prediction of crosswind inlet ﬂows: some numerical and...

Prediction of crosswind inlet flows:

some numerical and modelling challenges

Yann Colin!, Bertrand Aupoix†, Jean-Francois Boussuge‡ and Philippe Chanez§

CERFACS, Toulouse, 31000, France

The study is motivated by the need of engine designers to have a robust, accurate and

e!cient tool capable of simulating complex flows around and inside an isolated, or close to

the ground, nacelle in a crosswind. Such crosswind flows exhibit four distinctive features

challenging from a numerical and modelling point of view. First, this application is fea-

tured by the cohabitation of incompressible and transonic areas around the inlet lip. Local

preconditioning procedures are used to compute low Mach number regions with a com-

pressible solver. The second flow feature of this application is the considerable hysteresis

phenomenon occurring in the separation and reattachment processes, conditioning the time

integration techniques. Lastly, an accurate description of complex three-dimensional sepa-

rations requires the investigation of Reynolds Averaged Navier-Stokes turbulence models

along with the study of transition phenomena. Fully turbulent air intake flow computa-

tions show that none of the investigated turbulence models was fully satisfactory and able

to predict the distortion levels for the whole engine range. However, it is shown that the

use of local transition criteria is fundamental to predict accurately the boundary-layer de-

velopment along the nacelle external walls. This has strong consequences on the separation

line location and thus on fan plane distortion levels.

Nomenclature

A inviscid flux Jacobians in the x direction

!Research engineer, CFD Department, 42 Av. Gaspard Coriolis, [email protected].†Research director, ONERA DMAE, 2 Av. Edouard Belin, 31055 Toulouse, [email protected]‡Research engineer, CFD Department, 42 Av. Gaspard Coriolis, [email protected]§Research engineer, SNECMA, Villaroche, 77550 Moissy-Cramayel, [email protected]

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American Institute of Aeronautics and Astronautics

B inviscid flux Jacobians in the y direction

C inviscid flux Jacobians in the z direction

Cf skin-friction coeeficient

c speed of sound

d artificial dissipation flux

E total energy

H total enthalpy

M Mach number

Mis isentropic Mach number

Mlim limit Mach number

Mr Turkel reference Mach number

p static pressure

pt total pressure

q conductive heat flux

R Residual vector

Re! Reynolds number based on boundary-layer momentum thickness

s surface vector

U Euler symmetrizing variables vector

(u, v, w) Cartesian velocity components

u+ reduced velocity in wall variables

W state vector in conservative variables

!x Variable displacement vector

! Mr scaling factor

" Weiss-Smith parameter

# preconditioning parameter

" Weiss-Smith/Choi-Merkle preconditioner

$ specific-heat ratio

% density

&pgr pressure gradient free parameter

' stress tensor

( kinematic viscosity

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Subscript

i variable number

v viscous

W in conservative variable system

! infinite values

I. Introduction

An issue related to the development of subsonic aircraft engine nacelles is the design of e#cient air intakes

which have to fulfill both geometrical constraints and engine requirements. One of the engine requirements

is focused notably on the homogeneity of the flow in front of the fan which is quantified by the distortion

levels of the total pressure in this plane. Airplane on the ground with crosswind is a critical case for the

nacelle design. Subsonic or supersonic separations occur in the inlet, according to the engine mass flowrate.

The resulting heterogeneity of the flow may account for the outbreak of aerodynamic instabilities of the

fan blades and, if the distortion is large enough, the fan might stall. Figure 1 provides some insight of the

large separation that takes place in the inlet due to the crosswind and illustrates the resulting total pressure

distortion in the fan plane.

Figure 1. Flow heterogeneity in the fan plane induced by crosswind flow.

The goal of this study is to have a robust, accurate and e#cient tool capable of simulating complex flows

around and inside a nacelle in a crosswind and to predict the distortion levels. There are few studies related

to the numerical simulation of the distortion. Most of them deal with theoretical1, 2 or experimental3–5 issues.

Chen et al.6 performed Euler computations for general nacelle configurations focusing on meshing tools and

outlet boundary conditions prescriptions. Mullender et al.7 also used Euler computations but coupled to a

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boundary layer code for laminar nacelles design. These tools are adapted for attached flows only and are

thus ine#cient to predict distorsion levels accurately.

It is found that such crosswind flows exhibit four distinctive features challenging from a numerical and

a modelling point of view. Firstly, this application is featured by the cohabitation of incompressible and

transonic areas around the inlet lip. Indeed the infinite crosswind velocity varies between 15 and 30 kt

which yield Mach numbers of the order of 10!2 whereas the Mach number may be larger than unity at

the inlet lip. It turns out that the convergence of the pseudo-unsteady methods applied to the system of

the Euler or Navier- Stokes equations in compressible flow is degraded at low velocities. This performance

loss is due to the large disparity between the fast acoustic modes and the slow convective modes. Local

preconditioning procedures8–12 in which the time derivatives of the compressible equations are altered to

control the eigenvalues and to accelerate convergence must be used.

The second flow feature of this application is the considerable hysteresis phenomenon occurring in the

separation and reattachment processes as the engine mass flowrate evolves in the subsonic range. This

behaviour has been experimentally highlighted by Raynal13 or Quemard et al.14 They indicate that large

hysteresis can be observed when testing model intakes by varying angle of attack. Recently, Hall and

Hynes15 carefully measured the hysteresis associated with separation and reattachment and showed that it

is particularly sensitive to fan operating point and the location of the ground plane. At present there are

few theoretical bases for analyzing aerodynamic hysteresis and it remains a di#cult phenomenon to examine

numerically. This phenomenon raises interrogations on the method to conduct time integration. Special care

must be taken on convergence acceleration techniques, which imply a loss of time consistency.

Then, crosswind intake flows feature complex three-dimensional separations starting from the leading edge

of the nacelle down to the fan. Fast and accurate computations are required by engineers in nacelle design

context. Therefore computational predictions for such flows are obtained by solving the Reynolds-averaged

Navier-Stokes (RANS) equations in combination with popular turbulence models. Three eddy-viscosity

turbulence models are considered to assess their e#ciency in computing separated intake flows for di$erent

engine mass flowrates: the one-equation model of Spalart-Allmaras,16 the k " ) BSL and SST models by

Menter.17 A more detailed study on turbulence modelling assessment for this application may be found in.18

Lastly, intake flows are confronted with laminar-turbulent transition phenomena. The reduced size of the

scale model along with the use of non-pressurized wind tunnel tests may account for infinite low Reynolds

numbers and the development of laminar boundary layers on external walls. The transition towards a

turbulent state may also be delayed by the strong acceleration of the flow field as it gets close to the inlet

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lips. This has strong consequences on the position of the separation line and thus on the intake separation.

In this study, transition phenomena are taken into account through the use of local critera based on empirical

data.

The present work thus aims to assess some numerical and modelling tools to provide an accurate descrip-

tion of the intake distortion levels as the engine mass flowrate evolves. The test case and the experimental

setup are first introduced. Then, the governing equations and the numerical methods are briefly described.

The stress is put on local preconditioning techniques for low Mach numbers, spatial discretization and time

integration. In the last section, numerical results are presented and discussed.

II. Problem description and experimental setup

II.A. Experimental facility

The configuration consists of the LARA nacelle tested at the pressurized F1 ONERA Fauga wind tunnel as

illustrated in Fig. 2. This nacelle was originally designed to reduce significantly the external viscous drag

by using a laminar flow technique. Experimental tests are performed in order to characterize the intake

separation area and to quantify the heterogeneity of the flow in front of the fan plane. The nacelle is set

vertically and di$erent crosswind velocities (from 15 to 30 kts) are considered for the entire engine flowrate

range. The test instrumentation consists of wall static pressure tappings and total pressure probes at the

Figure 2. Crosswind tests at the F1 ONERA Fauga wind tunnel.

fan face.

The static tappings are located at four angular positions 0", 45", 90" and 135", along both the external

and internal walls, as illustrated in Fig. 3(a). The goal of the tappings along the external wall is notably to

capture the external separation for windmilling tests. Steady total pressure probes are allocated in the fan

plane on 12 arms at 10 di$erent radii locations. The probes are equally spaced around the circumference

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with a pitch of 30" and their radial distribution is summarized in Tab. 1. In particular, the comparisons

with numerical results will be made at the four specific radii locations R2, R3, R5 and R10, as described in

Fig. 3(b).

o

θ

90

135

x

y

z

0

45o

o

o

(a)

C2C3

C5

C10

(b)

Figure 3. Repartition of the (a) wall static pressure tappings and (b) fan total pressure probes.

Table 1. Location of the crowns

Crown i C1 C2 C3 C4 C5 C6 C7 C8 C9 C10

Ri/Rext 0.385 0.529 0.644 0.736 0.822 0.902 0.960 0.971 0.983 0.99

It should be noticed that these tests were conducted without the presence of a rotating fan. Fan-inlet flow

field coupling were experimentally studied by Hodder19 or Motycka.4 They observed that the magnitude of

distortion is reduced by the favorable coupling e$ect of the fan and inlet. The performance of small-scale

inlet model without engine is thus assumed to be conservative.

II.B. Distortion levels definition

The influence of the total pressure distortion can be measured with the introduction of the circumferential

distortion index (IDC) to characterize the heterogeneity of the flow. This coe#cient is defined as

IDC =nradius!1MAX

i=1

!

0, 5

"

(Pi " Pmini)

P+

(Pi+1 " Pmini+1)

P

#$

(1)

where nradius is the number of crowns, P the average pressure within the plane and Pmini the minimal

pressure of the ith crown. This index is devoted to assess the e$ect of the intake flow on the stability of

the fan and enables to define surge margin. The experiment consists of measuring the distortion in the fan

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plane as the mass flowrate (MFR) increases. Then the evolution of the distortion in terms of the flowrate

may be represented, as depicted in Fig. 4. At low MFR, subsonic separation takes place in the intake. As

MFR increases, the separation extent tends to reduce but total pressure losses become higher, resulting in

IDC increase. At intermediate MFR, the boundary layer reattaches in the di$user which leads to the IDC

drop. The flow is homogeneous in front of the fan plane and this flowrate range defines the working range.

Then, at high MFR, the flow becomes supersonic on the lip and brings about a shock wave associated with

strong total pressure losses, which explains the sudden increase of the IDC coe#cient. This shock wave may

induce a separation of the boundary layer: the resulting high heterogeneity of the flow causes aerodynamic

instabilities responsible for strong vibrations which can damage the fan blades or lead to surge.

Another common quantitative measure of the intake flow quality is given by the Distortion Coe#cient

DC(*), defined notably in Ref.1 The sector * is usually 60" and defines the “worst” sector of the face, related

to distortion e$ects. The common point of IDC and DC(60) coe#cients is that they are minima when the

flow is reattached and they yield similar working flowrate range.

0 500 1000 1500MFR (engine scale) in kg/s

0

0.1

0.2

0.3

IDC

max

Subsonic separation

Reattachment

Supersonic separationMFR increaseMFR decrease

Hysteresis region

33

38

Figure 4. Evolution of IDC in terms of the mass flowrate.

III. Governing equations

The governing equations are the unsteady compressible Navier-Stokes equations which describe the con-

servation of mass, momentun and energy of the flow field. In conservative form, they can be expressed in

three-dimensional Cartesian coordinates (x, y, z) in semi-discrete form as

+W

+t+ R(W ) = 0, R(W ) =

+

+xifi(W ) (2)

where W is the state vector given by

W = (%, %u1, %u2, %u3, %E)T , (3)

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and R(W ) is the residual vector resulting from spatial discretization of the convective and viscous fluxes.

The fluxes fi are thus given by

fi = fci " fvi (4)

where the convective fluxes fci and viscous fluxes fvi are defined as

fci =

%

&

&

&

&

&

&

&

&

&

&

&

&

&

'

%u1

%u1ui + p"i1

%u2ui + p"i2

%u3ui + p"i3

%uiH

(

)

)

)

)

)

)

)

)

)

)

)

)

)

*

, fvi =

%

&

&

&

&

&

&

&

&

&

&

&

&

&

'

0

'i1

'i2

'i3

U · 'i " qi

(

)

)

)

)

)

)

)

)

)

)

)

)

)

*

. (5)

Here % is the density, U = (u1, u2, u3) are the Cartesian velocity components, p is the pressure, E is the total

energy , H is the total enthalpy and " the Kronecker symbol.

The stress tensor ' is calculated by assuming a Newtonian fluid and the validity of Stokes hypothesis.

The temperature dependency of the viscosity was taken into account using Sutherland’s law. The heat flux qi

due to conduction is expressed according to Fourier’s law. For Reynolds-Averaged Navier-Stokes equations,

the turbulent fluxes are modelled with classical eddy viscosity assumptions or assessed with second-order

closure models.

IV. Numerical methods

The numerical platform employed for the simulation is routinely used for steady aerodynamic calculations

of industrial interest and is the Navier-Stokes multi-block parallel flow solver elsA.20 It was found that the

numerical results were extremely sensitive to the chosen methods. Notably, the stress is put on deriving a

convective scheme with low artificial dissipation. A small amount of di$usion has a strong e$ect on external

boundary layer thicknesses and thus on the separation line position.

IV.A. Finite Volume Method

The Navier-Stokes equations (2) are discretized using a cell-centered finite volume technique using structured

multi-block meshes. Integration of Eq. (2) over an arbitrary volume leads to the semi-discretized scheme

applied to one cell:

V+W

+t+

NS+

n=1

Fn + R" = 0 (6)

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where Fn is the inviscid numerical normal flux at a side of the finite volume V and R" is the residual of the

second order centrally discretized viscous terms.

IV.B. Low-speed preconditioning techniques

Preconditioning techniques involve the alteration of the time-derivatives used in time-marching CFD methods

with the primary objective of enhancing their convergence. The original motivation for the development of

these techniques arose from the need to e#ciently compute low speed compressible flows. At low Mach

numbers, the performances of traditional time-marching algorithms su$er because of the wide disparity that

exists between the particle and acoustic wave speeds. Preconditioning methods introduce artificial time-

derivatives which alter the acoustic waves so that they travel at speeds that are comparable in magnitude to

the particle waves. Thereby good convergence characteristics may be obtained at all speeds. The alteration

of the propagation velocities is done by multiplying the time-derivative of Eq. (6) by a preconditioning matrix

"W as follows:

V "W+W

+t+

NS+

n=1

Fn + R" = 0 (7)

A generic Weiss-Smith/Choi-Merkle preconditioner based on Merkle/Weiss workgroups8, 9, 12 was imple-

mented and validated in elsA. Using the Euler symmetrizing variables dU = [dp/%c, du, dv, dw, dS], the

preconditioner can be written as follows:

" =

%

&

&

&

&

&

&

&

&

&

&

&

&

&

'

1# 0 0 0 $

%c

0 1 0 0 0

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

(

)

)

)

)

)

)

)

)

)

)

)

)

)

*

(8)

where # is the preconditioning parameter and " is a free parameter varying from 0 to 1. For " = 0, the

preconditioner is the Weiss-Smith preconditioner, which is a member of Turkel’s family.

It turns out that the use of preconditioning techniques greatly reduces the robustness of the flow solver.

Numerical test cases show that the preconditioning parameter # is the critical factor influencing robustness

issues. The implementation of # is done as follows:

# = min

!

1, max

!

M2lim, M2,&pgr

|!p|

%c2,!M2

r , M2is

$$

(9)

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where the limiting factor &pgr|!p|

%c2is introduced to avoid large pressure fluctuations in the vicinity of

stagnation points.21 The limitation !M2r is suggested by Turkel22 to reduce preconditioning for viscous-

dominated flows in boundary layers. Such regions are indeed dominated by di$usion processes and this

formulation avoids deriving too large time steps in this region. Mr is usually taken as the inflow Mach

number so that # becomes constant in the boundary layer region. In this case, ! = 1.0 and Mr = 0.04, which

corresponds to infinite crosswind velocities of 30 kt.

The problematic of this restriction is the prescription of the reference Mach number. For crosswind inlet

flows, the boundary layer expands at very low Mach numbers whereas it develops at much higher Mach

numbers in the intake. This is why a restriction based on isentropic Mach number has been introduced with

M2is =

2

$ " 1

,

!

pt#p

$!!1

!

" 1

-

(10)

Outside the boundary layer, the isentropic Mach number is equivalent to the Mach number. Local precondi-

tioning is carried out with # # M2. Inside the boundary layer, the normal pressure gradient is approximately

zero, thus Mis is pretty constant and equal to the Mach number at the edge of the boundary layer. Therefore

the preconditioning parameter # is constant and global preconditioning is achieved. A detailed analysis of

the preconditioning formulation along with its application to air intake flow computations may be found in

Ref.23

IV.C. Spatial discretization

The use of preconditioning does not only reduce the sti$ness of the system of equations; it also improves

accuracy at low speeds. Turkel et al.24 showed that the loss of accuracy of the original convective schemes is

due to an ill-conditioning of artificial dissipation fluxes which become extremely large for very low velocities.

The modification of the fluxes required to take into account the new characteristics of the preconditioned

system results in a well conditioned dissipation formulation and ensures reliable accuracy. The results

presented in this study employed the scalar artificial dissipation scheme of Jameson, Schmidt and Turkel

(JST).25 The Jameson’s scheme involves a numerical flux at the interface between cells j and j + 1

Fj+1/2 =1

2(Fj + Fj+1) " "W,j+1/2 dj+1/2 (11)

where the artificial dissipation flux d is

dj+1/2 = ,(2)j+1/2(Wj+1 " Wj) " ,(4)j+1/2(Wj+2 " 3Wj+1 + 3Wj " Wj!1) (12)

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The coe#cients ,(2) and ,(4) are used to locally adapt the dissipative flux and are directionally scaled by the

scaling factor rj+1/2:

,(2)j+1/2 = k(2)rj+1/2 (j+1/2 (13)

,(4)j+1/2 = max(0, k(4)rj+1/2 " ,(2)j+1/2) (14)

where k(2) and k(4) are real numbers fixing the amount of di$usion brought up by the second - and fourth-

order dissipative operators. The sensor (j+1/2 is constructed using the absolute value of the normalized

second-order di$erences for the pressure to control the second-order dissipation near shock waves. The

scaling factor rj+1/2 is calculated as the average of the spectral radii of the Jacobian matrix AW = +F/+W

at the cell face

rj+1/2 =1

2(%("!1

W AW )j + %("!1W AW )j+1) (15)

The order of magnitude of the factor ri+1/2 is now the flow velocity and not the speed of sound as in the

original model. However, as explained above, the preconditioning parameter # has been reduced in the

boundary layer for sti$ness issues, which may account for high values of artificial dissipation close to the

wall. Thus the strategy consists of damping the artificial dissipation d near the wall by multiplying this flux

by (M/Mis)2.

IV.D. Time integration

As pointed out above, crosswind inlet flows exhibit considerable hysteresis in the separation and reattachment

processes as the engine mass flowrate evolves. As illustrated in Fig. 4, when the flow is separated, increasing

the mass flowrate tends to reduce the separated area, bringing the flowfield closer to reattachment. Once

the flow is reattached, if the mass flowrate is reduced, separation occurs at a much lower flowrate than

that required for reattachment. At present, theoretical bases for analyzing aerodynamic hysteresis are not

well developed and it remains a di#cult phenomenon to investigate numerically. In our study, it turns out

that steady computations failed to yield steady distortion in fan plane. Indeed these methods, involving

local time stepping or preconditioning procedures alter time derivatives of the original equations. The loss

of time consistency in the hysteresis region may account for the ine#ciency of these methods. On the

contrary, unsteady time integration techniques such as Dual Time Stepping (DTS) methods were successful

in converging to a steady separated solution.26 This technique enables to capture the two possible states of

the flow field for a given flowrate.

Introducing a pseudotime ' , the linear system (6) may be rewritten to provide a DTS procedure with a

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second-order backward di$erencing:

!

"WV

!'I +

3

2

V

!tnI +

+R

+W

.

.

.

.

"$

!W " =

3

2

Wn+1,"

!tnV + R(Wn+1,")

"V

2

!

3

!tn+

1

!tn!1

$

Wn "V

2!tWn!1 = R$

(16)

where R$ represents the discretized inviscid and viscous terms of the Navier-Stokes equations. ( is the

subiteration index and !W " = Wn+1,"+1 " Wn+1," . This linearized system may be solved using the scalar

version of the LU-SGS (Lower-Upper Symmetric Gauss-Seidel) relaxation scheme.27 The advantage of the

DTS approach is its ability to compute unsteady flows while keeping convergence acceleration techniques

such as local time stepping or preconditioning procedures. The physical time step is set to !t = 10!2. For

the convergence of the inner loop, the pseudotime step !' is determined by considering both the CFL and

von Neumann stability conditions. The convergence of the inner loop is function of two criteria. If the norm

of the residual R$ has decreased by two orders of magnitude, the internal loop is stopped. If this criterion

is not reached, the maximum number of subiterations is fixed to Nin = 10.

V. Numerical results

V.A. Computational Setup

The computational domain, illustrated in Fig. 5, is designed to match the wind tunnel facility. A crosswind

velocity of 30 kt (corresponding to a Mach number of 0.04) and a Reynolds number (based upon the crosswind

velocity) of 4.5 · 106 are considered.

The various boundary conditions are described in Fig. 5. They consist of an inflow condition at the

facility entrance while a static pressure is imposed at the exit. On the nacelle walls a no-slip condition and

a zero heat flux (adiabatic wall) are imposed whereas a Euler wall condition is applied to the spinner and

the wind tunnel wall. Numerical tests26 showed indeed that the spinner boundary layer development has

no e$ect on the intake separation. In order to avoid interaction of the separation in the intake with the

boundary condition, the outlet condition is imposed far more inside the inlet than in the wind tunnel test,

as shown Fig. 5. Then, for powered nacelle simulations and to control the intake flow rate of the nacelle,

three di$erent options for specifying fan plane boundary conditions are implemented.

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Figure 5. Computational domain and boundary conditions for the LARA air intake computation.

1. The first one is to specify the global mass flux MFR at the outlet plane %:

MFR =

/

!%-q · -n dS (17)

where -q is the velocity vector and -n is the outward pointing unit normal to the surface. From this

specified value, a local mass flux MFRloc may be calculated for each node of the fan plane by homo-

thety:

MFRloc =

!

MFR

MFRsch

$

%sch-q sch · -n (18)

where the superscript sch denotes the flow variables estimated by the numerical scheme. The inte-

gration of this equation over the fan plane surface clearly verifies Eq. (17). The advantage of this

formulation is that it allows us to simulate a specific MFR and to compare it directly with exper-

imental data. However, the lack of robustness of this condition, especially in the initial phase of a

simulation, makes it di#cult to use.

2. The second option is thus to specify the constant static pressure p at the fan face. The di#culty

associated with this condition is that it is dependent on the numerical scheme and model used, which

yield di$erent boundary layer thicknesses thus di$erent flow rates for the same outlet static pressure.

Therefore some iterations are required to simulate a specific MFR. However, this formulation is much

more robust than the mass flux one: this condition is thus kept for performing the computations.

13 of 27


3. A third option is the throttle condition given by

pout = p# + . Q2 (19)

where pout is the outlet pressure, Q the instantaneous flowrate given by the scheme and . the throttle

parameter. This condition is often used by turbomachinists to simulate the characteristic of a com-

pressor. It is equivalent to impose a non-constant static pressure in the outlet plane. This formulation

did not bring any improvements compared to the constant static pressure.

x

z

-0.8 -0.6 -0.4 -0.2 0 0.2

-0.2

0

0.2

(a)

(d)(c)

Fan plane location

Figure 6. Illustration of the meshing strategy (left) and partial view of the LARA nacelle mesh, representation one

point over two (right).

An essential element for the succesful simulation of the distortion is the capability of generating smooth

and well distributed grids in the intake flow region. In an industrial context, time constraints may enforce

the use of relative coarse grids. The meshing strategy consists of cutting the computational domain into

several regions, as described in Fig. 6, in order to achieve the best tradeo$ between computation time and

reliable accuracy. Four regions, listed in table 2, were thus studied carefully. In particular, the influence

of the number of points in the boundary layer wall normal direction (a), in the azimutal direction of the

intake (b), in the longitudinal direction around the lips (c) and within the di$user (d) was investigated. A

convergence study is then carried out separately for each region with three refinement levels M1, M2 and

M3 detailed in table 2. The complete convergence analysis is detailed in Ref.26

Concerning boundary layer meshing study, Fig. 6 shows parts of the C-mesh around the nacelle, which

is suitable to treat boundary layer separation. The fine Euler mesh is a structured multi-block mesh with

32 blocks and contains about 3.5 million grid points. The viscous grid is generated by remeshing the Euler

grid close to the walls such that the first cell height in wall unit, based upon the internal Reynolds number,

is lower than unity. Sensitivity study showed notably that at least 40 points are required in the wall normal

direction. Finally, numerical simulations yield identical results with M2 and M3 node distributions. The M2

14 of 27


distribution is thus selected to perform the RANS computations and results in a final viscous mesh with 5.2

million grid points.

Table 2. LARA meshing features

M1 M2 M3

Boundary layer (a) 25 41 51

1/4 azimutal region (b) 17 33 65

Lips (c) 21 41 81

Intake (d) 41 81 121

V.B. Fully turbulent air intake flow simulations

The relative high values of the Reynolds number encountered during the tests account for the initial choice to

perform fully-turbulent computations. One recalls that the goal of the present study is to be able to predict

the distortion levels in front of the fan plane for the entire engine mass flowrate range. These distortion

levels are determined by the total pressure losses induced by the inlet three-dimensional separation. Thus

an adequate turbulence modelling is required to predict accurately the separation extent. In the present

study, we focus on eddy-viscosity transport models (EVMs) only. These models are presently very popular in

computational fluid-dynamics applications and constitute the aircraft industry work horses. Three di$erent

models are considered and consist of the Spalart-Allmaras (SA) one-equation model, the two-equation k")

BSL and SST models by Menter. The e#ciency of SA and SST for computing separated flows has been

enhanced for various academic and industrial configurations.28–30 However, it should be noted that EVMs,

due to the Boussinesq hypothesis, are unable to reproduce stress anisotropy. This shortcoming may be

particularly penalizing for highly separated flow. A study of higher order models such as Di$erential Reynolds

Stress Models (DRSMs) may be found in Ref.18

The simulation of the increasing engine flowrate range is done identically for each model: first a steady

computation is performed at a low mass flowrate outside of the hysteresis region. Then simulations are

conducted by running a series of increasing MFR. The flowrate within the intake is increased by lowering

the outlet plane static pressure. One recalls that unsteady DTS simulations are performed to converge

towards steady state at one specific MFR. The convergence is checked by studying both fan plane IDC and

mass flow rate evolutions. The results for the three eddy-viscosity models are presented for two engine mass

flowrates corresponding respectively to points PT33 and PT38 of the experiment as illustrated in Fig. 4.

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-0.2 0 0.2x

0

0.2

0.4

0.6

0.8

1

Mis

Expe.SABSLSST

0o

-0.2 0 0.2x

0

0.2

0.4

0.6

0.8

1

Mis

45o

-0.2 0 0.2x

0

0.2

0.4

0.6

0.8

1

Mis

90o

-0.2 0 0.2x

0

0.2

0.4

0.6

0.8

1

Mis

135o

Figure 7. Wall isentropic Mach number distributions at PT33.

These two mass flowrate values bound the expected reattachment flowrate and constitute challenging test

cases for the assessment of turbulence model behaviour.

Firstly, wall isentropic Mach number distributions are computed at four angular positions 0", 45", 90"

and 135" as illustrated in Fig. 3(a) for both external and internal flows. The crosswind direction follows the

y-axis direction. These distributions provide information about the Mach peak values at the lips, the position

of the separation line and the stagnation area extent for a given angular position. Indeed, according to the

definition of the isentropic Mach number given by Eq. (10), this parameter turns to be inversely proportional

to the static pressure. Thus, a boundary layer separation is enhanced by the presence of a Mis distribution

plateau and the starting point of this plateau refers to the position of the separation line. Alternatively, a

linearly decreasing Mis distribution within the intake is a feature of a reattached boundary layer. The adverse

pressure gradients are indeed weaker and the flow recompression is done without separation. Complementary

to isentropic Mach number studies, fan plane total pressure drops are plotted in terms of the circumferential

angle * at the four radii locations described in Fig. 3(b). They yield details on the three-dimensional

separation extent and losses due to fan plane distortion.

Figures 7 and 8 compare the three models SA, BSL and SST at PT33, corresponding to an engine mass

16 of 27


0 90 180 270 360 θ

0.85

0.9

0.95

1

1.05

Pt

Expe.SABSLSST

R/Rext= 0.529

0 90 180 270 360θ

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.644

0 90 180 270 360θ

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.822

0 90 180 270 360θ

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.99

Figure 8. Fan plane total pressure distributions at PT33.

flowrate of 800 kg/s. Firstly, it turns out that the k " ) BSL model of Menter predicts a reattachment of

the boundary layer for much lower flowrates. The isentropic Mach number is linearly decreasing at the four

angular positions and denotes a reattached boundary layer. Besides, no total pressure drop may be seen in

Fig. 8 and the predicted flow is perfectly homogeneous in front of the fan plane. On the contrary, SA and

SST models tend to overestimate the separated area extent. Fig. 7 reveals that these models tend to predict

a separation line upstream of the experimental line, notably at the angular positions * = 45" and 135". In

particular, the separation occurs at the inlet lip for SST model. A consequence is the underestimation of

the Mach peak values on the lips. These overpredictions may also be appreciated with the total pressure

distributions given by Fig. 8. SA and SST predict higher total pressure losses in the azimutal direction at

radii R/Rext = 0.822 and 0.99, resulting in an overestimation of the fan plane distortion.

Figures 9 and 10 compare the previous models at PT38, corresponding to an engine mass flowrate of

950 kg/s. The BSL model already predicted a reattachment solution at PT33, it is not surprising that this

model provides a similar solution at PT38. No total pressure losses may be seen and the flow is perfectly

homogeneous in front of the fan plane. Conversely, SA and SST models, which were able to predict quite

accurate distortion levels at PT33, turn to be ine#cient to predict a boundary layer reattachment. Fig. 10

17 of 27


-0.2 0 0.2x

0

0.5

1

1.5

Mis

Expe.SABSLSST

0o

-0.2 0 0.2x

0

0.5

1

1.5

Mis

45o

-0.2 0 0.2x

0

0.5

1

1.5

Mis

90o

-0.2 0 0.2x

0

0.5

1

1.5

Mis

135o

Figure 9. Wall isentropic Mach number distributions at PT38.

points out strong distortion e$ects associated with total pressure losses higher than 20%.

To summarize the e#ciency of the models used for the fully-turbulent simulations, the IDC coe#cient is

plotted in Fig. 11 for an increasing MFR. The IDC evolution confirms that fully turbulent computations

with SA, BSL or SST models are not capable to yield accurate distortion levels for the entire flowrate range.

Besides, Colin et al.18 studied six other turbulence models for this application. They include the algebraic

model of Baldwin-Lomax,31 the rotation-curvature corrected version of Spalart-Allmaras model (SARC),32

k" l33 and k ") Wilcox34 two-equation models, a version of the non-linear eddy-viscosity model (EARSM)

of Wallin and Johansson35 coupled with a k"kL model36 and the di$erential Reynolds stress model (DRSM)

of Speziale, Sarkar and Gatski.37 This study also shows that none of these models is fully satisfactory and

may be classified into two categories:

• some models (including the Baldwin-Lomax, k" l, k") Wilcox, k") BSL and DRSM models) predict

a reattachment mass flowrate which is much lower than the one inferred from experimental data,

• some models (including SA, SARC, SST and EARSM models) overestimate the separation area extent,

which may account for the failure of reattached flow prediction.

18 of 27


0 90 180 270 360 θ

0.75

0.8

0.85

0.9

0.95

1

1.05

Pt

Expe.SABSLSST

R/Rext= 0.529

0 90 180 270 360θ

0.75

0.8

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.644

0 90 180 270 360θ

0.75

0.8

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.822

0 90 180 270 360θ

0.75

0.8

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.99

Figure 10. Fan plane total pressure distributions at PT38.


0

0.1

0.2

0.3

0.4

IDC

max

Expe.SABSLSST

Subsonic separation

Reattachment

Supersonic separation

Figure 11. IDC assessment with increasing MFR for a 30 kt crosswind speed.

V.C. Transition flow simulations

Fully turbulent computations are thus ine#cient to predict correct distortion levels for the entire flowrate

range. It is thought that the boundary layer development along the external walls of the intake has a major

role on the position of the separation line and thus on the fan plane distortion. Therefore some simulations

are performed in order to take into account transition phenomena. An issue concerning such computations is

19 of 27


X Y

Z

intermittency10.80.60.40.20

Y

Z

X

intermittency10.80.60.40.20

(a) (b)

Figure 12. Intermittency area for SA model at PT33.

related to the choice of transition criteria. The first choice was dedicated to non-local criteria, a priori more

attractive since they take into account the boundary layer history. However, the definition of the transition

computation lines is restricted to the mesh lines in elsA. This simplification is not satisfying for crosswind

inlet flows. The external streamlines are severely distorted as the flow approaches the inlet lips, as described

by Fig. 12(a). In this region, the streamlines do not match the mesh lines, and these criteria cannot be used.

Therefore, two local criteria, based on empirical data are employed to assess the intermittency region.

Also, the laminar boundary layer along the intake external walls may feature two instability modes:

streamwise (or longitudinal) and crossflow (or transversal). The streamwise instability in a three-dimensional

boundary layer is similar to the Tollmien-Schlichting (TS) waves in two-dimensional flows. Crossflow insta-

bility arises as a result of the inflectional crossflow velocity profile produced by transverse pressure gradients.

Two local criteria are finally employed for predicting the transition:

• Abu-Ghannam and Shaw (AGS) criterion38 for longitudinal instabilities,

• Coustols and Arnal (C1) criterion39 for transversal instabilities,

and transition process occurs when at least one of the two criteria is satisfied.

Figures 12(a)-(b) describe the intermittency region along with the wall friction lines obtained with SA

model at PT33. A value of zero for the intermittency function accounts for a laminar boundary layer whereas

a value of one corresponds to a turbulent region. Thus, the boundary layer turns to be laminar along the

external wall close to the leading edge, where a strong acceleration of the flow field takes place, as depicted

20 of 27


in Fig. 12(a). In this region, the negative pressure gradients tend to damp the TS waves and stabilize the

boundary layer. Transition intervenes slightly upstream the leading edge position, where the flow starts

to decelerate. However, at the angular position * = 0" and 180", transition occurs far upstream of the

lips location. In this region, the curvature of the streamlines accounts for the occurence of a transverse

pressure gradient, which may amplify crossflow disturbances. Figure 12(b) compares the positions of the

separation line (given by the friction lines) with the transition location in the intake. For this Reynolds

number, the separation occurs downstream of the transition line. The boundary layer is thus fully turbulent

when it separates, as in the previous fully-turbulent computations. Only the history of the boundary layer

has changed and the issue is now to study the e$ect of transition on the distortion levels.

t

x

0 45 90 135 180-0.6

-0.4

-0.2

0

0.2

0.4

0.6

t0 45 90 135 180

t

x

0 45 90 135 180-0.6

-0.4

-0.2

0

0.2

0.4

0.6

t0 45 90 135 180

x x

θ θ

Figure 13. Comparison of the prediction of the wall friction lines at PT33 for fully turbulent (left) and transition

(right) computations.

The influence of the transition processes on the intake separation is shown Figs. 13-15 with SA model.

Figure 13 compares the internal and external wall friction lines, predicted by SA model for fully-turbulent

and transitional simulations. These lines are projected in the two-dimensional plane (x, *) so that the

separation extent along with the vortex focus may be simultaneously represented. The location of the

leading edge is represented by the dashed red line, subdividing the external wall (x > 0.18) from the internal

wall (x < 0.18). The fan plane is located at x = "0.048. The intake transition simulation predicts a

separation line further downstream than the one found with fully-turbulent computation. Consequently, it

leads to a smaller recirculation zone, especially in the azimutal direction. This e$ect is confirmed by the wall

isentropic Mach number and fan plane total pressure distributions given by Figs. 14 and 15 respectively. The

separation line is better predicted at PT33 notably at * = 135" where the starting point of the plateau is in

good agreement with the experimental one. The azimutal separation extent along with total pressure losses

21 of 27


-0.2 0 0.2x

0

0.2

0.4

0.6

0.8

1

Mis

Expe.SANon Trans.SA Trans.

0o

-0.2 0 0.2x

0

0.2

0.4

0.6

0.8

1

Mis

45o

-0.2 0 0.2x

0

0.2

0.4

0.6

0.8

1

Mis

90o

-0.2 0 0.2x

0

0.2

0.4

0.6

0.8

1

Mis

135o

Figure 14. Influence of transition modelling on the Wall isentropic Mach number distributions at PT33.

are slightly underestimated, as it may be seen at particular radii locations R/Rext = 0.822 and 0.99. Finally,

the influence of the transition on the distortion is summarized in Fig. 16. One recalls that the fully-turbulent

computation with SA model was unable to predict any reattachment flowrate and thus unable to predict

any working range. The transition simulation predicts a reattachement at a mass flowrate (corresponding to

780 kg/s) slightly inferior to the experimental one (corresponding to 850 kg/s), which gives a relative error

inferior to 8%. Besides, the upper bound of the working range predicted by the simulation is in very good

agreement with the experimental one, with a relative error inferior to 2%.

The disparities encountered between the fully-turbulent and transition simulations prove that the external

wall boundary-layer development has a strong e$ect on inlet distortion. Considering the transition simula-

tion, the initially laminar boundary layer turns out to be much thinner around the inlet lips. Therefore, it

is more encline to counteract the adverse pressure gradient. Consequently, the separation line is predicted

further downstream and the resulting separation area is smaller than the one derived from fully-turbulent

computations.

22 of 27


0 90 180 270 360 θ

0.85

0.9

0.95

1

1.05

Pt

Expe.SANon Trans.SA Trans.

R/Rext= 0.529

0 90 180 270 360θ

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.644

0 90 180 270 360θ

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.822

0 90 180 270 360θ

0.85

0.9

0.95

1

1.05

Pt

R/Rext=0.99

Figure 15. Influence of transition modelling on the fan plane total pressure distributions at PT33.

VI. Conclusion

A methodology to compute crosswind inlet flows and fan plane distortion is derived. The stress is put

on four distinctive flow features challenging from a numerical and modelling point of view.

Firstly, the cohabitation of incompressible zones outside the nacelle along with high speed flow within

the intake has been computed using a generic Weiss-Smith/Choi-Merkle preconditioner. The computation of

the preconditioning parameter turns out to be essential for ensuring a robust tool capable of simulating such

flows. In particular, some specific cuto$ values are required to reduce preconditioning in the low Reynolds

number region.

The second flow feature of this application is the considerable hysteresis phenomenon occuring in the

separation and reattachment processes. The presence of the hysteresis region turns out to have strong

consequences on the relevant time integration techniques. Indeed, traditional stationnary methods are unable

to yield steady distortion levels. On the contrary, the use of time consistent techniques, such as Dual Time

Stepping techniques, allows us to converge to steady state. Since the use of acceleration techniques is

responsible for the loss of time consistency, it is assumed that the hysteresis region is responsible for the

failure of such techniques.

23 of 27



0

0.1

0.2

0.3

0.4

IDC

max

Expe.SA Non Trans.SA Trans.

Subsonic separation

Reattachment

Supersonic separation

Figure 16. Influence of transition modelling on IDC assessment for a 30 kt crosswind speed.

Thirdly, fully-turbulent RANS simulations are pursued for the prediction of intake separation. For

this purpose, the stress is put on meshing strategy, boundary conditions prescription and eddy-viscosity

turbulence models assessment. The mesh convergence study revealed the need to mesh carefully the boundary

layer in the wall normal direction along with the intake in the azimutal direction. A comparative study of

three eddy-viscosity turbulence models is performed. It is found that none of these models is fully satisfactory.

The k " ) BSL model predicts flow reattachment at much lower mass flowrate than the one inferred from

experimental data. The Spalart-Allmaras and k") SST models are more accurate in separated flow regions

but they fail to predict boundary-layer reattachment.

The failure of the fully-turbulent approach brings out the importance to take into account transition

e$ects. This study uses two local criteria to compute the intermittency region: the Abu-Ghannam and Shaw

model for longitudinal instability and the Arnal-Coustols criterion for transversal instability. Transition

simulations reveal the existence of a laminar region on the external walls, prior to the lips, where strong

acceleration of the flowfield occurs. As the flow follows the lips, transition occurs mainly due to the adverse

pressure gradients which trigger longitudinal instability. The flow separates downstream of the transition

region. Thus, the boundary layer is much thinner around the lips. It is less sensitive to the adverse pressure

gradient and the separation line is located downstream of the position given by fully-turbulent simulations.

Finally, as these crosswind inlet flow computations are very sensitive to the external Reynolds number,

it is thought that the use of pressurized wind tunnels is more appropriate to ensure conservative engine

evaluations.

24 of 27


Acknowledgments

This work was supported by Snecma on behalf of Safran group. The authors would like to acknowledge

G. Puigt, H. Deniau, M. Montagnac from CERFACS and K. Zeggai from Snecma for their support and

suggestions.

References

1Seddon, J. and Goldsmith, E., Intake Aerodynamics, Blackwell Science Oxford, 1999.

2Longley, J. and Greitzer, E., “Inlet distortion e!ects in aircraft propulsion system integration,” In AGARD, Steady and

Transient Performance Prediction of Gas Turbine Engines, 1992.

3Felderman, E. and Albers, J., “Comparison of Experimental and Theoretical Boundary-Layer Separation for Inlets at

Incidence Angle at Low Speed Conditions,” NASA TM X-3194, NASA Lewis Research Center, 1975.

4Motycka, D., “Reynolds number and fan/inlet coupling e!ects on subsonic transport inlet distortion,” Journal of Propul-

sion and Power (ISSN 0748-4658), Vol. 1, 1985, pp. 229–234.

5Hall, C. and Hynes, T., “Nacelle Interaction with Natural Wind Before Takeo!,” J. Propulsion and Power , Vol. 21, 2005,

pp. 784–791.

6Chen, H., Yu, N., Rubbert, P., and Jameson, A., “Flow Simulations for General Nacelle Configurations Using Euler

Equations.” AIAA Paper AIAA-83-0539, 1983.

7Mullender, A., Lecordix, J., Lecossais, E., Godard, J., and Hepperle, M., “The ELFIN II and LARA HLF nacelles:

design, manufacture and test.” Communication to 20 th European forum on laminar flow technology, Bordeaux (France)

ONERA-TAP-96-162, 1996.

8Choi, Y. and Merkle, C., “The Application of Preconditioning in Viscous Flows,” J. of Comput. Phys., Vol. 105, 1993,

pp. 207–223.

9van Leer, B., Lee, W., and Roe, P., “Characteristic time-stepping or local preconditioning of the Euler equations,” AIAA

paper AIAA-91-1552, 1991.

10Turkel, E., Radespiel, R., and Kroll, N., “Assessment of Preconditioning Methods for Multidimensional Aerodynamics,”

Computers & Fluids, Vol. 26, 1997, pp. 613–634.

11Weiss, J. and Smith, W., “Preconditioning Applied to Variable and Constant Density Flows,” AIAA J., Vol. 33, 1995.

12Venkateswaran, S. and Merkle, L., Analysis of Preconditioning Methods for the Euler and Navier-Stokes Equations, von

Karman Institute for Fluid Dynamics, Lecture Series, 1999.

13Raynal, J., “LARA laminar Flow Nacelle O!-Design Performance Tests in the ONERA F1 Wind Tunnel,” Test report

4365AY178G, ONERA, 1994.

14Quemard, C., Garcon, F., and Raynal, J., “High Reynolds Number Air Intake Tests in the ONERA F1 Wind Tunnel,”

TP 1996-213, ONERA, 1996.

15Hall, C. and Hynes, T., “Measurements of Intake Separation Hysteresis in a Model Fan and Nacelle Rig,” J. Propulsion

and Power , Vol. 22, 2006, pp. 872–879.

25 of 27


16Spalart, P. and Allmaras, S., “A One-Equation Turbulence Transport Model for aerodynamic flows.” AIAA Paper 92-0439,

1992.

17Menter, F., “Two-equation eddy-viscosity turbulence models for engineering applications,” AIAA J., Vol. 32, 1994,

pp. 1598–1605.

18Colin, Y., Aupoix, B., Boussuge, J.-F., and Chanez, P., “Numerical Simulation of the Distortion Generated by Crosswind

Inlet Flows,” 18th ISABE , Beijing, China, September 2007.

19Hodder, B., “An investigation of engine influence on inlet performance (conducted in the Ames 40- by 80-foot wind

tunnel),” Tech. Rep. NASA CR 166136, 1981.

20Cambier, L. and Gazaix, M., “elsA: An E"cient Object-Oriented Solution to CFD Complexity,” AIAA-paper , Vol. 2002-

0108, Januay 2002, Reno, Nevada.

21Darmofal, D. and Siu, K., “A robust Multigrid Algorithm for the Euler equations with Local Preconditioning and Semi-

coarsening,” J. of Comput. Phys., Vol. 151, 1999, pp. 728–756.

22Turkel, E., “Preconditioning Techniques in Computational Fluid Dynamics,” Ann. Rev. Fluid Mech., Vol. 31, 1999,

pp. 385–416.

23Colin, Y., Deniau, H., and Boussuge, J.-F., “A robust low speed preconditioning formulation: application to air intake

flows,” AIAA J., 2008, submitted for publication.

24Turkel, E., Fiterman, A., and van Leer, B., “Preconditioning and the limit to the incompressible flow equations,” Icase

report 93-42, 1993.

25Jameson, A., Schmidt, R. F., and Turkel, E., “Numerical Solutions of the Euler Equations by Finite Volume Methods

Using Runge-Kutta Time Stepping,” AIAA paper AIAA-81-1259, 1981.

26Colin, Y., Simulation numerique de la distorsion generee par une entree d’air de moteur civil par vent de travers, Ph.D.

Thesis, ENSAE, 2007.

27Yoon, S. and Jameson, A., “A Multigrid LU-SSOR Scheme for Approximate Newton Iteration Applied to the Euler

Equations,” Tech. Rep. NASA CR 179524, 1986.

28Huang, P., “Validation of turbulence models - Uncertainties and measures to reduce them,” Proc. of the ASME Fluids

Engineering Division Summer Meeting, Vancouver, Canada FEDSM97-3121, 1997.

29Bardina, J., Huang, P., and Coakley, T., “Turbulence modelling validation, testing and development,” NASA TM110446,

1997.

30Marvin, J. and Huang, G., “Turbulence Modeling - Progress and Future Outlook,” Fifteenth International Conference

on Numerical Methods in Fluid Dynamics, 1996.

31Baldwin, B. and Lomax, H., “Thin Layer Approximation and Algebraic Model for Separated Turbulent flows,” AIAA

Paper AIAA-78-257, 1978.

32Spalart, P. and Shur, M., “On the sensitization of turbulence models to rotation and curvature.” Aerospace Science and

Technology, Vol. 5, 1997, pp. 297–302.

33Smith, B., “A near wall model for the k " l two equation turbulence model.” AIAA Paper AIAA-94-2386, 1994.

34Wilcox, D., “Reassessment of the Scale-Determining Equation for Advanced Turbulence Models,” AIAA J., Vol. 26, 1988,

pp. 1299–1310.

26 of 27


35Wallin, S. and Johansson, A., “An Explicit Algebraic Reynolds Stress Model for Incompressible and Compressible Tur-

bulent Flows,” J. Fluid Mech., Vol. 403, 2000, pp. 89–132.

36Bezard, H. and Daris, T., Calibrating the Length Scale Equation with an Explicit Algebraic Reynolds Stress Constitutive

Relation, edited by W. Rodi and M. M. editors, Elsevier, 2005, pp. 77–86, Engineering Turbulence Modelling and Measurements

(ETMM6).

37Speziale, C., Sarkar, S., and Gatski, T., “Modelling the pressure-strain correlation of turbulence: An invariant dynamical

system approach,” J. Fluid Mech., Vol. 227, 1991, pp. 245–272.

38Abu-Ghannam, B. and Shaw, R., “Natural transition of boundary layers. The e!ects of turbulence, pressure gradient,

and flow history,” Journal of Mechanical Engineering Science, Vol. 22, 1980, pp. 213–228.

39Coustols, E. and Arnal, D., Criteres de transition en ecoulement tridimensionnel (aile en fleche infinie), TO OA, 21/5018

AYD, 1982.

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prediction of crosswind inlet ﬂows: some numerical and...

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