mirror of
https://github.com/CoolProp/CoolProp.git
synced 2026-04-01 03:00:13 -04:00
PlanckEinstein and PlanckEinstein2 classes replaced with PlanckEinsteinGeneralized. Docs to follow.
Aly-Lee not yet removed. Next step. Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
@@ -183,13 +183,16 @@
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"c": [
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0.6666666666666666
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],
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"d": [
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1
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],
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"n": [
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-0.197938904
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],
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"t": [
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87.31279
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-87.31279
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],
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"type": "IdealGasHelmholtzPlanckEinstein2"
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"type": "IdealGasHelmholtzPlanckEinsteinGeneralized"
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}
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],
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"alphar": [
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@@ -174,15 +174,18 @@
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},
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{
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"c": [
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1
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],
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"d": [
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-1
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],
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"n": [
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1.012767
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],
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"t": [
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8.9057501
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-8.9057501
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],
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"type": "IdealGasHelmholtzPlanckEinstein2"
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"type": "IdealGasHelmholtzPlanckEinsteinGeneralized"
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},
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{
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"a1": 0,
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@@ -193,13 +193,16 @@
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"c": [
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0.6666666666666666
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],
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"d": [
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1
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],
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"n": [
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0.944365
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],
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"t": [
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74.91476960299131
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-74.91476960299131
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],
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"type": "IdealGasHelmholtzPlanckEinstein2"
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"type": "IdealGasHelmholtzPlanckEinsteinGeneralized"
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}
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],
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"alphar": [
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@@ -168,7 +168,7 @@
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"type": "IdealGasHelmholtzLogTau"
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},
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{
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"T0": 309.213623675,
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"T0": 298,
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"Tc": 469.7,
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"c": [
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4,
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@@ -180,7 +180,7 @@
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"type": "IdealGasHelmholtzCP0AlyLee"
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},
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{
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"T0": 309.213623675,
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"T0": 298,
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"Tc": 469.7,
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"c": [
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0,
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@@ -12,7 +12,28 @@
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"level": 1,
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"metadata": {},
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"source": [
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"Conversion of Aly-Lee form to Planck-Einstein"
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"Derivation and Conversion of Planck-Einstein Terms"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Start with a generalized Helmholtz energy from \n",
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"$$\\alpha^0 = a_k\\log\\left[c_k + d_k\\exp\\left(\\frac{b_k\\tau}{T_c}\\right)\\right]$$\n",
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"\n",
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"The ideal-gas specific heat can be obtained from \n",
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"$$\\frac{c_p^0}{R} = -\\tau^2\\alpha^0_{\\tau\\tau}$$\n",
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"\n",
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"After some math shown below (and some manual grouping):\n",
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"$$\\frac{c_p^0}{R} = - \\frac{a_{k} (b_{k}\\tau/T_c)^{2} c_k d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}}{ \\left(c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}\\right)^2} $$\n",
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"\n",
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"Two important identities:\n",
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"$$ \\left(\\frac{1}{\\cosh x}\\right) = \\frac{2e^{-x}}{1+e^{-2x}}$$\n",
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"$$ \\left(\\frac{1}{\\sinh x}\\right) = \\frac{2e^{-x}}{1-e^{-2x}}$$\n",
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"which yield\n",
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"$$ \\left(\\frac{x}{\\cosh x}\\right)^2 = \\frac{4x^2e^{-2x}}{(1+e^{-2x})^2} = \\frac{(-2x)^2e^{-2x}}{(1+e^{-2x})^2}$$\n",
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"$$ \\left(\\frac{x}{\\sinh x}\\right)^2 = \\frac{4x^2e^{-2x}}{(1-e^{-2x})^2} = \\frac{(-2x)^2e^{-2x}}{(1-e^{-2x})^2}$$"
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]
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},
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{
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@@ -35,58 +56,155 @@
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]
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}
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],
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"prompt_number": 2
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"prompt_number": 4
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"a_k,b_k,c_k,d_k,tau,T_c = symbols('a_k,b_k,c_k,d_k,tau,T_c',real=True)\n",
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"alpha0 = a_k*log(c_k + d_k*exp(b_k*tau/T_c))\n",
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"display(diff(alpha0, tau, 2)*(-tau**2).together().ratsimp())"
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"print 'No derivatives'\n",
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"display(alpha0)\n",
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"print 'First partial w.r.t. tau'\n",
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"display(diff(alpha0, tau, 1).simplify())\n",
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"print 'Second partial w.r.t. tau'\n",
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"display(diff(alpha0, tau, 2).simplify())\n",
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"print latex(diff(alpha0, tau, 2).simplify()*(-tau**2))\n",
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"print 'Third partial w.r.t. tau'\n",
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"display(diff(alpha0, tau, 3).simplify())"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
|
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"No derivatives\n"
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]
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},
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{
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"latex": [
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"$$- \\frac{a_{k} b_{k}^{2} d_{k} \\tau^{2} e^{\\frac{b_{k} \\tau}{T_{c}}}}{T_{c}^{2} \\left(c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}\\right)} \\left(- \\frac{d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}}{c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}} + 1\\right)$$"
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"$$a_{k} \\log{\\left (c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}} \\right )}$$"
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],
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"metadata": {},
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"output_type": "display_data",
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|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAALYAAAAoBAMAAAChsh0EAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nNK64R/yf8j+av+zHorG6yAAAAABJRU5ErkJggg==\n",
|
||||
"text": [
|
||||
" \u239b b_k\u22c5\u03c4 \u239e \n",
|
||||
" \u239c \u2500\u2500\u2500\u2500\u2500 \u239f b_k\u22c5\u03c4 \n",
|
||||
" \u239c T_c \u239f \u2500\u2500\u2500\u2500\u2500 \n",
|
||||
" 2 2 \u239c d_k\u22c5\u212f \u239f T_c \n",
|
||||
"-a_k\u22c5b_k \u22c5d_k\u22c5\u03c4 \u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + 1\u239f\u22c5\u212f \n",
|
||||
" \u239c b_k\u22c5\u03c4 \u239f \n",
|
||||
" \u239c \u2500\u2500\u2500\u2500\u2500 \u239f \n",
|
||||
" \u239c T_c \u239f \n",
|
||||
" \u239d c_k + d_k\u22c5\u212f \u23a0 \n",
|
||||
"\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
|
||||
" \u239b b_k\u22c5\u03c4\u239e \n",
|
||||
" \u239c \u2500\u2500\u2500\u2500\u2500\u239f \n",
|
||||
" 2 \u239c T_c \u239f \n",
|
||||
" T_c \u22c5\u239dc_k + d_k\u22c5\u212f \u23a0 "
|
||||
" \u239b b_k\u22c5\u03c4\u239e\n",
|
||||
" \u239c \u2500\u2500\u2500\u2500\u2500\u239f\n",
|
||||
" \u239c T_c \u239f\n",
|
||||
"a_k\u22c5log\u239dc_k + d_k\u22c5\u212f \u23a0"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"First partial w.r.t. tau\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"latex": [
|
||||
"$$\\frac{a_{k} b_{k} d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}}{T_{c} \\left(c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}\\right)}$$"
|
||||
],
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAJsAAABMBAMAAACIdNgoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nm+3fsAlYAAAAAElFTkSuQmCC\n",
|
||||
"text": [
|
||||
" b_k\u22c5\u03c4 \n",
|
||||
" \u2500\u2500\u2500\u2500\u2500 \n",
|
||||
" T_c \n",
|
||||
" a_k\u22c5b_k\u22c5d_k\u22c5\u212f \n",
|
||||
"\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
|
||||
" \u239b b_k\u22c5\u03c4\u239e\n",
|
||||
" \u239c \u2500\u2500\u2500\u2500\u2500\u239f\n",
|
||||
" \u239c T_c \u239f\n",
|
||||
"T_c\u22c5\u239dc_k + d_k\u22c5\u212f \u23a0"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Second partial w.r.t. tau\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"latex": [
|
||||
"$$\\frac{a_{k} b_{k}^{2} c_{k} d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}}{T_{c}^{2} \\left(c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}\\right)^{2}}$$"
|
||||
],
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAKgAAABQBAMAAAB/pCPzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nNFxuru+P1H8Bv/Dea92wCuIAAAAASUVORK5CYII=\n",
|
||||
"text": [
|
||||
" b_k\u22c5\u03c4 \n",
|
||||
" \u2500\u2500\u2500\u2500\u2500 \n",
|
||||
" 2 T_c \n",
|
||||
"a_k\u22c5b_k \u22c5c_k\u22c5d_k\u22c5\u212f \n",
|
||||
"\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
|
||||
" 2\n",
|
||||
" \u239b b_k\u22c5\u03c4\u239e \n",
|
||||
" \u239c \u2500\u2500\u2500\u2500\u2500\u239f \n",
|
||||
" 2 \u239c T_c \u239f \n",
|
||||
"T_c \u22c5\u239dc_k + d_k\u22c5\u212f \u23a0 "
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"- \\frac{a_{k} b_{k}^{2} c_{k} d_{k} \\tau^{2} e^{\\frac{b_{k} \\tau}{T_{c}}}}{T_{c}^{2} \\left(c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}\\right)^{2}}\n",
|
||||
"Third partial w.r.t. tau\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"latex": [
|
||||
"$$\\frac{a_{k} b_{k}^{3} c_{k} d_{k} \\left(c_{k} - d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}\\right) e^{\\frac{b_{k} \\tau}{T_{c}}}}{T_{c}^{3} \\left(c_{k}^{3} + 3 c_{k}^{2} d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}} + 3 c_{k} d_{k}^{2} e^{\\frac{2 b_{k}}{T_{c}} \\tau} + d_{k}^{3} e^{\\frac{3 b_{k}}{T_{c}} \\tau}\\right)}$$"
|
||||
],
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": "iVBORw0KGgoAAAANSUhEUgAAAZYAAABUBAMAAABTgQyuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
|
||||
"text": [
|
||||
" \u239b b_k\u22c5\u03c4\u239e b_k\u22c5\u03c4 \n",
|
||||
" \u239c \u2500\u2500\u2500\u2500\u2500\u239f \u2500\u2500\u2500\u2500\u2500 \n",
|
||||
" 3 \u239c T_c \u239f T_c \n",
|
||||
" a_k\u22c5b_k \u22c5c_k\u22c5d_k\u22c5\u239dc_k - d_k\u22c5\u212f \u23a0\u22c5\u212f \n",
|
||||
"\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
|
||||
" \u239b b_k\u22c5\u03c4 2\u22c5b_k\u22c5\u03c4 3\u22c5b_k\u22c5\u03c4\u239e\n",
|
||||
" \u239c \u2500\u2500\u2500\u2500\u2500 \u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\n",
|
||||
" 3 \u239c 3 2 T_c 2 T_c 3 T_c \u239f\n",
|
||||
"T_c \u22c5\u239dc_k + 3\u22c5c_k \u22c5d_k\u22c5\u212f + 3\u22c5c_k\u22c5d_k \u22c5\u212f + d_k \u22c5\u212f \u23a0"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 4
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"And then with some manual simplification:\n",
|
||||
"$$\\frac{c_p^0}{R} = - \\frac{a_{k} (b_{k}\\tau/T_c)^{2} c_k d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}}{ \\left(c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}\\right)^2} $$\n",
|
||||
"Aly-Lee starts as\n",
|
||||
"$$\\frac{c_p^0}{R_u} = A + B\\left(\\frac{C/T}{\\sinh(C/T)}\\right)^2 + D\\left(\\frac{E/T}{\\cosh(E/T)}\\right)^2$$\n",
|
||||
"and generalized Plank-Einstein term is given by\n",
|
||||
"$$\\frac{c_p^0}{R_u} = - \\frac{a_{k} b_{k}^{2} c_{k} d_{k} \\tau^{2} e^{\\frac{b_{k} \\tau}{T_{c}}}}{T_{c}^{2} \\left(c_{k} + d_{k} e^{\\frac{b_{k} \\tau}{T_{c}}}\\right)^{2}}$$\n",
|
||||
"\n",
|
||||
"Two important identities:\n",
|
||||
"$$ \\left(\\frac{1}{\\cosh x}\\right) = \\frac{2e^{-x}}{1+e^{-2x}}$$\n",
|
||||
"$$ \\left(\\frac{1}{\\sinh x}\\right) = \\frac{2e^{-x}}{1-e^{-2x}}$$\n",
|
||||
"which yield\n",
|
||||
"$$ \\left(\\frac{1}{\\cosh x}\\right)^2 = \\frac{4e^{-2x}}{(1+e^{-2x})^2}$$\n",
|
||||
"$$ \\left(\\frac{1}{\\sinh x}\\right)^2 = \\frac{4e^{-2x}}{(1-e^{-2x})^2}$$"
|
||||
"Constant is separated out, and handled separately. sinh part can be expanded as\n",
|
||||
"$$B\\left(\\frac{C/T}{\\sinh(C/T)}\\right)^2 = \\frac{B(-2C/T)^2\\exp(-2C/T)}{(1-\\exp(-2C/T))^2}$$\n",
|
||||
"where\n",
|
||||
"$$a_k = B$$\n",
|
||||
"$$b_k = -2C$$\n",
|
||||
"$$c_k = 1$$\n",
|
||||
"$$d_k = -1$$\n",
|
||||
"\n",
|
||||
"cosh part can be expanded as\n",
|
||||
"$$D\\left(\\frac{E/T}{\\cosh(E/T)}\\right)^2 = \\frac{D(-2E/T)^2\\exp(-2E/T)}{(1+\\exp(-2E/T))^2}$$\n",
|
||||
"where\n",
|
||||
"$$a_k = -D$$\n",
|
||||
"$$b_k = -2E$$\n",
|
||||
"$$c_k = 1$$\n",
|
||||
"$$d_k = 1$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -102,7 +220,7 @@
|
||||
"display(diff1.rewrite(exp).subs(B, 2*D).simplify())\n",
|
||||
"term2 = (2*D/T)**2*exp(2*D/T)/(exp(2*D/T)-1)**2\n",
|
||||
"display(term2)\n",
|
||||
"print 'which is the same as the Aly-Lee sinh term with b_k = 2*D'\n",
|
||||
"print 'which is the same as the Aly-Lee sinh term with a_k = C, b_k = 2*D, c_k = -1, d_k = 1'\n",
|
||||
"\n",
|
||||
"B, F, T = symbols('B, F, T', real = True, positive = True)\n",
|
||||
"# From Aly-Lee:\n",
|
||||
|
||||
@@ -14,25 +14,24 @@ Residual Helmholtz Energy Terms:
|
||||
|
||||
Term | Helmholtz Energy Contribution
|
||||
---------- | ------------------------------
|
||||
ResidualHelmholtzPower | \f$ \alpha_r=\left\lbrace\begin{array}{cc}\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} & l_i=0\\ \displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}) & l_i\neq 0\end{array}\right.\f$
|
||||
ResidualHelmholtzExponential | \f$ \alpha_r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\gamma_i\delta^{l_i}) \f$
|
||||
ResidualHelmholtzGaussian | \f$ \alpha_r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\eta_i(\delta-\epsilon_i)^2-\beta_i(\tau-\gamma_i)^2)\f$
|
||||
ResidualHelmholtzGERG2008Gaussian | \f$ \alpha_r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\eta_i(\delta-\epsilon_i)^2-\beta_i(\delta-\gamma_i))\f$
|
||||
ResidualHelmholtzLemmon2005 | \f$ \alpha_r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}) \exp(-\tau^{m_i})\f$
|
||||
ResidualHelmholtzNonAnalytic | \f$ \begin{array}{c}\alpha_r&=&\displaystyle\sum_i n_i \Delta^{b_i}\delta\psi \\ \Delta & = & \theta^2+B_i[(\delta-1)^2]^{a_i}\\ \theta & = & (1-\tau)+A_i[(\delta-1)^2]^{1/(2\beta_i)}\\ \psi & = & \exp(-C_i(\delta-1)^2-D_i(\tau-1)^2) \end{array}\f$
|
||||
ResidualHelmholtzSAFTAssociating | \f$ \alpha_r = am\left(\ln X-\frac{X}{2}+\frac{1}{2}\right); \f$
|
||||
ResidualHelmholtzPower | \f$ \alpha^r=\left\lbrace\begin{array}{cc}\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} & l_i=0\\ \displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}) & l_i\neq 0\end{array}\right.\f$
|
||||
ResidualHelmholtzExponential | \f$ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\gamma_i\delta^{l_i}) \f$
|
||||
ResidualHelmholtzGaussian | \f$ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\eta_i(\delta-\epsilon_i)^2-\beta_i(\tau-\gamma_i)^2)\f$
|
||||
ResidualHelmholtzGERG2008Gaussian | \f$ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\eta_i(\delta-\epsilon_i)^2-\beta_i(\delta-\gamma_i))\f$
|
||||
ResidualHelmholtzLemmon2005 | \f$ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}) \exp(-\tau^{m_i})\f$
|
||||
ResidualHelmholtzNonAnalytic | \f$ \begin{array}{c}\alpha^r&=&\displaystyle\sum_i n_i \Delta^{b_i}\delta\psi \\ \Delta & = & \theta^2+B_i[(\delta-1)^2]^{a_i}\\ \theta & = & (1-\tau)+A_i[(\delta-1)^2]^{1/(2\beta_i)}\\ \psi & = & \exp(-C_i(\delta-1)^2-D_i(\tau-1)^2) \end{array}\f$
|
||||
ResidualHelmholtzSAFTAssociating | \f$ \alpha^r = am\left(\ln X-\frac{X}{2}+\frac{1}{2}\right); \f$
|
||||
|
||||
|
||||
Ideal-Gas Helmholtz Energy Terms:
|
||||
|
||||
Term | Helmholtz Energy Contribution
|
||||
---------- | ------------------------------
|
||||
IdealHelmholtzLead | \f$ \alpha_0 = n_1 + n_2\tau + \ln\delta \f$
|
||||
IdealHelmholtzEnthalpyEntropyOffset | \f$ \alpha_0 = \displaystyle\frac{\Delta s}{R_u/M}+\frac{\Delta h}{(R_u/M)T}\tau \f$
|
||||
IdealHelmholtzLogTau | \f$ \alpha_0 = n_1\log\tau \f$
|
||||
IdealHelmholtzPower | \f$ \alpha_0 = \displaystyle\sum_i n_i\tau^{t_i} \f$
|
||||
IdealHelmholtzPlanckEinstein | \f$ \alpha_0 = \displaystyle\sum_i n_i\log[1-\exp(-\theta_i\tau)] \f$
|
||||
IdealHelmholtzPlanckEinstein2 | \f$ \alpha_0 = \displaystyle\sum_i n_i\log[c_i+\exp(\theta_i\tau)] \f$
|
||||
IdealHelmholtzLead | \f$ \alpha^0 = n_1 + n_2\tau + \ln\delta \f$
|
||||
IdealHelmholtzEnthalpyEntropyOffset | \f$ \alpha^0 = \displaystyle\frac{\Delta s}{R_u/M}+\frac{\Delta h}{(R_u/M)T}\tau \f$
|
||||
IdealHelmholtzLogTau | \f$ \alpha^0 = n_1\log\tau \f$
|
||||
IdealHelmholtzPower | \f$ \alpha^0 = \displaystyle\sum_i n_i\tau^{t_i} \f$
|
||||
IdealHelmholtzPlanckEinsteinGeneralized | \f$ \alpha^0 = \displaystyle\sum_i n_i\log[c_i+d_i\exp(\theta_i\tau)] \f$
|
||||
*/
|
||||
class BaseHelmholtzTerm{
|
||||
public:
|
||||
@@ -107,7 +106,7 @@ struct ResidualHelmholtzPowerElement
|
||||
/*!
|
||||
Term of the form
|
||||
\f[
|
||||
\alpha_r=\left\lbrace\begin{array}{cc}\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} & l_i=0\\ \displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}) & l_i\neq 0\end{array}\right.
|
||||
\alpha^r=\left\lbrace\begin{array}{cc}\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} & l_i=0\\ \displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\delta^{l_i}) & l_i\neq 0\end{array}\right.
|
||||
\f]
|
||||
*/
|
||||
class ResidualHelmholtzPower : public BaseHelmholtzTerm{
|
||||
@@ -162,7 +161,7 @@ struct ResidualHelmholtzExponentialElement
|
||||
};
|
||||
/**
|
||||
Term of the form
|
||||
\f[ \alpha_r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\gamma_i\delta^{l_i}) \f]
|
||||
\f[ \alpha^r=\displaystyle\sum_i n_i \delta^{d_i} \tau^{t_i} \exp(-\gamma_i\delta^{l_i}) \f]
|
||||
*/
|
||||
class ResidualHelmholtzExponential : public BaseHelmholtzTerm{
|
||||
|
||||
@@ -573,7 +572,7 @@ public:
|
||||
/// The leading term in the EOS used to set the desired reference state
|
||||
/**
|
||||
\f[
|
||||
\alpha_0 = \log(\delta)+a_1+a_2\tau
|
||||
\alpha^0 = \log(\delta)+a_1+a_2\tau
|
||||
\f]
|
||||
*/
|
||||
class IdealHelmholtzLead : public BaseHelmholtzTerm{
|
||||
@@ -632,7 +631,7 @@ public:
|
||||
/// The term in the EOS used to shift the reference state of the fluid
|
||||
/**
|
||||
\f[
|
||||
\alpha_0 = a_1+a_2\tau
|
||||
\alpha^0 = a_1+a_2\tau
|
||||
\f]
|
||||
*/
|
||||
class IdealHelmholtzEnthalpyEntropyOffset : public BaseHelmholtzTerm{
|
||||
@@ -682,7 +681,7 @@ public:
|
||||
|
||||
/**
|
||||
\f[
|
||||
\alpha_0 = a_1\ln\tau
|
||||
\alpha^0 = a_1\ln\tau
|
||||
\f]
|
||||
*/
|
||||
class IdealHelmholtzLogTau : public BaseHelmholtzTerm
|
||||
@@ -735,7 +734,7 @@ public:
|
||||
|
||||
/**
|
||||
\f[
|
||||
\alpha_0 = \displaystyle\sum_i n_i\tau^{t_i}
|
||||
\alpha^0 = \displaystyle\sum_i n_i\tau^{t_i}
|
||||
\f]
|
||||
*/
|
||||
class IdealHelmholtzPower : public BaseHelmholtzTerm{
|
||||
@@ -793,33 +792,42 @@ public:
|
||||
|
||||
/**
|
||||
\f[
|
||||
\alpha_0 = \displaystyle\sum_i n_i\log[1-\exp(-\theta_i\tau)]
|
||||
\alpha^0 = \displaystyle\sum_i n_i\log[c_i+d_i\exp(\theta_i\tau)]
|
||||
\f]
|
||||
*/
|
||||
class IdealHelmholtzPlanckEinstein : public BaseHelmholtzTerm{
|
||||
class IdealHelmholtzPlanckEinsteinGeneralized : public BaseHelmholtzTerm{
|
||||
|
||||
private:
|
||||
std::vector<long double> n,theta; // Use these variables internally
|
||||
std::vector<long double> n,theta,c,d; // Use these variables internally
|
||||
std::size_t N;
|
||||
bool enabled;
|
||||
public:
|
||||
IdealHelmholtzPlanckEinstein(){N = 0; enabled = false;}
|
||||
IdealHelmholtzPlanckEinsteinGeneralized(){N = 0; enabled = false;}
|
||||
// Constructor with std::vector instances
|
||||
IdealHelmholtzPlanckEinstein(std::vector<long double> n, std::vector<long double> theta)
|
||||
:n(n), theta(theta)
|
||||
IdealHelmholtzPlanckEinsteinGeneralized(std::vector<long double> n, std::vector<long double> theta, std::vector<long double> c, std::vector<long double> d)
|
||||
:n(n), theta(theta), c(c), d(d)
|
||||
{
|
||||
N = n.size();
|
||||
enabled = true;
|
||||
};
|
||||
|
||||
//Destructor
|
||||
~IdealHelmholtzPlanckEinstein(){};
|
||||
// Destructor
|
||||
~IdealHelmholtzPlanckEinsteinGeneralized(){};
|
||||
|
||||
// Extend the vectors to allow for multiple instances feeding values to this function
|
||||
void extend(std::vector<long double> n, std::vector<long double> theta, std::vector<long double> c, std::vector<long double> d)
|
||||
{
|
||||
this->n.insert(this->n.end(), n.begin(), n.end());
|
||||
this->theta.insert(this->theta.end(), theta.begin(), theta.end());
|
||||
this->c.insert(this->c.end(), c.begin(), c.end());
|
||||
this->d.insert(this->d.end(), d.begin(), d.end());
|
||||
}
|
||||
|
||||
bool is_enabled(){return enabled;};
|
||||
|
||||
void to_json(rapidjson::Value &el, rapidjson::Document &doc)
|
||||
{
|
||||
el.AddMember("type","IdealHelmholtzPlanckEinstein",doc.GetAllocator());
|
||||
el.AddMember("type","IdealHelmholtzPlanckEinsteinGeneralized",doc.GetAllocator());
|
||||
cpjson::set_long_double_array("n",n,el,doc);
|
||||
cpjson::set_long_double_array("theta",theta,el,doc);
|
||||
};
|
||||
@@ -828,81 +836,22 @@ public:
|
||||
long double base(const long double &tau, const long double &delta) throw(){
|
||||
if (!enabled){return 0.0;}
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){
|
||||
s += n[i]*log(1.0-exp(-theta[i]*tau));
|
||||
} return s;
|
||||
s += n[i]*log(c[i]+d[i]*exp(theta[i]*tau));
|
||||
}
|
||||
return s;
|
||||
};
|
||||
long double dTau(const long double &tau, const long double &delta) throw(){
|
||||
if (!enabled){return 0.0;}
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*theta[i]*(1.0/(1.0-exp(-theta[i]*tau))-1.0);} return s;
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*theta[i]*d[i]*exp(theta[i]*tau)/(c[i]+d[i]*exp(theta[i]*tau));}
|
||||
return s;
|
||||
};
|
||||
long double dTau2(const long double &tau, const long double &delta) throw(){
|
||||
if (!enabled){return 0.0;}
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s -= n[i]*pow(theta[i],2)*exp(theta[i]*tau)/pow(1.0-exp(theta[i]*tau),2);} return s;
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*pow(theta[i],2)*c[i]*d[i]*exp(theta[i]*tau)/pow(c[i]+d[i]*exp(theta[i]*tau),2);} return s;
|
||||
};
|
||||
long double dTau3(const long double &tau, const long double &delta) throw(){
|
||||
if (!enabled){return 0.0;}
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*pow(theta[i],2)*theta[i]*exp(theta[i]*tau)*(exp(theta[i]*tau)+1)/pow(exp(theta[i]*tau)-1,3);} return s;
|
||||
};
|
||||
long double dDelta(const long double &tau, const long double &delta) throw(){return 0.0;};
|
||||
long double dDelta2(const long double &tau, const long double &delta) throw(){return 0.0;};
|
||||
long double dDelta2_dTau(const long double &tau, const long double &delta) throw(){return 0.0;};
|
||||
long double dDelta_dTau(const long double &tau, const long double &delta) throw(){return 0.0;};
|
||||
long double dDelta_dTau2(const long double &tau, const long double &delta) throw(){return 0.0;};
|
||||
long double dDelta3(const long double &tau, const long double &delta) throw(){return 0;};
|
||||
};
|
||||
|
||||
/**
|
||||
\f[
|
||||
\alpha_0 = \displaystyle\sum_i n_i\log[c_i+\exp(\theta_i\tau)]
|
||||
\f]
|
||||
*/
|
||||
class IdealHelmholtzPlanckEinstein2 : public BaseHelmholtzTerm{
|
||||
|
||||
private:
|
||||
std::vector<long double> n,theta,c; // Use these variables internally
|
||||
std::size_t N;
|
||||
bool enabled;
|
||||
public:
|
||||
IdealHelmholtzPlanckEinstein2(){N = 0; enabled = false;}
|
||||
// Constructor with std::vector instances
|
||||
IdealHelmholtzPlanckEinstein2(const std::vector<long double> &n,
|
||||
const std::vector<long double> &theta,
|
||||
const std::vector<long double> &c)
|
||||
:n(n), theta(theta), c(c)
|
||||
{
|
||||
N = n.size();
|
||||
enabled = true;
|
||||
};
|
||||
|
||||
//Destructor
|
||||
~IdealHelmholtzPlanckEinstein2(){};
|
||||
|
||||
bool is_enabled(){return enabled;};
|
||||
|
||||
void to_json(rapidjson::Value &el, rapidjson::Document &doc)
|
||||
{
|
||||
el.AddMember("type","IdealHelmholtzPlanckEinstein2",doc.GetAllocator());
|
||||
cpjson::set_long_double_array("n",n,el,doc);
|
||||
cpjson::set_long_double_array("theta",theta,el,doc);
|
||||
cpjson::set_long_double_array("c",c,el,doc);
|
||||
};
|
||||
|
||||
// Term and its derivatives
|
||||
long double base(const long double &tau, const long double &delta) throw(){
|
||||
if (!enabled){return 0.0;}
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*log(c[i]+exp(theta[i]*tau));} return s;
|
||||
};
|
||||
long double dTau(const long double &tau, const long double &delta) throw(){
|
||||
if (!enabled){return 0.0;}
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*theta[i]*exp(tau*theta[i])/(c[i]+exp(theta[i]*tau));} return s;
|
||||
};
|
||||
long double dTau2(const long double &tau, const long double &delta) throw(){
|
||||
if (!enabled){return 0.0;}
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*pow(theta[i],2)*c[i]*exp(tau*theta[i])/pow(c[i]+exp(tau*theta[i]),2);} return s;
|
||||
};
|
||||
long double dTau3(const long double &tau, const long double &delta) throw(){
|
||||
if (!enabled){return 0.0;}
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*pow(theta[i],2)*c[i]*(-theta[i])*exp(theta[i]*tau)*(exp(theta[i]*tau)-c[i])/pow(exp(theta[i]*tau)+c[i],3);} return s;
|
||||
long double s=0; for (std::size_t i=0; i < N; ++i){s += n[i]*pow(theta[i],3)*c[i]*d[i]*(c[i]-d[i]*exp(theta[i]*tau))*exp(theta[i]*tau)/pow(c[i]+d[i]*exp(theta[i]*tau),3);} return s;
|
||||
};
|
||||
long double dDelta(const long double &tau, const long double &delta) throw(){return 0.0;};
|
||||
long double dDelta2(const long double &tau, const long double &delta) throw(){return 0.0;};
|
||||
@@ -986,6 +935,13 @@ public:
|
||||
N = c.size();
|
||||
};
|
||||
|
||||
void extend(const std::vector<long double> &c, const std::vector<long double> &t)
|
||||
{
|
||||
this->c.insert(this->c.end(), c.begin(), c.end());
|
||||
this->t.insert(this->t.end(), t.begin(), t.end());
|
||||
N += c.size();
|
||||
}
|
||||
|
||||
/// Destructor
|
||||
~IdealHelmholtzCP0PolyT(){};
|
||||
|
||||
@@ -1147,100 +1103,89 @@ public:
|
||||
IdealHelmholtzEnthalpyEntropyOffset EnthalpyEntropyOffset;
|
||||
IdealHelmholtzLogTau LogTau;
|
||||
IdealHelmholtzPower Power;
|
||||
IdealHelmholtzPlanckEinstein PlanckEinstein;
|
||||
IdealHelmholtzPlanckEinstein2 PlanckEinstein2;
|
||||
IdealHelmholtzPlanckEinsteinGeneralized PlanckEinstein;
|
||||
|
||||
IdealHelmholtzCP0Constant CP0Constant;
|
||||
IdealHelmholtzCP0PolyT CP0PolyT;
|
||||
IdealHelmholtzCP0AlyLee CP0AlyLee;
|
||||
|
||||
long double base(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.base(tau, delta) + EnthalpyEntropyOffset.base(tau, delta)
|
||||
+ LogTau.base(tau, delta) + Power.base(tau, delta)
|
||||
+ PlanckEinstein.base(tau, delta) + PlanckEinstein2.base(tau, delta)
|
||||
+ PlanckEinstein.base(tau, delta)
|
||||
+ CP0Constant.base(tau, delta) + CP0PolyT.base(tau, delta)
|
||||
+ CP0AlyLee.base(tau, delta)
|
||||
);
|
||||
};
|
||||
long double dDelta(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dDelta(tau, delta) + EnthalpyEntropyOffset.dDelta(tau, delta)
|
||||
+ LogTau.dDelta(tau, delta) + Power.dDelta(tau, delta)
|
||||
+ PlanckEinstein.dDelta(tau, delta) + PlanckEinstein2.dDelta(tau, delta)
|
||||
+ PlanckEinstein.dDelta(tau, delta)
|
||||
+ CP0Constant.dDelta(tau, delta) + CP0PolyT.dDelta(tau, delta)
|
||||
+ CP0AlyLee.dDelta(tau, delta)
|
||||
);
|
||||
};
|
||||
long double dTau(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dTau(tau, delta) + EnthalpyEntropyOffset.dTau(tau, delta)
|
||||
+ LogTau.dTau(tau, delta) + Power.dTau(tau, delta)
|
||||
+ PlanckEinstein.dTau(tau, delta) + PlanckEinstein2.dTau(tau, delta)
|
||||
+ PlanckEinstein.dTau(tau, delta)
|
||||
+ CP0Constant.dTau(tau, delta) + CP0PolyT.dTau(tau, delta)
|
||||
+ CP0AlyLee.dTau(tau, delta)
|
||||
);
|
||||
};
|
||||
long double dDelta2(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dDelta2(tau, delta) + EnthalpyEntropyOffset.dDelta2(tau, delta)
|
||||
+ LogTau.dDelta2(tau, delta) + Power.dDelta2(tau, delta)
|
||||
+ PlanckEinstein.dDelta2(tau, delta) + PlanckEinstein2.dDelta2(tau, delta)
|
||||
+ PlanckEinstein.dDelta2(tau, delta)
|
||||
+ CP0Constant.dDelta2(tau, delta) + CP0PolyT.dDelta2(tau, delta)
|
||||
+ CP0AlyLee.dDelta2(tau, delta)
|
||||
);
|
||||
};
|
||||
long double dDelta_dTau(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dDelta_dTau(tau, delta) + EnthalpyEntropyOffset.dDelta_dTau(tau, delta)
|
||||
+ LogTau.dDelta_dTau(tau, delta) + Power.dDelta_dTau(tau, delta)
|
||||
+ PlanckEinstein.dDelta_dTau(tau, delta) + PlanckEinstein2.dDelta_dTau(tau, delta)
|
||||
+ PlanckEinstein.dDelta_dTau(tau, delta)
|
||||
+ CP0Constant.dDelta_dTau(tau, delta) + CP0PolyT.dDelta_dTau(tau, delta)
|
||||
+ CP0AlyLee.dDelta_dTau(tau, delta)
|
||||
);
|
||||
};
|
||||
long double dTau2(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dTau2(tau, delta) + EnthalpyEntropyOffset.dTau2(tau, delta)
|
||||
+ LogTau.dTau2(tau, delta) + Power.dTau2(tau, delta)
|
||||
+ PlanckEinstein.dTau2(tau, delta) + PlanckEinstein2.dTau2(tau, delta)
|
||||
+ PlanckEinstein.dTau2(tau, delta)
|
||||
+ CP0Constant.dTau2(tau, delta) + CP0PolyT.dTau2(tau, delta)
|
||||
+ CP0AlyLee.dTau2(tau, delta));
|
||||
);
|
||||
};
|
||||
long double dDelta3(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dDelta3(tau, delta) + EnthalpyEntropyOffset.dDelta3(tau, delta)
|
||||
+ LogTau.dDelta3(tau, delta) + Power.dDelta3(tau, delta)
|
||||
+ PlanckEinstein.dDelta3(tau, delta) + PlanckEinstein2.dDelta3(tau, delta)
|
||||
+ PlanckEinstein.dDelta3(tau, delta)
|
||||
+ CP0Constant.dDelta3(tau, delta) + CP0PolyT.dDelta3(tau, delta)
|
||||
+ CP0AlyLee.dDelta3(tau, delta)
|
||||
);
|
||||
};
|
||||
long double dDelta2_dTau(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dDelta2_dTau(tau, delta) + EnthalpyEntropyOffset.dDelta2_dTau(tau, delta)
|
||||
+ LogTau.dDelta2_dTau(tau, delta) + Power.dDelta2_dTau(tau, delta)
|
||||
+ PlanckEinstein.dDelta2_dTau(tau, delta) + PlanckEinstein2.dDelta2_dTau(tau, delta)
|
||||
+ PlanckEinstein.dDelta2_dTau(tau, delta)
|
||||
+ CP0Constant.dDelta2_dTau(tau, delta) + CP0PolyT.dDelta2_dTau(tau, delta)
|
||||
+ CP0AlyLee.dDelta2_dTau(tau, delta)
|
||||
);
|
||||
};
|
||||
long double dDelta_dTau2(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dDelta_dTau2(tau, delta) + EnthalpyEntropyOffset.dDelta_dTau2(tau, delta)
|
||||
+ LogTau.dDelta_dTau2(tau, delta) + Power.dDelta_dTau2(tau, delta)
|
||||
+ PlanckEinstein.dDelta_dTau2(tau, delta) + PlanckEinstein2.dDelta_dTau2(tau, delta)
|
||||
+ PlanckEinstein.dDelta_dTau2(tau, delta)
|
||||
+ CP0Constant.dDelta_dTau2(tau, delta) + CP0PolyT.dDelta_dTau2(tau, delta)
|
||||
+ CP0AlyLee.dDelta_dTau2(tau, delta)
|
||||
);
|
||||
};
|
||||
long double dTau3(const long double &tau, const long double &delta)
|
||||
{
|
||||
return (Lead.dTau3(tau, delta) + EnthalpyEntropyOffset.dTau3(tau, delta)
|
||||
+ LogTau.dTau3(tau, delta) + Power.dTau3(tau, delta)
|
||||
+ PlanckEinstein.dTau3(tau, delta) + PlanckEinstein2.dTau3(tau, delta)
|
||||
+ PlanckEinstein.dTau3(tau, delta)
|
||||
+ CP0Constant.dTau3(tau, delta) + CP0PolyT.dTau3(tau, delta)
|
||||
+ CP0AlyLee.dTau3(tau, delta)
|
||||
);
|
||||
};
|
||||
};
|
||||
|
||||
@@ -143,20 +143,36 @@ protected:
|
||||
long double a = cpjson::get_double(contribution,"a");
|
||||
EOS.alpha0.LogTau = IdealHelmholtzLogTau(a);
|
||||
}
|
||||
else if (!type.compare("IdealGasHelmholtzPlanckEinsteinGeneralized"))
|
||||
{
|
||||
// Retrieve the values
|
||||
std::vector<long double> n = cpjson::get_long_double_array(contribution["n"]);
|
||||
std::vector<long double> t = cpjson::get_long_double_array(contribution["t"]);
|
||||
|
||||
std::vector<long double> c = cpjson::get_long_double_array(contribution["c"]);
|
||||
std::vector<long double> d = cpjson::get_long_double_array(contribution["d"]);
|
||||
if (EOS.alpha0.PlanckEinstein.is_enabled() == true){
|
||||
EOS.alpha0.PlanckEinstein.extend(n, t, c, d);
|
||||
}
|
||||
else{
|
||||
EOS.alpha0.PlanckEinstein = IdealHelmholtzPlanckEinsteinGeneralized(n, t, c, d);
|
||||
}
|
||||
}
|
||||
else if (!type.compare("IdealGasHelmholtzPlanckEinstein"))
|
||||
{
|
||||
if (EOS.alpha0.PlanckEinstein.is_enabled() == true){throw ValueError("Cannot add ");}
|
||||
// Retrieve the values
|
||||
std::vector<long double> n = cpjson::get_long_double_array(contribution["n"]);
|
||||
std::vector<long double> t = cpjson::get_long_double_array(contribution["t"]);
|
||||
EOS.alpha0.PlanckEinstein = IdealHelmholtzPlanckEinstein(n, t);
|
||||
}
|
||||
else if (!type.compare("IdealGasHelmholtzPlanckEinstein2"))
|
||||
{
|
||||
if (EOS.alpha0.PlanckEinstein2.is_enabled() == true){throw ValueError("Cannot add");}
|
||||
std::vector<long double> n = cpjson::get_long_double_array(contribution["n"]);
|
||||
std::vector<long double> t = cpjson::get_long_double_array(contribution["t"]);
|
||||
std::vector<long double> c = cpjson::get_long_double_array(contribution["c"]);
|
||||
EOS.alpha0.PlanckEinstein2 = IdealHelmholtzPlanckEinstein2(n, t, c);
|
||||
// Flip the sign of theta
|
||||
for (std::size_t i = 0; i < t.size(); ++i){ t[i] *= -1;}
|
||||
std::vector<long double> c(n.size(), 1);
|
||||
std::vector<long double> d(c.size(), -1);
|
||||
if (EOS.alpha0.PlanckEinstein.is_enabled() == true){
|
||||
EOS.alpha0.PlanckEinstein.extend(n, t, c, d);
|
||||
}
|
||||
else{
|
||||
EOS.alpha0.PlanckEinstein = IdealHelmholtzPlanckEinsteinGeneralized(n, t, c, d);
|
||||
}
|
||||
}
|
||||
else if (!type.compare("IdealGasHelmholtzCP0Constant"))
|
||||
{
|
||||
@@ -177,11 +193,45 @@ protected:
|
||||
}
|
||||
else if (!type.compare("IdealGasHelmholtzCP0AlyLee"))
|
||||
{
|
||||
if (EOS.alpha0.CP0AlyLee.is_enabled() == true){std::cout << "Cannot add IdealGasHelmholtzCP0AlyLee\n";}
|
||||
std::vector<long double> c = cpjson::get_long_double_array(contribution["c"]);
|
||||
|
||||
std::vector<long double> constants = cpjson::get_long_double_array(contribution["c"]);
|
||||
long double Tc = cpjson::get_double(contribution, "Tc");
|
||||
long double T0 = cpjson::get_double(contribution, "T0");
|
||||
EOS.alpha0.CP0AlyLee = IdealHelmholtzCP0AlyLee(c, Tc, T0);
|
||||
|
||||
// Take the constant term if nonzero and set it as a polyT term
|
||||
if (fabs(constants[0]) > 1e-14){
|
||||
std::vector<long double> c(1,constants[0]), t(1,0);
|
||||
if (EOS.alpha0.CP0PolyT.is_enabled() == true){
|
||||
EOS.alpha0.CP0PolyT.extend(c,t);
|
||||
}
|
||||
else{
|
||||
EOS.alpha0.CP0PolyT = IdealHelmholtzCP0PolyT(c, t, Tc, T0);
|
||||
}
|
||||
}
|
||||
|
||||
std::vector<long double> n, c, d, t;
|
||||
if (fabs(constants[1]) > 1e-14){
|
||||
// sinh term can be converted by setting a_k = C, b_k = 2*D, c_k = -1, d_k = 1
|
||||
n.push_back(constants[1]);
|
||||
t.push_back(-2*constants[2]/Tc);
|
||||
c.push_back(1);
|
||||
d.push_back(-1);
|
||||
}
|
||||
|
||||
if (fabs(constants[3]) > 1e-14){
|
||||
// cosh term can be converted by setting a_k = C, b_k = 2*D, c_k = 1, d_k = 1
|
||||
n.push_back(-constants[3]);
|
||||
t.push_back(-2*constants[4]/Tc);
|
||||
c.push_back(1);
|
||||
d.push_back(1);
|
||||
}
|
||||
|
||||
if (EOS.alpha0.PlanckEinstein.is_enabled() == true){
|
||||
EOS.alpha0.PlanckEinstein.extend(n, t, c, d);
|
||||
}
|
||||
else{
|
||||
EOS.alpha0.PlanckEinstein = IdealHelmholtzPlanckEinsteinGeneralized(n, t, c, d);
|
||||
}
|
||||
}
|
||||
else if (!type.compare("IdealGasHelmholtzEnthalpyEntropyOffset"))
|
||||
{
|
||||
|
||||
@@ -1715,42 +1715,50 @@ long double HelmholtzEOSMixtureBackend::calc_alphar_deriv_nocache(const int nTau
|
||||
long double HelmholtzEOSMixtureBackend::calc_alpha0_deriv_nocache(const int nTau, const int nDelta, const std::vector<long double> &mole_fractions,
|
||||
const long double &tau, const long double &delta, const long double &Tr, const long double &rhor)
|
||||
{
|
||||
long double val;
|
||||
if (is_pure_or_pseudopure)
|
||||
{
|
||||
if (nTau == 0 && nDelta == 0){
|
||||
return components[0]->pEOS->base0(tau, delta);
|
||||
val = components[0]->pEOS->base0(tau, delta);
|
||||
}
|
||||
else if (nTau == 0 && nDelta == 1){
|
||||
return components[0]->pEOS->dalpha0_dDelta(tau, delta);
|
||||
val = components[0]->pEOS->dalpha0_dDelta(tau, delta);
|
||||
}
|
||||
else if (nTau == 1 && nDelta == 0){
|
||||
return components[0]->pEOS->dalpha0_dTau(tau, delta);
|
||||
val = components[0]->pEOS->dalpha0_dTau(tau, delta);
|
||||
}
|
||||
else if (nTau == 0 && nDelta == 2){
|
||||
return components[0]->pEOS->d2alpha0_dDelta2(tau, delta);
|
||||
val = components[0]->pEOS->d2alpha0_dDelta2(tau, delta);
|
||||
}
|
||||
else if (nTau == 1 && nDelta == 1){
|
||||
return components[0]->pEOS->d2alpha0_dDelta_dTau(tau, delta);
|
||||
val = components[0]->pEOS->d2alpha0_dDelta_dTau(tau, delta);
|
||||
}
|
||||
else if (nTau == 2 && nDelta == 0){
|
||||
return components[0]->pEOS->d2alpha0_dTau2(tau, delta);
|
||||
val = components[0]->pEOS->d2alpha0_dTau2(tau, delta);
|
||||
}
|
||||
else if (nTau == 0 && nDelta == 3){
|
||||
return components[0]->pEOS->d3alpha0_dDelta3(tau, delta);
|
||||
val = components[0]->pEOS->d3alpha0_dDelta3(tau, delta);
|
||||
}
|
||||
else if (nTau == 1 && nDelta == 2){
|
||||
return components[0]->pEOS->d3alpha0_dDelta2_dTau(tau, delta);
|
||||
val = components[0]->pEOS->d3alpha0_dDelta2_dTau(tau, delta);
|
||||
}
|
||||
else if (nTau == 2 && nDelta == 1){
|
||||
return components[0]->pEOS->d3alpha0_dDelta_dTau2(tau, delta);
|
||||
val = components[0]->pEOS->d3alpha0_dDelta_dTau2(tau, delta);
|
||||
}
|
||||
else if (nTau == 3 && nDelta == 0){
|
||||
return components[0]->pEOS->d3alpha0_dTau3(tau, delta);
|
||||
val = components[0]->pEOS->d3alpha0_dTau3(tau, delta);
|
||||
}
|
||||
else
|
||||
{
|
||||
throw ValueError();
|
||||
}
|
||||
if (!ValidNumber(val)){
|
||||
calc_alpha0_deriv_nocache(nTau,nDelta,mole_fractions,tau,delta,Tr,rhor);
|
||||
throw ValueError(format("calc_alpha0_deriv_nocache returned invalid number with inputs nTau: %d, nDelta: %d", nTau, nDelta));
|
||||
}
|
||||
else{
|
||||
return val;
|
||||
}
|
||||
}
|
||||
else{
|
||||
// See Table B5, GERG 2008 from Kunz Wagner, JCED, 2012
|
||||
|
||||
@@ -1691,10 +1691,11 @@ long double IdealHelmholtzCP0AlyLee::dTau(const long double &tau, const long dou
|
||||
}
|
||||
long double IdealHelmholtzCP0AlyLee::anti_deriv_cp0_tau2(const long double &tau)
|
||||
{
|
||||
return -c[0]/tau + 2*c[1]*c[2]/(Tc*(exp(-(2*c[2]*tau)/Tc)-1)) + 2*c[3]*c[4]/(Tc*(exp(-(2*c[4]*tau)/Tc)+1));
|
||||
return -c[0]/tau + 2*c[1]*c[2]/Tc/(exp(-2*c[2]*tau/Tc)-1) - 2*c[3]*c[4]/Tc*(exp(2*c[4]*tau/Tc)+1);
|
||||
}
|
||||
long double IdealHelmholtzCP0AlyLee::anti_deriv_cp0_tau(const long double &tau)
|
||||
{
|
||||
long double lnarg =-1 + exp(-2*c[2]*tau/Tc);
|
||||
long double term1 = c[0]*log(tau);
|
||||
long double term2 = 2*c[1]*c[2]*tau/(-Tc + Tc*exp(-2*c[2]*tau/Tc)) + c[1]*log(-1 + exp(-2*c[2]*tau/Tc)) + 2*c[1]*c[2]*tau/Tc;
|
||||
long double term3 = -c[3]*(Tc*exp(2*c[4]*tau/Tc)*log(exp(2*c[4]*tau/Tc) + 1) + Tc*log(exp(2*c[4]*tau/Tc) + 1) - 2*c[4]*tau*exp(2*c[4]*tau/Tc))/(Tc*(exp(2*c[4]*tau/Tc) + 1));
|
||||
@@ -1716,7 +1717,6 @@ long double IdealHelmholtzCP0AlyLee::dTau3(const long double &tau, const long do
|
||||
|
||||
/*
|
||||
IdealHelmholtzEnthalpyEntropyOffset EnthalpyEntropyOffset;
|
||||
IdealHelmholtzCP0AlyLee CP0AlyLee;
|
||||
*/
|
||||
|
||||
#ifdef ENABLE_CATCH
|
||||
@@ -1728,8 +1728,8 @@ class HelmholtzConsistencyFixture
|
||||
public:
|
||||
long double numerical, analytic;
|
||||
|
||||
std::tr1::shared_ptr<CoolProp::BaseHelmholtzTerm> Lead, LogTau, IGPower, PlanckEinstein, PlanckEinstein2,
|
||||
CP0Constant, CP0PolyT, CP0AlyLee, Gaussian, Lemmon2005, Power, SAFT, NonAnalytic, Exponential, GERG2008;
|
||||
std::tr1::shared_ptr<CoolProp::BaseHelmholtzTerm> Lead, LogTau, IGPower, PlanckEinstein,
|
||||
CP0Constant, CP0PolyT, Gaussian, Lemmon2005, Power, SAFT, NonAnalytic, Exponential, GERG2008;
|
||||
|
||||
HelmholtzConsistencyFixture(){
|
||||
Lead.reset(new CoolProp::IdealHelmholtzLead(1,3));
|
||||
@@ -1739,12 +1739,8 @@ public:
|
||||
IGPower.reset(new CoolProp::IdealHelmholtzPower(n,t));
|
||||
}
|
||||
{
|
||||
std::vector<long double> n(4,0), t(4,1); n[0] = 0.1; n[2] = 0.5; t[1] = 1; t[2] = 2; t[3] = 2;
|
||||
PlanckEinstein.reset(new CoolProp::IdealHelmholtzPlanckEinstein(n, t));
|
||||
}
|
||||
{
|
||||
std::vector<long double> n(4,0), t(4,1), c(4,1); n[0] = -0.1; n[2] = 0.1; t[1] = -1; t[2] = -2; t[3] = 2;
|
||||
PlanckEinstein2.reset(new CoolProp::IdealHelmholtzPlanckEinstein2(n, t, c));
|
||||
std::vector<long double> n(4,0), t(4,1), c(4,1), d(4,1); n[0] = 0.1; n[2] = 0.5; t[1] = 1; t[2] = 2; t[3] = 2;
|
||||
PlanckEinstein.reset(new CoolProp::IdealHelmholtzPlanckEinsteinGeneralized(n, t, c, d));
|
||||
}
|
||||
{
|
||||
long double T0 = 273.15, Tc = 345.857, c = 1.0578, t = 0.33;
|
||||
@@ -1752,11 +1748,6 @@ public:
|
||||
std::vector<long double>(1,t),
|
||||
Tc, T0));
|
||||
}
|
||||
{
|
||||
long double T0 = 518.109977174843, Tc = 645.78, c[] = {56.37158920013201, 118.0111016069331, 1792.1, 82.5909330141469, 786.8};
|
||||
CP0AlyLee.reset(new CoolProp::IdealHelmholtzCP0AlyLee(std::vector<long double>(c, c+sizeof(c)/sizeof(c[0])),
|
||||
Tc, T0));
|
||||
}
|
||||
CP0Constant.reset(new CoolProp::IdealHelmholtzCP0Constant(4/8.314472,300,250));
|
||||
{
|
||||
long double beta[] = {1.24, 0.821, 15.45, 2.21, 437, 0.743},
|
||||
@@ -1871,10 +1862,8 @@ public:
|
||||
else if (!t.compare("LogTau")){return LogTau;}
|
||||
else if (!t.compare("IGPower")){return IGPower;}
|
||||
else if (!t.compare("PlanckEinstein")){return PlanckEinstein;}
|
||||
else if (!t.compare("PlanckEinstein2")){return PlanckEinstein2;}
|
||||
else if (!t.compare("CP0Constant")){return CP0Constant;}
|
||||
else if (!t.compare("CP0PolyT")){return CP0PolyT;}
|
||||
else if (!t.compare("CP0AlyLee")){return CP0AlyLee;}
|
||||
|
||||
else if (!t.compare("Gaussian")){return Gaussian;}
|
||||
else if (!t.compare("Lemmon2005")){return Lemmon2005;}
|
||||
|
||||
@@ -154,8 +154,8 @@ int main()
|
||||
}
|
||||
if (1)
|
||||
{
|
||||
double rrr0 = PropsSI("O","T",350,"Q",0,"REFPROP::Water");
|
||||
double rrr2 = PropsSI("O","T",350,"Q",0,"Water");
|
||||
double rrr0 = PropsSI("C","T",350,"D",1e-13,"REFPROP::MDM");
|
||||
double rrr2 = PropsSI("C","T",350,"D",1e-13,"MDM");
|
||||
double rrr =0 ;
|
||||
}
|
||||
if (1)
|
||||
@@ -171,7 +171,8 @@ int main()
|
||||
}
|
||||
if (1)
|
||||
{
|
||||
double h1 = PropsSI("H","T",273.15,"Q",0,"CO2");
|
||||
double h1 = PropsSI("S","P",101325,"Q",0,"n-Pentane");
|
||||
std::string er = get_global_param_string("errstring");
|
||||
set_reference_stateS("n-Propane","NBP");
|
||||
double h2 = PropsSI("H","P",101325,"Q",0,"n-Propane");
|
||||
|
||||
|
||||
@@ -72,16 +72,6 @@ cpdef ndarray_or_iterable(object input):
|
||||
# if retval < 0:
|
||||
# raise ValueError('Unable to set reference state')
|
||||
#
|
||||
# cpdef add_REFPROP_fluid(string_like FluidName):
|
||||
# """
|
||||
# Add a REFPROP fluid to CoolProp internal structure
|
||||
#
|
||||
# example::
|
||||
#
|
||||
# add_REFPROP_fluid("REFPROP-PROPANE")
|
||||
#
|
||||
# """
|
||||
# _add_REFPROP_fluid(FluidName)
|
||||
#
|
||||
# cpdef long get_Fluid_index(string_like Fluid):
|
||||
# """
|
||||
@@ -116,9 +106,9 @@ cpdef ndarray_or_iterable(object input):
|
||||
|
||||
cpdef get_global_param_string(string param):
|
||||
return _get_global_param_string(param)
|
||||
#
|
||||
# cpdef get_fluid_param_string(string_like fluid, string_like param):
|
||||
# return _get_fluid_param_string(fluid, param)
|
||||
|
||||
cpdef get_fluid_param_string(string_like fluid, string_like param):
|
||||
return _get_fluid_param_string(fluid, param)
|
||||
#
|
||||
# cpdef __Props_err1(in1,in2,errstr):
|
||||
# if not len(errstr) == 0:
|
||||
@@ -155,53 +145,53 @@ cpdef PropsSI(in1, in2, in3, in4, in5, in6, in7 = None):
|
||||
else:
|
||||
return _PropsSI(in1, in2, in3, in4, in5, in6, in7)
|
||||
|
||||
# cpdef list FluidsList():
|
||||
# """
|
||||
# Return a list of strings of all fluid names
|
||||
#
|
||||
# Returns
|
||||
# -------
|
||||
# FluidsList : list of strings of fluid names
|
||||
# All the fluids that are included in CoolProp
|
||||
#
|
||||
# Notes
|
||||
# -----
|
||||
#
|
||||
# Here is an example::
|
||||
#
|
||||
# In [0]: from CoolProp.CoolProp import FluidsList
|
||||
#
|
||||
# In [1]: FluidsList()
|
||||
#
|
||||
# """
|
||||
# return _get_global_param_string("FluidsList").split(',')
|
||||
cpdef list FluidsList():
|
||||
"""
|
||||
Return a list of strings of all fluid names
|
||||
|
||||
Returns
|
||||
-------
|
||||
FluidsList : list of strings of fluid names
|
||||
All the fluids that are included in CoolProp
|
||||
|
||||
Notes
|
||||
-----
|
||||
|
||||
Here is an example::
|
||||
|
||||
In [0]: from CoolProp.CoolProp import FluidsList
|
||||
|
||||
In [1]: FluidsList()
|
||||
|
||||
"""
|
||||
return _get_global_param_string("FluidsList").split(',')
|
||||
|
||||
# cpdef get_aliases(str Fluid):
|
||||
# """
|
||||
# Return a comma separated string of aliases for the given fluid
|
||||
# """
|
||||
# cdef bytes _Fluid = Fluid.encode('ascii')
|
||||
# return [F.encode('ascii') for F in (_get_fluid_param_string(_Fluid,'aliases').encode('ascii')).decode('ascii').split(',')]
|
||||
cpdef get_aliases(str Fluid):
|
||||
"""
|
||||
Return a comma separated string of aliases for the given fluid
|
||||
"""
|
||||
cdef bytes _Fluid = Fluid.encode('ascii')
|
||||
return [F.encode('ascii') for F in (_get_fluid_param_string(_Fluid,'aliases').encode('ascii')).decode('ascii').split(',')]
|
||||
|
||||
#
|
||||
# cpdef string get_REFPROPname(str Fluid):
|
||||
# """
|
||||
# Return the REFPROP compatible name for the fluid (only useful on windows)
|
||||
#
|
||||
# Some fluids do not use the REFPROP name. For instance,
|
||||
# ammonia is R717, and propane is R290. You can still can still call CoolProp
|
||||
# using the name ammonia or R717, but REFPROP requires that you use a limited
|
||||
# subset of names. Therefore, this function that returns the REFPROP compatible
|
||||
# name. To then use this to call REFPROP, you would do something like::
|
||||
#
|
||||
# In [0]: from CoolProp.CoolProp import get_REFPROPname, Props
|
||||
#
|
||||
# In [1]: Fluid = 'REFPROP-' + get_REFPROPname('R290')
|
||||
#
|
||||
# In [2]: Props('D', 'T', 300, 'P', 300, Fluid)
|
||||
# """
|
||||
# cdef bytes _Fluid = Fluid.encode('ascii')
|
||||
# return _get_fluid_param_string(_Fluid,'REFPROP_name')
|
||||
cpdef string get_REFPROPname(str Fluid):
|
||||
"""
|
||||
Return the REFPROP compatible name for the fluid
|
||||
|
||||
Some fluids do not use the REFPROP name. For instance,
|
||||
ammonia is R717, and propane is R290. You can still can still call CoolProp
|
||||
using the name ammonia or R717, but REFPROP requires that you use a limited
|
||||
subset of names. Therefore, this function that returns the REFPROP compatible
|
||||
name. To then use this to call REFPROP, you would do something like::
|
||||
|
||||
In [0]: from CoolProp.CoolProp import get_REFPROPname, PropsSI
|
||||
|
||||
In [1]: get_REFPROPname('R290')
|
||||
|
||||
In [2]: PropsSI('D', 'T', 300, 'P', 300, Fluid)
|
||||
"""
|
||||
cdef bytes _Fluid = Fluid.encode('ascii')
|
||||
return _get_fluid_param_string(_Fluid,'REFPROP_name')
|
||||
|
||||
# cpdef string get_BibTeXKey(str Fluid, str key):
|
||||
# """
|
||||
@@ -230,31 +220,31 @@ cpdef PropsSI(in1, in2, in3, in4, in5, in6, in7 = None):
|
||||
# Return the current error string
|
||||
# """
|
||||
# return _get_global_param_string("errstring")
|
||||
# cpdef set_debug_level(int level):
|
||||
# """
|
||||
# Set the current debug level as integer in the range [0,10]
|
||||
#
|
||||
# Parameters
|
||||
# ----------
|
||||
# level : int
|
||||
# If level is 0, no output will be written to screen, if >0,
|
||||
# some output will be written to screen. The larger level is,
|
||||
# the more verbose the output will be
|
||||
# """
|
||||
# _set_debug_level(level)
|
||||
cpdef set_debug_level(int level):
|
||||
"""
|
||||
Set the current debug level as integer in the range [0,10]
|
||||
|
||||
Parameters
|
||||
----------
|
||||
level : int
|
||||
If level is 0, no output will be written to screen, if >0,
|
||||
some output will be written to screen. The larger level is,
|
||||
the more verbose the output will be
|
||||
"""
|
||||
_set_debug_level(level)
|
||||
|
||||
# cpdef get_debug_level():
|
||||
# """
|
||||
# Return the current debug level as integer
|
||||
#
|
||||
# Returns
|
||||
# -------
|
||||
# level : int
|
||||
# If level is 0, no output will be written to screen, if >0,
|
||||
# some output will be written to screen. The larger level is,
|
||||
# the more verbose the output will be
|
||||
# """
|
||||
# return _get_debug_level()
|
||||
cpdef int get_debug_level():
|
||||
"""
|
||||
Return the current debug level as integer
|
||||
|
||||
Returns
|
||||
-------
|
||||
level : int
|
||||
If level is 0, no output will be written to screen, if >0,
|
||||
some output will be written to screen. The larger level is,
|
||||
the more verbose the output will be
|
||||
"""
|
||||
return _get_debug_level()
|
||||
#
|
||||
# cpdef bint IsFluidType(string Fluid, string Type):
|
||||
# """
|
||||
@@ -286,8 +276,8 @@ cdef dict paras = {iDmass : 'D',
|
||||
iCpmass : 'C',
|
||||
# iC0 : 'C0',
|
||||
iCvmass : 'O',
|
||||
# iV : 'V',
|
||||
# iL : 'L',
|
||||
iV : 'V',
|
||||
iL : 'L',
|
||||
iSmass : 'S',
|
||||
iUmass : 'U',
|
||||
# iDpdT : 'dpdT'
|
||||
@@ -307,16 +297,16 @@ cdef class State:
|
||||
to calculate the enthalpy and pressure. Since the Equations of State are
|
||||
all explicit in temperature and density, each time you call something like::
|
||||
|
||||
h = Props('H','T',T','P',P,Fluid)
|
||||
s = Props('S','T',T','P',P,Fluid)
|
||||
h = PropsSI('H','T',T','P',P,Fluid)
|
||||
s = PropsSI('S','T',T','P',P,Fluid)
|
||||
|
||||
the solver is used to carry out the T-P flash calculation. And if you wanted
|
||||
entropy as well you could either intermediately calculate ``T``, ``rho`` and then use
|
||||
``T``, ``rho`` in the EOS in a manner like::
|
||||
|
||||
rho = Props('D','T',T','P',P,Fluid)
|
||||
h = Props('H','T',T','D',rho,Fluid)
|
||||
s = Props('S','T',T','D',rho,Fluid)
|
||||
rho = PropsSI('D','T',T','P',P,Fluid)
|
||||
h = PropsSI('H','T',T','D',rho,Fluid)
|
||||
s = PropsSI('S','T',T','D',rho,Fluid)
|
||||
|
||||
Instead in this class all that is handled internally. So the call to update
|
||||
sets the internal variables in the most computationally efficient way possible
|
||||
@@ -332,7 +322,7 @@ cdef class State:
|
||||
phase : string
|
||||
DEPRECATED : this input is ignored
|
||||
backend : string
|
||||
The CoolProp backend that should be used
|
||||
The CoolProp backend that should be used, one of "HEOS" (default), "REFPROP", "INCOMP", "BRINE", etc.
|
||||
"""
|
||||
cdef string _Fluid = Fluid
|
||||
|
||||
|
||||
Reference in New Issue
Block a user