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Learning Differential Equation Aspects Of Fluid Mechanics With Spreadsheet Facilitated Computational Fluid Dynamics

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2001 Annual Conference


Albuquerque, New Mexico

Publication Date

June 24, 2001

Start Date

June 24, 2001

End Date

June 27, 2001



Page Count


Page Numbers

6.675.1 - 6.675.16



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Paper Authors

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Robert Kee

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Jean-Pierre Delplanque

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It is well known that continuum fluid flow is described at its most fundamental level by the Navier-Stokes equations, a system of nonlinear, second-order, partial differential equations. In spite of this solid foundation, the equations themselves are sufficiently difficult to under- stand and solve that they are often introduced only superficially in fluid-mechanics courses. Because it is difficult to connect mathematical theory to engineering practice, a differential- equation perspective is often perceived as “too mathematical,” or “too disconnected” to be of any value. It is our view that the differential-equation view does have value in facilitating the fundamental understanding of fluid flow, but it needs to be made accessible to the stu- dents with a reasonable level of effort. The intent of this paper is to describe how we have incorporated computational fluid dynamics (CFD) into fluid-mechanics courses, especially at the advanced levels. In graduate-level fluid mechanics, the students must work with theoretically and math- ematically complex vector and vector-tensor concepts. While such concepts and operators are understandable in a purely mathematical sense, it is usually a challenge to relate the mathematical abstractions to a practical flow field. We use CFD simulation as a de-facto laboratory that permits the students to explore the flow field. In a class that is primarily oriented to the theoretical aspects of fluid mechanics, it is impractical to dedicate enough time for the students to create their own CFD simulations and to write the post-processors required to explore theoretical aspects of the flow. Instead, we computationally solve certain physically interesting problems beforehand and write the flow field (i.e., velocities, temperatures, pressures, etc.) into a spreadsheet (e.g., Excel) that is distributed electronically to the students. The CFD computation is usually done on a logically rectangular mesh network, which simplifies the student effort in the subsequent formation of the derivatives required to represent certain operations (e.g., forming the vor- ticity field). Based on the computed flow fields as represented in the spreadsheets, we assign homework exercises to reinforce theoretical concepts that are being developed in the lectures. It is relatively easy for the students to form vector or tensor operators by manipulating the solution fields in the spreadsheets. Also, Excel graphing features facilitate visualization of results. Overall, the students can understand theoretical complexities of a flow field, with a modest time investment. The paradigm proposed here combines the advantages of laboratory teaching (e.g., hands- on experience) with an effective teaching of scientific methods and problem solving [1]. Of course, a primary benefit of this method is that students play an active role in tackling ab- stract concepts, which have not been traditionally conducive to such participation. Further- more, these exercises result in an improved competency of the students in using spreadsheets for engineering purposes, thus preparing them better for their future professional endeav- ors. [1] The novelty of the proposed technique resides in its objective to illustrate abstract concepts. This is a departure from prior efforts to use spreadsheets, CFD, or software tools such as Mathcad in the engineering curriculum, since such efforts have typically focused on reducing the amount of repetitive calculations that are associated with certain engineering tasks such as pump selection [2], replacing traditional coding of numerical solutions by the use of “engineering arithmetic tools” [3, 4], or familiarizing the students with the new tools of their future trade (e.g., CFD) [5].

Kee, R., & Delplanque, J. (2001, June), Learning Differential Equation Aspects Of Fluid Mechanics With Spreadsheet Facilitated Computational Fluid Dynamics Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--9502

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