Flow Categorization in Supersonic Flows with Large Roughness Heights

In the present research the flow over large roughness elements, representative of a rocket nozzle inner contour, is investigated. From the rocket nozzle inner surface roughness, three simplified roughness shapes were defined and tested: a forward facing step, a cavity, and a forward facing step plus cavity. The geometries vary in height from 6 to 46 percent of the boundary layer thickness. The flow over these roughness elements is studied at a free stream Mach number of 2. This was done numerically by means of RANS simulations and experimentally by means of Schlieren and PIV. For these geometries it was found that three flow classes can be distinguished. For large roughness heights, with a large length to depth ratio, the flow disruptions center around the steps, while the sections between the elements show flat-plate flow. Drag and heat transfer show large increases for these elements. At smaller roughness heights a smoother behavior of the flow can be seen which more resembles boundary layer behavior. For cases where the length to depth ratio of the elements becomes small, a third flow class can be defined. Here the flow is separated between the roughness elements, and the gap from element top to element top is bridged by a shear layer. It was observed that a boundary layer was formed on top of the elements. Based on these observations, a classification system is proposed which divides the roughness in different categories, for each of which it is recommended to use a separate modelling approach. Introduction To evaluate the thermal loading of a rocket nozzle, a good predictive capability of the heat transfer on the gas side is mandatory. For a smooth wall multiple design formulations are available to calculate the heat transfer, see White [5]. If the surface is rough the heating is likely to be different from the smooth case. The interest of the current research lies in the regime of large roughness heights (relative to the boundary layer thickness) since this is not well covered in literature. Jimenez [1] is one of the few sources that describes flows over larger roughnesses. In practice these rough wall geometries can have various forms and shapes. They can range from the distributed wall texture roughness, to discrete roughness elements. Material roughness has been extensively researched. It was shown by Nikuradse [3] that the turbulent boundary layer flow on a rough surface can be described by adapting the standard law of the wall. In this study, however, we consider discrete wall patterns that are designed to represent the surface irregularities on the inside of the baseline rocket nozzle due to the employed manufacturing technique. We will investigate the effects of such surface irregularities on the flow, focusing in particular on the size of these roughness profiles. The final goal is to find a model that can explain the observed effects. Different physical behavior has been observed in different configurations, and therefore a system will be proposed which classifies the roughness into categories with the same behavior. The investigation was carried out using a combined computational and experimental approach. First a CFD study has been performed on these geometries. These simulations where made for a turbulent flow over an adiabatic, heated and cooled wall. The non-adiabatic wall simulations, were run with a wall temperature of 0.5 and 1.5 times the adiabatic wall temperature, i.e. , 137.5 K and 412.5 K, respectively. In the experiments the flow was visualized using Schlieren. Particle Image Velocimetry (PIV) was subsequently used to measure the velocity in the flow field. Rough geometries To investigate the effect of element geometry on the wall shear and heat transfer, multiple geometries have been defined. These are variations on the baseline nozzle geometry. For optical access to the geometries in the experiments they have been implemented as spanwise two-dimensional shapes in a nominal flat-plate configuration. Fig. 1 A shows several elements of the baseline nozzle shape extrapolated to a flat plate with the free-stream from left to right.