1

Put paper number here

SENSITIVITY ANALYSIS TO FLOW SEPERATION OVER NACA4412 AEROFOIL USING RANS SIMULATIONS.

Krishna Zore1 ANSYS, Inc

Pune, Maharashtra, India

Ishan Verma2

ANSYS, Inc Pune, Maharashtra, India

Patrick Sharkey3

ANSYS, Inc Milton Park Oxfordshire, United

Kingdom

ABSTRACT This paper discusses the influence of mesh topology,

turbulence models and various solver numeric settings on

prediction of separated flows over standard NACA4412 aerofoil

at critical angle of attack using ANSYS Fluent flow solver. To

understand the impact of mesh topology the results are compared

between block structured Hex mesh generated in ANSYS

ICEMCFD with prism-tetrahedral and prism-hexcore mesh from

ANSYS Fluent meshing. k-ω based turbulence closure variants

like SST (with default and modified value of a1 coefficient) and

BSL are studied for adverse pressure gradient predictions.

Solution initializations technique, governing equations

discretization methods (first and second order), Under

Relaxation Factors (URFs) and Algebraic Multigrid (AMG)

settings are studied for solver convergence, speed and accuracy.

Computational results were validated against experimentally

available data in the form of aerodynamic forces, pressure

coefficient and velocity profiles. Also, the influence of cross

flow (yaw angle) on the side of body separation were studied by

modeling NACA4412 airfoil, attaching two side plates across

each end. The solver numeric settings, URFs controls and time

advancement (Courant-Friedrichs-Lewy (CFL) and pseudo

transient) methods were explored to better understand side of

body separation bubble prediction.

INTRODUCTION NACA4412 aerofoil is selected for this study due to its

popularity among various applications and easy availability of

geometric profiles and experimental data. The hot-wire

measurement data in the boundary layer and separated region

near wake, acquired for flow past an NACA4412 aerofoil at

maximum lift by Coles & Wadcock5 are used for comparisons.

Figure 1. Shows the development and movement of trailing edge

separation region with increase in angle of attack. For lower

angle of attack less than 50 flow remains fully attached with very

weak link between viscous and in-viscous interactions. For

higher angle of attacks between 50 to 160 the adverse pressure

gradients becomes stronger, which moves separation point

upward and alter flow pattern significantly, making stronger

viscous and in-viscous interactions. After, 160 angle of attack

separations point moves upward more than half of chord length

and destroy suction peak, increasing wake resulting into stall. At

200 angle of attack, flow is completed separated and forms large

turbulent wake resulting into reduction of lift and increase in

pressure drag. Robust solution settings are available for attached

flows but for modeling separated flows needs more

investigation1-3. Mesh resolution, turbulence models and solver

numeric settings plays vital role in accurate predictions for

separated flows.

Figure 1. NACA4412 flow separation phenomenon w.r.t angle of

attack.

2

In this paper, the mesh sensitivity study is performed to

understand its impact on the numerical predictions of separated

flows. Block-structured hexahedral meshes are most preferable,

with most RANS turbulence models calibrated on these

structured meshes. However, practical engineering geometries

are very complex and sometimes it’s tedious to generate

structured grids on these geometries. In ANSYS Fluent mesher,

it is now possible to generate hybrid mesh, with surface triangles

to capture the complex geometric features, then extrude prism

wedge cells from the surface, and fill the empty volume with

hexahedral cells, which can leverage some of the benefits of pure

hexahedral mesh. Also, hybrid prism plus tetrahedron meshes are

generated. Results from these unstructured grids (prism hexcore

and prism tetrahedral) are compared to understand the mesh

topology impact. Solution initialization, URFs and advanced

AMG settings are also explored to understand the impact on

solution convergence. Faster convergence leads to reduced

solver iteration requirement, thereby reducing computational

cost. These understandings from flow over an aerofoil led to

generation of best practices for modeling separation due to

adverse pressure gradients. A more complex body separation

phenomenon is also studied which features cross flow (yaw

angle) boundary conditions over NACA 4412 aerofoil with two

side plates attached at the ends. This allows to model complex

flow structures generated due to separation from adverse

pressure gradients, cross flow boundary conditions and side

plates. Finally, the results are compared to the experimental data

in the form of aerodynamic force coefficient (lift and drag),

pressure coefficients and velocity profiles.

NOMENCLATURE

k = Turbulent kinetic energy.

ε = Dissipation rate. SST = Shear Stress Transport.

ω = Specific rate of dissipation.

M = Mach number.

α = Angle of attack.

U = Velocity.

𝜌 = Density.

𝜇 = Molecular viscosity.

T = Temperature.

P = Pressure.

𝛾 = Gas constant.

RESULTS AND DISCUSSION This section is divided into multiple sub-sections based on

the sensitivity studies performed.

Mesh Sensitivity Study

Adverse Pressure Gradient Separation Prediction

The mesh topologies are as showed in Figure 2. Where

Figure 2 (a) depicts the prism-tetrahedral mesh and Figure 2 (b)

depicts the prism-hexcore mesh with similar prism cells from the

airfoil surface. Computations are performed at 150 angles of

attack and lift force coefficient is compared between different

grid types.

(a) (b)

Figure 2. NACA4412, Computational domain a) Prism-tetrahedral

mesh and b) Prism-hexahedral mesh.

Figure 3 shows separation due to adverse pressure gradient at 150

angles of attack for a) Prism-tetrahedral mesh and b) Prism-

hexcore mesh. Figure 4. shows the prediction of adverse pressure

gradient separation on the upper surface of NACA4412 aerofoil,

using SST turbulence model at 150 angles of attack. Figure 4 (a)

and (b) represents the separation region modeled by prism-

tetrahedral and prism-hexahedral mesh respectively.

(a)

(b)

Figure 3. NACA4412, α=150, Separation Prediction a) Prism-

tetrahedral mesh and b) Prism-hexcore mesh.

It is clearly seen, that onset prediction of separation by prism-

tetrahedral mesh is not smooth and infer certain waviness,

whereas the onset separation prediction by prism-hexahedral

mesh is smooth. The reason being the shape of tetrahedral cells,

which are not properly align with the flow direction and might

have some influence on the gradient calculations. Whereas

hexahedral cells remain properly align with the flow directions

and might have very little influence on the gradient calculations.

However, the most important thing is both the meshes predict

3

onset separation at same location and this is due to same surface

triangular mesh and the same number of prism cells.

Figure 4. NACA4412, α=150, Lift force convergence, Prism-tetrahedral

and Prism-hexahedral mesh.

Turbulence Model First and Second Order Discretization

Flow separation prediction from SST k-w turbulence model with

first and second order upwind discretization using tetrahedron

and hexcore meshes is shown in Figure 5 and 6. The first order

upwind discretization fails to capture adverse pressure gradient

separation accurately with tetrahedron mesh, whereas hexcore

grid predicts accurately. However, both the meshes shows

accurate separation prediction with second order upwind

discretization methods.

(a)

(b)

Figure 5. NACA4412, α=150, Separation Prediction, Prism-tetrahedral

mesh a) First order turbulence discretization and b) Second order

turbulence discretization.

Figure 7 and 8 shows the lift force coefficient comparison

between first and second order upwind discretization of SST

turbulence model with tetrahedron and hexahedron mesh

respectively.

(a)

(b)

Figure 6. NACA4412, α=150, Separation Prediction, Prism-hexcore

mesh a) First order turbulence discretization and b) Second order

turbulence discretization.

Figure 7. NACA4412, α=150, Prism-tetrahedral mesh, Lift force

convergence, First and Second Order Turbulence Discretization.

For tetrahedral mesh separation region predicted by first order

discretization method shows unsteady behavior with large

separation region moving over upper surface, resulting in

oscillation of lift coefficient curve, whereas, second order

discretization predict steady separation, resulting in constant lift

coefficient curve, as seen in Figure 7. For hexcore mesh, first and

second order discretization produce steady separation, resulting

into constant lift coefficient curve with second order predicting

higher lift coefficient value as shown in Figure 8.

4

Figure 8. NACA4412, α=150, Prism-hexcore mesh, Lift force

convergence, First and Second Order Turbulence Discretization.

Total height of prism padding.

Figure 9 (a) and (b). shows the hexcore mesh with prism padding

total height of 5mm and 26mm respectively. The first layer

height and the growth rates are similar between the paddings.

Reason for this study is to access the impact of total prism

padding height on the separation prediction and the integral force

coefficient. Since to have thicker prism padding more numbers

of prism layers needs to be added, which increases the total

number of cell count.

(a) (b) Figure 9. NACA4412, α=150, Prism-hexahedral mesh, (a) 5mm total

prism height (b) 26mm total prism height.

Figure 10 (a) & (b). shows the comparison of adverse pressure

gradient separation region predicted by 5mm and 26mm prism

total height using SST turbulence model. It is observed that both

the meshes predict similar separation regions. However, looking

at Figure 11. the lift coefficient predicted by 5mm prism total

height is slightly higher than 26mm prism total height. Which

indicates 26mm total height predicts slightly more separation.

Since the difference is not huge user can take a call based on his

experience what prism total height is best.

Solution Convergence and Speed Sensitivity Study

Solution Initialization Sensitivity

To understand impact of solution initialization on flow

separation, angle of attack used is 180 at which NACA 4412

configuration stalls. Three different strategies have been used

which are assessed based on faster convergence. Figure. 12

shows convergence behavior of lift coefficient using Hexcore

mesh with 2nd order turbulence discretization. Standard

initialization (red) computes domain values based on inlet

boundary specification. Hybrid initialization (green) solves for

20 iterations of methods which are recipes and boundary

interpolation methods. Velocity field is calculated with Laplace

equation using velocity potential, with velocity components

obtained from gradient of velocity potential. Most efficient way

of initializing external aero flows is by using Full Multigrid

Initialization (FMG) which provides appropriate solution at

minimum cost (blue). It can be seen from Figure. 12 that FMG

initialized solution converges faster and is more robust for flows

with separation.

(a)

(b)

Figure 10. NACA4412, α=150, Separation region, Prism-hexahedral

mesh (a) 5mm total prism height (b) 26mm total prism height.

Figure 11. NACA4412, α=150, Prism-hexahedral mesh, lift coefficient

5mm and 26mm total prism height.

Figure 32. Convergence trace of RANS solution of lift coefficient with

a) standard (red), b) hybrid (green) and c) FMG (blue) initialization.

5

Advance Algebraic Multi-grid (AMG) sensitivity

Algebraic Multigrid (AMG) schemes are popular for

efficient usage with unstructured grids, with solution from coarse

level equations without use of geometry or re-discretization.

Scalar system of equations is solved by using Gauss-Seidel or

Incomplete Lower upper (ILU) point smoother methods, while

coupled system of equations are solved with block-method

(Gauss-Seidel or ILU) smoothers. Pressure Based Coupled

Solver (PBCS) Baseline AMG settings are very conservative

which are based on internal knowledge. These settings provide

deeper convergence while supporting different grid types.

Baseline settings use ILU for both point and block method

smoothers. Optimised AMG settings in this study are termed ad

Modified AMG settings which use Gauss-seidel for point-

method smoother and ILU for block-method smoother. Table 1

shows comparison between solver time for convergence of lift

coefficient for PBCS AMG settings (Default and New) and

Pseudo transient methods.

Table 1. Impact of AMG settings on convergence.

Modified AMG settings for flow over aerofoil at α=150 provide

faster convergence for solution with improvement in run time by

35%. Figure. 13 shows that both PBCS settings predict lift

coefficient with less sensitivity, but time taken per iteration is

less for case-specific modifications to scalar and coupled system

of AMG solver.

Figure 14. Convergence of lift coefficient with x-axis representing solver

time per iteration.

CFL and URF relaxation sensitivity

Convergence of PBCS solution largely depends upon CFL

number used. In this section two approaches have been used- a)

3-step approach, CFL 50 with pressure and momentum relaxed

to 0.25 for 1st 30 iterations followed by CFL 200 with pressure

and momentum relaxed to 0.5 for 120 iterations and rest

simulation with CFL 100; b) 2-step approach, CFL 100 with

pressure and momentum relaxed to 0.4 for 200 iterations

followed by CFL 200 for complete solution. Other two

approaches used in this study are a) 2-step approach with fast

AMG, where above mentioned less conservative AMG settings

are used with FMG initialization and b) 2-step approach with

turbulence URF are relaxed to 0.8 for 1st 200 iterations followed

by URF of 0.95.

It can be seen from Figure. 14 that 2-step and 3-step approaches

produce similar convergence behavior. However, 3-step

approach is preferred for case where larger sensitivity to flow

separation is encountered. For most cases 2-step approach is

robust since minimum CFL is >= 100. FAST AMG settings

converge slightly early however as discussed earlier cpu-time of

fast AMG setting is 34% faster. The main impact on cpu-time to

convergence is of relaxation of turbulence quantities. With

relaxation solver takes more number of iterations and more cpu-

time to converge the problem.

Figure 15. convergence of lift coefficient with different CFL and URF

settings.

Complex Cross Flow (yaw angle) Investigations

To investigate the prediction of side of body separations due to

cross flow (yaw angle), two end plates are attached to the

NACA4412 aerofoil with finite span, Figure 15. The

computational domain with boundary conditions are shown in

Figure 16. The mesh resolution with prism-hexahedral and pure

hexa block mesh are shown in Figure 17.

The results are obtained with SST turbulence model at α = 200

and β = 60 with prism-hexahedral and pure hexa block mesh. It

is observed that the turbulence URFs values plays very important

role in predicting side of body corner flow separations. Figure 18

shows lift coefficient curve comparison with two different URFs

values on prism-hexahedral mesh, where lower value of URFs

predict lower lift coefficients. The reason being the over

prediction of separation region with smaller values of URFs

compared to the larger values, Figure 19. Similar impact of

URFs is also observed with pure hexa block mesh. However, the

averaged integrated lift coefficient values are closed (Figure 18),

6

the side of body separation predicted with lower URFs is higher.

The reason is for such a complex flow with corner plates under

relaxing the solution with lower URFs values locks the solution

at different levels and does not come out of it. Thus, it is very

important, to increase the URFs to ~1 while modeling such

complex flow physics. Pseudo transient results and more details

will be present in final paper.

Figure 15. NACA4412 aerofoil, with end plates on either side.

Figure 16. NACA4412 aerofoil, computational domain with boundary

conditions to modeled cross flow.

(a) (b) Figure 17. NACA4412 aerofoil mesh resolution (a) prism-hexahedral

(b) pure block hexa.

Figure 18. NACA4412, α=150, 𝛽 = 60, lift coefficient, prism-

hexahedral mesh.

(a) (b) Figure 18. NACA4412, α=150, 𝛽 = 60, lift coefficient, prism-

hexahedral mesh (a) turbulence urfs 0.8 and (b) turbulence urfs 0.95.

Figure 19. NACA4412, α=150, 𝛽 = 60, lift coefficient, pure hexa block

mesh.

(a) (b) Figure 20. NACA4412, α=150, 𝛽 = 60, lift coefficient, pure hexa block

mesh (a) turbulence urfs 0.8 and (b) turbulence urfs 0.95.

7

A section including results comparison with experimental data

will be covered in the final paper.

Acknowledgments

The authors would like to thank Domenico Caridi, Matteo

Aroni and Florian Menter from ANSYS for reviewing the results

and providing valuable suggestions.

REFERENCES 1. Wu, J. C., Sampath, S., and Sankar, N. L., “Dynamic

tall of and Oscillating Airfoil,” Proceedings of AGARD

conference on Un-steady Aerodynamics, NATO,

advisory Group of Aero. Research & Development,

977, pp. 24-1 to 24-18.

2. Steger, J. L., ‘'Implicit Finite Difference Simulation

of Flow About Arbitrary Two-dimensional

Geometries,” AIAA Journal, Vol. 16, July 978, pp.

679-686.

3. Gibeling, H. J., Shamroth, S. J., and Eiseman, P. R.,

"Analysis of Strong Interaction Dynamic Stall for

Laminar Flow of Airfoils, "NASA CR-2969, 1978.

4. Donald Coles and Alan J. Wadcock. "Flying-Hot-wire

Study of Flow Past an NACA 4412 Airfoil at Maximum

Lift", AIAA Journal, Vol. 17, No. 4 (1979), pp. 321-

329.

5. Menter, F. R., “Influence of Freestream Values on the

6. K-w Turbulence Model Predictions,” AIAA Journal ,

Vol. 30, No. 6, 1992, pp. 1651–1659.

7. Menter, F. R., “Two-Equation Eddy-Viscosity

Turbulence Models for Engineering Applications,”

AIAA Journal , Vol. 32, No. 8, 1994, pp. 1598 – 1605.