Inclined slow acoustic waves incident to stagnation point probes in supersonic flow

Abstract

Tunnel noise in supersonic testing facilities is known to be a decisive factor in boundary layer transition experiments. It defines initial conditions for the growth of modal instabilities by the receptivity mechanism. That is, to interpret experimental results, the determination of tunnel noise is of crucial importance. It is common to use stagnation point probes equipped with pressure transducers in supersonic flows, but since tunnel noise undergoes modulation during the measurement, the probes must be calibrated. The predominant component of tunnel noise is caused by the nozzle boundary layer which radiates highly inclined slow acoustic waves. Therefore, the calibration of stagnation point probes for these disturbances is essential. For quasi-steady deviations from the free stream, an analytic reduced-order method holds. A corresponding conflicting model derived by Stainback & Wagner (1972, AIAA Paper 72-1003) is revised and corrected. Inclined slow acoustic waves generate higher pressure perturbations at the probe than non-inclined waves. In general, costly three-dimensional direct numerical simulations can be used for calibration. In this study, however, new axisymmetric boundary conditions are proposed to reduce the problem to two dimensions to efficiently investigate the detection of incident inclined slow acoustic waves by stagnation point probes. A cylindrical probe with a rounded edge is investigated in supersonic flow at a Mach number $Ma=5.9$. For the inclination angle of radiated slow acoustic waves, stagnation point pressure fluctuations abruptly decay with increasing Strouhal number and a similar behaviour can be seen at constant Strouhal number with increasing inclination angle. Two simple criteria for the onset of decay based on the radial wavenumber are deduced. Furthermore, stagnation point pressure fluctuations were decomposed into an initial pulse impact and resonant amplification to separately investigate the effects. The initial pulse determines the overall pressure signal. At high inclination angles, a new mechanism for resonance caused by a surface pressure wave travelling at the phase speed of the incident wave was found to supersede resonance caused by oscillating acoustic waves prevailing at low inclination angles.

Algorithmic differentiation of hyperbolic flow problems

“…ZFS is a highly efficient multi-physics simulation framework and developed by the numerical group of the Institute of Aerodynamics and Chair of Fluid Mechanics (AIA), RWTH Aachen University. Flows with shocks were computed for several applications, i.e., a transonic airfoil in [43], a cone in supersonic flow in [48], a blunt stagnation point probe in supersonic flow in [46,47], and a reentry capsule in supersonic flow in [49].…”

“…Three steps are required to obtain the full tangent (v, ξ) from the numerical simulation. First, the CFD code is modified to solve the additional equation for the shock location (47). Second, the modified method is enhanced by AD to yield the first component of the tangent v, i.e., the numerical discretization of equation (13).…”

“…An example is shown in Figure 5. A blunt body, e.g., defined by a stagnation point probe (SPP), is exposed to supersonic flow in a wind tunnel to measure stagnation pressure fluctuations caused by flow perturbations [46,47]. The flow is characterized by lines of constant Mach number and a detached shock wave.…”

Experimental investigation of boundary layer instabilities and transition on sharp and blunt cones in Oxford’s High-Density Tunnel

“…Additionally, previous studies found the post-shock pressure-based turbulence intensity measured with pitot probes to vary as much as 300% between plateau #1 and #2 [32]. Both discrepancies can be explained by bow shock receptivity, or bow shock transfer functions, which vary significantly with the inclination angle of the disturbance [52][53][54] and were not applied to the data reported previously [32]. To investigate the inclination angles of the freestream disturbances, we will use correlations between signals in the two-dimensional FLDI array.…”

“…The definition of 𝜃 𝑛 is chosen to be consistent with the definitions used by others [50,[52][53][54] for backwards facing slow acoustic waves. The spanwise convection velocity, 𝑣 𝑐 , is assumed negligible in the following analysis.…”