values of pressure and heat flux differ from one another and from the experiments, too. While the non-adiabatic approach over-predicts the heat flux at a downstream position of 200 mm by about 40%, the adiabatic flamelet simulation yielded results similar to the experiment. Pressures however were underpredicted by 5% and 3%, respectively; see Fig. 23. Full-scale cases often consist of more than 100 injection elements with propellants injected at sub- or super-critical conditions. The latter requires different modeling strategies, namely the inclusion of

**Fig. 23** Comparisons of measured and predicted wall pressure (left) and heat-flux (right) distributions

**Fig. 24** Temperature distribution for TCD1 of project TP K4 using RANS. Black line indicates stoichiometric mixture fraction

a spray code and application of a real-gas equation of state. Such simulations were also performed, see Fig. 24 which depicts the predicted temperature distribution in the central in a plane of the Thrust Chamber Demonstrator (TCD1) of project K4 [58].

## *6.2 Dual Bell Nozzle*

Experimental and numerical investigation of dual bell nozzles have been the key focus of project K2 (see Génin et al. in this volume). Previous investigations revealed that flow separation transition can be influenced not only by the variation of total propellant mass-flow rate but by a variation of the propellant mixture ratio r*of* as well. While its increase yielded in a reduction of the transition pressure ratio, lowering of r*of* produces an opposite result [59, 60]. However, these effects are accompanied by a reduction of the width of the hysteresis, the pressure ratio gap between transition

**Fig. 25** Additive manufactured, film-cooled dual-bell nozzle at P8 test facility

and re-transition occurs. This effect is reducing the margin of stable operation in one particular mode in the presence of minor pressure and flow fluctuations around the nozzle. Recently, K2 put the focus on a combination of a classical convective cooled base nozzle and a film cooled nozzle extension with a dual-bell contour which was tested at DLR test facility P8, see Fig. 25. the operation with LOX/GH2 was tested in a subscale combustion chamber, equipped with a GH2 film cooled dual-bell nozzle [61].

## *6.3 Thrust-Chamber Demonstrators*

ArianeGroup as a major European actor in space transportation activities has been involved in the TRR40 from the very beginning supporting the activities with its expertise and through contributions to the combustion modeling workshops of the summer program. ArianeGroup thus provided an industrial benchmark for the highfidelity modeling approaches. In the final program period, ArianeGroup contributed and fully funded project K4 (see Eiringhaus et al. in this volume) to define virtual thrust-chamber demonstrators which covered all technical fields investigated within TRR40 and served as numerical test cases. As the design of a thrust chamber depends highly on its application, i.e. main or upper stage, and the chosen engine cycle, e.g. gas generator or expander cycle, not all relevant design features can be covered by a single demonstrator and therefore three different concepts were defined [62]. They have

**Fig. 26** Hot-gas temperature field of demonstrator TCD1 illustrated at several axial and lateral slices as well as for the stoichiometric mixture surface. Additional axial slices at selected positions display the strong temperature gradients to be resolved in the structure

been used as well for the continuous maturation of the in-house tool Rocflam3. As already mentioned, Rocflam3 has been extended with a new conjugate heat transfer (CHT) environment for fully 3D analyses of full-scale liquid rocket combustion chambers unique within the TRR40. The resulting hot-gas temperature field as well as selected axial slices of the structure and coolant temperatures of such a CHT simulation of demonstrator TCD1 are illustrated in Fig. 26. Further investigations show a circumferential wall temperature stratification stemming from a superposition of injection pattern as well as cooling channel effects. These variations reach up to 100 K on the hot-gas wall [58]. Additionally, the individual cooling channels show only minor variances in coolant heat up and pressure loss, making this stratification difficult to detect in full-scale experiments.

## **7 Central Research and Education Support**

Cooperation within TRR40 as well as with people and entities outside the center employed several instruments, ranging from individually arranged working-group meetings, weekly seminars with national and international experts, graduate education and summer research programs to frequent and regular bi-annual, or quarterly, research area meetings. Meetings of project groups at the TRR40 sites allowed doctoral students to acquire knowledge from across the different divisions and to establish new and improve existing collaborations.

A particular event of TRR40 was the biennual summer program with the main objective to establish cooperation between visiting scientists (preferably early postdocs or experienced doctoral students) and members of TRR40 project groups. The number of working teams grew from 11 in 2011 to 15–20 in the past years with participation of 20–30 visiting scientists from up to 9 different countries. Special lectures for the summer program on launcher-related topics have been delivered in the course of the summer program. The projects reports can be found in the four summer-program volumes [63–67].

A combustion modelling workshop was integrated into the 2015, 2017 and 2019 summer programs, where the project K1 provided test cases [68, 69] and a reference reaction mechanism [70] to foster competitive numerical comparison with experimental heat transfer and pressure data. In addition to TRR40 members, participants from universities, research labs, agencies and industry took up the challenge and generated valuable data for the evaluation and improvement of their numerical methods.

The special education for PhD students within the TRR40 took place locally for the different universities and research institutions involved. Annually, the PhD students and interested researchers in the field of rocket propulsion and related topics were invited to a week-long seminar exposing them to challenges of current launcher technologies brought forth by international experts in the field. Material science, combustion modelling, thermodynamics, computational fluid dynamics are just a few of the focal points of these graduate seminars. During the course of the involvement with the TRR40, the PhD students had to spend at least 4 weeks abroad or with an industrial partner. Most students took advantage of this unique opportunity and went abroad for 2–3 months which helped to establish a scientific network as well as towards an international visibility of the program itself. As a service task to all the projects involved, the TRR40 has undergone a rigorous evaluation of the turbulence modelling activities involved in the computational fluid-dynamic projects. The outcome has been documented in a best-practice guide [71] for all groups to ensure comparability and transferability of the results from within the TRR40.

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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**Structural Cooling**

## **A Coupled Two-Domain Approach for Transpiration Cooling**

**Valentina König, Michael Rom, and Siegfried Müller**

**Abstract** Transpiration cooling is an innovative cooling concept where a coolant is injected through a porous ceramic matrix composite (CMC) material into a hot gas flow. This setting is modeled by a two-domain approach coupling two models for the hot gas domain and the porous medium to each other by coupling conditions imposed at the interface. For this purpose, appropriate coupling conditions, in particular accounting for local mass injection, are developed. To verify the feasibility of the two-domain approach numerical simulations in 3D are performed for two different application scenarios: a subsonic thrust chamber and a supersonic nozzle.

## **1 Motivation**

In order to bring higher loads into orbit, rocket engines have to be designed with significantly higher thrust. Such engines will experience high thermal loads. In this context transpiration cooling is an innovative cooling concept that gained attention with the development of carbon fiber materials. The general setup is the orthogonal injection of a cooling gas through a porous material. The advantage of this concept is twofold: The porous wall is cooled down by convection energy within the wall while the coolant passes through it. The second cooling mechanism is the development of a cooling film at the interface of the porous sample. This cooling film thickens the incoming boundary layer leading to a reduction of the heat flux at the wall.

V. König · M. Rom · S. Müller (B)

IGPM, RWTH Aachen University, Templergraben 55, Aachen 52056, Germany e-mail<EMAIL_ADDRESS>
V. König e-mail<EMAIL_ADDRESS>
M. Rom e-mail<EMAIL_ADDRESS>
N. A. Adams et al. (eds.), *Future Space-Transport-System Components under High Thermal and Mechanical Loads*, Notes on Numerical Fluid Mechanics and Multidisciplinary Design 146, https://doi.org/10.1007/978-3-030-53847-7\_2

In the 1950s Eckert and Livingood [7] identified the superior characteristics of this active cooling technique. Terry and Caras [27] summarized the possibilities of applying these to rocket nozzles. Transpiration cooling experiments for metallic nozzle applications were performed in [13] and numerical simulations for metallic nozzles can be found in [18].

The development of light-weight permeable high-temperature fiber ceramics, in particular composite carbon/carbon (C/C) materials, investigated for instance by Selzer et al. [26], led to increased interest in transpiration cooling. Transpiration cooled thrust chambers were investigated by Ortelt et al. [24] or Herbertz and Selzer [10]. Experiments in a subsonic hot gas channel were performed by Langener et al. [19]. Additive manufactured porous plates for transpiration cooling applications were recently analyzed in [11].

Numerical simulations of subsonic hot gas channel flow exposed to transpiration cooling were conducted by Jiang et al. [12] and more recently by Liu et al. [20]. Non-uniform injection was investigated by Wu et al. [31]. In Yang et al. [34] each injection channel is simulated separately. In [28] the coupling with a fully resolved pore-network for low Reynolds numbers without heat transfer is used to investigate the effect at the hot gas interface. A monolithic approach for a laminar hot gas flow with a resolved porous medium is presented in [33].

In [4] we developed a two-domain approach where two solvers for the hot gas flow and the porous medium flow are solved in alternation. Data between those solvers are exchanged at the coupling interface. Originally the development of appropriate coupling conditions focused on uniform mass injection [6]. These are modified in [17] to account also for non-uniform mass injection.

In the present work we report on the latest changes on the design of the coupling conditions. Furthermore, we perform numerical simulations for two different application scenarios for transpiration cooling: a subsonic thrust chamber and a supersonic nozzle. For the first scenario we investigate the influence of non-uniform mass injection on the cooling film, whereas for the second scenario the challenge lies in the extension of the range of application.

We first summarize in Sect. 2 the models of the two-domain approach. In particular, the coupling conditions at the interface between the two domains are presented in detail. The numerical methods used are briefly described in Sect. 3. In Sect. 4 numerical results for a subsonic thrust chamber and a supersonic nozzle flow can be found. We conclude with a summary and an outlook in Sect. 5.

## **2 Mathematical Modeling**

For the investigation of transpiration cooling we use a two-domain approach where the flows in the hot gas domain -HG and the porous medium domain -PM are solved in alternation. At the coupling interface Int boundary conditions for one domain use data from the other domain. Exemplarily, the scenario for a thrust chamber is shown in Fig. 1. Note that the flow in the cooling gas reservoir is not simulated. This model

**Fig. 1** General transpiration cooling setup

was already presented in detail in previous publications [4, 6, 15]. In the meantime, the coupling conditions have been modified to account also for non-uniform injection. Therefore we focus here on these modifications, see Sect. 2.3, whereas the models in the hot gas domain and the porous medium are only addressed very briefly for the sake of completion, see Sects. 2.1 and 2.2, respectively.

## *2.1 Hot Gas Domain*

The flow in the hot gas domain is assumed to be turbulent. Therefore, we apply a RANS model that formally can be written as

$$\mathcal{L}\_{\rm HG}(\mathbf{U}\_{\rm HG}) = 0. \tag{l}$$

In our numerical investigations we will consider both the flow in a subsonic thrust chamber at moderate temperatures and a supersonic nozzle at high temperatures. These investigations are motivated by experiments performed in the wind tunnel [19, 25] at University Stuttgart and the detonation-based facility for rocket-engine-like flows [9, 21, 32] at the Shock Wave Laboratory at RWTH Aachen. Therefore, the system (1) of RANS equations will differ for the two scenarios.

**Scenario 1: Subsonic thrust chamber.** In this scenario the gas is treated as a thermally and calorically perfect gas. The turbulence is modeled by the Wilcox *k*-ω model [29]. Thus, the system (1) consists of the continuity equation, the momentum equation and the energy equation for density ρ, momentum ρ**v** and total energy *E* as well as two equations for the turbulence kinetic energy *k* and the specific dissipation rate ω with **v** the fluid velocity. The vector of conserved quantities is determined by

$$\mathbf{U\_{HG}} = \left(\rho, \,\rho\mathbf{v}, \,\rho E, \,\rho k, \,\rho\omega\right), \tag{2}$$

where the density is Reynolds-averaged and all other quantities are Favre-averaged. The system is closed by an equation of state for a thermally perfect gas. For further details, in particular on the modeling of the Reynolds stress tensor as well as the mean and the turbulent heat flux, we refer to previous work [4, 6, 17]. The following additional quantities enter the model: the specific heat capacity at constant pressure *cp*, the dynamic viscosity μ and the turbulent viscosity μ*<sup>t</sup>* , the Prandtl number *Pr* and the turbulent Prandtl number *Prt* , the specific gas constant *R* and the isentropic exponent γ .

**Scenario 2: Supersonic nozzle.** In this scenario the hot gas model has to account for a thermally perfect but calorically imperfect gas mixture of *Ns* non-reacting species. For this purpose, the RANS equations (1) are extended by additional *Ns* species equations for the partial densities ρα, i.e., the vector of conserved quantities is now determined by

$$\mathbf{U\_{HG}} = (\rho, \rho\_1, \dots, \rho\_{N\_z}, \rho \mathbf{v}, \rho E, \rho k, \rho \alpha). \tag{3}$$

Here the turbulent quantities are modeled by Menter's SST *k*-ω model [22]. The system (1) is closed by an equation of state for a thermally perfect gas mixture. For details we refer to [3, 30].

The system (1) is complemented by suitable boundary conditions for the two scenarios:

**Scenario 1: Subsonic thrust chamber.** At the inflow boundary <sup>I</sup> the Mach number, the density and the temperature are prescribed by *M* = *M*∞, ρ = ρ<sup>∞</sup> and *<sup>T</sup>* <sup>=</sup> *<sup>T</sup>*∞. The turbulence kinetic energy is defined by the turbulent intensity *T u*<sup>∞</sup> <sup>=</sup> <sup>√</sup>2/<sup>3</sup> *<sup>k</sup>*∞/|**v**∞|, where **<sup>v</sup>**<sup>∞</sup> is the inflow velocity vector. The turbulent dissipation rate ω<sup>∞</sup> is computed by ρ∞*k*∞/μ*<sup>t</sup>* , where the ratio of the turbulent dynamic viscosity to the laminar dynamic viscosity (μ*t*/μ)<sup>∞</sup> is used in combination with a viscosity curve fit model. At the outflow boundaryO, only the pressure is prescribed by setting *p* = *p*∞. For the wallsW,HG,iso of the channel we use isothermal boundary conditions motivated by the thermal wall behavior observed in the experiments in [25]. For the walls W,HG,ad downstream of the porous sample adiabatic boundary conditions account for the changing wall temperature due to the cooling.

**Scenario 2: Supersonic nozzle.** At the nozzle entry <sup>I</sup> we additionally set the mass fractions *X*α,<sup>∞</sup> = ρα,∞/ρ<sup>∞</sup> of each species α. At the nozzle exit <sup>O</sup> only the outflow pressure is prescribed by setting *p* = *p*out. Due to the short test duration of a few milliseconds in the corresponding experiments [9, 21, 32], there is no wall temperature increase. Hence, all nozzle walls are modeled as isothermal walls (W,HG,iso).

## *2.2 Porous Medium Domain*

The porous medium flow is characterized by the porosity ϕ of the material. We assume that the entire void space is connected. Thus, we do not have to deal with isolated cavities. Furthermore, the porosity is constant in the entire domain. For our two scenarios the flow in the porous medium is laminar. Furthermore, we have to account for the drag that evolves due to the solid obstacle using a Darcy-Forchheimer velocity equation. In short form, the resulting system of equations for a steady state flow reads

$$
\mathcal{L}\_{\rm PM}(\mathbf{U}\_{\rm PM}) = 0. \tag{4}
$$

It consists of the continuity equation for the density ρ *<sup>f</sup>* of the coolant, the Darcy-Forchheimer equation for the Darcy velocity **v***<sup>D</sup>* and two heat equations for the temperatures *Ts* and *Tf* of the solid and the coolant, respectively, i.e.,

$$\mathbf{U\_{PM}} = (\rho\_f, \mathbf{v\_D}, T\_s, T\_f). \tag{5}$$

Considering two temperatures allows to account for a potential thermal non-equilibrium of the solid and the fluid. The model is complemented with a perfect gas law for the coolant. Again, we refer to previous work [4] for further details.

The model is supplemented with boundary conditions. Assuming that the conditions in the reservoir are constant and homogeneous we can derive the pressure and the temperatures on the reservoir boundary <sup>R</sup> from a fixed coolant temperature *Tc*, e.g., given by measurements. Furthermore let *Tb* be the temperature of the solid on the backside of the porous material. Then the boundary conditions on the reservoir boundary <sup>R</sup> read *Ts* = *Tb*, *Tf* = *Tc* and ρ *<sup>f</sup>* = *p*R/(*Rc Tc*), where *Rc* denotes the specific gas constant of the coolant. Furthermore, the solid side walls at W,PM are assumed to be adiabatic, i.e., ∇*Ts* · **n** = ∇*Tf* · **n** = 0, and the slip conditions to hold, i.e., **n** · **v***<sup>D</sup>* = 0. Note that at W,PM no boundary conditions for the density ρ *<sup>f</sup>* have to be imposed because viscous effects are neglected in the continuity equation and the Darcy-Forchheimer equation.

## *2.3 Coupling Conditions*

So far we have not yet addressed boundary conditions at the coupling interface Int for the hot gas flow and the porous medium flow. Note that in the present work we only consider injection normal to the porous wall without entrainment of hot gas into the porous medium. At the coupling interface Int the flow quantities **U**HG, see (2) or (3), in the hot gas domain -HG and **U**PM, see (5), in the porous medium domain -PM are coupled. Since our model is based on a two-domain approach, we impose boundary conditions for both domains at the interface Int where the boundary conditions for the porous medium domain access data of the hot gas domain (PM ← HG) and vice versa (HG ← PM). The coupling conditions, which are specified in the following, make use of the equation of state and the formula for the mass flow rate, in general notation given by *p* = ρ*RT* and *m*˙ = ρ*v A*, respectively.

**PM** ← **HG**: The coupling conditions at the interface Int for -PM use the pressure *p*HG, the temperature *T*HG and the temperature gradient ∇*T*HG of the hot gas at the interface computed from the conservative quantities in **U**HG. They are given by

$$
\nu\_{D,n} = \frac{\dot{m}\_c}{A\_c} \frac{R\_c T\_f}{p\_{\rm HG}} \,, \tag{6}
$$

where *vD*,*<sup>n</sup>* = **v***<sup>D</sup>*,*<sup>n</sup>* · **n** denotes the absolute value of the injection velocity vector **v***<sup>D</sup>*,*<sup>n</sup>* normal to the porous wall with outer unit normal vector **n**, *m*˙ *<sup>c</sup>* the prescribed coolant mass flow rate and *Ac* the surface area of the porous medium, and

$$(\mathbf{l} - \boldsymbol{\varphi}) \left( \mathbf{k}\_s \nabla T\_s \right) \cdot \mathbf{n} = c\_{p,f} \, \rho\_f \, \upsilon\_{D,n} \left( T\_f - T\_{\rm HG} \right) + \kappa\_{\rm HG} \nabla T\_{\rm HG} \cdot \mathbf{n}.\tag{7}$$

Here *κ<sup>s</sup>* and κHG denote the heat conduction tensor of the solid in the porous medium and the heat conduction coefficient of the hot gas fluid, respectively, and *cp*, *<sup>f</sup>* the heat capacity at constant pressure of the hot gas fluid.

**HG** ← **PM**: The coupling conditions at the interface Int for -HG use the Darcy velocity normal component *vD*,*<sup>n</sup>* and the fluid temperature *Tf* of the porous medium at the interface such that

$$\rho = \frac{p\_{\rm HG}}{R\_c \, T\_f}, \quad \nu\_n = \nu\_{D,n} \cdot \bar{o}, \quad E = c\_v T\_f + \frac{1}{2} \nu\_{D,n}^2. \tag{8}$$

In contrast to original work where we investigated **uniform** mass injection [3, 4, 8] we recently added the parameter *o*¯ to account for **non-uniform** injection that is set to 1 for uniform injection. Furthermore, the turbulence kinetic energy *k* at the interface is set to zero. The specific dissipation rate is determined by

$$
\omega = \frac{\rho u\_\tau^2}{\mu} \frac{25}{\frac{\nu\_{D,\text{s}}}{u\_\tau} \left(1 + \mathfrak{F} \frac{\nu\_{D,\text{s}}}{u\_\tau}\right)},\tag{9}
$$

as proposed by Wilcox [29] to account for mass injection at the modeled porous surface. Here *<sup>u</sup>*<sup>τ</sup> <sup>=</sup> <sup>√</sup>τ*w*/ρ denotes the friction velocity with the wall shear stress <sup>τ</sup>*w*.

For the supersonic nozzle flow the mass fractions of the coolant *X*α,*<sup>c</sup>* are set at the interface to compute ρα = ρ · *X*α,*<sup>c</sup>* with ρ from (8). Note that for foreign gas injection the mass fraction at the interface is 1 for the coolant species and 0 for all species contained in the hot gas flow.

We would like to emphasize that originally in [5] the injection velocity (6) was prescribed to simulate non-uniform injection. For a better control of a specific mass flow rate the parameter *o*¯ representing a local fraction or a percentage of a given mass flow was introduced in [16]. There it was incorporated in the coupling conditions for the porous medium. However, this caused modeling errors in the pressure distribution in the porous medium. Therefore, we recently incorporated this parameter in the coupling conditions for the hot gas [17].

Finally, we emphasize that in the case of uniform injection and thermal equilibrium in the porous material our coupling conditions enforce pressure continuity across the interface. For non-uniform injection and thermal equilibrium the local pressure continuity is lost because of the factor *o*¯ in (8), but due to

$$\frac{1}{|\Gamma\_{\text{Int}}|} \int\_{\Gamma\_{\text{Int}}} \bar{o} \, d\mathcal{y} = 1 \tag{10}$$

we obtain integral pressure continuity instead. For thermal non-equilibrium, regardless of the injection type, the pressure is not continuous which is in agreement with the literature considering the interface as an idealization of a thin layer in which the pressure can change significantly because of the presence of the porous material [23].

## **3 Numerical Methods**

For the two-domain approach we use two different solvers to discretize the RANS equations (1) and the porous medium model (4).

**Porous medium solver**. A finite element solver is used to solve the porous medium model. It has been implemented using the deal.II library [1]. For this purpose a weak formulation for the system (4) was derived, see [4, 8]. The resulting system of variational equations is split into two parts:

The nonlinear system is linearized and solved by a Newton iteration to which we refer as the inner iteration. The two systems are solved iteratively until the residual of the complete system drops below a chosen tolerance (outer iteration).

**Hot gas solver**. For the discretization of the RANS equations (1) we use the flow solver Quadflow [2]. This fully adaptive finite volume scheme operates on locally refined B-Spline meshes.

**Two-domain solver**. For the solution of the coupled problem, we iteratively solve the RANS equations and the porous medium equations for the hot gas flow and the porous medium flow, respectively, by applying the two solvers in alternation and exchanging data at the interface as described in Sect. 2.3. This provides solutions **U**HG and **U**PM in the two flow regimes. The iterative process is summarized in

#### **Algorithm 1**:

Step 1: Initialize the flow solver.

	- Step 3: Converge the porous medium solver.
	- Step 4: Transfer data (*vD*,*<sup>n</sup>*, *Tf* ) from the porous medium solver to the flow solver.
	- Step 5: Converge the flow solver.

In contrast to previous work [4, 6, 8] we use the reservoir pressure *p*<sup>R</sup> as a fitting parameter to ensure that the given mass flow rate *m*˙ *<sup>c</sup>* is met at the interface Int and the continuity of the pressure distribution at the interface is established. For this purpose we perform an outer iteration on the flow solver until the target mass flow rate *m*˙ *<sup>c</sup>* is met following [17]. In each iteration *<sup>i</sup>*, the mass flow rate *<sup>m</sup>*˙ *<sup>i</sup>* Int at the interface Int is compared with the given target mass flow rate *m*˙ *<sup>c</sup>* and *p*R,num is updated by

$$p\_{\text{R,num}}^{i+1} = p\_{\text{R,num}}^i + p\_{\text{R,num}}^i \cdot \left(1 - \frac{\dot{m}\_{\text{Int}}^i}{\dot{m}\_c}\right). \tag{11}$$

For an initial guess *p*<sup>0</sup> R,num we use either experimental data or an approximation determined by the Darcy-Forchheimer equation [16].

## **4 Numerical Results**

In this section we present numerical results for two application scenarios where the two-domain approach is applied to investigate transpiration cooling in a subsonic thrust chamber and a supersonic nozzle.

## *4.1 Non-uniform Injection into a Subsonic Hot Gas Channel Flow*

In the first scenario we investigate non-uniform injection coupling conditions and compare the results with uniform injection. This is motivated by developments in manufacturing allowing to design specific injection patterns of porous materials. This leads to the necessity of affordable non-uniform injection simulations for transpiration cooling. For this purpose, we consider the following configuration: the domains for the porous medium and the hot gas channel are -PM = 48 mm × 10.9 mm × 48 mm and -HG = 1, 120 mm × 60 mm × 90 mm, respectively, where the porous medium is mounted to the bottom side of the hot gas channel 580 mm downstream of the channel entrance and centrally in lateral direction. To investigate the influence of the injection pattern on the cooling and, thus, the effectivity of the transpiration cooling, we consider two injection patterns: the first one depends on the lateral coordinate *<sup>z</sup>* and is given by *<sup>o</sup>*¯ <sup>=</sup> <sup>0</sup>.887(sin( <sup>5</sup> <sup>48</sup>π · (*z* + 24)) + 1), while the second one depends on the streamwise coordinate *<sup>x</sup>* and is given by *<sup>o</sup>*¯ <sup>=</sup> <sup>0</sup>.887(sin( <sup>5</sup> <sup>48</sup>π · *x*) + 1). We refer to these as the lateral and the streamwise wave pattern, respectively. For (*x*,*z*) ∈ [0, 48] × [−24, 24] the wave patterns consist of three peaks and two sinks corresponding to high and low injection rates. The factor 0.887 scales *o*¯ such that (10) holds. A similar pattern was numerically and experimentally investigated in [17] where *o*¯ depends on experimental outflow measurements. The disadvantage of *o*¯ depending on experimental data lies in the necessity to project the discrete data onto the computational mesh.

The porous medium domain is discretized by a mesh with 60 × 30 × 60 cells. The mesh lines are concentrated towards the hot gas and towards the reservoir side by applying a stretching technique.

For the hot gas domain we use a coarse mesh of about 135,000 cells in the first coupling step, i.e., Steps 2–5 of Algorithm 1. Then the data in the hot gas domain are prolongated to a uniformly refined mesh consisting of 1.08 million cells as an initial guess for the solution process on the finer mesh. Another four coupling steps are performed to obtain a converged coupled solution in the hot gas flow domain. Additionally a mesh convergence study was performed with a hot gas mesh of 8.64 million cells.

We perform three computations: uniform injection and non-uniform injection with lateral and streamwise wave pattern. Both the hot gas and the coolant are air. The parameters for the coupled simulations can be found in Table 1.

In Fig. 2 (left) we show the temperature distribution at the wall in the hot gas domain where the porous medium is mounted. In Fig. 2a, b the simulation results for the two non-uniform configurations are presented. We use the same integral mass

**Table 1** Flow and porous material parameters for test scenario 1

**Fig. 2** Comparison of uniform injection and non-uniform injection patterns

flow rate for both the uniform and the non-uniform injection. Therefore, the porous areas with weak injection (light blue on the blowing insert in Fig. 2a, b are balanced by those with high injection. This has a strong effect on the cooling of the porous material itself and on the wake of the sample.

In Fig. 2a the areas with almost no injection can be seen over the porous material. In the wake of the sample the cooling film exhibits three streaks. The temperatures in the wake of areas with higher injection are lower than in the uniform injection case. In the wake of areas with almost no injection almost no cooling film is observed leading to high temperatures.

In Fig. 2b the areas with almost no injection can also be seen over the porous material. The cooling film in the wake of the sample is more uniform compared to the lateral wave pattern. The cooling film is slightly extended in streamwise direction compared with the uniform injection case.

To get a better understanding of the cooling film, especially in the wake of the sample, we perform a more detailed investigation by means of temperature data extracted in streamwise direction and lateral to the flow in the wake in Fig. 2 (right). A comparison of the wall temperature for the uniform injection and the lateral wave pattern is presented in Fig. 2d. Temperature data are extracted along the centerline (*z* = 0 mm) for the uniform injection and at a peak (*z* = 0 mm) and at a sink (*z* = 14.4 mm) for the lateral wave pattern. Due to almost no injection at the sink the temperature above the porous material is significantly higher than in the uniform case. It is also significantly higher in the wake (*x* > 48 mm), and at position *x* ≈ 70 mm the temperature increases to the isothermal wall temperature *T*<sup>W</sup> = 362.6 K. For *x* > 70 mm the temperature is larger than *T*<sup>W</sup> due to the adiabatic boundary condition in the wake of the porous medium and therefore no cooling film can be observed. For the peak the temperatures above the porous material are similar to the uniform injection. In the wake the temperatures are significantly lower due to a thicker cooling film resulting from the higher injection rate.

In Fig. 2e the uniform injection is compared with the streamwise wave pattern along the centerline (*z* = 0 mm). Above the porous material two areas with almost no injection can be identified for the streamwise wave pattern case. Here the temperatures are similar to the temperatures at the sink in the lateral wave pattern case. In the wake of the sample (*x* > 48 mm) the streamwise wave pattern shows a slightly thicker cooling film, probably due to the injection rate peak close to the trailing edge.

In Fig. 2f a comparison of uniform and non-uniform injection temperature data downstream of the sample (*x* = 65 mm) is presented. For the lateral wave pattern three troughs can be observed in the simulations. For the streamwise wave pattern the cooling film is uniform and very similar to the uniform injection. The mean values of the three curves are 348.4, 346.5 and 348.0 K for the lateral wave, streamwise wave and uniform case, respectively.

## *4.2 Uniform Injection into a Supersonic Nozzle Flow*

The second scenario is motivated by the nozzle test facility [9, 21, 32] of the Shock Wave Laboratory at RWTH Aachen. The facility consists of a detonation tube, an attached axisymmetric nozzle, a vacuum tank and a damping section. The detonation tube provides hot water vapor for a quasi-steady nozzle flow for 7–10 ms. In this work, we concentrate on the simulation of the flow in the expansion part of the nozzle which has a length of 340 mm, a throat diameter of 16 mm, a half-opening angle of 15◦, a throat radius of curvature of 12 mm and an expansion ratio *A*exit/*A*<sup>∗</sup> of 156. The nozzle has a slot with a length of 110.25 mm and a width of 8 mm in which a porous medium can be installed for transpiration cooling. The leading edge of the slot is positioned about 98 mm behind the nozzle throat (measured on the nozzle centerline).

We perform two simulations with (*i*) a porous medium with a cross-section surface corresponding to the dimensions of the slot and (*ii*) a porous medium of the same length but comprising the whole circumference of the nozzle. Due to the short test duration, analogously to the aforementioned isothermal nozzle wall there is no temperature increase of the fluid or the solid temperature in the porous material, i.e., we have *Tf* = *Ts* = *Tc*. Hence, for our two simulations the coupling conditions (8) and (9) for the hot gas flow can be directly calculated without simulating the porous medium flow.

To account for the quasi-steady behavior, we couple the nozzle flow with the calculated porous medium data only once. In particular, we first of all perform a fully adaptive nozzle flow simulation without cooling which provides a final mesh with about 26 million cells. Based on the resulting hot gas data, (8) and (9) are calculated and used as boundary conditions for the subsequent slot and circumferential injection simulations, both with uniform cooling gas injection. These are then conducted by converging the flow solver once more on the final mesh.

The gas in the supersonic nozzle flow is water vapor with initial mass fractions *X*H,<sup>∞</sup> = 0.00251, *X*H2,<sup>∞</sup> = 0.01176, *X*H2O,<sup>∞</sup> = 0.842, *X*O,<sup>∞</sup> = 0.01231, *X*O2,<sup>∞</sup> = 0.08668 and *X*OH,<sup>∞</sup> = 0.04474. The injected cooling gas is helium. The two simulations only differ in the dimensions of the porous medium and are conducted with the parameters listed in Table 2. Note that no parameters regarding the porous material are given because the porous medium flow is not simulated. The flow data are based on experiments planned at the Shock Wave Laboratory for a porous medium with dimensions 110.25 mm × 8 mm × 7 mm and characteristics similar to those of the first scenario, see Table 1.

The temperature distribution in the nozzle for slot and circumferential injection can be seen in Fig. 3a and b, respectively, on six slices through the nozzle. The par-

**Table 2** Flow parameters for test scenario 2

**Fig. 3** Comparison of slot and circumferential injection into nozzle flow

ticular positions of the slices are indicated in the figures. Note that only temperatures between 350 K and 1,150 K are displayed. The leading and the trailing edge of the porous medium are positioned at *x* ≈ 98 mm and *x* ≈ 208 mm, respectively. The formation of a narrow cooling film in the case of slot injection is visible in Fig. 3a, in particular on the slices *x* = 190 mm and *y* = *y*min + 0.8 mm, where *y*min refers to the local *y*-coordinate on the nozzle wall at *z* = 0 depending on *x*. In contrast, in the case of circumferential injection, there is a continuous cooling film on the nozzle wall, see for instance the slices *x* = 190 mm or *y* = 0 mm in Fig. 3b. Since a cooling film is an obstacle to the hot gas flow, a stronger flow deceleration can be observed for the circumferential injection. Hence, the temperatures in the interior of the nozzle away from the walls are slightly higher compared with the slot injection case. This effect is visible in Fig. 3a and b, e.g., on slice *y* = 0 mm between *x* = 190 mm and *x* = 280 mm or on slice *x* = 280 mm.

An interesting phenomenon can be observed when comparing the temperatures in the cooling film boundary layers: With slot injection, lower temperatures can be achieved, as visible around the intersection point of the slices *z* = 0 mm, *y* = *y*min + 0.8 mm and *x* = 190 mm. This is probably due to the slot being only a narrow obstacle which can be avoided by the hot gas flow by flowing around it. A comparison of the streamlines on the slice *y* = *y*min + 0.8 mm in Fig. 3c, d confirms this conjecture. As a consequence, the slot cooling film can become thicker than the circumferential cooling film and, hence, results in a better cooling effectiveness at selective positions. Figure 3c, d also show the distribution of helium in the nozzle flow. In the slot injection case, the cooling film widens towards the trailing edge of the porous medium at *x* ≈ 208 mm and narrows downstream of the trailing edge.

Temperature boundary layer profiles in wall-normal direction in the wake of the porous medium at *x* = 280 mm on the centerline *z* = 0 mm are depicted in Fig. 4a. According to expectations, a better overall cooling is obtained by circumferential injection despite selective lower temperatures achieved by slot injection as described above. However, the comparison with the temperature profile for nozzle flow without any cooling gas injection reveals a significant cooling also in the slot injection case. The temperature peak in the lower part of the boundary layer (wall distance less than 2 mm) is reduced from 945 K (no cooling) to 853 K (slot injection) and 746 K (circumferential injection).

Figure 4b shows the wall heat fluxes for the line *y* = *y*min, *z* = 0 mm, which corresponds to the centerline of the slot, with and without cooling gas injection. Due to the isothermal nozzle walls, the wall temperature and the temperature of the cooling gas are the same (333.15 K). Hence, the wall temperature gradients up- and downstream of the leading edge of the porous medium are similar. However, the thermal conductivity of helium is about 3.5 times higher than that of water vapor which leads to the peak of the wall heat fluxes at the leading edge of the injection. Further downstream the heat fluxes rapidly decrease with a value close to zero at the trailing edge of the porous medium in the case of slot injection. The larger wall heat flux over the porous medium for circumferential injection is again explained by the thicker cooling film for slot injection. In the wake of the injection, both heat fluxes slowly increase, but the cooling effect persists up to the nozzle exit.

**Fig. 4** Temperature boundary layer and wall heat flux for slot and circumferential injection into nozzle flow

## **5 Conclusion**

Transpiration cooling, especially using C/C material, is an active field of research. So far, the heat transfer process of a porous medium flow interacting with a hot gas flow is not yet fully understood. In this paper we presented coupling conditions taking into account non-uniform injection. The numerical results for the subsonic thrust chamber confirm that the injection pattern has a strong influence on the cooling film and therefore needs to be considered in the technical design of a cooling system. This is in accordance with experimental investigations of C/C material characteristics at the DLR Stuttgart and of a wind tunnel setting at the University of Stuttgart in [17] where numerical results are compared with infrared measurements.

The numerical results of cooling gas injection into the nozzle show that our approach is suitable for rocket-engine-like flows even though the porous medium was not simulated in this case. By studying two arrangements of the porous medium (slot or circumferential injection), the simulations led to further insight into the behavior of transpiration cooling. A corresponding experimental study would come at a high cost. Since the experiments at the Shock Wave Laboratory at RWTH Aachen have not yet been conducted, further simulations could help set up the experiments, e.g., by applying different coolant mass flow rates. The experiments will provide data for the wall heat flux on top and in the wake of the porous medium. These will be compared with our numerical results.

So far, the micro-scale behavior of the injection through the porous surface has not been considered. Since a direct simulation is not feasible due to prohibitively high computational costs, effective coupling conditions need to be designed that model the influence of the micro-scale effects on macro-scale quantities, e.g. average of the skin friction coefficient, without resolving the micro-structures. Preliminary work on this is reported in [14] where an upscaling approach for a porous material surface is developed.

**Acknowledgements** Financial support has been provided by the German Research Foundation (Deutsche Forschungsgemeinschaft – DFG) in the framework of the Sonderforschungsbereich Transregio 40.

## **References**

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

## **Innovative Cooling for Rocket Combustion Chambers**

**Jonas Peichl, Andreas Schwab, Markus Selzer, Hannah Böhrk, and Jens von Wolfersdorf**

**Abstract** Transpiration cooling in combination with permeable ceramic-matrix composite materials is an innovative cooling method for rocket engine combustion chambers, while providing high cooling efficiency as well as enhancing engine life time as demanded for future space transportation systems. In order to develop methods and tools for designing transpiration cooled systems, fundamental experimental investigations were performed. An experimental setup consisting of a serial arrangement of four porous carbon fiber reinforced carbon (C/C) samples is exposed to a hot gas flow. Perfused with cold air, the third sample is unperfused in order to assess the wake flow development over the uncooled sample as well as the rebuilding of the coolant layer. Hereby, the focus is on the temperature boundary layer, using a combined temperature/pitot probe. Additionally, the sample surface temperature distribution was measured using IR imaging. The experiments are supported by numerical simulations which are showing a good agreement with measurement data for low blowing ratios.

## **1 Introduction**

During the three funding periods (FP) of the TRR40 extensive investigations have been conducted in subproject A5 (SP A5) regarding transpiration cooling. Using detailed experimental analysis on single transpiration cooled samples, analytical 1Dmodels have been developed describing the cooling efficiency of the transpiration

Institute of Aerospace Thermodynamics, Pfaffenwaldring 31, Stuttgart 70569, Germany

© The Author(s) 2021

J. Peichl (B) · M. Selzer · H. Böhrk

DLR Institute of Structures and Design, Pfaffenwaldring 38-40, Stuttgart 70569, Germany e-mail<EMAIL_ADDRESS>
A. Schwab · J. von Wolfersdorf

N. A. Adams et al. (eds.), *Future Space-Transport-System Components under High Thermal and Mechanical Loads*, Notes on Numerical Fluid Mechanics and Multidisciplinary Design 146, https://doi.org/10.1007/978-3-030-53847-7\_3

cooled sample, but neglecting the coolant film development of upstream transpiration cooling (FP 1) [6]. To get a better understanding of the physical coupling mechanisms of the transpired coolant and the hot cross flow, the measurement apparatus was extended to measure the boundary layer characteristics using pitot tubes and thermocouples in the hot gas flow. Schlieren visualizations gave further insight into the interaction between coolant and hot gas flow [13]. The experimental data also served to validate numerical models coupling the hot gas flow and the porous wall [1, 8].

In contrast to film cooling, the pores in the material are very small and distributed over the surface. To be able to characterize this property, a test bench to measure this distribution has been developed, where the dynamic pressure distribution of the outflowing coolant is measured using a pitot tube [16]. Additionally, application of electro-coating processes allowed for improvements in the design of the samples [15]. This led to more robust samples, which made it possible to characterize fully instrumented samples and use these identical samples in the hot gas channel for transpiration cooling experiments. Thus, the effects of inhomogeneities in the outflow distribution on the cooling behaviour of the sample and the wake flow were demonstrated and even further incorporated into numerical results showing a good agreement in cooling behaviour [4]. Whilst the investigations in FP 1 and FP 2 have been focused on a single transpiration cooled sample, transpiration cooling offers the opportunity to adapt the local coolant mass flow by supplying different pressures, varying the porous wall thickness or stacking materials with different permeabilities. Thus, in a real combustion chamber an additional efficiency gain is expected by adjusting the coolant mass flow distribution to the local heat load and only replenishing the coolant film layed by upstream transpiration cooling as needed [2, 9, 10]. This concept is visualized in Fig. 1, depicting the approach of adjusting coolant mass flow to the local thermal situation.

Especially when taking into account the whole thrust chamber system with additional constraints like coolant supply pressure, injection temperature and highly varying thermal loads from injector to nozzle exit, it is evident that the most efficient cooling will be achieved by an optimized combination of different cooling techniques like transpiration-, film-, and regenerative cooling.

Using the combined approach of sample characterization, transpiration cooling experiments, analytical modelling and numerical simulations developed in FP 1 and FP 2, the current research is focused on local variations of coolant mass flow rate. Thereby, the effects of accumulating coolant film through transpiration cooling and degeneration of that film on low or non-perfused sections as well as replenishment of this coolant film can be studied in detail.

## **2 Experimental Setup**

In order to experimentally determine the accumulation of coolant film and degeneration of the coolant layer over non-perfused samples, a new stacked ceramic test bed consisting of four independent samples has been developed. The specimen and

**Fig. 1** Envisioned optimized cooling scheme for rocket combustion chambers

its characterization are described in Sect. 2.1. From preliminary numerical studies operating conditions have been identified that show the phenomena of accumulating coolant film, degeneration of the coolant film over a non-transpiration cooled section and subsequent regeneration of the coolant film [5]. The test channel and the operating conditions are described in Sect. 2.2.

## *2.1 Stacked Transpiration Cooling Specimen*

The specimen shown in Fig. 2 contains four permeable Carbon/Carbon (C/C) samples of *AC* = *L* × *W* = 67 × 52 mm2 size and *t* = 10 mm thickness each. Each of the samples exhibit a ply-parallel through-flow direction. Visible at the edges of the C/C samples, a galvanic copper layer is used to prevent lateral mass flow and to solder the individual sample into the sample holder. From the sample holder a 1 mm stainless steel plate can be seen at the leading and trailing edge. Additionally, to separate the coolant supplies of the four samples, a dividing plate is placed between each sample as shown in Fig. 2.

For temperature measurements ten Type K thermocouples are integrated into each sample. Four surface thermocouples at the outlet of the C/C-sample (see Fig. 2), one thermocouple at the backside surface and five thermocouples located at various depths inside the sample. These serve to capture the temperature distribution inside the C/C-samples when exposed to a hot gas flow. Each fully integrated and instrumented sample has been characterized at the AORTA (Advanced Outflow Research

**Fig. 2** Specimen setup and characterization

facility for Transpiration Applications) [16] test bench regarding permeability and outflow distribution.

Figure 2 shows the outflow distribution measured with a pitot tube with an inner diameter of 0.8 mm on a grid with a step size of 0.4 mm in x- and y-direction and a mass flow of 1.7 g/s. A detailed description of the measurement procedure is given in [15]. The contour graphs show the measured dynamic pressure at each point, where the colour scale has been adjusted to the same maximum value of 200 Pa, to best show the general outflow pattern. Typical for a ply-parallel through-flow are the line like patterns, stemming from the plies of the material as well as the regions with very little to no through-flow at the joints of the plates. This general pattern is similar for each sample, but the measurements also reveal some other outflow inhomogeneities between the samples. While sample 1 for example exhibits a homogeneous outflow distribution, sample 3 exhibits increased throughflow at the leading edge due to imperfections in the galvanic and soldering process.

The permeability of the samples is described by the Darcy-coefficient *kD* and the Forchheimer-coefficient *kF* , using the Darcy-Forchheimer equation in its compressible formulation given by Innocentini et al. [3] as

$$\frac{P\_i^2 - P\_o^2}{2P\_o t} = \frac{\mu\_o}{k\_D} \nu\_o + \frac{\rho\_o}{k\_F} \nu\_o^2. \tag{1}$$

Thereby, *Pi* and *Po* are the inlet and the outlet pressure. Further parameters are the thickness of the sample *t*, the dynamic viscosity of the coolant μ*o*, the density of the fluid ρ*<sup>o</sup>* and the superficial velocity *vo* where the subscript *<sup>o</sup>* denotes values at the outlet of the sample. To determine the Darcy coefficient *kD* and Forchheimer coefficient *kF* , steady state measurements with different mass flow rates are conducted. The permeability coefficients are then fitted to the resulting pressure - massflow curve using a "least squares algorithm". The uncertainties are calculated using a Monte-Carlo method with a sample size of 200,000 [16]. With the current samples, measurements could be conducted with mass flows up to 10 g/s. The maximum pressures at 10 g/s ranges from 4.75 bar to 5.2 bar between the ceramic samples. The resulting permeability coefficients are also given in Fig. 2.

## *2.2 Hot Gas Channel and Measurement Setup*

The described specimen is exposed to a hot gas flow within the Medium Temperature Facility (MTF). This suction mode driven test facility is heated up by an electrical heater and operating at test conditions of up to *TH G* = 373.15 K for a maximum measurable mass flow rate of *m*˙ *H G* = 0.568 kg/s, a more detailed description is given in [12, 17]. Accelerated by a nozzle,the hot gas passes through a test section of a cross-section size of *AH G* = *WxH* = 60 × 90 mm2 and a final length of 290 mm [12, 14].

In order to obtain information about the boundary layer development above the effused porous samples a measurement rake is inserted in the test section with an axially and vertically traversable apparatus and depicted encircled in Fig. 3. A pitot tube ( 0.5 mm ±0.01 OD, 0.3 mm −0 + 0.02 ID) for stagnation pressure measurements and a Type-K sheath thermocouple with a diameter of 0.5 mm recording a recovery temperature form a measurement rake which protrudes 20 mm oriented blunt into the undisturbed hot gas flow. Due to the inflow on the thermocouple, stem conduction caused measurement errors are neglectable small. A recalculation of the measured data into velocity and temperature profiles is done following the descriptions of [12]. In this investigation five different locations for temperature and velocity profile measurements have been chosen. The numbers 7, 8, 9, 10 and 12 in Fig. 3 refer to these measurement points at axial positions of 148 mm, 164 mm, 182 mm, 216 mm and

**Fig. 3** Test section of the medium temperature facility and the various measuring positions for temperature and velocity boundary layers

**Table 1** Summary of the derived steady-state test case parameters with the according inlet temperature and pressure

240 mm, respectively. These positions are selected due to the main objective of this measurement campaign as mentioned in Sect. 1 with an uncooled third sample, while samples 1, 2 and 4 are cooled by an identical mass flow of coolant air *m*˙ *<sup>C</sup>*1,2,<sup>4</sup> , varied for different testing conditions. Considering the mass fluxes of hot gas and transpired coolant through the porous samples the dimensionless blowing ratio

$$F\_C = \frac{\text{transspired mass flux}}{\text{hot gas mass flux}} = \frac{\dot{m}\_{C\_{1-4}}/A\_C}{\dot{m}\_{HG}/A\_{HG}}\tag{2}$$

can be defined. All steady state operating conditions are listed in details in Table 1.

In this context the pressures *PSi* represent the back plenum pressure in order to perfuse the various samples with their corresponding permeabilities according to Fig. 2 with the appropriate blowing ratios. Furthermore, the temperatures *TSi* pertain to the sample backside temperature, measured by thermocouples positioned on each sample back side. For *TS*<sup>1</sup> , the measurement data showed a significant deviation due to a loose contact to the sample. The measurement data are therefore omitted. Since for the boundary conditions for the simulation, as seen from plenum temperature measurements, no significant deviation has to be expected for sample 1, *TS*<sup>1</sup> is approached as *TS*<sup>2</sup> . On the outlet side the porous samples are exposed to main flow conditions at a hot gas temperature *TH G* = 373.15 K and a hydraulic diameter based Reynolds number Re*Dh* = 200,000. Knowing the test section cross size as well as the static channel pressure *pH G* = 80 kPa inside the test section the hot gas mass flow amounts to *m*˙ *H G* = 0.327 g/s. This results in a bulk velocity of *ubulk* = 80 m/s and a Mach number of *Ma* = 0.2 emphasizing incompressibility of the flow.

Besides boundary layer measurements with the measurement rake, the test section also provides optical access for an areal non-intrusive surface temperature measurement through a Calcium Fluoride window with a thickness of 5 mm. An infrared camera type FLIR SC7600 with a resolution of 640 × 512 pixels and sensitive for

**Fig. 4** Exemplary fit functions for transformation of recorded digital levels to a spatial temperature distribution for the third and fourth sample

wavelengths between 1.5µm and 5µm is installed aside the test section at an angle of α = 33◦ to the porous sample surface. In order to reduce optical warping the infrared camera is traversed parallel to the test section and focused on every sample's center axis individually resulting in four serial recordings per steady-state operational point in Table 1. For quantitative analysis of the infrared data an in-situ calibration according to Martiny et al. [7] with application of an empirical simplification of Planck's law is used. The latter one is fitted by a differential method on the basis of Prokein et al. [11] using the case without cooling, respectively number "0" in Table 1, as reference. This approach is visualized in Fig. 4 for the third and fourth ceramic sample.

For each test case the four surface thermocouples per sample as mentioned in Sect. 2.1 are correlated with the radiation intensity in direct vicinity of each thermocouple. Because of the high volumetric heat transfer coefficient, it is assumed that the porous wall and the coolant are in thermal equilibrium for this experimental setup [13]. Hence, the temperature measured by the thermocouples is roughly the wall temperature. Applying the differential method the latter ones are relating the surface temperature reductions to reductions of the measured radiation intensity recorded as Digital Levels, an intensity unit of the infrared camera linked to the chosen integration time. Thereby, external disturbances are eliminated due to the stationary operating points associated with constant disturbance.

## **3 Numerical Setup**

For the simulation of transpiration cooled systems, numerical models were developed in cooperation with Dahmen et al. [1]. Thereon, a Computational Fluid Dynamics (CFD) design tool using the industry standard simulation software ANSYS CFX 17.2 has been developed. Latter one solves the Reynolds-averaged Navier–Stokes (RANS)

**Fig. 5** Numerical setup

equations using a Finite-Volume method. The investigated problem is separated into two domains, representing the hot gas duct and the porous samples, respectively. Each domain is solved separately until local convergence is obtained. The results at the interface between the domains are transferred as boundary conditions, therefore coupling both domains externally via a Python script instead of a monolithic approach using ANSYS-internal coupling mechanisms. This approach has been validated using experimental data [8]. Global convergence is obtained when the difference of both temperatures at the interface reaches 0.1K.

For the hot gas domain, the given inlet boundary conditions are the measured inlet temperature and velocity profiles as well as the averaged outlet pressure provided by the vacuum pump [12]. The duct walls are either set as isothermal or adiabatic according to Fig. 5. Turbulence is modelled by the Shear Stress Transport (SST) turbulence model implemented in CFX, combining the κ-ω-model described by Wilcox [18] for the boundary layer region and the κ--model for the free stream region. The iteratively changed boundary conditions provided by the porous domain are the sample surface temperatures *TP M*,*<sup>s</sup>* for the solid and *TP M*, *<sup>f</sup>* for the fluid as well as the outlet velocity vector −→*v P M*,*out* . The sample domain is modelled using the porous model implemented in CFX based on the Darcy-Forchheimer equation. The reservoir-side sample wall temperature boundary condition *in* is taken from experimental data according to Table 1, assuming thermal equilibrium between fluid and solid on the sample reservoir interface. The coolant mass flow is being calculated using the definition of the Blowing Ratio as given in Eq. 2, while assuming a fixed hot gas mass flow. On the duct side interface, the calculated heat flux stemming from the hot gas domain calculation is applied as a boundary condition *int*,1. The gaps between the samples are being modelled by setting a rather conservative thermal resistance of 3.84 · 10−<sup>2</sup> m2K W−<sup>1</sup> on the sample interfaces as described in [5].

**Fig. 6** Measured (symbol) and simulation (lines) velocity boundary profiles in streamwise direction at their corresponding axial position for various blowing ratios F in %

## **4 Results and Interpretation of the Serial Transpiration Cooling Experiment**

The following section discusses the experimental and numerical results. In order to obtain an all-encompassing impression on the thermal situation in context of the non perfused ceramic sample, Fig. 7 illustrates the temperature boundary layer situation. Followed by an analysis of the surface temperature distribution measured by infrared thermography in Figs. 8 and 9, the temperature progression is continued with the sample-internal temperature distribution depicted in Fig. 10 assuming thermal equilibrium of fluid and solid. To complete the picture of the overall thermal structure a visualization of the fluid mechanical boundary layer situation is added in Fig. 6. As the comparison to the numerical simulations is the main purpose here, the presented data focuses mainly on cases 1, 3-5 described in Table 1, where the agreement is seen as acceptable. For higher blowing ratios additional investigations are needed.

In order to gain an overview of the overall fluid mechanical situation the velocity boundary layer profiles are shown in Fig. 6. Last mentioned are corrected in height by 0.3 mm as described in [12] because of placing the measuring probe under pretension near the wall. Visible in experimental data is an increase of near wall velocities due to a reduction of the coolant layer with increasing axial positions on top of the non cooled sample, until the fourth sample at *x* = 240 mm that is perfused again. However, the near wall measurements need to be considered carefully due to the finite dimension of the pitot tube with an outer diameter of 0.5 mm as described in Sect. 2.2. Nevertheless, a good agreement can be stated for the wall remote area in transition to the undisturbed free stream velocity in the channel center region with the numerical data. But in the range of the last 10–15% dimensionless distance to the wall the velocities differ significantly numerically predicting higher velocities in the velocity boundary layer. This mismatch motivates for a more profound insight of the mechanical boundary layer description and consequently needs to be investigated further.

Continuing on from that, the temperature profiles are also shown in Fig. 7 both experimentally and numerically up to a dimensionless channel height of 0.25. Addi-

**Fig. 7** Measured (symbol) and simulation (lines) temperature boundary profiles in streamwise direction at their corresponding axial position for various blowing ratios F in %

tionally, the surface temperatures, recorded by infrared thermography and averaged over a length of ±1mm in the direct vicinity of the five profile measurement points according to Fig. 3 in Sect. 2.2 along the median axis, are depicted in the temperature profile plots of Fig. 7 with a cross. It has to be noted that the agreement of the temperature profiles up to blowing ratios of *F* = 0.5% and a progressed axial position is quite decent. Even though three-dimensional channel side effects are neglected numerically, the difference of absolute values is rather small. However, the measured profiles show a slight kink between thickened boundary layer and non cooled, reheating wall, which is not visible in the simulated profiles. This experimentally measured thermal boundary layer behavior reflects the context of Fourier's law, considering the proportionality of heat flux and temperature gradient [13]. Due to missing coolant the heat flux into the wall is reduced in accordance with an increased surface wall temperature. Combined with a further increase of the thermal boundary layer thickness due to turbulent mixing effects within the hot gas flow, the kink occurs in the temperature profiles. Besides the numerically optimizable thermal boundary layer in the wake above the non-cooled ceramic sample, the boundary layer profiles of the cooled fourth sample are met well even for higher blowing ratios. Nevertheless, it has to be said, that also thermal near wall measurements need to be considered carefully due to the experimental setup explained in Sect. 2.2 with a measurement rake placed on the surface in contact to the wall with slight pretension. This and the extremely small size of the thermal viscous sublayer can further explain the discrepancy of the measured near wall temperatures and the infrared temperature data. Whereas the measured temperature profiles and the infrared thermography show slight differences to the numerical data the good agreement of the simulated data for blowing ratios up to *F* = 0.5% is even more remarkable. While at the beginning of the uncooled sample at a position of *x* = 148 mm the agreement is still rather poor, more downstream this agreement is convincing and is meeting the measured infrared surface temperatures perfectly.

**Fig. 8** Surface temperature distribution measured via infrared imaging (note different color scales per blowing ratio)

The temperature distribution on the sample surface determined via infrared imaging is shown in Fig. 8. For the perfused samples, it can be seen that the streamwise peripheral edges are at a higher temperature level compared to the sample center line, which is attributed to heat conduction from the hot channel walls. Further visible is a characteristic stripe pattern orthogonal to the flow direction which corresponds to the carbon fiber plies. The four thermocouples per sample used for calibrating the infrared camera as described in Sect. 2.2 can clearly be seen. The white spaces between the samples represent the non cooled metallic parts of the specimen, where the calibration of the infrared camera is not valid, and therefore no temperature data is available.

Due to the transpiration cooling, samples 1 and 2 are continuously cooled down, with across the gap could be observed, indicating that the gap has no significant influence on the cooling effect. In contrast, the trailing edge of sample 2 shows a slight increase of the surface temperature. For the non cooled sample 3, the surface temperature already increased over the gap and is further increasing over the first parts of the sample. While not reaching the temperature of the non cooled test case of *TS*,*uncooled* = 367 K, the temperatures increase over the whole sample length. Especially for low blowing ratios, the temperature on sample 4 is almost immediately

**Fig. 9** Sample surface temperature distribution - measured data and numerical results

down or even below the temperatures of sample 2. The increase of the blowing ratio does only decrease the temperature level of the specimen.

In order to further investigate these effects, the surface temperature profiles along the sample center line marked red in Fig. 8 are depicted in Fig. 9 and compared to numerical simulations. Noticeable from these measurements, the amplitudes of the visible temperature oscillations are higher for the cooled samples compared to the uncooled sample. Comparing the experimental infrared temperature data to the simulated surface temperatures shows a good agreement. For low blowing ratios *F* ≤ 0.5%, the simulations match the cooling effect remarkably well on the first two samples as well as the third sample. In contrast, on the fourth sample the simulations overestimate the cooling effect. With increasing blowing ratios the simulations start to deviate from the measurement, as the cooling effect is significantly overestimated.

The measured sample-internal temperatures of samples 3 and 4 in comparison with the simulated sample temperature distribution are shown in Fig. 10. Subsequently focusing on the internal sample temperatures similar effects can be recognized. With the non perfusion of the third sample low temperature gradients through the channel height occur relatively to the much higher gradients in the cooled sample. This is directly related to the higher surface temperatures due to the kinking temperature profiles as explained above. In accordance with this, also on the backside a temperature gradient occurs. Despite a well isolated stack of samples, with heat conduction by the metallic mounting the entering compressed coolant of ambient air at ambient temperature is heated up and leads to a temperature layering within the sample back plenum. Comparing the simulation results to measurement data, the perfused sample 4 shows a significant deviation for blowing ratios of *F* ≥ 0.5%. For the unperfused sample, the simulated temperatures fit the measurement data for every investigated blowing ratio well.

**Fig. 10** Temperature profiles in porous samples 3 and 4 for various blowing ratios F

## **5 Summary and Outlook**

The focus of the presented work was to investigate the cooling efficiency of a serial transpiration cooling arrangement. This was accomplished by setting up a serial arrangement of four identical CMC samples which could be independently perfused with cooling air. Measurements of the boundary layer were conducted using a measurement rake consisting of a pitot tube and a Type-K thermocouple. Additionally, the sample surface and internal temperature were measured using both thermocouples and infrared imaging. CFD simulations using ANSYS CFX were performed to support the experimental data. The cooling effect can be seen in infrared images. The described methods could be used to investigate the different phenomena linked with the cooling effect (coolant film, conduction in the specimen and sample internal heat transfer). Simulation results were compared with the experimental data, showing good agreement at low blowing ratios *F* ≤ 0.5% for both flow temperature profiles and the surface temperatures provided by infrared measurement data. For higher blowing ratios, the numerical setup will be further improved in order to accurately simulate transpiration cooled systems.

In future investigations, the results will be transferred in an application-near environment, using the Sub-scale Validation Experiment (SVE), a cylindrical serial transpiration cooling experiment which is both capable of performing tests in a hot gas duct as well as using combustion processes in order to create an realistic environment comparable to rocket engine combustion chambers.

## **References**

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## **Film Cooling in Rocket Nozzles**

**Sandra Ludescher and Herbert Olivier**

**Abstract** In this project supersonic, tangential film cooling in the expansion part of a nozzle with rocket-engine like hot gas conditions was investigated. Therefore, a parametric study in a conical nozzle was conducted revealing the most important influencing parameter on film cooling for the presented setup. Additionally, a new axisymmetric film cooling model and a method for calculating the cooling efficiency from experimental data was developed. These models lead to a satisfying correlation of the data. Furthermore, film cooling in a dual-bell nozzle performing in altitude mode was investigated. The aim of these experiments was to show the influence of different contour inflection geometries on the film cooling efficiency in the bell extension.

## **1 Motivation**