{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Sagemath derivation of added mass coeficient for circular shape\n",
"\n",
"Model includes finite depth of the channel"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import csv\n",
"\n",
"# MatPlotLib set LaTeX font\n",
"plt.rcParams['text.usetex'] = True"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def write_csv(data):\n",
" \n",
" file_name = 'results_circ.csv'\n",
" Nr = len(data)\n",
" \n",
" with open(file_name, 'w', newline='') as csvfile:\n",
" fieldnames = ['x','y']\n",
" writer = csv.DictWriter(csvfile, fieldnames=fieldnames)\n",
"\n",
" writer.writeheader()\n",
" \n",
" for i in range(Nr): \n",
" writer.writerow({\n",
" 'x':'{:.2f}'.format(data[i][0]),\n",
" 'y':'{:.2f}'.format(data[i][1]),\n",
" })"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"%display latex\n",
"V,A,h,a,b,x,y,th,rh, Hw = var('V A h a b x y theta rho H_w', domain='real')\n",
"z = var('z')"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/2*A*coth(1/2*pi*z/h)/h"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"PP = A/(2*h) * coth(pi*z/(2*h))\n",
"display(PP)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"-1/4*pi*A/(h^2*sinh(1/2*pi*(x + I*y)/h)^2)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"4*V*h^2*sinh(1/2*pi/h)^2/pi"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dpdx = diff(PP.subs(z=x+I*y),x)\n",
"display(dpdx)\n",
"sol = solve(dpdx.subs(x=1,y=0) - V, A)\n",
"As = -sol[0].right()\n",
"display(As)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"2*h*coth(1/2*pi*z/h)*sinh(1/2*pi/h)^2/pi"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"4*h^2*sin(theta)*sinh(1/2*pi/h)^2/pi^2 + 1/3*sin(theta)*sinh(1/2*pi/h)^2"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/180*pi^2*sin(3*theta)*sinh(1/2*pi/h)^2/h^2 + 4*h^2*sin(theta)*sinh(1/2*pi/h)^2/pi^2 + 1/3*sin(theta)*sinh(1/2*pi/h)^2"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/7560*pi^4*sin(5*theta)*sinh(1/2*pi/h)^2/h^4 + 1/180*pi^2*sin(3*theta)*sinh(1/2*pi/h)^2/h^2 + 4*h^2*sin(theta)*sinh(1/2*pi/h)^2/pi^2 + 1/3*sin(theta)*sinh(1/2*pi/h)^2"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"691/326918592000*pi^10*sin(11*theta)*sinh(1/2*pi/h)^2/h^10 + 1/11975040*pi^8*sin(9*theta)*sinh(1/2*pi/h)^2/h^8 + 1/302400*pi^6*sin(7*theta)*sinh(1/2*pi/h)^2/h^6 + 1/7560*pi^4*sin(5*theta)*sinh(1/2*pi/h)^2/h^4 + 1/180*pi^2*sin(3*theta)*sinh(1/2*pi/h)^2/h^2 + 4*h^2*sin(theta)*sinh(1/2*pi/h)^2/pi^2 + 1/3*sin(theta)*sinh(1/2*pi/h)^2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f = PP.subs(A=As).subs(V=1)\n",
"display(f)\n",
"fnc_3 = f.series(z,3).subs(z=I*exp(-I*th)).simplify()\n",
"fnc_5 = f.series(z,5).subs(z=I*exp(-I*th)).simplify()\n",
"fnc_7 = f.series(z,7).subs(z=I*exp(-I*th)).simplify()\n",
"fnc_N = f.series(z,12).subs(z=I*exp(-I*th)).simplify()\n",
"\n",
"re_fnc_3 = real(fnc_3).simplify()\n",
"re_fnc_5 = real(fnc_5).simplify()\n",
"re_fnc_7 = real(fnc_7).simplify()\n",
"re_fnc_N = real(fnc_N).simplify()\n",
"\n",
"display(re_fnc_3)\n",
"display(re_fnc_5)\n",
"display(re_fnc_7)\n",
"display(re_fnc_N)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/lib/python3/dist-packages/sage/plot/graphics.py:2327: MatplotlibDeprecationWarning: \n",
"The OldScalarFormatter class was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
" x_formatter = OldScalarFormatter()\n",
"/usr/lib/python3/dist-packages/sage/plot/graphics.py:2352: MatplotlibDeprecationWarning: \n",
"The OldScalarFormatter class was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
" y_formatter = OldScalarFormatter()\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"Graphics object consisting of 4 graphics primitives"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Hw = 1.1\n",
"plot((re_fnc_3.subs(h=Hw),re_fnc_5.subs(h=Hw),re_fnc_7.subs(h=Hw),re_fnc_N.subs(h=Hw)),(th,-pi/2,pi/2))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/lib/python3/dist-packages/sage/plot/graphics.py:2327: MatplotlibDeprecationWarning: \n",
"The OldScalarFormatter class was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
" x_formatter = OldScalarFormatter()\n",
"/usr/lib/python3/dist-packages/sage/plot/graphics.py:2352: MatplotlibDeprecationWarning: \n",
"The OldScalarFormatter class was deprecated in Matplotlib 3.3 and will be removed two minor releases later.\n",
" y_formatter = OldScalarFormatter()\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot((re_fnc_7 - re_fnc_N).subs(h=Hw),(th,-pi/2,pi/2))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/12*pi*sinh(1/2*pi/h)^2 + h^2*sinh(1/2*pi/h)^2/pi"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/12*(pi^2*sinh(1/2*pi/h)^2 + 12*h^2*sinh(1/2*pi/h)^2)/pi"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/12*(pi^2*sinh(1/2*pi/h)^2 + 12*h^2*sinh(1/2*pi/h)^2)/pi"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
""
],
"text/plain": [
"1/12*(pi^2*sinh(1/2*pi/h)^2 + 12*h^2*sinh(1/2*pi/h)^2)/pi"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"intf_3 = (integral(re_fnc_3*sin(th),(th,0,pi/2))).simplify()\n",
"intf_5 = (integral(re_fnc_5*sin(th),(th,0,pi/2))).simplify()\n",
"intf_7 = (integral(re_fnc_7*sin(th),(th,0,pi/2))).simplify()\n",
"intf_N = (integral(re_fnc_N*sin(th),(th,0,pi/2))).simplify()\n",
"\n",
"display(intf_3)\n",
"display(intf_5)\n",
"display(intf_7)\n",
"display(intf_N)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"int_phi = lambda x: np.sinh(np.pi/(2*x))**2 * (1/3 + (2*x/np.pi)**2)\n",
"\n",
"hv = np.linspace(int(1.0), int(2.0), int(100))\n",
"data = []\n",
"c22 = []\n",
"for hi in hv:\n",
" vh1 = int_phi(hi)\n",
" c22.append(vh1*100)\n",
" data.append([vh1*100,(hi-1)*100])\n",
" \n",
"plt.plot(c22,(hv-1)*100)\n",
"plt.xlabel(r'$c_{22}$ [\\%]')\n",
"plt.ylabel(r'UKC/R [\\%]')\n",
"plt.title(r'Added mass coefficient for circle shape ($R=1$)')\n",
"plt.grid(True)\n",
"plt.savefig(r'result_circ.pdf')\n",
"\n",
"write_csv(data)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.0",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}