! Copyright (c) 2023 Gregorio Gerardo Spinelli <gregoriogerardo.spinelli@dlr.de> ! ! Redistribution and use in source and binary forms, with or without ! modification, are permitted provided that the following conditions are met: ! ! 1. Redistributions of source code must retain the above copyright notice, ! this list of conditions and the following disclaimer. ! ! 2. Redistributions in binary form must reproduce the above copyright notice, ! this list of conditions and the following disclaimer in the documentation ! and/or other materials provided with the distribution. ! ! THIS SOFTWARE IS PROVIDED BY THE UNIVERSITY OF SIEGEN “AS IS” AND ANY EXPRESS ! OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES ! OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. ! IN NO EVENT SHALL UNIVERSITY OF SIEGEN OR CONTRIBUTORS BE LIABLE FOR ANY ! DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES ! (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; ! LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ! ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT ! (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ! SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ! **************************************************************************** ! !> This module contains data types, function and routines for wall function !! computations relative to Reichardt profile. !! Haussmann, Marc; BARRETO, Alejandro CLARO; KOUYI, Gislain LIPEME; !! Rivière, Nicolas; Nirschl, Hermann; Krause, Mathias J. (2019): !! Large-eddy simulation coupled with wall models for turbulent channel !! flows at high Reynolds numbers with a lattice Boltzmann method !! — Application to Coriolis mass flowmeter. In Computers & Mathematics !! with Applications 78 (10), pp. 3285–3302. DOI: 10.1016/j.camwa.2019.04.033. !! !! The explicit power-law in terms of friction velocity given in Eq. 33 in !! S. Wilhelm, J. Jacob, and P. Sagaut, "An explicit power-law-based wall !! model for lattice Boltzmann method–Reynolds-averaged numerical simulations !! of the flow around airfoils", Physics of Fluids 30, 065111 (2018) !! https://doi.org/10.1063/1.5031764 !! !! The model constants are chosen according to Werner and Wengle: !! Wengle, H. and Werner, H. (1993) ‘Large-eddy Simulation of Turbulent Flow !! Over Sharp-edged Obstacles in a Plate Channel’, (1985), pp. 192–199. !! !! author: Gregorio Gerardo Spinelli module mus_wall_function_reichardt_module ! include treelm modules use env_module, only: rk use mus_wall_function_abstract_module, only: mus_wall_function_type implicit none private !! Constant parameters for Reichardt's law real(kind=rk), parameter :: vonKA = 0.4_rk real(kind=rk), parameter :: oneOvervonKA = 1.0_rk / vonKA public :: mus_wall_function_reichardt_type !> extend the abstract subclass mus_wall_function_type type, extends(mus_wall_function_type) :: mus_wall_function_reichardt_type contains !> function to get uPlus procedure, nopass :: get_uPlus !> function to apply the newon method ! F = uPlus_n - uPlus_(n+1) ! here we compute the derivative of uPlus_(n+1) w.r.t. u_tau ! this function computes the derivative of uPlus with respect to uTau procedure, nopass :: get_d_uPlus_d_uTau end type mus_wall_function_reichardt_type contains !> function to get uPlus pure function get_uPlus( yPlus ) result( uPlus ) !> yPlus real(kind=rk), intent(in) :: yPlus !> output: uPlus real(kind=rk) :: uPlus ! ------------------------------------------------------------------------------ !uPlus = oneOvervonKA * log( 1.0_rk + vonKA*yPlus ) & ! & + 7.8 * ( 1.0_rk-exp(-yPlus/11._rk) & ! & - (yPlus/11._rk) * exp(-yPlus/3._rk) ) ! above expression simplified with sympy in python uPlus = -0.709090909090909_rk * yPlus * exp(-yPlus / 3._rk) & & + log(vonKA*yPlus + 1._rk) + 7.8_rk & & - 7.8_rk * exp(-yPlus/11._rk) + oneOvervonKA end function get_uPlus !> function to get the derivative of uPlus with respect to uTau pure function get_d_uPlus_d_uTau( y, uTau, nu ) result( d_uPlus_d_uTau ) !> vertical distance from the wall real(kind=rk), intent(in) :: y !> uTau at iteration n real(kind=rk), intent(in) :: uTau !> dynamic viscosity real(kind=rk), intent(in) :: nu !> output: derivative of uPlus with respect to uTau real(kind=rk) :: d_uPlus_d_uTau ! ------------------------------------------------------------------------------ real(kind=rk) :: inv_nu, yPlus, nu_sqr, y_inv_nu, A, B inv_nu = 1._rk / nu y_inv_nu = y * inv_nu yPlus = uTau * y_inv_nu nu_sqr = nu**2 A = 0.709090909090909_rk * y_inv_nu B = exp( -yPlus / 3._rk) ! obtained as diff from sympy in python d_uPlus_d_uTau = vonKA * y / ( nu * ( vonKA * yPlus + 1._rk ) ) & & + A * ( exp( -yPlus / 11._rk) - B ) & & + 0.236363636363636_rk * yPlus * y_inv_nu * B end function get_d_uPlus_d_uTau end module mus_wall_function_reichardt_module