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April 18, 2016 20:27
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Shear heating and diffusion modeling.
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# System Thermal Model With Shear Heating\n", | |
"\n", | |
"We model the system as two steel sideblocks, an acrylic center block, and two layers of quartz representing the gouge. \n", | |
"\n", | |
"## Thermal Properties\n", | |
"* __Steel__ $\\kappa$ = 1.172x10$^{-5}$ m$^2$/s\n", | |
"* __Acrylic__ $\\kappa$ = 1.12x10$^{-7}$ m$^2$/s\n", | |
"* __Quartz__ $\\kappa$ = 1.4x10$^{-6}$ m$^2$/s\n", | |
"\n", | |
"\n", | |
"\n", | |
"## Model\n", | |
"* 1-D Model\n", | |
"* Fixed room temperature at the right and left boundaries\n", | |
"* Uniform temperature anomaly in the gouge layers at the beginning of simulation\n", | |
"\n", | |
"$\\frac{\\partial T}{\\partial t} = \\kappa \\frac{\\partial ^2T}{\\partial x^2} + \\frac{Q(x,t)}{\\rho c_p}$\n", | |
"\n", | |
"## Shear Heating\n", | |
"Heat is generated in the gouge layers due to shearing with friction $\\mu$ at effective normal stress $\\sigma'_n$ at velocity $V$. \n", | |
"\n", | |
"$q = \\tau V = \\mu \\sigma'_n V$\n", | |
"\n", | |
"Knowing that the zone generating the heat has width $w$, we can determine the rate of heat generation per unit volume as \n", | |
"\n", | |
"$Q(x_0,t_0) = \\frac{\\mu \\sigma'_n V}{w}$ \n", | |
"\n", | |
"in the shear zone interval and zero elsewhere." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Admin Code" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"from fipy import *\n", | |
"import matplotlib.pyplot as plt\n", | |
"import numpy as np" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"plt.rcParams['figure.figsize'] = 10, 7.5\n", | |
"plt.rcParams['xtick.labelsize'] = 16\n", | |
"plt.rcParams['ytick.labelsize'] = 16\n", | |
"plt.rcParams['font.sans-serif'] = 'Helvetica'\n", | |
"plt.rcParams['text.color'] = 'black'\n", | |
"plt.rcParams['font.size'] = 18\n", | |
"plt.rcParams['lines.linewidth'] = 2\n", | |
"plt.rcParams['axes.facecolor'] = 'white'\n", | |
"plt.rcParams['axes.edgecolor'] = 'black'\n", | |
"plt.rcParams['axes.labelcolor'] = 'black'\n", | |
"plt.rcParams['axes.axisbelow'] = True\n", | |
"plt.rcParams['xtick.major.size'] = 10\n", | |
"plt.rcParams['xtick.minor.size'] = 5\n", | |
"plt.rcParams['xtick.major.width'] = 1\n", | |
"plt.rcParams['xtick.minor.width'] = 1\n", | |
"plt.rcParams['ytick.major.size'] = 10\n", | |
"plt.rcParams['ytick.minor.size'] = 5\n", | |
"plt.rcParams['ytick.major.width'] = 1\n", | |
"plt.rcParams['ytick.minor.width'] = 1\n", | |
"plt.rcParams['xtick.color'] = 'k'\n", | |
"plt.rcParams['ytick.color'] = 'k'\n", | |
"\n", | |
"%matplotlib inline" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Setup Model Grid" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Model Length : 0.146000 m\n", | |
"Model Spatial Step : 0.000100 m\n", | |
"Number of Cells : 1460\n" | |
] | |
} | |
], | |
"source": [ | |
"# Setup Model Grid\n", | |
"L = .146 # Model length in meters\n", | |
"dx = 0.0001 # Spatial step in meters (0.1 mm)\n", | |
"nx = L/dx + 1\n", | |
"mesh = Grid1D(nx=nx, dx=dx)\n", | |
"\n", | |
"print \"Model Length : %f m\" %L\n", | |
"print \"Model Spatial Step : %f m\" %dx\n", | |
"print \"Number of Cells : %d\" %nx" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Set Spatially Varying Diffusion Coefficients" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"# Setup Diffusion Coefficients\n", | |
"D = FaceVariable(mesh=mesh, value=1.172e-5) # Set all to Steel Values\n", | |
"\n", | |
"X = mesh.faceCenters[0]\n", | |
"\n", | |
"# Set 50> and <=53 mm as quartz\n", | |
"D.setValue(1.4e-6, where=(X > 0.050) & (X<=0.053))\n", | |
"\n", | |
"# Set >53 and <=93 mm as acrylic\n", | |
"D.setValue(1.12e-7, where=(X > 0.053) & (X<=0.093))\n", | |
"\n", | |
"# Set 93> and <=96 mm as quartz\n", | |
"D.setValue(1.4e-6, where=(X > 0.093) & (X<=0.096))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(0, 146.00000000000003)" | |
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}, | |
"execution_count": 5, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"/Users/jleeman/anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:1282: UserWarning: findfont: Font family [u'sans-serif'] not found. Falling back to Bitstream Vera Sans\n", | |
" (prop.get_family(), self.defaultFamily[fontext]))\n" | |
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"data": { | |
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G4BLgIuDqiLi8eu9ZETGQQHGe/DwoIo6PiEsj4uqI+HlEPHnY6UqSJI1KzwFW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\nF11D8ONfNi6puqRCk1m/XXJ5PYDFZraiBpd6prq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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10b08ab90>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Setup figure and axes\n", | |
"# Generally plots is ~1.33x width to height (10,7.5 or 12,9)\n", | |
"fig = plt.figure(figsize=(10,7.5))\n", | |
"ax1 = plt.subplot(111)\n", | |
"\n", | |
"# Set labels and tick sizes\n", | |
"ax1.set_xlabel(r'Model Distance [mm]', fontsize=20)\n", | |
"ax1.set_ylabel(r'Thermal Diffusivity [x $10^{-6}$ m$^2$/s]', fontsize=20)\n", | |
"\n", | |
"# Plotting\n", | |
"ax1.plot(X*1000., D.value*1e6, color='k')\n", | |
"\n", | |
"plt.title('Thermal Diffusivity Model', fontsize=24)\n", | |
"\n", | |
"# Set limits\n", | |
"ax1.set_xlim(0,np.max(X.value*1000.))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Boundary Conditions" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"# Setup model boundary conditions\n", | |
"valueLeft = 20.\n", | |
"valueRight = 20.\n", | |
"\n", | |
"phi = CellVariable(name=\"Temperature\", mesh=mesh, value=20.)\n", | |
"phi.constrain(valueRight, mesh.facesRight)\n", | |
"phi.constrain(valueLeft, mesh.facesLeft)\n", | |
"\n", | |
"\n", | |
"# Introduce anomalies on the layers for testing\n", | |
"\n", | |
"X = mesh.cellCenters[0]\n", | |
"# Set 50> and <=53 mm as quartz\n", | |
"phi.setValue(21, where=(X > 0.050) & (X<=0.053))\n", | |
"\n", | |
"# Set 93> and <=96 mm as quartz\n", | |
"phi.setValue(21, where=(X > 0.093) & (X<=0.096))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(19.8, 21.2)" | |
] | |
}, | |
"execution_count": 7, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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HeZO2MpswfeuY1uz6u/e5/4dTzOR/MdO3jzkNePS4X7uPOetTZ9H9jhcbUQR6a9sea5i+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\n4eQFQRAEQRBUkP8BbGL38w9MrJsAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10dd3aad0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Setup figure and axes\n", | |
"# Generally plots is ~1.33x width to height (10,7.5 or 12,9)\n", | |
"fig = plt.figure(figsize=(10,7.5))\n", | |
"ax1 = plt.subplot(111)\n", | |
"\n", | |
"# Set labels and tick sizes\n", | |
"ax1.set_xlabel(r'Model Distance [mm]', fontsize=20)\n", | |
"ax1.set_ylabel(r'Temperature [C]', fontsize=20)\n", | |
"\n", | |
"# Plotting\n", | |
"ax1.plot(X*1000., phi.value, color='k')\n", | |
"\n", | |
"plt.title('Temperature Initial Condition', fontsize=24)\n", | |
"\n", | |
"# Set limits\n", | |
"ax1.set_xlim(0,np.max(X.value*1000.))\n", | |
"ax1.set_ylim(19.8,21.2)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## State and Solve Problem" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"# Setup the Crank-Nicholson Scheme\n", | |
"X = mesh.cellCenters[0]\n", | |
"mask_left = X > 0.05\n", | |
"mask_right = X <= 0.053\n", | |
"mask = mask_left & mask_right\n", | |
"\n", | |
"mu = 0.6\n", | |
"sigma_n = 7.e6\n", | |
"v = 10.e-6\n", | |
"w = 0.003\n", | |
"rho = 2650.\n", | |
"cp = 830.\n", | |
"\n", | |
"eqX = TransientTerm() == ExplicitDiffusionTerm(coeff=D) + (mask * ((mu*sigma_n*v/w) / rho*cp))\n", | |
"eqI = TransientTerm() == DiffusionTerm(coeff=D) + (mask * ((mu*sigma_n*v/w) / rho*cp))\n", | |
"eqCN= eqI + eqX" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [ | |
"timeStepDuration = 0.01 # How long of a timestep we take\n", | |
"steps = 100 # Number of timesteps" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"for step in range(steps):\n", | |
" eqCN.solve(var=phi, dt=timeStepDuration)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(0, 145.94999999999999)" | |
] | |
}, | |
"execution_count": 11, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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dyj1mX5yZ357qXNN5/h7a9/I91rXNlnyNenzeqfo0lY9WHw+pqpHlwMwvUgLUWZQq2nrK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\nrkJggg==\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x10d47ed90>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Setup figure and axes\n", | |
"# Generally plots is ~1.33x width to height (10,7.5 or 12,9)\n", | |
"fig = plt.figure(figsize=(10,7.5))\n", | |
"ax1 = plt.subplot(111)\n", | |
"\n", | |
"# Set labels and tick sizes\n", | |
"ax1.set_xlabel(r'Model Distance [mm]', fontsize=20)\n", | |
"ax1.set_ylabel(r'Temperature [C]', fontsize=20)\n", | |
"\n", | |
"# Plotting\n", | |
"ax1.plot(X*1000., phi.value, color='k')\n", | |
"\n", | |
"plt.title('Temperature Final Result', fontsize=24)\n", | |
"\n", | |
"# Set limits\n", | |
"ax1.set_xlim(0,np.max(X.value*1000.))\n", | |
"#ax1.set_ylim(19.8,21.2)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 2", | |
"language": "python", | |
"name": "python2" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 2 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython2", | |
"version": "2.7.11" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 0 | |
} |
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