【物理应用】基于Matlab模拟RANS湍流

1 内容介绍

传统RANS湍流模型大多基于Boussinesq湍流涡粘本构模型,该本构模型是在研究半无限大平板流构型中得到的.

2 部分代码

Turbulence - Project 2: RANS numerical simulation of a turbulent flow

through a channel.

Numerical models:

- Length mixing (0 equation)

- TKE (1 equation)

- k-epsilon (2 equations)

Problem description:

Data extracted from direct numerical simulations of fully developed plane

turbulent channel flow. URL:http://torroja.dmt.upm.es/channels/data/

Re_tau = 180 || Re_tau = 550 ||Re_tau = 950 || Re_tau = 2000

clear; clc; help main; addpath(genpath(pwd));

% Figures save path

mkdir figures; addpath('.\figures\'); fpath = strcat(pwd,'\figures\');

savefigure = false;

% ------------------------------------------------------------------------%

% Problem configuration

% ------------------------------------------------------------------------%

global Re lm n nfrec sigma_k c cd c_mu c_ep1 c_ep2 sigma_ep h

Re = 180; % Re_tau

eps = 1e-3; % Right Hand Side (RHS) error -> stadistically stationary

nfrec = 1000; % Plot frecuency

h = 1; % Half of the channel (Dimensionless h==h^*=1)

n = round(Re/4); % Number of nodes of the mesh

CFL = 1; % Corant number associated with the viscous term

a = 1.5; % Exponent amplificator of nodes

mplot = true; % Mesh plot?

x0 = 0; % Left bound

xf = h; % Right bound

itmax = 2e6; % Max number of iterations

% ------------------------------------------------------------------------%

% DNS Data

% ------------------------------------------------------------------------%

% y/h || y+ || U+ || u'+ || v'+ || w'+ || -Om_z+ || om_x'+

% om_y'+ || om_z'+ || uv'+ || uw'+ || vw'+ || pr'+ || ps'+ || psto'+ || p'

load(strcat('Re', num2str(Re), '.prof'));

d(1).d(:,:) = evalin('base', strcat('Re', num2str(Re)));

% y/h || y+ || dissip || produc || p-strain || p-diff || t-diff

% v-diff || bal || tp-kbal

load(strcat('Re', num2str(Re), '.bal.kbal'));

d(2).d(:,:) = evalin('base', strcat('Re', num2str(Re), '_bal'));

% ------------------------------------------------------------------------%

err = 1; err1 = err; err2 = err; err3 = err; it = 1;

y(:,1) = mesh1D(n,a,x0,xf,mplot);

% y(:,1) = d(1).d(:,1); % Copy mesh DNS

% n = length(y);% Copy mesh DNS

yplus = y.*Re./h;

deltay(:,1) = y(2:end)-y(1:end-1);

deltaymax = max(deltay);

mu = deltay(1:end)./deltaymax;

% dt = CFL*min(deltay.^2*Re);

% ------------------------------------------------------------------------%

% Initialization

% ------------------------------------------------------------------------%

% Initialization by functions

% u = 15.*y.^(0.25); % Initialization: Mixing & TKE & k-epsilon

% k = 8.*y.^(0.25).*exp(-2.5.*y); % Initialization: TKE & k-epsilon

% ep = 0.75.*y.^(0.25).*exp(-5.*y); % Initialization: k-epsilon

ep = 500.*y.^(0.25).*exp(-5.*y); % Initialization: k-epsilon

% ep = 750*y.^(0.25).*exp(-5.*y); % Initialization: k-epsilon

% Accurate initialization - 1

y_dns = d(1).d(:,1);

u_dns = d(1).d(:,3);

k_dns = 0.5.*(d(1).d(:,4).^2 + d(1).d(:,5).^2 + d(1).d(:,6).^2);

ep_dns = -Re.*d(2).d(:,3);

u = spline(y_dns,u_dns,y);

k = spline(y_dns,k_dns,y);

% ep = spline(y_dns,ep_dns,y);

% Accurate initialization - 2

% load('kepsilon_2000.mat')

% u = spline(y_kepsilon,u_kepsilon,y);

% k = spline(y_kepsilon,k_kepsilon,y);

% ep = spline(y_kepsilon,ep_kepsilon,y);

% ------------------------------------------------------------------------%

% Turbulent viscosity from DNS data:

dudy_dns = difx(u_dns,y_dns);

tau12_dns = d(1).d(:,11);

nut_dns = -tau12_dns./dudy_dns;

nut_dns = nut_dns(1:end-1); % Remove wrong value

% ------------------------------------------------------------------------%

nut_spline = spline(y_dns(1:end-1),nut_dns,y);

dt = CFL.*(1/Re+abs(nut_spline(1:end-1))).^(-1).*deltay.^2;

dt = [dt;dt(end)];

nyplus1 = find(yplus<1,1,'last');

% dt = min(CFL.*(1/Re+abs(nut_spline(1:end-1))).^(-1).*deltay.^2); % Fixed step size

% ------------------------------------------------------------------------%

% Display configuration

disp('---- Configuration ----')

fprintf('y = %.3e \n', h)

fprintf('n = %d \n', n)

fprintf('dy_min = %.3e \n', min(deltay))

fprintf('dy_max = %.3e \n', deltaymax)

fprintf('dt_min = %.3e \n', min(dt))

fprintf('CFL = %.3e \n', CFL)

fprintf('Re = %.3e \n', Re)

fprintf('eps = %.3e \n', eps)

fprintf('Nodes y+< 1 = %d \n', nyplus1)

disp('-----------------------')

if nyplus1 < 2

disp('ATTENTION! number of nodes in y+ < 1 is less than 2.')

end

%% Mixing length model

mixing;

%% TKE model

tke;

%% k-epsilon

% kepsilon; % Chien

% kepsilonRM; % Chien + fmu Rodi & Mansour

% kepsilon2; % Nagano-Tagawa

kepsilon3; % Launder-Sharmar

% kepsilon4; % Lam-Bremhorst

%% k-omega

% komega; % Not yet

%% Load results for plotting

npoint = 1; % Plot per npoint

load_results;

%% Plot Mixing, TKE and k-epsilon

plotallu;

plotallk;

plotallep;

plotallnut;

%% Plot in wall units (dots)

dnsplot1 = 20;

dnsplot2 = 8;

plotalluplus;

plotallkplus;

plotallepplus;

plotallnutplus;

%% Plot in wall units (lines)

dnsplot1 = 16;

dnsplot2 = 8;

plotalluplus2;

plotallkplus2;

plotallepplus2;

plotallnutplus2;

%% Plot Viscous vs Reynolds stresses

plottau;

%% Plot Production vs Dissipation

plotalllep_prod_dis_plus

%% Velocity-defect law

plotvelocity

%% Plot only k-epsilon models

% plotkep_uplus;

% plotkep_kplus;

% plotkep_epplus;

% plotkep_nutplus;

3 运行结果

4 参考文献

[1]郭永涛, 徐弘一. 基于方、矩形环管直接数值模拟结果的各向异性RANS湍流模型构建[J]. 复旦学报(自然科学版), 2019, 58(01):5-17.

[2]王翔宇. RANS/LES混合方法在湍流精细数值模拟中的应用与改进[D]. 西北工业大学.

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