TURBULENCE_WALL

Specifies a turbulent boundary layer wall.

Type

AcuSolve Command

Syntax

TURBULENCE_WALL("name") {parameters...}

Qualifier

User-given name.

Parameters

shape (enumerated) [no default]

Shape of the surfaces in this set.

three_node_triangle or tri3: Three-node triangle.
four_node_quad or quad4: Four-node quadrilateral.
six_node_triangle or tri6: Six-node triangle.

element_set or elem_set (string) [no default]

User-given name of the parent element set.

surfaces (array) [no default]

List of element surfaces.

surface_sets (list) [={}]

List of surface set names (strings) to use in this command. When using this option, the connectivity, shape, and parent element of the surfaces are provided by the surface set container and it is unnecessary to specify the shape, element_set and surfaces parameters directly to the TURBULENCE_WALL command. This option is used in place of directly specifying these parameters. In the event that both of the surface_sets and surfaces parameters are provided, the full collection of surface elements is read and a warning message is issued. The surface_sets option is the preferred method to specify the surface elements. This option provides support for mixed element topologies and simplifies pre-processing and post-processing.

type (enumerated) [=low_reynolds_number]

Type of the turbulence wall modeling.

low_reynolds_number or low_re: Low Reynolds number damping functions.
wall_function or func: Turbulence wall function.
running_average_wall_function: Turbulence wall function based on running average field.

roughness_height (real) >=0 [=0]

Average wall roughness height. Used with low_reynolds_number, wall_function, and running_average_wall_function type.

wall_function_heat_flux_factor >=1 [=1]

Constant factor used to scale the turbulent thermal conductivity within the first element off the wall. Used with type = wall_function and running_average_wall_function.

active_type (enumerated) [=all]

Type of the active flag. Determines which surfaces in this set will be active as turbulence boundary layer walls.

all: All surfaces in this set are active.
none: No surface in this set is active.
no_interface: Only surfaces that are not in an interface surface set or do not find a contact surface of an appropriate medium are active.

Description

This command specifies the surfaces (element faces) bounding a turbulent boundary layer.

The turbulence wall surfaces are defined with respect to the elements of an element set. For example,

ELEMENT_SET( "interior" ) {
    shape             = four_node_tet
    elements          = { 1, 8, 3, 4, 9 ;
                          3, 3, 4, 9, 5 ;
                          ... }
    ...
}
TURBULENCE_WALL( "no-slip wall" ) {
    shape             = three_node_triangle
    element_set       = "interior"
    surfaces          = { 1, 12, 9, 3, 4 ;
                          3, 52, 5, 3, 4 ; }
    type              = wall_function
    roughness_height  = 0.001
    active_type       = all
}

specifies that two surfaces of the element set "interior" are on a no-slip boundary, that a turbulence wall function with an average wall roughness height of 0.001 is to be used to capture the turbulent boundary layer, and that both surfaces are active.

There are two main forms of this command. The legacy version (or single topology version) of the command relies on the use of the surfaces parameter to define the surfaces. When using this form of the command, all surfaces within a given set must have the same shape, and it is necessary to include both the element_set and shape parameters in the command. shape specifies the shape of the surface. This shape must be compatible with the shape of the "parent" element set whose user-given name is provided by element_set. The element set shape is specified by the shape parameter of the ELEMENT_SET command. The compatible shapes are:

Element Shape: Surface Shape
four_node_tet: three_node_triangle
five_node_pyramid: three_node_triangle
five_node_pyramid: four_node_quad
six_node_wedge: three_node_triangle
six_node_wedge: four_node_quad
eight_node_brick: four_node_quad
ten_node_tet: six_node_triangle

The surfaces parameter contains the faces of the element set. This parameter is a multi-column array. The number of columns depends on the shape of the surface. For three_node_triangle, this parameter has five columns, corresponding to the element number (of the parent element set), a unique (within this set) surface number, and the three nodes of the element face. For four_node_quad, surfaces has six columns, corresponding to the element number, a surface number, and the four nodes of the element face. For six_node_triangle, surfaces has eight columns, corresponding to the element number, a surface number, and the six nodes of the element face. One row per surface must be given. The three, four, or six nodes of the surface may be in any arbitrary order, since they are reordered internally based on the parent element definition.

The surfaces may be read from a file. For the above example, the surfaces may be placed in a file, such as wall.srf:

1 12 9 3 4
3 52 5 3 4

and read by:

TURBULENCE_WALL( "no-slip wall" ) {
 shape       = three_node_triangle
 element_set = "interior"
 surfaces    = Read( "free.srf" )
 ...
}

The mixed topology form of the TURBULENCE_WALL command provides a more powerful and flexible mechanism for defining the surfaces. Using this form of the command, it is possible to define a collection of surfaces that contains different element shapes. This is accomplished through the use of the surface_sets parameter. The element faces are first created in the input file using the SURFACE_SET command, and are then referred to by the TURBULENCE_WALL command. For example, a collection of triangular and quadrilateral element faces can be defined using the following SURFACE_SET commands.

SURFACE_SET( "tri faces" ) {
   surfaces     = { 1, 1, 1, 2, 4 ;
                    2, 2, 3, 4, 6 ;
                    3, 3, 5, 6, 8 ; }
   shape        = three_node_triangle
   volume_set   = "tetrahedra"
}
SURFACE_SET( "quad faces" ) {
    surfaces    = { 1, 1, 1, 2, 4, 9 ;
                    2, 2, 3, 4, 6, 12 ;
                    3, 3, 5, 6, 8, 15 ; }
    shape       = four_node_quad
    volume_set  = "prisms"

Then, a single TURBULENCE_WALL command is defined that contains the tri and quad faces as follows:

TURBULENCE_WALL ( "no-slip wall" ) {
   surface_sets  = {"tri_faces", "quad_faces"}
   ...
}

The list of surface sets can also be placed in a file, such as surface_sets.srfst:

tri faces
quad faces

and read using:

TURBULENCE_WALL ( "no-slip wall" ) {
   surface_sets       = Read("surface_sets.srfst")
   ...
}

The mixed topology version of the TURBULENCE_WALL command is preferred. This version provides support for multiple element topologies within a single instance of the command and simplifies pre-processing and post-processing. In the event that both the surface_sets and surfaces parameters are provided in the same instance of the command, the full collection of surface elements is read and a warning message is issued. Although the single and mixed topology formats of the commands can be combined, it is strongly recommended that they are not.

A low_reynolds_number type specifies that the low Reynolds number damping functions are to be used in modeling the boundary layer. This model integrates the turbulence flow all the way to the boundary. As a result, this option is more accurate, provided that sufficient mesh density is used. For the Spalart-Allmaras turbulence model, (defined below) of the first mesh point must be less than 10 (preferably 5); otherwise, gross errors in traction, heat flux, and mass transfer may result.

A wall_function type specifies that the turbulence "law of the wall" is to be assumed near the wall. Turbulence wall functions allow for coarser meshes. For the Spalart-Allmaras turbulence model, for example, of the first mesh point may be as large as 300. On the other hand, the law of the wall applies only to simple turbulent boundary layers. The implemented wall function is valid only for non-separated flows with mild pressure gradients.

Unlike some wall function implementations there is no minimum

requirement in AcuSolve. For small values of

the two types become equivalent. The velocity law of the wall is given by:(1)

with a transition region for 5 <

< 30 . These two parts are referred to as the "viscous sublayer" and the "logarithmic layer". The non dimensional distance to the wall

and velocity

are defined by:(2)

where is the kinematic viscosity, is the turbulent friction velocity, is the wall shear, ρ is the density, U is the velocity parallel to the wall, and y is the normal distance to the wall. The logarithmic layer requires two experimentally determined parameters:

The temperature law of the wall is similar:(3)

plus a transition region. The non dimensional temperature is defined by(4)

where, in addition to the velocity parameters, T is the temperature,

is the wall temperature,

is the friction temperature,

is the wall heat flux, and

is the heat capacity. The molecular Prandtl number is

where μ is the dynamic viscosity and k is the thermal conductivity. The turbulent Prandtl number is modeled as a constant: the default is

but can be changed in CONDUCTIVITY_MODEL. The curve fit for the intercept A is:(5)

The species law of the wall has the same form as for temperature:(6)

plus a transition region. The nondimensional species is defined by(7)

where, in addition to the parameters defined above, Φ is the species, is the wall species, is the friction species, and is the wall species flux. The molecular Schmidt number is where D is the species diffusivity. The turbulent Schmidt number is modeled as a constant: the default is Sct = 0.91, but can be changed in DIFFUSIVITY_MODEL. The function A is the same as for the temperature law of the wall.

For simple attached turbulent boundary layers the required distance from the wall of the first mesh point can be estimated given a desired

value. The Reynolds number is(8)

where x is the streamwise distance from the beginning of the boundary layer and

is the freestream velocity. An approximate correlation for the wall shear is given by:(9)

From this the distance to the first node may be derived:(10)

The extremely weak dependence on Reynolds number allows this procedure to work well with only a rough estimate of the Reynolds number. For pipe flow a similar relationship valid for

may be derived:(11)

where is the average pipe velocity and the Reynolds number is based on and the pipe diameter.

Normally, designing a mesh based on the turbulent velocity profile is sufficient to resolve the temperature and species boundary layers as well.

Specification of a turbulence wall via this command does not enforce a no-slip condition on the given surface. The no-slip velocity and proper conditions for the turbulence variables must be separately imposed using NODAL_BOUNDARY_CONDITION commands. Wall roughness may be modeled by specifying an average wall roughness height for equivalent sand grains, given by roughness_height.

In some circumstances it is necessary to "turn off" or "deactivate" a previously-defined turbulence boundary layer wall. This is accomplished by setting the active flag through active_type. A value of all is the default and means that all surfaces in the set are active (active flag = 1) as turbulence boundary layer walls. A value of none means that no surface is active (active flag = 0).

A no_interface active type is used to automatically turn on and off each surface's status as a turbulence boundary layer wall in the presence of interfaces. Each surface is such a wall (active flag = 1) if the surface does not belong to an INTERFACE_SURFACE set or if it does not find a contact surface of fluid medium. That is, each surface will fall into one of four possible cases:

The surface is not in any INTERFACE_SURFACE set; active flag = 1.
The surface is in an INTERFACE_SURFACE set, but it does not find a contact surface; active flag = 1.
The surface finds a contact surface of fluid medium; active flag = 0.
The surface finds a contact surface of solid/shell medium; active flag = 1.