Scoop optimization: A preliminary study

IN

DEGREE PROJECT VEHICLE ENGINEERING, SECOND CYCLE, 30 CREDITS

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STOCKHOLM SWEDEN 2019

Scoop optimization

A preliminary study

BIXENTE ARTOLA

KTH ROYAL INSTITUTE OF TECHNOLOGY

Abstract

Scoops are important parts in an aircraft engine design, as they provide airflow to different equipment and subsystems. The optimization of such a component is essential in order to find a design that can perform properly within a range of flight conditions, with a minimum impair of main flow aerodynamic performances. Scoop design methods are generally based on previous experimental results and are usually constrained by the limited space available. The studied configuration concerns the flush scoop located inside the secondary flow of turbofans which provides flow for a turbine cooling equipment. Depending on flight conditions and engine working point, this scoop will experience various flow regimes, from low mass flow rates to choke flows. Therefore, the study of several scooped mass flow rates is mandatory to extract the scoop behaviour. The thesis concerns the preliminary step before a 3D CFD optimization : a study of influence is run on the baseline geometry in order to investigate the robustness of the solution computed using different methods and to determine the parameters to be optimized. Firstly, the full post-processing methodology is defined to properly evaluate the performance of a design (scoop efficiency, induced pressure losses). A second step consists in analysing the ability of CFD solvers to capture the different flow behaviour. This point is addressed by comparing solvers (Fluent, elsA, PowerFLOW), meshes (structured, unstructured) and turbulence models. The third step deals with the optimization strategy definition to improve the scoop design and thus the engine fuel consumption.

Keywords

Abstrakt

Skopar är viktiga delar i en flygplansmotordesign eftersom de ger luftflöde till olika utrustningar och delsystem. Optimeringen av en sådan komponent är avgörande för att hitta en design som kan fungera ordentligt inom en rad flygförhållanden med en minimal försämring av huvudflödes aerodynamiska prestanda. Skopdesignmetoder är generellt baserade på tidigare experimentella resultat och är vanligtvis begränsade tillgängliga utrymme. Den studerade konfigurationen avser spolskopan placerad inuti det sekundära flödet av turbofans som ger flöde för en turbinkylningsutrustning. Beroende på flygförhållanden och motorbearbetning kommer denna skopa att uppleva olika flödesregimer, från låga massflöden till chokeflöden. Därför är studien av flera skopade massflöden obligatorisk för att extrahera skopbeteendet. Avhandlingen handlar om det preliminära steget före en 3D CFD-optimering: En studie av inflytande drivs på baslinjegeometrin för att undersöka robustheten i lösningen beräknad med olika metoder och för att bestämma parametrar som ska optimeras. Först definieras den fullständiga efterbehandlingsmetoden för att korrekt utvärdera prestanda hos en design (skopeffektivitet, inducerade tryckförluster). Ett andra steg består i att analysera CFD-lösare förmåga att fånga upp olika flödesbeteenden. Denna punkt behandlas genom att jämföra lösare (Fluent, elsA, PowerFLOW), nät (strukturerad, ostrukturerad) och turbulensmodeller. Det tredje steget handlar om optimeringsstrategins definition för att förbättra skopdesignen och därigenom motorns bränsleförbrukning.

Nyckelord

Acknowledgements

I wish my deepest gratitude to my local supervisor Mrs Amélie Placko for her guidance, for her advice and criticism throughout the thesis.

I would like to thank my supervisor Professor Paul Petrie-Repar for his encouragements and supports, and Mr Grégory Millot for his relevant remarks and expertise.

I would also like to thank Mr Nicolas Sirvin and Mrs Jagoda Worotynska for welcoming me in Paris and following my job from there. Thank you Mr Emmanuel Vanoli for helping me to use PowerFLOW and answer to all my questions.

I am using this opportunity to express my gratitude to the fondation ISAE-supaero that supported me to follow a double degree at KTH.

I want to express my best wishes to Matthieu Becquet, Antoine Bayle, Thomas Pommier, Christophe Stevenin, Cesare Andriano, Rémi Magnon, Sébastien Magnabal, Olivier Scholz, Morgan Croixmarie and all my colleagues in Aerothermical team for their friendship and help during this study.

I am very grateful to Mrs Linnea Gabrielsson and my family for their unlimited love, support and motivation.

Author

Bixente Artola - bixente@kth.se KTH Royal Institute of Technology ISAE Supaéro

Local supervisor

Supervisor

Contents

2.2 Early experiment work . . . 6

2.3 Recent studies . . . 6

2.4 Fluid model . . . 8

3 Method 14 3.1 Presentation of the studied scoop . . . 14

3.2 Study of influence . . . 16

4 Implementation 19 4.1 Meshing . . . 19

4.2 Numerical parameters and strategy . . . 22

4.3 Checking of the calculations . . . 24

5 Results 27 5.1 Solver influence . . . 27

5.2 Mesh influence . . . 33

5.3 Turbulence model influence . . . 34

5.4 Summary . . . 37

5.5 First step towards optimization . . . 37

6 Conclusions 40

References 42

List of Figures

1.1 Examples of different scoop inlet design . . . 1

2.1 Schematic representation of the scoop inlet (simplified geometry) . . . 4

2.2 Schematic representation of the particle interactions with LBM . . . 12

3.1 Scoop design . . . 14

3.2 Upstream plane used for Mach number calculation . . . 15

3.3 Fitting curve for the reference ram pressure efficiency . . . 18

3.4 Cutting planes in the scoop . . . 18

4.1 Three mesh methods for three solvers . . . 19

4.2 Bodies of influence at the intake of the scoop . . . 21

4.3 Different levels of Variable Resolution in PowerFLOW . . . 21

4.4 Convergence strategy applied . . . 23

4.5 Convergence of the mass flow rate closure - Low MFR/High MFR . . . 24

4.6 Convergence of the throat mass flow rate - Low MFR/High MFR . . . . 25

4.7 Convergence of the scoop outlet total pressure - Low MFR/High MFR . 25 4.8 y+_{distribution on the body . . . 26}

5.1 Comparison elsA/Fluent of the permeability and pressure discharge . . 27

5.2 Ram pressure efficiency of the scoop . . . 28

5.3 Mach distribution on the middle plane for high MFR . . . 29

5.4 Mach distribution on the middle plane for low MFR . . . 30

5.5 Mach distribution at high MFR -Realizable k-ϵ . . . 30

5.6 Mach distribution at low MFR -Realizable k-ϵ . . . 31

5.7 Streamlines model . . . 31

5.8 Influence of the mesh on the scoop performances . . . 33

5.8 Influence of the mesh on the total pressure distribution for a high MFR 34 5.9 Influence of the turbulence on the scoop performances . . . 34

5.10 Influence of the turbulence on the total pressure discharge . . . 35

5.11 Low MFR effect of the turbulence model on the total pressure . . . 36

5.12 Automatic simplified geometry generated with ∆θ = 10◦and ∆c/c = 0.1 38 5.13 Visualization of the real captured part of the flow . . . 39

List of Tables

2.1 Different averages used . . . 5

4.1 Prism layer parameters used by Fluent . . . 20

4.2 Tetrahedron parameters used by Fluent . . . 20

4.3 Summary of the final meshes used by the solvers . . . 22

4.4 Numerical parameters for the baseline computations . . . 23

5.1 i/θdistribution along the blades . . . 32

5.2 Computation cost depending on the solver . . . 32

5.3 Mean gap δη/δ0 depending on the MFR region . . . 35

5.4 Summary of the influence of each parameter on the pressure recovery (MWA) . . . 37

List of Symbols

a Microscopic acceleration

e Microscopic velocity

δ0 Mean ram pressure efficiency difference between elsA and Fluent

˙

m′_∞ Captured inlet mass flow rate ˙

m_∗ Throat mass flow rate ˙

m_∞ Inlet mass flow rate

ϵ Turbulence dissipation rate

µ Dynamic viscosity

µt Turbulent dynamic viscosity

ν Kinematic viscosity

νt Turbulent eddy viscosity

ω Specific dissipation rate

δη Mean ram pressure efficiency difference

ϕ Generic scalar

ρ′_∞ Captured inlet density

ρ_∗ Throat density

τt Turbulent relaxation scale

τij Reynold stress tensor

θ Angle of a blade along x

ξ Pressure recovery

A′_∞ Captured inlet area

A_∗ Throat area

A_∞ Inlet area

c Blade chord

i Angle of attack of a blade

k Turbulent kinetic energy

M_∗ Throat mach number

M_∞ Inlet mach number

Mup Upstream mach number

p′_0∞ Captured inlet total pressure

p0∞ Inlet total pressure

p0scoop Scoop outlet total pressure

p_∞ Inlet static pressure

pout Static pressure of the scoop outlet

rLE Leading edge radius

Sij Mean strain tensor

u Macroscopic velocity

u′_∞ Captured inlet velocity

u_∗ Throat velocity

y+ _{Non-dimensional wall distance}

1

1

Introduction

1.1

Background

Internal scoop inlets are necessary sub-parts of an engine by providing air flow for many purposes, from equipment cooling, to bleed air system supply and fire zone ventilation. These intakes can take different shapes depending on its application and the speed of the flow from which the air is deviated. If we focus on inlets designed for subsonic flow, which is the range of the thesis, three main categories can be find in the literature [1] :

(a) Pitot intake (b) NACA intake (c) Flush intake

Figure 1.1: Examples of different scoop inlet design

• Dynamic (or Pitot) design (Figure 1.1a) is the most commonly used because of its simplicity. This type of intake is placed outside of the geometry : this intrusive form has the advantage to be efficient as it avoids capturing the boundary layer. However, it is also its disadvantage as it results in a excessive induced drag and disturbs the main flow.

• NACA intake (Figure 1.1b), developed by the National Advisory Committee for Aeronautics (NACA) in the 1940’s, is widely used in aeronautical industry because of its low drag characteristics. Its geometry consists in a flush with a long ramp opening : it generates two counter-rotating vortices improving the ingestion efficiency. The major drawback of this design is the important internal volume needed to integrate in a geometry.

2 Introduction

• Flush (or submerged) intakes (Figure 1.1c) can be seen as a mix between the two previous designs and resemble to NACA-type intake with a short approach ramp. They have unique advantages including less external drag, decreased aircraft weight and lower observability. However they have a lower stagnation pressure intake due to the boundary layer ingestion.

A crucial step during the design of a scoop is that while optimizing its purpose (a target mass flow rate or a pressure recovery for example), it has to minimize the aerodynamic performances loss due to the flow deviation [1].

1.2

Problem

For the study of very integrated designs and out of experience, it is necessary to set up a CFD optimization if we do not want to go through expensive tests. As a matter of fact, the studied configuration concerns a flush scoop, which is located inside the secondary flow of a turbofan and has a high curvature due to limited space available (more than the 7◦advised by the ESDU [2]). This high ramp angle causes the scoop to occupy a shorter intake surface area and to possess a cascade of 5 blades to guide the flow into it. Due to its special geometry, the considered scoop inlet is quite different from what it can be found in previous research papers that are often simple NACA flush. In order to obtain an optimal scoop configuration, a preliminary study is needed to assess the performance of the scoop in its original configuration. The present thesis will therefore determine to what extent these performances of the studied scoop depend to the computational method used.

1.3

Purpose

This study takes part in a more global project which can be epitomized as follow : while creating an optimal design for the scoop using a technology developed by Altran, new abaqus for high ramp angle flush scoop inlets will be created. The goal being to conceive methods for the design of future scoops, using the newly expanded 1D model.

1.4 Methodology 3

Moreover, the benchmark between solvers that is evaluated in the thesis will be beneficial in 2 ways :

• Check whether or not the design depend on the solver used

• Challenge the traditional methodology and use a faster reliable solver

Finally, this preliminary step is crucial in order to make trustable conclusions that could be drawn after the optimization.

1.4

Methodology

The thesis covers the preliminary study before the optimization of a scoop inlet using 3D CFD simulations. The study of several scooped mass flow rates is mandatory to extract the scoop behaviour as it will experience various flow regimes, from low mass flow rates to choke flows depending of the flight conditions and the engine working point. Therefore, the study will be divided in 3 main steps in order to achieve the optimization :

• Describe the criteria used to analyse the scoop quality regarding its own function (scoop recovery coefficient) and its impact on the engine performance. Given the secondary flow is conditioned with a radial pressure profile, the generating pressure of scooped flow stream tube needs to be computed accurately

• The CFD methodology will be highlighted by comparison of solver results, both quantitatively and qualitatively. Cross checking solver, mesh and model effects will allow defining adapted modelling for the whole working range and the remaining bias. The analysis includes the compromise between accuracy and computational cost taking into account the optimization process which needs the evaluation of a large number of configurations.

• The settings are presented to perform a parametric optimization with an automated CAD-CFD workflow. The optimization process will rely on Surrogate Based Optimization (SBO) techniques with Efficient Global Optimization algorithm.

4 Theoretical Background

2

Theoretical Background

2.1

Figures of merit

Different quantities are generally computed to assess the performance of the studied scoop [3]. The physical quantities used are summarized in the figure 2.1 :

Figure 2.1: Schematic representation of the scoop inlet (simplified geometry)

Total pressure recovery It models the global efficiency of the scoop. It is affected by viscous losses such as boundary layer, shear layer and separations.

ξ = p0∗ p0∞

(2.1)

Ram pressure efficiency This is a representation of the amount of the freestream dynamic pressure that is recovered by the air inlet :

η = p0∗− p∞ p0∞− p∞

(2.2)

Mass flow ratio The MFR is defined as the ratio between the mass flow rate at the throat ˙m_∗ = ρ_∗u_∗A_∗ and the ideal mass flow rate ˙m′_∗ = ρ′_∞u′_∞A_∗ which corresponds to the maximum theoretical value that would be ingested by the intake at freestream conditions.

2.1 Figures of merit 5

Therefore, this ratio represents the magnitude of the captured area of the incoming stream air A′_∞compared the area of the scoop throat A_∗.

MFR = m˙∗ ˙

m′_∗ = A′_∞

A_∗ (2.3)

If we consider an ideal gas in an isentropic flow in absence of work or body force, the MFR can be estimated as : MFR = p0∗ p′_0∞ M_∗ M_∞ ( 1 + γ−1₂ M2 ∞ 1 + γ−1₂ M2 ∗ ) γ+1 2(γ−1) (2.4)

Total pressure drop The drop in total pressure in the secondary flow of the turbofan corresponds to the losses induced by the scoop :

∆p0

p0∞

= p0∞− p0,d

p0∞

(2.5) With p0,dthe total pressure downstream in the secondary flow.

It is important to realize that because they are not uniformly distributed, the quantities used in the formulas correspond to their average on the associated surface. Furthermore, it depends on the type of averaging it is used :

Average Expression Area Weighted ϕ_{AW A} = ∫∫ Sϕ dS ∫∫ S dS Mass Weighted ϕ_{M W A} = ∫∫ Sρvnϕ dS ∫∫ SρvndS

Entropy Weighted p_{0EW A} =   ∫∫ Sρvnp γ−1 γ 0 dS ∫∫ SρvndS   γ γ−1 Dynalpy Weighted p_{0DW A} = p_{AW A} ( 1 + γ−1₂ M2_{AW A} ) γ γ−1

Table 2.1: Different averages used

6 Theoretical Background

2.2

Early experiment work

Most of the experimental references have been produced in the mid-20th century by the National Advisory Committee for Aeronautics. In 1945 was introduced the NACA-type submerged intake : the experimental investigation aimed at presenting the important geometrical and flow parameters for the design of the intake, such as the ramp design, the lip design, the Mach number, the mass flow ratio and the boundary layer thickness [4]. High ram recovery was observed for all intakes located upstream where the boundary layer is thinner. It was at this moment that the theory behind the performance of the scoop was created (see part 2.1) and it appeared the shape of the entry ramp was as well affecting the efficiency of the scoop [5]. In 1948, the approach ramp was proven to play an important role as the submerged intakes with divergent walls had better performances than the parallel walls [6]. As a matter of fact, the studies indicated that at the top of the divergent ramp walls, where the air flow changes direction suddenly, a rotational flow is generated. Even though the vortices engender a total pressure loss when entering in the NACA intake, this effect is counteracted by the thinning of the boundary layer along the ramp floor, thus improving the efficiency of the intake [7]. The divergent wall design was observed to have higher performances for both subsonic and transonic speeds [8] : variation of the Mach number (as well as the angle of attack) has generally a limited impact in the ram pressure efficiency, contrary to the mass flow ratio that significantly affects it.

2.3

Recent studies

After these experimental studies, research on submerged scoop stopped until the 2000s with the development of Computational Fluid Dynamics (CFD) techniques and the increasing computational power. Most of the studies are using CFD to enhance the efficiency of the air intake. One of the first attempts was to use a vortex generator on a NACA inlet, as it is able to thin the boundary layer through the mixing of high-momentum air and forcing the resulting energized flow to be ingested in the inlet. Vortex generators was later used in many other NACA inlet applications to improve the scoop performances [9, 10, 11]. After investigating the physics of the flow for

2.3 Recent studies 7

air vehicle submerged inlets through numerical simulation [12], vortex generators have been also adapted for the same purpose on this geometry. Not surprisingly, it succeeded to increase the efficiency of the scoop while minimizing the inlet mixing loss (produced by the ingestion of the counter-rotating vortex pair observed in the early NACA experiments) and with no drag penalty [13].

Other studies chose to improve the duct shape itself : a submerged inlet was deformed to change the characteristics of the flow [14]. Later, the same geometry was investigated over a wide range of flight conditions by both experiments and numerical simulations. It was concluded that the angle of attack, the side edge angle and the ramp angle have significant impacts on the aerodynamic performance of the submerged inlet : for the inlet embedded into the belly of the fuselage, the increase of the angle of attack is beneficial to the total pressure recovery [15].

In 2007, these improvements that were made manually truly became automatized. The global shape of a S-shaped intake was improved using a discrete adjoint approach with a NURBS shape modification function [16], a method that was already used in other applications such as airfoil and wing/body design [17, 18, 19]. By applying the k-ω SST model, key characteristics of a flow in a S-shaped diffuser - such as strong vortex and flow separation - could be better captured than other turbulence models.

In 2015, a surrogate-assisted evolutionary optimization was conducted on a NACA duct to test the influence of two geometric parameters (divergence angle and mass flow ratio) on performance responses [20]. First, a set of samples in the design space is generated using space-filling Latin Hypercube Design (LHD) in order to maximize the amount of information gained from a limited number of samples. Then, with the use of Kriging surrogate models, that provides an estimate for prediction errors, the optimization could be performed in a greatly reduced computational time. In 2017, Altran used as well a surrogate-assisted optimization applied for an engine air intake design of a helicopter [21]. Altran chose to adopt an Efficient Global optimization (EGO) approach, a Kriging-based method developed by Jones et al [22]. They succeeded to create a workflow management system called OptiMind that uses this method, that can handle failures during the process (such as failed mesh generation or diverged CFD calculations) and that link all the different softwares used during the optimization process.

8 Theoretical Background

2.4

Fluid model

CFD simulations can be run on many different softwares, solvers, with different resolution methods or implementations. This part exposes the fluid model theory used later in the thesis : elsA and Fluent are both solving the so-called RANS equations by a finite-volume method while PowerFLOW solves the Boltzmann equations by a Lattice Boltzmann Method.

2.4.1 Overview of the calculation solvers

2.4.1.1 elsA

This solver has been developed at Onera (a french national aerospace research center) since 1997 and can be used both for complex external and internal flow aerodynamics [23]. It is used for a large variety of applications, such as aircraft, turbomachinery, helicopters, missiles. elsA is based on an Object-Oriented (OO) design method that makes possible to partition problems into well-separated parts specialized for a given CFD task. This OO concept is implemented in such a way that the CPU efficiency is not impaired [24]. It solves the compressible 3D Navier-Stokes equations, possesses a large variety of turbulence models and the system of equations is solved by a cell centered finite-volume method [25].

2.4.1.2 Fluent

Fluent is typically handled by Altran and more generally, it is used worldwide by many companies from any industry. It is the CFD solver of ANSYS since 2006, a powerful general-purpose finite element modelling package that can combine many physical problems into one [26]. For all flows, ANSYS Fluent solves conservation equations for mass and momentum and can additionally solve compressible flows, heat transfer, species mixing or reactions. Depending of the speed of the flow, two numerical methods are possible (pressure-based or density-based) but in either case, a finite-volume method is used. Finally, Fluent is famous for its robustness and accurate turbulence models for RANS, Reynolds stress models (RSM), Large eddy simulation (LES) or Detached eddy simulation (DES), particularly in near-wall regions via the use of extended wall functions and zonal models [27].

2.4 Fluid model 9

2.4.1.3 PowerFLOW

PowerFLOW uses different calculation methods compared to the “traditionnal” finite-volume methods : the enhanced particle-based method DIGITAL PHYSICS® technology patented by Exa, allows PowerFlow to address a wide range of modeling and analysis capabilities, including : aerodynamics, thermal or aeroacoustics simulations. PowerFLOW main characteristic is to be based on extensions of the Lattice Boltzmann model (LBM), another CFD technology developed over the last 30 years [28], and is capable of addressing subsonic, transonic and supersonic unsteady compressible flows. The LBM approach is solved on Cartesian meshes, which is generated automatically for any geometrically complex shape. Variable refinement regions (VR) can be defined for local mesh refinement of the grid by successive factors of two.

2.4.2 Reynolds-averaged Navier-Stokes

Because solving the instantaneous Navier-Stokes equations would require too much computation time, Reynolds-averaged Navier-Stokes (RANS) computations are generally used in the industry. This averaging describes statistically the velocity field

u by decomposing its components ui into mean and fluctuating terms. Likewise,

other scalar variables denoted ϕ (such as pressure) are decomposed :

ui = ¯ui+ u′i and ϕ = ¯ϕ + ϕ′ (2.6)

Substituting expressions of this form for the flow variables into the instantaneous continuity and momentum equations and taking a time average yields the averaged momentum equations. They can be written in Cartesian tensor form as :

∂ρ ∂t + ∂(ρui) ∂xi = 0 (2.7a) ∂ ρui ∂t + ∂ ρuiuj ∂xi =−∂p ∂xj + ∂ ∂xj [ 2µ ( Sij − 1 3Skkδij )] −∂ ρu′iu′j ∂xj (2.7b) Where Sij = 1₂ [ ∂ui ∂xj + ∂uj ∂xi ]

is the mean Strain tensor and τij = u′iu′jthe Reynolds Stress

tensor. The system (2.7) composed of 4 equations involving 4 dependent variables

10 Theoretical Background

(uiand p) augmented with six additional independent unknowns from the

stress tensor is therefore not closed. The problem of the closure of the Reynolds-averaged Navier–Stokes equations consists in expressing the Reynolds-stress tensor as a function of the mean-field and other variables.

Different classes of RANS turbulence models exist [29], but one in particular will be covered during this thesis as it is widely used : two separate transport equations are solved for two independent turbulent quantities (the turbulent kinetic energy k with either the turbulence dissipation rate ϵ or the specific dissipation rate ω). For this method, the Boussinesq hypothesis is used to model the Reynolds stress tensor as it is of relatively low computational cost associated with the computation of the turbulent kinematic viscosity, νt.

− τij = 2νtSij − 2 3(k + νtSkk) δij with k = 1 2u ′ ku′k (2.8)

The choice of the two transport equations to close the problem depends on the application of the simulation. Three different methods will be covered in the thesis : Realizable k-ϵ (used in the provided calculations by SAE with elsA and then compared on Fluent), Shear Stress Transport (SST) k-ω and Transition SST model (both on Fluent to investigate their influence). The equations followed by these models are not presented here but it can be found in literature [30, 31, 32]. The expression of turbulent eddy viscosity can be summarized as :

νt =      Cµfµ k2 ϵ , α∗k ω, for k− ϵ models for k− ω models (2.9)

With Cµand α∗ coefficients from the model chosen and fµa damping function.

The first model is based on the satisfaction of the realizability constraints on the normal Reynolds stresses and the Schwartz inequality for turbulent shear stresses. Beside this, the Cµ constant of Standard k-ϵ model is not anymore a constant but

it is computed in this improved model by an eddy-viscosity equation. Performance is substantially improved for jets and mixing layers, channels, boundary layers and separated flows compared to theStandard k-ϵ model.

The more advanced k-ω SST turbulent model was developed by Menter [33] and

2.4 Fluid model 11

combines the advantages of k-ϵ and Wilcox k-ω models in predicting aerodynamic flows, and in particular in predicting boundary layers under strong adverse pressure gradients. It mixes the accurate formulation of the k-ω model in the near-wall region with the free-stream independence of the k-ϵ model in the far field. The model has been validated against many other applications with good results such as turbomachinery blades, wind turbines, free shear layers, zero pressure gradient and adverse pressure gradient boundary layers.

Finally, the Transition SST model is based on the coupling of the k-ω SST transport equations with two other transport equations, one for the intermittency and one for the transition onset criteria, in terms of momentum-thickness Reynolds number.

On one hand, k- ϵ models are primarily valid for the flow in the regions far from walls. Consideration therefore needs to be given as to how to make these models suitable for wall-bounded flows by using various wall functions. On the other hand

k- ω models were designed to be applied throughout the boundary layer, provided that the near-wall mesh resolution is sufficient.

2.4.3 Implementation of the Lattice Boltzman Method in PowerFLOW

The LBM method used by PowerFLOW, an alternative method to simulate fluid dynamics, is based on microscopic models and mesoscopic kinetic equations rather than macroscopic level, like “conventional” CFD methods. It rises from Ludwig Boltzmann’s kinetic theory of gases, which central idea is to assimilate gases/fluids as a collection of a large number of small particles moving with random motions, exchanging momentum and energy through particle streaming (or advection) and particle collision. LBM simplifies it by confining the particles to n nodes of a lattice (see Appendix for more details), discretizing the process.

Hence, the process is governed by the Boltzmann transport equation : (

∂

∂t+ e·∇x+ a·∇e

)

f (x, e, t) = Ω (2.10)

12 Theoretical Background

(a) Timestep 1 (b) Timestep 1a : Particles moved from their current voxel to an adjacent one

(c) Timestep 2 : Collision of the particles in the same voxel

Figure 2.2: Schematic representation of the particle interactions with LBM

Where f (x, e, t) is the particle distribution function at the position x, with microscopic velocity e and microscopic acceleration a. The collision operator Ω can be rather complicated as it contains all the parameters necessary to approximate the macroscopic behavior of a wide range of partial differential equations, including the Navier Stokes Equations, and can be described using different methods.

PowerFlow discretizes (2.10) with the so-called Lattice Bhatnagar-Gross-Krook (LBGK) method that describes the collision operator in terms of a single relaxation parameter τ [34] : f (x + e∆t, e, t + ∆t)− f(x, e, t) | {z } Advection =−f (x, e, t)− f eq_{(x, e, t)} τ | {z } Collision (2.11)

where feq_{(x, e, t) is the local equilibrium distribution function derived from the}

Boltzmann Maxwellian distribution function. Its formulation is given in Appendix but without the derivation that can be found in literature [34].

Macroscopic quantities, such as the macroscopic density ρ(x, t) and velocity

u(x, t)are then defined as a summation of microscopic particle distribution function. The macroscopic pressure p is determined from the equation of state of an ideal gas. ρ = n−1 ∑ i=0 fi ρu = n−1 ∑ i=0 eifi (2.12)

PowerFLOW is based on the principle of performing very large eddy simulations (VLES) that directly simulate resolvable flow scales while modeling unresolved scales,

2.4 Fluid model 13

i.e near wall regions, with an extended wall law formulation that account for the effects of local adverse pressure gradients. PowerFLOW implements the LGBK procedure by replacing τ by an effective turbulent relaxation time scale τt derived

by applying a systematic renormalization group (RNG) procedure :

τt = τ + Cµ

k2_/ϵ

T (1 + ˜η)1/2 (2.13)

Where Cµ= 0.085, T the static temperature, k and ϵ determined according to the

RNG k-ϵ transport and ˜η a combination of local strain parameter and local helicity parameters.

All in all, the concept of this method of resolution is similar to hybrid RANS/LES methods, such as DES, for really high Reynolds numbers [35]. Furthermore we can point out that τtis containing the definition of the eddy viscosity νt, which relates the

macroscopic Navier Stokes equation with the microscopic kinetic theory.

14 Method

3

Method

The work realized with SAE is subject to a confidentiality clause and is therefore restricted. Physical quantities are non-dimensional, the images don’t show the global geometry and are deformed intentionally.

3.1

Presentation of the studied scoop

The geometry of the studied scoop was given and already simplified by SAE. It consists in a 45◦sector of the turbofan secondary airflow, a generic geometry provided by SAE. The scoop itself is extruded as well to prevent backflow issues during calculations. Only the connection between those two part has been made, using the software Spaceclaim.

(a) Up view (b) Side view

Figure 3.1: Scoop design

The scoop has a high ramp angle and is not symmetrical along the x axis. A cascade of 5 blades are positioned at the inlet of the scoop in order to guide the flow. A diffuser follows the scoop ramp to slow down rapidly the fluid, making possible to use the airflow for cooling purpose. It is expected a strong flow separation at this point as it is the best way to obtain a quick energy dissipation.

3.1.2 Boundary conditions

3.1.2.1 Total pressure inlet

The inlet of geometry is positioned just after a fan that produces a non-uniform profile of total pressure that needs to be correctly imposed radially. This profile was given by

3.1 Presentation of the studied scoop 15

SAE. The flow for this study is supposed to be directed only along the x axis without any swirl. Moreover, a constant total temperature T0∞is fixed.

The turbulence is characterized via the turbulence intensity I (the ratio of the root-mean-square of the velocity fluctuations u′ to the mean flow velocity ¯u) and viscosity ratio µt/µ: I = u ′ ¯ u = 0.05 µt µ = 500 3.1.2.2 Pressure outlet

The two outlets of the geometry are pressure outlets : a constant static pressure is imposed. A range of pressure was applied in order to obtain the whole MFR range that the scoop will experience, from really low MFR to high MFR choked flow. However these pressures were only a guideline, a modification was necessary so that the average Mach number Mupin a plane at the scoop inlet upstream was constant

for all studied cases (see Figure 3.2).

The value of Mup was obtained through analytic calculation on the full 360◦ engine

and corresponds to a precise flight condition. It ensures that the results can be compared : the incoming flow is considered the same, only the scooped mass flow rate will differs.

Figure 3.2: Upstream plane used for Mach number calculation

Only the pressure at the outlet of the secondary airflow pmain was modified as

it was found that this pressure is controlling the incoming mass flow rate ˙m_∞, and consequently Mup. As a matter of fact, if we consider the total quantities to be

constant for all cases in the upstream plane, it can be shown that the variation of ˙ m_∞is expressed as : ∆ ˙m_∞ ˙ m_∞ = 1− M2 up 1 + γ−1₂ M2 up ∆Mup Mup (3.1) The static pressure of the scoop pout is only governing the scooped mass flow

rate.

16 Method

3.1.2.3 Walls and side faces

A no-slip condition was applied on all the walls of the geometry, unless for the upper part of the secondary airflow extrusion and for the extrusion at the scoop outlet, where a slip condition was applied.

The side faces are imposed as a symmetry in both Fluent and elsA. However this boundary condition is not possible with PowerFlow as it only handles cartesian symmetries : a frictionless condition was instead applied. It shouldn’t change the behaviour of the fluid as the flow doesn’t have any swirl components.

3.2

Study of influence

As discussed in introduction part, this thesis concerns the preliminary step before the scoop optimization. The goal is to discuss the influence of parameters, which are categorized in three groups : solver influence, mesh influence and turbulence influence. The differences are assessed comparing quantitatively the performances of the scoop and qualitatively the behaviour of the flow by analyzing the Mach number and total pressure distribution at the intake.

3.2.1 Work plan

Considering that the optimization process will be run with Fluent and not with elsA, a benchmark between those two solvers has been accomplished over the range of scooped conditions. These calculations were made using the exact same numerical conditions exposed in the next sections. Because this part did show some unexpected differences, a more detailed influence has been pursued.

First, more simulations are run with Fluent to test the influence of the mesh and the turbulent model. The mesh realized with Fluent is unstructured and composed of tetrahedrons, while the mesh of elsA is structured and composed with hexahedrons. The mesh influence study will thereupon consist in solving the flow using the structured mesh on Fluent. As a result, the bias induced by the meshing method is overcome.

3.2 Study of influence 17

From literature review it has been shown that other turbulence models are used in turbomachinery than the Realizable k-ϵ model. Consequently two other turbulence models will be run on Fluent : k-ω SST and Transition SST previously introduced.

Then, some chosen cases (because of a limited license time) are solved with PowerFLOW in order to have a third comparison :

• The lowest MFR case proved to be the major difference between Fluent and elsA. The goal is to check whether the flow direction inverts or not.

• The highest MFR case exhibit the same flow behaviors with Fluent or elsA, but the scoop performances are not similar. The goal is to obtain a third comparison point.

• The flow with the highest MFR can locally be greater than the maximum Mach number allowed by PowerFLOW. Therefore, the flow behavior doesn’t exactly match the one observed with Fluent or elsA. For the same reasons the previous case was chosen to be tested, the second highest MFR case is simulated because of lower Mach number values.

3.2.2 Quantitative analysis

The quantitative analysis of the influence of each factor is performed by comparing the performances of the scoop. However, three performances are computed by four averages in terms of the MFR : a choice needed to be done to model efficiently, yet in a representative way, the differences between each model.

To summarize the data collected, an average difference δ is computed between the result curve obtained by the influence factor and the reference curve of Fluent. As the performances curves are only shifted (see the result section), this way of modeling corresponds to finding the mean gap between the curve and the reference curve. Only the mass weighted average difference is chosen as it is usually used to compute the total quantities and as it represent correctly the trend from the other averages (the others are calculated in order to check that the values are reasonable).

Because the Ram pressure efficiency expresses the overall performance trend of

18 Method

the scoop, only the average difference δη is compared between all the influence

parameters.

Concretely, the Fluent reference performance curve is approximated by a polynomial of order 3, then the mean gap δη is calculated as being the

average of:

δη = ηcomputed(MFR)− ηf it−fluent(MFR) (3.2)

All in all, at each influence factor corresponds an unique number δηthat quantify how

much the performance curve is shifted compared to the reference curve.

Figure 3.3: Fitting curve for the reference ram pressure efficiency (MFRref and ηref are

defined in Result section)

3.2.3 Qualitative analysis

The qualitative analysis is performed on both performances curves and the flow behavior at different regions from the scoop inlet as the general trend of the curves is usually linked to flow behavior. Visualizations of both the Mach number and total pressure are taken along the middle plane of the scoop and at several levels in the scoop: inlet, throat and diffuser outlet. The latter two have a flow distribution that is not symmetrical because of the geometry of the scoop.

Figure 3.4: Cutting planes in the scoop

19

4

Implementation

4.1

Meshing

The preliminary study was really rich in terms of meshing method as the three solvers used different techniques. The following figure compares the three final meshes :

(a) Fluent

(b) elsA

(c) PowerFlow

Figure 4.1: Three mesh methods for three solvers

4.1.1 Fluent

Fluent Meshing v16.2 is used to make the non-structured mesh, composed of tetrahedron and a prism layer to model properly the boundary layer.

The resolution of the prism layer is highly connected to the method used to solve the RANS equation : theRealizable k-ϵ turbulence model needs a precise model of the near-wall region and consequently theEnhanced wall treatment of Fluent is applied.

20 Implementation

Nonetheless, the near-wall mesh is required to be fine enough to be able to resolve the viscous sublayer. A typical parameter to express the non-dimensional wall distance

y+_{is express as :} y+= yuτ ν with uτ = √ τw ρ (4.1)

With y the dimensional wall distance, uτ the friction velocity and τw the wall shear

stress. For the chosen wall treatment, we must have y+ _{≈ 1. Using this information}

and approximating τwwith Schlichting skin-friction correlation (Re < 109) :

uτ = 0.5 CfρU with Cf ≈ [2 log10(Re)− 0.65]−2.3 (4.2)

We find that the height of the first prism needs to be equal to approximately 2 µm. Some liberties were taken regarding this value, that was only an approximation, to keep a relatively small size mesh : the final values for the design of the prism layer is summarized in the Table 4.1. Values of y+_{is checked in section 4.3.}

No First height

Blades/Other walls Last ratio

Expansion rate

18 2 µm/5 µm 30 % 1.35

Table 4.1: Prism layer parameters used by Fluent

The tetrahedral mesh fills the rest of the volume using parameters exposed in Table 4.2. Three Body Of Influence (BOI) are added for more refinement around the inlet region (see Figure 4.2)

General Blades BOI

Upstream/Intake/Downstream Expansion rate 1.2 Max size s/c = 5% Max size s/c = 16%/6%/12% Max size s/c = 5% Min size s/rLE = 40%

Min size s/rLE = 40%

Curvature 10◦

Table 4.2: Tetrahedron parameters used by Fluent

With s the corresponding mesh size, c the chord length of the blades and rLE the

Leading Edge radius of the blades.

4.1 Meshing 21

(a) Side view (b) Front view

Figure 4.2: Bodies of influence at the intake of the scoop

All in all, the final non-structured mesh is composed of 8 million tetrahedrons and 7.6 million prisms. The quality of meshes conforms to the recommendations in terms of skewness (< 0.95) but the orthogonal quality is hardly respected because of sharp angles at the entrance of the scoop. The meshes of low quality are nevertheless very localized and do not degrade the convergence of the computations.

4.1.2 PowerFlow

PowerFLOW discretizes the space by generating automatically a cartesian mesh, only composed of cubes named voxels, in a “russian doll” fashion. Note that even if the lattice has a regular cubic structure, the geometry of the surface can be arbitrary as the final mesh surface is the intersection of the solid with the fluid. Variable Resolution regions (VR) can be set to refine the mesh at specific part, always refining the grid by a factor of two.

Eight VR are designed for this study and are inspired by the BOI from Fluent calculations. For the first coarse calculation, the finest voxel size is set to be 0.6 rLE.

Figure 4.3: Different levels of Variable Resolution in PowerFLOW

The two finest VR corresponds to offsets of the scoop inlet, containing 8 local voxel per inflation. The other walls are also successively inflated starting by the VR5 and containing 6 local voxels per layer.

22 Implementation

4.1.3 Summary

Fluent

Power-FLOW elsA

Number of

cells 17 million 40 million 10 million Mesh type Unstructured Cartesian Structured

Cell type Tetrahedron + Prism Cube Hexahedron Smallest cell

size 0.4 rLE 0.6 rLE 0.6 rLE

Quality Max skewness : 0.95

Min orthogonality 0.05 N/A

Max determinant

0.98 Max y+_at

the walls 1 N/A 1

Table 4.3: Summary of the final meshes used by the solvers

4.2

Numerical parameters and strategy

This part mainly covers the work that has been produced during the thesis by presenting the way the characteristic of the meshing and the calculations were managed on both Fluent and PowerFLOW. The way in which elsA simulations have been implemented is not covered here in much details. The numerical models used for the computations are summarized in Table (4.4). elsA used the same parameters as Fluent, with the corresponding options from the solver.

For RANS solving equations, a convergence strategy is applied (PowerFLOW computations are unsteady and don’t need any type of convergence). The Courant– Friedrichs–Lewy (CFL) number models the distance that any information travels during the timestep length within the mesh. A small CFL means that the solution will be really stable and will have slow changes : this is used at the beginning for stability reason. A high CFL number allows for more rapid variations and is used at the end of the simulation for a finest result.

4.2 Numerical parameters and strategy 23

Fluent PowerFLOW elsA

General Pressure based Steady Double precision 3D External flow Unsteady Single precision Steady Model Energy ON RANS k-ϵ Realizable : Enhanced wall treatment Pressure gradient effects Thermal effects Viscous heating Curvature correction Compressibility effects Production limiter VLES Turbulence modeling k-ϵ RNG (near wall regions) High subsonic RANS k-ϵ Realizable Mesh Unstructured Boundary layer 18 cells y+ ≈ 1 Cartesian mesh Boundary layer 16 cells No y+_requirement Structured Boundary layer 18 cells y+ ≈ 1

Table 4.4: Numerical parameters for the baseline computations

Furthermore, the pressure-based solver uses under-relaxation of equations to control the update of computed variables at each iteration, to control the dampling. The general form of these coefficients CU RF for any quantity ϕ = ϕold+CU RF∆ϕ.

0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 10 20 30 40 50 60 70 80 90 100 110 0 0.1 0.2 0.3 0.4 0.5

Figure 4.4: Convergence strategy applied : CFL and CU RF of pressure/momentum

24 Implementation

PowerFLOW doesn’t need any strategy of convergence as it is an unsteady flow solver. However, unsteady behaviour of the fluid is not of interest in this thesis as we need to compare results between the solvers. In order to achieve this, we first estimate the number of timesteps Ntneeded by a particle to go from the inlet to an

outlet : Nt = L U 1 ttimestep (4.3) With L and U characteristic length and speed from the problem. Computations are run during 3Ntsteps and results are averaged over the last fluid passage to not take

into account the transient effects at the beginning of the computations.

4.3

Checking of the calculations

Convergence is checked with conservation of mass ( ˙m_∞− ˙mout)/ ˙m∞(oscillation less

than 0.1%), mass flow rate at the throat ˙m_∗/ ˙m_∞and an integral of the total pressure

p0scoop/p0∞. The lowest MFR operating point, even if it does not diverge, converges to a

solution with an inverted flow in the scoop. For this reason, the scoop pressure outlet is changed to an imposed mass flow rate condition, the same obtained with elsA, in order to compare the results. Here are presented the convergences of the two extreme MFR “pressure imposed” cases of Fluent : second lowest MFR and highest MFR. The other intermediate cases have similar convergences than the fastest case.

Figure 4.5: Convergence of the mass flow rate closure - Low MFR (left) High MFR (right)

4.3 Checking of the calculations 25

Figure 4.6: Convergence of the throat mass flow rate - Low MFR (left) High MFR (right)

Figure 4.7: Convergence of the scoop outlet total pressure - Low MFR (left) High MFR (right)

We notice that oscillations appear for the low-flow case, proof that the system is close to its unstable equilibrium. However, the oscillations remain below 0.1%, the convergence is validated.

26 Implementation

We also need to check for near wall treatment, that necessitates y+ _{≈ 1 (see}

section 4.1.1). The test is done on the operating point with the highest scooped mass flow rate, as shown in Figure 4.8, y+

max= 1:

(a) Global view of the y+_distribution

(b) y+_{scoop intake distribution}

Figure 4.8: y+_{distribution on the body}

27

5

Results

The result part only exposes the most relevant results obtained during the thesis. None of the absolute values or scales are given in order to protect the confidentiality clause of Safran. A reference case is chosen to compare the performances : the one that has the highest Ram pressure efficiency ηref at MFRref.

5.1

Solver influence

Firstly, we note that for a same operating point, the scoop captures more flow when computed with Fluent : the difference ∆MFR between Fluent and elsA remains globally constant. At really low MFR, the air flow is at the limit to become unstable due to the high slope of the curve : a slight change in pressure outlet can reverse the flow direction. Hence it explains why the flow was reversed with Fluent : the result depends very strongly on the output pressure imposed.

(a) Permeability of the scoop (b) Pressure discharge in the main flow

Figure 5.1: Comparison elsA/Fluent of the permeability and pressure discharge

The curves have the same trend, but the one calculated with Fluent is translated and the very low flow case converges to an unstable solution. These results are contradictory because one would have thought that on the contrary, the lowest MFR

28 Results

case on Fluent would have a MFR more important and would thus be less unstable. Secondly, the performances computed with PowerFLOW are placed between the two curves. The points are even overlapping the elsA permeability curve : for the same pressure conditions, the scoop is capturing the same amount of air. At the opposite, for low MFR, PowerFLOW has difficulties to converge towards a stable solution and necessitate longer calculations : it proves once again the unstable nature of the flow at this mass flow rate.

The translation of the curves is also observed for the pressure drop. Fluent calculates a lower pressure drop (on average 0.1 percentage point), except for the lowest MFR case where the pressure drops meet. It is important to note that the pressure loss values are not representative of reality, the geometry of the vein being largely simplified. However, it is interesting to compare these values relatively.

Finally, pressure recovery and ram pressure efficiency are calculated using the 4 averages. Here again, we observe a translation of the performance curves: Fluent obtains better Ram pressure performances, with a quasi-constant improvement δ0.

Figure 5.2 shows the MWA comparison of the Ram pressure efficiency between the three solvers, because representing the trend of the averages. Pressure recovery follows the same trend can be found in Appendix. PowerFLOW computes performances that are between the two curves : no conclusion can be drawn, apart from the fact that the results are reasonable.

(a) Ram pressure efficiency - Fluent (b) MWA comparison

Figure 5.2: Ram pressure efficiency of the scoop depending on the average and the solver

5.1 Solver influence 29

5.1.2 Evolution of the flow distribution

At high flow rate, the recirculation bulb under the inlet edge is very flattened and acts as the fictitious extension of the inclination of the vein before the blades. A strong acceleration before the diffuser is also noticeable.

(a) Fluent

(b) elsA

(c) PowerFLOW

Figure 5.3: Mach distribution on the middle plane for high MFR

The three solvers obtain globally the same flow behavior for high MFR. The difference with elsA comes from a different color scale, not from the flow itself. PowerFLOW has lower Mach numbers because of software limitations : the solver strictly restrict it below Mmax(Mmax < 1).

As flow decreases, the bulb tends to expand and almost touches the first blade. In addition, the stagnation point on the vein, behind the last blade, gradually goes down: the captured current tube thins. Finally, the detachment after the diffuser becomes much more massive. The thickness of the recirculation bulb is one of the major differences with calculations made with elsA. With Fluent calculations, it becomes so large that the scoop becomes impervious if mass flow is not imposed: the separation at the blades is total and even spreads in the vein.

30 Results

(a) Fluent

(b) elsA

(c) PowerFLOW

Figure 5.4: Mach distribution on the middle plane for low MFR

For high MFR the flow is almost two dimensional at the scoop inlet : the cutting plane is representative of the overall flow (Figure 5.5). On the other hand, 3D effects appear as the MFR decreases, contributing to a quicker degradation of the efficiency parameters. No major difference between solvers is detected.

(a) Fluent (b) elsA

(c) PowerFLOW

Figure 5.5: Mach distribution at high MFR -Realizable k-ϵ

5.1 Solver influence 31

(a) Fluent (b) elsA

(c) PowerFLOW

Figure 5.6: Mach distribution at low MFR -Realizable k-ϵ

5.1.3 Streamlines evolution

Noting α, the angle relative to x of the flow at the stagnation point of a blade , θ the angle of the blades relative to x. Thus the angle of attack of a blade relative to the flow is equal to i = θ− α.

(a) Schematic representation of the angles

(b) Streamlines for a high MFR simulation

Figure 5.7: Streamlines model

The last blade captures the upper part of the current tube: the particles are more strongly deflected. Therefore, the angle α is increasing along x (α5−α1

θ ≈ 0.35). For a

case with low MFR, as the captured current tube is thinner, the flow is less deviated and is therefore more importantly directed along the x axis.

32 Results

As a result, the angle of attack increases because α decreases. Moreover, the difference between α1and α5has increased (α5−α_θ 1 ≈ 0.58).

Blade 1 Blade 2 Blade 3 Blade 4 Blade 5 High

MFR −0.08 −0.15 −0.23 −0.35 −0.42

Low

MFR +0.54 +0.23 +0.15 +0.08 +0.01

Table 5.1: i/θ distribution along the blades

It can be seen that at very high MFR, the angle of attack is always negative and that, on the contrary, at very low MFR, the angle of attack is always positive. By conservation of the momentum and considering the flow at the trailing edge to be constant (the flow follows the shape of the scoop), the resultant forces are directed to the pressure face for high MFR, to the suction face for low MFR.

5.1.4 Computational cost

Finally, Table 5.2 summarizes the computation cost, quantified in HCPU, the amount of CPU hours needed by the three solvers. From these results, it is clear that PowerFLOW necessitates a large amount of HCPU as it solves unsteady flow. Both Fluent and PowerFLOW calculations were run during the master thesis on the known Altran’s calculation server : its specification are given thereafter. On the contrary, elsA calculations were run by SAE : no specifications could be given.

Fluent PowerFLOW elsA

HCPU 380 745 250

Nodes 15 8 N/A

CPU per node 32 16 N/A

Type Sandy bridge Ivy bridge N/A Frequency 2.1GHz 2.6GHz N/A RAM 15*512 Go 7*128 + 1*256 Go N/A

Table 5.2: Computation cost depending on the solver

5.2 Mesh influence 33

5.2

Mesh influence

(a) Comparison of the scoop permeability (b) Comparison of the MWA Ram pressure efficiency

Figure 5.8: Influence of the mesh on the scoop performances

Figure 5.8 shows that the mesh has no influence on the permeability of the scoop, the scoop with Fluent always captures more flow than elsA calculations. With the exception of low flow rates: the scoop becomes impervious at lower pressure outlet. The structured mesh allows to slightly reduce the performance but it does not explain at all the gap that exists between the solver Fluent and elsA. On the other hand, it makes possible to reach lower flow rates in the scoop, even though the lowest MFR case always converges towards an inverse flow solution.

The flow at the entrance of the scoop confirms that the type of mesh used has little influence on the results.

(a) Unstructured mesh - Fluent

(b) Structured mesh - elsA

34 Results

(c) Structured mesh - Fluent

Figure 5.8: Influence of the mesh on the total pressure distribution for a high MFR

5.3

Turbulence model influence

The turbulence model has a noticeable effect on scoop performance calculations, especially for low flow rates. Two main regions can be examined : for a MFR greater than MFRref, the results are similar to those obtained with k-ϵ. For a lower MFR,

the performances drop quickly and are close to those obtained with elsA. It once again proves the low MFR instability, the result fluctuating strongly depending on the model or the solver used. The last points do not follow the trend of the permeability curve but they are not intended to be compared to other cases, the pressure is not imposed in a similar way (non-homogeneous pressure because of the mass flow rate imposed).

(a) Comparison of the scoop permeability (b) Comparison of the MWA Ram pressure efficiency

Figure 5.9: Influence of the turbulence on the scoop performances

5.3 Turbulence model influence 35

Note also that theTransition SST model provides similar results to k-ϵ over a wider MFR range, but for low flow rates, performance drops more sharply. The total pressure discharge calculated withTransition SST is almost identical with the one obtained with Fluent, while k-ω SST computes less discharge.

Figure 5.10: Influence of the turbulence on the total pressure discharge

The following table summarizes the mean difference between the MWA performance curves obtained, depending on the region from which it is computed. These deviations are divided by the mean gap δ0between Fluent and elsA to measure

the “intensity” of the influence of the studied parameters. Average calculation

range Whole range MFR < MFRref MFR > MFRref

k-ω SST -0.45 -0.78 -0.11 Transition SST -0.26 -0.52 +0.01

Table 5.3: Mean gap δη/δ0depending on the MFR region

5.3.2 Evolution of flow distribution

The visualizations of the low MFR cases make possible to understand why their performances are degraded quickly: the flow separation at the entrance of the scoop propagates until the second, even the third blade. This phenomenon was not present with k-ϵ with Fluent and was less important with elsA.

We can also see that the separation is greater with the SST transition model,

36 Results

but at higher flow, the recirculation bulb flattens more, hence the curves obtained previously.

(a)Realizable k-ϵ

(b) k-ω SST

(c)Transition SST

Figure 5.11: Low MFR effect of the turbulence model on the total pressure distribution- Fluent

Thus, even if the performance curves with k-ω and Transition SST are close to those obtained with elsA, the characteristics of the flow are totally different at low flow. Indeed, the fall in performance with Fluent with these turbulence models is mainly explained by the massive separation at the entrance of the scoop. Two additionnal operating point were added to obtain additional pressure conditions in the low MFR region.

5.4 Summary 37

5.4

Summary

The characterization of the influence of the parameters is done on the MWA ram pressure efficiency of the scoop, because being representative of the overall performance of the scoop. The following table shows the average difference between different pressure recovery obtained and the reference curve computed with Fluent. Factor of influence δη/δ0[-] elsA -1 PowerFLOW -0.49 Structured mesh -0.24 k-ω SST -0.45 Transition SST -0.26

Table 5.4: Summary of the influence of each parameter on the pressure recovery (MWA)

5.5

First step towards optimization

The optimization process necessitate a set of parameters in order to create the design space that will be explored during the surrogate-assisted optimization process. Based on the results obtained, the easiest method to implement would be to vary the angles of the blades θ and the chord length c. As a matter of fact, the flow at the inlet of the scoop have been observed to behave differently along each blade.

Intuitively, a larger angle θ at the last blade would allow the flow to penetrate more easily inside the scoop and to ingest a higher region of the boundary layer. On the contrary, a smaller angle θ at the first blade could position it along the flow direction, thus reducing the angle of attack and diminishing the risk of a flow separation.

An automatic simplified geometry, linked to an auto-meshing procedure have been tested for this strategy. The procedure is following a simple law that necessitate four parameters : the average angle of the blades θ, the average chord of the blades

c, the maximum angle deviation ∆θ = θ− θmin and the maximum chord deviation

38 Results

∆c = c − cmin. Once those four parameters given, a constant angle and chord

increment between each consecutive blade is computed. The spacing between the blades is proportional to the chord.

Finally, the diffuser outlet is moved away as the strong flow separation could impair the optimization results.

Figure 5.12: Automatic simplified geometry generated with ∆θ = 10◦and ∆c/c = 0.1

5.5.2 Improvement of the post-processing

Another part that needed to be assessed was to automatically post-process the efficiency of the scoop, in order for the optimization to be run by itself. The crucial part is to compute p′_0∞which is the average total pressure at the inlet of the captured stream tube to compute the MFR (Equation 2.4). For this thesis, this was realized as follows :

• The height of the captured tube in the middle plane is measured using streamlines.

• The total pressure is integrated, presuming this height is constant in the entire inlet.

The two steps had two major drawbacks : they are manual and the hypothesis that the height is constant, is incorrect. The captured area has an arbitrary shape and doesn’t necessarily extend to the limit of the geometry.

The solution found is to use a User Defined Scalar (UDS) with Fluent. This tool solves a transport equation for any scalar. The ruse is to first solve the flow as usual, then stop the calculations, reverse the three speed components and diffuse the scalar

ϕ from the two outlets. The source term Sϕ of the scoop outlet is set to 1 and the

source term of the main flow outlet to 0.

5.5 First step towards optimization 39

The convective flux is then computed with mass flow rate using the transport equation : ∂ ∂xi ( ρuiϕ− Γ ∂ϕ ∂xi ) = Sϕ (5.1)

With Γ the diffusion coefficient, chosen to be equal to be arbitrarily small, 10−6kg · s−1· m−1, for low diffusion. The captured area is therefore the inlet region where the UDS is greater than 0.5. This method has the advantage to find the precise shape of the captured tube and to directly obtain the MFR with the ratio of areas.

(a) 2D view of the UDS diffusion in the middle plane

(b) Shell of the captured tube - UDS = 0.5

Figure 5.13: Visualization of the real captured part of the flow