A consistent small‐perturbation theory for the aligned‐fields, steady, magnetogasdynamic two‐dimensional and axisymmetric flow of an inviscid conductor in the sonic, Alfvénic, and hypercritical regimes is developed, and approximate shock relations derived by a simple method. This results in nonlinear relatively simple systems of equations and shock relations for mixed flows around bodies in the transition regimes. It is found that transonic magnetogasdynamic problems can be reduced to gasdynamic ones; each gasdynamic transonic flow around a given body implies an infinite number of magnetogasdynamic patterns around the same body for all values of Alfvén numbers different from zero and one, and each of these, in turn, yields another family of flows around similar bodies, according to a modified von Kármán similarity rule. The hypercritical and transonic systems are mathematically similar and obey the same similarity rule. An explicit correspondence between specific transonic and hypercritical flows does not exist, but transonic arguments and methods can be used to infer qualitative properties of hypercritical flows and to obtain exact solutions of hypercritical flow patterns.
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April 1963
Research Article|
April 01 1963
Magnetogasdynamic Flows with Shock Waves
Nima Geffen
Nima Geffen
Graduate School of Aerospace Engineering, Cornell University, Ithaca, New York
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Phys. Fluids 6, 566–571 (1963)
Article history
Received:
September 13 1962
Citation
Nima Geffen; Magnetogasdynamic Flows with Shock Waves. Phys. Fluids 1 April 1963; 6 (4): 566–571. https://doi.org/10.1063/1.1706774
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