MECH E4320 (Fall 2024): Homework #4
Please turn in your homework before the date and time indicated in Courseworks. Please show andexplain 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 viacourseworks. This pdf must contain all relevant work, equations, intermediate steps, intermediate andfinal results, plots, tables, and explanations – andonly this pdf will be graded. Any additional files youuse to generate the results presented and explained in the pdf (e.g. ipyn or xlsx) must also be uploadedas well (as supplemental information for your pdf file) but will not be explicitly graded.
- Ignition delay time is the time it takes for a homogenous mixture at some given initialtemperature 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 aspecific species reaches a maximum. For this homework, use the maximum time derivative inthe 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 delaytimesfor various mixtures in a homogenous, closed, adiabatic vessel (also known as a constantvolume, adiabatic “batch” reactor). You may find the“batch_reactor_ignition_delay_NTC.ipynb” Jupyter notebook under the “reactors” folder on theCantera Jupyter notebook site (https://github.com/Cantera/cantera-jupyter) helpful. For thesecalculations, 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 workingdirectory.For a mixture of 3.47% H2, 3.47% 2, and 93.6% Argon, please plot the ignition delaytime (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 to100 atm, on the y-axis in log scale). You can compare your calculations and plot to thisfigure belowFrom: H. Hashemi, J.M. Christensen, S. Gersen, P. Glarborg, Proceedings of theCombustion Institute 35 (2015), 553-560, https://doi.org/10.1016/j.proci.2014.05.101b. Explain the reasons for the trends you find for ignitiondelaytime as a function oftemperature and pressure within the context of the H2
- In order to obtain a better understanding of the distinct effects of pressure and concentration onignition delay times, plot the ignition delay times (on the y-axis in log scale) for three differentcases (different lines on the same plot) that yield at a mixture 3.47% H, 3.47% O2, and 93.6%Argon at 1100K and 1 atm but with different variables held constant or varied in case. Plot theignition delay time for mixtures with an initial temperature of 1100 K:as a function of P/P0(from 代写 MECH E4320 Batch_Reactor_Ignition1 to 13 where P0= 1 atm, on the x-axis in log scale) for amixture where the mole fractions are held constant while varying pressure (label thisline as ‘X fixed’).as a function of P/P0 (from 1 to 13 where P0= 1 atm, on the x-axis in log scale) for amixture where the reactant concentrations are held constant (at their 1 atm values) whilevarying the pressure (label this line as ‘[X] fixed’)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/XO2is held fixed at 1when varying XH2(label this line as ‘P fixed’).Explain the reasons for the distinct trends in each caseNote: For this plot the y axis should still be the log scale of the ignition delay time but the x-axisis P/P0or X/X0depending on which line is being plotted.