Gas Dynamics

Based on the pre-knowledge of Fluidmechanics I the compressible Navier-Stokes equations and the main theorems of thermodynamics are introductorily repeated. Bottom-up on this, the stationary theory of quasi one dimensional nozzle flow (laval-equation) and the stationary normal shock theory are derived, analysed and applied for the solution of compressible fluid problems in subsonic and supersonic area. Based on the stationary theory of one dimensional flow, unsteady linear and non-linear wave dynamics is introduced and applied for the analysis of the fundamental principle of charge change. With the theory of non-linear wave dynamics the analysis of processes in a shock tube (Ludwieg-tube) are performed. Finally, technics for analysis of multidimensional effects in supersonic flows are discussed and applied to several problems related to wings and jet engines. The lecture and the exercise are supplemented through simulation examples and visualisations.

After successfully passing the module in gas dynamics, the students are able to: (1) apply fundamental procedures in the formulation of simplifications to the equations in compressible fluid mechanics as well as in thermodynamics, (2) analyze stationary and transient gas-dynamic problems with analytical methods (3) to qualitatively determine and evaluate the behavior of supersonic flows around slender bodies by means of the solution of linear differential equations, (4) to recall wave dynamic processes including transient shock formation, (5) to understand experimental devices for the analysis of compressible gas flows, (6) to apply the learned theories (from the analysis of the Concorde accident to the prediction of the characteristic wave-drag in transonic flow to the description of the transient behavior of the flow in piston-cylinder systems).

Necessary are the basic study courses Fluidmechanics I and Thermodynamics, recommended but in no case obligatory are the courses Fluidmechanics II, Thermodynamics II, Applied CFD also courses in the area Aerodynamics / Fluidmechanics.

The module includes a lecture and an exercise as courses. The lecture explains the theoretical basics of gas dynamics through a teaching process. For example, the students learn to apply the basic procedure in the formulation of simplifications to the equations in compressible fluid mechanics as well as in thermodynamics.
In the exercise lecture sample exercises are calculated and can be discussed together with the trainer. The students learn to analyze stationary and unsteady gas-dynamic problems with analytical methods and to apply the learned theories (e.g. prediction of characteristic wave-drag in transonic flows, description of unsteady behavior of the flow in piston-cylinder systems).

Multimedia-based supported frontal teaching

Lecture scripts, lecture slides, exercise collection, additional materials on the web platform.
John D. Anderson: “Modern Compressible Flow: With Historical Perspective”, McGraw-Hill Education; 3 edition (July 19, 2002), ISBN: 9780071241366

The exam (written exam, 90 min) consists of extended short questions that cover the entire range of topics discussed in the lectures. In the exam no aids are allowed - except for writing / drawing equipment and a non-programmable calculator. The extended short questions have the advantage of being able to test a well-balanced mix of knowledge questions (i.e., important elementary formulas and contexts), practice questions (i.e., the use of techniques comparable to the exercises), and transfer questions across the entire range of topics. The students should thus demonstrate that they analyze, for example, stationary and unsteady gas-dynamic problems with analytical methods, qualitatively determine and evaluate the behavior of supersonic flows around slender bodies with the help of the solution of linear differential equations, and the learned theories (e.g. prediction of the wave-drag in transonic flow and the description of the transient behavior of the flow in piston-cylinder systems).