**2. Treatment of Radiation Lesions with Stem Cells**

Radiation lesions is amenable to treatment by methods that result in repairing or regeneration of the damaged tissue. In fact, stem cell transplantation in medical practice is not new and have been used for decades in bone marrow transplantation [4].

Stem cell treatment of radiation damage is based on the assumption that the transplanted cells integrate with the damaged host tissue to replace the damaged/lost cells or stimulate the host cells to prevent the damage or regenerate the damaged tissue. The later will obviously be more efficient before establishment of the radiation damage. Transplanting the stem cells before the full establishment of radiation lesion can prevent the development of radiation damage or shorten the duration of the manifestation of the lesion.

Bone marrow transplantation has been successfully used in the treatment of leukaemia, lymphoma, and certain types of anaemia procedures. Initial efforts in this field were directed towards transplantation of pre-differentiated stem cells and a good example of this is bone marrow transplantation that started as early as 1951 with the work of Lorenz [5] who found that infusion of the spleen or marrow cells could protect the irradiated mice. Bone marrow transplantation is based on allogenic use of stem cells. Whole marrow or stem cells of the marrow are extracted from a donor and transplanted to the host to

reconstruct the haemopoietic tissues of cancer patients. The patient, prior to bone-marrow transplantation, is myeloablated by radiation or chemotherapy. The process of bone marrow transplantation is reviewed by [4].

Later, non-tissue specific or naive stem cells were transplanted on the basis of the opinion that the niche, or local microenvironment, consisting of surrounding cells, will define the fate of the transplanted cells and direct the administered stem cells to lodge into target tissue and differentiate into the required cells to restore structural and functional deficits.

In this article, a number of papers indicating the application of stem cells in the treatment of radiation-induced lesions are reviewed. It is also argued that the beneficial effect of transplanted stem cells in irradiated bodies is not necessarily due to the lodging of the transplanted stem cells in the irradiated tissue to replace the lost/damaged cells. It is suggested that perhaps the result is by paracrine effect; i.e., transplanted stem cells secrete bioactive substances that are capable of stimulating the host cells to reproduce and repair the damaged tissue. This means that the transplanted stem cells, besides integrating in the structure of damaged tissues, secrete biologically active factors, mainly in the form of extracellular vesicles, such as exosomes and microvesicles, that stimulate and mobilise the endogenous stem cells to repair the damage. Recently, it was shown by many researchers including ourselves, that the effect of stem cells is exerted in a paracrine fashion [6–8]. Transplanted stem cells, by integration with the host tissue, mobilisation of endogenous stem cells, or a combination of both mechanisms, result in functional and structural improvements of injured tissues. For a review on extracellular vesicles, see [9,10].


**1. Introduction**

Water is the most ubiquitous substance on this planet and has probably received more scientific and technological attention than any other substance. *Water clusters*, in particular, the groups of water molecules held together by hydrogen bonds, have been the subject of a number of intense experimental and theoretical investigations for the past century due to their importance in chemistry [1], atmospheric chemistry [2], understanding cloud and ice formation, as well as a large number of physicochemical and biochemical processes [3]. The exploration of the structural and binding properties of water clusters is the first step to understand the properties of bulk water, the essence of life. The difficulty in obtaining a rigorous molecular scale description of the structure of liquid and solid water is mainly due to the constantly fluctuating hydrogen-bonding network therein. This cooperative hydrogen-bonding in water molecules gives rise to the fascinating arrays of anomalous properties. Also, the cooperativity in aggregates of water molecules is particularly important towards understanding the behavior of the liquid and ionic as well as molecular hydration.

A look at the available literature reveals several monographs as well as reviews [4–9] providing detailed understanding of structures as well as binding, spectral and chemical properties of water and its related clusters. The following discussion comprises a brief review of earlier benchmarking studies on water clusters with a special reference to the structure, energetics and the spectra.

Almost six decades ago, Clementi and co-workers [10] performed benchmarking studies on the water clusters, (H2O)n,n=2–8 within Hartree-Fock (HF) framework. The water dimer, the smallest member of the water cluster family has been studied extensively within experimental [11–13] as well as theoretical framework [9, 14–17] (ΔE = 5.5 0.7 kcal.mol1 and Cs symmetry) since it forms a classical case of hydrogen bond.

According to several experimental [18–22] as well as theoretical studies, the energetically most favorable structure of the water trimer has been confirmed to be cyclic with C1 symmetry. This structure has one external hydrogen atoms on one side of the O-O-O plane and two hydrogen bonds on the other side of the plane. Also, each monomer in this case behaves as a donor as well as an acceptor. Several *ab initio* quantum chemical investigations [4, 6, 7, 14–16, 23–27] have advocated a cyclic, homodromic structure with S4 symmetry of Water tetramer, (H2O)4 which corresponds to the global minimum. The cyclic water tetramer has the free hydrogen atoms in alternate fashion above and below the plane of the O-O-O-O ring. This structure has also been observed in IR-studies of benzene-(H2O)4 and VRT spectra of (D2O)4 and (H2O)4 [28, 29]. Pentagonal rings of (H2O)5 are quite common in clathrate hydrates and in the solvation of hydrophobic groups of small molecules as well as in proteins and in DNA molecules.

Interestingly, the most stable structure for the pentamer follows the puckered cyclic ring pattern [1, 14, 30–32] whereas the *ab initio* studies [4, 6, 15, 16, 23–27] also predicted such a ring structure. Wales [33] pointed out the existence of different ring structures that can be interconverted through low energy barrier pathways consisting of the flipping of hydrogen atoms and bifurcation mechanisms.

The hexamer of water, (H2O)6 shows a transition from cyclic to threedimensional geometries, and could be yet another cluster which has been studied extensively by theory [4, 6, 15, 16, 24–27, 34] and experiments [22, 35, 36]. Several studies [4, 6, 15, 16, 22, 24–27, 34–36] have demonstrated that a large number of alternative three-dimensional structures, such as chair, boat, book, jaws, ring and cage, are likely to be of comparable energies. The study of C6H6 … (H2O)6 by Pribble and Zwier [35] could be considered as the first experimental evidence for the cage structure. Later on, Liu *et al*. [36, 37] also have verified the cage structure of isolated water hexamer through their FIR-VRT spectroscopy. Zero-point vibrational energy (ZPE) seems to play an important role in deciding the preferred geometry of the hexamer. In a recent studies due to Bates and Tshumper [38] proposed that the prism structure is marginally by 0.06 kcal.mol-1 and 0.25 kcal. mol1 at MP2/CBS and CCSD(T)/CBS corrected for zero-point vibrational energy (ZPE) respectively.

Size-specific IR spectra of benzene-(H2O)7 clusters [35] suggest a compact noncyclic structure for (H2O)7 whereas IR-UV and UV–UV double resonance spectra of jet-cooled phenol-(H2O)7 clusters supported a cuboid structure for the heptamer, with one corner being occupied by the phenolic oxygen atom [39]. The vibrational spectrum of pure (H2O)7 [40] indicate the existence of two isomers derived from the S4 octamer cube by the removal of either a double-donor or a double-acceptor water molecule.

Extensive *ab initio* calculations [4, 10, 16, 41–47] suggest that, at low temperatures, (H2O)8 would stabilize into a cube with D2d or S4 symmetry and that, at higher temperatures, entropy considerations could favor the other geometries. Experiments involving pure water clusters [48] as well as hydrated molecules, such as and phenol-(H2O)8, [39] and C6H6-(H2O)8 [49] also support the cubic structure of (H2O)8. Maeda and Ohno [30] explored 164 local minima of (H2O)8 employing MP2/6-311++G(3df,2p)//B3LYP/6-311 + G\*\* level. They have observed that the *D*2*d* isomer was energetically most stable than the *S*4 isomer of (H2O)8. Thus, it may be seen that the smaller water clusters, (H2O)n, n < 8 have been subject of intense investigation within theoretical framework.

*Unraveling Hydrogen Bonded Clustering with Water: Density Functional Theory Perspective DOI: http://dx.doi.org/10.5772/intechopen.99958*

Several possible conformers of various water clusters, (H2O)n, up to nonamer were explored employing continuum solvation model by Malloum and Conradie [31]. They used MN15 DFT framework [32] with 6-31++G(d,p) basis set. According to this study the structures of (H2O)n in continuum solvation (IEF-PCM) framework qualitatively similar to their gas phase counterpart. However, the hydrogen bonds show elongation in continuum solvent. The authors also suggested the effectiveness of MN15/6-31++G(d,p) density functional theory model chemistry for studying water clusters Jensen *et al*. [50] explored 44 possible structures of water nonamer using extensive HF calculations using the 6-311G(d) and 6-311G(d,p) basis sets. It was observed that the energetically favorable structure of water nonamer consist of stacked pair of cyclic water tetramer and pentamer which could be thought of as an extended cube. The computational predictions are in qualitative agreement with the available experimental result [51].

About a decade ago, Shields and coworkers [52] performed a detailed investigations on (H2O)n,n=2–10; employing a combined molecular dynamics and quantum mechanical framework. The focus of the work was on the structures and energetics of water heptamer, nonamer and decamer structures. They observed that the 30 conformers of (H2O)10 spanned within the short range of 2 kcal.mol1 of Gibb's free energy computed at 298 K. They used least-squares fitting based extrapolation and a new approach (MP2/CBS-e) incorporating counterpoise (CP) correction to basis set superposition error. The O-H stretch spectra [51, 53] of (H2O)10 seem to support a butterfly structure and not a fused cage.

For larger clusters viz. (H2O)n, n > 8 there exist some notable computational studies [4–6, 8, 16, 31, 54–59] with employing different levels of theory including the Gold-Standard CCSD(T) level of theory in conjugation with complete basis set (CBS) extrapolation for some structurally important prototype clusters. Todorova and coworkers on the basis of a detailed study involving modified B3LYP, X3LYP, and PBE0 functionals concluded that the modified functionals show better agreement with the experimental structures (in terms of radial distribution function) and dynamics (in terms of self-diffusion constant) properties of liquid water.

Lee and coworkers [60] studied (H2O)11 (undecamer) and (H2O)12 (dodecamer) employing Møller–Plesset second order perturbation theory (MP2) with TZ2P++ basis set. The undecamer structure is though as a combination of cyclic (H2O)5 and (H2O)6 with 16 hydrogen bonds. Similar structure for (H2O)11 has been confirmed by Bulusu *et al*. [61] in their study at B3LYP/6-311+G(d,p) level. They also extended their study for (H2O)13. In case of (H2O)12, the isomer arising from stacking of three cyclic tetramers with 20 hydrogen bonds and patterns (D2d)2 or (D2d)(S4) or (S4)2 are energetically favorable conformers [4, 46] on potential energy surface. There also exists another low-lying conformer comprising two fused hexameric units held together by 18 hydrogen bonds. The (H2O)13 structure as confirmed by Bulusu et al. [61] is composed of an addition of isolated water molecule to the (H2O)12 cluster with cuboid conformation.

CCSD(T) level study on dipole polarizability of water clusters upto (H2O)12 has been reported by Hammond *et al*. [62]. This study also involve performance assessment of six density functionals namely. PBE, PBE0, B3LYP, BLYP, X3LYP and PW91. The authors concluded that the density functional PBE0 with aug-cc-pVDZ yield better agreement with the results from CCSD(T) level of theory than the other density functionals.

In a benchmarking study, Bryantsev and coworkers [16] investigated some structurally important neutral and charged water clusters viz. (H2O)n,n=2–8, and 20, H3O+ (H2O)n,n=1–6, and OH-(H2O)n,n=1–6. They employed B3LYP, X3LYP, M06, M06-L and M06-2X density functionals as well as Møller-Plesset perturbation theory (MP2) and coupled-cluster theory with single, double, and perturbative

triple excitations CCSD(T) levels of theory with various extended basis sets. The basis sets employed were aug-cc-pVnZ, where n = 2, 3, 4 and 5. It was concluded that Minnesota density functionals namely M06 and M06-L used with aug-cc-pV5Z basis set yield vary small mean unsigned error (MUE) of 0.73–0.84 kcal.mol1 . However, these methods are computationally very expensive even for mediumsized water clusters. In a detailed benchmarking investigation on (H2O)16 and (H2O)17, Leverentz and coworkers [54] employed 61 levels of density functionals, 12 computational methods combining DFT with molecular mechanics (MM) damped dispersion (DF-MM), seven semiempirical methods, as well as semiempirical methods with MM- damped dispersion. The results from their study were compared with those from CCSD(T)/aug-cc-pVTZ level of theory [63]. They advocated that the density functionals viz. M06-2X, M05-2X, ωB97X-D, SCC-DFTB-g are good for binding energies.

A generalized energy-based fragmentation (GEBF) approach was used by Wang and Li [64] to compute the interaction energies of (H2O)20 conformers at explicitly correlated version of coupled-clusters with singles, doubles and triple excitation (CCSD(T)-F12) level of theory. They have also computed interaction energies of these conformers using 32 different levels of DFT-framework. Based on the detailed investigation it was concluded that the functionals ωB97X-D and M05-2X functional show good agreement in absence of empirical dispersion correction. Also, the functionals including the empirical dispersion corrections viz. LC-ωPBE-D3 and B97-D show very close agreement with the CCSDT results. The same approach was employed by Yuan and coworkers [65] to investigate relative energies of large water clusters namely (H2O)n, n = 32, and 64.The energies computed with GEBF method were compared with CCSD(T) and MP2-levels of theories combined with CBSlimit. It was concluded that the popular functionals viz. B3LYP, PBE0, and DFTB3 do not yield accurate energies whereas the functionals viz. LC-ωPBE-D3 and ωB97X-D yield better agreement of relative energies when compared with CCSD (T)/CBS-level of theory. They advocated use of at-least aug-cc-pVTZ basis set for computational studies on water clusters as well as clusters in aqueous solutions.

Mallhoun *et al*. [8] on performed a careful study of (H2O)n,n=2–30 employing the M06-2X functional with aug-cc-pVTZ basis set. They observed that the cage structures are energetically more dominating as compared to the stacked structures comprising tetrameric and pentameric units for (H2O)n, where n = 26–30. The computed relative energies of their study are in good agreement with the earlier results with CCSD(T)/CBS level of theory. On the basis of their results, it was concluded that performance of the density functional when compared with CCSD(T)/CBS in the increasing order is: MN15 [32], ωB97X-D, M06-2X and APFD. The density functional, MN15 from Truhlar and coworkers outperforms all other density functionals.

Thus, it may be seen from above discussion that a study comprising a short review of benchmarking studies on structures, and energetics of water clusters, (H2O)n is warranted. The present work also involves an unbiased assessment of some well-known density functionals for small prototype water clusters, as well as the understanding of basic building blocks for building bigger clusters.

### **2. Computational methodology**

#### **2.1 Benchmarking of the DFT framework**

In order to benchmark the density functionals, the present work involves use of two *ab initio* theories, namely Hartree-Fock (HF), Moller-Plesset second order perturbation theory (MP2) and eleven different density functionals, viz. B3LYP

*Unraveling Hydrogen Bonded Clustering with Water: Density Functional Theory Perspective DOI: http://dx.doi.org/10.5772/intechopen.99958*

[66–68], B3PW91, BHandHLyp, BLYP, PBE0, M06 [69, 70], M06-2X [69, 70], M06-L [69, 70], τ-HCTHHyb [71], ωB97X [72], AND ωB97X-D [73]. These methods were used in combination with a variety of basis sets viz. 6-31G(d,p), 6-311++G(d,p), 6-311++G(2d,2p), aug-cc-pVDZ, aug1-cc-pVTZ (aug-cc-pVTZ on Oxygen atoms and cc-pVTZ on Hydrogen atoms), aug-cc-pVTZ as well as def2- TZVP for benchmarking the density functionals. Thus, the benchmarking of smaller clusters was done with 91 different model chemistries against the Goldstandard method, coupled-cluster theory with singles, doubles and triples excitation (CCSD(T)/aug-cc-pVQZ). The water clusters, (H2O)2 and (H2O)3 and the isolated water molecules were selected for benchmarking the interaction energy and structural parameters.

#### **2.2 Structure generation**

The prototype structures viz. isolated water molecule, water dimer and trimer were selected for this benchmarking. The initial structures of the energetically favorable water clusters, (H2O)n were taken from the earlier benchmarking studies which are based on the supermolecular approach [4, 14, 27, 62]. These structures were subjected to further geometry optimization within the judiciously shortlisted DFT-framework.

#### **2.3 Computational framework**

Initial optimization of all the structures at Hartree-Fock (HF), and Moller Plesset second order perturbation theory (MP2) level with computationally decent and manageable basis set, 6-31G(d,p) was performed employing Gaussian 09 [74] and GAMESS [75]. For standardization of the results, the geometry optimization, vibrational frequency computations were carried out using Gaussian 09 suite of program with default options. However, for all the density functional theory calculations the integration grid specified was an ultrafine pruned grid with 99 radial shells and 590 angular points per shell as defined in the Gaussian 09 suite [74].

### **3. Results and discussion**

The present work embarks on providing an extensive overview of notable investigations on water clusters, (H2O)n within quantum chemical as well as density functional theory framework. The results of present work are summarized below.

Selection of an appropriate computational framework which is also known as model chemistry (that is a combination of a computational theory and a basis set) for a given problem is an extremely tough task due to availability of wide range of methods and variety of basis sets. The same fact is evident in the Introduction section that outlines a wide range of computational methodologies including DFT framework employed for water clusters.

In order to understand the trends in energetics and structures, some structurally important prototype clusters, viz. (H2O)n,n=1–6, 8, 20 were selected for which some data at high-levels of theory is available. Also, for benchmarking of density functionals the smaller clusters viz. (H2O)2, and (H2O)3 were studied employing 91 model chemistries (as mentioned in the Methodology Section) against the Goldstandard method, coupled-cluster theory with singles, doubles and triples excitation (CCSD(T)/aug-cc-pVTZ) [16]. The various (H2O)n clusters considered for reviewing are depicted in **Figure 1**. The details of interaction energy data compiled from the present investigation as well as other notable studies is compiled in **Table 1**.

#### **Figure 1.**

*Schematic representation of B3LYP/6-311++G(2d,2p) optimized structures of (H2O)n,n=2–6. Data derived from ref. [16]. Oxygen atoms are denoted by Red spheres, Hydrogen atoms by White-Grey color. Dotted lines represent hydrogen bonds.*

The mean unsigned errors for structural parameters viz. bond lengths, bond angle as well as energetics of (H2O)2 and (H2O)3 are presented in **Tables 2**–**4** respectively. The energies for larger clusters were adapted from other references as mentioned in the respective Tables. It may be seen from the **Table 1** that all the computational model chemistries involve an extensive aug-cc-pVTZ basis set that make use of 92 basis functions per water molecule. Thus, as an example studying a water clusters (H2O)30 would require 2760 basis functions, which makes the exploring and scanning of several energetically favorable conformers, rather an arduous task.

In order to explore a convenient alternative to a computationally demanding, aug-cc-pVTZ basis set, a truncated version of aug-cc-pVTZ basis set was employed which involve the use of aug-cc-pVTZ basis set on Oxygen atoms and cc-pVTZ basis set on Hydrogen atoms. This exercise reduces the number of basis functions per water molecule to 74.

It is clear from **Tables 1**–**4** that the decent basis set, viz. 6-31G(d,p) is good only for the initial structure optimization for larger clusters. Though the MUE for interaction energies for various quantum chemical and DFT framework are large the overall trends and structures show qualitative trends similar to the other extended basis sets.

Taking a cue from the earlier studies [16, 54, 77] as well as the basic computational insights from the present investigation it may be concluded that the density functional theory in combination with appropriate basis sets can predict interaction energies at par or even with better accuracy when compared with MP2-level of theory. On the basis of review of earlier studies and present work, the density


*3.1. Flow Deflection in the Guide Vane Domain*

Figure 7 shows an example of a typical flow state in the shutdown process (GVO = 6.5◦~1.82◦), including the velocity contour and streamline at the Z = 0 plane (middle plane of the GV domain). It can be observed that the main stream in the GV domain is deflected when it passes through the gap in the GVs.

At GVO = 6.5◦, the water from the runner outlet flows out along the channel between the movable guide vanes, and its direction is consistent with the overflow channel. When the GVO decreases to 3.1◦, it can be seen that the direction of the water flow is no longer towards the right side of GV #4, but is deflected by nearly 90◦ and flows towards the fixed guide vane. The main flow in the deflection process is very unstable. When the GVO is further reduced to 1.82◦, the water flow is completely attached to the right wall of GV #5. According to the streamline distribution, a clockwise circulation is formed between the movable guide vane and the fixed guide vane.

The reverse process is found during the startup, as shown in Figure 8. At GVO = 2◦, the water flow from the runner outlet is completely attached to the right wall of GV #5. When the GVO increases to 3.3◦, it can be seen that the direction of the water flow is no longer attached to GV #5, but is deflected by nearly 90◦, and the water flows towards the fixed guide vane. There are vortices with opposite rotation directions on both sides of the main stream. When the GVO is further decreased to 4.45◦, the main stream flows out along the channel between the movable guide vanes, and its direction is consistent with the overflow channel.

We gave definitions for the two flow types in the pump mode, which are sketched in Figure 9. Type I is defined as the flow type with a direction consistent with the incoming flow direction, while Type II is the flow type with a deflected direction that is attached to the guide vane head. This belongs to the state of the transition between the two.

**Figure 7.** Global velocity contours of the shutdown process (Z = 0 plane).

**Figure 8.** Global velocity contours of the startup process (Z = 0 plane).

**Figure 9.** A schematic diagram of the flow pattern definitions.

The main flow in the gap of GVs #26 and #1 was chosen to demonstrate the formation of these two flow patterns. Figure 10 shows the velocity resolution of the main flow near the tailing edge of GV #26. *Vr* is the radial velocity, and *Vθ* is the tangential velocity. In the plot, a subscript of 1 stands for a small opening, and 2 stands for a large opening. It can be seen that, near the tailing edge of the GV, the radial velocity is greater than the tangential velocity. At the small opening, the incidence angle is too large, and this large incidence angle can lead to flow separation near the tailing edge of GV #26. Then, this separation forces the main flow to turn toward the leading edge of GV #1. Because the curvature radius of the GV surface is too large, the Coanda effect [24,25] can make the main flow adhere to the surface of GV #1 so that the main flow stays in Type II. However, at the large opening, the incidence angle can be reduced with a change in the vane angle; thus, the flow separation is weakened and the main flow eventually stays in Type I.

**Figure 10.** Analysis of the resultant velocity: (**a**) small opening; (**b**) large opening.

#### *3.2. Flow-Field Characteristics of Startup and Shutdown*

Because the flow pattern of each guide vane has little difference, we selected some guide vanes (GV03, GV04, GV05, GV06) for the flow-field analysis. In order to analyze the characteristics of flow deflection between moving and stationary guide vanes in detail, Figure 11 shows the local velocity contours and pressure contours of the shutdown process. During this process, the GVs gradually closed from a max opening of 19.69% to a max opening of 5.91% (decrease in the GVO from 6.5◦ to 1.95◦).

**Figure 11.** *Cont*.

**Figure 11.** Local velocity contours (**left**) and pressure contours (**right**) of the shutdown process (Z = 0 plane, GVO = 6.5◦~1.95◦).

When GVO = 6.5◦~4.58◦, the main flow stays in Type I. At GVO = 6.5◦, the direction of the main flow is towards the left side of the fixed guide vane directly in front of the flow channel. The velocity coefficient *kv* is about 0.9. The velocity at the throat between the two GVs is the highest where *kv* is about 1.2. Therefore, the pressure here is also the lowest relative to the flow field inside and outside the GV. The velocity on the right side of the main stream is very low with *kv* ≈ 0.1.

As the GVO decreases, the main flow tends to shift away from the left movable guide vane, as shown at GVO = 4.58◦. When the GVO decreases, the velocity at the throat gradually increases and the pressure further decreases, which is caused by the decrease in the cross-sectional area of the overflow.

In the range of GVO = 4.58◦~2.08◦, the main flow is in the transition stage between Type I and Type II. When GVO = 3◦, the direction of the main flow is deflected by nearly 90 degrees. At the same time, there is a high-pressure area at the left GV, where *cp* ≈ 0.8. The trailing-edge of the main stream impinges on the other fixed guide vane (transferred from left to right) and flows along the fixed guide vane wall to both sides. With the decrease in the GVO, the deflection angle of the main flow increases further and changes to flow in the flow channel between the fixed guide vanes, as shown at GVO = 2.08◦. At this time, the pressure coefficient inside the GV increases to *cp* ≈ 1.2.

When the GVO further decreases to 1.95◦, the main flow state changes to Type II. At this opening, the main stream flows around the leading edge of the GV. The throat position becomes the boundary between the high-pressure area and low-pressure area.

Moreover, the main flow stays in Type I when the GVO is more than 6.24◦, and the flow pattern stays in Type II when the GVO is less than 1.95◦. The pressure plot shows that the pressure at the tailing edge of the GV is higher than that at the leading edge of the GV; thus, the water coming from the runner domain pushes the GV to close, and the resultant moment should be positive. Furthermore, with the decrease in the GVO, the HT must theoretically increase.

During startup, the flow goes through the process of opposite deflection, as shown in Figure 12. With the increase in the GVO, the main flow starts deflecting from Type II to Type I. Unlike in the shutdown process, when GVO = 2.8◦, the main flow is still in Type II, while the main flow is converted to Type I.

**Figure 12.** *Cont*.

**Figure 12.** Local velocity contours (**left**) and pressure contours (**right**) of the startup process (Z = 0 plane).

The pressure plot shows that the pressure at the tailing edge of the GV is larger than the pressure at the leading edge of the GV; thus, the resultant moment on the GV helps the GV to close. In this paper, the moment that forces the GV to close is defined as a positive moment (HT > 0).

The behaviors of the deflections during the startup and shutdown processes are not the same. Figure 13 shows a comparison of the GVO ranges of the deflections between the shutdown and startup processes. The specific deflecting range of the shutdown process is larger than that of the startup process. For the shutdown process, the deflection angle ranges from 1.99◦ to 5.32◦ on average. For the startup process, the range is reduced to 2.83◦ to 4.11◦ on average.

**Figure 13.** A comparison of GVO ranges of the deflections between the shutdown and startup processes.

During the shutdown process, the GVO of the starting deflection fluctuates greatly on different guide vanes. However, for the ending deflection, the fluctuation is small.

#### *3.3. Hydraulic Torque on the Guide Vanes*

Several GVs were chosen for analysis in this part because the torque change trends of most GVs are similar.

Figure 14 presents the GVO-*Cm* plot for GV03, GV04, GV05, GV06, and GV10 during the simulation of the startup process. In the beginning, *Cm* gradually decreases with the increase in the GVO, but when the GVO goes up to 2.8◦, *Cm* abruptly increases. This sudden increase in *Cm* is indicated by the red line. When the GVO is about 4.05◦, which is indicated by the blue line, *Cm* of GV10 is larger than that of the others. As can be seen in Figure 15, when GVO = 4.05◦, the deflection speed of the main stream of GV10 is faster than that of GV06, so the torque of GV10 at this time is greater than that of the other GVs. When the GVO is around 4.22◦ (indicated by the green line), the flow deflection is complete, and the trend of *Cm* slows down. In addition, it can be seen that during the deflection process (GVO ranging from 2.8◦ to 4.2◦), the values of *Cm* have phase differences between each other. This difference is caused by the unstable flow behavior of the main flow during the deflection process, as mentioned above.

**Figure 14.** GVO-*Cm* plot of the startup process.

By comparing the *Cm* plot with the velocity contours of the main flow (Figure 12), it can be seen that the main flow deflection and the increase in *Cm* occur at the same opening. When the deflection occurs abruptly, the velocity near the GV surface on the side of the stay vane decreases quickly; thus, the pressure on the surface of the GV increases. In addition, the resultant moment on the GV suddenly increases.

The GVO-*Cm* plot for GV01, GV03, GV04, GV05, and GV06 obtained from the calculation of the shutdown process shows that *Cm* increases with the gradual decrease in the GVO. However, when the GVO ranges from 5.26◦ to 3.15◦ (which is indicated by the red line and blue line in Figure 16), *Cm* has a turbulent trend, and the GV near the nose of the spiral case (GV01) has a large moment value. This phenomenon is due to the instability of the main flow when the GVO is in the specific range (from a max opening of 19.39% (about 6.4◦) to a max opening of 5.91% (about 1.95◦)) that was mentioned before. The velocity near the surface of the GV fluctuates, and this fluctuation leads to the turbulent fluctuation of *Cm*. When the GVO is less than 3.15◦, *Cm* has a stable trend. Moreover, when the GVO

is about 2.2◦, *Cm* descends sharply, as indicated by the green line in the plot. In addition, the main flow stays in Type II when *Cm* flattens (which is indicated by the yellow line in Figure 16).

**Figure 15.** Comparison of deflection speeds between the main flow of GV10 (**right**) and that of GV06 (**left**) at GVO = 4.05◦.

**Figure 16.** GVO-*Cm* plot of the shutdown process.

It can be inferred that the deflection led to a sudden change in the velocity near the GV, and the pressure on the GV's surface abruptly changed. Consequently, the change in pressure resulted in a sudden increase in the *Cm*; if the transmission of the distributer cannot immediately adapt to this change, there will be a relative displacement between the shaft of the GV and the friction device, which will produce violent friction. This violent friction will lead to vibrations and abnormal sounds.

## **4. Conclusions**

Numerical studies were presented for the startup and shutdown processes of an RPT in the pump mode when GVO is between 1.5 and 6.5 degrees. A dynamic meshing technique was used to investigate the flow deflection of the main flow between the guide vanes. The primary findings include:

**Author Contributions:** Methodology, Q.J., G.W.; formal analysis, Q.J., H.F., W.L.; investigation, G.W.; resources, H.F.; data curation, Q.J., G.W.; writing—original draft preparation, Q.J.; writing—review and editing, Q.J., H.F., W.L.; supervision, H.F., W.L.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by [National Natural Science Foundation of China] [Grant No. 51879140, No. 51679196], [State Key Laboratory of Hydroscience and Hydraulic Engineering] [Grant No. 2021-KY-04], [Creative Seed Fund of Shanxi Research Institute for Clean Energy of Tsinghua University], and [Tsinghua-Foshan Innovation Special Fund(TFISF)] [Grant No. 2021THFS0209].

**Acknowledgments:** The authors would like to thank the National Natural Science Foundation of China (No. 51879140, No. 51679196), State Key Laboratory of Hydroscience and Hydraulic Engineering (Grant No. 2021-KY-04), Creative Seed Fund of Shanxi Research Institute for Clean Energy of Tsinghua University and Tsinghua-Foshan Innovation Special Fund(TFISF) 2021THFS0209 for their financial support.

**Conflicts of Interest:** The authors declare no conflict of interest.