Session F04: Compressible Flows: Supersonic, Hypersonic and General (3:55pm - 4:40pm CST)

Stepped aerospike for enhanced drag reduction using multiple intermediate shocks.

Drag reduction in supersonic vehicles has been achieved using several techniques among which passive aerospikes are the most reliable solution. Various aerospike designs have been extensively studied where the fore-geometry is modified to enhance the drag reduction. In the present work aft-geometry modification in the form of a stepped spike is explored. Planar inviscid, axisymmetric viscous flow simulations and wind-tunnel tests are conducted at a Mach number of 2.43 to analyse the drag reduction of the two spikes of aspect ratio 1.5. The inviscid flow features like shocks and expansion fans are studied using the inviscid simulation, whereas the viscous flow simulations incorporate the effects of the separated shear layer. Viscous flow results are validated with schlieren images from wind tunnel experiments. The steps introduce multiple shocks which eventually reduce the strength of the re-attachment shock. The effect of the re-circulation zones and the interaction of shocks and expansion fans are studied using different step locations. Wave drag reduction over a conventional aerospike ranges from 9.32\% to 21.06\% as step locations are varied.   

Dynamics of compound, compressible flow contractions

Sudden axisymmetric flow contractions lead to a local acceleration of the flow which causes large pressure gradients and, ultimately, can cause local flow separation. For a single stream contracting flows, the dynamics of the problem are well understood--even in the turbulent, compressible regime. In compound compressible flows, which are defined by co-flowing, axisymmetric streams, the differential flow acceleration among the streams results in non-negligible radial pressure gradients and varying compressibility effects. This causes non-linear coupling among the dynamics of the co-flowing stream. We investigate the dynamics in the compound, compressible contractions using low-order models and high-fidelity computational fluid dynamics. We show the emergence of a bifurcation point which is governed by the compound flow properties and the geometric features of the contraction. We investigate the sensitivity of the bifurcation point and the dynamics of this highly unstable system.   

Experimental analysis of diffuser terminal shock motion and associated acoustics in vacuum objective supersonic air ejectors

Diffuser shock motion in vacuum objective ejectors is problematic for many industries due to excessive noise generation. This experimental study characterizes the terminal shock motion through simultaneous schlieren and wall pressure measurements in a rectangular ejector. The primary flow is driven by stagnation pressures ranging from 2.0 to 8.0 bar. Experiments are performed for both zero and non-zero suction flow rates. Low frequency oscillations are shown to have a strong correlation with upstream instability near the primary nozzle due to the combination of mixing layer instabilities and secondary stream static pressure fluctuations during restricted suction flow conditions. Various iterations of wall geometry modifications are tested using the experimental apparatus in tandem with CFD simulations to reduce the strength of this terminal shock. Increasing the mixing chamber length and bore diameter is shown to dramatically reduce shock motion in the diffuser, though motion remains more pronounced in the zero secondary flow case. Additionally, small protrusions near the diffuser entrance stabilize the terminal shock location further upstream, which reduces the generated noise.   

Shock Wave Oscillation at Cylindrical Cavity on Wedge Surface in Mach-7 Hypersonic Flow.

This study explores the shock wave oscillation observed near a cylindrical cavity placed on the surface of a wedge model at a 30-degree angle in Mach-7 hypersonic flow. Since the behavior of such a shock wave is key to understanding the aerodynamic heating on space vehicles, a wind tunnel test was carried out to clarify this shock oscillation problem. Flow stagnation pressure and temperature were set to 950kPa and 500K respectively. A high-speed schlieren video showed that, with a 1-cm diameter cavity, the main oscillation frequency was around 5.4 kHz. Further measurements were done to quantify this phenomenon and these detailed results will be reported in a DFD 2020 presentation.   

Self-sustained Shock Oscillations over Axisymmetric Bodies in Hypersonic Flow

The phenomenon of shock oscillations over conical bodies with a blunt axisymmetric base has been investigated experimentally at Mach 6. The experiments were carried out in the 0.5 m diameter enclosed free-jet hypersonic wind tunnel at IISc; this facility can achieve a unit Reynolds number of $9\times 10^{6}\,\,\mathrm{m}^{-1}$ at Mach 6. The axisymmetric test models consist of a base circular cylinder with a $25^\circ$ half-angle conical forebody that is 40 mm in length ($L$). The base diameter ($D$) was varied to obtain different $L/D$ ratios in the range 0.4 to 0.9 to study the effects of the geometric parameter on the oscillation dynamics. Time-resolved schlieren imagery from these experiments shows distinct ``pulsation'' and ``oscillation'' modes of shock oscillations, similar to previous observations from literature on spiked forebodies (the terminology for modes is borrowed from the same). The ``pulsation mode'' is seen at low $L/D$ ratios, and a switch to ``oscillation mode'' occurs above a $L/D$ ratio of 0.8. Detailed experimental results including an analysis of the different stages of shock oscillations will be presented at the meeting.   

Reynolds number dependency on Lagrangian Coherent Structures (LCS) over supersonic turbulent boundary layers

Lagrangian coherent structures (LCS) have received a lot of attention recently due to its advantages over Eulerian coherent structure identification schemes. Transport barriers revealed by LCS have the capability to enhance mixing for many engineering applications. This study utilizes a high-fidelity Direct Numerical Simulation database of spatially-developing turbulent boundary layers (SDTBL) at the supersonic regime (\textbf{$M_\infty = 2.5$}) to evaluate the effects of Reynolds number on LCS. The analysis is performed by prescribing realistic turbulent information at the computational domain inflow for SDTBL simulations. The methodology is based on the Dynamic Multiscale Approach by Araya et al. (JFM, Vol. 670, pp. 581-605, 2011) adapted to compressible flow. Furthermore, identification of LCS structures is performed by computing the Finite-Time Lyapunov Exponent (FTLE). Preliminary results reveal that zones with large FTLE values, after performing a backward time integration of particle trajectories (attraction material lines), can be linked to the local presence of hairpin vortex packets. At the larger Reynolds number, coherent motions exhibit a finer structure, more isotropic but less organized structures. Behavior at low Reynolds numbers depicts a more organized pattern.   

Influences of forebody size on supersonic retropropulsion flowfield dynamics

Supersonic retropropulsion (SRP) is an enabling technology for landing large payloads on planets such as Mars. To be successful, the retropropulsive jets must establish a stable flowfield that retains as much aerodynamic drag as possible, for efficiency. We lack a detailed understanding of SRP flowfield dynamics and how it varies with jet pressure and thrust. This is especially true for low thrust operation or for complicated geometries. A series of experiments have been undertaken to examine the influences of jet pressure and thrust on jets of different sizes relative to the vehicle forebody. All current experiments were conducted at zero angle of attack. Using a Mach 2 Ludweig tube and high-speed schlieren photography, flowfield topology and variability are investigated. Scaling of shock standoff distance with jet pressure and thrust coefficient is examined. Finally, we explore the conditions for flowfield unsteadiness, analyzing bow shock motion, its dominant frequencies and POD modes.   

Input/output Analysis of Hypersonic Boundary Layers using the One-Way Navier-Stokes (OWNS) Equations

Input/output (resolvent) analysis is used to examine the most amplified linear disturbances in hypersonic flat-plate boundary layers. Owing to the large computational expense of the resulting singular value decomposition for PDEs discretized in two inhomogeneous directions, we apply an approximate fast marching technique, the One-Way Navier-Stokes (OWNS) Equations, in iterative fashion to solve for the optimal disturbances. In this way, we are able to systematically investigate the full parametric space for this class of boundary layers over a range of hypersonic Mach numbers, while varying the input and output metrics that determine the corresponding receptivity problems, and highlight different transition scenarios depending on the spatial support, frequency, and physical nature of the external disturbances. We also highlight extensions of the OWNS methodology to complex three-dimensional geometries.   

Delay of high-speed boundary-layer transition by isolated roughness

Direct numerical simulations of Mach 4.5 boundary layers demonstrate sensitivity of transition to turbulence to the placement and shape of roughness elements. The examined elements alter the growth rate of second-mode instabilities relative to flow over smooth plates, with minimal impact on the first-mode instability. Two key flow parameters influence the outcome: (i) the relative position of synchronization of the slow and fast modes and (ii) the height of the near-wall region where the second-mode phase speed is supersonic relative to the flow. Downstream of synchronization protruding roughness effectively delays transition, whereas cratering the surface is more effective upstream of synchronization. Post-synchronization, the protrusion thickens the supersonic region leading to stabilization, but the same thickening pre-synchronization is destabilizing. Using ensemble-variational optimization of the roughness height, width and slope, we effectively mitigate the nonlinearly most dangerous route to turbulence (Jahanbakhshi, R., and Zaki, T. A., Nonlinearly most dangerous disturbance for high-speed boundary-layer transition, J. Fluid Mech. 876 (2019): 87-121), and maintain laminar flow throughout the computational domain.   

Numerical subgrid-scale modeling of supersonic spatially-developing turbulent boundary layers

We investigate the performance of numerically implicit subgrid-scale modeling provided by the well-known streamline upwind/Petrov-Galerkin stabilization for finite element discretization of advection-diffusion problems. While its original purpose was to provide sufficient algorithmic dissipation for a stable and convergent numerical method, more recently it has been utilized as subgrid-scale (SGS) model to account for the effect of small scales, unresolvable by the discretization. In addition, here we consider a physics-based SGS model, namely the popular dynamic Smagorinsky model. These two LES modelling efforts are evaluated by direct comparison with a DNS database of adiabatic supersonic spatially-turbulent turbulent boundary layers at high Reynolds numbers (Re$_{\delta2}$ $\approx$ 3,000) based on the freestream velocity, momentum thickness and wall viscosity. The freestream Mach number is 2.5. In all cases, turbulent inflow conditions are generated via the dynamic rescaling-recycling approach (JFM, 670, pp. 581-605, 2011) extended to compressible flows. Focus is given to the assessment of the resolved Reynolds stresses, turbulent heat fluxes and turbulent Prandtl number. Also, the influence of coherent structures on the thermal transport phenomena is scrutinized.