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General Card #2527
CourseDeck: EM Approach to Teaching Compressible Flow Course
By Sid G
Updated: 10/14/2022 3:12 PM by Michael Johnson
Reviewed: 10/14/2022 3:12 PM by Michael Johnson
This is one such course where the power of math is blatantly visible where the equations narrates the connection between the model and the real world.

1. Introduction: 

This course is all about exposing students to the fundamentals of compressible flow in different internal and external environments such as nozzle, ducts, airfoils, etc. The inherent and blatant connections between the equations and the real world applications makes it easier to naturally integrate EM components into various levels and aspects of the course. It is the author's hope that the weekly modules presented in this "master" card makes it easier for any instructor teaching this course to adapt it to his/her own flavor with ease. 

2. Weekly Card Structure:

In all the weekly modules cards presented below, a clear description of the course content is given interspersed with curiosity, connections and creating value questions that the instructor can use in the beginning of the class or anywhere in between. A short description of the weekly HW assignments were also given which briefly describes the intention behind the homework assignment and how and WHY students will benefit from answering the questions in the assignments. The attachments contain the slides with all the relevant equations, guided notes that were used in class as well as videos that were created. In some weekly course materials, the instructors can use the equations given in the slides to create guided notes of their own flavor for the students to go through the derivation. 

3. EM Tools used in the course:

It is vital to give a platform for the students to show their curiosity, make connections and understand the value of the concepts they are learning. It also gives the instructors a way to assess it. Therefore the following tools were used throughout the course progression as a way for the students to demonstrate their 3C's. 

a) Setting Proper Context

I can't overstate the importance of setting proper context for the concepts/derivations which are covered in the course. As instructors, we constantly be thinking about "WHY DO THE STUDENTS CARE ABOUT ANY OF THIS"? While there is be a strong argument that students are the ones who need to find the importance of the topics discussed, setting a bit of context to the concepts through thought provoking questions or using techniques such as QFT, helps a lot for the students to get some grip on the "alien" topics. Given them something to care about so that they are pulled into the subject. Throughout the weekly modules, questions are dispersed within the narrative to invoke curiosity, connections and creating value so that they have a reason to care about the subject. 

b) Guided Notes

In a math and derivation heavy class, the use of guided notes can provide a platform for the students to become curious and make connections between several concepts. Guided notes are instructor-prepared handouts provided to all students in the class with necessary background information and cues with unfilled spaces to write key facts, equations, concepts, assumptions, etc. during the lecture. The guided notes prepared by the author is attached to most of the weekly modules presented below which the instructors can modify and use in their own classes. Some of the important assumptions, derivation steps, and equations were intentionally left out from the notes so that the students can discuss in groups and fill in the blanks. Through this method, students were able to play complete attention to the class and were able to ask important questions to the author. The guided notes surprisingly provided a faster way to go through the derivations when compared to us writing equations on the board. It is easy for the students to misinterpret some of the mathematical symbols and variables which are written on the board which can be overcome through the use of guided notes. The focus is turned away from simple copying to truly understanding the material because they have to figure out the steps inorder to move forward. This forces them to make connections and forces them to ask questions. A short video on the use of guided notes is presented in the resources section below.

c) NOT using compressible flow tables

It is very common for students who takes this course to rely a lot on the compressible flow tables for various concepts such as shock wave relations, Rayleigh flow, Fanno flow relations, etc. While that makes it easier for the students, there is very little learning once they figure out which numbers to see. Therefore, in this course, the students are required to program all the relations that were discussed using Matlab, Python or any other programming language. Programming these equations increases the skillset of the students as well as forces them to make connections between the equations relating different properties such as temperature, Mach number, density, pressure, etc. They can plot these relations and understand not just the magnitude of these variables but also the trends. By NOT using the compressible flow tables, it is possible to push the students to think deeply about the connections and perform sanity checks on the results they get.

d) Not give back of the chapter HW problems

More often than not, there is little to no context behind the questions posed in the back of the chapter HW problems in any text books. As such, the instructor should tailor the HW so that students are constantly reminded of the "VALUE" that these simple concepts adds to the field of engineering. In this course, students work on problems involving space shuttle main engines, dehydration of natural gas (use of shock waves in CD nozzle), vertical tail of X-15, wing of F-104 Starfighter, natural gas pipelines, supersonic wind tunnels, cold spray nozzles, wings of Cessna 152, etc. where students work on the actual design involving these applications where they get to analyze or optimize certain functions. 

e) Using Portfolio as a means of assessment 

The benefits of using "portfolios" as a means of assessment is well documented in literature. Over the years, the author has taught several technical courses with portfolio based learning. A detailed descriptions of the portfolio and the case studies are documented in two ASEE papers which are attached in the resources section.  A couple of example student portfolios are included for the instructors to get an idea of the level of knowledge, understanding, evaluation and synthesis (pretty much all levels of Bloom's taxonomy) that the students take out of this course through the use of portfolios. The use of portfolios as a means to assess 3C's is also shown in this card

Weekly Modules:

Week 1 - Reynolds Transport Theorem: Insight into Conservation of... well, anything!

Week 2 - What is the Role of Thermodynamics in Compressible Flow?

Week 3 - A Mind Bending Relationship between Area and Flow Speed

Week 4 - The Role of Back Pressure

Week 5 - The What, How and the Why of Shock Waves

Week 6 - What do Supersonic Engine Inlets and Supersonic Wind Tunnels have in Common? - The Oblique Shocks

Week 7 - A Look Into Detached Shocks (An Interactive Approach)

Week 8 - Prandtl Meyer Flow + Bonus Material (Connection between Water Flow and Shock Waves)

Week 9 - Rayleigh Flow (Flow with Heat Addition) with NASA's Turbine-less Ducted Fan

Week 10 - Fanno Flow and the Role it Plays in the Transport of the Natural Gas across the Country

Week 11 - Linearized Flow (Method of Small Perturbations for Subsonic and Supersonic Flows)

  • Demonstrate constant curiosity about our changing world
  • Explore a contrarian view of accepted solution
  • Integrate information from many sources to gain insight
Creating Value
  • Identify unexpected opportunities to create extraordinary value
  • Persist through and learn from failure
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