Contents
Study the heat exchanger between the plasma and the magnets
The heat exchanger is modeled as a flat plate with a uniform flux q on one side and a cooling gas flow. The other side has radiation heat loss. In this case, we model the wall with layers for turbulent gas flow, a ceramic wall, and an MLI blanket.
%-------------------------------------------------------------------------- % See also RFromCPAndGamma, HeatExchangerWithLosses, HeatTransferCoeff, % KinematicViscosity, NusseltTurbulent, PrandtlNumber, % ReynoldsNumberKinematic, OptimalMLIDensity %-------------------------------------------------------------------------- %-------------------------------------------------------------------------- % Copyright (c) 2018 Princeton Satellite Systems, Inc. % All rights reserved. %-------------------------------------------------------------------------- d = HeatExchangerWithLosses; % Compute the thermal conductivity with an MLI blanket tH = 1589; % hot end d.tB0 = 300; % cold end d.qDot = 10787; % W/m, this is for one channel % approximate conductivity of a 4 mm ceramic wall kW = 20.7; % W/m K % SJT: source? % thermal conductance kW = kW/0.004; % W/m^2 K % turbulent flow heat exchanger % Assume a mix of 70% He and 30% Xe gamma = d.cP/300; % SJT: what is 300? u = 8.8; % m/s (??) should this be computed? % SJT: memo says 2 ATM but an ATM is 14.7 psi. 6895 is psi to N/m2 p = 2*14.7*6895; % 2 psi to N/m2 mu = 5.95e-5; % (??) viscosity, kg/m-s r1 = 0.3; % wall radius (m) kF = 0.0262; % conductivity (W/m-K) ?? R = RFromCPAndGamma(d.cP,gamma); rho = p/(R*d.tB0); nu = KinematicViscosity( mu, rho ); pR = PrandtlNumber( mu, d.cP, kF ); rE = ReynoldsNumberKinematic( u, 2*r1, nu ); nU = NusseltTurbulent( rE, pR ); h = HeatTransferCoeff( nU, kF, 2*r1 ); % W/m^2 K % MLI - compute layers/cm and total conductance dMLI = OptimalMLIDensity; dMLI.n = 200; % number of layers [nD,~,kMLI] = OptimalMLIDensity(tH,d.tB0,dMLI); % sum the thermal conductances % SJT: conductance or conductivity??? d.k = 1/(1/kW + 1/h + 1/kMLI); % assumed mass flow rate d.mDot = 0.2; % kg/s % calculate the temperatures and fluxes % NOTE: header says input k is thermal conductivity [tB,tS4,q4] = HeatExchangerWithLosses( d );
Display output
disp('----') disp('Fusion Heat Exchanger Design') disp('----') fprintf('Input heat flux: %g W/m\n',d.qDot) fprintf('Flow rate: %g kg/s\n\n',d.mDot) fprintf(1,"Thickness of MLI blanket = %.2f cm\n",dMLI.n/nD); fprintf('Thermal conductance wall: %g W/m2 deg-K\n',kW) fprintf('Thermal conductance MLI: %g W/m2 deg-K\n',kMLI) fprintf('Thermal conductance flow: %g W/m2 deg-K\n',h) fprintf('Total conductance: %g W/m2 deg-K\n',d.k) fprintf('Max radiative flux: %g W/m2\n',max(q4)) fprintf('Start/end wall temps: %g, %g K\n',tS4(1),tS4(end)) fprintf('Start/end gas temps: %g, %g K\n',tB(1),tB(end)) %--------------------------------------
---- Fusion Heat Exchanger Design ---- Input heat flux: 10787 W/m Flow rate: 0.2 kg/s Thickness of MLI blanket = 2.27 cm Thermal conductance wall: 5175 W/m2 deg-K Thermal conductance MLI: 0.133934 W/m2 deg-K Thermal conductance flow: 31.7535 W/m2 deg-K Total conductance: 0.133368 W/m2 deg-K Max radiative flux: 175.859 W/m2 Start/end wall temps: 139.411, 235.991 K Start/end gas temps: 300, 1554.59 K