{ "cells": [ { "cell_type": "markdown", "id": "3a4276eb", "metadata": {}, "source": [ "### TP Wind Tunnel\n", "## Signal processing (3 hours approx.)\n", "## Calibration\n", "We can read the data files in the following way. Start by installing the necessary packages:" ] }, { "cell_type": "code", "execution_count": 1, "id": "80a072a6", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy import signal as sig\n", "import scipy as sc\n", "\n", "import netCDF4\n", "from netCDF4 import Dataset\n", "\n", "# static figures (can be exported to pdf):\n", "#%matplotlib inline\n", "\n", "# dynamic figures:\n", "\n", "# for jupyter-notebook\n", "#%matplotlib notebook\n", "# for jupyter-lab (the package ipympl is needed) if not installed type: conda install ipympl\n", "%matplotlib widget" ] }, { "cell_type": "markdown", "id": "4ae37569", "metadata": {}, "source": [ "To load the data from the file `filename.nc`, the following operations must be excecuted" ] }, { "cell_type": "code", "execution_count": 2, "id": "6fb9c677", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "root group (NETCDF4_CLASSIC data model, file format HDF5):\n", " a: 0.83\n", " b: 1.79\n", " vitessemoyenne: 7.611776850683432\n", " ecarttypevitesse: 2.1170192527160587\n", " title: acquisition fil chaud\n", " subtitle: soufflerie\n", " dimensions(sizes): time(12000000)\n", " variables(dimensions): float32 time(time), float32 tensionsfilchaud(time), float32 vitessesfilchaud(time)\n", " groups: \n" ] } ], "source": [ "ncfile = Dataset('E:/Group1/90M_u=3mps_active01102024 155406.nc', mode='r')\n", "print(ncfile)" ] }, { "cell_type": "code", "execution_count": 3, "id": "abaec1be", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dict_keys(['time', 'tensionsfilchaud', 'vitessesfilchaud'])\n" ] } ], "source": [ "print(ncfile.variables.keys())" ] }, { "cell_type": "markdown", "id": "d09db6a6-8c46-465d-aec4-ae46c3a6b270", "metadata": {}, "source": [ "Load variables from the structure into arrays" ] }, { "cell_type": "code", "execution_count": 4, "id": "aedd0a55-e3c8-423b-83fb-47881e9481f7", "metadata": {}, "outputs": [], "source": [ "time = ncfile.variables['time'][:]\n", "voltage = ncfile.variables['tensionsfilchaud'][:]\n", "velocity = ncfile.variables['vitessesfilchaud'][:]" ] }, { "cell_type": "markdown", "id": "816180e1", "metadata": {}, "source": [ "The calibration law for hot-wire anemometers is $e^2=A\\sqrt{u}+B$ where $e$ is the voltage output of the hot-wire and $A$ and $B$ are the calibration constants. From your calibration spread sheet, create an array of mean voltage and mean velocity (from dP given by the Pitot tube) to estimate the constants $A$ and $B$ using python this time. You can make use of the command `np.polyfit` to obtain a linear fit. Then, you can make use of the command `np.polyval` to apply a polynomial transformation to the voltage signal from the hot-wire. " ] }, { "cell_type": "code", "execution_count": null, "id": "4cfddd83", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "80e51e41", "metadata": {}, "source": [ "Display the adjusted calibration law along with the calibration points" ] }, { "cell_type": "code", "execution_count": null, "id": "a3736918", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6f63551e-f4a9-4a0d-b0dd-eb817fb09eb3", "metadata": {}, "source": [ "Compare a voltage signal transformed to velocity through the calibration using `np.polyval` with a velocity signal recorded directly from the labVIEW program, display both of them as a function of time. Are they similar? What is the difference in mean value between them?" ] }, { "cell_type": "code", "execution_count": null, "id": "fb963b2b-c45f-42de-8243-311cf7f144ac", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9d5be796", "metadata": {}, "source": [ "# Statistical analysis of the hot-wire signals\n", "## Probability\n", "For one of the active-grid files of your choice, calculate the mean value, the root-mean-square deviation and the probability distribution function (PDF) of the speed measured by the anemometer (apply the calibration law). \n", "\n", "To estimate the PDF, calculate a histogram of the signal. Use the `np.histogram` function. Read the documentation. Start with a number of bins of 100 and use the `density='true'` option for correct PDF normalization. As the `np.histogram` function outputs the boundary values of the bins (and not the center positions), the `bin_edges` output is one point higher than the `hist` output. Hence, you can calculate first the central positions of the bins by simply `(bin_edges[0:-1]+bin_edges[1:])/2`." ] }, { "cell_type": "code", "execution_count": 7, "id": "d7ec457b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "6f261ed33a53420eaf4f37b90c9ffce4", "version_major": 2, "version_minor": 0 }, "image/png": 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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Start by assigning variable for specific case (3 m/s, active grid)\n", "u3a = velocity\n", "plt.figure()\n", "plt.plot(u3a[0:10000])" ] }, { "cell_type": "code", "execution_count": null, "id": "39e8e578-5f48-4e4c-931e-e88b1a966dae", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "73d94ab4", "metadata": {}, "source": [ "For one of the signals, vary the number of bins and comment on the effect of this parameter on the probability density estimate." ] }, { "cell_type": "code", "execution_count": null, "id": "a0f71aed", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "e4607b75", "metadata": {}, "source": [ "Which classic functional form can be used to approximate the data? Display this functional form with your data to visualize the comparison." ] }, { "cell_type": "code", "execution_count": null, "id": "5c52475c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "82c94360", "metadata": {}, "source": [ "## Spectral analysis\n", "Compute the Fourier spectrum. Use the `sig.welch` function in scipy.signal. Read the documentation. All you need to do is specify the sampling frequency and the `nperseg` parameter. Choose `axis=0`. The default values for the other parameters are suitable.\n", "\n", "For one of the experiments, calculate the spectrum of the signal from the hot wire. Display the spectrum in logarithmic scale on each axis (use `plt.loglog`). Observe the effect of the `nperseg` parameter on spectrum estimation and comment." ] }, { "cell_type": "code", "execution_count": null, "id": "b7451d0f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "84571222", "metadata": {}, "source": [ "Calculate the Fourier spectrum for the different wind tunnel speeds you have recorded, for an optimum `nperseg` number." ] }, { "cell_type": "code", "execution_count": null, "id": "e665b231", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2db7c838", "metadata": {}, "source": [ "What is the shape of the spectrum decay predicted by Kolmogorov's theory of isotropic homogeneous turbulence? Is your data compatible with this prediction?" ] }, { "cell_type": "code", "execution_count": null, "id": "0d21cbaf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "454cf4bc", "metadata": {}, "source": [ "For the hot-wire signal, calculate the velocity derivative $\\dfrac{\\partial u}{\\partial t}$. \n", "\n", "In reality, as the mean velocity of the flow is large compared with the fluctuations, we can consider that the flow is transported over the sensor and that the time derivative is actually a spatial gradient by performing the operation: $\\dfrac{\\partial u}{\\partial x}=-\\dfrac{1}{\\overline u}\\dfrac{\\partial u}{\\partial t}$ (this is known as Taylor's frozen turbulence hypothesis). \n", "\n", "As the signal contains noise (especially at high frequencies, as can be seen from the spectra you have plotted above), low-pass filtering is required. A simple way to do this is to decimate the signal by a factor $N$ using the `sig.decimate` function (which includes a low-pass filter) with the command `ud=sig.decimate(ufc4,N,axis=0)` for an initial signal `ufc4`. Note that the sampling frequency is reduced by this factor $N$. You can choose the value of this decimation factor by observing the spectra. You can plot the spectrum of the decimated signal for comparison.\n", "\n", "For homogeneous, isotropic turbulence, we can then calculate the dissipation rate $\\epsilon$ with $\\epsilon=15\\nu \\overline{\\dfrac{\\partial u}{\\partial x}^2}$. Calculate $\\epsilon$ and display its value. What effect does Reynold's number have on $\\epsilon$?\n", "\n", "\n", "Deduce the Kolmogorov scale $\\eta$ which is the typical size of the smallest vortices in the flow according to the formula $\\eta=\\left(\\dfrac{\\nu^3}{\\epsilon}\\right)^{1/4}$. Display its value and comment on the effect of Reynolds number." ] }, { "cell_type": "code", "execution_count": null, "id": "13e16df3", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f59fbc39", "metadata": {}, "source": [ "For the highest wind tunnel speed, calculate the probability density function of the velocity gradient $g=\\dfrac{\\partial u}{\\partial x}$. Display the probability in semilogarithmic scale. Comment on the shape of the distribution." ] }, { "cell_type": "code", "execution_count": null, "id": "4d3b3858", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "b691255c", "metadata": {}, "source": [ "Compute the skewness of the gradient signal, defined by $$S=\\dfrac{\\langle g^3 \\rangle }{\\langle g^2 \\rangle^{3/2}}$$." ] }, { "cell_type": "code", "execution_count": null, "id": "2da40959", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 5 }