Large Eddy Simulation (LES) with dynamic sub-grid scale eddy viscosity model has been applied to numerically investigate the evolution of complicated flow structures in supersonic base flow with mass bleed. Mean flow properties obtained from numerical simulations, such as axial velocity, pressure on the base surface, have been compared with the experimental measurements to show that LES is able to predict the mean flow properties with acceptable accuracy. The data obtained from LES has been further analyzed to understand the evolution of coherent structures in the flow field. Periodical shedding of vortical structures from the outer shear layer has been observed and it has also been found that this vortex shedding is associated with the flapping of the outer shear layer. The frequency of flapping of the outer shear layer has been found out and the phase-averaged streamlines have been analyzed to further study the evolution of vortical structures associated with this flapping. The phase-averaged streamline plots clearly elucidate the evolution of vortical structures along the outer shear layer. Further, the study of these structures is investigated by performing Proper Orthogonal Decomposition (POD) analysis of the data, obtained along the central plane in the wake region. The POD results also seem to agree well with the observations made in the phase averaged streamline plots, as the concentrated energy and enstropy are observed in the outer shear layer with fewer POD modes.
The appearance of detached recirculation regions in wakes with base bleed determines the aerodynamic properties of many natural organisms and technological applications. In this work we introduce an analytical model which captures certain key dimensions of the recirculation region in the wake of porous plates of infinite aspect ratio, along with the porosity range \ks{over which} it exists, when vortex shedding is absent or suppressed. The model is used to interpret why the recirculation region (i) emerges, (ii) migrates away from the body with increasing base bleed, (iii) disappears at a crit…
We study the large-scale helical vortex shedding regime in the wake of an axisymmetric body with a blunt trailing edge at high Reynolds numbers, both experimentally and by means of local, linear, spatiotemporal stability analysis. In the instability analysis we take into account the detailed downstream evolution of the basic flow behind the body base. The study confirms the existence of a finite region of absolute instability for the first azimuthal number in the near field of the wake. Such instability is believed to trigger the large scale helical vortex shedding downstream of the recirculat…
Base pressure control is often employed on drag reduction design, but the interaction of the jet with the base region flow topology can generate undesired or uncontrolled flow configurations. The ejected flow can drive pressure bifurcations at the trailing edge, that without a correct optimization can affect the aerodynamic performance of the system. The purpose of this work is to fully understand the physical mechanisms related with the use of injected base bleed employing global stability analysis and adjoint methodologies. Moreover, the results of the sensitivity analysis are used to identi…
The unsteady three-dimensional separated flow on a wall induced by a square protrusion (approximately twice the local boundary layer thickness in width and height), and its control by means of passive suction through holes, is investigated using wind tunnel experiments at Mach $2.87$. The baseline flow without any control was characterized and compared against the cases with bleed. A bow-shaped separation line on the wall with a mid-span separation length of $5.57δ$ from protrusion face was traced from oil-flow visualization. The averaged pressure distribution surveyed using static pressure po…
The resolvent formulation of McKeon & Sharma (2010) is applied to supersonic turbulent boundary layers to study the validity of Morkovin's hypothesis, which postulates that high-speed turbulence structures in zero pressure-gradient turbulent boundary layers remain largely the same as its incompressible counterpart. Supersonic zero-pressure-gradient turbulent boundary layers with adiabatic wall boundary conditions at Mach numbers ranging from 2 to 4 are considered. Resolvent analysis highlights two distinct regions of the supersonic turbulent boundary layer in the wave parameter space: the rela…
How to determine accurately and efficiently the aerodynamic forces of the aircraft in high-speed flow is one of great challenges in modern aerodynamics. In this Letter we propose a new similarity law for steady transonic-supersonic flow over thin bodies. The new similarity law is based on the local Mach number frozen principle. It depends on both the specific heat ratio and the free-stream Mach number. The new similarity law enables one to determine the lift and drag coefficients of the aircraft from that of a reference state which is more reachable. The validity of the new similarity law has …
We use resolvent analysis to determine an unsteady active control setup to attenuate pressure fluctuations in turbulent supersonic flow over a rectangular cavity with a length-to-depth ratio of 6 at a Mach number of 1.4 and a Reynolds number based on cavity depth of 10,000. Large-eddy simulations (LES) and dynamic modal decomposition (DMD) of the supersonic cavity flow reveal the dominance of two-dimensional Rossiter modes II and IV. These predominantly two-dimensional vortical structures generate high-amplitude unsteadiness over the cavity through trailing-edge impingement and create oblique …
Experimental studies are carried out to investigate the effects of the geometrical parameters with a drag reducing spike on a hemispherical forebody in a supersonic freestream of $M_\infty=2.0$ at $0^{\circ}$ angle of attack. The spike length $(l/D=0.5,1.0,1.5,2.0)$, spike stem diameter $(d/D=0.06,0.12,0.18)$, and spike tip shapes are varied and their influence on the time-averaged, and time-resolved flow field are examined. When $l/D$ increases, a significant reduction in drag ($c_d$) is achieved at $l/D=1.5$, whereas the variation in $d/D$ has only a minor effect. The intensity of the shock-…
The origin of a vortex structure generated during the shock-plasma interaction is investigated. A two-dimensional model based on the shock refraction mechanism successfully unifies the vortex generation with major co-processes typical for the interaction and thus well fits in their cause-and-consequence relationship. Numerical simulations demonstrated the possibility of an intense vortex generation with a continuous positive dynamics as the shock crosses the interface. It was shown that while the vorticity is triggered by the shock refraction on the interface, it is the gas parameter distribut…
The impinging shock of varying strengths on the free shear layer in a confined supersonic cavity flow is studied numerically using the detached-eddy simulation. The resulting spatiotemporal variations are analyzed between the different cases using unsteady statistics, $x-t$ diagrams, spectral analysis, and modal decomposition. A cavity of length to depth ratio $[L/D]=2$ at a freestream Mach number of $M_\infty = 1.71$ is considered to be in a confined passage. Impinging shock strength is controlled by changing the ramp angle ($θ$) on the top-wall. The static pressure ratio across the impinging…
Phase-based analysis and control of supersonic turbulent cavity flows
University of California, Los Angeles（加州大学洛杉矶分校）；Japan Agency for Marine-Earth Science and Technology（日本海洋地球科学技术机构）；University of Florida（佛罗里达大学）；Illinois Institute of Technology（伊利诺伊理工学院）
A combined analytical and numerical study is conducted to investigate the asymmetric cap-shock non-uniform Mach Reflection (csMR) phenomenon outside of an over-expanded supersonic jet. Prior analytical works have only considered the wedge-induced steady symmetric and asymmetric Mach reflection (MR) configurations, as well as symmetric MR in an open jet. However, there is another structure occurring in nozzle flow fields known as a non-uniformity induced cap-shock pattern. We derive a new analytical model to predict the wave structure of the asymmetric csMR in the absence of internal shocks by …
Noise measurements of heated axisymmetric jets at fixed supersonic acoustic Mach number indicate that the acoustic spectrum reduces when the temperature ratio increases. The `spectral quietening' effect has been observed both experimentally and computationally using Large Eddy Simulations (LES). It was explained by Afsar {\it et al}. (M. Z. Afsar and M. E. Goldstein $\&$ A. M. Fagan AIAAJ., Vol. 49, p. 2522, 2011) through the cancellation introduced by enthalpy flux/momentum flux coupling term using the generalized acoustic analogy formulation. But the parallel flow assumption is known to give…
Large Eddy Simulation (LES) with dynamic Smagorinsky model has been applied to numerically investigate the complicated flow structures that evolve in the near wake of a cylindrical after body aligned with a uniform Mach 2.46 flow. Mean flow field properties obtained from numerical simulations, such as axial velocity, pressure on base surface, have been compared with the experimental measurements as well as with other published results. It has been found that standard k-epsilon model fails to predict the flow properties in the recirculation region where better agreement has been observed betwee…
We perform direct numerical simulations of shock-wave/boundary-layer interactions (SBLI) at Mach number M = 1.7 to investigate the influence of the state of the incoming boundary layer on the interaction properties. We reproduce and extend the flow conditions of the experiments performed by Giepman et al., in which a spatially evolving laminar boundary layer over a flat plate is initially tripped by an array of distributed roughness elements and impinged further downstream by an oblique shock wave. Four SBLI cases are considered, based on two different shock impingement locations along the str…
Control surface deployment in a supersonic flow has many applications, including flow control, mixing, and body-force regulation. The extent of control surface deflections introduces varying flow unsteadiness. The resulting fluid dynamics influence the downstream flow characteristics and fluid-structure interactions severely. In order to understand the gas dynamics, an axisymmetric cylindrical body with a sharp-tip cone at zero angles of attack ($α=0^\circ$) is examined in a free stream Mach number of $M_\infty=2.0$ and Reynolds number of $Re_{D}=2.16 \times 10^6$ ($D=50$ mm). Four static cont…
Shock related unsteadiness over axisymmetric spiked body configurations is experimentally investigated at a freestream supersonic Mach number of 2.0 at 0$^\circ$ angle of attack. Three different forebody configurations mounted with a sharp spike-tip ranging from blunt to streamlined (flat-face, hemispherical, and elliptical) are considered. Steady and unsteady pressure measurements, short-exposure high-speed shadowgraphy, shock footprint analysis from $x-t$ plots, and identification of dominant spatiotemporal modes through modal analysis are carried out to explain the unsteady flow physics. Th…
The flow structure obtained when Localized Arc Filament Plasma Actuators (LAFPA) are employed to control the flow issuing from a perfectly expanded Mach 1.3 nozzle is elucidated by visualizing coherent structures obtained from Implicit Large-Eddy Simulations. The computations reproduce recent experimental observations at the Ohio State University to influence the acoustic and mixing properties of the jet. Eight actuators were placed on a collar around the periphery of the nozzle exit and selectively excited to generate various modes, including first and second mixed (m = +/- 1 and m = +/- 2) a…
We study compressible turbulent flow in a circular pipe, at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies.Regarding velocity statistics, we find that Huang's transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of den…
A D2Q9 Hybrid Lattice Boltzmann Method (HLBM) is proposed for the simulation of both compressible subsonic and supersonic flows. This HLBM is an extension of the model of Feng et al: [12], which has been found, via different test cases, to be unstable for supersonic regimes. The improvements consist of: (1) a new discretization of the lattice closure correction term making possible to properly simulate supersonic flows, (2) a corrected viscous stress tensor that takes into account polyatomic gases, and (3) a novel discretization of the viscous heat production term fitting with the regularized …
A double-distribution-function based lattice Boltzmann method (DDF-LBM) is proposed for the simulation of polyatomic gases in the supersonic regime. The model relies on an extended equilibrium state that is constructed to reproduce the first 13 moments of the Maxwell-Boltzmann distribution exactly. This extends the validity of the standard 5-constraint (mass, momentum and energy) approach and leads to the correct simulation of thermal, compressible flows with only 39 discrete velocities in 3D. The stability of this BGK-LBM is reinforced by relying on Knudsen-number-dependent relaxation times t…
Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and $α$-damping schemes introduced by Chamarthi (2022) [1] for simulating high-speed flows in generalized curvilinear and dynamic mesh domains with the freestream preservation property. In the first part of this paper, the algorithms are detailed within the generalized curvilinear coordinate framework, with a focus on demonstration through stationary and dynamic mesh test…
The performance of high-order gas-kinetic scheme (HGKS) has been investigated for the direct numerical simulation (DNS) of isotropic compressible turbulence up to the supersonic regime. Due to the multi-scale nature and coupled temporal-spatial evolution process, HGKS provides a valid tool for the numerical simulation of compressible turbulent flow. Based on the domain decomposition and message passing interface (MPI), a parallel HGKS code is developed for large-scale computation in this paper. The standard tests from the nearly incompressible flow to the supersonic one, including Taylor-Green…
The physics of shock-boundary layer interactions (SBLIs) in a supersonic turbine cascade at Mach 2.0 and Reynolds number 395,000, based on the axial chord, is investigated through a wall-resolved large eddy simulation. Special attention is given to the characterization of the low-frequency dynamics of the separation bubbles using flow visualization, spectral analysis, space-time cross correlations, and flow modal decomposition. The mean flowfield shows different shock structures formed on both sides of the airfoil. On the suction side, an oblique shock impinges on the turbulent boundary layer,…
In present work, we report an experimental setup that has been developed to characterize highly under-expanded helium and nitrogen jets confined in a vacuum chamber. The evolution of Zone of Silence (ZOS) is studied and found that experimentally measured ZOS for helium and nitrogen jets are in agreement with empirical relation and mathematical model. The velocity of the jet inside ZOS is measured using a developed time of flight (TOF) probe without using a skimmer. We are able to measures the velocity of the gas jet itself compared to a skimmer-based method which measures the velocity of gas t…
The slope of the power spectrum of the density field in isothermal supersonic compressible turbulence
ENS de Lyon, CRAL UMR5574, Universite Claude Bernard Lyon 1, CNRS（里昂高等师范学校，CRAL UMR5574，克洛德·贝尔纳里昂大学，法国国家科学研究中心）；School of Physics, University of Exeter（埃克塞特大学物理学院）
Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS
Pennsylvania State University（宾夕法尼亚州立大学）；CSIR-National Aerospace Laboratories（印度国家航空航天实验室）；Case Western Reserve University（凯斯西储大学）；National Research Council Canada（加拿大国家研究委员会）
We present a design for high energy density laboratory experiments studying the interaction of hypersonic shocks with a large number of inhomogeneities. These ``clumpy'' flows are relevant to a wide variety of astrophysical environments including the evolution of molecular clouds, outflows from young stars, Planetary Nebulae and Active Galactic Nuclei. The experiment consists of a strong shock (driven by a pulsed power machine or a high intensity laser) impinging on a region of randomly placed plastic rods. We discuss the goals of the specific design and how they are met by specific choices of…
We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are governed by the steady isothermal Euler equations for potential flow with axisymmetry so that the equations contain a singular geometric source term. We first formulate the shock stability problem as an initial-boundary value problem with the leading conical shock-front as a free boundary, and then establish the existence and asymptotic behavior of global entropy s…
