Contents

Size the channels for heat transfer with He/Xe

Create a set of circumferential channels around the fusion region. Compute the flow rate to achieve the desired temperatures.

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% See also: HeatTransferChannel
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%	Copyright (c) 2017 Princeton Satellite Systems, Inc.
%   All rights reserved.
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Inputs

Waste heat, for a 1.1 MW fusion reactor

Q = 0.61e6;       % W
l = 1.5;          % length of radiating plasma, m
r = 0.35;         % radius of inner wall, m

nChannels = 20;   % how many ducts

tIn  = 300;       % inlet (cold) temperature
tOut = 1589;      % out temperature, GE ceramic blades
pR   = 2;         % inlet pressure, ATM

gas  = {'xe', 0.3, 'he', 0.7};
cP   = 494;       % 70/30 He/Xe, specific heat/pressure
cV   = 300;       % 70/30 He/Xe, specific heat/volume

Calculate heat per channel

This assumes the flux is uniform around the channel perimeter.

c = 2*pi*r;             % circumference
w = c/nChannels;        % channel width
h = 0.5*w;              % channel height
q = Q/nChannels;        % wall loading, W/m, per channel

d = struct( 'name',     'Helium/Xenon 70/30',...
            'length',   l,...       % m
            'w',        w,...       % m
            'h',        h,...       % m
            'q',        q,...       % MW
            'cP',       cP,...     % J/kg-K
            'gamma',    cP/cV,...   % ratio
            'kC',       0,...       %
            'kE',       0,...       %
            'tInlet',   tIn,...     % K
            'tOutlet',  tOut,...    % K
            'tube',     'square',...
            'pressure', pR	);        % ATM

d.gas = gas;

[out, ltx] = HeatTransferChannel( d, true );

k = size(ltx,1)+1;
ltx{k,1} = 'Total $\dot{m}$';
ltx{k,2} = sprintf('%12.2e',nChannels*out.mDot);
ltx{k,3} = 'kg/s';
fprintf(1,'\n\n');
DisplayLatexTable(ltx);

       Gas Helium/Xenon 70/30          
    height               5.50       cm 
     width              11.00       cm 
         Q           45750.00        W 
     $C_p$             494.00   J/kg-K 
  $\gamma$               1.65          
     $T_i$             300.00        K 
     $T_o$            1589.00        K 
 $\dot{m}$           0.047898     kg/s 
  $\rho_o$               3.48 kg/m$^3$ 
  $\rho_i$               0.66 kg/m$^3$ 
     $a_c$              60.45   cm$^2$ 
       $u$              12.05      m/s 
         q           30500.00        W 
$\Delta P$          -2.45e-04      Atm 
      Tube             square          


            Gas Helium/Xenon 70/30          
         height               5.50       cm 
          width              11.00       cm 
              Q           45750.00        W 
          $C_p$             494.00   J/kg-K 
       $\gamma$               1.65          
          $T_i$             300.00        K 
          $T_o$            1589.00        K 
      $\dot{m}$           0.047898     kg/s 
       $\rho_o$               3.48 kg/m$^3$ 
       $\rho_i$               0.66 kg/m$^3$ 
          $a_c$              60.45   cm$^2$ 
            $u$              12.05      m/s 
              q           30500.00        W 
     $\Delta P$          -2.45e-04      Atm 
           Tube             square          
Total $\dot{m}$           9.58e-01     kg/s 

Flow rate and pressure as a function of heat

Keep the channel size the same, how does the flow vary?

qs = linspace(0.5*q,2*q);
for k = 1:length(qs)
  d.q = qs(k);
  out = HeatTransferChannel( d );
  us(k) = out.u;
  mDots(k) = out.mDot;
end
Plot2D(qs,[us;mDots;nChannels*mDots],'Channel Heat Flux (W/m)',...
  {'Flow Speed (m/s)','Mass Flow (kg/s)','Total Mass Flow'},'Channel Flow')


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Published with MATLAB® R2020a