A study of wall-injected flows into closed–open rectangular cylinders

The present work concerns with the study of the fluid motion within a channel when a gas is injected from its wall. This kind of flow appears in a wide variety of engineering applications and it is realized either with low or high injection velocity. The most fruitful scientific production about this argument comes from the propulsive community. In fact, a Solid Rocket Motor (SRM) is a hollowed cylinder, whose inner walls burn and hence inject gas into a channel. Thus, propulsive applications involves wall-injected flows and combustion. Actually, the most of combustion takes place in a very thin limited region near the propellant (the flame) and it is often neglected in modeling. However, pressure and temperature are extremely high in a SRM. Therefore, due to this extreme condition, real firing tests provide a number of dataset limited to the number of probes. Usually, sophisticated pressure transducers, withstanding high temperature, placed at the head-end and aft-end of the motor and ultra-sound pads are employed in order to gauge pressure oscillations and monitor the radial regression of the propellant surface. As stated in [1], it is extremely hard to equip model rocket motor to allow for visual access to its interior and also punctual temperature are of limited interest. A first simplification had been to employ a cold flow injected into a hollow cylinder. Although it has been very useful to confirm theoretical predicted instabilities, also this experimental equipment was limited to punctual measurements. A further simplification leads to a closed-open rectangular cylinder, which can be seen as a bi-dimensional approximation of what happens in three-dimensions. Despite this kind of configuration have been developed, moreover with visual access, it has been mostly used for visualizations and no global flowfield measurements were conducted. In this work, a closed-open rectangular cylinder has been adopted in order to obtain a global velocity flowfield by means of Particle Image Velocimetry (PIV). The test section of the experiment is a 24 cm-long, 4 cm-wide and 2 cm-high rectangular channel into which a mixture of air and oil droplets, necessary to the PIV measure- ment, is injected through a porous material in order to simulate the propellant gas injection. As the propellant heterogeneity, the injection due to the flame presents a non-trivial spatial pattern and unsteady temporal behavior. Therefore, the porosity of the adopted material has been investigated in order to understand whether it yields a simulative phenomenon of the propellant flame evolution and, if so, which is the mechanism behind it. Since porosity implies morphological structures of the material of the dimensions of tens of a micron, a high resolution measuring technique is required for the analysis of the flow generated from the injection through this porous material. Hence, Single Pixel Ensemble Correlation PIV, which has a resolution as small as one pixel, has been applied in addition to the more classical Window Correlation technique, which has instead a resolution related to the window size, usually around 16 pixel. The velocity field of the whole channel, reconstructed by means of Window Correlation PIV, is then compared with analytical models opportunely presented. The influence of the flow structure due to porosity has been analyzed. The injection Reynolds number, based on the injection velocity and the height of the channel, for the present set-up is around 100 and the flowfield does not seems to show any transition to turbulence within the full length of the channel. The presence of corners and cavities is a fundamental point of interest for a better comprehension of the internal fluid dynamics of a SRM. Therefore, a second configuration has been taken into account. It presents a ninety degrees corner backward facing step, on the injecting wall, doubling the port area, and a subsequent non-porous, movable block forming a cavity. Investigations have been performed for different cavity lengths and in presence or not of injection from the bottom of the cavity itself. This aspect is strictly related to the flow structure at the aft region of a segmented grain with a tubular segment at the head followed by a star-shaped segment. In fact, the star-shaped segment and the nozzle form a cavity that injects until the propellant of the star-shaped segment burns, thereafter the cavity becomes inert and the flow is due to the tubular segment. The capability of a numerical scheme to accurately solve acoustic waves is fundamental in this circumstance, because the acoustical interaction plays a crucial role in the fluid dynamics of cavities. Definitely, numerical simulations provide a more complete outline and will be also employed in order to compare and go beyond the limitations of the experimental apparatus. A numerical code has been developed implementing high order centered finite difference schemes for the compressible Navier-Stokes equations. Since the physical phenomenon is confined into a bounded region with several boundary con- ditions, the Navier-Stokes Characteristics Boundary Conditions (NSCBC) technique has been adopted. It consists in a local one-dimensional approximation near the boundary, where the method of the characteristics is adopted in order to adequately compute the quantities deriving from the boundary conditions. Since a fourth-order finite difference scheme has been adopted, a selective low-pass filtering process was mandatory in order to overcome the spurious naturally arising oscillations. More- over, the coefficients of the schemes and filters have been chosen so that the scheme minimizes the dispersion error in order to solve the acoustical waves as accurately as possible.