ANALYSIS OF INJECTION - INDUCED FLOWS IN POROUS - WALLED DUCTS WITH APPLICATION TO THE AEROTHERMOCHEMISTRY OF SOLID - PROPELLANT MOTORS

A theoretical analysis of the flow in porous-walled tubes and channels with appreciable injection through the duct wall is presented. Emphasis is placed on flows induced solely from injection by closure of a duct end. Application of the theory to the aerothermochemistry of the solid-propellant rocket motor (viz., the erosive burning problem) is extensively examined. The analysis employs a second-order closure model of turbulence, with single-step gas and condensed-phase reactions utilized to model the combustion of a homogeneous propellant. A finite-difference procedure is used to solve the parabolic equation system.; Theoretical results together with existing experimental data indicate that the flows in porous tubes at large injection Reynolds number can undergo three regimes of flow development, proceeding from the closed head end. In the first regime the velocity field develops in accordance with laminar similarity theory. In the second, high levels of turbulence are developed while the mean velocity field continues to correspond with laminar theory for several radii. The third regime commences with transition (change in shape) of the mean axial velocity distribution, a process occuring at extremely large Reynolds numbers. Factors infuencing the development of the latter regime are assessed. For the reactive flows in solid propellant motors, the results show qualitatively similar flow development with, however, a change in scaling of the mean flow transition process due to combustion. The results for erosive burning are shown to be sensitive to imprecisely-known physical conditions such as surface roughness and the parameters governing the height of the combustion zone, although selection of these parameters within acceptable ranges allows favorable agreement with laboratory motor data. The absence of erosive burning observed in larger motors is theoretically related to the scaling of the erosion threshold condition, and consequently, to the preceding mean-flow transition process. The effects of reaction-rate correlations on erosive burning (combustion-turbulence interaction) have also been investigated. The results show that CTI has a surprisingly negligible effect on the propellant burning rate under erosion conditions, although the effects on mean reaction-rate and thermal transport processes can be substantial.