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**Shock-Induced Turbulent Boundary Layer** 

**Separation in Over-Expanded Rocket Nozzles: Physics, Models, Random Side Loads, and the** 

**Diffusive Character of Stochastic Rocket Ascent** 

Contrary to popular belief, and notwithstanding two hundred years of scientific study (Gruntman , 2004), the problem of accurately predicting rocket ascent remains largely unsolved. The difficulties trace to a variety of altitude-, speed-, and launch-site-dependent random forces that act during rocket ascent, including: i) aerodynamic forces (Sutton & Biblarz, 2001), ii) forces due to wind and atmospheric turbulence (Flemming et al., 1988; Justus & Johnson, 1999; Justus et al., 1990; Leahy, 2006), iii) forces produced by rocket construction imperfections (Schmucker, 1984), and iv) impacts with air-borne animals and debris (McNaughtan, 1964). Significantly, our physical understanding and ability to model

By contrast, understanding of the *physical origins,* as well as the *dynamical effects* of altitude-dependent, in-nozzle *random side loads,* has only recently begun to emerge (Keanini et al., 2011; Ostlund, 2002; Srivastava et al., 2010). Referring to figures 1 through 3, we find that side loads represent the end result of a chain of in-nozzle fluid dynamic processes. During low altitude flight, under over-expanded flight conditions, a pressure gradient can exist between the high pressure ambient air surrounding the rocket and nozzle, and the low pressures extant within the nozzle. This pressure gradient can force ambient air *upstream* along the nozzle wall; eventually, inertia of the ambient inflow is overcome by the pressure and inertial forces associated with the outflow, producing a near-wall recirculation region. To the supersonic flow outside the near-wall boundary layer, the recirculation zone functions as a virtual compression corner, producing an oblique shock (Keanini & Brown, 2007; Ostlund, 2002; Summerfield et al., 1954). See figures 1 through 3. Due to the altitude dependence of *Pa* = *Pa*(*H*(*t*)), where *Pa* is the ambient pressure and *H*(*t*) is the rocket's time-dependent altitude, the nominal location of the oblique shock, *xshock* = *xshock*(*H*(*t*)), also varies with

Random side loads arise due to two coupled flow features: i) The oblique shock produces a sharp, adverse pressure rise within the near-wall outflow boundary layer, forcing the boundary layer to separate from the nozzle wall; see figure 1. ii) The *shape* of the boundary

the dynamical effects of each of these random features is fairly well-developed.

**1. Introduction**

altitude.

Sam Hellman, P. T. Tkacik and P. Douglas Knight *Department of Mechanical Engineering & Engineering Science*

*The University of North Carolina at Charlotte*

*USA*

**7**
