solution to industry benchmark problems with the … · 2018. 11. 30. · the lattice boltzmann...

European Congress on Computational Methodsin Applied Sciences and Engineering (ECCOMAS 2012)

J. Eberhardsteiner et.al. (eds.)Vienna, Austria, September 10-14, 2012

SOLUTION TO INDUSTRY BENCHMARK PROBLEMS WITH THELATTICE-BOLTZMANN CODE XFLOW

David M. Holman1, Ruddy M. Brionnaud1, and Zaki Abiza1

1Next Limit TechnologiesAngel Cavero, 228043 Madrid

[email protected]

Keywords: Lattice-Boltzmann, Lagrangian, particle-based, Ahmed body, NASA trapezoidalwing

Abstract. This contribution presents some of the capabilities of the Computational Fluid Dy-namics (CFD) code XFlow, which uses a proprietary particle-based kinetic solver based on theLattice-Boltzmann Method. Using traditional CFD software, industrial problems require timeconsuming meshing process which often leads to errors or even divergence of the simulation.Due to its particle-based and fully Lagrangian approach, the complexity of the geometry sur-faces is not a limiting factor in XFlow even in the presence of moving parts, allowing to solvereal industrial problems. The performance of XFlow will be demonstrated for different industrybenchmarks. The first example is the Ahmed body which is a classical benchmark in the auto-motive industry. The second benchmark presented will be the NASA trapezoidal wing. XFlowresults will be described and show good agreement with experimental data.

David M. Holman, Ruddy M. Brionnaud, and Zaki Abiza

1 INTRODUCTION

For the past 20 years, the field of Computational Fluid Dynamics (CFD) has reached a highlevel of maturity, but it has only been recently that CFD has been broadly applied to the improve-ment of several processes at different stages: research, design, manufacturing, optimization, etc.The need for robust and reliable analysis tools is therefore growing rapidly, in proportion to theincreasing complexity of simulations. To provide quick, accurate feedback to realistic engineer-ing problems is consequently essential for companies to be competitive.

The traditional numerical methodologies employed so far are based on methods involvingfinite volumes and finite elements, applied to Navier-Stokes equations. However, even thoughsuch methods have been widely investigated, they still hold major drawbacks, limiting their ca-pacity to solve real industrial problems: uncertainties induced by the meshing process; highlyempirical approaches to the turbulence modeling (RANS); the treatment of the nonlinear con-vective term; artificial stabilization parameters; and so on. Because of this, in most cases engi-neers are not able to model real systems; they are forced to fall back on simplified models andapproximations. These methods require a time-consuming meshing process, are not tolerant tomoving parts, and are usually limited to steady-state analysis, ignoring transient dynamics.

Particle-based methods have been in development for several decades, and are now startingto come to the fore. Among them, the promising Lattice-Boltzmann Method (LBM) surmountsmany of the drawbacks of traditional CFD methods. XFlow CFD uses a particle-based andfully Lagrangian approach based on LBM. With this method, classic fluid-domain meshing isnot required and surface complexity is not a limiting factor.

XFlow has been validated in several benchmarks, demonstrating the validity of the methodto solve industrial problems. The first example presented in this paper is the Ahmed body, aclassic benchmark for the automotive industry. The car’s geometry has a variable slant angleand is a challenging test case in terms of turbulence modelling and drag estimation. The NASAtrapezoidal wing is the second benchmark presented in this paper, a three element airfoil com-posed of a slat, a main blade and a flap. The goal is to assess the aerodynamic coefficients on alarge range of incidence angles, including the post-stall region.

2 NUMERICAL METHODOLOGY

Over the last few years, schemes based on minimal kinetic models for the Boltzmann equa-tion are becoming increasingly popular as a reliable alternative to conventional CFD approaches.

The Lattice Boltzmann method (LBM) was originally developed as an improved modifica-tion of the Lattice Gas Automata to remove statistical noise and achieve better Galilean invari-ance [7, 10]. Due to the flexibility afforded by its close connection to kinetic theory, the LBMcan be adapted to model several physical phenomena. Recent research has led to major im-provements, including physically consistent models for multiphase and multicomponent flowand fully compressible flow [3, 17, 13].

2.1 Lattice Gas Automata

The Lattice Gas Automata (LGA) is a simple scheme for modeling the behavior of gases. Thebasic idea behind the LGA is that particles with specific velocities (ei, i = 1, ..., b) propagatethrough a d-dimensional lattice, at discrete times t = 0, 1, 2, ... and collide according to specificrules designed to preserve the mass and the linear momentum when different particles reach thesame lattice position.

The simplest LGA model is the HPP approach, introduced by Hardy, Pomeau and de Pazzis,

2


in which particles move in a two-dimensional square lattice and in four directions (d = 2,b = 4). The state of an element of the lattice at instant t is given by the occupation numberni(r, t), with ni = 1 being presence and ni = 0 absence of particles with velocity ei.

The stream-and-collide equation that governs the evolution of the system is

ni(r + ei, t+ dt) = ni(r, t) + Ωi(n1, ..., nb), i = 1, ..., b, (1)

where Ωi is the collision operator that computes a post-collision state conserving mass and linearmomentum. If one were to assume Ωi = 0, only an streaming operation would be performed.

From a statistical point of view, the system is made up of a large number of elements whichare macroscopically equivalent to the problem investigated. The macroscopic density and linearmomentum can be computed as:

ρ =1

b

b∑i=1

ni (2)

ρv =1

b

b∑i=1

niei (3)

2.2 Lattice Boltzmann method

While the LGA schemes use boolean logic to represent the occupation stage, the LBMmethod makes use of statistical distribution functions fi with real variables, preserving by con-struction the conservation of mass and linear momentum.

The Boltzmann transport equation is defined as follows:

∂fi∂t

+ ei · ∇fi = Ωi, i = 1, ..., b, (4)

where fi is the particle distribution function in the direction i, ei the corresponding discretevelocity and Ωi the collision operator.

The stream-and-collide scheme of the LBM can be interpreted as a discrete approximationof the continuous Boltzmann equation. The streaming or propagation step models the advectionof the particle distribution functions along discrete directions, while most of the physical phe-nomena are modeled by the collision operator which also has a strong impact on the numericalstability of the scheme.

In the most common approach, a single-relaxation time (SRT) based on the Bhatnagar-Gross-Krook (BGK) approximation is used

ΩBGKi =1

τ(f eqi − fi), (5)

where τ is the relaxation time parameter, related to the macroscopic viscosity as follows

ν = c2s(τ −1

2). (6)

f eqi is the local equilibrium function usually defined as

f eqi = ρwi

(1 +

eiαuαc2s

+uαuβ2c2s

(eiαeiβc2s− δαβ

)). (7)

3


Here cs is the speed of sound, u the macroscopic velocity, δ the Kronecker delta and the wiare weighting constants built to preserve the isotropy. The α and β subindexes denote thedifferent spatial components of the vectors appearing in the equation and Einstein’s summationconvention over repeated indices has been used.

By means of the Chapman-Enskog expansion the resulting scheme can be shown to repro-duce the hydrodynamic regime for low Mach numbers [13, 12, 8].

The single-relaxation time approach is commonly used because of its simplicity. However itis not well-posed for high Mach number applications and it is prone to numerical instabilities.Some of the limitations of the BGK are addressed with multiple-relaxation-time (MRT) colli-sion operators where the collision process is carried out in moment space instead of the usualvelocity space

ΩMRTi = M−1ij Ŝij(m

eqi −mi), (8)

where the collision matrix Ŝij is diagonal, meqi is the equilibrium value of the moment mi and

Mij is the transformation matrix [15, 4].An alternative method that aims to overcome the limitations of the BGK approach is the

entropic lattice Boltzmann (ELBM) scheme, which may rely on a single-relaxation-time wherethe attractors of the particle distribution functions are based on the minimization of a Lyapunov-type functional enforcing the H-theorem locally in the collision step. However, this method isexpensive from the computational point of view [2] and thus not used in practical engineeringapplications.

The collision operator in XFlow is based on a multiple relaxation time scheme. However, asopposed to standard MRT, the scattering operator is implemented in central moment space. Therelaxation process is performed in a moving reference frame by shifting the discrete particlevelocities with the local macroscopic velocity, naturally improving the Galilean invariance andthe numerical stability for a given velocity set [11].

Raw moments can be defined as

µxkylzm =N∑i

fiekixe

liye

miz (9)

and the central moments as

µ̃xkylzm =N∑i

fi(eix − ux)k(eiy − uy)l(eiz − uz)m (10)

2.3 Turbulence modeling

The approach used for turbulence modeling is the Large Eddy Simulation (LES). This schemeintroduces an additional viscosity, called turbulent eddy viscosity νt, in order to model the sub-grid turbulence. The LES scheme we have used is the Wall-Adapting Local Eddy viscositymodel, that provides a consistent local eddy-viscosity and near wall behavior [5].

The actual implementation is formulated as follows:

νt = ∆2f

(GdαβGdαβ)

3/2

(SαβSαβ)5/2 + (GdαβGdαβ)

5/4(11)

Sαβ =gαβ + gβα

2(12)

Gdαβ =1

2(g2αβ + g

2βα)−

1

3δαβg

2γγ (13)

4


gαβ =∂uα∂xβ

(14)

where ∆f = Cw∆x is the filter scale, S is the strain rate tensor of the resolved scales and theconstant Cw is typically 0.325.

A generalized law of the wall that takes into account for the effect of adverse and favorablepressure gradients is used to model the boundary layer [16]:

U

uc=

U1 + U2uc

=uτuc

U1uτ

+upuc

U2up

(15)

=τwρu2τ

uτucf1

(y+uτuc

)+

dpw/dx

|dpw/dx|upucf2

(y+upuc

)(16)

y+ =ucy

ν(17)

uc = uτ + up (18)

uτ =√|τw| /ρ (19)

up =

(ν

ρ

∣∣∣∣∣dpwdx∣∣∣∣∣)1/3

. (20)

Here, y is the normal distance from the wall, uτ is the skin friction velocity, τw is the turbulentwall shear stress, dpw/dx is the wall pressure gradient, up is a characteristic velocity of theadverse wall pressure gradient and U is the mean velocity at a given distance from the wall.The interpolating functions f1 and f2 given by Shih et al. [16] are depicted in figure 1.

100 101 102

y+ uτ/uc

0

5

10

15

20

25

f 1

f1 (y+ uτ/uc )

100 101 102

y+ up /uc

0

5

10

15

20

25

30

35

40

45

f 2

f2 (y+ up /uc )

Figure 1: Unified laws of the wall

3 AHMED BODY BENCHMARK

The Ahmed Body is a classic benchmark for the automotive industry. It was first definedand its characteristics described in the experimental work of Ahmed [1]. The car geometrywas studied at various slant angles from 0 to 40 degrees. The experimental measurements wereconducted by Ahmed in the DFVLR subsonic wind tunnels at Braunschweig and Göttingenwhich have a square nozzle of (3 x 3) m and a length of 5.8 m.

The first goal of this study is to validate the curve of the drag coefficient against the slant an-gle obtained by Ahmed in [1], and the second one is to analyze the mean recirculation structureson the slant surface of the Ahmed body and in the downstream region.

5


Table 1: Simulation specifications of the Ahmed body benchmark

Inlet velocity 60 m/sDensity 1 kg/m3

Dynamic viscosity 1.46014× 10−5 Pa.sCar length 1044 mm

Reynolds number 4.29× 106Slant angles 0 ; 5 ; 10 ; 12.5 ; 15 ; 20 ; 25 ; 30 ; 40 degrees

Turbulence intensity 0.5%

3.1 Simulation setup

A strictly identical geometry to the one used by Ahmed was imported into the virtual windtunnel featured in XFlow. This virtual wind tunnel consists of a rectangular domain and wasset to dimensions of (8 x 2 x 2) m. A far-field velocity boundary condition was used at the inletand the top boundaries, and zero gauge pressure was imposed at the outlet. Periodic boundaryconditions were set on the side walls, and a free-slip wall with no velocity was imposed at thebottom boundary.

The geometry of the Ahmed body was separated into two parts in order to simplify the setupmodification for variable slant angles. The first part is the fore body that has an invariablegeometry. The second part is the rear body which is replaced when the slant angle changes.These two parts are shown on figure 2.

Figure 2: Fore body geometry and rear geometry

The simulation settings are gathered in table 1, and correspond to a Reynolds number basedon the car length equal to 4.29 million. The simulation time was two seconds and the time step∆t = 7.69231× 10−5 s is automatically estimated by XFlow to ensure the numerical stability.

3.2 Spatial discretization

Since XFlow is a particle based technology it does not require a time-consuming meshingprocess. The preprocessor generates the initial octree lattice structure based on the input geome-tries and the user-specified resolution for each geometry. The lattice may have several levelsof detail which are hierarchically arranged. Each level solves spatial and temporal scales twotimes smaller than the previous level, thus forming the aforementioned octree structure.

The lattice structure may be modified later by the solver if the computational domain changes(due to the presence of moving parts) or if the resolution changes dynamically in order to adaptto the flow patterns (adaptive wake refinement). The adaptive wake refinement feature in XFlow

6


Table 2: Near walls and wake resolutions used in the resolution dependency study

h h/2 h/22 h/23

Resolution (m) 0.04 0.02 0.01 0.005# of Elements at t = 0.3 s 88,316 222,337 1,132,292 8,316,626

is based on the module of the vorticity field: in the lattice elements where the vorticity reachesa threshold value the lattice is automatically refined. Similarly, when the vorticity is lower thananother threshold, eight adjacent lattice elements are merged to form a coarser lattice element.This saves computational resources and removes the need to refine your solution in advance.Consequently, as in illustrated figure 3, three resolutions are required by the user: the far field,the wake and the near wall resolutions.

Figure 3: Example of lattice structure using the near wall and adaptive wake refinement

In order to select the best resolution near the walls and within the wake that allows us to getgood results in an acceptable time, a resolution dependency study is conducted before startingthe validation of the Ahmed body. This preliminary study consists in refining the resolutions andseeing how this affects the accuracy of the results, but also checking if the code is convergingto the right solution. It is done by measuring the drag coefficient predicted by XFlow for aslant angle of 35 degrees which is a reference angle for this benchmark. The far field is takenconstant as 0.08 m, and four resolutions are considered for the walls and the wake as describedtable 2.

The drag coefficient is computed for the four cases and compared with the experimentalvalue measured by Ahmed [1]. The drag points from the simulations are plotted in figure 4in function of the number of elements at t = 0.3 s. The point corresponding to the resolutionh/22 = 0.01 m gives good results and in an acceptable time for a slant angle φ = 35◦, and willtherefore become the reference near wall resolution for the rest of the study. The figure 4 alsoconfirms the convergence of the code to the correct solution.

A second question arises regarding the value of the wake resolution. As the wake refinementalgorithm creates a significant number of elements as it develops, its importance in the dragcontribution must be assessed accurately to get a good compromise between solution qualityand computational time. Hence, a second study is conducted on the wake resolution startingfrom the elected near wall resolution (0.01 m) and then increasing by multiples of two, due tothe lattice structure. The figure 5 demonstrates the importance of solving the wake accurately:using the same resolution near the walls and within the wake the drag coefficient history showsa nice prediction, but as soon as the wake resolution is the double or quadruple of the near wall

7


0 1000 2000 3000 4000 5000 6000 7000 8000 9000N (103 nodes)

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

Dra

g Co

effic

ient

, Cx

h/23h/22

h/2

h

Figure 4: Drag coefficient against the number of lattice nodes for different resolutions at φ = 35◦

resolution affects the results quite dramatically. Hence, for all our runs, the spatial discretiza-tion chosen for all the different slant angles is done with an automatic wake refinement with aresolution of 0.08 m for the far field, and 0.01 m around the Ahmed body and within the wake.

0.0 0.1 0.2 0.3 0.4 0.5Time (s)

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Dra

g Co

effic

ient

, Cx

Wake 0.01mWake 0.02mWake 0.04mExperimental

Figure 5: Drag coefficient history for different wake refinement resolution at φ = 35◦

3.3 Numerical results

The time required in XFlow to set up the case is about 10 minutes and mainly consistsin geometry importation, the flow and boundary specifications, and the resolution setup. Thecalculation time is almost the same for all the slant angles and varies between 6 and 8 hourswith the previously selected resolutions on two Intel Xeon E5620 (2.4GHz).

The first result given by Ahmed is the curve representing the drag coefficient against the slant

8


angle φ, and gives the drag contributions of every part of the Ahmed body: the front Ck, therear vertical surface Cb, the rear slant surface Cs and the friction drag Cr. The total drag Ahmedfound was Cw and was the sum of the different contributions. Hence, the total drag obtainedfrom XFlow for the different slant angles is superimposed with the Cw from Ahmed, as shownin figure 6.

Figure 6: Drag coefficient against the slant angle φ

From the figure 6 we observe a good overall drag prediction by the code: the drag breakdownoccurs right after 30 degrees and the minimum drag point is the critical angle 12.5 degrees, asmeasured by Ahmed. The absolute drag values predicted by XFlow are accurate and the relativeerror varies from only 0.4% to 3.2% for most of the angles, except around the drag breakdownand at 0 degree angle where it reaches a maximum of only 7.1%. These small discrepancies canbe explained, on the one hand, by the complexity around the flow around 30 degrees of slant

9


angle which is switching from a massive 3D separation in the near-wake region to an almost 2Dattached structure at higher angles [6], and, on the other hand, by stronger gradients producedby the rear of the car at 0 degree angle.

3.4 Flow field results

The second part of the results analysis is done by analyzing the main recirculation structuresresulting from the flow around the Ahmed body. For this study, the averaging of the flow fieldsis required in order to filter the temporal fluctuations and to identify the main structures of theturbulent wake. The averaging of the fields started from t = 0.3 s when the flow was established,as indicated for example by figure 5, to cut off the transient period.

Ahmed provides pictures of the oil flow on the slanted surface for φ = 12.5, 25 and 30degrees. It can be compared with XFlow which features Line Integral Convolution (LIC) thatapproximates the surface streamlines on a body. The figure 7 shows similar structure for thethree angles: a quite smooth and attached flow at 12.5 degrees, smooth flow patterns with twosmall and symmetric fringes on the sides at 25 degrees, and two large and symmetric separationbubbles at 30 degrees.

Figure 7: Averaged Line Integral Convolution (LIC) on the slanted surface from Ahmed (left) and XFlow (right)

Ahmed also provides different velocity vectors plots in the symmetry plane of the car, show-

10


ing the near-wake region. This allows the study of the separation bubble on the rear slant andwithin the wake for different slant angles.

Figure 8: Near-wake structure at scale for: a) φ = 5◦, b) φ = 25◦

Figure 8 compares the near-wake region for a slant angle of 5 degrees between the exper-imental results measured by Ahmed and results obtained by XFlow at the same scale. Thisallows us to check the length of the bubble separation located around the non-dimensional co-ordinate x/Lref = 0.375, predicted in an extremely similar way in the two pictures. Two maineddy structures are detected - highlighted in red boxes on figure 8 - which are symmetrical fromthe top and bottom of the separation bubble. The code tends to locate them slightly furtherdownstream, though with reasonable overall flow patterns.

The near-wake structure for a slant angle of 25 degrees also show good similarities. Thisfigure 8 shows an equivalent triangular separation bubble, ending around the non-dimensionalcoordinate x/Lref = 0.2 for both cases.

4 NASA TRAPEZOIDAL WING BENCHMARK

The NASA trapezoidal wing benchmark comes from the 1st AIAA CFD High Lift Predic-tion Workshop (HiLiftPW-1), sponsored by the Applied Aerodynamics Technical Committee,which took place in June 2010 in Chicago, IL. The challenge was to simulate a half aircraftconfiguration composed of a body and a 3-element airfoil with a plane of symmetry as shownin figure 9 for a wide range of angles of attack. The trapezoidal wing is composed of slat,main element and flap. The latter can be in two different configurations: Configuration 1 at 25degrees and Configuration 8 at 20 degrees of angle-of-attack.

The objectives of the benchmark are multiple [14]:

• Assess the prediction capability of CFD codes in landing/taking-off configuration,

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Figure 9: NASA trapezoidal wing geometry

Table 3: Resolutions used for the resolution-dependency at 13 degrees incidence

h h/2 h/22 h/23

Near wall (m) 0.04 0.02 0.01 0.005Wake (m) 0.08 0.04 0.02 0.01

# of Elements at t = 0.3 s 201,513 653,211 2,893,687 21,880,186

• Develop practical modeling guidelines for the analysis of high-lift configurations,

• Provide an impartial forum for evaluating the effectiveness of existing CFD codes andmodeling techniques,

• Identify areas that require additional research and development.

4.1 Simulation setup

XFlow simulations were run for the Configuration 1 with no brackets. The Mach numberwas 0.2, the Reynolds number based on the mean aerodynamic chord (MAC) was 4.3 million.The angles of attack run for this benchmark were: -4, 1, 6, 13, 21, 25, 28, 32, 34 and 37 degrees.The hardware used in all the computations was a single workstation with two Intel Xeon E5620@ 2.4 GHz processors (8 cores) and 12GB of RAM.

A resolution dependency study has also been performed for this benchmark using the fourresolutions described in Table 3 and a constant far field resolution of 1.28 m. An incidenceangle of 13 degrees which is one of the reference angles of the first workshop was employed.

The drag coefficient obtained with each of the four simulations is plotted in figure 10 as afunction of the number of elements at t = 0.3 s. The point corresponding to resolution h/23

gives the best estimation of the drag compared to the experimental data, with only 1% of relativeerror. This value will therefore be used as the reference near wall resolution for the rest of thestudy.

However, two different wake resolutions have been used depending on the incidence of theNASA trapezoidal wing. Indeed, for large angles of attack, a significant wake develops andthe number of lattice elements introduced by the adaptive wake refinement increases. At 32degrees, the simulation reaches 25 million lattice elements, which is the maximum number ofelements that can fit in the 12 GB of RAM available on the workstation. Special care is thus

12


0 5 10 15 20 25Number of Lattice Nodes (106 )

0.30

0.32

0.34

0.36

0.38

0.40

Dra

g Co

effic

ient

, CD

h/23

h/22

h/2

h XFlowExperiment

Figure 10: Drag coefficient against the number of lattice nodes for different resolutions at α = 13◦

Table 4: Resolutions used for the 1st High Lift Prediction Workshop

Walls (m) Wake (m) Far Field (m) Max. # of Particles AnglesResolution 1 0.005 0.01 1.28 25× 106 [-4◦; 32◦]Resolution 2 0.005 0.02 1.28 10× 106 [34◦; 37◦]

required in order to keep this number within the memory constraints for higher angles. Thewake resolution has been limited to double the normal value for those cases (Resolution 2 intable 4).

4.2 Numerical results

The experimental data were produced at the 14x22 wind-tunnel at the well-known NASALangley. Forces, moments, and Cp distribution were provided with free transition [9]. Datawere provided as lower and upper values which are assumed to be the range of uncertainty inthe wind tunnel measurements.

On figure 11, the drag coefficient against the angle of attack α is shown. XFlow results showvery good agreement with the experimental data along the whole range of angles. The dragslope is accurate and still behaves correctly at both low and high incidences, with a slight slopedecrease.

The lift coefficient is also very well predicted for the whole range of angles. Within therange [1, 28] degrees, XFlow predicts accurately both slope and absolute lift coefficient values.Starting from 32 degrees, the critical angle is reached and the code also succeeds in predictingthis: the wind tunnel data indicates the maximum lift point at around 33 degrees, and it happensbetween the point of 32 degrees and 34 degrees. Starting from that point, the lift drops, due to alarge bubble of separation on the wing. The bubble of separation grows on the tip of the wing,as shown in the Figure 12.

Since both drag and lift coefficients are quite well predicted, the polar curve on Figure 11 ishence matching the experimental results, especially in the pre-stall region.

The pitching moment coefficients also lie between the upper and lower limits of the experi-

13


10 0 10 20 30 40α (deg)

0.0

0.2

0.4

0.6

0.8

1.0D

rag

Coef

ficie

nt, C

D

(a)

ExperimentalExperimental LowerExperimental UpperXFlow

10 0 10 20 30 40α (deg)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Lift

Coef

ficie

nt, C

L

(b)

0.0 0.2 0.4 0.6 0.8 1.0Drag Coefficient, CD

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Lift

Coef

ficie

nt, C

L

(c)

10 0 10 20 30 40α (deg)

0.5

0.4

0.3

0.2

0.1

0.0

Pitc

hing

Mom

ent,

C m

(d)

Figure 11: Drag (a) and lift (b) coefficients against the angle of attack, the polar curve (c), and the pitching momentcoefficient (d)

mental results within almost the whole range.

5 CONCLUSION

The CFD code XFlow features a kinetic particle-based solver that differs from the traditionalapproaches, which are usually mesh-based. The lattice-Boltzmann method employed is ableto solve advanced industrial problems even in the presence of complex geometries or movingparts.

The methodology has demonstrated it can solve industrial benchmarks efficiently. For in-stance the Ahmed body is a classic benchmark for the automotive industry that XFlow solvedwith a high degree of accuracy. XFlow did not face convergence issues even for extreme slantangles, and changing the rear of the car did not add additional workload. The code has beendemonstrated to be robust and accurate in terms of drag and flow pattern prediction, and closelymatches the data measured by Ahmed in the DFVLR subsonic wind tunnel of Braunschweigincluding the drag breakdown around 30 degrees and the low slant angles where gradients arestronger.

The High Lift Prediction Workshop benchmark has also been successfully validated byXFlow. The NASA trap wing geometry was tested within a range of incidence between -4and 37 degrees, which includes the post-stall region. The drag, lift and pitching moment coef-ficients predicted by the code are in good agreement with the experimental tests conducted inthe NASA Langley 14x22 wind tunnel. The stall angle is also accurately predicted around 33degrees.

XFlow has therefore demonstrated its robustness and accuracy in different benchmarks. Themethod is well-suited for external aerodynamics and shows strong potential for more advanced

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Figure 12: Averaged Line Integral Convolution (LIC) at 37 degrees incidence

topics, such as analysis involving complex geometries, the presence of moving parts and fluid-structure interaction.

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INTRODUCTIONNUMERICAL METHODOLOGYLattice Gas AutomataLattice Boltzmann methodTurbulence modeling

AHMED BODY BENCHMARKSimulation setupSpatial discretizationNumerical resultsFlow field results

NASA TRAPEZOIDAL WING BENCHMARKSimulation setupNumerical results

CONCLUSION

solution to industry benchmark problems with the … · 2018. 11. 30. · the lattice boltzmann...

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