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## Computer Project With C Code And One-Dimensional Flow Analysis.

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Computer Project with C code and one-dimensional flow analysis.

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### Additional Instructions

Grading Rubric for ABE Computer Project – Spring 2022*
Score X/100
Part 1
Results from Part 1 not submitted, -50
Raw computer output not submitted, -12
Missing column of required data, -7 per column
Missing column headers, -4
Incorrect numbers, -5 per column
o If M is wrong, -10 but no further deduction for answers if provided
Wrong significant figures, -2 per column up to -8
Poor alignment, -5
Plots
o Wrong curve but numbers above are correct, -4 per curve
o Wrong curve because numbers are incorrect, no additional point loss
o Missing required curves, -7 per curve
o No title or inappropriate title, -4
o No legend or poorly labeled legend, -5
o Improper or no axis titles; Improper axis labeling, -2 per axis per error type
o Cannot distinguish curves, -5
o Poor plot size relative to page size, -4
o Curves not on a single plot, -4
o Plot not submitted, but data provided, -20
Part 2
Results from Part 2 not submitted, -35
Data not submitted, -20
(Because only inlet and exit values are needed, raw data not necessary, only inlet and exit values.)
Incorrect numbers:
o If numbers in Part 1 are incorrect, no additional point loss
o If numbers in Part 1 are correct, -2 per number
Wrong significant figures, -2 per column
Poor alignment, -5
Plots, same as in Part 1
o Plot not submitted for Part 2, -10
No code submitted but data and plots provided, -30; Code submitted only electronic or hardcopy but not
both, -15
No results at all submitted, but a (reasonable) code is submitted, -40 with no further deduction
*This represents the expected grading rubric. The instructor reserves the right to add to or modify it at any time to account for
circumstances not explicitly stated herein.
In class, we treated area changes, friction, and heat addition separately. However, in an engine component several effects can occur simultaneously. The technique used to analyze this situation is the so-called generalized one-dimensional flow method derived in many gas dynamics texts. It is a differential equation analysis from which influence coefficients are derived. These coefficients relate changes of one variable on another. You were provided with a handout showing a table of the influence coefficients. You will now use that table along with your lecture notes to solve a combined heat addition and friction problem for an aircraft engine combustion chamber.
Flow with an incoming Mach number of 0.4 and an inlet total pressure of 1.5 MPa enters a combustion chamber 0.75 m long with an inlet diameter of 0.4 m, which increases linearly to 0.6 m, and a friction factor of 0.045. The total temperature increases linearly from 700 K to 1700 K. What is the total pressure ratio across the burner if the specific heat ratio is 1.32? Also determine the burner ratios for static temperature and pressure, and the exit Mach number. On a single graph, plot the changes of these ratios and the Mach number as a function of axial position in the chamber (for incoming Mach number of 0.4 only).
Now investigate the effects of these ratios with different incoming Mach numbers. Vary the Mach number from 0 to 0.9 in increments of 0.1. On a single graph, plot each variable ratio (total pressure, static pressure, static temperature) and the exit Mach number against the incoming Mach number. Do not plot non-physical results, but instead explain why these results are non-physical.
For both graphs, you will want to use a double-y-axis plot, with the exit Mach number and pressure ratios on one axis, and the temperature ratio on the other axis.
To solve this problem, you will need to numerically integrate the equations you develop from the table of influence coefficients. This is relatively easy if you replace all the differential terms (dM2, dT, etc.) with delta terms (AM2, AT, etc.) where a delta term represents a change in the variable in space. Divide the chamber into 100 increments, and use a backwards difference for each delta term (i.e. AM2 = M2i—M2i 1). All terms on the right-hand side of the equations should be evaluated at the i — I node. In this fashion, you can numerically integrate your way across the burner.
You may choose any computer language you prefer provided you are not using a commercial or other pre-written application (i.e., Mathematica, Excel, and other available software are not acceptable, though MATLAB is acceptable) and the numerical integration is coded as described above without using pre-written functions that do the integration for you. While working in small groups to set up the problem and determine how to solve it is acceptable, all code must be original work. Code that is copied or substantially similar to other students' work will be rejected and no credit for the project received.
To complete this project, you must turn in the code listing, tabulated numerical results from your code (appropriately formatted and aligned for readability with exactly 3 decimal places), and your plots (with appropriate titles, axis labels, labeled legends, etc.) in both hard copy and electronically on Canvas. No screenshots of results...your code must provide an output file.
See attachments for homework instructions, grading rubrics, one-dimensional flowchart, chapter 9 examples, and appendix H.
Use textbook: Fundamentals of Jet Propulsion with application. Chapter 9 and appendix H provide good examples of how to use the one-dimensional flow chart. Remember, in the burner heat addition and friction occurs simultaneously. See also attachments for copies of chapter 9 and appendix H.
Important Notes:
Your code must generate the raw scores. You must also show how (handwritten) you computed the raw scores for the following:
Total pressure ratio across the burner if the specific heat ratio is 1.32. Static temperature, static pressure, and exit Mach number.
You must provide 2 graphs:
(Graph 1) On a single graph, plot the changes of these ratios and the Mach number as a function of axial position in the chamber (for incoming Mach number of 0.4 only).
(Graph 2) Vary the Mach number from 0 to 0.9 in increments of 0.1. On a single graph, plot each variable ratio (total pressure, static pressure, static temperature) and the exit Mach number against the incoming Mach number. Do not plot non-physical results, but instead explain why these results are non-physical
For both graphs, you will want to use a double-y-axis plot, with the exit Mach number and total pressure and static pressure ratios on the left y-axis, and the temperature ratio on the right y-axis. On graph 1, the x-axis is axial positions and graph 2, the x-axis is incoming Mach number.

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