Large Eddy Simulation of a Pseudo-Shock System Within a Laval Nozzle

Principal Investigator:
Stefan Hickel

Technische Universität München (Germany)

Local Project ID:

HPC Platform used:
SuperMUC of LRZ

Date published:

Laval nozzles (such as rocket engines) consist of a convergent-divergent geometry. By definition, the flow speed inside a Laval nozzle is accelerated from sub- to supersonic conditions. A high backpressure at the outlet can lead to an instantaneous deceleration of the flow within the divergent part of the nozzle. Then a jump discontinuity (shock) appears in the pressure, temperature and density distribution along the nozzle. In contrast to the quasi-1-D inviscid theory, this shock interacts in practice with the turbulent boundary layers at the channel walls and causes flow separation. Flow separation and reattachment is a particularly challenging subject of enduring fluid dynamics research and results in a complex 3-D system of interacting oblique shocks, compression and expansion waves, which is referred to as pseudo-shock system.

These pseudo-shock systems influence reliability and performance of a wide range of flow devices, such as ducts and pipelines in the field of process engineering and supersonic aircraft inlets. Thus, the optimization of pseudo-shock systems is of great academic and commercial interest.

The purpose of this project is the numerical investigation of a pseudo-shock system. Prior simulations using the common Reynolds averaged Navier-Stokes (RANS) approach showed that the results are very sensitive on the applied modeling parameters. Thus, more elaborate large-eddy simulations (LES) have to be performed for the analysis of this highly unsteady flow phenomenon. The upper panel of the figure shows the density gradient in the flow and reveals that the pseudo-shock system consists of a shock-train counting five serial shocks. The initial shock is bifurcated while the subsequent shocks are curved. The lower part of the figure shows the complex flow pattern of the pseudo-shock system, which is visualized by means of time-averaged Mach number distribution. The shocks separate the supersonic regions (M>1) clearly from the subsonic flow (M<1). Downstream of the primary shock flow separation occurs at the channel walls. The simulations are validated against experimental data with the same parameter set and show excellent agreement. In the next step we the scientists will analyze the unsteady behavior to better understand the underlying flow physics and flow control mechanisms.

The simulations have been performed with the flow solver INCA at the LRZ SuperMUC Phase 1 and 2 system.

Research Team & Contact Information:
J.F. Quaatz, S. Hickel, M. Giglmaier & N.A. Adams
Technische Universität München
Fakultät für Maschinenwesen
Boltzmannstr. 15, 85748 Garching
E-mail: sh [at]