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VORTEX GENERATOR - Vortex generator model (block)

Structured Grids

 VORTEX [GENERATOR]    {MODEL WENDT        ZONE iz1 BOUNDARY {I1 | IMAX | J1 | JMAX | K1 | KMAX} \             [SUBSET I range J range K range]        ZONE iz2 BOUNDARY {I1 | IMAX | J1 | JMAX | K1 | KMAX} \             [SUBSET I range J range K range]        NUMBER ival           vg_boundary {XLOC xl | YLOC yl | ZLOC zl} chord height alpha \              [VEL vmax] [DEL delta] |     MODEL BAY        ZONE izone        NUMBER ival        VANE_SPEC imin imax jmin jmax kmin kmax vg_boundary alpha area \                  [model_constant]} ENDVORTEX

This keyword block is applicable to three-dimensional cases with structured grids, and enables the user to specify the effects of vortex generators in the flow using a choice of two models:

The Wendt model

• [Wendt, B. J. (2001) "Initial Circulation and Peak Vorticity Behavior of Vortices Shed from Airfoil Vortex Generators," NASA CR-2001-211144]
• [Dudek, J. C. (2006) "An Empirical Model for Vane-Type Vortex Generators in a Navier-Stokes Code," AIAA Journal, Vol 44, No. 8, pp. 1779-1853.]
or the BAY model
• [Bender, E. E., Anderson, B. H., and Yagle, P. J. (1999) "Vortex Generator Modeling for Navier-Stokes Codes," FEDSSM99-69 19, 3rd Joint ASME/JSME Fluids Engineering Conference, San Francisco, California.]
• [Dudek, J. C. (2011) "Modeling Vortex Generators in a Navier-Stokes Code," AIAA Journal, Vol 49, No. 4, pp. 748-759.]
Both models simulate the vortices produced by an array of vane-type vortex generators. A vortex generator array consists of one or more vortex generators mounted on viscous wall boundaries. A separate vortex generator keyword block must be used for each array. The models are only applicable to generators placed on viscous wall boundaries. It is the user's responsibility to check this - Wind-US currently has no mechanism for flagging this input error.

The various elements of the VORTEX GENERATOR input block are defined as follows:

 VORTEX [GENERATOR]

Defines the beginning of the vortex generator keyword input block.

 ENDVORTEX

Ends the vortex generator input block.

 {MODEL WENDT | MODEL BAY}

The main part of the VORTEX GENERATOR block is divided into two sections, corresponding to input for the Wendt and BAY models. Either MODEL WENDT or MODEL BAY must be specified, but not both.

Wendt Model

The Wendt model uses a discontinuous change in secondary velocity across a zonal interface boundary in order to simulate the vortices produced by an array of vane-type vortex generators. The model determines the strength of each vortex based on the generator chord length, height and angle of incidence with the incoming flow, as well as the incoming flow core velocity and boundary layer thickness. Each vortex center is placed at the grid point closest to the location determined by the user-specified generator location on the boundary, and the generator height.

Note that the Wendt vortex generator model is derived from experimental data taken at axial stations which were one chord length downstream of the trailing edge of the generators, and therefore the secondary velocities produced by the model simulate vortices at this station, rather than at the generator trailing edges. For most accurate results, the boundary where the vortex generator boundary condition is applied should be at this one chord length station.

The following restriction applies:

• The BOUNDARY TVD FACTOR 0 keyword option should be used at all interface boundaries containing vortex generators.

The elements of the VORTEX GENERATOR input block applicable to the Wendt model are defined as follows:

 ZONE iz1 BOUNDARY {I1 | IMAX | J1 | JMAX | K1 | KMAX} \      [SUBSET I range J range K range] ZONE iz2 BOUNDARY {I1 | IMAX | J1 | JMAX | K1 | KMAX} \      [SUBSET I range J range K range]

These two lines define the location of the vortex generator array. The relevant zones are given by the values of iz1 and iz2, and the relevant boundaries within zones iz1 and iz2 are specified via the BOUNDARY keyword parameter.

iz1 The "upstream" zone. The secondary velocities will be increased when passing information from this zone to iz2. The "downstream" zone, i.e., the zone receiving increased secondary velocities from zone iz1. Secondary velocities will be decreased when passing information from this zone back to zone iz1.

Note: Currently, the vortex generators must be located at either an i1 or imax boundary. Thus, the only valid choices with the BOUNDARY keyword parameter are I1 and IMAX.

Note that the secondary velocity is the flow in a plane normal to the primary velocity. For example, for a vortex generator array at an i-interface boundary, the primary flow is in the i direction, and the secondary velocity is in the j and k directions.

The SUBSET parameter may be used to specify that the change in secondary velocity occurs only over a part of the zone boundary. Otherwise, it is assumed that the change occurs over the entire boundary. The range parameters define the part of the zone boundary over which the change occurs, and take one of the following forms:

index1 index2 Starting and ending indices in the specified direction. LAST may be used for the last index. Equivalent to 1 LAST.

The starting and ending indices for the appropriate I, J, or K parameter (depending on the boundary specified) must be the same, and correspond to that boundary.

 NUMBER ival

This defines the number of vortex generators in the vortex generator array (i.e., on the specified boundary).

 vg_boundary {XLOC xl | YLOC yl | ZLOC zl} chord height alpha \    [VEL vmax] [DEL delta]

Defines the location and geometric parameters of each vortex generator. A separate line of input must be included for each generator.

vg_boundary The minimum or maximum index, specified as IM, IX, JM, JX, KM, or KX, within the specified boundary surface (as specified by ZONE and SUBSET) where the generator is mounted. This boundary must have been defined as a viscous wall. As an example, for a vortex generator array at an i-interface boundary, either JM, JX, KM, or KX should be specified, where JM means the generator is at the j = 1 interface boundary, JX means it's at the j = jmax boundary, etc. xl, yl, or zl is the x, y, or z coordinate location in inches of the base of the vortex generator on the already specified boundary surface and wall boundary. (Currently, only one coordinate direction and location may be specified. This may lead to ambiguity in specifying the locations for generators placed in complex duct geometries. This shortcoming will be addressed in future code updates.) The chord length of the vortex generator in inches. Must be greater than zero. The height of the vortex generator in inches. Must be greater than zero. The angle of incidence of the generator in degrees. Must be non-zero. More specifically, it is defined as the angle the generator chord line makes with the primary flow direction. The sign of alpha is determined using the "right-hand rule" of vector mechanics. For a given generator, use a normal vector pointing into the wall (the thumb), and the primary flow direction (fingers). If the rotation from the primary flow direction towards the generator follows the right-hand rule, then the sign of alpha is positive. Otherwise, it is negative. A positive value of alpha generally results in a vortex with a counterclockwise rotation, and conversely. The recommended range of magnitudes for alpha is between 8 and 20°. vmax is the maximum velocity at the vortex generator station, in ft/sec. The default is for Wind-US to compute this value from the flow. It is currently recommended that this value be specified by the user. Must be greater than zero. delta is the boundary layer thickness of the incoming flow, in inches. The default is for Wind-US to compute this value from the flow. It is currently recommended that this value be specified by the user. Must be greater than zero.

In selecting values for the above described parameters, keep in mind that the vortex generator model was derived from conservation of momentum and inviscid theory, correlated with experimental data having height/chord ratios between 0.13 and 2.62, height/delta ratios between 0.12 and 2.60, and for duct flows with core Mach numbers ranging from 0.20 to 0.60. Because of the theory used in its derivation, the model is intended to work well outside of the range of the experiments. However, there is one caveat: past experience indicates that the model does not work when the vortex generators are placed in regions of sonic flow.

Example

The following example illustrates the use of the Wendt vortex generator model for one vortex generator array located between zones 2 and 3. The interface between zones 2 and 3 corresponds to the imax boundary of zone 2 and the i1 boundary of zone 3. The array contains two vortex generators, both mounted on the jmax viscous wall boundary of the zone interface with z coordinate values of −0.52 inches and 0.52 inches. The generators have the same geometric parameters: the chord length is 1.6 inches, the height is 0.4 inches, and the angle of incidence is 16°.

VORTEX GENERATOR
MODEL WENDT
ZONE 2 BOUNDARY IMAX
ZONE 3 BOUNDARY I1
NUMBER 2
JX ZLOC -0.52 1.6 0.4 16.0
JX ZLOC  0.52 1.6 0.4 16.0
ENDVORTEX

BAY Model

The BAY model is a source term model which models the side force produced by the vortex generator and adds it to the momentum and energy equations. This side force automatically adjusts its strength based on the local flow. The user specifies the grid points over which the force is to be applied (i.e., enclosing each vortex generator).

The elements of the VORTEX GENERATOR input block applicable to the BAY model are defined as follows:

 ZONE izone

This line defines the zone containing the vortex generator array.

 NUMBER ival

This defines the number of vortex generators in the vortex generator array.

 VANE_SPEC imin imax jmin jmax kmin kmax vg_boundary alpha area [model_constant]

This keyword line must be specified ival times, i.e. once for each vane. It is used to specify the grid points over which the model acts for each vane and the accompanying vane angle of incidence, planform area and model constant. These parameters are described in more detail below.

imin, imax Minimum and maximum i indices defining the grid region enclosing the vortex generator Minimum and maximum j indices defining the grid region enclosing the vortex generator Minimum and maximum k indices defining the grid region enclosing the vortex generator The minimum or maximum index, specified as IM, IX, JM, JX, KM, or KX, indicating the viscous wall where the generator is mounted. Here JM means the vane is on the j = 1 boundary, JX means it's on the j = jmax boundary, etc. The angle of incidence of the vane chord line (in degrees) with respect to the coordinate grid line in the primary flow direction. Note: In instances where the leading edge of the vane corresponds to the maximum index of the VANE_SPEC range rather than the minimum (i.e., jmax or kmax approximately specify the leading edge of the vane), the sign of the angle must be negative in order to produce the correct directional rotation of the vortex. The vane area (in2) The model constant. The default value is 10.

Example

The following example illustrates the use of the BAY vortex generator model for one vortex generator array located in zone 2. The array contains two vortex generators, both mounted on the jmax viscous wall boundary. The VANE_SPEC values of the zones are shown below. They both act over the same i and j indices but at different k indices on the wall. Both generators have the same angle of incidence with the primary flow direction grid line, 16°, and have planform areas of 0.21 in2.

VORTEX GENERATOR
MODEL BAY
ZONE 2
NUMBER 2
VANE_SPEC 15 25 45 65 20 25 JX 16.0 0.21
VANE_SPEC 15 25 45 65 35 40 JX 16.0 0.21
ENDVORTEX

Last updated 1 Apr 2016