计算可压缩流和不可压缩流的位移、动量、能量和99%边界层厚度 matlab代码.rar

function varargout = thickness(y,u,r) % THICKNESS(Y,U,R): Calculates the different boundary layer thicknesses % for a rake of coordiantes Y, velocities U, and densities R (optional) % in COLUMN form. The integral thicknesses from Schlichting are derived % from trapezoidal integrations. The 99% thicknesses are robust metrics % for the standard 'delta99'. Three BL profiles are provided as sample. % % INTEGRAL, INCOMPRESSIBLE: % (1) Displacement (incompressible) % (2) Momentum (incompressible) % (3) Energy (incompressible) % % INTEGRAL, COMPRESSIBLE % (4) Displacement (compressible: ONLY when R is passed) % (5) Momentum (compressible: ONLY when R is passed) % (6) Energy (compressible: ONLY when R is passed) % % GEOMETRIC, ROBUST DELTA 99 % (7) 99% variance thickness (4 for incompressible) % (8) 99% asymptotic thickness (5 for incompressible) % % If zero outputs are passed, a plot is generated with all thicknesses. % If one output is passed, all thicknesses are returned in vector form. % If multiple outputs are passed, the indexed thicknesses are returned. % % % EXAMPLES: % % thickness; % t = thickness(Y,U); % t = thickness(Y,U,R); % t = thickness([Y,U,R]); % [t1,...,tn] = thickness(...); % % % Miguel Moreno, August 2024 %% PARSE INPUTS if nargin==0 % Load sample BL data [y,u,r] = sample(1); % CHANGE: 1, 2 or 3 compressible = true; n = length(y); % Compressible mode elseif nargin==3 compressible = true; n = length(y); % Incompressible mode elseif nargin==2 compressible = false; n = length(y); % Parse matrix else [y,u,r,n,compressible] = checkinputs(y); end %% CALCULATE THICKNESSES % INTEGRAL THICKNESSES u = u/u(n); if compressible % Calculate [displacement, momentum, energy] for INCOMP. and COMP. m = 8; r = r/r(n); t(m) = 0; t(1:6) = trapz(y-y(1), [1-u, u.*(1-u), u.*(1-u.*u), 1-r.*u, ... r.*u.*(1-u), r.*u.*(1-u.*u)]); else % Calculate incompressible [displacement, momentum, energy] m = 5; t(m) = 0; t(1:3) = trapz(y-y(1),[1-u, u.*(1-u), u.*(1-u.*u)]); end % VARIANCE DELTA 99 for i = n:-1:1 % Find index with maximum cumulative self-variance from freestream if max(abs(u(i:n)-sum(u(i:n))/(n-i+1)))>1e-2 % When maximum variance exceeds 1%, stop search t(m-1) = y(i+1); break end end % ASYMPTOTIC DELTA 99 % Use last 10% of the data points to calculate asymptote i = ceil(0.9*n); % Asymptotic delta99: 1% discrepancy with freestream asymptote t(m) = y(min(n,find(abs(u-lval(lfit(y(i:n),u(i:n)),y))>1e-2,1,'last')+1)); %% PARSE OUTPUTS % No-input case n = nargout; if nargin==0 % Display sample results createfigure(y,u,t,m) % Empty workspace switch n case 0 clear otherwise for i = 1:n varargout{i} = []; %#ok end end return end % Return thicknesses switch n case 0 % Prompt to workspace and PLOT results varargout{1} = t; createfigure(y,u,t,m) case 1 % Vector mode varargout{1} = t; otherwise % Individual entries for i = 1:n if i>m varargout{i} = []; %#ok else varargout{i} = t(i); %#ok end end end end %% SUBFUNCTIONS % Load sample BL function [y,u,r] = sample(n) % Three examples of turbulent BLs switch n % Accelerated BL with SBLIs case 1 y = [0;1.99999999495049e-06;4.15308113588253e-06;6.47095794192865e-06;8.96624169399729e-06;1.16525061457651e-05;1.45443646033527e-05;1.76575504156062e-05;2.10089947358938e-05;2.46169256570283e-05;2.85009682556847e-05;3.26822446368169e-05;3.71834867110010e-05;4.20291762566194e-05;4.72456558782142e-05;5.28612836205866e-05;5.89065821259283e-05;6.54144096188247e-05;7.24201381672174e-05;7.99618283053860e-05;8.80804509506561e-05;9.68201056821272e-05;0.000106228268123232;0.000116356015496422;0.000127258346765302;0.000138994422741234;0.000151627929881215;0.000165227422257885;0.000179866663529538;0.000195625019841827;0.000212587925489061;0.000230847290367819;0.000250502052949742;0.000271658616838977;0.000294431491056457;0.000318943930324167;0.000345328473486006;0.000373727700207382;0.000404295074986294;0.000437195616541430;0.000472606858238578;0.000510719662997872;0.000551739416550845;0.000595887016970664;0.000643399835098535;0.000694533227942884;0.000749561819247901;0.000808780547231436;0.000872506760060787;0.000941081438213587;0.00101487082429230;0.00109426875133067;0.00117969815619290;0.00127161329146475;0.00137050217017531;0.00147688854485750;0.00159133540000767;0.00171444611623883;0.00184686866123229;0.00198929803445935;0.00214248010888696;0.00230721384286881;0.00248435628600419;0.00267482572235167;0.00287960562855005;0.00309974886476994;0.00333638256415725;0.00359071278944612;0.00386402895674109;0.00415770849213004;0.00447322381660342;0.00481214607134461;0.00517615070566535;0.00556702492758632;0.00598667142912746;0.00643711583688855;0.00692051183432341;0.00743914581835270;0.00799544714391232;0.00859198812395334;0.00923149287700653;0.00991684012115002;0.0106510706245899;0.0114373881369829;0.0122791621834040;0.0131799355149269;0.0141434157267213;0.0151734827086329;0.0162741821259260;0.0174497254192829;0.0187044795602560;0.0200429558753967;0.0214698072522879;0.0229898076504469;0.0246078334748745;0.0263288393616676;0.0281578414142132;0.0300998743623495;0.0321599654853344;0.0343430899083614;0.0366541221737862;0.0390977896749973;0.0416786149144173;0.0444008558988571;0.0472684428095818;0.0502848960459232;0.0534532591700554;0.0567760281264782;0.0602550692856312;0.0638915300369263;0.0676857829093933;0.0716373175382614;0.0757447183132172;0.0800055488944054;0.0844163522124291;0.0889725461602211;0.0936684533953667;0.0984972491860390;0.103450976312160;0.108520574867725;0.113695889711380;0.118965782225132;0.124318152666092;0.129740089178085;0.135217934846878;0.140737473964691;0.146284013986588;0.151842594146729;0.157398104667664;0.162935495376587;0.168439894914627;0.173896789550781;0.179292127490044;0.184612601995468;0.189845591783524;0.194979354739189;0.200003176927567;0.204907327890396;0.209683179855347;0.214323252439499;0.218821167945862]; u = [-0.551870584487914;-0.851362402229443;-0.616410248775832;0.211779454477307;1.62932274355219;3.51114881673560;5.58005730356145;7.53683961063929;9.23286236295779;10.6722495724363;11.9145172276030;13.0177871338018;14.0253934586106;14.9673981026777;15.8642899976517;16.7302962650622;17.5747383372861;18.4036303169777;19.2257806368195;20.0472645223029;20.8705675749267;21.6984100425310;22.5334569043569;23.3779135117346;24.2339127894409;25.1033702800103;25.9879955932996;26.8894163925308;27.8091097351745;28.7484497651058;29.7087134433067;30.6910023530747;31.6964239135751;32.7262554298042;33.7818926085127;34.8644356628873;35.9747064908296;37.1134546921931;38.2817161884409;39.4809124375051;40.7135905669582;41.9841177543230;43.3001577142940;44.6734643671199;46.1192868932895;47.6562440573638;49.3071599672873;51.0913807544153;53.0218369689450;55.1124258842637;57.3814645256371;59.8506562