Posted onMay 13, 2017|Comments Off on GES 554: Partial Differential Equations
At the University of Alabama, I taught the GES 554 course Partial Differential Equations from 2014-2017. The course investigated theory, classification, formulation, relevancy, analysis, and solutions of PDEs. Both analytical and computational methods were studied with a special focus on PDEs commonly seen in engineering.
Textbook: Partial Differential Equations for Scientists and Engineers, S. Farlow, Dover ($12 from Amazon) Reviewed here
In the Fall of 2016, I taught AEM 313 Aerodynamics I.
Objectives: Introduction to subsonic aerodynamics, including properties of the atmosphere; aerodynamic characteristics of airfoils, wings, and other components; lift and drag phenomena; and topics of current interest.
Required Book: Fundamentals of Aerodynamics, John Anderson, McGraw-Hill, 5th ed, 2010
We will cover subsonic and transonic topics in the textbook. Selected topics and sources supplement the text.
Prandtl Lifting Line theory remains an excellent tools for preliminary design and gaining intuition about the aerodynamics of unswept wings.
Implementing a PLL solver is relatively simple; I made this version in a few hours with Fortran. The solver generates SVG files displaying the wing geometry, gamma and lift distributions as well as the integrated lift and drag coefficients for arbitrary wing geometries (as approximated by linear sections). The program and input files are available at: https://charles-oneill.com/code/prandtl/prl2.zip
A flat elliptical wing demonstrates the flat sectional lift coefficient distribution resulting from an elliptical lift distribution.
The beauty of the Prandtl lifting line theory is the ability to modify the wing geometry and airfoil sections. For example, given a 20% flap deflected 20 degrees on inner wing sections, the sectional lift distribution reflects the flap deflection. Of particular interest is that the shed vorticity is proportional to the slope of the green lift distribution.
The PLL theory is also instructive for understanding control surface behaviors. In the following image, the 20% ailerons are deflected approximately +-10 degrees (Thin airfoil theory is used to determine the equivalent zero lift line.). Of particular concern is that aileron deflections at high AOA can push the local angle of attack into a stalled state.
Back in 2006 as part of an independent study course, I used an inviscid CFD solver to estimate the aerodynamic performance of actual low aspect ratio wing configurations. The report (lowargeometryco2006.pdf) was written in a handbook style inspired by the classic Hoerner Lift and Drag books. The configurations were: monoplane, biplane, joined-tip biplane “box”, disc, monoplane with endplates, and a shroud cowl. Biplane gap, stagger, and decalage were considered. Performance criteria such as lift slope, induced drag, lift to drag ratio (L/D) were compared for multiple configurations and aspect ratios.The final portion of the report provides a visual display of the pressures and flow fields near the configurations.
Wake rollup of an AR=1 wing:
Wake aft of a biplane:
Pressure field interference with respect to biplane gap.
A brief description of IEEE 754 floating point numbers
Spacecraft Attitude (Guest Lecture)
Propulsion (Guest Lecture)
The notes contain numerous hand drawn images of systems and references to many books.
Detailed Aircraft Systems of Particular Aircraft were analyzed through flight manuals, NTSB accident reports, AIAA case-studies, and expert guest lectures.
Cessna 170 & 310
VTOL: VJ101 and VAK191B
WW2 Dam Busters (system development case study)
DHC-7 (aka. EO-5C / RC-7B)
A behind-the-scenes guided tour of the Southern Museum of Flight in Birmingham by two (2) PhDs in History and Engineering.
The course also included a set of lectures titled “Failure Fridays” which investigated aircraft incidents and accidents by tracking the failure points and symptoms with a special emphasis on systems. These included:
Cessna 182 Fuel Contamination
A320 Fly By Wire
Boeing 737 Rudder Actuator
Advisory Circulars (AC)
The largest non-nuclear explosion known to man. (Not aerospace, but still an impressive and covertly intentional systems failure!)
This course was particularly interesting; as the instructor, I learned a great deal about many topics. I had to work hard to stay ahead of the students. The students gave one of the best ratings that I have ever received. One student said:
The course was very interesting and likely one of the most valuable classes I have had in college. Rather than sticking strictly to theory as most of the Aerospace curriculum does, this class covers details about the what, why, and how for a wide range of
systems that will be particularly useful in any aerospace career.
Another student said:
This course provided me with an otherwise unobtainable insight into the real world of engineering systems, something not talked
about in other courses. This class is great for the industry engineer.
Not every comment was so positive. One student mentioned that this course required several prerequisites and that “newly transferred” students would find the course “difficult”.
More information and the full course notes are available by contacting Charles O’Neill.