turbulentDigitalFilterInlet

Table of Contents

Properties

  • Digital-filter based inlet boundary condition for velocity, i.e. U, to generate synthetic turbulence-alike time-series for LES and turbulent DES flow computations from input turbulence statistics.
  • Theoretical expressions of the implementation are based on
    • the digital-filter method (DFM) [32]
    • the forward-stepwise method (FSM) [96]
    • the mass-inflow rate correction [31]
  • In DFM or FSM, a random number set (mostly white noise), and a group of target statistics (mostly mean flow, Reynolds stress tensor profiles and length-scale sets) are merged into a new number set (stochastic time-series, yet consisting of the statistics) by a chain of mathematical operations whose characteristics are designated by the target statistics, so that the realised statistics of the new sets could match the target. 
    Random number sets ---->-|
                         |
                     DFM or FSM ---> New stochastic time-series consisting
                         |           turbulence statistics
Turbulence statistics ->-|
  • The main difference between DFM and FSM is that FSM replaces the expensive-to-run streamwise convolution summation in DFM by a simpler and an almost-equivalent-in-effect numerical procedure in order to reduce computational costs. Accordingly, FSM potentially brings computational resource advantages for computations involving relatively large streamwise length-scale sets and small time-steps.
  • Synthetic turbulence is generated on a virtual rectangular structured-mesh plane, which is parallel to the chosen patch, and is mapped onto this patch by the selected mapping method.

Required fields: 

U    | Velocity    [m/s]

Usage

Example of the boundary condition specification: 

<patchName>
{
    // Mandatory entries (unmodifiable)
    type                turbulentDigitalFilterInlet;
    n                   (<nHeight> <nWidth>);
    L                   (<L1> <L2> ... <L9>);
    R                   uniform (<Rxx> <Rxy> <Rxz> <Ryy> <Ryz> <Rzz>);
    UMean               uniform (1 0 0);
    Ubulk               10.0;

    // Optional entries (unmodifiable)
    fsm                 false;
    Gaussian            true;     // always false for FSM
    fixSeed             true;
    continuous          false;
    correctFlowRate     true;
    mapMethod           nearestCell;
    perturb             1e-5;
    C1                  -1.5707;  //-0.5*PI;
    C1FSM               -0.7854   //-0.25*PI;
    C2FSM               -1.5707;  //-0.5*PI;

    // Optional (inherited) entries
    ...

where the entries mean:

Property Description Type Required Default
type Type name: turbulentDigitalFilterInlet word yes -
n Number of cells on turbulence generation plane tuple of labels yes -
L Integral length-scale set (Lxu Lxv Lxw Lyu Lyv Lyw Lzu Lzv Lzw) [m] tensor yes -
R Reynolds stress tensor set (xx xy xz yy yz zz) [m2/s2] symmTensorField yes -
UMean Mean velocity profile [m/s] vectorField yes -
Ubulk Characteristic patch-normal bulk flow speed [m/s] scalar yes -
fsm Flag to turn on the forward-stepwise method bool no false
Gaussian Autocorrelation function form bool no true
fixSeed Flag to fix random-number generator seed to 1234 or generate a new seed based on clock-time per simulation bool no true
continuous Flag to write random-number sets at output time, and to read them on restart. Otherwise, generate new random-number sets of restart bool no false
correctFlowRate Flag to correct mass-inflow rate on turbulence plane in (only) streamwise direction bool no true
mapMethod Interpolation-to-patch method word no nearestCell
perturb Point perturbation for planarInterpolation mapMethod scalar no 1e-5
C1 Model constant shaping autocorrelation function (KSJ:Eq. 14) scalar no -0.5*PI
C1FSM Model coefficient in FSM (XC:Eq. 14) scalar no -0.25*PI
C2FSM Model coefficient in FSM (XC:Eq. 14) scalar no -0.5*PI

The inherited entries are elaborated in:

Options for the fsm entry: 

false | Method due to (Klein et al., 2003)
true  | Method due to (Xie-Castro, 2008)

Options for the Gaussian entry: 

true  | Gaussian function
false | Exponential function (only option for FSM)

Options for the mapMethod entry: 

nearestCell         | One-to-one direct map, no interpolation
planarInterpolation | Bilinear interpolation

Patch-profile input is available for two entries: 

R     | Reynolds stress tensor
UMean | Mean velocity

where the input profiles and profile coordinates are located in: 

Coordinates | $FOAM_CASE/constant/boundaryData/<patchName>/points
R/UMean     | $FOAM_CASE/constant/boundaryData/<patchName>/0/{R, UMean}

points file contains a list of three-dimensional coordinates, and profile data files provide a value corresponding to each coordinate.

Notes on entries

  • mapMethod=planarInterpolation option needs point coordinates that can form a plane.
  • adjustTimeStep=true option is currently not fully supported.
  • In order to obtain Reynolds stress tensor information, experiments, RANS simulations or engineering relations can be used.
  • continuous=true means deterministic-statistical consistent restart (relatively more expensive), and continuous=false means deterministic discontinuity in synthetic turbulence time-series by keeping statistical consistency (relatively cheaper).
  • For L, the first three entries should always correspond to the length scales in association with the convective (streamwise) mean flow direction.
  • Streamwise integral length scales are converted to integral time scales by using Taylor's frozen turbulence hypothesis, and Ubulk.

Further information

Tutorial:

Source code:

History

  • Introduced in version v1906