Response from Program IdealAdiabatic v.3.2

Your Input

Working Gas Helium 
Specific gas constantRspec2076.9000J/(kg K)
Ratio of specific heatsκ1.6670-
Average pressurepave1000.0000kPa
Net work per cycleWnet12.5208J
Rotations per second of crankfreq30.00001/sec
Heater temperatureTh873.0000K
Heater volumeVh45.0000cm³
Kooler temperatureTk303.0000K
Kooler volumeVk90.0000cm³
Regenerator volumeVr141.0000cm³
Regenerator,eff TempTr538.6491°
Drive type s 
Volume phase lagvpl85.0000°
Clearance volume, compressionVclc5.5000cm³
Clearance volume, expansionVcle12.0000cm³

The following output shows various quantities of interest as function of the swept volume of the compression space. The net work per cycle remains constant at 12.520796 [J] as does the average pressure 10.000000 [bar] and all other input parameters.

The items listed are (from left to right) :
Vswc [cc] : Swept Volume of Compression Space
Vswe [cc] : Swept Volume of Expansion Space
Vtot [cc] : Vswc + Vswe
eta [] : Actual Efficiency
Wtot [J] : Net Work per Cycle (nominally equal to 12.520796)
pmin [bar] : Minimum Pressure
pmax [bar] : Maximum Pressure
Tcmin [K] : Minimum Temperature in Compression Space
Tcmax [K] : Maximum Temperature in Compression Space
Wc [J] : Work done by Compression Space *
dQkneg [W] : Most negative Heat Flow Rate , Kooler
dQkpos [W] : Most positive Heat Flow Rate , Kooler
Qr [J] : Heat transfered into Gas , Regenerator
dQrneg [W] : Most negative Heat Flow Rate , Regenerator
dQrpos [W] : Most positive Heat Flow Rate , Regenerator
dQhneg [W] : Most negative Heat Flow Rate , Heater
dQhpos [W] : Most positive Heat Flow Rate , Heater
Temin [K] : Minimum Temperature in Expansion Space
Temax [K] : Maximum Temperature in Expansion Space
We [K] : Work done by Expansion Space *
* The net heat load in the kooler is equal to Wc and the net heat load in the heater equals We

Please be patient. The computations are numerically intensive.
They will proceed until Vswe ≥ 2.00 * (Th/Tk) * Vswc is reached.

Which will be approximately at Vswc = 3.280968e+01 ; Vswe = 1.890617e+02

   Vswc[cc]    Vswe[cc]    Vtot[cc]       eta[]     Wtot[J]   pmin[bar]   pmax[bar]    Tcmin[K]    Tcmax[K]       Wc[J]   dQkneg[W]   dQkpos[W]       Qr[J]   dQrneg[W]   dQrpos[W]   dQhneg[W]   dQhpos[W]    Temin[K]    Temax[K]       We[J]
 8.7208e+01  6.9766e+01  1.5697e+02  6.0267e-01  1.2521e+01  8.0960e+00  1.2197e+01  2.8299e+02  3.3431e+02 -8.2548e+00 -4.4707e+03  3.6126e+03  1.0832e+02 -1.0039e+04  1.1531e+04 -1.7680e+03  2.1395e+03  7.5337e+02  8.8518e+02  2.0776e+01
 8.6120e+01  7.0497e+01  1.5662e+02  6.0344e-01  1.2521e+01  8.1123e+00  1.2175e+01  2.8328e+02  3.3415e+02 -8.2281e+00 -4.4210e+03  3.5768e+03  1.0833e+02 -9.9901e+03  1.1598e+04 -1.7492e+03  2.1274e+03  7.5449e+02  8.8504e+02  2.0749e+01
 8.5032e+01  7.1249e+01  1.5628e+02  6.0420e-01  1.2521e+01  8.1286e+00  1.2153e+01  2.8356e+02  3.3399e+02 -8.2020e+00 -4.3717e+03  3.5411e+03  1.0839e+02 -9.9435e+03  1.1668e+04 -1.7303e+03  2.1154e+03  7.5562e+02  8.8490e+02  2.0723e+01
 8.3944e+01  7.2025e+01  1.5597e+02  6.0495e-01  1.2521e+01  8.1448e+00  1.2131e+01  2.8384e+02  3.3384e+02 -8.1763e+00 -4.3227e+03  3.5057e+03  1.0849e+02 -9.8988e+03  1.1740e+04 -1.7114e+03  2.1035e+03  7.5675e+02  8.8476e+02  2.0697e+01
 8.2856e+01  7.2823e+01  1.5568e+02  6.0569e-01  1.2521e+01  8.1609e+00  1.2109e+01  2.8412e+02  3.3368e+02 -8.1512e+00 -4.2741e+03  3.4705e+03  1.0863e+02 -9.8561e+03  1.1815e+04 -1.6923e+03  2.0917e+03  7.5788e+02  8.8462e+02  2.0672e+01
 8.1768e+01  7.3647e+01  1.5542e+02  6.0641e-01  1.2521e+01  8.1770e+00  1.2088e+01  2.8440e+02  3.3353e+02 -8.1266e+00 -4.2260e+03  3.4355e+03  1.0882e+02 -9.8156e+03  1.1892e+04 -1.6732e+03  2.0800e+03  7.5901e+02  8.8449e+02  2.0647e+01
 8.0680e+01  7.4496e+01  1.5518e+02  6.0712e-01  1.2521e+01  8.1930e+00  1.2067e+01  2.8468e+02  3.3338e+02 -8.1025e+00 -4.1783e+03  3.4007e+03  1.0906e+02 -9.7772e+03  1.1973e+04 -1.6540e+03  2.0683e+03  7.6014e+02  8.8436e+02  2.0623e+01
 7.9592e+01  7.5373e+01  1.5496e+02  6.0781e-01  1.2521e+01  8.2089e+00  1.2045e+01  2.8497e+02  3.3324e+02 -8.0789e+00 -4.1310e+03  3.3662e+03  1.0935e+02 -9.7412e+03  1.2057e+04 -1.6347e+03  2.0567e+03  7.6127e+02  8.8423e+02  2.0600e+01
 7.8504e+01  7.6277e+01  1.5478e+02  6.0850e-01  1.2521e+01  8.2247e+00  1.2024e+01  2.8525e+02  3.3310e+02 -8.0558e+00 -4.0842e+03  3.3320e+03  1.0968e+02 -9.7076e+03  1.2144e+04 -1.6154e+03  2.0452e+03  7.6240e+02  8.8410e+02  2.0577e+01
 7.7416e+01  7.7211e+01  1.5463e+02  6.0916e-01  1.2521e+01  8.2404e+00  1.2003e+01  2.8553e+02  3.3297e+02 -8.0333e+00 -4.0379e+03  3.2981e+03  1.1007e+02 -9.6767e+03  1.2235e+04 -1.5960e+03  2.0338e+03  7.6352e+02  8.8398e+02  2.0554e+01
 7.6328e+01  7.8175e+01  1.5450e+02  6.0982e-01  1.2521e+01  8.2560e+00  1.1983e+01  2.8581e+02  3.3284e+02 -8.0113e+00 -3.9920e+03  3.2645e+03  1.1052e+02 -9.6485e+03  1.2329e+04 -1.5765e+03  2.0225e+03  7.6464e+02  8.8387e+02  2.0532e+01
 7.5240e+01  7.9172e+01  1.5441e+02  6.1046e-01  1.2521e+01  8.2715e+00  1.1962e+01  2.8609e+02  3.3271e+02 -7.9898e+00 -3.9467e+03  3.2312e+03  1.1102e+02 -9.6233e+03  1.2427e+04 -1.5569e+03  2.0113e+03  7.6577e+02  8.8376e+02  2.0511e+01
 7.4152e+01  8.0203e+01  1.5435e+02  6.1108e-01  1.2521e+01  8.2868e+00  1.1942e+01  2.8637e+02  3.3259e+02 -7.9689e+00 -3.9019e+03  3.1983e+03  1.1158e+02 -9.6011e+03  1.2528e+04 -1.5372e+03  2.0002e+03  7.6688e+02  8.8365e+02  2.0490e+01
 7.3064e+01  8.1268e+01  1.5433e+02  6.1169e-01  1.2521e+01  8.3020e+00  1.1922e+01  2.8666e+02  3.3247e+02 -7.9485e+00 -3.8577e+03  3.1658e+03  1.1219e+02 -9.5823e+03  1.2634e+04 -1.5175e+03  1.9892e+03  7.6800e+02  8.8355e+02  2.0469e+01
 7.1976e+01  8.2372e+01  1.5435e+02  6.1228e-01  1.2521e+01  8.3169e+00  1.1903e+01  2.8694e+02  3.3236e+02 -7.9286e+00 -3.8141e+03  3.1337e+03  1.1287e+02 -9.5669e+03  1.2744e+04 -1.4977e+03  1.9783e+03  7.6911e+02  8.8345e+02  2.0449e+01
 7.0888e+01  8.3514e+01  1.5440e+02  6.1286e-01  1.2521e+01  8.3317e+00  1.1883e+01  2.8722e+02  3.3226e+02 -7.9094e+00 -3.7711e+03  3.1021e+03  1.1361e+02 -9.5553e+03  1.2858e+04 -1.4778e+03  1.9675e+03  7.7021e+02  8.8336e+02  2.0430e+01
 6.9801e+01  8.4697e+01  1.5450e+02  6.1342e-01  1.2521e+01  8.3463e+00  1.1864e+01  2.8750e+02  3.3216e+02 -7.8907e+00 -3.7288e+03  3.0709e+03  1.1441e+02 -9.5477e+03  1.2977e+04 -1.4578e+03  1.9569e+03  7.7131e+02  8.8328e+02  2.0411e+01
 6.8713e+01  8.5923e+01  1.5464e+02  6.1396e-01  1.2521e+01  8.3606e+00  1.1846e+01  2.8777e+02  3.3208e+02 -7.8726e+00 -3.6871e+03  3.0403e+03  1.1527e+02 -9.5444e+03  1.3101e+04 -1.4378e+03  1.9463e+03  7.7240e+02  8.8321e+02  2.0393e+01
 6.7625e+01  8.7195e+01  1.5482e+02  6.1449e-01  1.2521e+01  8.3747e+00  1.1827e+01  2.8805e+02  3.3199e+02 -7.8551e+00 -3.6462e+03  3.0102e+03  1.1620e+02 -9.5457e+03  1.3230e+04 -1.4179e+03  1.9359e+03  7.7349e+02  8.8314e+02  2.0376e+01
 6.6537e+01  8.8515e+01  1.5505e+02  6.1500e-01  1.2521e+01  8.3885e+00  1.1809e+01  2.8833e+02  3.3192e+02 -7.8381e+00 -3.6060e+03  2.9808e+03  1.1720e+02 -9.5520e+03  1.3364e+04 -1.3983e+03  1.9256e+03  7.7456e+02  8.8309e+02  2.0359e+01
 6.5557e+01  8.9747e+01  1.5530e+02  6.1545e-01  1.2521e+01  8.4006e+00  1.1794e+01  2.8858e+02  3.3186e+02 -7.8235e+00 -3.5705e+03  2.9548e+03  1.1817e+02 -9.5621e+03  1.3489e+04 -1.3809e+03  1.9165e+03  7.7553e+02  8.8305e+02  2.0344e+01
 6.4578e+01  9.1021e+01  1.5560e+02  6.1588e-01  1.2521e+01  8.4125e+00  1.1778e+01  2.8883e+02  3.3181e+02 -7.8093e+00 -3.5360e+03  2.9295e+03  1.1919e+02 -9.5770e+03  1.3620e+04 -1.3638e+03  1.9075e+03  7.7648e+02  8.8302e+02  2.0330e+01
 6.3599e+01  9.2341e+01  1.5594e+02  6.1629e-01  1.2521e+01  8.4241e+00  1.1763e+01  2.8907e+02  3.3177e+02 -7.7956e+00 -3.5022e+03  2.9047e+03  1.2027e+02 -9.5968e+03  1.3755e+04 -1.3471e+03  1.8987e+03  7.7742e+02  8.8300e+02  2.0316e+01
 6.2718e+01  9.3570e+01  1.5629e+02  6.1665e-01  1.2521e+01  8.4343e+00  1.1750e+01  2.8929e+02  3.3174e+02 -7.7838e+00 -3.4725e+03  2.8830e+03  1.2129e+02 -9.6192e+03  1.3881e+04 -1.3323e+03  1.8909e+03  7.7827e+02  8.8299e+02  2.0305e+01
 6.1837e+01  9.4839e+01  1.5668e+02  6.1700e-01  1.2521e+01  8.4441e+00  1.1738e+01  2.8951e+02  3.3171e+02 -7.7724e+00 -3.4434e+03  2.8618e+03  1.2237e+02 -9.6463e+03  1.4012e+04 -1.3179e+03  1.8832e+03  7.7910e+02  8.8299e+02  2.0293e+01
 6.0955e+01  9.6151e+01  1.5711e+02  6.1733e-01  1.2521e+01  8.4537e+00  1.1725e+01  2.8973e+02  3.3170e+02 -7.7615e+00 -3.4150e+03  2.8412e+03  1.2351e+02 -9.6785e+03  1.4147e+04 -1.3038e+03  1.8756e+03  7.7992e+02  8.8301e+02  2.0282e+01
 6.0162e+01  9.7370e+01  1.5753e+02  6.1762e-01  1.2521e+01  8.4621e+00  1.1714e+01  2.8993e+02  3.3169e+02 -7.7520e+00 -3.3900e+03  2.8233e+03  1.2457e+02 -9.7120e+03  1.4273e+04 -1.2914e+03  1.8689e+03  7.8066e+02  8.8303e+02  2.0273e+01
 5.9369e+01  9.8627e+01  1.5800e+02  6.1789e-01  1.2521e+01  8.4702e+00  1.1704e+01  2.9012e+02  3.3169e+02 -7.7430e+00 -3.3657e+03  2.8058e+03  1.2569e+02 -9.7503e+03  1.4403e+04 -1.2794e+03  1.8624e+03  7.8138e+02  8.8307e+02  2.0264e+01
 5.8576e+01  9.9923e+01  1.5850e+02  6.1816e-01  1.2521e+01  8.4780e+00  1.1694e+01  2.9031e+02  3.3169e+02 -7.7343e+00 -3.3419e+03  2.7890e+03  1.2685e+02 -9.7937e+03  1.4537e+04 -1.2678e+03  1.8560e+03  7.8210e+02  8.8312e+02  2.0255e+01
 5.7783e+01  1.0126e+02  1.5904e+02  6.1841e-01  1.2521e+01  8.4855e+00  1.1684e+01  2.9050e+02  3.3171e+02 -7.7261e+00 -3.3188e+03  2.7728e+03  1.2806e+02 -9.8425e+03  1.4676e+04 -1.2566e+03  1.8497e+03  7.8280e+02  8.8318e+02  2.0247e+01
 5.7069e+01  1.0250e+02  1.5957e+02  6.1862e-01  1.2521e+01  8.4920e+00  1.1676e+01  2.9068e+02  3.3173e+02 -7.7190e+00 -3.2987e+03  2.7587e+03  1.2920e+02 -9.8914e+03  1.4805e+04 -1.2469e+03  1.8442e+03  7.8343e+02  8.8325e+02  2.0240e+01
 5.6355e+01  1.0378e+02  1.6014e+02  6.1883e-01  1.2521e+01  8.4982e+00  1.1668e+01  2.9085e+02  3.3176e+02 -7.7123e+00 -3.2791e+03  2.7452e+03  1.3038e+02 -9.9454e+03  1.4938e+04 -1.2375e+03  1.8389e+03  7.8404e+02  8.8333e+02  2.0233e+01
 5.5641e+01  1.0510e+02  1.6074e+02  6.1902e-01  1.2521e+01  8.5041e+00  1.1661e+01  2.9101e+02  3.3179e+02 -7.7060e+00 -3.2601e+03  2.7323e+03  1.3160e+02 -1.0005e+04  1.5074e+04 -1.2286e+03  1.8337e+03  7.8465e+02  8.8343e+02  2.0227e+01
 5.4999e+01  1.0632e+02  1.6132e+02  6.1919e-01  1.2521e+01  8.5091e+00  1.1654e+01  2.9117e+02  3.3183e+02 -7.7006e+00 -3.2435e+03  2.7213e+03  1.3274e+02 -1.0064e+04  1.5201e+04 -1.2210e+03  1.8292e+03  7.8518e+02  8.8353e+02  2.0221e+01
 5.4357e+01  1.0757e+02  1.6193e+02  6.1934e-01  1.2521e+01  8.5139e+00  1.1648e+01  2.9132e+02  3.3187e+02 -7.6955e+00 -3.2275e+03  2.7107e+03  1.3391e+02 -1.0127e+04  1.5332e+04 -1.2138e+03  1.8248e+03  7.8571e+02  8.8364e+02  2.0216e+01
 5.3714e+01  1.0886e+02  1.6258e+02  6.1949e-01  1.2521e+01  8.5184e+00  1.1643e+01  2.9146e+02  3.3193e+02 -7.6908e+00 -3.2121e+03  2.7007e+03  1.3513e+02 -1.0196e+04  1.5466e+04 -1.2069e+03  1.8205e+03  7.8623e+02  8.8377e+02  2.0212e+01
 5.3072e+01  1.1019e+02  1.6326e+02  6.1962e-01  1.2521e+01  8.5226e+00  1.1637e+01  2.9161e+02  3.3198e+02 -7.6864e+00 -3.1973e+03  2.6913e+03  1.3639e+02 -1.0271e+04  1.5604e+04 -1.2006e+03  1.8164e+03  7.8673e+02  8.8392e+02  2.0207e+01
 5.2493e+01  1.1141e+02  1.6391e+02  6.1973e-01  1.2521e+01  8.5261e+00  1.1633e+01  2.9174e+02  3.3204e+02 -7.6827e+00 -3.1844e+03  2.6833e+03  1.3756e+02 -1.0343e+04  1.5732e+04 -1.1953e+03  1.8129e+03  7.8718e+02  8.8407e+02  2.0203e+01
 5.1915e+01  1.1267e+02  1.6459e+02  6.1984e-01  1.2521e+01  8.5294e+00  1.1629e+01  2.9187e+02  3.3211e+02 -7.6793e+00 -3.1721e+03  2.6759e+03  1.3876e+02 -1.0421e+04  1.5863e+04 -1.1904e+03  1.8095e+03  7.8762e+02  8.8423e+02  2.0200e+01
 5.1337e+01  1.1397e+02  1.6530e+02  6.1993e-01  1.2521e+01  8.5323e+00  1.1625e+01  2.9200e+02  3.3218e+02 -7.6762e+00 -3.1604e+03  2.6690e+03  1.4000e+02 -1.0504e+04  1.5997e+04 -1.1859e+03  1.8063e+03  7.8805e+02  8.8441e+02  2.0197e+01
 5.0759e+01  1.1530e+02  1.6605e+02  6.2002e-01  1.2521e+01  8.5350e+00  1.1621e+01  2.9213e+02  3.3226e+02 -7.6735e+00 -3.1491e+03  2.6626e+03  1.4127e+02 -1.0593e+04  1.6136e+04 -1.1820e+03  1.8032e+03  7.8847e+02  8.8460e+02  2.0194e+01
 5.0239e+01  1.1652e+02  1.6676e+02  6.2009e-01  1.2521e+01  8.5372e+00  1.1619e+01  2.9224e+02  3.3234e+02 -7.6712e+00 -3.1395e+03  2.6574e+03  1.4246e+02 -1.0678e+04  1.6263e+04 -1.1789e+03  1.8006e+03  7.8883e+02  8.8479e+02  2.0192e+01
 4.9718e+01  1.1778e+02  1.6750e+02  6.2015e-01  1.2521e+01  8.5391e+00  1.1616e+01  2.9236e+02  3.3242e+02 -7.6693e+00 -3.1304e+03  2.6527e+03  1.4367e+02 -1.0768e+04  1.6394e+04 -1.1762e+03  1.7982e+03  7.8919e+02  8.8500e+02  2.0190e+01
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 3.3945e+01  1.8106e+02  2.1501e+02  6.1509e-01  1.2521e+01  8.3946e+00  1.1801e+01  2.9499e+02  3.3995e+02 -7.8352e+00 -3.2445e+03  2.9123e+03  2.0391e+02 -1.6890e+04  2.2868e+04 -1.5450e+03  1.8988e+03  7.9254e+02  9.0335e+02  2.0356e+01
 3.3764e+01  1.8229e+02  2.1605e+02  6.1489e-01  1.2521e+01  8.3893e+00  1.1808e+01  2.9501e+02  3.4013e+02 -7.8419e+00 -3.2532e+03  2.9229e+03  2.0502e+02 -1.7018e+04  2.2990e+04 -1.5593e+03  1.9043e+03  7.9244e+02  9.0374e+02  2.0363e+01
 3.3582e+01  1.8353e+02  2.1711e+02  6.1468e-01  1.2521e+01  8.3837e+00  1.1815e+01  2.9503e+02  3.4032e+02 -7.8488e+00 -3.2621e+03  2.9338e+03  2.0615e+02 -1.7148e+04  2.3114e+04 -1.5741e+03  1.9099e+03  7.9233e+02  9.0414e+02  2.0370e+01
 3.3401e+01  1.8479e+02  2.1819e+02  6.1446e-01  1.2521e+01  8.3781e+00  1.1822e+01  2.9504e+02  3.4050e+02 -7.8560e+00 -3.2714e+03  2.9449e+03  2.0729e+02 -1.7280e+04  2.3240e+04 -1.5894e+03  1.9158e+03  7.9221e+02  9.0454e+02  2.0377e+01
 3.3219e+01  1.8608e+02  2.1930e+02  6.1424e-01  1.2521e+01  8.3723e+00  1.1830e+01  2.9506e+02  3.4070e+02 -7.8633e+00 -3.2810e+03  2.9564e+03  2.0845e+02 -1.7414e+04  2.3368e+04 -1.6051e+03  1.9219e+03  7.9209e+02  9.0495e+02  2.0384e+01
 3.3038e+01  1.8739e+02  2.2042e+02  6.1401e-01  1.2521e+01  8.3663e+00  1.1837e+01  2.9507e+02  3.4089e+02 -7.8710e+00 -3.2908e+03  2.9682e+03  2.0963e+02 -1.7551e+04  2.3499e+04 -1.6213e+03  1.9282e+03  7.9196e+02  9.0537e+02  2.0392e+01
 3.2875e+01  1.8858e+02  2.2146e+02  6.1380e-01  1.2521e+01  8.3608e+00  1.1845e+01  2.9509e+02  3.4107e+02 -7.8780e+00 -3.3000e+03  2.9791e+03  2.1070e+02 -1.7676e+04  2.3618e+04 -1.6363e+03  1.9340e+03  7.9184e+02  9.0575e+02  2.0399e+01
 3.2711e+01  1.8979e+02  2.2251e+02  6.1358e-01  1.2521e+01  8.3552e+00  1.1852e+01  2.9510e+02  3.4126e+02 -7.8853e+00 -3.3094e+03  2.9902e+03  2.1179e+02 -1.7803e+04  2.3738e+04 -1.6517e+03  1.9401e+03  7.9172e+02  9.0613e+02  2.0406e+01
 4.6692e+01  1.2577e+02  1.7247e+02  6.2031e-01  1.2521e+01  8.5446e+00  1.1609e+01  2.9299e+02  3.3305e+02 -7.6638e+00 -3.0883e+03  2.6364e+03  1.5142e+02 -1.1401e+04  1.7225e+04 -1.1707e+03  1.7876e+03  7.9107e+02  8.8658e+02  2.0185e+01

ALL DONE : Vswe > 2.000000e+00 * (Th/Tk) * Vswc reached and precise location of optimum efficiency determined ( last line of data with Vswc = 4.6692e+01 )


Zig Herzog © 2005
hgn@psu.edu