Inception of Turbulence in the Stokes Boundary Layer Over a Transpiring Wall

Abstract

In this work, the onset of turbulence inside a rectangular chamber is investigated, with and without side-wall injection, in the presence of an oscillatory pressure gradient. Two techniques are used to define the transition from laminar to turbulent regimes: statistical analysis and flow visualization. Calibrated hot film anemometry and a computer data acquisition system are used to record and analyze acoustical flow data. Four classifications of flow regimes are reported: (a) laminar, (b) distorted laminar, (c) weakly turbulent, and (d) conditionally turbulent. Despite numerous attempts to promote turbulence, a fully turbulent flow does not develop at any of the driving frequencies tested. Statistical measurements reveal that a periodic drop in standard deviation of axial velocity fluctuations always occurs, indicating relaminarization within each cycle. Transition between flow regimes is assessed from the standard deviation of velocity data correlated as a function of the acoustic Reynolds number ReA. Under predominantly laminar conditions, the standard deviation is found to vary approximately with the square of the acoustic Reynolds number. Under turbulent conditions, the standard deviation becomes almost directly proportional to the acoustic Reynolds number. Inception of turbulence in the oscillatory flow with side-wall injection is found to be reproducible at the same critical value of ReA≅200.

Hydrodynamic Stability Analysis of Solid Rocket Motors with Arbitrary Grain Design

“…Through the present work, the analytic models developed by Abu-Irshaid, Majdalani and Casalis, 5 Bhatia et al, 6 and Chedevergne et al [1][2][3][4] will be implemented in an improved combustion instability framework originating from the efforts of Flandro et al 7,8 The need to incorporate hydrodynamic instability waves in combustion instability computations has been recently emphasized by Casalis and co-workers, particularly by Chedevergne et al, [1][2][3][4] Griffond and Casalis, 9,10 Griffond, 11 Féraille and Casalis, 12 and others. The importance of accounting for unsteady vorticity in general has been emphasized by Fischbach et al, [13][14][15][16] Flandro et al, 7,8 Flandro and Majdalani, 17 Majdalani et al, [18][19][20][21][22][23][24][25][26][27][28][29] Balachandar et al, 30 Wasistho et al, 31 and others. [32][33][34] Our chief purpose will be to extend and implement their techniques in a general 3D capable linear stability tool that has been under development by French et al [35][36][37]…”

Acoustic Instability of the Slab Rocket Motor

“…The use of the (opposed plane) slab configuration in combustion stability related studies may be traced back to the work of Brownlee and Marble [1][2][3] who employed blocks of propellant in some of their laboratory experiments. More recent investigations that adopt the slab geometry include those by Casalis et al [4][5][6][7], Liou et al [8][9][10], Yang et al [11][12][13], Van Moorhem et al [14][15][16][17][18], Wasistho et al at the Center for Simulation of Advanced Rockets (CSAR) [19], and Vuillot et al at the Office National d'Études et de Recherches Aérospatiales (ONERA) [20][21][22][23][24][25]. In that vein, scientists at both CSAR and ONERA have often utilized the planar/slab configuration as the preferred geometry to either validate their full-scale threedimensional codes or to concentrate on one particular aspect of motor gas dynamics.…”