Julianne C. Dudek

Glenn Research Center, Cleveland, Ohio

Modeling Vortex Generators in the Wind-US Code

NASA/TM—2010-216744

July 2010

AIAA–2010–32
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Julianne C. Dudek

Glenn Research Center, Cleveland, Ohio

Modeling Vortex Generators in the Wind-US Code

NASA/TM—2010-216744

July 2010

AIAA–2010–32

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

48th Aerospace Sciences Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Orlando, Florida, January 4–7, 2010
Acknowledgments

The author would like to sincerely thank Rodrick Chima, Mary Jo Long-Davis and Charles Towne of the NASA Glenn 

Research Center, and Chris Nelson of Innovative Technology Applications Company, LLC.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2010-216744 1 

Modeling Vortex Generators in the Wind-US Code 

Julianne C. Dudek 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract

A source term model which simulates the effects of vortex generators was implemented into the 

Wind-US Navier Stokes code. The source term added to the Navier-Stokes equations simulates the lift 

force which would result from a vane-type vortex generator in the flowfield. The implementation is userfriendly, requiring the user to specify only three quantities for each desired vortex generator: the range of 

grid points over which the force is to be applied and the planform area and angle of incidence of the 

physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single 

vane vortex generator, supersonic flow in a rectangular duct with a counter-rotating vortex generator pair, 

and subsonic flow in an S-duct with 22 co-rotating vortex generators. The validation results indicate that 

the source term vortex generator model provides a useful tool for screening vortex generator 

configurations and gives comparable results to solutions computed using a gridded vane. 

Introduction 

In modern aircraft engine inlets, vortex generators (VGs) are frequently used to improve performance 

by minimizing the effects of adverse pressure gradients, boundary layer separations and shock-boundary 

layer interactions. Vortex generators come in many shapes and sizes, but in this paper, vane-type VGs are 

the focus. These VGs are small vane-shaped devices mounted at an angle to the local flow, and introduce 

streamwise vortices which act to mix the high-momentum flow in the freestream with the low-momentum 

flow near the wall. This can be an effective means of preventing or reducing flow separation, thereby 

improving the performance of an inlet or wing. 

Computational Fluid Dynamics (CFD) is used to simulate inlet flow and predict inlet performance, 

and together with experiments and statistical methods, is a useful tool in designing new inlets. Inlets 

occasionally include multiple VGs, and in studies where multiple VG arrays must be evaluated, it is very 

time-consuming and impractical to generate computational grids for each VG. Therefore, it is highly 

desirable to be able to model the effects of the VGs without including their geometry in the computational 

mesh.

With this in mind, NASA Glenn has implemented two vortex generator models into the Wind-US 

Navier-Stokes code (Refs. 1 to 3). Previous work describes the Wendt empirical VG model and its 

implementation (Refs. 4 and 5). This model was primarily developed for subsonic flows with adverse 

pressure gradients, and simulates the VG by adding vorticity as a step change at a give axial station. More 

recently, a lift-force model, developed by Bender, Anderson and Yagle (Ref. 6) and referred to in this 

paper as the “BAY” model was implemented into Wind-US. This is a more robust model applicable to a 

wider range of flows, including supersonic flows and sub-boundary layer VGs. It acts over the length of 

the VG, rather than at a single axial station, allowing it to accurately simulate longer VGs. Both models 

are user-friendly; the user only needs to specify the generator location, dimensions and angle of 

incidence. 

In this paper, the implementation of the BAY vortex generator model into the Wind-US code is 

described. The differences between the Wendt and BAY models are highlighted. Validation results for a 

single vane in subsonic flow, a pair of counter-rotating vanes in supersonic flow and also an array of 

vanes in a subsonic S-duct diffuser are given. 
NASA/TM—2010-216744 2 

Nomenclature 

b

ˆ unit vector in the direction of the span of the vortex generator 

cVG model constant 

c vortex generator chord length 

DC60 pressure distortion index 

E total energy 

FE inviscid and viscous fluxes in energy equation 

FM

 inviscid and viscous fluxes in momentum equations 

h vortex generator height 

Li

 vortex generator source term on cell i 

l

ˆ a unit vector in the direction of the lifting force acting on the flow 

nˆ unit vector normal to the vortex generator 

p static pressure 

0 p freestream total pressure 

Sj area of cell face j 

SVG vortex generator planform area 

u

 velocity vector 

uˆ unit velocity vector 

Vi volume of cell i 

t

ˆ unit vector tangent to the vortex generator planform 

x, y, z Cartesian coordinates 

y

+

 nondimensionalized y-coordinate 

 vortex generator angle of incidence 

t time step 

 boundary layer thickness 

 density 

max peak vorticity 

 computational coordinates 

The Wind-US CFD Code 

The Wind-US CFD code (Refs. 1 to 3) may be used to solve the Euler or Navier-Stokes equations of 

fluid mechanics, along with supporting equation sets governing turbulent and chemically reacting flows. 

The code has structured, unstructured and hybrid grid capability, although all cases described in this paper 

use structured grids and the current implementation of the vortex generator models is valid only for 

structured grids. The Wind-US code is the production solver of the NPARC Alliance, which is a 

partnership between NASA Glenn Research Center (GRC), the USAF Arnold Engineering Development 

Center (AEDC), and the Boeing Company. The mission of the Alliance is to develop, validate and 

support an integrated, general purpose, computational flow simulator for the U.S. aerospace community; 

the work described in this paper contributes to these efforts. The code itself uses a finite-volume 

formulation and allows the user to select from several schemes to compute both the right-hand-side 

inviscid terms, as well as the left-hand-side viscous terms. 

Wind-US has two vortex generator models: the Wendt model (Refs. 4 and 5) and the recently added 

BAY model (Ref. 6). Both models may be used to model a single vane-type vortex generator, or an array 

of vortex generators. The Wendt model was developed primarily for subsonic flows with vanes having 

heights on the order of the boundary layer thickness and having moderate height-to-chord ratios. It must 
NASA/TM—2010-216744 3 

be applied at a coupled zonal interface boundary, where the effects of the vortex generators are simulated 

by a step change in the secondary velocities (Ref. 5). The strength of each vortex is based on the user 

input vortex generator chord length, height and angle of incidence with the primary flow, as well as the 

local velocity and boundary layer thickness. These vortex generator parameters are shown in Figure 1. 

The BAY model was developed to handle a wider range of vortex generator geometric parameters 

including "micro-vanes" which have small heights (25 to 40 percent of boundary layer thickness) and 

vanes with large chord lengths, and may be used in subsonic and supersonic flows. The details of the 

BAY model are given below. 

The BAY Vortex Generator Model 

The vortex generator model implemented in the Wind-US Navier-Stokes code adds a source term to 

the momentum and energy equations which simulates the lift force introduced by a vane VG in the 

flowfield. This source term was developed by Bender, Anderson and Yagle (Ref. 6) and acts to align the 

local flow velocity with the vane VG. The lifting force source term, Li , acting at grid point i, is added to 

the governing discretized finite volume momentum and energy equations: 

ij

j

M

i

i LSF

t

u V j

  

 



   )(

ij

j

E

i

i LuSF

t

E V j

   



   )(

where, 

lu

V

V ScL

i

i

i VGVG ˆ  2   

and l

ˆ is a unit vector in the direction of the lifting force acting on the flow. This force is equal and 

opposite to the force which would act on the vane. u

 is the local velocity,  is the local density,  is the 

angle of incidence of the vane with the primary flow, Vi is the volume of the grid cell, and Vi is the sum 

of the volumes of all of the cells over which the model is being applied, SVG is the VG planform area, and 

cVG is an empirical constant. The model constant, cVG controls the strength of the side force and the 

intensity with which the local velocity aligns with the vane. 

The vane VG is described by three unit vectors, as shown in Figure 2, where b

ˆ is along the span of 

the vane, t

ˆ is tangent to the vane and nˆ is normal to the vane and perpendicular to b

ˆ and t

ˆ. Using the 

small angle approximation, the unit vector l

ˆ is assumed to be normal to the velocity vector and the unit 

vector b

ˆ along the VG span, 

bub

u

u l ˆ ˆ ˆˆ  



where uˆ is a unit vector in the flow direction and 

nu ˆˆ 2

cossin  

 










NASA/TM—2010-216744 4 

The lift force source term is also multiplied by a factor of 

uˆ  t

ˆ

to approximate the loss of side force at higher angles of attack. The resulting equation for the lift force 

source term is 

)(ˆ ˆ) ˆ ( ˆˆ )(ˆ 2 tubunuu

V

V ScL

i

i

VGVGi 













 



 

In determining the value of the constant cVG, Bender et al. (Ref. 6) calibrated it by examining the 

integrated cross-flow kinetic energy,  . They found that for large values of cVG ,  approaches an 

asymptotic value because the VG model source term, Li



, starts to dominate the other terms in the 

governing equations. This causes the flow to align itself with the vortex generator, resulting in a local 

angle of attack which approaches zero, i.e.  nu ˆˆ  0 , so that the lift force goes to zero when the local flow 

becomes aligned with the vane. Bender et al. suggest that this asymptotic behavior is reached for cVG > 5. 

Jirasek (Ref. 7) found that the flow in an s-duct is independent of the value of cVG for values greater than 

7. The default value for cVG in Wind-US is 10, but may be changed by the user. 

This implementation of the BAY vortex generator model into the Wind-US code was designed to be 

user- friendly. The unit vectors b

ˆ , t

ˆ, and nˆ , are computed within the code based on the user inputs, 

reducing the time and effort needed to set up inputs. Within the standard Wind-US keyword input file, the 

user specifies the following information for each vortex generator to be modeled: the range of grid points 

over which the model is to be applied, the planform area of the physical vane, and the angle of incidence 

the vane makes with the primary grid direction. 

Test Cases 

A Single Vane in Subsonic Flow 

The first validation case run with the BAY VG model was a single vortex generator on a flat plate in 

subsonic flow. For comparison, simulations were also run with the vane gridded in the computational 

mesh. Results are compared with the experimental data of Yao, et al. (Ref. 8). 

Experimental Configuration 

In the experiment of interest, a single vane VG with an angle of incidence of 16° was mounted on a 

long flat plate at a location where the local boundary thickness, , is approximately 35 mm. (See Fig. 3) 

The flow was turbulent with a freestream velocity of U = 35 m/s. Stereo digital particle image 

velocimetry measurements were taken using two cameras taking simultaneous pictures of the cross-flow 

plane from opposite angles and directions. All three velocity components were obtained through 

stereoscopic reconstruction. The VG was a rectangular flat plate with a height of 7 mm (h/ = 0.2) and a 

chord length of 49 mm (c/h = 7). It is considered a “low-profile” VG (Ref. 8) (or “sub-boundary layer” 

VG (Ref. 9)) since the height is much less than the boundary layer thickness (Ref. 8). 

Computational Strategy 

The boundary layer at the vane was set up by creating a long duct section (266 cm long) upstream of 

the specified vane location; this was the length required for the boundary layer thickness to grow to the 

desired 35 mm at the vane leading edge. The model was applied at the station where  = 35 mm. The 

farfield boundaries were defined to be sufficiently far from the vane to avoid influence: the grid height is 

30 cm, and the grid width is 40 cm. In the experiment, the dimensions of the duct were 51- by 71-cm. A 
NASA/TM—2010-216744 5 

smaller computational grid was used to reduce the number of grid points, thereby reducing the 

computational time. Inviscid wall boundary conditions were set at the side and top boundaries. A viscous 

wall boundary was set at the lower wall, and the grid was clustered such that y

+ = 0.8 at the first point 

from the wall. Freestream atmospheric conditions were specified at the inflow with the total temperature 

and pressure held constant. The mass flow rate at the outflow was specified as 10.75 lbm/sec (4.88 kg/s). 

This produced the desired Mach number of 0.1 in the duct. 

For the gridded vane solution the vane had zero thickness. Two grids were created: one which was 

nearly identical to that used for the BAY model calculations and used inviscid boundary conditions on the 

vane, and another which used viscous wall boundary conditions on the vane. The latter grid was packed at 

the vane wall (y

+ ≈ 1.6) with viscous wall boundary conditions specified. The grid using the viscous wall 

boundary condition had dimensions 27910164 for a total of 1,803,456 grid points. The grid for the 

inviscid vane boundary condition case had dimensions 2799164 and 1,625,796 total points, a reduction 

of only 10 percent, since fairly fine resolution is required to capture the vortex, as described below. In 

both grids, the vane grid size was 22236. 

Local time stepping was used to integrate to a steady state flowfield. The default second-order 

upwind-biased Roe scheme with modifications for stretched grids was used for the explicit right-handside terms and the default full block implicit scheme was used to compute the viscous terms. The Mentor 

shear stress transport (SST) turbulence model was used. The solution was considered converged when the 

L2 residuals had leveled off and the peak vorticity was no longer changing. 

For the simulations performed using the BAY model, the model was applied to the rectangularshaped region where the vane was located within the grid, as shown in Figure 4(c). These points envelop 

the region of the physical vane inclined at 16°, and have grid dimensions 22936. Generally in the 

vicinity of the vortex generator, a grid spacing of 30 percent of the vane chord in each coordinate 

direction is adequate, based on Reference 5. However, these recommendations were based on vanes 

which had more than double the height-to-chord ratio of the sub-boundary-layer vane, and heights which 

were on the order of the boundary layer thickness. To make sure the vortex details were captured for a 

vane with a smaller height, a maximum spacing of 30 percent of the vane height was used instead. At the 

vane trailing edge tip, the resulting grid spacing in each coordinate direction was: x/h = 0.32, y/h = 

0.24, z/h = 0.17. To confirm that the current grid resolution was adequate simulations were run using a 

grid where the number of points was halved in each direction, and another grid where the number of 

points was doubled in each direction. The corresponding grid dimensions of the rectangular-cylindershaped region where the BAY model was specified were 12518 and 441972, respectively. Based on 

these results the current grid was determined to have sufficient resolution for these calculations. Doubling 

the number of points gave neglible benefit, while halving the grid did not provide sufficient resolution to 

capture the details of the vortex upstream quite as well as the chosen grid. The grid used for the model 

simulations is shown in Figure 4; the cross-plane region where contours of velocity and vorticity are 

shown in later figures is also highlighted, for perspective. 

Simulation Results 

Velocity contours downstream of the vane are shown for the experiment, the two gridded vane 

solutions, and the BAY model solution in Figure 5. Six axial stations are shown, measured from the vane 

trailing edge and nondimensionalized by the vane height. The gridded vane solution with viscous walls 

does the best job of simulating the vortex shape and detail for x/h < 10. Progressing downstream, the 

differences between the viscous vane solution and the inviscid vane and BAY model solutions diminish. 

For all stations shown, the velocity contours for the inviscid vane solution are nearly identical to those of 

the BAY model solution. Note that due to limitations of the plotting software, it was not possible to match 

the color distribution within the velocity scale for the CFD results exactly to that shown from Reference 8 

for the experimental data, however a best effort was made. 

Vorticity contours are shown in Figure 6. (Note that three different scales are used.) All simulation 

results underpredict the maximum vorticity magnitude, indicating a less concentrated vortex than shown 
NASA/TM—2010-216744 6 

experimentally. All of the simulation results are very similar in magnitude and shape, indicating that there 

is little benefit to using viscous wall vanes to generate a tip vortex. Note that the BAY model, unlike a 

viscous vane calculation, does not model the losses generated by the VGs, and may thus give optimistic 

answers. For predicting these vorticity contours, the BAY model gives essentially the same result as both 

gridded vane solutions. 

The axial decay of the peak vorticity is plotted in Figure 7. The gridded vane solutions and the BAY 

model solution underpredict the initial peak vorticity shown in the experiment. The experimental value of 

peak vorticity at the first experimental measurement station at x/h = 1.6 is approximately 7200 1/s. The 

corresponding values for the CFD simulations are significantly less; the resulting values are 2400 1/s for 

the gridded vane, 2700 1/s for the gridded vane with viscous walls, and 2600 1/s for the BAY model 

simulation. Of the simulations, the gridded vane solutions have slightly higher vorticity in the upstream 

region where x/h is between 3 and 20, but further downstream, it decays to the levels of the BAY model. 

This rapid decay of the peak vorticity is also seen in References 8 and 10 and is currently unexplained. 

Also, since vorticity is defined as the difference between velocity gradients, it is also very sensitive to 

grid resolution. To see if a grid finely packed at the location of the vane tip would significantly improve 

the result, a simulation was run with a grid very finely packed at the location of the vane tip see 

(Fig. 7(b)). The cross-plane resolution was 75 percent finer in the horizontal direction and 94 percent finer 

in the vertical direction. The peak vorticity resulting from the simulation using this grid is included in 

Figure 7(a), as the “fine tip grid” case. The initial peak vorticity is much higher than previous simulations 

as well as the experiment, however, it also decays very quickly, as in the previous simulations. This 

indicates the complexity of accurately predicting the peak vorticity and its axial decay. A more accurate 

comparison of peak vorticity would be found by interpolating the CFD results onto the same “grid” used 

to compute the vorticity in the experiments. Unfortunately, the experimental grid information was not 

available for this comparison. But in summary, one sees that, in general, in Reynolds-averaged NavierStokes CFD results, the vortex decays more rapidly than experimental results. Overall, for these 

calculations, the BAY model is easier to use than gridding the vanes, and produces a very similar result. 

A Counter-Rotating Vortex Generator Pair in Supersonic Flow 

This validation case was run to demonstrate that the BAY model may also be used to simulate vanes 

in supersonic channel flow. The case for counter-rotating vanes in Mach 2.0 flow was simulated and 

results were compared with a solution computed with the vanes gridded within the computational mesh. 

At the time of this writing, experimental data for a single or multiple vanes in shock-free supersonic flow 

could not be obtained. Data does exist for vanes in the vicinity of normal and oblique shocks, however the 

computation of shock waves introduces its own challenges and may be studied in conjunction with vane 

VGs at a later date. 

Configuration and Computational Strategy 

The flow conditions for this case were Mach 2.0 with a freestream velocity of 506 m/s, total pressure 

of 101.4 KPa, and total temperature of 287.2 K. The VG array consisted of two low-profile flat plate vane 

VGs at angles of incidence of +16° and –16°, with a chord length c of 3.6 cm and a height h of 0.36 cm 

(c/h = 10). The leading edge of the vanes was located 100 cm from the inflow boundary where the 

boundary layer thickness  was 1.05 cm (h/ = 0.34). A schematic of this configuration is shown in 

Figure 8. 

The boundary layer at the vane was set up in a manner similar to that of the vane in subsonic flow. A 

long duct section (100 cm long) was created upstream of the vanes to allow the boundary layer thickness 

to grow to 1.05 cm at the vane leading edge. Since the geometry was symmetric about the centerline plane 

between the vanes, only half of the duct was gridded, with a symmetry boundary condition applied on the 

plane midway between the vanes as well as on the opposite sidewall. The lower wall was specified as a 

viscous wall and at the first grid point from the wall, y

+ was equal to 0.5; the upper boundary was set to an 
NASA/TM—2010-216744 7 

inviscid wall. Inviscid wall boundary conditions were used on the vane for the gridded vane case. The 

inflow was set to freestream conditions, and at the outflow boundary the pressure was extrapolated. The 

duct was 195 cm long, 15.25 cm high and 2.5 cm wide. The grid had four zones. Zone 1 had dimensions 

of 412164; zone 2 had dimensions of 1004564; zone 3 had dimensions of 214564; and zone 4 had 

dimensions of 212164 for a total of 431,808 points. The vane was located in zone 2, and so a denser 

grid was used in zones 2 and 3 to capture the vortex features. The vane was specified within zone 2 and 

had dimensions 23636. 

The Wind-US code was run using local time stepping with the Mentor SST turbulence model in a 

manner similar to the vane in subsonic flow. The solution was considered converged when the L2 

residuals had leveled off and area averaged total pressure recovery was changing by less than 0.0001. 

Simulation Results 

The Mach number at five axial locations in the duct is shown in Figure 9 for the solutions computed 

using the gridded vane and the BAY model. The axial stations given are nondimensionalized by the vane 

height. The VG pair produces a counter-rotating “upward” pair of vorticies, meaning that the two 

vorticies are rotating in the upward and outward direction in the centerplane where they meet. At the first 

axial station of x/h=5, the two vortex shapes can be seen fairly distinctly. For the gridded vane case the 

shape of the vortices is more clearly defined. As the vortex pair moves downstream the two vorticies 

move closer together and upward, away from the wall. The differences in the BAY model solution from 

the gridded vane solution diminish with downstream progression, and at x/h = 100, the shape of the Mach 

contours is very similar. 

The counter-rotating upward pair of vortices produced by the vane pair is similar to the vortex pair 

produced by a micro-ramp VG. Figure 10 shows the experimental data of Hirt et al (Ref. 11). for a microramp VG and the corresponding Mach contours at an axial station of x/h = 15. The similarity of the 

shape for the Mach contours indicates that it is likely that, with proper calibration, the BAY model is a 

likely candidate for simulating micro-ramp vortex generators by treating them as a pair of vanes at 

opposite angles of incidence. 

Flow in a Circular S-Duct 

In this study, flow in a circular S-duct was examined for throat Mach numbers ranging from 

approximately 0.35 to 0.80. The purpose of the study was to evaluate Wind-US with the BAY VG model 

for an aggressively diffusing flow containing vane-type VGs. The results were compared with 

experimental data and with Wind-US simulations with the VGs represented as gridded flat plate vanes, 

and with previous results of simulations using the Wendt VG model (Ref. 5). 

Experimental Configuration 

The geometry which was tested experimentally is test case 3 from the AGARD study of Reference 12 

and was labeled the M2129 duct in the experimental investigations of Anderson and Gibb (Ref. 13). This 

duct has a circular cross-section and an S-shaped centerline, as shown in Figure 11. The duct was 

approximately 2 ft (0.61 m) in length, and the throat, which is located at the end of the upstream straight 

section, was 5.06 in. (12.9 cm) in diameter. The engine face, or aerodynamic interface plane (AIP) was 

located at 19.27 in. (48.9 cm), its diameter is 6.0 in. (15.2 cm), and the duct offset was 5.4 in. (13.7 cm). 

The duct had a length to inlet diameter, L/Di of 4.74, and the engine face to inlet area ratio, Aef /Ai, was 

1.40, with an offset of z/D of 1.07. A centerbody with a cross-sectional area of about 7 percent of the 

AIP, not shown, protruded upstream from the duct outlet and extended through the AIP. This centerbody 

was not modeled in the CFD investigation. A 72-probe pitot rake positioned at the engine face, was used 

to measure the engine face total pressure recovery and distortion. It consisted of twelve 6-probe rakes 

spaced 30° apart. 
NASA/TM—2010-216744 8 

The VG configuration tested is referred to as VG170 in Ref. 13 and contains 11 flat plate vanes per 

half duct, located two inlet radii downstream of the inlet throat. Each VG had a height-to-chord ratio of 

0.25, where the chord was approximately 0.7 in. (1.8 cm), and an angle of incidence of 16°. The incidence 

was chosen in order to turn the flow near the wall away from the bottom of the duct, to counteract the 

formation of the duct vortex. 

Computational Strategy 

The computational grids used for the simulations with the VGs gridded as flat plates and with the VG 

effects simulated with the VG model were very similar in terms of the number of points and clustering. 

The grid used for the BAY model simulations is shown in Figure 12. Since the duct is symmetric about 

the x-z-plane only half of the duct was gridded. The grids include a straight, 10.14 in. (25.76 cm) long 

constant-area section at the upstream end of the duct, in order to allow a boundary layer to develop, and 

another 5.07 in. (12.88 cm) constant-area section at the downstream end, so that the computational 

boundary is aft of the AIP. For the gridded vane simulations the vanes were specified using inviscid wall 

boundary conditions, and the grid had 718,000 points, with the sections upstream and downstream of the 

vane each having dimensions of 1327750 and the VG section having dimensions of 1127750. The 

value of y

+

 at the duct wall was 0.8. The BAY model was specified over the 11 individual grid regions 

containing each VG, each region having dimensions of 10225. The grid spacing at the VG trailing edge 

nondimensionalized by the VG chord length was 0.10 in the axial direction, 0.05 in the radial direction, 

and 0.04 in the circumferential direction. For the cases computed using the Wendt VG model, the grid 

was split at the vane trailing edge station, and the Wendt model was applied at this zonal interface. For 

simulations using the VG models the grid had a total of 679,000 points, 6 percent fewer points than used 

for the gridded vane. Again, a fine grid resolution near the vortices was desired to accurately capture the 

features of the vortices. 

Five cases, with throat Mach numbers ranging from 0.35 to 0.80, were run with the VGs specified. 

The different throat Mach numbers were a result of the set value of the outflow static pressure, and the 

downstream pressure ratios 0 pp were those used by Mohler (Ref. 14): 0.938, 0.877, 0.861, 0.841, and 

0.826. The corresponding throat Mach numbers were 0.40, 0.62, 0.68, 0.75 and 0.82. 

Local time stepping was used to integrate to a steady state flowfield. The default second-order 

upwind-biased Roe scheme with modifications for stretched grids was used for the explicit right-handside terms and the default full block implicit scheme was used to compute the viscous terms. The SpalartAllmaras (SA) turbulence model was used. The cases converged after approximately 15,000 iterations, 

based on the criteria that the total pressure recovery at the AIP as well as the Mach number at the throat 

had converged to within at least 3 significant figures. 

Results 

In the discussion of results which follows, the Wind-US results computed with the BAY model are 

compared with experimental data (Ref. 13) and previously computed results using gridded vanes and the 

Wendt model (Ref. 5). 

The total pressure recovery versus throat Mach number is plotted in Figure 13(a) for the baseline 

cases and Figure 13(b) for the cases with VG’s in the duct. Note that neither the Wendt model nor the 

BAY model formulations explicitly model the total pressure losses caused by the drag forces present on 

the vane. This shortcoming is more apparent in the Wendt model total pressure recovery values, which are 

significantly higher than the experimental values; more so than the other computational results. For the 

lower throat Mach numbers, the vortex generators have little to no effect on recovery. At the higher throat 

Mach numbers ranging from 0.65 to 0.8, however, there is a slight improvement. The VGs redistribute the 

low pressure flow more uniformly around the duct, resulting in a slight improvement in the area averaged 

total pressure. This behavior can be better understood by examining the total pressure contours and 

streamline plots of Figure 14(a) to (d) for a throat Mach number of 0.82. 
NASA/TM—2010-216744 9 

In the streamline plots shown in Figure 14(a) to (d), the streamlines were released at the VG trailing 

edge station, and the total pressure contours are plotted at an axial location of x/c = 1, or one chord 

length downstream of the VG trailing edge, and at the AIP station (x/c = 20). In the baseline case shown 

in Figure 14(a), flow separates on the lower surface of the duct, but reattaches just upstream of the AIP, 

however at the AIP a significant low pressure region remains at the base of the duct. This large region of 

low pressure results in an undesirable high level of distortion. The streamlines show that the low pressure 

flow at the VG station remains near the lower surface of the duct along the axial length of the duct and 

through the low pressure region at the AIP. 

The total pressure contours from the experiment and the CFD solutions at the AIP show that the vanes 

have redistributed the flow and removed the low pressure region at the bottom of the duct. The 

streamlines illustrate the movement of the low energy flow up around the circumference of the duct, 

resulting in an overall more uniform total pressure distribution. The BAY model AIP total pressure 

contour distribution gives a slightly better match to the gridded vane solution than the Wendt model 

result, but the two model solutions are very similar. 

The DC60 distortion is plotted in Figure 15. The DC60 distortion parameter is defined at the AIP to 

be the difference between the mean total pressure and the mean total pressure in the “worst” 60° sector, 

normalized by the mean dynamic pressure (Ref. 15). The average improvement in DC60 as a result of the 

addition of the VGs was 82 percent for the experiment, 86 percent for the simulations using the gridded 

vane, 86 percent for the simulations using the Wendt model and 86 percent for the simulations using the 

BAY model. So in terms of the DC60 distortion parameter, there appears to be no added benefit to 

gridding the vane versus using either VG model. 

In summary, the VG’s have a minimal impact on the total pressure recovery in this duct, with only a 

slight benefit at the higher throat Mach numbers, so use of the BAY VG model versus gridded vanes 

makes little difference. For the distortion, the VG’s greatly improve the distortion by redistributing the 

low pressure region around the circumference of the duct. The results using the BAY model versus the 

gridded vanes were essentially equivalent, however using the BAY model was much easier than gridding 

up vanes. 

Conclusion 

A lift-force source term vortex generator model for vane-type VGs was implemented into the WindUS CFD code for structured grid applications. The magnitude of the lift-force is based on the local flow 

conditions and the size and angle of orientation of the vane. The model is user-friendly and allows the 

user to specify the vanes by inputting the range of grid points enveloping each vane, the planform area of 

the vane and its angle of incidence. Validation results have been shown for a single vane in a subsonic 

channel, a counter rotating pair of vanes in supersonic flow, and an S-duct with a co-rotating array. For 

these test cases, the CFD results using the model were comparable to CFD results using a gridded vane. 

Since the model is easier to use than a gridded vane, the VG model is recommended as an efficient 

alternative to gridding vanes. 

References 

1. Bush, R.H., Power, G.D. and Towne, C E., “WIND: The Production Flow Solver of the NPARC 

Alliance,” AIAA–98–0935, Jan. 1998. 

2. Towne, C.E., “Wind-US User’s Guide, Version 2.0,” NASA/TM—2009-215804, Oct. 2009. 

3. Nelson, C.C., Lankford, R. H., Nichols, R. H., “Recent Improvements to the Wind (-US) Code at 

AEDC,” AIAA–2004–527, Jan. 2004. 

4. Wendt, B.J., “Initial Circulation and Peak Vorticity Behavior of Vortices Shed from Airfoil Vortex 

Generators,” NASA/CR—2001-211144, Aug. 2001. 
NASA/TM—2010-216744 10 

5. Dudek, J.C., “Empirical Model for Vane-Type Vortex Generators in a Navier-Stokes Code,” AIAA 

Journal, Vol. 44, No. 8, 2006, pp. 1779–1789. 

6. Bender, E.E., Anderson, B.H., Yagle, P.J., “Vortex Generator Modeling for Navier-Stokes Codes,” 

ASME Paper FEDSM99–6929, Jul. 1999. 

7. Jirasek, A., “Vortex-Generator Model and Its Application to Flow Control,” Journal of Aircraft, 

Vol. 42, No. 6, Nov.-Dec. 2005. 

8. Yao, C-S, Lin, J.C., and Allan, B.G., “Flow-Field Measurement of Device-Induced Embedded 

Streamwise Vortex on a Flat Plate,” AIAA–2002–3162, Jun. 2002. 

9. Wik, E., and Shaw, S.T., “Numerical Simulation of Micro Vortex Generators,” AIAA–2004–2697, 

Jan. 2004. 

10. Dudek, J.C., “An Empirical Model for Vane-type Vortex Generators in a Navier-Stokes Code,” 

AIAA–2005–1003, Jan. 2005. 

11. Hirt, S.M., and Anderson, B.H., Experimental Investigation of the Application of Microramp Flow 

Control to an Oblique Shock Interaction,” AIAA–2009–0919, Jan. 2009. 

12. AGARD Fluid Dynamics Panel, Working Group 13, “Air Intakes for High Speed Vehicles,” 

AGARD-AR-270, Sep. 1991. 

13. Anderson, B.H., and Gibb, J., “Vane Effector Installation Studies on Steady State and Dynamic Inlet 

Distortion,” AIAA–1996–3279. 

14. Mohler, R.S., “WIND-US Flow Calculations for the M2129 S-Duct Using Structured and 

Unstructured Grids,” NASA/CR—2003-212736, Jan. 2003. 

15. Wendt, B.J., and Dudek, J.C., “Development of Vortex Generator Use for a Transitioning High-Speed 

Inlet,” Journal of Aircraft, Vol. 35, No. 4, Jul. 1998. 

 
NASA/TM—2010-216744 11 

Figure 2.—Orientation of unit vectors on vane.

Figure 3.—Schematic of the single vane in subsonic flow test 

case of Yao et al. (Ref. 8). 

Umax





c

h

Figure 1.—Vortex generator model parameters. 
NASA/TM—2010-216744 12 

Figure 4.—Grid used for the BAY model simulations of the Yao single vane experiment (Ref. 8). Region where 

contours are shown in later figures given for perspective. (a) Cross-plane grid. (b) Isometric view showing 

axial grid spacing and (c) Region showing grid points (in red) where the BAY model is applied. 

Region where source term 

model is specified 

(a) (b) 

(c) 
NASA/TM—2010-216744 13 

x/h













Experiment Gridded Vane BAY Model Gridded Vane/ 

Viscous Walls 

Figure 5.—Velocity contours at six stations downstream of the VG for the experiment and three 

simulations. 
NASA/TM—2010-216744 14 

x/h













Experiment Gridded Vane BAY Model Gridded Vane/ 

Viscous Walls 

Figure 6.—Vorticity contours at six stations downstream of VG for the experiment and three simulations. 
NASA/TM—2010-216744 15 

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 20 40 60 80 100 120

Dimensionless Axial Distance, x/h

Peak Vorticity (1/s)

Experiment

Viscous Vane

Vane

BAY Model

BAY Model - Fine Tip

(a) Peak vorticity for the experiment and four CFD simulations. 

(b) Grid resolution for the BAY model original grid and BAY model grid packed finely at the vane tip. 

Figure 7.—Peak vorticity versus axial direction (a) and cross-plane grids to illustrate grid resolution used for 

BAY model simulations (b). 

Cross Plane Grid at x/h = 3 BAY Model Original Grid BAY Model Fine-Tip Grid 
NASA/TM—2010-216744 16 

Figure 8.—Schematic of counterrotating vortex generators 

producing an upward vortex pair. 
NASA/TM—2010-216744 17 

x/h

5 

15 

25 

50 

100 

Gridded Vane BAY Model 

Figure 9.—Mach contours for a pair of counter-rotating vortex generators in Mach 2.0 

flow for solutions computed with the gridded vane and using the BAY model. 
NASA/TM—2010-216744 18 

 

Figure 11.—Schematic of M2129 S-duct (Ref. 13). 

throat

“engine face”

vane vortex generators

Figure 12.—Computational mesh. 

Figure 10.—Mach 2 flow over a microramp vortex generator x/h = 15. 

(a) Schematic. (b) Experimental data of Hirt et al. (Ref. 11). 

(a) (b) 
NASA/TM—2010-216744 19 

(a) Baseline Duct 

(b) Duct with VGs 

Figure 13.—Total pressure recovery in the M2129 S-duct. 

0.95

0.96

0.97

0.98

0.99

1.00

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Total Pressure Recovery

Throat Mach Number

Experiment

Wind-US

0.95

0.96

0.97

0.98

0.99

1.00

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Total Pressure Recovery

Throat Mach Number

Experiment

Gridded Vanes

Wendt Model

BAY Model
NASA/TM—2010-216744 20 

Baseline

Experiment

No Vanes

Gridded Vanes

Experiment

with Vanes

Wind-US 

Results Experimental Results 

Figure 14.—Total pressure contours for flow through an S-duct with throat Mach number of 0.82 for: (a) the 

baseline case (no VGs), (b) solution with gridded vanes, (c) solution computed using the Wendt VG model and 

(d) solution computed using the BAY model. 

(b)

(a)

(c)

(d)
NASA/TM—2010-216744 21 

Figure 15.—DC60 distortion at the AIP for the M2129 S-duct, shown with and without 

vortex generators. 

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1

DC60

Throat Mach Number

Experiment, Baseline

Wind-US, Baseline

Experiment, With VGs

Wind-US, Gridded Vanes

Wind-US, Wendt Model

Wind-US, BAY Model

With VGs

Baseline
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14. ABSTRACT

A source term model which simulates the effects of vortex generators was implemented into the Wind-US Navier Stokes code. The source 

term added to the Navier-Stokes equations simulates the lift force which would result from a vane-type vortex generator in the flowfield. 

The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid 

points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was 

evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, supersonic flow in a rectangular duct with a counterrotating vortex generator pair, and subsonic flow in an S-duct with 22 co-rotating vortex generators. The validation results indicate that the 

source term vortex generator model provides a useful tool for screening vortex generator configurations and gives comparable results to 

solutions computed using a gridded vane. 

15. SUBJECT TERMS

Vortex generators; Computational fluid dynamics; Inlet flow; Subsonic flow; Aerodynamics; Supersonic inlets 

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