Daily Archives: May 19, 2016

Finally Solving the Matrix

Posted on May 19, 2016 by R.P. Churchill

Once we get all the parameters calculated and the matrix loaded, then we can finally solve the thing. Here’s how the code looks:

    function loadMatrix(index,fceTemp)
    {
      var i; var j; var k;
      var tsa; var tfa; var ts3; var tf4;

      tfa = arrayTfce[index] + Tabs;
      tf4 = tfa * tfa * tfa * tfa;

      for (k = 0; k <= sizeNodes; k++)
      {
        ZSRCE[k] = 0.0;
        ZAUX[k] = 0.0;
        for (i = 0; i <= sizeBandWidth; i++)
          ZMATX[k][i] = 0.0;
      }

      k = 0;
      for (j = 0; j < nodesHigh; j++)
        for (i = 0; i < nodesWide; i++)
        {
          k++;

          //nodal energy
          ZMATX[k][1] += arrayRho[i][j] * arrayCp[i][j];
          ZSRCE[k] += arrayRho[i][j] * arrayCp[i][j] * arrayT[i][j];

          //conduction to right
          if (arrayKright[i][j] > 0.0)
          {
            ZMATX[k][1] += arrayKright[i][j];
            ZMATX[k][2] -= arrayKright[i][j];
            ZMATX[k+1][1] += arrayKright[i][j];
          }

          //conduction up
          if (arrayKup[i][j] > 0.0)
          {
            ZMATX[k][1] += arrayKup[i][j];
            ZMATX[k][1+nodesWide] -= arrayKup[i][j];
            ZMATX[k+nodesWide][1] += arrayKup[i][j];
          }

          //radiation
          if (arrayRad[i][j] > 0.0)
          {
            tsa = arrayT[i][j];
            ts3 = tsa * tsa * tsa;
            ZMATX[k][1] += arrayRad[i][j] * ts3;
            ZSRCE[k] += arrayRad[i][j] * tf4;
          }

        }
    }     //loadMatrix

    function oneCalc(index) {
      calcParams(index);

      for (var i=0; i<nodesWide; i++) {
        for (var j=0; j<nodesHigh; j++) {
          arrayT[i][j] = arrayTpieces[index][i][j] + Tabs;
        }
      }
      
      loadMatrix(index);
      calcMatrix();
      
      k = 0;
      for (var j=0; j<nodesHigh; j++) {
        for (var i=0; i<nodesWide; i++) {
          k++;
          arrayTpieces[index][i][j] = ZSRCE[k] - Tabs;
        }
      }
    }  //oneCalc

    var loopCount = 0;
    
    var s="Temperatures after "+loopCount+" time steps<br />";
    for (var j=nodesHigh-1; j>=0; j--) {
      for (var i=0; i<=nodesWide-1; i++) {
        s += arrayTpieces[0][i][j].toPrecision(7) + ", ";
      }
      s += "<br />";
    }
    document.getElementById("stuff").innerHTML = s;

    function runOneTime() {
      if (loopCount == 0) {
        for (var i=0; i< pieceCount; i++) {
          for (var j=0; j<nodesWide; j++) {
            for (var k=0; k<nodesHigh; k++) {
              arrayTpieces[i][j][k] = 70.0;
            }
          }
        }
      } else {
        oneCalc(0);
      }
      var s="Temperatures after "+loopCount+" time steps<br />";
      for (var j=nodesHigh-1; j>=0; j--) {
        for (var i=0; i<=nodesWide-1; i++) {
          s += arrayTpieces[0][i][j].toPrecision(7) + ", ";
        }
        s += "<br />";
      }
      document.getElementById("stuff").innerHTML = s;
      loopCount++;
      if (loopCount > 20) {
        loopCount = 0;
      }
    }

    var intervalID = setInterval(runOneTime, 1000);

100

101

102

103

104

105

106

107

108

109

110

111

112

113

function loadMatrix(index,fceTemp)

{

var i; var j; var k;

var tsa; var tfa; var ts3; var tf4;

tfa = arrayTfce[index] + Tabs;

tf4 = tfa * tfa * tfa * tfa;

for (k = 0; k <= sizeNodes; k++)

{

ZSRCE[k] = 0.0;

ZAUX[k] = 0.0;

for (i = 0; i <= sizeBandWidth; i++)

ZMATX[k][i] = 0.0;

}

k = 0;

for (j = 0; j < nodesHigh; j++)

for (i = 0; i < nodesWide; i++)

{

k++;

//nodal energy

ZMATX[k][1] += arrayRho[i][j] * arrayCp[i][j];

ZSRCE[k] += arrayRho[i][j] * arrayCp[i][j] * arrayT[i][j];

//conduction to right

if (arrayKright[i][j] > 0.0)

{

ZMATX[k][1] += arrayKright[i][j];

ZMATX[k][2] -= arrayKright[i][j];

ZMATX[k+1][1] += arrayKright[i][j];

}

//conduction up

if (arrayKup[i][j] > 0.0)

{

ZMATX[k][1] += arrayKup[i][j];

ZMATX[k][1+nodesWide] -= arrayKup[i][j];

ZMATX[k+nodesWide][1] += arrayKup[i][j];

}

//radiation

if (arrayRad[i][j] > 0.0)

{

tsa = arrayT[i][j];

ts3 = tsa * tsa * tsa;

ZMATX[k][1] += arrayRad[i][j] * ts3;

ZSRCE[k] += arrayRad[i][j] * tf4;

}

} //loadMatrix

function oneCalc(index) {

calcParams(index);

for (var i=0; i<nodesWide; i++) {

for (var j=0; j<nodesHigh; j++) {

arrayT[i][j] = arrayTpieces[index][i][j] + Tabs;

}

loadMatrix(index);

calcMatrix();

k = 0;

for (var j=0; j<nodesHigh; j++) {

for (var i=0; i<nodesWide; i++) {

k++;

arrayTpieces[index][i][j] = ZSRCE[k] - Tabs;

}

} //oneCalc

var loopCount = 0;

var s="Temperatures after "+loopCount+" time steps<br />";

for (var j=nodesHigh-1; j>=0; j--) {

for (var i=0; i<=nodesWide-1; i++) {

s += arrayTpieces[0][i][j].toPrecision(7) + ", ";

}

s += "<br />";

}

document.getElementById("stuff").innerHTML = s;

function runOneTime() {

if (loopCount == 0) {

for (var i=0; i< pieceCount; i++) {

for (var j=0; j<nodesWide; j++) {

for (var k=0; k<nodesHigh; k++) {

arrayTpieces[i][j][k] = 70.0;

}

} else {

oneCalc(0);

}

var s="Temperatures after "+loopCount+" time steps<br />";

for (var j=nodesHigh-1; j>=0; j--) {

for (var i=0; i<=nodesWide-1; i++) {

s += arrayTpieces[0][i][j].toPrecision(7) + ", ";

}

s += "<br />";

}

document.getElementById("stuff").innerHTML = s;

loopCount++;

if (loopCount > 20) {

loopCount = 0;

}

var intervalID = setInterval(runOneTime, 1000);

We start with a 7×7-node workpiece where the interior nodes are two inches wide and two … Continue reading →

Posted in Tools and methods | Tagged matrix solution techniques, sim_presentation_series, thermodynamics | Leave a comment

Search for:
Recent Posts
Recent Comments
Categories
Meta
May 2016

M T W T F S S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30 31

« Apr Jun »

Daily Archives: May 19, 2016

Finally Solving the Matrix

Recent Posts

Recent Comments

Categories

Meta