From 388daec1aa0df672689dbe2e55833fe7c621a0aa Mon Sep 17 00:00:00 2001 From: rockfool Date: Mon, 6 Apr 2020 18:33:25 -0400 Subject: [PATCH] add flux_3d.png --- examples/jupyter/expansion-filters.ipynb | 33 ++++++++++++----------- examples/jupyter/images/flux3d.png | Bin 0 -> 100719 bytes 2 files changed, 18 insertions(+), 15 deletions(-) create mode 100644 examples/jupyter/images/flux3d.png diff --git a/examples/jupyter/expansion-filters.ipynb b/examples/jupyter/expansion-filters.ipynb index 4f28e5cfd..13150d342 100644 --- a/examples/jupyter/expansion-filters.ipynb +++ b/examples/jupyter/expansion-filters.ipynb @@ -151,7 +151,7 @@ { "data": { "text/plain": [ - "PosixPath('/mnt/d/MIT_CRPG/openmc_develop/openmc/examples/jupyter/statepoint.210.h5')" + "0.30282347701347406+/-0.0006325501096712208" ] }, "execution_count": 7, @@ -160,7 +160,7 @@ } ], "source": [ - "model.run(output=False)" + "sp_file = model.run(output=False)" ] }, { @@ -176,7 +176,7 @@ "metadata": {}, "outputs": [], "source": [ - "with openmc.StatePoint('statepoint.210.h5') as sp:\n", + "with openmc.StatePoint(sp_file) as sp:\n", " df = sp.tallies[flux_tally.id].get_pandas_dataframe()" ] }, @@ -444,15 +444,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Alternatively, Zernike polynomials provided in OepnMC to represent continuous functions of space or angle can be reconstructed from the tallied moments.\n", + "## Zernike polynomials\n", "\n", - "In this example, we will determine the spatial dependence of the flux along the radial direction $r'$ and / or azimuthal angle $\\theta$ by making a Zernike polynomial expansion. Let us represent the flux along the radial and azimuthal direction, $\\phi(r', \\theta)$, by the function\n", + "Now let's look at an example of functional expansion tallies using Zernike polynomials as the basis functions.\n", + "\n", + "In this example, we will determine the spatial dependence of the flux along the radial direction $r'$ and $/$ or azimuthal angle $\\theta$ by making a Zernike polynomial expansion. Let us represent the flux along the radial and azimuthal direction, $\\phi(r', \\theta)$, by the function\n", "\n", "$$ \\phi(r', \\theta) = \\sum\\limits_{n=0}^N \\sum\\limits_{m=-n}^n a_n^m Z_n^m(r', \n", "\\theta) $$\n", "\n", "where $r'$ is the position normalized to the range [0, r], and the azimuthal lies within the range [0, $ 2\\pi$]. \n", - "Since $Z_n^m(r', \\theta)$ are known functions, what we need to do is to determine the expansion coefficients, $a_n^m$. By the orthogonality properties of the Zernike polynomials, one can deduce that the coefficients, $a_n^m$, are given by\n", + "\n", + "Since $Z_n^m(r', \\theta)$ are known functions, we need to determine the expansion coefficients, $a_n^m$. By the orthogonality properties of the Zernike polynomials, one can deduce that the coefficients, $a_n^m$, are given by\n", "\n", "$$ a_n^m = k_n^m \\int_{0}^r dr' \\int_{0}^{2\\pi} d\\theta Z_n^m(r',\\theta) \\phi(r', \\theta).$$\n", "$$ k_n^m = \\frac{2n + 2}{\\pi}, m \\ne 0. $$\n", @@ -465,7 +468,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "To begin, let us first create a simple model. The model will be a pin-cell fuel material with vacuum boundary condition in both radial direction and axial direction." + "To begin with, let us first create a simple model. The model will be a pin-cell fuel material with vacuum boundary condition in both radial direction and axial direction." ] }, { @@ -596,7 +599,7 @@ } ], "source": [ - "model.run(output=False)" + "sp_file = model.run(output=False)" ] }, { @@ -612,7 +615,7 @@ "metadata": {}, "outputs": [], "source": [ - "with openmc.StatePoint('statepoint.100.h5') as sp:\n", + "with openmc.StatePoint(sp_file) as sp:\n", " df1 = sp.tallies[flux_tally_legendre.id].get_pandas_dataframe()" ] }, @@ -789,7 +792,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Since the scaling factors for expansion coefficients will be given in Python API, thus, we do not need to multiply the moments by scaling factors." + "Since the scaling factors for expansion coefficients will be provided by the Python API, thus, we do not need to multiply the moments by scaling factors." ] }, { @@ -864,7 +867,7 @@ "metadata": {}, "source": [ "A rough cosine shape is obtained. \n", - "One can also conduct numerically integrating using the trapezoidal rule." + "One can also numerically integrate the function using the trapezoidal rule." ] }, { @@ -900,7 +903,7 @@ "metadata": {}, "outputs": [], "source": [ - "with openmc.StatePoint('statepoint.100.h5') as sp:\n", + "with openmc.StatePoint(sp_file) as sp:\n", " df2 = sp.tallies[flux_tally_zernike.id].get_pandas_dataframe()" ] }, @@ -1166,7 +1169,7 @@ "metadata": {}, "outputs": [], "source": [ - "with openmc.StatePoint('statepoint.100.h5') as sp:\n", + "with openmc.StatePoint(sp_file) as sp:\n", " df3 = sp.tallies[flux_tally_zernike1d.id].get_pandas_dataframe()" ] }, @@ -1437,7 +1440,7 @@ " phi = np.arctan2(y, x)\n", " return(rho, phi)\n", "\n", - "# reconstruct 3-D flux based on azimuthal Zernike and Legendre polynomials\n", + "# Reconstruct 3-D flux based on azimuthal Zernike and Legendre polynomials\n", "z_n = np.array(df2['mean'])\n", "zz = openmc.Zernike(z_n, radius=radius) \n", "#\n", @@ -1539,7 +1542,7 @@ } ], "source": [ - "f1 = plt.imread('flux3d.png')\n", + "f1 = plt.imread('./images/flux3d.png')\n", "plt.imshow(f1, cmap='jet')" ] }, diff --git a/examples/jupyter/images/flux3d.png b/examples/jupyter/images/flux3d.png new file mode 100644 index 0000000000000000000000000000000000000000..4f706f9a2305ccf6e6083a242d796e7bc78dd201 GIT binary patch literal 100719 zcmeFZ*I!d>)GZvhZKEP80tN(Bn)DKiG|`Qe(2MjY0)Y^U2n6XiP`dOaG-*LfKp=pW zfQW>afV6~;iiQ%Z^nO-+zxP~!f55p4KQGp^o>|5mbIiGnGBVI&KF4_u1OhQbwI7&( zK&N^^pp(x3{sa8W=bp7wAkYmE^uhgy&+Hc`t-Se1!)e<>5OlC$-L2AwwDJ~fcc@dF zJn{HN+?rsU{G+z#6@D`TKhm)l-(N($@DOKr9^sIejWe$+i7ESO(w;@qqy3C&`#1Y7 z>t&%^GD(yCExeb8yPT!0Y#Tb?wEP}AItV{<0L}z~?)fh?pJ)65x*hp}iShg4nlUTm z*GM`~kn#Ke@dJIv@4fc77{>4O=*w~^7=N(wxij7#B%(R=_fZdH|K9`tpAA5u|7U~$ zKQ^F*Z~(b^@_ zk7X#&%GN$Wc&IORm0IH}hidF=e~I^RGf0AO>M29zaa9G}+*;8e)v@&+c3tI3%LhNF zMZFlb}iK(W+qmK3?`#as&bWuy^}k)RIo^qh zzeoz5JXBp;L60M0bZcA@d_B$Ui)^J-nw0vXTjvFD2LS=nyTiJw(aRfmeq%npG6aD6 za|Hu+pMCxEFfgdpj$fK|bWpkCbR_DUx5*XQv+<=^&k;zP 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