*Article* **Kriging-Based Framework Applied to a Multi-Point, Multi-Objective Engine Air-Intake Duct Aerodynamic Optimization Problem**

**Przemysław S. Dr ˛ezek ˙ 1,2,\*, Sławomir Kubacki 2 and Jerzy Z˙ ółtak 1**

**Abstract:** The forecasted growth in dynamic global air fleet size in the coming decades, together with the need to introduce disruptive technologies supporting net-zero emission air transport, demands more efficient design and optimization workflows. This research focuses on developing an aerodynamic optimization framework suited for multi-objective studies of small aircraft engine air-intake ducts in multiple flight conditions. In addition to the refinement of the duct's performance criteria, the work aims to improve the economic efficiency of the process. The optimization scheme combines the advantages of Kriging-based Efficient Global Optimization (EGO) with the Radial Basis Functions (RBF)-based mesh morphing technique and the Chebyshev-type Achievement Scalarizing Function (ASF) for handling multiple objectives and design points. The proposed framework is applied to an aerodynamic optimization study of an I-31T aircraft turboprop engine intake system. The workflow successfully reduces the air-duct pressure losses and mitigates the flow distortion at the engine compressor's front face in three considered flight phases. The results prove the framework's potential for solving complex multi-point air-intake duct problems and the capacity of the ASF-based formulation to guide optimization toward the designer's preferred objective targets.

**Keywords:** optimization; multi-objective; multi-point; Kriging; metamodel; surrogate; intake; aerodynamics; CFD; mesh morphing; achievement scalarizing function


**4. The historical role of the built environment in pandemics before the advent of antibiotics**

Until the arrival of antibiotics in the middle of the 20th century, the main historical methods against bacterial pandemics were limiting the contacts between individuals through **isolation, quarantine and confinement** (**lockdown**) and, from the 19th century, the architectural and urban measures concerning air quality and sunlight.

In the case of leprosy, containment led to the appearance of the first dedicated architectural program, the leprosarium. The measure was common in Medieval Europe [6], although "less uniform and prescriptive [7]".

Plagues were the deadliest pandemics. The 1346–1353 Black Death supposedly killed up to half of Europe's population [8]. They pushed to a diversification of measures aiming the limitation of contacts between individuals, such as isolation, quarantine, confinement, the use of plague mask and the introduction of the medical passport. They also led to dedicated constructions, such as the 27 km long, six feet tall, Plague Wall in the French Vaucluse mountains traced in 1721 [9, 10]. Since the 19th century, plagues impact diminished.

The tuberculosis, "the white plague", took the relay, with a peak mortality rate in Western Europe in 1800 [11]. Tuberculosis deaths counts for 45% between 1790 and 1796 in Bristol, 33.2% of deaths between 1751 and 1778 in Marseille [12] and for 25% of death between 1810 and 1815 in New York City [13]. In 1900, it remained the third cause of mortality after cardiovascular diseases and influenza–pneumonia in the US [14].

In France, the backbone of the fight against tuberculosis was the **Hygiene movement** in which public health was supposed to scientifically guide political decisions, architecture and urbanism. The movement started in the 1820s, continued with the creation of the Hygiene Commissions (1848) and of the Commission for Unhealthy Housing (1950) [15] and reached its peak in the urban renewal during the Haussmann period as Seine (Paris) prefect (1853–1870). The French capital applied the hygiene reform at the largest scale ever seen: **sewage, wastewater treatment, waste removal, air circulation inside and between buildings, sunlight**.

**Hygiene movement derived principles definitively marked architecture and urbanism.** The sunlight that kills bacteria imposed the sanatoriums as general architectural models, with vast windows stretching from one side to the other of the room and terraces for sun baths. Sunlight and ventilation at the 45th parallel north are the reason for imposing distances in between buildings greater than the building height.

At the turn of the 20th century emerged the British **Garden City movement**, started with the Ebenezer Howard's 1898 book, republished in 1902 as *Garden Cities of To-morrow*. In Germany and Switzerland appeared the *Lebensreform* (Life Reform) movement.

The turn of the 20th century brought the first *International Congresses on Tuberculosis*: Berlin (1899), London (1901), Paris (1905). The *First International Congress for Sanitation and Housing Health Safety* was held in Paris (1904). The congress report correlates population density and health. The European research of the French dr. Samuel Bernheim concludes that "The tuberculosis mortality is proportional to the housing density; the danger of infection is all the greater when the residents are more cramped in their housings [15]".

The hygiene measures led to a decline of tuberculosis and, at the turn of the 20th century, mortality was reduced at half in Paris between 1872–1900 and 1901–1925 periods [12].

The 19th century Hygiene movement marked the Interwar modernist architecture. Architect's **Le Corbusier** *Five Points of a New Architecture* are derived from Hygiene movement theories. The **house on** *pilotis*, reinforced concrete columns raising the house from the ground, allows aeration. The **roof garden** is inspired by the sanatorium sunbath terraces. The **free plan** allows the liberation from being the "slave of the load-bearing walls". The **horizontal window**, "essential goal of the house", which "runs from one end to the other of the façade" is directly taken from the 19th century recommendations. The **free façade** in front of the columns is a "lightweight membrane made of isolating walls or windows". Modernist urbanism is synthesized by the Le Corbusier architect book *Athens Charter* (1933) and the Josep Lluís Sert architect *Can our cities survive?* (1942). Hygiene movement principles were employed, emphasizing lighting and sunlight, light-oriented buildings and air circulation inside and between buildings.

One year later, in 1943, the discovery of the streptomycin antibiotic brought the first effective treatment for tuberculosis. The health strategies against bacterial pandemics no longer needed the support of architecture and urbanism.

#### **5. Architecture and urbanism after the emancipation of medicine**

As human health ceased to be an architectural and urban issue, Modernist movement, that promoted air, sun and light, was judged by social and environmental concerns determined by the functional segregation and the automobile-based traffic. In 1972 was symbolically declared the death of the modernist movement with the demolishment of a 1955 modernist US housing planned according to the principles of Le Corbusier [16].

The environmental counterreaction appeared in the late 1960s with the **green architecture**, as a reaction to the suburban sprawl and to the energy crisis. Different approaches are green city, sustainable city, eco city, zero & low carbon cities, zero energy city, livable city, compact city, smart city or resilient city. They concern pollution, carbon emission, energy, water, waste management and recycling, green-space ratios, forests and agricultural land loss.

The counterreaction to the social environment led in the US to the **New Urbanism** movement, in the 1980s. It emphasized mixed-use neighborhood and encouraged walking and bicycle transportation [17]. At the same time emerged in Europe the **Urban Village** movement that also promotes mixed use zoning aiming for partial self-containment by combining working, leisure and living, leads to medium-density housing, encourages walking and bicycling as well as public space encounters.


**Acknowledgements**

such as hunting and disease control impacts by boundary fencing of the park, culling operations and water provisioning, have influenced the dynamics of large herbivore population trends in the Kruger National Park (KNP) over the past century [83, 84]. Thus, the interactive effects of disease and climate-induced factors have the potential to affect many iconic African wildlife species under a changing climate. Changing climatic conditions are therefore likely to affect safari hunting and the wildlife tourism sector due to changes in the abundance of such iconic species. Mawdsley et al. [81, 82] suggest that effective climate change adaptation incorporates protec-

Generally, in Southern Africa, augmenting natural water supplies by providing artificial water points is an intervention commonly adopted by managers of national parks and other large protected areas. In addition, some of the most commonly used adaptation strategies to

**i.** Expansion of protected areas to include migration corridors and seasonal feeding areas

**ii.** Improving connectivity of habitats to facilitate dispersal to appropriate habitats [27]. In view of the magnitude of impacts, in future it will be important to incorporate predicted and observed climate change impacts into overall wildlife management plans and to review and modify existing laws, regulations and policies regarding wildlife management. Kupika and Nhamo [84] noted that most countries in Southern Africa do not mainstream climate change in their biodiversity-related policies. Thus, lack on enabling policy framework retards progress in as far as responding to climate-related disasters is concerned. Other countries, e.g. Zimbabwe, rely on a centralized system towards disaster risk reduction. Although the implementation on the ground is multi-sectoral, disaster response is hampered by bureaucracy within the Parks and Wildlife Management Authority. Thus, protected area managers are not flexible to directly implement any short-term or long-term

Apart from mainstreaming enabling laws and regulations, consideration should also be given to managing protected areas for climate change mitigation through carbon storage and sequestration, as well as for other ecosystem services. Despite all efforts to adapt to the changing climate, efforts are hampered by several factors related to technical and financial constraints to implement the strategies. Africa as a continent is highly vulnerable to the impacts of climate change because of other multiple stressors such as poverty; illiteracy and lack of skills; weak institutions; lack of political will to confront climate change challenges; limited infrastructure; lack of technology and information; poor health care; armed conflicts; rampant corruption and host of other human anthropogenic activities [13]. Thus, managing threats to the wildlife

resources consequently include managing other confounding stressors to biodiversity.

Generally, climate-induced extreme events such as prolonged and frequent drought periods influenced the abundance and distribution of wildlife resources across Southern

tionist and interventionist approaches (**Table 2**).

[27].

16 Selected Studies in Biodiversity

**4. Conclusion**

deal with impacts of climate change in the wildlife sector include:

adaptation strategies to ensure improved species conservation.

This work was conducted within the framework of the Research Platform "Production and Conservation in Partnership (HYPERLINK "http://www.rp-pcp.org" www.rp-pcp.org). This research was supported by funding from the European Union under the Delivering Innovation and technology through the Reinforcement of Agricultural and Multidisciplinary research capacity (DREAM) project & the Chinhoyi University of Technology (CUT), Zimbabwe.


*4.3.3 Lipids*

Diabetes results in a decrease in the levels of poly-unsaturated fatty acids especially docosohexanoic acid (DHA) and these changes are associated with chronic inflammation. Long term administration of omega 3 fatty acids has been linked to retinal capillary degeneration. DHA, resolvins and autocoids have shown to have critical antiinflammatory properties. Li et al. noted that administration of statins (HMG-CoA inhibitor) inhibited diabetes induced changes in the blood retinal barrier [28].


**3.6. Thermal posttreatment**

After the aging phase, titania thin films are calcinated at high temperature. In this step, a sequence of transformations takes place: evaporation of the remaining solvent and acid (T < 200°C) which activates consolidation of the framework (this step is accompanied by an uniaxial shrinkage of the mesostructure along the z axis); template pyrolysis (T= 250–300°C), which generates the porosity; and crystallite nucleation and growth on walls (T > 300°C) [9].

Typically with mesoporous TiO2 , the thermal posttreatment effectuated to convert the amorphous titania walls into crystalline walls usually results in the partial or total collapse of the mesoporous network [46, 47]. To circumvent such a drawback, several post-synthesis treatments have been developed mainly devoted to increase the thermal stability of the mesoporous TiO2 . In particular, Cassiers et al. [48] reported that the posttreatment of an uncalcinated mesoporous titania powder with ammonia resulted in the formation of mesoporous crystalline titania with thermal stability up to 600°C. Sanchez and coworkers [49] claimed that the mesoporous anatase network could be retained with a porosity of 35% above 650°C by applying a specific post-synthesis delayed rapid crystallization (DRC) treatment. Another study demonstrates that the thermal stability of these crystalline films can be enhanced, up to 850°C, by posttreatment of the film in supercritical carbon dioxide (sc-CO2 ) with the presence of a small amount of precursor, such as tetramethoxysilane (TMOS) [50].

The thermal posttreatment has to be therefore carefully done and monitored especially if a specific TiO2 polymorph is sought. Most of the reported literature data available are dedicated to the preferential formation of anatase vs. the rutile polymorph. Although through the literature a large inhomogeneity in temperature range over the control of a selected polymorph is present and reflects the influence of secondary important factors such as the Ti precursor, the template, the deposition technique, and the experiment conditions used to form the TiO2 mesoporous material [51], most of the reports agree in the temperature range of 350–450°C to promote the exclusive crystallization of the anatase polymorph, while at higher temperature, the rutile phase transformation initiate [42, 52].


**5. Pathophysiology**

The presentation and pathophysiology of Ebstein's anomaly depend on the severity of the morphology and associated congenital heart defects. Symptomatic neonates generally present with cyanosis, cardiomegaly, arrhythmias, and congestive heart failure [18]. At the extreme end in Carpentier type C and D of Ebstein's anomaly, there is severe displacement of the tricuspid valve that results in severe tricuspid regurgitation and an ineffective functional right ventricle. With the physiological elevation in pulmonary vascular resistance typically seen in neonates, the small and ineffective functional right ventricle is unable to generate antegrade pulmonary blood flow, especially when the ductus arteriosus is still patent, which leads to "functional pulmonary atresia." True anatomic pulmonary valve atresia is also associated with Ebstein's anomaly and requires a patent ductus (PDA) to provide pulmonary blood flow.

Another serious condition observed in neonatal Ebstein's patients is a "circular shunt," where there is ineffective systemic output due to recirculation of blood with a poorly functioning right ventricle and severe tricuspid regurgitation in association with an atrial septal defect and a patent ductus arteriosus. Retrograde flow from the ductus arteriosus (**Figure 7** arrow 1) through a regurgitant pulmonary valve

**Figure 7.** *Diagram illustrating the "circular shunt" physiology.*

(**Figure 7** arrow 2) circulates into the right atrium due to severe tricuspid regurgitation (**Figure 7** arrow 3) and then passes into the left heart (**Figure 7** arrow 5, 6) through an atrial septal defect (**Figure 7** arrow 4) for another cycle through this circular shunt via the ductus arteriosus (**Figure 7**). High perinatal mortality is associated with the presence of a "circular shunt"; in utero NSAIDs constrict the ductus arteriosus improving fetal survival and resulting in greater gestational age at delivery [19]. In neonates, a "circular shunt" creates unstable hemodynamics with severe hypoxia and low-cardiacoutput syndrome. Patients may be temporized with mechanical ventilation and inotropic support, but more definitive correction of the physiology with surgical intervention, typically the Starnes procedure may be required [7].

The goal of medical treatment during the neonatal period is to assist with the generation of antegrade pulmonary blood flow by supporting the functional right ventricle. Antegrade pulmonary flow improves as the pulmonary vascular resistance falls and can be augmented by the initiation of pulmonary vasodilators, such as inhaled nitric oxide (iNO). Prostaglandin infusion is crucial to maintain patent ductus in neonates with anatomic pulmonary atresia. A trial of withdrawing prostaglandin may be required to assess for the presence of functional pulmonary atresia. Early prostaglandin withdrawal may also be necessary for neonates with a "circular shunt." With less severe forms of Ebstein's anomaly (Carpentier type A and B), the functional right ventricular can generate antegrade pulmonary blood flow. These neonates may recover out of the neonatal period without any intervention. Such neonates need to be followed into infancy as the tricuspid regurgitation may worsen over time leading to worsening cardiomegaly from worsening right atrial dilatation and thinning out of the atrialized right ventricle [7].

In the neonatal period, cyanosis due to inadequate pulmonary flow and/or right to left shunting, as well as congestive heart failure are the main issues. Neonates with adequate antegrade pulmonary blood flow and a reasonable size functional right ventricle are candidates for a biventricular repair beyond the neonatal period.

Neonates with pulmonary atresia fall into two groups: true anatomic pulmonary valve atresia and "functional pulmonary atresia." In neonates with Ebstein's anomaly and anatomic pulmonary atresia, initial prostaglandin administration followed by either stenting of the ductus arteriosus or placement of a surgical Blalock-Tausig shunt may be the option to get out of the neonatal period in patients with an adequate functional right ventricle. When the functional right ventricle is small, patients may undergo a Starne's repair followed subsequently by a Cone procedure and/or a Fontan procedure.

Neonates with functional pulmonary atresia are often very unstable, as some patients may develop a "circular shunt" with retrograde flow back through the pulmonary valve. Such neonates usually present in extremis and need a Starne's repair. The strategy for stable patients depends again on the size of the functional right ventricle.