Session ZC06: Compressible Flows: Instability and Turbulence

Multi-mode compressible Rayleigh-Taylor instability under strong isothermal background stratification

This study explores the compressibility effects of the background isothermal stratification strength on multi-mode two-dimensional Rayleigh–Taylor instability (RTI) using fully compressible multi-species direct numerical simulations. Cases with three different isothermal Mach numbers are investigated to explore weakly, moderately, and strongly stratified compressible RTI at an Atwood number of 0.04. Unlike incompressible RTI, an increase in the flow compressibility through the background stratification strength can suppress the RTI growth and can lead to a saturation of the RTI mixing layer growth with highly molecularly mixed fluids. Our findings show that even at the chosen relatively low Atwood number, variable-density effects can be significantly increased with the background stratification strength for the compressible RTI, especially different spatial profiles become more asymmetric across the mixing layer for the strongly stratified case. Furthermore, the chaotic behavior of the cases is studied with the transport of the turbulent kinetic energy and the vortex dynamics.   

Self-similarity scaling of second and third velocity moments due to compressibility

The influence of compressibility on turbulence attenuation and self-preservation of axisymmetric turbulent free jets are investigated. Second and third velocity moments containing the streamwise, u, and radial velocity fluctuations, v, are obtained using 2-D planar Particle Image Velocimetry (PIV). Two Mach numbers are chosen, at Mach 0.3 and Mach 1.25, to compare the effect of compressibility.  Interest is capturing the influence of compressibility on Reynolds stress anisotropy, which remains an important challenge to the development of reliable turbulence models. Using the jet half-width, b, and the centerline velocity,Um, as length and velocity scales, the mean streamwise velocity profile collapses. For self-preserving turbulent axisymmetric jets the Reynolds shear stress scales according to uv ∝  U²_m db/dx [1]. Our recent study [2] have shown that in the compressible axisymmetric jet, the attenuation on the Reynolds shear stress and the shear layer thickness growth rate are proportional - allowing for a collapse of the Reynolds shear stress profiles. Although there is agreement on scaling of uv, the effect of compressibility on other turbulent moments remains unclear. By performing an order-of-magnitude analysis, self-similarity solutions of the Reynolds stress transport equation are investigated which find that the radial and azimuthal velocity moments are attenuated by compressibility, while the streamwise velocity moment remains unaffected.  Moreover, the analysis allows for the inference of the effect of pressure-strain correlations as related to compressibility. Comparisons between the supersonic and subsonic cases will be provided to highlight the influence of compressibility.   

ML for fast assimilation of wall-pressure measurements from hypersonic flow over a cone

The performance of hypersonic vehicles is sensitive to environmental disturbances, especially in the transitional flow regime. Accurate and efficient prediction of the flow state from limited sensor data is a pacing item in both fundamental studies and practical applications. Recent data assimilation demonstrated the integration of scarce measurements into direct numerical simulations (Buchta et al, J. Fluid Mech., 947, R2, 2022). Solving the inverse problem unveiled the realistic flow hidden within limited measurements, granting access to every flow quantity. However, the computational cost associated with direct simulations hinders wide adoption, for example for a large number of experiments or in practical applications. Here, we introduce a deep-learning approach that can accelerate assimilation by two orders of magnitude in terms of the number of experiments assimilated using the same wall-clock time.  We minimize the number of required numerical simulations by optimally sampling the space of possible solutions, deploy a deep operator network (DeepONet) as proxy of the compressible Navier-Stokes equations to continuously span and search high-dimensional noisy spaces of solutions, and efficiently reach an optimal result with a gradient-free technique. The successful application of this method is demonstrated for data assimilation of wind-tunnel measurements in boundary-layer flow over a 7-degree half-angle cone, at Mach 6.   

Flow Instability in a Hypersonic Boundary Layer Behind a Propagating Shock Wave

Instability of a boundary layer developed behind a propagating shock wave is theoretically and numerically investigated. A numerical simulation of the boundary layer behind the propagating shock wave is conducted using a shock stationary frame method, efficiently solving the flow field around the propagating shock wave in an inertial frame where the shock wave seems to be stationary. An analysis of a linear stability theory based on the averaged flow field obtained by the numerical simulation finds that a wall cooling effect of an isothermal wall makes the boundary layer unstable. Moreover, an artificial disturbance is introduced on the wall in the numerical simulation to investigate the growth of the disturbance. The introduced disturbance grows downstream as it supports the analysis result of the linear stability theory. It is suggested that this flow instability causes the laminar-turbulent transition in the boundary layer behind the propagating shock wave.   

Atwood number effects on isothermally stratified compressible single-mode Rayleigh-Taylor instability

The coupled effects of variable density and background isothermal stratification strength on the growth of the fully compressible single-mode two-fluid Rayleigh–Taylor instability (RTI) is examined using two-dimensional direct numerical simulations (DNS). Varying Atwood numbers and background isothermal Mach numbers are used to differentiate between cases. The Hydrodynamics Adaptive Mesh Refinement Simulator (HAMeRS) is used to solve the fully compressible, multi-species Navier–Stokes equations in the DNS of single-mode RTI cases at low, intermediate, and high Atwood numbers, which are cases under weak, moderate, and strong stratifications. At the low Atwood number, it is observed that the growth of the heavy (spike) and light (bubble) fluid penetration regions remains nearly symmetric, and this growth begins to experience suppression as the stratification strength is increased. At higher Atwood numbers, the asymmetry between the growth rates of the spikes and bubbles becomes evident. As stratification strength increases, the bubbles experience more growth suppression while spikes grow for a longer time and retain more small-scale vortical structures. These findings suggest that the asymmetry in the growth of the RT unstable interface and the vortical dynamics are highly related to the coupled effects of Atwood and isothermal Mach numbers.   

Excitation and evolution of subsonic Gortler vortices induced by free-stream vortical disturbances

We study the nonlinear development of subsonic Gortler vortices which are excited by free-stream vortical disturbances (FSVD) in compressible boundary layers over concave walls. The free-stream Mach number is assumed to be of O(1) and the FSVD are strong enough for compressibility and nonlinearity to be taken into account. The focus is on low-frequency (long-wavelength) components of FSVD, which excite the Gortler vortices in the boundary layers. The formation and evolution of Gortler vortices are governed by the compressible nonlinear boundary-region equations, supplemented by appropriate initial and boundary conditions that characterise the impact of the FSVD on the boundary layer. The numerical computations are performed for parameters typical of flows over pressure surfaces of high-pressure turbine blades, where the Gortler number and the turbulence Reynolds number are both of order-one quantities. For low-intensity FSVD, increasing the Gortler number or intensifying the FSVD render the boundary layers more unstable, while increasing the Mach number or frequency of the FSVD stabilizes the flows. Raising the FSVD level deactivates the effects of the studied parameters. In particular, the deactivation effect of high-level FSVD leads to the formation of streaks over a convex wall. The theoretical prediction captures well the experimental measurement of the enhancement of the wall-heat transfer and the skin friction. The mean-flow distortion is found to play a crucial role in the nonlinearly generated extra drag and heat transfer.   

Compressible turbulence density gradient spectra using schlieren imaging

Scramjet engines and astrophysical flows require the understanding of turbulent Mach number (M_t) effects on turbulence. M_t values as low as 0.1 begin to exhibit compressible behaviors. Simulations show that the slope of the spectra steepens with increasing M_t. Since compressibility is changes in density, measurements of density gradients are sensitive to subtle aspects of compressible turbulence. In a pressurized vessel with a fan-generated jet, the speed of sound is adjusted using different gases including sulfur-hexafluoride (SF₆), to increase M_t up to 0.15 while holding the Taylor-Reynolds number constant at values up to 1000. This way, the role of the Reynolds number and Mach number can be distinguished independently. Schlieren imaging is implemented to visualize the density gradients, which are quantifiable with calibration techniques. With a high-speed camera, the density gradients are recorded, both spatially and temporally, to obtain the spectra at various conditions, and observe the behavior of the slope.