[American Institute of Aeronautics and Astronautics 49th AIAA/ASME/SAE/ASEE Joint Propulsion...

American Institute of Aeronautics and Astronautics

1

Pressure-based Coupled Simulation of Pressure Recovery

and Distortion in an S-shaped Intake Diffuser

Saravana Kumar1 and Balasubramanyam Sasanapuri

2

ANSYS Fluent India Pvt Ltd., Pune - 411057, India

Konstantin A. Kurbatskii3 and Angela Lestari

4

ANSYS Inc., Lebanon, NH 03766, USA

The problem of a compressible flow through an S-shaped compact offset intake diffuser

is studied computationally using the general purpose CFD code ANSYS Fluent. Steady-state

converged solutions are calculated using second-order upwind discretizations. A hierarchy

of four computational meshes, one unstructured and three block-structured, is applied to

evaluate grid independence. The near-wall resolution in all four meshes is fine enough to

resolve the viscosity-affected near-wall region all the way to the laminar sublayer.

Performance of four turbulence RANS models are compared: Spalart-Allmaras, SST k-,

Realizable k-, and Reynolds Stress model with low-Re stress-omega formulation of the

pressure-strain term. Numerical predictions of total pressure recovery and pressure

distortion are compared with the experimental data. An excellent agreement is presented for

pressure recovery, and favorable agreement is found in the prediction of distortion. An

additional configuration of the S-duct model incorporating test probes is considered to

evaluate the effects of experimental instrumentation at the Aerodynamic Interface Plane

(AIP) on predicting distortion.

I. Introduction

here has been a wide use of S-shaped inlets in military and commercial aircraft where design constraints require

the engine to be buried into the fuselage. Other advantages of using S-shaped inlets include reduction in drag

and pitching moment, and a more ergonomic inlet integration into the airframe which reduces the use of aircraft

space and leaves more room for payloads and passengers.

The flow inside an S-duct inlet is complicated because of its curved shape, and such flow complexity may

introduce undesired losses into the system. The flow inside the S-duct turns and diffuses, creating pressure gradients

in the streamwise and circumferential directions. These gradients cause the flow to separate and induce undesired

secondary flows. Total pressure losses due to flow separation and distortion due to secondary flows negatively affect

the compressor performance and may even lead to compressor stall. Broad-spectrum easy-to-implement numerical

models of S-shaped inlet configurations are being sought to augment the design process of engine inlet systems.

The main goal of the present study is on assessing the accuracy of the pressure-based coupled algorithm

implemented in the general purpose CFD code ANSYS Fluent1 in simulating aerodynamics of compact offset intake

diffusers. The work focuses on steady-state computations using different RANS methods with the purpose of

comparing their performance in predicting total pressure recovery and steady-state pressure distortion for S-duct

geometries.

II. Problem Description

The geometry of the S-shaped duct was proposed as a benchmark test of the 1st

AIAA Propulsion Aerodynamics

Workshop (PAW)2. The model consists of a bellmouth, a constant diameter pipe, and an S-shaped duct (Figures 1 –

5). The area ratio of the S-duct (ratio between the outlet and inlet sections) is equal to 1.52. The offset of the intake

1 Engineer.

2 Senior Technology Specialist.

3 Lead Technical Services Engineer, Senior AIAA Member.

4 Technical Services Engineer.

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49th AIAA/ASME/SAE/ASEE Joint PropulsionConference

July 14 - 17, 2013, San Jose, CA

AIAA 2013-3794

Copyright © 2013 by ANSYS, Inc.. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


2

resulting from centerline curvature is 1.34 x D1, where D1 =

133.15 mm is the inlet diameter. The length of the S-duct is 5.23 x

D1. The outlet diameter D2 is 164 mm, and a 164 mm diameter

pipe connects the outlet station to the AIP equipped with a 40

Kulite instrumentation system. Kulite probes were not included in

the baseline model proposed by the PAW. The bulk of the

numerical study was carried out on the baseline geometry. In order

to assess effects of the test probes placed at the AIP on pressure

distortion prediction, an additional model with the probes (Fig. 2)

is also considered in the study and a limited number of numerical

runs are performed on this model.

III. Numerical Model

Many numerical approaches to compressible flows through

intakes, e.g.3-4

, employ density-based coupled formulations where

the governing equations of continuity, momentum, energy and

(where appropriate) species transport are solved simultaneously as

a set, or vector, of equations. In this approach, density is used as a

primary variable found from the continuity equation, and then

pressure is deduced from it using an equation of state. Density-

based techniques are found to be efficient when used for high

subsonic, transonic or supersonic flows; however, they often

require modifications, such as preconditioning 5-6

, in low Mach

number flow regions (e. g. wakes and boundary layers close to the

walls) to overcome the problem of the system matrix becoming

singular in the incompressible limit.

As an alternative to the density-based approach, a number of

coupled pressure-based methods have been proposed 7- 11

to extend

applicability of traditional pressure-based segregated techniques to

flow regimes where the inter-equation coupling is strong. Unlike a segregated algorithm, in which the momentum

equations and pressure correction equation are solved sequentially in a decoupled manner, a pressure-based coupled

algorithm solves a coupled system of equations comprising the momentum equations and pressure correction

equation. Since the momentum and pressure equations are solved in a closely coupled manner, the rate of solution

convergence significantly improves when compared to a segregated solver. The coupling also makes pressure-based

coupled algorithms more robust for subsonic, supersonic and even hypersonic problems, which can be very difficult

to solve by a segregated approach. A pressure-based coupled double-precision solver1 is employed in this study.

A. Pressure-based Coupled Solver

The governing equations for the conservation of mass, momentum and energy are discretized using a control-

volume-based technique. Face values in convection terms are interpolated from the cell centers using a second-order

upwind scheme12

. Gradients needed for constructing values of a scalar at the cell faces and for computing secondary

diffusion terms and velocity derivatives are calculated using the least squares cell-based gradient evaluation1

preserving a second-order spatial accuracy.

An implicit discretization of pressure gradient terms in the momentum equations, and an implicit discretization

of the face mass flux, including the Rhie-Chow pressure dissipation terms, provide fully implicit coupling between

the momentum and continuity equations. This discretization yields a system of algebraic equations whose matrix

depends on the discretization coefficients for momentum equations1, and it is then solved using the coupled

algebraic multigrid (AMG) scheme1, 13

. Incomplete Lower Upper (ILU) smoother is applied to smooth residuals

between levels of AMG. ILU smoother is more expensive than standard Gauss-Seidel, but has better smoothing

properties, especially for block-coupled systems solved by the coupled AMG, which allows for more aggressive

coarsening of AMG levels. Additional details of the pressure-based coupled algorithm are provided in Ref. 1.

Figure 1. Baseline S-shaped intake model

Figure 2. S-shaped intake model with

Kulite probes at the AIP.

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B. Physical Models and Boundary Conditions

Air is modeled as a single-species calorically perfect gas.

Air viscosity is defined as a function of temperature by

Sutherland's viscosity law. Pressure inlet boundary condition at

the far-field boundary (Fig. 3) specifies total pressure P0 =

88744 Pa and total temperature T0 = 286.2 K which correspond

to the test conditions2. The far-field boundary is placed at the

radial distance of about 1,400 mm from the axis of the inlet

duct, and extends to 1,000 mm upstream from the duct

entrance. The flow is induces through the mass flow condition

defined at the duct outlet which imposes the mass flow rate of

2.427 kg/s (full model). This flow rate through the outlet

produces Mach number ~ 0.4 at the AIP and Mach number ~

0.6 at the duct entrance.

C. Computational Meshes

A half model about the symmetry

plane is simulated. Two baseline

computation meshes, 7.55 million

cell structured mesh and 7.36 cell

unstructured mesh, were provided to

PAW participants2 (Fig. 4). In

addition, two extra structured

meshes, 19 million cell medium and

44 million cell fine mesh, were

constructed using ANSYS ICEM

CFD1 for a grid-independence study

(Fig. 5). The meshes along the walls

contain a boundary layer type mesh

fine enough to resolve the viscosity-

affected near-wall region all the way

to the laminar sublayer to ensure y+

in the wall-adjacent cell is on the

order of one.

D. Turbulence Models

Four RANS-based models are

applied to investigate the effects of

turbulence modeling: one equation

Spalart-Allmaras14

(SA), two

equation shear-stress transport (SST)

k- model15

and Realizable k-

(RKE) model16

, and seven-equation

Reynolds Stress Model (RSM)17-19

.

The RSM accounts for the

effects of streamline curvature, swirl,

rotation, and rapid changes in strain

rate in a more rigorous manner than one-equation and two-equation models, and it has greater potential to give

accurate predictions for flows in S-shaped inlets. RSM predictions are still limited by the closure assumptions

employed to model various terms in the exact transport equations for the Reynolds stresses. The modeling of the

pressure-strain and dissipation-rate terms is particularly challenging. In addition, the RSM rely on scale equations (ε-

or ω-) and inherits deficiencies resulting from the underlying assumptions in these equations. In a version of the

RSM used in the study, the pressure-strain term is modeled by the low-Re stress-omega model based on the omega

equations and LRR model20

.

Unlike SA, SST and the RSM, the RKE model is not directly integrable all the way to the wall due to a lack of a

Figure 4. Structured (left) and unstructured (right) baseline

computational meshes.

Figure 5. Medium (left) and fine (right) meshes for grid independent

study.

Figure 3. Computational domain and

boundary conditions.

Pressure inlet P0 = 88744 PaT0 = 286.2 K

Mass flow outlet (1.2135 kg/s)

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well-defined wall boundary condition for the dissipation rate . To make the RKE model applicable to y+ ~ 1

meshes, an enhanced wall treatment is used to blend a law-of-the-wall for compressible flows and a two-layer zonal

approach for the laminar sublayer based on the combination of approaches21-22

.

IV. Numerical Results and Comparison with Test Data

All the numerical solutions are initialized with the ambient conditions. Then the full multigrid (FMG)

initialization1 is utilized to obtain the initial solution. The FMG initialization is based on the full-approximation

storage (FAS) multigrid algorithm1, 23

. The FMG procedure constructs several grid levels to combine groups of cells

on the finer grid to form coarse grid cells. FAS multigrid cycle is applied on each level until a given order of

residual reduction is obtained, then the solution is interpolated to the next finer grid level, and the FAS cycle is

repeated again from the current level all the way down to the coarsest level. This process is continued until the finest

grid level is reached. FMG initialization is relatively inexpensive since most of computational work is done on

coarse levels, which allows one to obtain a good initial solution that already recovers some flow physics. Once the

initialization is complete, the solver is iterated until a steady-state solution is reached.

A. Comparison of Structured and Unstructured Mesh Results

Boundary layer profiles at the duct entrance are examined along the

three radial lines at azimuth angles = 0, 90 and 180 deg (Fig. 6).

Numerical profiles calculated on the baseline structured and

unstructured meshes using SA, RKE, SST and RSM turbulence models

are compared with experimental distributions in Fig. 7 and 8. The RKE

and SA models exhibit closer comparison with the test distributions at

the entrance for wall distances greater than 0.002 m. The SST model

generates higher turbulent viscosity near the duct inlet which explains its

deviation from the experimental curves. Eventually, as the flow evolves

downstream, the SST performs better, as will be shown in subsequent

sections. All the numerical profiles collapse into one curve for wall

distances smaller than 0.002 m. A more careful examination of the

experimental profiles revels slight asymmetry in the three profiles at =

0, 90 and 180 deg, while numerical profiles are nearly axisymmetrical, suggesting a uniform distribution of

calculated flow field at the duct entrance.

Figure 7. Boundary layer profile comparison – structured baseline mesh.

Figure 8. Boundary layer profile comparison – unstructured baseline mesh.

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.75 0.80 0.85 0.90 0.95 1.00

Wal

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ce (m

)

Pi/Pi0

BL profile at phi = 0 (exp)

BL profile at Phi = 0 (RKE)

BL profile at Phi = 0 (SST)

BL profile at Phi = 0 (RSM)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.75 0.80 0.85 0.90 0.95 1.00

Wal

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ce (m

)

Pi/Pi0


BL profile at phi = 90 (RKE)



0.000

0.001

0.002

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0.005

0.006

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0.008

0.75 0.80 0.85 0.90 0.95 1.00

Wal

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ce (m

)

Pi/Pi0


BL profile at Phi = 180 (RKE)



0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.75 0.80 0.85 0.90 0.95 1.00

Wal

l dis

tan

ce (m

)

Pi/Pi0

BL profile at phi = 0 (exp)BL profile at Phi = 0 (SA)BL profile at Phi = 0 (RKE)BL profile at Phi = 0 (SST)BL profile at Phi = 0 (RSM)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.75 0.80 0.85 0.90 0.95 1.00

Wal

l dis

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ce (m

)

Pi/Pi0

BL profile at Phi = 90 (exp)BL profile at Phi = 90 (SA)BL profile at Phi = 90 (RKE)BL profile at Phi = 90 (SST)BL profile at Phi = 90 (RSM)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.75 0.80 0.85 0.90 0.95 1.00

Wal

l dis

tan

ce (m

)

Pi/Pi0

BL profile at phi =180 (exp)BL profile at Phi = 180 (SA)BL profile at Phi = 180 (RKE)BL profile at Phi = 180 (SST)Bl profile at Phi = 180 (RSM)

Figure 6. Three radial lines at the

duct entrance used to plot

boundary profiles

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Comparison of Mach number contours at different cross sections is shown in Fig. 9, where s denotes streamwise

distance measured from the duct entrance. Mach numbers are qualitatively consistent for the all turbulence models,

and between structured and unstructured meshes.

Enlarged views of Mach number contours at different cross-sections are presented in Fig. 10 and 11. On this

scale, differences in the flowfields calculated by the three turbulence models become more visible. All the models

show very similar flowfield at s/D1 = 2 cross-section just before the duct bend. As the flow goes through the curved

portion of the duct, it separates which is reflected by the low-velocity region. The separation region grows in size

downstream. The separation zone predicted by the RKE model is smaller than that calculated by SST and RSM. The

latter two models predict qualitatively similar separation zones, with some slight differences between SST and RSM.

Closer to the AIP the flow begins to recover which is reflected by diminishing difference in velocities between the

core and separation zone.

Figure 9. Contours of Mach number at five cross-sections and at the outlet calculated by RKE, SST and RSM

turbulence models on baseline structured and unstructured meshes.

s/D1 = 2 s/D1 = 3

Figure 10. Mach contours at s/D1 = 2 and 3 cross-sections.

StructuredRKE

entrance

s/D1 = 2

s/D1 = 3

s/D1 = 4

AIP

StructuredSST k-

StructuredRSM

UnstructuredRKE

UnstructuredSST k-

RKE SST RSM

Unstructured

Structured

RKE SST RSM

Unstructured

RKE SST RSM

Structured

RKE SST RSM

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s/D1 = 4 AIP

Figure 11. Mach contours at s/D1 = 4 cross-section and AIP.

Experimental measurements were taken at a series

of probes on duct walls distributed along streamwise

and circumferential lines denoted in Fig. 12.

Streamwise pressure distributions along the three

lines φ = 0, 90, 180 deg calculated on structured and

unstructured meshes are shown in Fig. 13 and 14.

Predictions of the SST model are comparable with

those of the RSM along the three lines. Predicted

pressures are nearly the same before the flow separates

(~x = 350 mm). After its separation, the RKE predicts

higher pressures as compared to the SST and RSM.

Predictions of the SA model are very close to the SST

and RSM.

Circumferential pressure distributions at the three

cross section (s/D1 = 2, 3 and 4) predicted by different

turbulence models on structured and unstructured

meshes are shown in Fig. 15 and 16. All the profiles

match well before the flow separates (s/D1 = 2). After

its separation, the RKE predicts higher pressure

compared to other models.

Figure 13. Streamwise pressure distribution using different turbulent models at

φ = 0, 90, 180 deg. Structured mesh.

RKE SST RSM

RKE SST RSM

Structured

Unstructured

RKE SST RSM

Unstructured

Structured

RKE SST RSM

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 0 deg (RKE)Phi = 0 deg (SST)Phi = 0 deg (RSM)

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 90 deg (RKE)

Phi = 90 deg (SST)Phi = 90 deg (RSM)

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0.76

0.78

0.8

0.82

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0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 180 deg (RKE)

Phi = 180 deg (SST)Phi = 180 deg (RSM)

Figure 12. Positions of pressure probes on duct

walls along streamwise and circumferential lines,

and AIP.

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Figure 14. Streamwise static pressure distribution using different turbulent models at

φ = 0, 90, 180 deg. Unstructured mesh.

Figure 15. Circumferential static pressure distribution using different turbulent models at

s/D1 = 2, 3, 4. Structured mesh.

Figure 16. Circumferential static pressure distribution using different turbulent models at

s/D1 = 2, 3, 4. Unstructured mesh.

B. Grid Independence Study.

Contours of Mach number and static to total pressure ratio at the AIP calculated on the three structured meshes

(Fig. 4 and 5) using the RSM are compared in Fig. 17. Corresponding pressure profiles along the three streamwise

lines (Fig. 10) are plotted in Fig. 18 and 19. Mach numbers and pressures calculates on the coarse mesh differ

slightly from distributions obtained on the medium and fine meshes. There is no observable difference in the results

on the medium and fine meshes, suggesting the solution on the medium mesh qualitatively has reached a grid

independent state.

Mach number Pi/Pi0

Figure 17. Mesh independent study: contours of Mach number and static to total pressure ratio at the AIP.

0.74

0.76

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0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 0 deg (SA)Phi = 0 deg (RKE)Phi = 0 deg (SST)Phi = 0 deg (RSM) 0.74

0.76

0.78

0.80

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0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 90 deg (SA)Phi = 90 deg (RKE)Phi = 90 deg (SST)Phi = 90 deg (RSM) 0.74

0.76

0.78

0.80

0.82

0.84

0.86

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0.90

0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 180 deg (SA)Phi = 180 deg (RKE)Phi = 180 deg (SST)Phi = 180 deg (RSM)

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 25 50 75 100 125 150 175 200

P/P

i0

Degree

s/D1 = 2 (RKE)

s/D1 = 2 (SST)

s/D1 = 2(RSM)0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 25 50 75 100 125 150 175 200

P/P

i0

Degree

s/D1 = 3 (RKE)

s/D1 = 3 (SST)

s/D1 = 3 (RSM)0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 50 100 150 200

P/P

i0

Degree

s/D1 = 4 (RKE)

s/D1 = 4 (SST)

s/D1 = 4 (RSM)

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 25 50 75 100 125 150 175 200

P/P

i0

Degree

s/D1 = 2 (SA)s/D1 = 2 (RKE)s/D1 = 2 (SST)s/D1 = 2 (RSM)

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 25 50 75 100 125 150 175 200

P/P

i0

Degree

s/D1 = 3 (SA)

s/D1 = 3 (RKE)

s/D1 = 3 (SST)

s/D1 = 3 (RSM)0.74

0.76

0.78

0.8

0.82

0.84

0.86

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0.9

0 25 50 75 100 125 150 175 200

P/P

i0

Degree

s/D1 = 4 (SA)s/D1 = 4 (RKE)s/D1 = 4 (SST)s/D1 = 4 (RSM)

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Figure 18. Mesh independence study – streamwise pressure distribution (RSM).

Figure 19. Mesh independence study – circumferential pressure distribution (RSM).

C. Comparison with Experimental Data

Pressures along streamwise and circumferential lines predicted by the RSM model on the fine mesh are

compared with experimental distributions in Fig. 20 and 21. Numerical distributions agree favorably with the

experimental curves. There are some deviations of the numerical curves from the experiment near the duct entrance

and the S-duct bend, but further downstream pressure recovers and matches well with the test values close to the

AIP located at 730.68 mm.

Figure 20. RSM predictions on the fine mesh vs. experiment. Streamwise pressure distributions.

Figure 21. RSM predictions on the fine mesh vs. experiment. Circumferential pressure distributions.

Table 1 compares coefficients of total pressure recovery and distortion predicted by different turbulence models

on baseline structured and unstructured meshes. Pressure recovery is calculated as a ratio of area-weighted average

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 0 deg (8 Million)


Phi = 0 deg (44 Million)0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)



Phi = 90 deg (44 Million)0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 180 deg (8 Million)Phi = 180 deg (19 Million)Phi = 180 deg (44 Million)

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 25 50 75 100 125 150 175 200

P/P

i0

Degree

s/D1 = 2 (8 Million)s/D1 = 2 (19 Million)s/D1 = 2 (44 Million)

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0 25 50 75 100 125 150 175 200

P/P

i0

Degree


0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0 25 50 75 100 125 150 175 200

P/P

i0

Degree


0.74

0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)

Phi = 0 deg (Exp)Phi = 0 deg (RSM)

0.74

0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0 100 200 300 400 500 600 700

P/P

i0

X (mm)


0.74

0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0 100 200 300 400 500 600 700 800

P/P

i0

X (mm)


0.74

0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0 25 50 75 100 125 150 175 200

P/P

i0

Degree

s/D1 = 3 (Exp)s/D1 = 3 (RSM)

0.74

0.76

0.78

0.80

0.82

0.84

0.86

0.88

0.90

0 25 50 75 100 125 150 175 200

P/P

i0

Degree

s/D1 = 4 (Exp)s/D1 = 4 (RSM)

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values of total pressure at the AIP and duct inlet. Distortion coefficient (DC) is calculates using 40 locations at the

AIP, grouped into five rings (Fig. 22) as,

Where PAVi is the average total pressure at the ring i,

PAVLOWi is the average total pressure below PAVi at the

ring i.

Experimental values were presented at the PAW

workshop2: pressure recovery coefficient = 0.97 and

distortion coefficient = 0.02. All the models are more

uniform in predicting pressure recovery. Distortion is

somewhat over-predicted. One explanation to over-

predicting distortion is simplifications of the geometrical

model made in the CFD analysis. The results discussed so

far were obtained from CFD runs on a model which did not

include test pressure probes positioned at the AIP plane in

the experiment. An argument can be made these probes may

have an effect on distortion, and this will be discussed in

detail in the next section.

Out of the four models, the RSM yields the best

prediction of the distortion. Pressure recovery and distortion

coefficients calculated on the coarse, medium and fine

structured meshes using the RSM are compared in Table 2.

The values predicted on the medium and fine mesh are nearly identical, indicating the medium mesh solution has

reached quantitative grid independence.

Baseline structured mesh Baseline unstructured mesh

RKE SST RSM SA RKE SST RSM

Pressure recovery 0.9752 0.9724 0.9699 0.9717 0.9736 0.9700 0.9685

Distortion 0.0333 0.0365 0.0317 0.0335 0.0334 0.0341 0.0310

Table 1. Comparison of pressure recovery and distortion coefficients calculated by different turbulence

models on baseline structured and unstructured meshes.

Coarse Medium Fine

Pressure recovery 0.9699 0.9702 0.9706

Distortion 0.0317 0.0302 0.0302

Table 2. Comparison of pressure recovery and distortion coefficients calculated by the RSM on the coarse,

medium and fine structured meshes.

D. Comparison of the Models without and with the Test Probes

Effects of the test probes positioned at the AIP (Fig. 2) on pressure distortion are studied computationally on a

20 million cell unstructured mesh (Fig. 23), which was additionally constructed for the model with the probes. A

similar unstructured mesh of the same resolution was generated for the baseline model without the probes for a

consistent comparison between the two models.

Figure 24 compares contours of static to total pressure ratio at the AIP for the two models. There are some

observable differences in the pressure distribution, suggesting the probe effect is not entirely negligible and it may

affect distortion prediction.

Figure 22. Total pressure measurements in

the AIP - real rake used in the experiment.

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Quantitative comparison of pressure recovery and distortion for the two models without and with the probes is

presented in Table 3. Probes have no effect on total pressure recovery, but they reduced distortion coefficient by

about 16%, bringing it closer to its experimental value of 0.02.

Figure 23. Two views of the unstructured computation mesh of the model with the test probes.

Figure 24. Comparison of contours of static to total pressure ratio at the AIP between the models without and

with the probes.

Without Probes With Probes

Pressure recovery 0.9668 0.9680

Distortion 0.0300 0.0252

Table 3. Comparison of pressure recovery and distortion coefficients predicted by the baseline model without

test probes, and by the enhanced model with the test probes at the AIP.

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V. Conclusions

This study confirms the ability of RANS models implemented in the framework of a general purpose CFD solver

to accurately simulate steady-state subsonic flow in an S-shaped intake diffuser. Numerical predictions of total

pressure recovery are in excellent agreement with experimental data. Pressure distortion is slightly overpreicted in

the baseline model without the test probes. A grid-independence study is carried out to provide an additional

verification of the CFD results. It is found a Reynolds Stress Model is better suited for this type of flows, as

compared to one- and two-equations RANS models. Inclusion of the test probes brings the computational model

closer to the experimental set up and significantly improves pressure distortion prediction.

The results reported in this work show that the pressure-based coupled solver (PBCS) is a robust and effective

method for solving intake flow problems which can adequately resolve the physics and capture essential features of

a subsonic intake flow and accurately predict pressure recovery and distortion. PBCS is less memory and CPU

intensive than a traditional density-based approach, which makes it an economically attractive alternative to density-

based algorithms for obtaining steady-state solutions to intake flow problems.

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