In order to perform Schlieren visualizations of transonic nozzle flows, quartz glass windows are mounted on both sidewalls of the test section. However, to avoid strong stresses within the glass, these windows cannot be flush mounted to the facility. Thus, small gaps occur between the glass sidewalls and the metal contour.
During previous numerical and experimental investigations on pseudo-shock systems, we observed that small gaps of Δx = O(10−4) m between construction parts result in reproducible differences between measurement and simulations concerning the pressure distribution along the nozzle wall and the shock location [1].
We showed that these small geometrical uncertainties enable a bypass mass flow, which determines the size and the shape of the separation zones occurring at the foot of the oblique primary shock. Hence, the gaps determine the shape of the entire pseudo-shock system [2].
Extensive unsteady flow simulations of the nozzle geometry with gaps revealed that the shear layer between subsonic gap flow and supersonic core flow is subject to a Kelvin-Helmholtz instability resulting in small pressure fluctuations. We showed, that these fluctuations can trigger the low frequency shock oscillation [3].
Continuative simulations of the full channel geometry confirmed the assumption that the gaps also affect the orientation of the entire shock system [4]. In a slender Laval nozzle without gaps, experimental and numerical simulations demonstrated that the pseudo-shock system tends to break its symmetric behavior with increasing pre-shock Mach number. In contrast, geometries with small gaps along nozzle corner show a symmetric behavior. The induced corner separations shift the pseudo-shock system towards the center of the channel and suppress the breakage of symmetry.
These findings lead to the conclusion that the orientation of pseudo-shock systems can be defined by purposeful placed small gaps along the nozzle contour. This could be of interest for the intake of Ram and Scramjets, for example. Other conceivable applications are rocket engines: A way to increase propulsive nozzle performance is to enhance the expansion ratio of these nozzles. The flow regime at the ground is normally highly overexpanded and hence, flow separation inside the nozzle occurs. As Bourgoing and Reijasse [5, 6] state in their work, the shock structures coming along with the flow separation are often unsteady or asymmetric. In order to improve the understanding of this behavior, they analyzed a shock system occurring in a two-dimensional planar Mach 2 nozzle by LDV, wall pressure measurements, surface flow and Schlieren visualization. They observed three different flow configurations: two asymmetric and one symmetric case.
![Schlieren picture of the symmetric (left) and asymmetric shock system [5,6]](http://events.eventact.com/Ortra/16496/Schlierenbild2.png)
Schlieren picture of the symmetric (left) and asymmetric shock system (right) [5,6]
We reproduced these flow configurations by simulating the flow with RANS. It became apparent that for the asymmetric flow configurations, the shock systems remain stable at the upper or lower channel wall whereas the symmetric case is unstable and even small perturbations lead to the asymmetric case. We investigate the effect of small gaps along the nozzle contour and demonstrate their stabilizing effects. As a result, we were able to fix the shock system within the center of the nozzle. We show that the amount of bypass mass flow depends on the pressure gradient across the primary shock and determines the size and the shape of the flow separations and thus the shock strength. Unsteady RANS simulations are performed in order to manifest this assumption and to further analyze underlying mechanisms.
[1] Gawehn T., Gülhan A., Giglmaier M., Al-Hasan N.S., Quaatz J.F., Adams N.A.: Analysis of Pseudo-Shock System Structure and Asymmetry in Laval Nozzles with Parallel Side Walls. Proc. 19th International Shock Interaction Symposium (ISIS 19), Moscow, August 31 - September 3, 2010.
[2] Giglmaier, M., Quaatz, J.F., Gawehn, T., Gülhan, A., Adams, N.A.: Numerical and experimental investigation of the effect of bypass mass flow due to small gaps in a transonic channel flow; Proc. 28th International Symposium on Shock Waves (ISSW 28), Manchester, UK, July 17 – 22, 2011.
[3] Giglmaier, M., Quaatz, J.F., Gawehn, T., Gülhan, A., Adams, N.A.: Numerical and experimental investigations of pseudo-shock systems in a planar nozzle: Impact of bypass mass flow due to narrow gaps; Shock Waves; Volume 24, Issue 2, Pages 139-156, 2014.
[4] Giglmaier, M., Quaatz, J.F., Gawehn, T., Gülhan, A., Adams, N.A.: Impact of bypass mass flow on shock motion in pseudo-shock systems; Proc. 20th International Shock Interaction Symposium (ISIS 20), Stockholm, Sweden, August 20 - August 24, 2012.
[5] Bourgoing, A. and Reijasse, P. : Experimental investigation of an unsteady and asymmetrical supersonic separated flow. Tech. Rep.. ONERA-TP–01-95, 2001.
[6] Bourgoing, A. and Reijasse, P. : Experimental analysis of unsteady separated flows in a supersonic planar nozzle; Shock Waves; Volume 14, Pages 251–258, 2005.
