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trProp.m
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trProp.m
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% ________ ___ __ _____ ______
% |\ ____\|\ \|\ \ |\ _ \ _ \
% \ \ \___|\ \ \/ /|_ \ \ \\\__\ \ \
% \ \ \ \ \ ___ \ \ \ \\|__| \ \
% \ \ \____\ \ \\ \ \ __\ \ \ \ \ \
% \ \_______\ \__\\ \__\\__\ \__\ \ \__\
% \|_______|\|__| \|__\|__|\|__| \|__|
%
% Author: Andrea Somma;
% Politecnico of Milan
%
% trProp calculates transport properties as: viscosity (vi), binary
% diffusivity (diff), thermal conductivity (kt) of requested species, both
% from transport matrix (see trRed or trConv) and from fitted coefficients
% (see fitTransportCoefficients) in SI units.
%
% - out = trProp(specie,T,P,prop,data_trans,data,fittedOrCalc): where
% specie is the vector of the species, T the temperature [K], P the
% pressure [bar], see below for further informations.
%
% - fittedOrCalc == "calc", for calculated properties:
% - specie = name of the species in chemkin format in vertical vector;
% - T = temperature [K] (horizontal vector);
% - P = pressure [bar] (horizontal vector);
% - data_trans = transport data matrix from trRed or trConv;
% - data = thermodynamic data matrix from thRed or thConv;
%
% - fittedOrCalc == "fit", for fitted properties from fitTransportCoefficients:
% - specie = name of the species in chemkin format in vertical vector;
% - T = temperature [K] (horizontal vector);
% - P = pressure [bar] (horizontal vector);
% - data_trans = fitted coefficients in transport folder:
% - kt: ckK;
% - vi: ckV;
% - diff: ckD;
% - data = [];
%
% - prop = property to evaluate, based on collision integral:
% - vi = viscosity;
% - kt = thermal conductivity;
% - diff = diffusion mass coefficient (A in B, binary);
function out = trProp(specie,T,P,prop,data_trans,data,fitted)
ckm = CKM;
if fitted == "fit"
if size(T,1)>size(T,2)
T = T';
end
if size(P,1)>size(P,2)
P = P';
end
% choose the property
if prop == "vi"
coeff = cell2mat(data_trans(:,2:end));
[~,index] = ismember(specie,data_trans(:,1));
out = exp( coeff(index,1) + coeff(index,2).*log(T) + coeff(index,3).*(log(T)).*log(T) ...
+ coeff(index,4).*(log(T)).*log(T).*log(T) );
elseif prop == "kt"
coeff = cell2mat(data_trans(:,2:end));
[~,index] = ismember(specie,data_trans(:,1));
out = exp( coeff(index,1) + coeff(index,2).*log(T) + coeff(index,3).*(log(T)).*log(T) ...
+ coeff(index,4).*(log(T)).*log(T).*log(T) );
elseif prop == "diff"
coeff = cell2mat(data_trans(:,3:end));
out = zeros(size(specie,1),size(T,2));
for i = 1:size(specie,1)
index = all(data_trans(:,1:2)==specie(i,:),2);
if all(index==0)
index = all(data_trans(:,1:2)==[specie(i,2) specie(i,1)],2);
end
out(i,:) = exp( coeff(index,1) + coeff(index,2).*log(T) + coeff(index,3).*(log(T)).*log(T) ...
+ coeff(index,4).*(log(T)).*log(T).*log(T) )./P;
end
end
elseif fitted == "calc"
if size(specie,1)<size(specie,2) && length(specie)>2
specie = specie';
end
if length(T)>1
error("Temperature vector not supported for calculated properties, try using fitted ones")
end
if prop == "vi"
PM = ckm.PM(specie,data); %molecular mass Kg/mol
[~,index] = ismember(specie,data_trans(:,1));
epsonk = str2double(data_trans(index,3)); %K
lennar = str2double(data_trans(index,4))*1e-10; %m
mu = str2double(data_trans(index,5))*1e-21/299792458;
kb = 1.3806488e-23; %J/K
NA = 6.02214076e23;
Tred = T./epsonk;
R = 8.3144621;
delta = 1/2*(mu./sqrt(epsonk.*kb.*lennar.^3)).^2;
coll2_2 = collInt(2,Tred,delta);
coll2_2 = coll2_2';
out = 5/16*sqrt(pi*PM*kb*T/NA)./(pi*lennar.^2.*coll2_2);
elseif prop == "kt"
PM = ckm.PM(specie,data); %molecular mass Kg/mol
[~,index] = ismember(specie,data_trans(:,1));
type = str2double(data_trans(index,2));
epsonk = str2double(data_trans(index,3)); %K
lennar = str2double(data_trans(index,4))*1e-10; %m
mu = str2double(data_trans(index,5))*1e-21/299792458;
Zrot0 = str2double(data_trans(index,7));
kb = 1.3806488e-23; %J/K
NA = 6.02214076e23;
Tred = T./epsonk;
R = 8.3144621;
delta = 1/2*(mu./sqrt(epsonk.*kb.*lennar.^3)).^2;
cvtrans = 3/2*R;
index_type_0 = type==0;
index_type_1 = type==1;
index_type_2 = type==2;
cvrot = zeros(1,length(specie));
cvrot(index_type_0) = 0;
cvrot(index_type_1) = R;
cvrot(index_type_2) = 3/2*R;
cvrot = cvrot';
cv = ckm.thProp(specie,"cp",T,data) - R;
cvvib = cv-cvtrans-cvrot;
coll1_1 = collInt(1,Tred,delta);
coll1_1 = coll1_1';
pDii = 3/16*sqrt(2*pi*kb^3*(T^3)./(PM./2./NA))./(pi*lennar.^2.*coll1_1);
coll2_2 = collInt(2,Tred,delta);
coll2_2 = coll2_2';
vi = 5/16*sqrt(pi*PM.*kb*T/NA)./(pi*lennar.^2.*coll2_2);
fvib = PM./R/T.*pDii./vi;
A = 5/2 - fvib;
F = 1+(pi^1.5)./sqrt(Tred).*(0.5 + 1./Tred) + (0.25*pi*pi+2)./Tred;
Tred298 = 298./epsonk;
F298 = 1+(pi^1.5)./sqrt(Tred298).*(0.5 + 1./Tred298) + (0.25*pi*pi+2)./Tred298;
Zrot = Zrot0.*F298./F;
B = Zrot + 2/pi*(5/3*cvrot./R + fvib);
frot = fvib.*(1 + 2/pi*A./B);
ftrans = 5/2*(1 - 2/pi*cvrot./cvtrans.*A./B);
out = vi./PM.*(ftrans.*cvtrans + frot.*cvrot + fvib.*cvvib);
elseif prop == "diff"
PM = ckm.PM(specie,data); %molecular mass Kg/mol
[~,index] = ismember(specie,data_trans(:,1));
epsonk = reshape(str2double(data_trans(index,3)),size(specie)); %K
lennar = reshape(str2double(data_trans(index,4)),size(specie))*1e-10; %m
mu = reshape(str2double(data_trans(index,5)),size(specie))*1e-21/299792458;
alpha = reshape(str2double(data_trans(index,6)),size(specie))*1e-30;
out = zeros(size(specie,1),1);
kb = 1.3806488e-23; %J/K
NA = 6.02214076e23;
P = P*1e5; % [Pa] input in bar
index_alpha_0 = alpha==0;
polarity = (index_alpha_0(:,1)+index_alpha_0(:,2))==1; % 1=non polar + polar
for i = 1:length(polarity)
%if (alpha(i,1)==0 && alpha(i,2)~=0) || (alpha(i,2)==0 && alpha(i,1)~=0) %non polar + polar
if polarity(i)==1
% correction for non polar+polar
mij = (PM(i,1)*PM(i,2)/NA^2)/(PM(i,1)/NA+PM(i,2)/NA);
[alphan,inn] = min(alpha(i,:));
[~,inp] = max(alpha(i,:));
alphanred = alphan/lennar(i,inn)^3;
mupred = mu(i,inp)/sqrt(epsonk(i,inp)*kb*lennar(i,inp)^3);
mupredn = mu(i,inn)/sqrt(epsonk(i,inn)*kb*lennar(i,inn)^3);
roten = 1+1/4*alphanred*mupred*sqrt(max(epsonk(i,:))/min(epsonk(i,:)));
lennarij = 0.5*(lennar(i,1)+lennar(i,2))*roten^(-1/6);
epsonkij = roten^2*sqrt(epsonk(i,1)*epsonk(i,2));
Tred = T/epsonkij;
delta = 1/2*mupredn*mupred;
coll1_1ij = collInt(1,Tred,delta);
out(i) = 3/16*sqrt(2*pi*kb^3*T^3/(mij))/(pi*lennarij^2*coll1_1ij)/P;
else % non polar + non polar or polar + polar
lennarij = 0.5*(lennar(i,1)+lennar(i,2));
mij = (PM(i,1)*PM(i,2)/NA^2)/(PM(i,1)/NA+PM(i,2)/NA);
epsonkij = sqrt(epsonk(i,1)*epsonk(i,2));
Tred = T/epsonkij;
mupred = mu(i,:)./sqrt(epsonk(i,:).*kb.*lennar(i,:).^3);
delta = 1/2*mupred(1)*mupred(2);
coll1_1ij = collInt(1,Tred,delta);
out(i) = 3/16*sqrt(2*pi*kb^3*T^3/(mij))/(pi*lennarij^2*coll1_1ij)/P;
end
end
else
error('only vi,kt,diff supported and only 2 species at a time for diff coeff')
end
else
error('Choose fit or calc for fitted or calculated transport values')
end
function out = collInt(n,Tred,delta)
out = zeros(1,length(delta));
for k = 1:length(delta)
if n==1
if delta(k) == 0
cc1A = -1.1036729;
cc1B = [2.6431984 0.0060432255 -1.5158773/10 0.54237938/10 -0.90468682/100 0.61742007/1e3];
cc1C = [1.6690746 -6.9145890/10 1.5502132/10 -2.0642189/100 1.5402077/1e3 -0.49729535/1e4];
exponents = [1 2 3 4 5 6];
out(k) = cc1A + sum(cc1B./Tred(k).^exponents + cc1C.*log(Tred(k)).^exponents);
else
deltaV = [0.0, 0.25, 0.50, 0.75, 1.0, 1.5, 2.0, 2.5];
TredV = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0...
1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 3.5, 4.0...
5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0, 16.0...
18.0, 20.0, 25.0, 30.0, 35.0, 40.0, 50.0, 75.0, 100.0];
coll11 = [4.00791711465155 4.00187617260788 4.65606936416185 5.52115384615385 6.45158197507191 8.21333333333333 9.82889733840304 11.3130352045671
3.12989255564083 3.16267942583732 3.35496183206107 3.72053231939164 4.19791666666667 5.23004694835681 6.22607879924953 7.15977443609023
2.64940759399198 2.65791940018744 2.76981132075472 3.00284360189574 3.31852551984877 4.05337078651685 4.78618113912232 5.48459383753501
2.31437454279444 2.32014719411224 2.40111420612813 2.57156220767072 2.81273408239700 3.38604651162791 3.97217068645640 4.54081632653061
2.06613589070841 2.07377049180328 2.14062500000000 2.27777777777778 2.47217068645640 2.94547134935305 3.43819188191882 3.91974169741697
1.87662103746398 1.88496376811594 1.94343065693431 2.05968778696051 2.22559852670350 2.62809917355372 3.05412844036697 3.47339449541284
1.72935036890409 1.73803071364047 1.79090909090909 1.89223744292237 2.03568161024703 2.38721461187215 2.76277372262774 3.13698630136986
1.61221181556196 1.62149954832882 1.66969147005445 1.75978161965423 1.88524590163934 2.19727272727273 2.53454545454545 2.87170154686078
1.51749954898070 1.52712477396022 1.57259528130672 1.65304268846503 1.76566757493188 2.04343891402715 2.34932126696833 2.65670289855072
1.43984452680105 1.45018115942029 1.49048050770626 1.56391659111514 1.66485507246377 1.91696750902527 2.19567177637511 2.47833935018051
1.32041742286751 1.32940108892922 1.36355394378966 1.42443438914027 1.50858175248419 1.72032374100719 1.95605381165919 2.19820627802691
1.23359126081020 1.24203821656051 1.27157129881926 1.32336956521739 1.39350180505415 1.57309417040359 1.77747989276139 1.98928571428571
1.16788321167883 1.17609489051095 1.20200181983621 1.24569356300997 1.30595667870036 1.46057347670251 1.63960749330955 1.82651245551601
1.11660422187700 1.12420091324201 1.14558689717925 1.18511796733212 1.23646209386282 1.37153088630260 1.52983081032947 1.69804618117229
1.07526980062191 1.08226691042048 1.10209662716500 1.13520871143376 1.18066847335140 1.30017921146953 1.44078361531612 1.59131205673759
1.00064067362255 1.00548446069470 1.02005469462170 1.04640582347589 1.07963800904977 1.16950672645740 1.27782724844167 1.39646017699115
0.950064020486556 0.953424657534247 0.965360072926162 0.985441310282075 1.01177536231884 1.08176100628931 1.16755793226381 1.26483613817538
0.913070880526124 0.916058394160584 0.925318761384335 0.940909090909091 0.962828649138713 1.01888489208633 1.09025915996425 1.17036379769299
0.884523483812129 0.887146763901550 0.894449499545041 0.907447774750227 0.924818840579710 0.972072072072072 1.03130590339893 1.09769094138544
0.842738928798763 0.844636363636364 0.850136239782017 0.859618874773140 0.871312217194570 0.905405405405405 0.948028673835126 0.998219056099733
0.812843537414966 0.814052583862194 0.817934782608696 0.824796380090498 0.834538878842676 0.859909909909910 0.892825112107623 0.931311329170384
0.789791855203620 0.791040723981901 0.793851717902351 0.799006323396567 0.806407942238267 0.826372637263727 0.852466367713005 0.883303571428571
0.771125361271676 0.772267389340560 0.774368231046931 0.779061371841155 0.784761045987376 0.800449640287770 0.821883408071749 0.847363717605005
0.755522495717248 0.756357078449053 0.758701532912534 0.761801801801802 0.766426642664266 0.779694519317161 0.797757847533632 0.818588025022341
0.742189610155758 0.742664266426643 0.744644464446445 0.747794779477948 0.751438848920863 0.762387791741472 0.777419354838710 0.795442359249330
0.720237132848289 0.720287253141831 0.722282120395328 0.723967684021544 0.727199281867145 0.735515695067265 0.746374216651746 0.759964253798034
0.702555137170522 0.703139013452915 0.703584229390681 0.705376344086022 0.707795698924731 0.714055505819158 0.722808586762075 0.733214285714286
0.687737200143215 0.688182632050134 0.688988361683080 0.689803220035778 0.691681574239714 0.697137745974955 0.704021447721180 0.712767857142857
0.675111746826390 0.675067024128686 0.675781948168007 0.676943699731904 0.678462913315460 0.682931188561215 0.688482142857143 0.695539696699376
0.664023573533351 0.664107142857143 0.664732142857143 0.665625000000000 0.666964285714286 0.670115967885816 0.675200713648528 0.681105169340463
0.641379310344828 0.641711229946524 0.642067736185383 0.642691622103387 0.643582887700535 0.645592163846839 0.649065004452360 0.652935943060498
0.623472382815974 0.623754448398576 0.624021352313167 0.624466192170818 0.625088967971530 0.626957295373665 0.628977777777778 0.632177777777778
0.608801847410960 0.608792184724689 0.609058614564831 0.609325044404974 0.609857904085258 0.611278863232682 0.613232682060391 0.615630550621670
0.596398474230462 0.596628216503993 0.596805678793256 0.596983141082520 0.597426796805679 0.598314108251997 0.600000000000000 0.601418439716312
0.576250331946535 0.576106194690266 0.576283185840708 0.576371681415929 0.576637168141593 0.577345132743363 0.578230088495575 0.579805137289637
0.541467501543346 0.541534391534392 0.541710758377425 0.541409691629956 0.541585903083701 0.542151675485009 0.542151675485009 0.543021201413428
0.518039422738472 0.517941952506596 0.518381706244503 0.518453427065026 0.518261633011414 0.518541300527241 0.518469656992085 0.518502202643172];
[X,Y] = meshgrid(TredV,deltaV);
out(k) = interp2(X,Y,coll11',Tred(k),delta(k),"spline");
end
elseif n==2
if delta(k) == 0
exponents = [1 2 3 4 5 6];
cc2A = -0.92032979;
cc2B = [2.3508044 0.50110649 -4.7193769/10 1.5806367/10 -2.6367184/100 1.8120118/1e3];
cc2C = [1.6330213 -6.9795156/10 1.6096572/10 -2.2109440/100 1.7031434/1e3 -0.56699986/1e4];
out(k) = cc2A + sum(cc2B./Tred(k).^exponents + cc2C.*log(Tred(k)).^exponents);
else
deltaV = [0.0, 0.25, 0.50, 0.75, 1.0, 1.5, 2.0, 2.5];
TredV = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0...
1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 3.5, 4.0...
5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0, 16.0...
18.0, 20.0, 25.0, 30.0, 35.0, 40.0, 50.0, 75.0, 100.0];
coll22 = [4.1005, 4.266, 4.833, 5.742, 6.729, 8.624, 10.34, 11.89;
3.2626, 3.305, 3.516, 3.914, 4.433, 5.57, 6.637, 7.618;
2.8399, 2.836, 2.936, 3.168, 3.511, 4.329, 5.126, 5.874;
2.531, 2.522, 2.586, 2.749, 3.004, 3.64, 4.282, 4.895;
2.2837, 2.277, 2.329, 2.46, 2.665, 3.187, 3.727, 4.249;
2.0838, 2.081, 2.13, 2.243, 2.417, 2.862, 3.329, 3.786;
1.922, 1.924, 1.97, 2.072, 2.225, 2.614, 3.028, 3.435;
1.7902, 1.795, 1.84, 1.934, 2.07, 2.417, 2.788, 3.156;
1.6823, 1.689, 1.733, 1.82, 1.944, 2.258, 2.596, 2.933;
1.5929, 1.601, 1.644, 1.725, 1.838, 2.124, 2.435, 2.746;
1.4551, 1.465, 1.504, 1.574, 1.67, 1.913, 2.181, 2.451;
1.3551, 1.365, 1.4, 1.461, 1.544, 1.754, 1.989, 2.228;
1.28, 1.289, 1.321, 1.374, 1.447, 1.63, 1.838, 2.053;
1.2219, 1.231, 1.259, 1.306, 1.37, 1.532, 1.718, 1.912;
1.1757, 1.184, 1.209, 1.251, 1.307, 1.451, 1.618, 1.795;
1.0933, 1.1, 1.119, 1.15, 1.193, 1.304, 1.435, 1.578;
1.0388, 1.044, 1.059, 1.083, 1.117, 1.204, 1.31, 1.428;
0.99963, 1.004, 1.016, 1.035, 1.062, 1.133, 1.22, 1.319;
0.96988, 0.9732, 0.983, 0.9991, 1.021, 1.079, 1.153, 1.236;
0.92676, 0.9291, 0.936, 0.9473, 0.9628, 1.005, 1.058, 1.121;
0.89616, 0.8979, 0.903, 0.9114, 0.923, 0.9545, 0.9955, 1.044;
0.87272, 0.8741, 0.878, 0.8845, 0.8935, 0.9181, 0.9505, 0.9893;
0.85379, 0.8549, 0.858, 0.8632, 0.8703, 0.8901, 0.9164, 0.9482;
0.83795, 0.8388, 0.8414, 0.8456, 0.8515, 0.8678, 0.8895, 0.916;
0.82435, 0.8251, 0.8273, 0.8308, 0.8356, 0.8493, 0.8676, 0.8901;
0.80184, 0.8024, 0.8039, 0.8065, 0.8101, 0.8201, 0.8337, 0.8504;
0.78363, 0.784, 0.7852, 0.7872, 0.7899, 0.7976, 0.8081, 0.8212;
0.76834, 0.7687, 0.7696, 0.7712, 0.7733, 0.7794, 0.7878, 0.7983;
0.75518, 0.7554, 0.7562, 0.7575, 0.7592, 0.7642, 0.7711, 0.7797;
0.74364, 0.7438, 0.7445, 0.7455, 0.747, 0.7512, 0.7569, 0.7642;
0.71982, 0.72, 0.7204, 0.7211, 0.7221, 0.725, 0.7289, 0.7339;
0.70097, 0.7011, 0.7014, 0.7019, 0.7026, 0.7047, 0.7076, 0.7112;
0.68545, 0.6855, 0.6858, 0.6861, 0.6867, 0.6883, 0.6905, 0.6932;
0.67232, 0.6724, 0.6726, 0.6728, 0.6733, 0.6743, 0.6762, 0.6784;
0.65099, 0.651, 0.6512, 0.6513, 0.6516, 0.6524, 0.6534, 0.6546;
0.61397, 0.6141, 0.6143, 0.6145, 0.6147, 0.6148, 0.6148, 0.6147;
0.5887, 0.5889, 0.5894, 0.59, 0.5903, 0.5901, 0.5895, 0.5885];
% Astar = [1.0231, 1.0660, 1.0380, 1.0400, 1.0430, 1.0500, 1.0520, 1.0510;
% 1.0424, 1.0450, 1.0480, 1.0520, 1.0560, 1.0650, 1.0660, 1.0640;
% 1.0719, 1.0670, 1.0600, 1.0550, 1.0580, 1.0680, 1.0710, 1.0710;
% 1.0936, 1.0870, 1.0770, 1.0690, 1.0680, 1.0750, 1.0780, 1.0780;
% 1.1053, 1.0980, 1.0880, 1.0800, 1.0780, 1.0820, 1.0840, 1.0840;
% 1.1104, 1.1040, 1.0960, 1.0890, 1.0860, 1.0890, 1.0900, 1.0900;
% 1.1114, 1.1070, 1.1000, 1.0950, 1.0930, 1.0950, 1.0960, 1.0950;
% 1.1104, 1.1070, 1.1020, 1.0990, 1.0980, 1.1000, 1.1000, 1.0990;
% 1.1086, 1.1060, 1.1020, 1.1010, 1.1010, 1.1050, 1.1050, 1.1040;
% 1.1063, 1.1040, 1.1030, 1.1030, 1.1040, 1.1080, 1.1090, 1.1080;
% 1.1020, 1.1020, 1.1030, 1.1050, 1.1070, 1.1120, 1.1150, 1.1150;
% 1.0985, 1.0990, 1.1010, 1.1040, 1.1080, 1.1150, 1.1190, 1.1200;
% 1.0960, 1.0960, 1.0990, 1.1030, 1.1080, 1.1160, 1.1210, 1.1240;
% 1.0943, 1.0950, 1.0990, 1.1020, 1.1080, 1.1170, 1.1230, 1.1260;
% 1.0934, 1.0940, 1.0970, 1.1020, 1.1070, 1.1160, 1.1230, 1.1280;
% 1.0926, 1.0940, 1.0970, 1.0990, 1.1050, 1.1150, 1.1230, 1.1300;
% 1.0934, 1.0950, 1.0970, 1.0990, 1.1040, 1.1130, 1.1220, 1.1290;
% 1.0948, 1.0960, 1.0980, 1.1000, 1.1030, 1.1120, 1.1190, 1.1270;
% 1.0965, 1.0970, 1.0990, 1.1010, 1.1040, 1.1100, 1.1180, 1.1260;
% 1.0997, 1.1000, 1.1010, 1.1020, 1.1050, 1.1100, 1.1160, 1.1230;
% 1.1025, 1.1030, 1.1040, 1.1050, 1.1060, 1.1100, 1.1150, 1.1210;
% 1.1050, 1.1050, 1.1060, 1.1070, 1.1080, 1.1110, 1.1150, 1.1200;
% 1.1072, 1.1070, 1.1080, 1.1080, 1.1090, 1.1120, 1.1150, 1.1190;
% 1.1091, 1.1090, 1.1090, 1.1100, 1.1110, 1.1130, 1.1150, 1.1190;
% 1.1107, 1.1110, 1.1110, 1.1110, 1.1120, 1.1140, 1.1160, 1.1190;
% 1.1133, 1.1140, 1.1130, 1.1140, 1.1140, 1.1150, 1.1170, 1.1190;
% 1.1154, 1.1150, 1.1160, 1.1160, 1.1160, 1.1170, 1.1180, 1.1200;
% 1.1172, 1.1170, 1.1170, 1.1180, 1.1180, 1.1180, 1.1190, 1.1200;
% 1.1186, 1.1190, 1.1190, 1.1190, 1.1190, 1.1190, 1.1200, 1.1210;
% 1.1199, 1.1200, 1.1200, 1.1200, 1.1200, 1.1210, 1.1210, 1.1220;
% 1.1223, 1.1220, 1.1220, 1.1220, 1.1220, 1.1230, 1.1230, 1.1240;
% 1.1243, 1.1240, 1.1240, 1.1240, 1.1240, 1.1240, 1.1250, 1.1250;
% 1.1259, 1.1260, 1.1260, 1.1260, 1.1260, 1.1260, 1.1260, 1.1260;
% 1.1273, 1.1270, 1.1270, 1.1270, 1.1270, 1.1270, 1.1270, 1.1280;
% 1.1297, 1.1300, 1.1300, 1.1300, 1.1300, 1.1300, 1.1300, 1.1290;
% 1.1339, 1.1340, 1.1340, 1.1350, 1.1350, 1.1340, 1.1340, 1.1320;
% 1.1364, 1.1370, 1.1370, 1.1380, 1.1390, 1.1380, 1.1370, 1.1350];
[X,Y] = meshgrid(TredV,deltaV);
out(k) = interp2(X,Y,coll22',Tred(k),delta(k),"spline");
end
end
end
end
end