unsteady flow simulation of high-lift stall hysteresis using a lattice boltzmann approach

American Institute of Aeronautics and Astronautics

1

Unsteady Flow Simulation of High-Lift stall Hysteresis using

a Lattice Boltzmann Approach

Enrico Fabiano1, Ehab Fares

2 and Swen Nölting

3

Exa GmbH, Curiestrasse 4, D-70563 Stuttgart, Germany

A Lattice-Boltzmann flow solver is used for the prediction of the unsteady flow field around the

Trap Wing high–lift configuration used in the first High–Lift Prediction Workshop. The numerical

approach and the meshing technique are briefly described. The simulation model includes the

effects of wind tunnel walls, the geometries of the slat/flap brackets and the laminar to turbulent

transitional regions. Simulation results are compared to the uncorrected force and moment wind

tunnel measurements as well as the pressure distributions at various spanwise sections. The

numerical approach is further developed to include a time varying angle of attack resembling the

continuous measurements of increasing/decreasing incidence in the wind tunnel. This approach

aims at investigating the hysteresis effects which were documented during measurements. The

simulation predictions are compared to available measurements and the flow phenomena during

the hysteresis effects are analyzed based on the simulated unsteady flow structures, particularly the

stall behavior. Numerical predictions correctly capture the hysteresis effects around the stall region

and are shown to be related to the interaction between the slat and main wing separations near the

wing tip. The simulations furthermore indicate that a longer time period and dynamic

modifications of the laminar regions during simulation may be needed to further improve

quantitative predictions.

I. Introduction

ccurate prediction of the complex flow field around high lift devices of aircrafts has gained importance over the

past few years within the CFD community1,2,3

because of the significant effect the development of high lift

systems has on the overall aircraft performance and cost.

The 1st AIAA CFD High Lift Prediction Workshop (HiLiftPW-1) was held in June 2010 to address the capability of

the current-generation CFD codes to predict the complex flow field around a simplified three dimensional high lift

configuration1,4

. During the workshop the importance of grid refinement, turbulence modeling, geometrical details

and transition prediction has been highlighted, while the aerodynamics hysteresis seen in the experiment has not

been addressed yet.

Aerodynamic hysteresis is defined as the flow history effect that causes aerodynamic coefficients to be dependent on

the sense of change of angle of attack (AoA), so that they formed multi-valued rather than single-valued functions of

the AoA. Arguably the most common and most studied type of hysteresis occurs around stall, where the lift stall

cannot be recovered by reducing the AoA until the AoA is considerably below the angle at which the stall initially

occured. Aerodynamic hysteresis was studied previously in experiment5 for low Reynolds numbers flows and the

influence of transition and laminar separation and reattachment was also documented experimentally6. Similar flow

behavior at a higher Reynolds number of~2.2 million was observed also for a 2 element GA-(W)-2 airfoil7.

Hysteresis can also occur during a real flight mission representing an extremely dangerous flight condition from a

flight mechanics point of view. Therefore, it is of great interest for a state-of-the-art CFD code to be able to

accurately capture the unsteady flow phenomena associated with the aerodynamic hysteresis and to give insight into

the unsteady flow behavior associated with the hysteresis effect.

In this work, taking full advantage of the intrinsically unsteady nature of the Lattice Boltzmann approach

implemented in the commercial CFD code PowerFLOW, aerodynamic hysteresis around stall is investigated. To our

knowledge this is the first attempt to numerically investigate aerodynamic hysteresis for a full high lift

1 Application Engineer, Aerospace Applications, [email protected].

2 Technical Manager, Aerospace Applications, [email protected], Senior AIAA Member.

3 Managing Director, Aerospace Applications, [email protected], AIAA Member.

A

30th AIAA Applied Aerodynamics Conference25 - 28 June 2012, New Orleans, Louisiana

AIAA 2012-2922

Copyright © 2012 by Exa Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


2

configuration. Having shown in a previous work8 the importance of including the wind tunnel wall, the slat/flap

brackets and laminar regions in the simulation domain, this study will first describe the general numerical approach

used so far, and then it will move to the simulation of the aerodynamic hysteresis using a time varying AoA through

a sliding mesh region. Dynamic simulations results will be compared to experiment in terms of force and moment

measurements, pressure data as well as flow structures, giving particular attention to separated flow regions near the

wing tip.

This paper is organized as follows. The experimental findings used as a reference to the current study are briefly

summarized in section II. The details of the Lattice – Boltzmann and turbulence modeling approach are summarized

in section III. Results are presented in section IV and compared to experiments while conclusions are drawn in

section V.

II. Problem Description

The high-lift configuration used in this study is the semi-span, three-element untwisted trapezoidal wing (trap wing)

depicted in Figure 1 which is defined through the publicly available CAD geometries provided within the

framework of the high-lift prediction workshop10

. The model, characterized by a mean aerodynamic chord of 39.6”,

an aspect ratio of 4.56 and a leading edge sweep of 29.97°, was mounted on a body pod with full span slat and flap.

Wind tunnel measurements for this model were conducted at NASA Ames and NASA Langley as well as at Boeing

Seattle and Long Beach wind tunnels. The current study is based on the measurements at the NASA Langley

14’×22’ wind tunnel at a Reynolds number of ReMAC=4.3Million and a Mach number of 0.2 that included

uncorrected forces and moments measurements as well as surface pressures at several spanwise locations. The flow

over the wing was not tripped, i.e. a fixed transition was not enforced. A measurement of the laminar to turbulent

transitional behavior for this configuration using hot film is documented for a couple of angles of attack in11

while a

complete numerical investigation based on stability analysis is presented in10

. A comparison between stability

analysis and experiment reveals that the transition N-factor Ncritic for the NASA Langley wind tunnel is between 7

and 10. However it should be noted that the stability analysis code has been run for a free-air configuration without

taking the geometry of the slat and flap supporting brackets into account. The computations show that the transition

location on the upper surface is almost constant with the AoA while a more pronounced variation is seen on the

lower surface, as depicted in Figure 9.

The experimental force and moment repeatability and prediction intervals were determined applying the

methodology described in13

to three different test sessions in 1998, 2002, and 2003. Measurements for each AoA

take approximately 30 seconds. The first 20 seconds are used to pitch the model to the next AoA and to allow the

Figure 1. Trap wing geometry shown from upstream (left) and downstream (right) directions in the NASA Ames

tunnel


3

flow to settle. The following 8 seconds are the actual data acquisition, carried out at 50 samples per seconds for a

total of 400 samples per AoA. The remaining two seconds were used to write the acquired data32

. No information is

available about the movement of the model, but it is understood to be quick. It should be noted that hysteresis was

observed around CL,max and around α=0° depending on whether the AoA was increasing or decreasing during the

measurements as documented in Figure 2. The objective of the current study is to investigate the hysteresis effect at

stall.

Figure 2. Experimental lift polar showing hysteresis at stall and at zero incidence

III. Numerical Method

The numerical simulations were carried out using the commercial software PowerFLOW 4.3 which is based on the

three dimensional 19 state (D3Q19) lattice Boltzmann model. This lattice Boltzmann approach has been extensively

validated for a wide variety of applications ranging from academic cases using DNS14

to industrial flow problems in

the fields of aerodynamics15-19

, thermal management20

, and aeroacoustics3,21

.

A. The Lattice Boltzmann Approach

The lattice Boltzmann equation has the following form:

( , ) ( , ) ( , )i i i if x c t t t f x t C x t (1)

where fi is the particle distribution function moving in the i-th direction, according to a finite set of the discrete

velocity vectors { ic : i = 0, ... b}. ic t and t are space and time increments respectively. For convenience, we

choose the convention 1t in the subsequent discussions. The collision term on the right hand side of Eq. (1)

adopts the simplest and also the most popular form known as the Bhatnagar-Gross-Krook (BGK) form22

.

1( , ) ( , ) ( , )eq

i i iC x t f x t f x t (2)

Here is the single relaxation time parameter, and eq

if is the local equilibrium distribution function, which depends

on local hydrodynamic properties. The basic hydrodynamic quantities, such as fluid density and velocity u , are

obtained through summations; i.e.

( , ) ( , )i

i

x t f x t , ( , ) ( , )i i

i

u x t c f x t (3)

0

0.5

1

1.5

2

2.5

3

3.5

-5 0 5 10 15 20 25 30 35 40

CL

[-]

Experiment - Uncorrected forces- increasing Alpha

Experiment - Uncorrected forces- decreasing Alpha


4

The three-dimensional D3Q19 model22

shown in Figure 4 is used in the present three-dimensional study to represent

the possible discrete velocity directions.

The local equilibrium distribution function eq

if takes the following form

2 32

2

2 3 21

22 6 2

i ieq i i

i i

c u c uc u c uuf w u

T TT T T

(4)

where wi are weighting parameters:

1/18, in 6 coordinate directions;

1/ 36, in 12 bi-diagonal directions;

1/ 3, rest particles

iw

(5)

and T is the lattice temperature which is generally set to 1/3 for isothermal simulations. In the low frequency and

long-wave-length limit, one can recover the Navier-Stokes equations through Chapman-Enskog expansion. The

resulting equation of state obeys the thermally perfect gas law p T . The kinematic viscosity of the fluid is

related to the relaxation time parameter, by14,22

0 ( 1/ 2)T (6)

The combination of Eq. (1) to Eq. (6) forms our LBM scheme (LBM momentum solver) for fluid dynamics.

B. Turbulence Modeling

A modified k two-equation model based on the original RNG formulation describes the sub-grid turbulence

contributions23,24

and is given by

0

1 2

0

0

3 2

0 0

3

(1 / )

1

T

T

T

ij ij

j k k j

T

ij ij

j j

Dk kS

Dt x x

DC S C C

Dt x x k k

(7)

Figure 3. Schematic of the three dimensional D3Q19 model


5

The parameter 2 /T C k is the eddy viscosity in the RNG formulation. All dimensionless coefficients are the

same as in the original models23,24

. The above equations are solved on the same lattice using a modified Lax-

Wendroff explicit time marching finite difference scheme.

In order to model the turbulent fluctuations, the LBM is extended by replacing its molecular relaxation time scale

with an effective turbulent relaxation time scale; i.e., eff , where

eff can be derived from a systematic

renormalization group (RNG) procedure 24

as

2

2 1/ 2

/

(1 )eff

kC

T

(8)

where is a combination of a local strain parameter ( /k S ), local vorticity parameter ( /k ), and

local helicity parameters. This swirl correction for the local relaxation time, and hence the local eddy viscosity, is

fundamental in physically allowing the large vortical fluid structures to develop and persist without artificial

numerical damping. The swirl model together with the inherently unsteady nature of the lattice Boltzmann equation

adequately reproduces the large scale turbulent vortices. This represents, from a pragmatic point of view25

a key

factor in predicting LES similar solutions on coarse grids using an unsteady turbulence model, a methodology

referred to as Very Large Eddy Simulation (VLES). This LBM-VLES based description of turbulent fluctuation

carries flow history and upstream information, and contains high order terms to account for the nonlinearity of the

Reynolds stress26,27

. This is in contrast to its Navier-Stokes based methods, which generally use the conventional

linear eddy viscosity based Reynolds stress closure models.

C. Boundary Conditions and Wall Treatment

Inflow or outflow boundary conditions based on simple extrapolations or simplified characteristics are easily

defined using the assumption of local equilibrium fi=eq

if at the boundary. More complex non-reflecting unsteady

boundary conditions28

are also implemented but not used here. Usually velocity and turbulent kinetic energy is

imposed at the inflow boundaries, whereas the static pressure is kept constant at the outflow. Other values are

extrapolated from the simulation domain. The boundary conditions are used in an under-relaxed manner to avoid

large local gradients especially during the startup process.

The standard lattice Boltzmann bounce back boundary condition for no-slip or the specular reflection for free-slip

condition are generalized through a volumetric formulation29,30

near the wall for arbitrarily oriented surface elements

(Surfels) within the Cartesian volume elements (Voxels). In addition, in order to reduce the resolution requirements

near the wall, a hybrid wall function is used to model the boundary layer on solid surfaces. The wall function model

used in this work16

, is an extension of the standard log law of the wall, including the effect of favorable and adverse

pressure gradient and accounts for surface roughness through a length parameter. Its general form is

( ( ))

Where ut is the local tangential component of velocity and ks is the surface roughness length, while ( ) is the

function that accounts for pressure gradients. In addition for laminar boundary layers flow the wall model is adapted

to prescribe a laminar boundary layer, i.e. . The roughness length was not used in this work.

The combination of the LBM-VLES approach and the wall model allows an efficient and accurate prediction of

turbulent engineering flows at high Reynolds number.

D. Meshing Technique

The lattice Boltzmann approach is solved on Cartesian meshes which are generated automatically for any

geometrically complex shape. This greatly simplifies the tedious manual work usually associated with the volume

meshing step using other approaches. Furthermore, variable refinement regions (VR) can be defined to allow for

local mesh refinement of the grid size by successive factors of 2. The transfer of the velocity distributions fi across

the VR boundaries ensures the mass and momentum conservation via the volumetric formulation31

.


6

E. Sliding mesh approach

For all the hysteresis simulations the trap wing geometry is rotated during the simulation with respect to the wind

tunnel walls using a sliding mesh approach. The wind tunnel serves as an outer domain fixed with the ground, while

a cylindrical domain enclosing the trap wing geometry inside the wind tunnel (see Figure 4 ) serves as an inner

domain whose grid is fixed with the rotating geometry and slides against the outer domain. The fluxes across the

boundary from body fixed to ground fixed frames and vice versa, including mass, heat and momentum fluxes, are

exactly conserved as documented in31

.

IV. Results and Discussion

F. Generated mesh and case setup

In this work a numerical investigation of the hysteresis effect around stall will be performed for the trap wing

equipped with slat/flap brackets in the wind tunnel. The simulation model consists of the NASA Langley wind

tunnel and the trap wing at flap deflection of 25° (configuration one). The exact position of the trap wing in the wind

tunnel, including the .9” peniche offset is taken from32,33,34

. The computational model is equipped with supporting

brackets for the slat and the flap. The fuselage is assumed to be fully turbulent, while laminar to turbulent transition

location for the slat, main and flap is taken from10

with Ncritic = 10 chosen for the stability analysis because of the

better agreement with experiment at high angles of attack.

Transition location has been fixed in the current unsteady simulations to the one corresponding to 34 degrees AoA

because the focus of this study is biased towards very high angles of attack where the hysteresis is expected to occur.

Figure 4: Simulation model, the trap wing installed in the NASA Langley wind tunnel and the local rotation region

To accurately reproduce the wind tunnel blockage effect all the walls of the wind tunnel model used in the

simulation are set to a no slip boundary condition. The wind tunnel floor in the NASA Langley wind tunnel had a

boundary layer suction system shown in Figure 5. To reproduce a comparable starting position of the wall boundary

layer between simulations and experiments a free slip boundary condition was imposed on the corresponding

upstream region of the floor shown in Figure 5 as well.


7

Figure 5: Schematic of the NASA Langley wind tunnel (top) and simulation model (bottom).

The pitch-pause approach used in the wind tunnel has been reproduced here by means of a sliding mesh method. A

cylindrical region containing the trap wing is rotated according to a user specified AoA temporal variation.

The mandatory structured and unstructured meshes provided within the first high lift prediction workshop24

were not

used due to the Cartesian and automatic meshing technique implemented here for the lattice Boltzmann solver.

Instead, a locally refined mesh was employed (Setup1) similar to the one used in8. The definition of local resolution

regions (VR) was achieved through a simple offset from the wing geometry. Special attention has been given to the

resolution of the shear layer wake shed from the slat. A further optimization of the meshing approach (Setup2) was

performed to reduce the computational cost for the complete hysteresis loop. For Setup 1, the slat, the leading edge,

the upper surface and the tip of the main wing and the flap and the shear layer are resolved with the finest cell of

1.25mm size. The fuselage, the brackets and the lower surface of the main wing and the flap are set to the second

finest resolution. For Setup 2 the slat is left unchanged, but only the tip, and the leading and trailing edge of the main

and the flap have been kept to the finest VR region. The upper surface of the main and the flap have been moved to

the second finest VR. Differences between the two meshes in terms of number of voxels and computational

requirements are summarized in Table 1.

Setup 1 Setup 2

Finest voxel size [mm] 1.25 1.25

Total number of voxels [106] 127 79

Number of timesteps 500000 500000

CPU time [kCPUh] 32.5 24.6

Table 1: Computational requirement for the two setups

Free-slip wall No-slip wall


8

A comparison between the two meshing strategies is shown in Figure 6 and a quantitative comparison in terms of

computational results is shown in the next section.

Figure 6: Comparison between the two setups. Setup 1 on the left, setup 2 on the right.

G. Static simulations

Preliminary computations at 28° and 36° AoA have been performed to assess the quality of the results achieved with

the two different VR strategies. These two angles of attack are chosen since they are outside the experimentally

observed hysteresis.

Figure 7: Static pressure comparison. 28° AoA

Figure 8: Static pressure comparison. 36° AoA

A qualitative comparison is documented in Figure 7 and Figure 8 clearly showing that the two setups yield an almost

identical flow field at both 28° and 36° AoA and demonstrating that the computationally less demanding setup 2 can

be used for the hysteresis simulations. Similarly a comparison of the pressure distribution (not shown here) at

Setup 1 Setup 2

Setup 1 Setup 2


9

various spanwise sections indicate only a slight underprediction of the suction pressure on the main and flap for the

28° AoA and a slight modification of the separation behavior at 36° AoA. The integrated forces and moments are

summarized in Table 2 and show a maximum difference of ~1.5% in CL and ~1% in CD between the two setups.

AoA 28 degrees

CL CD CM

Setup 1 2.9302 0.5940 -0.3905

Setup 2 2.9220 0.5964 -0.3816

Experiment - Increasing 2.9676 0.6356 -.44370

AoA 36 degrees

Setup 1 2.1376 0.8600 -0.2032

Setup 2 2.1683 0.8687 -0.2102

Experiment - Increasing 2.2669 0.8395 -0.2086

Table 2: Aerodynamic coefficients for the two setups.

H. Laminar to turbulent transition location sensitivity

In this section the effect of specifying different transition locations is investigated. The current transition location

setup based on the stability analysis12

is compared to the laminar regions derived from experimental findings 11

used

in the previous numerical study8.

Figure 9: Laminar regions (green). Locations for 28° AoA (top) and for 34° AoA (middle) based on the stability

analysis (SA LR) compared to the one used in the previous work8 (bottom) based on experimental estimates at AoA

28°(LR from Exp)


10

Figure 10: Lift comparison for laminar regions based on stability analysis (SA LR) and Experiment (LR from EXP)

Figure 11: Drag comparison for laminar regions based on stability analysis (SA LR) and Experiment (LR from EXP)

2.10

2.30

2.50

2.70

2.90

3.10

3.30

26 27 28 29 30 31 32 33 34 35 36 37 38

CL

AOA [deg]

SA LR

LR from EXP

Experiment - Uncorrected - Increasing

Experiment - Uncorrected - Decreasing

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

26 27 28 29 30 31 32 33 34 35 36 37 38

CD

AOA [deg]

SA LR

LR from EXP




11

Figure 12: Pitching moment for laminar regions based on stability analysis (SA LR) and Experiment (LR from EXP)

Overall aerodynamic coefficients are shown in Figure 10, Figure 11 and Figure 12, for lift, drag and moment

coefficients, respectively. The current laminar region setup based on the stability analysis seems to be responsible

for a much more severe stall, also observed in experiment, than the former laminar region setup, which generates a

smoother stall as documented also in8. The pressure distributions at 28° AoA (not shown here) reveals that the

laminar regions used in the previous work allow for a better prediction of the pressure peak on the flap, while

sometimes slightly overpredicting the local pressure peaks on the slat and the main wing. This results in an

improved lift coefficient prediction. However, the flow pattern at this AoA between these two laminar regions

setups does not change significantly, as can be seen in Figure 13.

The results at 34° and 36° AoA show a much more pronounced difference in flow structures due to the different stall

behavior on the slat and the main wing. The loss in lift with the new laminar region definition based on the stability

analysis is significant and in better agreement with the stall observed in experiment but the stall AoA is

underpredicted by almost 1 degree when compared to the increasing AoA branch of the experiment. The pressure

distributions at 36° AoA are documented in Figure 14 and indicate a better agreement with experiment. This

generally confirms the assumption made in8 about the sensitivity of the stall behavior to the transitional behavior of

the flow. Due to the limited difference in the laminar definition on the nose of the main wing and the overall similar

contribution of the flap lift for all simulated angles of attack, it is likely that mainly the laminar region specification

on the slat suction side is responsible for the differences in separation behavior observed here.

-0.60

-0.55

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

26 27 28 29 30 31 32 33 34 35 36 37 38

CM

AOA [deg]

SA LR

LR from EXP




12

Figure 13: Flow structures for the two laminar regions setups at different AoA.

LR from EXP

AoA 28º SA LR

AoA 28º

LR from EXP

AoA 34º SA LR

AoA 34º

LR from EXP

AoA 36º SA LR

AoA 36º


13

Figure 14: Pressure distribution for the different laminar regions setups at η=17% (top), 50% (mid), 95% (bottom)

of the span. AoA = 36º

I. Hysteresis cases

In this section the hysteresis effect around stall observed in the wind tunnel measurements is investigated. Two

different meshes, summarized in Table 3, are used for this purpose. Results from these simulations are analyzed to

address the mechanism underlying stall and the hysteresis effect itself.

Coarse run Fine run

Finest voxel size [mm] 1.875 1.25

Total number of voxels [106] 37 68

Total number of surfels [106] 5.4 9.0

Covered AoA range 28°-36°-28° 32°-36°-32°

Number of timesteps 1 454 700 3 313 660

CPU time [kCPUh] 54.2 166

Table 3: Computational requirements and simulation range for the two hysteresis simulations

The simulations are performed around the hysteresis region for both the coarse and the fine cases starting from the

linear range into the stalled region and back. In order to reduce the overall computational cost for the fine case the

range of AoA was reduced further to start just before CL,max.


14

1. Coarse mesh, short settling time

Since the exact reproduction of the long experimental pitch-pause approach as described previously would not be

feasible, a much shorter time periods were used in the simulation. For the coarse simulation, the settling time for

each AoA is 0.250 seconds. The AoA time history is reported in Figure 15 together with the corresponding lift time

history. The almost instantaneous increase in AoA is achieved applying a pitching rotation velocity of 50 deg/s to

the rotation volume over 0.02 seconds.

Figure 15: Pitch-pause method implemented in the simulation

Aerodynamic CL and CD coefficients for this simulation are shown in Figure 16 and Figure 17 in comparison to the

experiment. The coarse simulation is first of all clearly able to capture the stall behavior observed in experiment.

The stall mechanism can be explained by investigating the lift contribution for the three lifting surfaces, as

documented in Figure 18, and surface flow structures, as depicted in Figure 19.

The lift of the flap remains almost constant over the full hysteresis cycle while the lift breakdown of the wing occurs

between 28° and 29° AoA, with a more significant drop observed between 34 and 35 degrees. On the other hand the

slat is still increasing lift as the AoA increases up till 34 degrees. This increase is effectively compensating the lift

drop on the main wing so that the stall for the complete wing is postponed until both the slat and the main are

simultaneously separating.


15

Figure 16: Lift vs. AoA, coarse simulation

Figure 17: Drag vs. AOA, coarse simulation

0

0.5

1

1.5

2

2.5

3

3.5

-10 -5 0 5 10 15 20 25 30 35 40

CL

AoA [deg]

Experiment - Uncorrected - increasing AlphaExperiment - Uncorrected - decreasing Alpha

PowerFLOW simulation - Increasing AlphaPowerFLOW simulation - decreasing Alpha

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-10 -5 0 5 10 15 20 25 30 35 40

CD

AoA [deg]

Experiment - Uncorrected - increasing Alpha

Experiment - Uncorrected - decreasing Alpha

PowerFLOW simulation - increasing Alpha

PowerFLOW simulation - decreasing Alpha


16

Figure 18: Lift contribution per component.

The lift drop of the main wing is caused by the separation region close to the wing tip, which is increasing slightly in

size with increasing AoA. The stall of the slat is more abrupt: the flow is attached up till 34° AoA, but between 34°

and 35° a big separation region appears starting from mid span to the wingtip. No separation is observed on the flap.

Figure 19: Stall progression for the hysteresis coarse case. The separation at the main wing tip tends to grow

slightly in size as incidence increases, but stall occurs only when the slat is massively separated.

The lift and drag vs. AoA curves, depicted in Figure 16 and Figure 17, show a pronounced hysteresis effect that

closely resembles the one seen in the wind tunnel. Right after stall, at 36° AoA, the separation on the main wing

0

0.5

1

1.5

2

2.5

3

28 29 30 31 32 33 34 35 36 35 34 33 32 31 30 29 28

CL

AoA [deg]

SlatMainFlapOverall

AoA 33 AoA 34

AoA 35 AoA 36


17

reduces in size allowing for a small lift recovery compared to the 35° incidence. This is assumed to be related to the

highly unsteady nature of the separated flow and could have changed slightly if the flow had been allowed to settle

for a longer time in the simulation. When the AoA starts to decrease, the lift on the slat remains almost constantly

reduced because of the size of its separation bubble which stays almost the same up till 34° AoA. The lift on the

main wing increases more rapidly because its separation bubble gets smaller as the incidence decreases. However,

the lift on the main wing is not able to recover its pre – stall value until also the separation bubble on the slat

disappears completely, and this happens only at 32° AoA. This behavior is evident when looking at the flow

progression juxtaposed for the increasing and decreasing branch in Figure 23 and especially for the AoA=33° and

34°.

Analysis of surface pressure distribution, Figure 20, Figure 21 and Figure 22 corroborates the previous findings. For

all angles of attack the agreement with experiment for the most inboard part of the wing is very good. Hysteresis in

these inboard sections, if present at all, is limited. The comparison in the outboard sections reproduce the trends

from the experiment between increasing and decreasing angles of attack whereas the magnitude is not fully captured

for this coarse simulation. This is expected to be caused by the lack of resolution and potentially the comparatively

very short settling time chosen. However, the separation pattern is in close agreement with experiment and this

confirms that the simulation is able to correctly reproduce the behavior observed in the wind tunnel.

Figure 20: Pressure distribution for increasing and decreasing 32° AoA at η=17% (top), 50% (mid), 95% (bottom)

of the span.


18


of the span.


of the span.


19

Figure 23: Hysteresis cycle. Increasing AoA on the left, decreasing AoA on the right

AoA 32 Inc AoA 32 Dec





20

2. Fine mesh, variable settling time

A second simulation was performed using the finer mesh and a variable settling time adapted to the force history and

hence allowing a longer settling time to be simulated especially in the stall regime. The AoA time history is depicted

in Figure 24. In order to reduce the overall run time the simulation was limited to an AoA range starting from 32° up

to 36°.

Figure 24: AoA time history for the finer hysteresis run

This finer simulation produces as expected overall a higher magnitude of lift and documents a similar stall and

hysteresis behavior as already discussed previously for the coarse simulation. The stall is shifted to 33°-34°

compared to experiment and coarse simulation as depicted in Figure 25 and Figure 26. The qualitative analysis as

well as the lift per component analysis depicted in Figure 27, shows the same stall mechanism described in the

coarse simulation. The lift contribution of the flap is almost constant over the whole hysteresis cycle. The stall of the

main wing occurs already between 32° and 33° AoA at the wing tip which is then enhanced by the separation of the

slat at 34° AoA and produces the massive stall between 33° and 34° AoA.

For this simulation the hysteresis is slightly different in size than the one observed in the coarse case, see Figure 25.

At 35° AoA there is no hysteresis effect simulated, in good agreement with experiment. This suggests that the lift

dip seen in the coarse simulation might be due to a too short settling time in that case.

At 34° and 33° AoA the hysteresis is more pronounced, especially at 33° AoA. While for the increasing incidence,

see Figure 29, the flow is mainly attached, for the decreasing AoA the slat is separated and consequently the main

wing. At 32° AoA lift has recovered almost all its pre-stall value and the difference between the two flow fields are

minimal.


21

The overall comparison of the pressure distribution at the hysteresis AoA is documented in Figure 28 for the

representative AoA 33° in simulation and 34° in experiment. The comparison indicates that the simulation correctly

captures the trends of the separation near the wing tip.

Figure 25: Lift vs. AoA. Fine simulation

Figure 26: Drag vs. AoA. Fine simulation

0

0.5

1

1.5

2

2.5

3

3.5

-10 0 10 20 30 40

CL

AoA [deg]

Experiment - Uncorrected - Increasing Alpha

Experiment - Uncorrected - Decreasing Alpha

PowerFLOW simulation - Increasing Alpha

PowerFLOW simulation - Decreasing Alpha

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-10 0 10 20 30 40

CD

AoA [deg]

Experiment - Uncorrected - Increasing Alpha



PowerFLOW simulation - Increasing Alpha


22

Figure 27: Lift contribution per component. Fine simulation

Figure 28: Pressure distribution for increasing and decreasing 34° AoA in experiment and 33° in Simulation at

η=17% (top), 50% (mid), 95% (bottom) of the span.

0

0.5

1

1.5

2

2.5

3

3.5

32 33 34 35 36 35 34 33 32

CL

AoA [deg]

Slat

Main

Flap

Overall


23

Figure 29: Hysteresis cycle, fine simulation. Increasing AoA on the left, decreasing AoA on the right

V. Conclusions

Numerical simulations of the hysteresis loop for the trapezoidal wing used in the first High–Lift Prediction

Workshop have been carried out taking advantage of the intrinsically unsteady nature of the Lattice Boltzmann

based PowerFLOW flow solver. A computational setup was developed to reduce the overall computational cost for

the hysteresis simulation. An investigation of the laminar region definition based on available experimental findings

at 28° AoA and based on stability flow analysis at 34° demonstrates a strong sensitivity of the stall behavior to the

size of these regions.

Full hysteresis simulations were performed using a coarse and a fine mesh. The comparison between computational

results and experiments reveals that these simulations are able to correctly capture the underlying physical

phenomena of the hysteresis. Simulations are in reasonable agreement with experiments and provide valuable

AoA 32 Inc

AoA 33 Inc

AoA 34 Inc

AoA 33 Dec

AoA 32 Dec

AoA 34 Dec


24

information on the stall behavior and the hysteresis effect, relating them to a complex interaction between the slat

and the main wing, whereas the flap seems to be overall unaffected.

In an attempt to improve the current results quantitatively, future studies will investigate the effects of a larger

settling time for each angle of attack and a dynamic modification of the laminar regions during the simulation. Also

smaller steps while changing the AoA can be included in the simulation to better resolve the CLmax region. These

additional investigations are expected to increase the comparability with the experimental setup.

Acknowledgments

The Authors would like to thank Judith A. Hannon from NASA Langley Research Center and the High-Lift

Prediction Workshop committee for providing the experimental and geometrical data of the Trapezoidal Wing as

well as detailed information on the wind tunnel installation. The authors would also like to acknowledge the

contributions from Bruno Moschetta in postprocessing the simulation data.

References 1 Rumsey C. L., Long M., Stuever R. A., Wayman T. R., “Summary of the first AIAA CFD high – lift prediction

workshop”, AIAA Paper, 2011-939, 2011. 2 Rumsey C.L. and Ying S.X., “Prediction of high-lift: Review of present CFD capability,” Progress in Aerospace

Sciences Vol.38, No.2, pp.145-180, 2002. 3 Satti R., Shock R., and Noelting S., “Aeroacoustic Analysis of a High Lift Trapezoidal Wing using lattice Boltzmann

Method”, AIAA Paper, 2008-3048, 2008. 4 Slotnick J. P., Hannon J. A., Chaffin M., “Overview of the first AIAA CFD high – lift prediction workshop”, AIAA

Paper, 2011-862, 2011. 5 Hu H., Yang Z. and Igarashi H., “Aerodynamic hysteresis of a low-Reynolds-number airfoil”, Journal of Aircraft , Vol

44, No. 6, 2007. 6 Mueller T.J., “The influence of laminar separation and transition on low Reynolds number airfoil hysteresis”, Journal

of Aircraft , Vol. 22, No. 9, 1985. 7 Biber K. and Zumwalt G.W., “Hysteresis effects on wind tunnel measuremnts of a two-element airfoil”, AIAA Journal,

Vol. 31, No. 3, 1993. 8 Fares E., Nölting S., “Unsteady flow simulation of a high – lift configuration using a Lattice Boltzmann approach”,

AIAA Paper, 2011-0869, 2011. 9 “High-Lift System Aerodynamics”, AGARD Conference Proceedings 515, September 1993. 10 Geyr H.F.v., and. Schade, N., “Prediction of Maximum Lift Effects on Realistic High-Lift-Commercial-Aircraft-

Configurations within the European project EUROLIFT II”, AIAA Paper, 2007-4299, 2007. 11 McGinley C.B., Jenkins L.N., Watson R.D., and Bertelrud A., “3-D High-Lift Flow-Physics Experiment – Transition

Measurements”, AIAA Paper, 2005-5148, 2005. 12 Eliasson P., Hanifi A., Peng S.-H., “Influence of transition on high – lift prediction for the NASA trap wing model”,

AIAA Paper, 2011-3009, 2011. 13 Wahls R.A., Adcock J.B., Witkowski D.P. and Wright F.L., “A Longitudinal Aerodynamic Data Repeatability Study

for a Commercial Transport Model Test in the National Transonic Facility”, NASA Technical Paper, TP 3522, 1995. 14 Li,Y., Shock, R., Zhang, R. and Chen, H., “Numerical Study of Flow Past an Impulsively Started Cylinder by Lattice

Boltzmann Method,” J. Fluid Mech., Vol. 519, pp. 273-300, 2004. 15 Satti R., Li Y., Shock R., and Noelting S, “Simulation of Flow over a 3-Element Airfoil using a Lattice-Boltzmann

Method”, AIAA Paper, 2008-34, 2008. 16 Fares E., “Unsteady Flow Simulation of the Ahmed Reference Body using a Lattice Boltzmann Approach”, J.

Computers and Fluids, vol.35, iss. 8-9,pp. 940-950, 2006. 17 Kotapati R., Keating A., Kandasamy S., Duncan B., Shock R., and Chen H., "The Lattice-Boltzmann-VLES Method

for Automotive Dynamics Simulation, a Review”, SAE Paper, 2009-26-057, 2009. 18 Li,Y., Shock, R., Zhang, R. and Chen, H., “Simulation of Flow over Iced Airfoil by Using a Lattice Boltzmann

Method”, AIAA Paper, 2005-1103, 2005. 19 Brès G.A., Williams D.R., and Colonius T., “Numerical Simulations of Natural and Actuated Flow over a 3D, Low-

Aspect-Ratio Airfoil”, AIAA Paper, 2010-4713, 2010. 20 Fares E., Jelic S., Kuthada T., and Schroeck D., “Lattice Boltzmann Thermal Flow Simulation and Measurements of a

modified SAE Model with Heated Plug”, Proceedings of FEDSM2006, FEDSM2006-98467, 2006. 21 Brès G.A., Freed D., Wessels M., and Noelting S., “Flow and noise predictions for the tandem cylinder aeroacoustic

benchmark”, Phys. Fluids, Vol. 24, 036101, 2012. 22 Qian, Y., d'Humieres, D. and Lallemand, P., “Lattice BGK Models for the Navier-Stokes Equation,” Europhys. Lett.,

Vol. 17, 1992, pp. 479-484.


25

23 Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S., and Yakhot, V., “Extended Boltzmann Kinetic Equation for

Turbulent Flows,” Science, Vol. 301, 2003, pp. 633-636. 24 Yakhot, V. and Orszag, S. A., “Renormalization Group Analysis of Turbulence. I. Basic Theory,” J. Sci. Comput., Vol

1, No. 2, 1986, pp. 3-51. 25 Menter F.R., Kuntz M., and Bender R., “A scale adaptive simulation model for turbulent flows prediction”, AIAA

paper, 2003-0767, 2003. 26 Shan X., Yuan X.-F, and Chen H. “Kinetic theory representation of hydrodynamics: a way beyond the Navier Stokes

equation”, J. Fluid Mech., Vol. 550, 2006, pp. 413-441 27 Chen H., Orszag S., Staroselsky I., and Succi S., “Expanded analogy between Boltzmann Kinetic Theory of Fluid and

Turbulence”, J. Fluid Mech., Vol 519, 2004, pp. 307-314 28 Thomson K.W., “Time Dependent Boundary Conditions for Hyperbolic Systems II”, J. Comp. Physics, vol.89, pp.439-

461, 1990. 29 Chen H., Teixeira C., and Molving K., “Realization of Fluid Boundary Condition via Discrete Boltzmann Dynamics”,

Int. J. Mod. Phys. C, vol.9, pp.1281-1292, 1998. 30 Chen J., “Volumetric formulation of the lattice Boltzmann method for fluid dynamics: Basic concept”, Physical Review

E, vol.58, no.3, pp.3955-3963, 1998. 31 Zhang R., Sun C., Li Y., Satti R., Shock R., Hoch J., Chen H., “Lattice Boltzmann approach for local reference

frames”, Communications in Computational Physics, Vol. 9, No. 5, 2011, pp 1193-1205 32 Hannon J.A., private communication, 2010. 33 Gentry G.L., Quinto P.F., Gatlin, G.M., and Applin Z.T., “The Langley 14- by 22-Foot Subsonic Tunnel: Description,

Flow Characteristics, and Guide for Users”, NASA Technical Paper, TP 3008, 1990. 34 Neuhart D.H., and McGinley C.B., “Free-Stream Turbulence Intensity in the Langley 14- by 22-Foot Subsonic

Tunnel”, NASA Technical Paper, TP-2004-213247, 2004.

unsteady flow simulation of high-lift stall hysteresis using a lattice boltzmann approach

Documents