Development of steady-state mixing in an aerodynamic wake
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We consider the unsteady, isothermal flow in the wake behind a body on which a shock wave has impinged. This flow is studied for sufficiently large distance from the body, when the effect of the latter on the external flow, as in the corresponding steady problem [1, 2], may be neglected. The analysis is performed for laminar and turbulent mixing with planar and axial symmetry.
In § 1 we use the characteristics of the system of equations consisting of the momentum equation written on the wake centerline and an integral equation to determine approximately the boundary separating the steady and unsteady flows. It is noted that the unsteady flow takes place between this boundary and the tagged particle line, which at the moment of detachment of the shock wave from the body coincided with it.
In §2 we show the possibility of calculating the flow in this region using the characteristics of the system of equations noted above. Some particular solutions of the latter are obtained.
Then, in §§ 3 and 4 the exact solutions corresponding to the flow regions identified in §§1 and 2 are presented.
Section 3 presents the exact solutions of the linear system of equations for large values of the time, when the velocity in the wake is close to the velocity of the particles behind the shock wave.
On the basis of the analysis made in §2, and previously in , §4 obtains the exact solution of the nonlinear system of equations which describes the development of the mixing near the tagged particle line for planar turbulent flow. This solution is compared with the corresponding approximate solution of §2. The accuracy of the latter is noted. Comparison of the horizontal component velocity profiles with the profiles obtained in the preceding section and used in  in the method of integral relations shows satisfactory agreement between them
KeywordsShock Wave Exact Solution Fluid Dynamics Nonlinear System Velocity Profile
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