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242 lines
8.8 KiB
Matlab
242 lines
8.8 KiB
Matlab
classdef CounterFlowDiffusionFlame < Sim1D
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% Create a counter flow diffusion flame stack. ::
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%
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% >> flame = CounterFlowDiffusionFlame(left, flow, right, tp_f, tp_o, oxidizer)
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%
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% :param left:
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% Object representing the left inlet, which must be
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% created using function :mat:class:`Inlet`.
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% :param flow:
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% Object representing the flow, created with
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% function :mat:class:`AxisymmetricFlow`.
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% :param right:
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% Object representing the right inlet, which must be
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% created using function :mat:class:`Inlet`.
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% :param tp_f:
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% Object representing the fuel inlet gas, instance of class
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% :mat:class:`Solution`, and an ideal gas.
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% :param tp_o:
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% Object representing the oxidizer inlet gas, instance of class
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% :mat:class:`Solution`, and an ideal gas.
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% :param oxidizer:
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% String representing the oxidizer species. Most commonly O2.
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% :return:
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% Instance of :mat:class:`CounterFlowDiffusionFlame` object
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% representing the left inlet, flow, and right inlet.
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methods
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function flame = CounterFlowDiffusionFlame(left, flow, right, ...
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tp_f, tp_o, oxidizer)
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% Constructor
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%% Check input parameters
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if nargin ~= 6
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error('CounterFlowDiffusionFlame expects six input arguments.');
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end
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if ~tp_f.isIdealGas
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error('Fuel gas object must represent an ideal gas mixture.');
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end
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if ~tp_o.isIdealGas
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error('Oxidizer gas object must represent an ideal gas mixture.');
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end
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if ~isa(left, 'Inlet')
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error('Left inlet object of wrong type.');
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end
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if ~isa(flow, 'Flow1D')
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error('Flow object of wrong type.');
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end
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if ~isa(right, 'Inlet')
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error('Right inlet object of wrong type.');
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end
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if ~ischar(oxidizer)
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error('Oxidizer name must be of format character.');
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end
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%% Define elMoles function
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function moles = elMoles(tp, element)
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% Determine the elemental moles in a gas object per unit mass.
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% Check input parameters
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if nargin ~= 2
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error('elMoles expects two input arguments.');
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end
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if ~tp.isIdealGas
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error('Gas object must represent an ideal gas mixture.');
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end
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if ~ischar(element)
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error('Element name must be of format character.');
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end
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% Calculate the moles per mass of mixture of an element within a gas
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% object. The equation used is:
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%
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% elMoles = elMassFrac/Mel
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%
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% where elMassFrac is the elemental mass fraction within the gas object
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% using the elementalMassFraction function; Mel is the atomic mass of
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% the element.
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elMassFrac = tp.elementalMassFraction(element);
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eli = tp.elementIndex(element);
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M = tp.atomicMasses;
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Mel = M(eli);
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moles = elMassFrac / Mel;
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end
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%% Get the density of both fuel and oxidizer streams.
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% To be used in determining velocity of each stream. Also get the
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% temperature of both inlet streams.
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rhof = tp_f.D;
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rho0 = tp_o.D;
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tf = left.T;
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tox = right.T;
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%% Find the species index of the oxidizer.
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% To be used in determining initial strain rate.
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ioxidizer = tp_o.speciesIndex(oxidizer);
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%% Calculate the stoichiometric mixture fraction.
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% Needed for determining location of flame edges and composition.
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% elMoles function used to calculate the number of moles of C, H, and O
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% atoms in the fuel and oxidizer streams:
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%
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% elMoles = elementalMassFraction/element atomic weight.
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%
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% From this, the stoichiometric Air/Fuel ratio can be determined.
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% 1 Mole of O needs 2 Moles of C and 0.5 Moles of H for stoichiometric
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% conditions. The stoichiometric mixture fraction, Zst, is then
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% calculated.
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sFuel = elMoles(tp_f, 'O') - 2 * elMoles(tp_f, 'C') - ...
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0.5 * elMoles(tp_f, 'H');
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sOx = elMoles(tp_o, 'O') - 2 * elMoles(tp_o, 'C') - ...
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0.5 * elMoles(tp_o, 'H');
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phi = sFuel / sOx;
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zst = 1.0 / (1.0 - phi);
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%% Compute the stoichiometric mass fractions of each species.
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% Use this to set the fuel gas object and calculate adiabatic flame
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% temperature and equilibrium composition.
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spec = tp_f.speciesNames; % Get all of the species names in gas object.
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nsp = tp_f.nSpecies; % Get total number of species in gas object.
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% Get the current mass fractions of both fuel and inlet streams.
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yox = tp_o.Y;
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yf = tp_f.Y;
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ystoich_double = zeros(1, nsp); % Create empty vector for stoich mass frac.
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for n = 1:nsp
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% Calculate stoichiometric mass fractions.
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ystoich_double(n) = zst * yf(n) + (1.0 - zst) * yox(n);
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% Convert mass fraction vector to string vector.
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ystoich_str{n} = num2str(ystoich_double(n));
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% Convert string vector to cell with SPECIES:MASS FRACTION format.
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y_stoich{n} = [spec{n}, ':', ystoich_str{n}];
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end
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% Initialize stoichiometric mass fraction cell with first SP:Y value.
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ystoich = [y_stoich{1}];
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for i = 2:nsp
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% Update cell to have format similar to N2:Yst,O2:Yst,...
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ystoich = [ystoich ',', y_stoich{i}];
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end
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% Set the fuel gas object as stoichiometric values and use equilibrate
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% function to determine stoichiometric equilibrium temperature and mass
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% fractions.
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tp_f.TPY = {tf, tp_f.P, ystoich};
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tp_f.equilibrate('HP');
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teq = tp_f.T;
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yeq = tp_f.Y;
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%% Estimate the strain rate.
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% Based on the inlet stream velocities and determine initial 'guess'
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% for mixture fraction based on mass flux ratio.
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zz = flow.gridPoints;
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dz = zz(end) - zz(1);
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mdotl = left.massFlux;
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mdotr = right.massFlux;
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uleft = mdotl / rhof;
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uright = mdotr / rho0;
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a = (abs(uleft) + abs(uright)) / dz;
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diff = tp_f.mixDiffCoeffs;
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f = sqrt(a / (2.0 * diff(ioxidizer)));
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x0num = sqrt(uleft * mdotl) * dz;
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x0den = sqrt(uleft * mdotr) + sqrt(uright * mdotr);
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x0 = x0num / x0den;
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%% Calculate initial values of temperature and mass fractions.
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% These values to be used for energy equation solution. Method is based
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% on the Burke-Schumann model.
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nz = flow.nPoints;
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zm = zeros(1, nz);
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u = zeros(1, nz);
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v = zeros(1, nz);
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y = zeros(nz, nsp);
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t = zeros(1, nz);
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for j = 1:nz
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x = zz(j);
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zeta = f * (x - x0);
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zmix = 0.5 * (1.0 - erf(zeta)); % Mixture fraction in flame.
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zm(j) = zmix;
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u(j) = a * (x0 - zz(j)); % Axial velocity.
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v(j) = a; % Radial velocity.
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if zmix > zst
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for n = 1:nsp
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y(j, n) = yeq(n) + (zmix - zst) * (yf(n) - yeq(n)) /...
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(1.0 - zst);
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end
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t(j) = teq + (tf - teq) * (zmix - zst) / (1.0 - zst);
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else
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for n = 1:nsp
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y(j, n) = yox(n) + zmix * (yeq(n) - yox(n)) / zst;
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end
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t(j) = tox + zmix * (teq - tox) / zst;
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end
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end
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zrel = zz / dz;
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%% Create the flame stack.
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% Set the profile of the flame with the estimated axial velocities,
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% radial velocities, temperature, and mass fractions calculated above.
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flame@Sim1D({left flow right});
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flame.setProfile(2, {'velocity', 'spread_rate'}, [zrel; u; v]);
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flame.setProfile(2, 'T', [zrel; t]);
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for n = 1:nsp
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nm = tp_f.speciesName(n);
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flame.setProfile(2, nm, [zrel; transpose(y(:, n))]);
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end
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end
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end
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end
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