{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Exploring grain settling with Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Grain settling is one of the most important problems in sedimentology (and therefore sedimentary geology), as neither sediment transport nor deposition can be understood and modeled without knowing what is the settling velocity of a particle of a certain grain size. Very small grains, when submerged in water, have a mass small enough that they reach a terminal velocity before any turbulence develops. This is true for clay- and silt-sized particles settling in water, and for these grain size classes Stokes' Law can be used to calculate the settling velocity:\n", "\n", "$$w = \\frac{RgD^2}{C_1\\nu}$$\n", "\n", "where $R$ = specific submerged gravity, $g$ = gravitational acceleration, $D$ is the particle diameter, $C_1$ is a constant with a theoretical value of 18, and $\\nu$ is the kinematic viscosity.\n", "\n", "For grain sizes coarser than silt, a category that clearly includes a lot of sediment and rock types of great interest to geologists, things get more complicated. The reason for this is the development of a separation wake behind the falling grain; the appearance of this wake results in turbulence and large pressure differences between the front and back of the particle. For large grains - pebbles, cobbles - this effect is so strong that viscous forces become insignificant and turbulent drag dominates; the settling velocity can be estimated using the empirical equation\n", "\n", "$$w = \\sqrt{\\frac{4RgD}{3C_2}}$$\n", "\n", "The important point is that, for larger grains, the settling velocity increases more slowly, with the square root of the grain size, as opposed to the square of particle diameter, as in Stokes' Law.\n", "\n", "Sand grains are small enough that viscous forces still play an important role in their subaqueous settling behavior, but large enough that the departure from Stokes' Law is significant and wake turbulence cannot be ignored. There are several empirical - and fairly complicated - equations that try to bridge this gap; here I focus on the simplest one, published in 2004 in the Journal of Sedimentary Research (Ferguson and Church, 2004):\n", " \n", "$$w = \\frac{RgD^2}{C_1\\nu+\\sqrt{0.75C_2RgD^3}}$$\n", "\n", "At small values of D, the left term in the denominator is much larger than the one containing the third power of D, and the equation is equivalent of Stokes' Law. At large values of D, the second term dominates and the settling velocity converges to the solution of the turbulent drag equation.\n", "\n", "But the point of this blog post is not to give a summary of the Ferguson and Church paper; what I am interested in is to write some simple code and plot settling velocity against grain size to better understand these relationships through exploring them graphically. So what follows is a series of Python code snippets, directly followed by the plots that you can generate if you run the code yourself. I have done this using the iPyhton notebook, a very nice tool that allows and promotes note taking, coding, and plotting within one document. I am not going to get into details of Python programming and the usage of iPyhton notebook, but you can check them out for example here.\n", "\n", "First we have to implement the three equations as Python functions:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi\n", "import numpy as np\n", "\n", "rop = 2650.0 # density of particle in kg/m3\n", "rof = 1000.0 # density of fluid in kg/m3\n", "visc = 1.002*1E-3 #8.9*1E-4 # dynamic viscosity in Pa*s (N*s/m^2)\n", "C1 = 18 # constant in Ferguson-Church equation\n", "C2 = 1 # constant in Ferguson-Church equation, valid for natural sand grains\n", "\n", "def v_stokes(rop,rof,d,visc,C1):\n", " R = (rop-rof)/rof # submerged specific gravity\n", " w = R*9.81*(d**2)/(C1*visc/rof)\n", " return w\n", "\n", "def v_turbulent(rop,rof,d,visc,C2):\n", " R = (rop-rof)/rof \n", " w = (4*R*9.81*d/(3*C2))**0.5\n", " return w\n", "\n", "def v_ferg(rop,rof,d,visc,C1,C2):\n", " R = (rop-rof)/rof \n", " w = (R*9.81*d**2)/(C1*visc/rof+(0.75*C2*R*9.81*d**3)**0.5)\n", " return w" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 109 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot these equations for a range of particle diameters:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "d = np.arange(0,0.0005,0.000001)\n", "ws = v_stokes(rop,rof,d,visc,C1)\n", "wt = v_turbulent(rop,rof,d,visc,C2)\n", "wf = v_ferg(rop,rof,d,visc,C1,C2)\n", "\n", "figure(figsize=(10,8))\n", "plot(d*1000,ws,label='Stokes',linewidth=3)\n", "plot(d*1000,wt,'g',label='Turbulent',linewidth=3)\n", "plot(d*1000,wf,'r',label='Ferguson-Church',linewidth=3)\n", "plot([0.25, 0.25],[0, 0.15],'k--')\n", "plot([0.25/2, 0.25/2],[0, 0.15],'k--')\n", "plot([0.25/4, 0.25/4],[0, 0.15],'k--')\n", "text(0.36, 0.11, 'medium sand', fontsize=13)\n", "text(0.16, 0.11, 'fine sand', fontsize=13)\n", "text(0.075, 0.11, 'v. fine', fontsize=13)\n", "text(0.08, 0.105, 'sand', fontsize=13)\n", "text(0.01, 0.11, 'silt and', fontsize=13)\n", "text(0.019, 0.105, 'clay', fontsize=13)\n", "legend(loc=2)\n", "xlabel('grain diameter (mm)',fontsize=15)\n", "ylabel('settling velocity (m/s)',fontsize=15)\n", "axis([0,0.5,0,0.15]);\n", "\n", "D = [0.068, 0.081, 0.096, 0.115, 0.136, 0.273, 0.386, 0.55, 0.77, 1.09, 2.18, 4.36]\n", "w = [0.00425, 0.0060, 0.0075, 0.0110, 0.0139, 0.0388, 0.0551, 0.0729, 0.0930, 0.141, 0.209, 0.307]\n", "err = [0.00009, 0.0001, 0.0001, 0.0002, 0.0001, 0.0002, 0.0005, 0.0010, 0.0016, 0.002, 0.002, 0.003]\n", "plot(D,w,'o',markerfacecolor=[0.6, 0.6, 0.6], markersize=8);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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iIhX57Tfg6lXx2NwcmDpVtfGQ5mACR0REpAI5OcBXXxWWZ84ETE1VFw9pFiZwpDbCw8PR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pyAvXvVJgV7qeEthBDWzCyPUGfNmoWfnx/x8fGMGDECFxcX/P39AfDz88PLy4s6depQo0YNnJ2d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\n9ersZPZCiKqXn5/P0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"text": [ "" ] } ], "prompt_number": 110 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The black dots are data points from settling experiments performed with natural river sands (Table 2 in Ferguson and Church, 2004). It is obvious that the departure from Stokes' Law is already significant for very fine sand and Stokes settling is completely inadequate for describing the settling of medium sand.\n", "\n", "This plot only captures particle sizes finer than medium sand; let's see what happens as we move to coarser sediment." ] }, { "cell_type": "code", "collapsed": false, "input": [ "d = np.arange(0,0.01,0.00001)\n", "ws = v_stokes(rop,rof,d,visc,C1)\n", "wt = v_turbulent(rop,rof,d,visc,C2)\n", "wf = v_ferg(rop,rof,d,visc,C1,C2)\n", "figure(figsize=(10,8))\n", "plot(d*1000,ws,label='Stokes',linewidth=3)\n", "plot(d*1000,wt,'g',label='Turbulent',linewidth=3)\n", "plot(d*1000,wf,'r',label='Ferguson-Church',linewidth=3)\n", "plot([0.25, 0.25],[0, 2],'k--')\n", "plot([0.5, 0.5],[0, 2],'k--')\n", "text(0.33, 1.0, 'medium sand', fontsize=13, rotation='vertical')\n", "text(0.09, 1.15, 'fine sand, silt and clay', fontsize=13, rotation='vertical')\n", "plot([1, 1],[0, 2],'k--')\n", "text(0.7, 1.0, 'coarse sand', fontsize=13, rotation='vertical')\n", "plot([2, 2],[0, 2],'k--')\n", "text(1.5, 1.0, 'very coarse sand', fontsize=13, rotation='vertical')\n", "plot([4, 4],[0, 2],'k--')\n", "text(3, 1.0, 'granules', fontsize=13, rotation='vertical')\n", "text(4.5, 1.0, 'pebbles', fontsize=13, rotation='vertical')\n", "legend(loc=2)\n", "xlabel('grain diameter (mm)',fontsize=15)\n", "ylabel('settling velocity (m/s)',fontsize=15)\n", "axis([0,5,0,2]);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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eJLJkrHvWrUiLx/r6+uLmzZsIDQ3FgAEDULNmTWie6gcSQuDMmTOYPXs2Zs+e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"text": [ "" ] } ], "prompt_number": 111 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A log-log plot is much better for looking at a wide spectrum of grain sizes." ] }, { "cell_type": "code", "collapsed": false, "input": [ "d = np.arange(0,0.01,0.00001)\n", "ws = v_stokes(rop,rof,d,visc,C1)\n", "wt = v_turbulent(rop,rof,d,visc,C2)\n", "wf = v_ferg(rop,rof,d,visc,C1,C2)\n", "figure(figsize=(10,8))\n", "loglog(d*1000,ws,label='Stokes',linewidth=3)\n", "loglog(d*1000,wt,'g',label='Turbulent',linewidth=3)\n", "loglog(d*1000,wf,'r',label='Ferguson-Church',linewidth=3)\n", "plot([1.0/64, 1.0/64],[0.00001, 10],'k--')\n", "text(0.012, 0.0007, 'fine silt', fontsize=13, rotation='vertical')\n", "plot([1.0/32, 1.0/32],[0.00001, 10],'k--')\n", "text(0.17/8, 0.0007, 'medium silt', fontsize=13, rotation='vertical')\n", "plot([1.0/16, 1.0/16],[0.00001, 10],'k--')\n", "text(0.17/4, 0.0007, 'coarse silt', fontsize=13, rotation='vertical')\n", "plot([1.0/8, 1.0/8],[0.00001, 10],'k--')\n", "text(0.17/2, 0.001, 'very fine sand', fontsize=13, rotation='vertical')\n", "plot([0.25, 0.25],[0.00001, 10],'k--')\n", "text(0.17, 0.001, 'fine sand', fontsize=13, rotation='vertical')\n", "plot([0.5, 0.5],[0.00001, 10],'k--')\n", "text(0.33, 0.001, 'medium sand', fontsize=13, rotation='vertical')\n", "plot([1, 1],[0.00001, 10],'k--')\n", "text(0.7, 0.001, 'coarse sand', fontsize=13, rotation='vertical')\n", "plot([2, 2],[0.00001, 10],'k--')\n", "text(1.3, 0.001, 'very coarse sand', fontsize=13, rotation='vertical')\n", "plot([4, 4],[0.00001, 10],'k--')\n", "text(2.7, 0.001, 'granules', fontsize=13, rotation='vertical')\n", "text(6, 0.001, 'pebbles', fontsize=13, rotation='vertical')\n", "legend(loc=2)\n", "xlabel('grain diameter (mm)', fontsize=15)\n", "ylabel('settling velocity (m/s)', fontsize=15)\n", "axis([0,10,0,10]);\n", "plot(D,w,'o',markerfacecolor=[0.6, 0.6, 0.6], markersize=8);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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999+93Sy3iIuLo1+/ftSoUYOqVasSERHB119/7fF2ZN1STAghcnPkCHTs6LjIb58+sGeP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\naCj79+9n/PjxTJo0ic2bNxe5QUL7sl8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80LNC7Zf6+ussTUiAQYNgyRJwYcs8IYQQ3uGR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\nj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"text": [ "" ] } ], "prompt_number": 112 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plot shows how neither Stokes' Law, nor the velocity based on turbulent drag are valid for calculating settling velocities of sand-size grains in water, whereas the Ferguson-Church equation provides a good fit for natural river sand.\n", "\n", "Grain settling is a special case of the more general problem of flow past a sphere. The analysis and plots above are all dimensional, that is, you can quickly check by looking at the plots what is the approximate settling velocity of very fine sand. That is great, but you would have to generate a new plot - and potentially do a new experiment - if you wanted to look at the behavior of particles in some other fluid than water. A more general treatment of the problem involves dimensionless variables; in this case these variables are the Reynolds number and the drag coefficient. The classic diagram for flow past a sphere is a plot of the drag coefficient against the Reynolds number. I will try to reproduce this plot, using settling velocities that come from the three equations above.\n", "\n", "At terminal settling velocity, the drag force equals the gravitational force acting on the grain:\n", "\n", "$$F_d = F_g$$\n", "\n", "We also know that the gravitational force is given by the submerged weight of the grain:\n", "\n", "$$F_g = (\\rho_p-\\rho_f)\\frac{4}{3}\\pi r^3g$$\n", "\n", "The drag coefficient is essentially a dimensionless version of the drag force:\n", "\n", "$$C_d = \\frac{F_d}{\\frac{\\rho_fw^2}{2}A} =\\frac{F_d}{\\rho_fw^2\\pi\\frac{d^2}{8}}$$\n", "\n", "At terminal settling velocity, the particle Reynolds number is\n", "\n", "$$Re = \\frac{\\rho_fwd}{\\mu}$$\n", "\n", "Using these relationships it is possible to generate the plot of drag coefficient vs. Reynolds number:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "d = np.arange(0.000001,0.3,0.00001)\n", "C2 = 0.4 # this constant is 0.4 for spheres, 1 for natural grains\n", "ws = v_stokes(rop,rof,d,visc,C1)\n", "wt = v_turbulent(rop,rof,d,visc,C2)\n", "wf = v_ferg(rop,rof,d,visc,C1,C2)\n", "Fd = (rop-rof)*4/3*pi*((d/2)**3)*9.81 # drag force\n", "Cds = Fd/(rof*ws**2*pi*(d**2)/8) # drag coefficient\n", "Cdt = Fd/(rof*wt**2*pi*(d**2)/8)\n", "Cdf = Fd/(rof*wf**2*pi*(d**2)/8)\n", "Res = rof*ws*d/visc # particle Reynolds number\n", "Ret = rof*wt*d/visc\n", "Ref = rof*wf*d/visc\n", "figure(figsize=(10,8))\n", "loglog(Res,Cds,linewidth=3, label='Stokes')\n", "loglog(Ret,Cdt,linewidth=3, label='Turbulent')\n", "loglog(Ref,Cdf,linewidth=3, label='Ferguson-Church')\n", "# data digitized from Southard textbook, figure 2-2:\n", "Re_exp = [0.04857,0.10055,0.12383,0.15332,0.25681,0.3343,0.62599,0.77049,0.94788,1.05956,\n", " 1.62605,2.13654,2.55138,3.18268,4.46959,4.92143,8.02479,12.28672,14.97393,21.33792,\n", " 28.3517,34.55246,57.57204,78.3929,96.88149,159.92596,227.64082,287.31738,375.98547,\n", " 516.14355,607.03827,695.8316,861.51953,1147.26099,1194.43213,1513.70166,1939.70557,\n", " 2511.91235,2461.13232,3106.32397,3845.99561,4974.59424,6471.96875,8135.45166,8910.81543,\n", " 11949.91309,17118.62109,21620.08203,28407.60352,36064.10156,46949.58594,62746.32422,\n", " 80926.54688,97655.00781,122041.875,157301.8125,206817.7188,266273,346423.5938,302216.5938,\n", " 335862.5313,346202,391121.5938,460256.375,575194.4375,729407.625]\n", "Cd_exp = [479.30811,247.18175,199.24072,170.60068,112.62481,80.21341,45.37168,39.89885,34.56996,\n", " 28.01445,18.88166,13.80322,12.9089,11.41266,8.35254,7.08445,5.59686,3.92277,3.53845,\n", " 2.75253,2.48307,1.99905,1.49187,1.27743,1.1592,0.89056,0.7368,0.75983,0.64756,0.56107,\n", " 0.61246,0.5939,0.49308,0.39722,0.48327,0.46639,0.42725,0.37951,0.43157,0.43157,0.40364,\n", " 0.3854,0.40577,0.41649,0.46173,0.41013,0.42295,0.43854,0.44086,0.4714,0.45225,0.47362,\n", " 0.45682,0.49104,0.46639,0.42725,0.42725,0.40171,0.31214,0.32189,0.20053,0.16249,0.10658,\n", " 0.09175,0.09417,0.10601]\n", "loglog(Re_exp, Cd_exp, 'o', markerfacecolor = [0.6, 0.6, 0.6], markersize=8)\n", "\n", "# Reynolds number for golf ball:\n", "rof_air = 1.2041 # density of air at 20 degrees C\n", "u = 50 # velocity of golf ball (m/s)\n", "d = 0.043 # diameter of golf ball (m)\n", "visc_air = 1.983e-5 # dynamic viscosity of air at 20 degrees C\n", "Re = rof_air*u*d/visc_air\n", "loglog([Re, Re], [0.4, 2], 'k--')\n", "text(3e4,2.5,'$Re$ for golf ball',fontsize=13)\n", "legend(loc=1)\n", "axis([1e-2,1e6,1e-2,1e4])\n", "xlabel('particle Reynolds number ($Re$)', fontsize=15)\n", "ylabel('drag coefficient ($C_d$)', fontsize=15);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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7UHJXwnTsCK98FUAnVnCeMgC4/HMMU+s2cOyYg6MTERGRwuY0yV1J2cQ4N3r0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"text": [ "" ] } ], "prompt_number": 143 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The grey dots are experimental data points digitized from the excellent textbook by John Southard, available through MIT Open Courseware. As turbulence becomes dominant at larger Reynolds numbers, the drag coefficient converges to a constant value (which is equal to C2 in the equations above). Note however the departure of the experimental data from this ideal horizontal line: at high Reynolds numbers there is a sudden drop in drag coefficient as the laminar boundary layer becomes turbulent and the flow separation around the particle is delayed, that is, pushed toward the back; the separation wake becomes smaller and the turbulent drag decreases. Golf balls are not big enough to reach this point without some additional 'help'; this help comes from the dimples on the surface of the ball that make the boundary layer turbulent and reduce the wake.\n", "\n", "References\n", "\n", "Ferguson, R. and Church, M. (2004) A simple universal equation for grain settling velocity. Journal of Sedimentary Research 74, 933\u2013937." ] } ], "metadata": {} } ] }