MECH E4320 代做、代写 Python 程序语言

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MECH E4320 (Fall 2024): Homework #4
Please turn in your homework before the date and time indicated in Courseworks. Please show and explain your work clearly and completely in order to earn full credit.
Please include all parts of the homework you want to be graded in a single (1) pdf file submitted via courseworks. This pdf must contain all relevant work, equations, intermediate steps, intermediate and final results, plots, tables, and explanations – and only this pdf will be graded. Any additional files you use to generate the results presented and explained in the pdf (e.g. ipyn or xlsx) must also be uploaded as well (as supplemental information for your pdf file) but will not be explicitly graded.
1. Ignition delay time is the time it takes for a homogenous mixture at some given initial temperature and pressure to ignite. This ignition delay time can be defined in a variety of ways, but it is often defined as the time at which the time derivative of temperature, pressure, or a specific species reaches a maximum. For this homework, use the maximum time derivative in the mass fraction of OH as the marker for the time of ignition.
In the following problems, you will calculate (using Cantera) and plot the ignition delay times for various mixtures in a homogenous, closed, adiabatic vessel (also known as a constant volume, adiabatic “batch” reactor). You may find the “batch_reactor_ignition_delay_NTC.ipynb” Jupyter notebook under the “reactors” folder on the Cantera Jupyter notebook site (https://github.com/Cantera/cantera-jupyter) helpful. For these calculations, use the kinetic mechanism from Hashemi et al. when defining the gas. To do this, download ‘H2mech.yaml’ from the files tab in courseworks and add it to your current working directory.
a. For a mixture of 3.47% H2, 3.47% O2, and 93.6% Argon, please plot the ignition delay time (on the x-axis in log scale) at temperatures of 900, 1000, 1050, 1100, 1200, 1300, and 1400 K (as different lines on the same plot) as a function of pressure (from 0.1 to 100 atm, on the y-axis in log scale). You can compare your calculations and plot to this figure below
From: H. Hashemi, J.M. Christensen, S. Gersen, P. Glarborg, Proceedings of the Combustion Institute 35 (2015), 553-560, https://doi.org/10.1016/j.proci.2014.05.101

b. Explain the reasons for the trends you find for ignition delay time as a function of temperature and pressure within the context of the H2/O2 explosion limits discussed in class.
2. In order to obtain a better understanding of the distinct effects of pressure and concentration on ignition delay times, plot the ignition delay times (on the y-axis in log scale) for three different cases (different lines on the same plot) that yield at a mixture 3.47% H2, 3.47% O2, and 93.6% Argon at 1100K and 1 atm but with different variables held constant or varied in case. Plot the ignition delay time for mixtures with an initial temperature of 1100 K:
a. as a function of P/P0 (from 1 to 13 where P0 = 1 atm, on the x-axis in log scale) for a mixture where the mole fractions are held constant while varying pressure (label this line as ‘X fixed’).
b. as a function of P/P0 (from 1 to 13 where P0 = 1 atm, on the x-axis in log scale) for a mixture where the reactant concentrations are held constant (at their 1 atm values) while varying the pressure (label this line as ‘[X] fixed’)
c. as a function of XH2/XH2,0 (from 1 to 13 where XH2,0 = 3.47 %, on the x-axis in log scale) for a mixture where pressure is held constant at 1 atm and XH2/XO2 is held fixed at 1 when varying XH2 (label this line as ‘P fixed’).
d. Explain the reasons for the distinct trends in each case
Note: For this plot the y axis should still be the log scale of the ignition delay time but the x-axis is P/P0 or X/X0 depending on which line is being plotted.