Shock acceleration with turbulence minimization

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We investigate whether there is an optimum way to accelerate an interface so as to minimize the generation of turbulence at the interface, using a k-{var epsilon}'' simplification of a one-point turbulence model. The problem is to use a finite number of shock waves to bring an interface, initially at rest, to a final velocity V after it has traveled a distance x. We restrict attention to the case of two shock waves, and treat the problem in three phases. The first phase is the initialization of turbulence at the discontinuous interface by the first shock wave, seeded by a ... continued below

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Hoffman, N.M. January 1, 1991.

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We investigate whether there is an optimum way to accelerate an interface so as to minimize the generation of turbulence at the interface, using a k-{var epsilon}'' simplification of a one-point turbulence model. The problem is to use a finite number of shock waves to bring an interface, initially at rest, to a final velocity V after it has traveled a distance x. We restrict attention to the case of two shock waves, and treat the problem in three phases. The first phase is the initialization of turbulence at the discontinuous interface by the first shock wave, seeded by a spectrum of perturbations on the interface. This sets the initial conditions for the second phase, which is the transport of turbulence and growth of the interface's thickness during the period between shocks. The third phase is the arrival at the interface of the next shock wave, generating turbulence from finite density self-correlation, density-velocity correlation, and turbulence kinetic energy. We assume dissipation of turbulence is negligible, and use a configurational approximation for the density self-correlation, rather than solving an evolution equation for this quantity. We derive an expression for the total turbulence energy after the passage of the second shock wave, as a function of the two variables V{sub 1} (the interface velocity after the passage of the first shock) and t{sub 2} (the time of arrival of the second shock), parametric in the final velocity V, a scale S characterizing the initial perturbation, and the Atwood number A. We find that in the high-Atwood-number, small-perturbation-scale limit, the turbulence energy is maximized if the first shock is somewhat weaker than the second. For accelerations in which 60% or more of the final velocity V is acquired in the first shock, the turbulence energy is less than half what it is when only 25% of the final velocity is acquired in the first shock. 4 refs., 7 figs.

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Pages: (20 p)

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OSTI; NTIS; GPO Dep.

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  • Workshop on physics of compressible, turbulent mixing, Royaumont (France), 17-19 Jun 1991

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  • Other: DE91014741
  • Report No.: LA-UR-91-1993
  • Report No.: CONF-9106222--1
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 5730067
  • Archival Resource Key: ark:/67531/metadc1093427

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  • January 1, 1991

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  • Feb. 10, 2018, 10:06 p.m.

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  • May 25, 2018, 5:12 p.m.

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Hoffman, N.M. Shock acceleration with turbulence minimization, article, January 1, 1991; New Mexico. (digital.library.unt.edu/ark:/67531/metadc1093427/: accessed October 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.