Regenerator functions

The regenerator connects the heater and cooler, hence in addition to evaluating the heat transfer from the regenerator matrix to the working gas, it is necessary to determine the conduction heat leakage through the regenerator housing. The housing can either be tubular or annular, and this learning resource includes two regenerator matrix types, either wire mesh matrix (as in the Ford-Philips 4-215 engine) or a wrapped foil matrix (as in the D-90 Ross Yoke-drive engine). We also consider the case of no regenerator matrix, in which the wetted area of the housing takes the role of the regenerator matrix (as in the Lehmann engine analyzed by Schmidt). The purpose of the regenerator functions is to specify values for the global variables subsequently used in the Schmidt analysis, Ideal Adiabatic or Simple simulations. Each global variable has the subscript r for heater and k for cooler (subscript c is used for compression space in the engine routines). The variables are defined as follows:

vr = void volume (cu.m) - used only in the Schmidt and Ideal Adiabatic functions
The following variables are used only in the Simple simulation.
lr = regenerator effective length (m)
cqwr = regenerator housing thermal conductance (W/K)
ar = regenerator internal free flow area (sq.m)
awgr0 = no matrix regenerator wetted area (sq.m)
awgr = regenerator wetted area (sq.m)
dr = regenerator hydraulic diameter (m) – refer to Chapter 5a - Scaling Parameters

The following five MATLAB functions in the regen.m function module specify all the above global variable values.

function regen
% Specifies regenerator geometric and thermal properties
% Israel Urieli 04/20/02 (modified 12/01/03)
% modified 2/12/2010 to include awgr0 (wetted area)
% modified 11/27/2010 to include 'no regenerator matrix'
global lr % regenerator effective length [m]
global awgr0 % no matrix regenerator wetted area [m^2]
global cqwr % regenerator housing thermal conductance [W/K]
global new fid % new data file
regen_type = 'u';
while(strncmp(regen_type,'u',1))
    if(strncmp(new,'y',1))
        fprintf('Available regenerator configurations are:\n')
        fprintf('   t, for tubular regenerator set\n')
        fprintf('   a, for annular regenerator\n')
        regen_type = input('enter regenerator configuration ','s');
        fprintf(fid, '%c\n', regen_type(1));
    else
        fscanf(fid, '%c',1); % bypass the previous newline character
        regen_type = fscanf(fid, '%c',1);
    end
    if(strncmp(regen_type,'t',1))
        printf('tubular regenerator housing\n')
        if(strncmp(new,'y',1))
            dout = input('enter tube housing external diameter [m] : ');
            domat = input('enter tube housing internal diameter [m] : ');
            lr = input('enter regenerator length [m] : ');
            num = input('enter number of tubes : ');
            fprintf(fid, '%.3e\n', dout);
            fprintf(fid, '%.3e\n', domat);
            fprintf(fid, '%.3e\n', lr);
            fprintf(fid, '%d\n', num);
        else
            dout = fscanf(fid, '%e',1);
            domat = fscanf(fid, '%e',1);
            lr = fscanf(fid, '%e',1);
            num = fscanf(fid, '%d',1);
        end
        dimat = 0; 
        awgr0 = num*pi*domat*lr;
    elseif(strncmp(regen_type,'a',1)) 
        fprintf('annular regenerator housing\n')
        if(strncmp(new,'y',1))
            dout = input('enter housing external diameter [m] : ');
            domat = input('enter housing internal diameter [m] : ');
            dimat = input('enter matrix internal diameter [m] : ');
            lr = input('enter regenerator length [m] : ');
            fprintf(fid, '%.3e\n', dout);
            fprintf(fid, '%.3e\n', domat);
            fprintf(fid, '%.3e\n', dimat);
            fprintf(fid, '%.3e\n', lr);
        else
            dout = fscanf(fid, '%e',1);
            domat = fscanf(fid, '%e',1);
            dimat = fscanf(fid, '%e',1);
            lr = fscanf(fid, '%e',1);
        end
        num = 1;
        awgr0 = pi*(dimat + domat)*lr;
    else
        fprintf('regenerator configuration is undefined\n')
        regen_type = 'u';
    end
end
amat = num*pi*(domat*domat - dimat*dimat)/4; % regen matrix area
awr = num*pi*(dout*dout - domat*domat)/4; % regen housing wall area
%########temporary fix (4/20/02):
kwr = 25; % thermal conductivity [W/m/K]
% note that stainless steel thermal conductivity is temp dependent
%   25 W/m/K for normal engine conditions,
%    6 W/m/K for cryogenic coolers.
cqwr = kwr*awr/lr; % regen wall thermal conductance [W/K]
matrix(amat);
%===============================================================
function matrix(amat)
% Specifies regenerator matrix geometric and thermal properties
% Israel Urieli 03/31/02
% modified 11/27/10 for no regenerator matrix

global matrix_type % m)esh, f)oil or n)o matrix
global new fid % new data file

matrix_type = 'u';
while(strncmp(matrix_type,'u',1))
     if(strncmp(new,'y',1))
         fprintf('Available matrix types are:\n')
         fprintf('   m, for mesh matrix\n')
         fprintf('   f, for foil matrix\n')
         fprintf('   n, for no matrix\n')
         matrix_type = input('enter matrix type ','s');
         fprintf(fid, '%c\n', matrix_type(1));
     else
         fscanf(fid, '%c',1); % bypass the previous newline character
         matrix_type = fscanf(fid, '%c',1);
     end
     if(strncmp(matrix_type,'m',1))
         mesh(amat); 
     elseif(strncmp(matrix_type,'f',1))
         foil(amat); 
     elseif(strncmp(matrix_type,'n',1)) 
         nomatrix(amat); 
     else        
         fprintf('matrix configuration is undefined\n')
         matrix_type = 'u';
     end
end
%===============================================================
function mesh(amat)
% Specifies mesh matrix geometric and thermal properties
% Israel Urieli 03/31/02
global vr % regen void volume [m^3]
global ar % regen internal free flow area [m^2]
global awgr % regen internal wetted area [m^2]
global awgr0 % no matrix regenerator wetted area [m^2]
global lr % regenerator effective length [m]
global dr % regen hydraulic diameter [m]
global new fid % new data file
fprintf(' stacked wire mesh matrix\n')
if(strncmp(new,'y',1))
    porosity = input('enter matrix porosity : ');
    dwire = input('enter matrix wire diameter [m] : ');
    fprintf(fid, '%.3f\n', porosity);
    fprintf(fid, '%.3e\n', dwire);
else
    porosity = fscanf(fid,'%f',1);
    dwire = fscanf(fid,'%e',1);
end
ar = amat*porosity;
vr = ar*lr;
dr = dwire*porosity/(1 - porosity);
awgr = 4*vr/dr + awgr0;
fprintf(' matrix porosity: %.3f\n', porosity)
fprintf(' matrix wire diam %.2f(mm)\n', dwire*1e3)
fprintf(' hydraulic diam %.3f(mm)\n', dr*1e3)
fprintf(' total wetted area %.3e(sq.m)\n', awgr)
fprintf(' regenerator length %.1f(mm)\n', lr*1e3)
fprintf(' void volume %.2f(cc)\n', vr*1e6)
%===============================================================
function foil(amat)
% Specifies foil matrix geometric and thermal properties
% Israel Urieli 03/31/02
global vr % regen void volume [m^3]
global ar % regen internal free flow area [m^2]
global awgr % regen internal wetted area [m^2]
global awgr0 % no matrix regenerator wetted area [m^2]
global lr % regenerator effective length [m]
global dr % regen hydraulic diameter [m]
global new fid % new data file
fprintf(' wrapped foil matrix\n')
if(strncmp(new,'y',1))
    fl = input('enter unrolled length of foil [m] : ');
    th = input('enter foil thickness [m] : ');
    fprintf(fid, '%.3f\n', fl);
    fprintf(fid, '%.3e\n', th);
else
    fl = fscanf(fid,'%f',1);
    th = fscanf(fid,'%e',1);
end
am = th*fl;
ar = amat - am;
vr = ar*lr;
awgr = 2*lr*fl + awgr0;
dr = 4*vr/awgr;
porosity = ar/amat;
fprintf(' unrolled foil length: %.3f(m)\n', fl)
fprintf(' foil thickness %.3f(mm)\n',th*1e3)
fprintf(' hydraulic diam %.3f(mm)\n', dr*1e3)
fprintf(' total wetted area %f(sq.m)\n', awgr)
fprintf(' void volume %.2f(cc)\n', vr*1e6)
fprintf(' porosity %.3f\n', porosity)
%===============================================================
function nomatrix(amat)
% Specifies conditions for no regenerator matrix
% Israel Urieli 11/27/10
global vr % regen void volume [m^3]
global ar % regen internal free flow area [m^2]
global awgr % regen internal wetted area [m^2]
global awgr0 % no matrix regenerator wetted area [m^2]
global lr % regenerator effective length [m]
global dr % regen hydraulic diameter [m]
fprintf(' no regenerator matrix\n')
ar = amat;
vr = ar*lr;
awgr = awgr0;
dr = 4*vr/awgr;
fprintf(' hydraulic diam %.3f(mm)\n', dr*1e3)
fprintf(' total wetted area %f(sq.m)\n', awgr)
fprintf(' void volume %.2f(cc)\n', vr*1e6)
%===============================================================

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Stirling Cycle Machine Analysis by Israel Urieli is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License