Understanding the fundamental equations of flow in the special regime of high speed (supersonic) internal and external flows at where compressibility of the medium plays a significant role and leads to special physical phenomena in the flow such as shock waves, and to sometimes counter-intuitive behaviour. The main driver in these mechanisms are first the speed exceeding the speed of sound, and secondly, the exchange between kinetic energy of the flow and internal energy. Applications range from high speed aeronautics to space technology. This is achieved in a mixed learning environment with a limited number of interactive lectures where the course material is discussed. We develop the ability to analyse the equations and rewrite, and use the relevant theory for problem analysis of specific physical phenomena and their impact, for practical cases. Work is done in group assignments. Develop the ability to independently study a practically relevant topic related to compressible flow/gasdynamics in a group, write a paper about it, and present results in a mini-conference setting.
Topic specific goals:
- Familiarize with physics and mathematical models for compressible flows starting from the most general framework, employing assumptions. Understand the derivation of physically more restrictive models derived, such as relations as Crocco’s and Bernoulli’s relations. Understand the relation with acoustics.
- Understand the derivations of the Rankine-Hugoniot relations for discontinuous (weak) solutions of inviscid flows: shock waves, contact surfaces, and develop the skills to analyse normal and oblique shock problems.
- Familiarize with the thermodynamics required for compressible flow problems: Maxwell’s thermodynamic relations, perfect gases, and non-perfect gases.
- Understand the hyperbolic character of unsteady compressible flows and be familiar with the method-of-characteristics technique to obtain the solution of compressible flow problems for one-dimensional unsteady isentropic and non-isentropic flow, two-dimensional steady supersonic flow.
- analytically obtain solutions of the linearized as well as the full Euler equations for 1D wave-propagation problems: linear acoustics, nonlinear wave propagation, expansion waves, normal and oblique shock waves.
- Develop the knowledge and the skills to study in detail and critically analyse and discuss a relevant recent scientific paper in the field of gasdynamics/compressible flow and in relation to the contents of the course.
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Description of physics and mathematical models for high speed (supersonic) flows from most general framework, employing assumptions. Understanding of the physics of flows faster than the speed of sound and the exchange in such flows of thermal and kinetic energy due to the compressibility. Derivation of, physically more restrictive models, as well as relations such as Crocco’s and Bernoulli’s relations. Rankine-Hugoniot relations for discontinuous (weak) solutions of inviscid flow equations: Analysis of shock waves normal and oblique, contact surfaces. Implications of shockwaves for performance of airfoils (external flow) and nozzles (internal flow). Thermodynamics required for compressible flow problems: Maxwell’s thermodynamic relations, perfect gases, and non-perfect gases may arise. Description of the hyperbolic character of unsteady compressible flows, method-of-characteristics to obtain the solution of compressible flow problems for one-dimensional unsteady isentropic and non-isentropic flow, two-dimensional steady supersonic flow. Solution techniques for one-, two- and three-dimensional compressible flow problems may come about. Analytical solutions of the linearized as well as the full Euler equations for 1D wave-propagation problems: linear acoustics, nonlinear wave propagation, expansion waves, normal and oblique shock waves. Possbile extensions involve: Application of gasdynamics to highway traffic. Elements of kinetic gas theory.
Organization: TWIN Teaching Dual Learning Concept
In a mixed learning environment with a limited number of interactive lectures the course material is discussed with teacher and assistents. Students have an active role in lecture preparation and discussion. Mixed learning environment. Lectures and discussion. Assignments. Technical Paper, and Mini conference.
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