A non-equilibrium kinetic description of shock wave structure

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dc.creator Battat, D.
dc.date 2015-10-22T09:47:11Z
dc.date 2015-10-22T09:47:11Z
dc.date 1968-06
dc.date.accessioned 2022-05-09T09:55:00Z
dc.date.available 2022-05-09T09:55:00Z
dc.identifier http://dspace.lib.cranfield.ac.uk/handle/1826/9580
dc.identifier.uri https://reports.aerade.cranfield.ac.uk/handle/1826.2/4266
dc.description A formulation for the shock wave structure is devised by viewing the transition as a phenomenon in which non-equilibrium effects play an important role. The essence of the method is the approximation of Boltzmann's equation by a simpler kinetic model. Initially, the distribution function in Boltzmann's collision integral is expressed in terms of a function of deviation from local equilibrium. Then, by suitably transforming the complete collision term, the molecular velocities after collision are eliminated. At this stage the formulation of the method is specialized to hard sphere molecules and the problem of deriving a model equation thus reduces to one of assigning an expression for the deviation function. In the first instance, this function is chosen to be zero and an exploratory model is obtained which, when its variable collision frequency is replaced by its mean value, reduces identically to the Bhatnagar-Gross-Krook model. However, it is found that the exploratory model provides a somewhat crude representation of Boltzmann's equation and is shown to imply a Prandtl number very nearly equal to unity. A more accurate model is then derived by choosing for the deviation function the first order term of Chapman-Enskog’s sequence, leading to the Navier-Stokes equations. Here, the specific form of Boltzmann's collision term is represented more accurately than hitherto and the model is found to possess all the known features of the Boltzmann equation. It is shown that this model contains a description of a gas in non-equilibrium state.
dc.language en
dc.publisher College of Aeronautics
dc.relation 154
dc.relation COA/M-154
dc.title A non-equilibrium kinetic description of shock wave structure
dc.type Report

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