Planar shock-wave boundary-layer interaction

Semi-confined Flows

Underlying Flow Regime 3-32

Test Case Study

Brief Description of the Study Test Case

The flow under investigation is an oblique shock reflection on a flat plate where a turbulent boundary layer is formed (see Figure 2). In this case, the flat plate is the floor of the test section. The shock wave is produced by a shock generator. The angle /?/ of the shock generator with respect to the external flow is supposed to be the same as the flow deflection; this is a very good approximation in the present flow conditions. Two cases are studied, corresponding to flow deflections /?/ of 8° and of 9.5° at the nominal Mach number 2.25. They are both separated. This experiment is designed to provide the characteristics of the low frequency unsteadiness found in such conditions, and affecting the reflected (or separation) shock wave and the separated zone itself. The deflection is produced by a shock generator, i.e. a tilted flat plate, fixed on the ceiling of the wind tunnel, and leaving a sufficient gap to let a passage to the ceiling boundary layer, without affecting the flow around the shock generator leading edge. The implementation of the shock generator is given in Figure 1.

A sketch of the configuration is given in Figure 2.

The external Mach number, i.e. in the external flow upstream of the interaction is /M//(/=2.25, stagnation pressure in the potential flow upstream of the interaction is /p//tref/=50 663 N/m2; the stagnation temperature in the outer flow /T//tref/ is typically atmospheric, and remains close to 300K. The incoming boundary layer is fully turbulent. It develops on a flat plate with nearly adiabatic constant wall temperature. The conditions in the incoming boundary layer are summed up in the following tables.

The first campaign of measurements called "case-2006" was performed with the following parameters:

The origin of the abscissa is taken at the end of the contoured part of the nozzle block. /R//?/ and /R//?/ are respectively the Reynolds numbers based on layer thickness and on momentum thickness. A second campaign called "case-2007" corresponds to the following conditions, in which the thickness of the incoming boundary layer is smaller than in the previous case.

The details of the geometry and of the flow conditions can be accessed in the UFAST data base in Doerffer (2009).

The measured quantities are the wall pressure (mean, rms value and spectra) along the interaction, and 2-d velocity fields in vertical planes obtained by Particle Image Velocimetry (PIV) and by Laser Doppler Velocimetry (LDV). The two components (longitudinal, normal to the wall) (/U/ , /V)/ of the mean velocity and (/u'/ , /v'/ ) of the fluctuating velocity have been measured. The Reynolds stresses [pic], [pic], [pic] have been determined. The spectra of the wall pressure, which are very sensitive to the shock system unsteadiness, have also been determined.

Test Case Experiments

The experiment was carried out in the hypo-turbulent supersonic wind tunnel at IUSTI. It is a continuous facility with a closed-loop circuit. It can be operated for 4 hours with well controlled operating conditions. It is operated at a nominal Mach number of 2.25. The air is dried and the perturbations produced by the machinery are damped by appropriate devices: a Helmholtz resonator to remove the frequencies related to the compressor rotation, a heat exchanger, a drier acting continuously and a settling chamber. A regulation system stabilizes the stagnation pressure to a prescribed setting. Typically, when the wind tunnel is operated at a stagnation pressure of 0.5 bar, its variations in time are less than ±0.2%. The stagnation temperature is typically atmospheric; with a typical drift of 1K/hour. The level of background turbulence in the outer flow is essentially due to aerodynamic noise radiated by the boundary layers. Its level is less than 0.1% for velocity turbulence intensity. The range of Reynolds numbers produced in this facility encompasses moderate values (typically /R//?/?5000); this makes the experiments well adapted to advanced modelling techniques like LES, which, in their present state are feasible for moderate Reynolds numbers.

The two-dimensional supersonic equilibrium turbulent boundary layer under investigation develops on the wind tunnel floor, which is a flat plate. The incoming conditions (inlet conditions for the interaction) are located at a distance larger than 25 cm downstream of the contoured part of the nozzle block (more than 25 boundary layer thicknesses). All /x/ coordinates in the following correspond to an origin taken at the beginning of the flat part of the nozzle wall, and located 388.6 mm downstream of the sonic neck. Downstream of the interaction a diverging diffuser brings the flow from supersonic to subsonic conditions. Various devices are placed in the loop to prevent the propagation of aerodynamic noise.

The incoming boundary layer is turbulent and fully developed. It is subjected to a shock wave produced by a shock generator placed in the external flow, as indicated in figures 1 and 2. A shock generator made of a sharp-edged plate is fixed on the ceiling of the wind tunnel. It is placed in the free-stream and its leading edge is located in the potential flow. It entirely spans the test section and generates an oblique shock wave impinging on the floor boundary layer. Its angle with respect to the potential flow /?/ is set at 8° and 9.5°, for the two cases documented here. The global organisation of the oblique shock wave boundary layer interaction visualised by spark Schlieren is presented in Figure 3, for which the external flow deviation is 8°, and the pressure gradient is strong enough for the boundary layer to separate. Two interactions are documented, corresponding to deviations of 8° and 9.5°.

Measurement accuracy

As mentioned in the previous section, wall pressure measurements were performed along the interaction with Kulite transducers (type XCW-062) mounted flush to the wall. Two components of velocity were measured in the incoming boundary layer, in the interaction and downstream of reattachment.

Pressure measurements

The Kulite transducers have a limited bandwidth, typically 40 kHz. They are unable to resolve turbulent fluctuations in the incoming boundary layer. However, they are convenient to measure the fluctuations induced by the shock motion (frequency about 500 Hz) or the large eddies in the separated zone (about 6 kHz).

CFD Methods

Provide an overview of the methods used to analyze the test case. This should describe the codes employed together with the turbulence/physical models examined; the models need not be described in detail if good references are available but the treatment used at the walls should explained. Comment on how well the boundary conditions used replicate the conditions in the test rig, e.g. inflow conditions based on measured data at the rig measurement station or reconstructed based on well-defined estimates and assumptions.

Discuss the quality and accuracy of the CFD calculations. As before, it is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However the following points should be addressed: