Jones Nozzle in Detonation

Detonation, Nonlinear Theory of Unstable One-Dimensional. J.J. Erpenbeck describes in PhysFluids 10(2), 274-89(1969) CA 66, 8180-R(1967) a method for calcg the behavior of 1-dimensional detonations whose steady solns are hydrodynamic ally unstable. This method is based on a perturbation technique that treats the nonlinear terms in the hydro-dynamic equations as perturbations to the linear equations of hydrodynamic-stability theory. Detailed calcns are presented for several ideal-gas unimol-reaction cases for which the predicted oscillations agree reasonably well with those obtd by numerical integration of the hydrodynamic equations, as reported by W. Fickett W.W. Wood, PhysFluids 9(5), 903-16(1966) CA 65, 

Cook (Ref 6) gave the following explanation of nozzle theory  

There were two steps in Jones determination of equations of his theory. He first solved the perturbed hydrodynamic equations for D, using a constant covolume equation of state. Then, using an expression for the ideal deton velocity D, he obtd the equation  

Jones final result of calculation is given by the equations  

Nozzle theory is also described in Russian (Ref 7) under the name teoriya sop la  

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