This experimental and numerical study examines transition to turbulence for a Cone-Cylinder-Flare geometry at Mach 7 and across a broad Reynolds number range. The focus is set on both attached boundary layers and separated shock-boundary layer interactions. The campaign is conducted in the R2Ch facility. Unsteady wall pressure fluctuations and high-speed schlieren images are analysed using data-driven techniques and compared with base flow computations and global linear stability analysis. The results distinguish two transition regimes. At high Reynolds numbers, transition is dominated by the second Mack mode and its non-linear interactions on the cone. High-frequency wall pressure measurements and schlieren imaging permit the capture of both fundamental waves and their non-linear harmonics. Non-linear interaction regions are resolved with unprecedented detail, clarifying the boundary-layer state before rapid breakdown at reattachment. At lower Reynolds numbers, the transition scenario is more intricate, marked by the coexistence of low- and high-frequency modes. A complex coupling between separated flow and convective instabilities is revealed, with trapped acoustic waves inside the recirculation region measured experimentally for the first time. Their linear origin is demonstrated through global stability analysis, and a simple acoustic duct model is provided to predict their frequencies. These waves offer a new interpretation of low-frequency pressure signatures and suggest a mechanism for energy transfer from high to low frequencies, ultimately driving transition on the flare. The findings advance understanding of hypersonic boundary-layer transition and its dependence on Reynolds number and flow separation.
In this paper, the relation between skin friction and heat transfer along windward sides of blunt-nosed bodies in hypersonic flows is investigated. The self-similar boundary layer analysis is accepted to figure out the distribution of the ratio of skin friction to heat transfer coefficients along the wall. It is theoretically obtained that the ratio depends linearly on the local slope angle of the wall surface, and an explicit analogy expression is presented for circular cylinders, although the linear distribution is also found for other nose shapes and even in gas flows with chemical reaction…
This study investigates the origin and sustenance of self induced oscillations of shock structures in a hypersonic flow over a double wedge configuration. Previously, various researchers have considered the double wedge flow configuration for inviscid flow with variations of different inflows as well as geometric parameters such as inflow Mach number , wedge angles, and wedge lengths. Few recently published articles reveal an unsteady flow physics involved with the hypersonic viscous flow for double wedge configuration with large second wedge angles. However, the reason for such self sustained…
The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impingement, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with h…
Due to the thick boundary layers in hypersonic flows, the state of the boundary layer significantly influences the whole flow field as well as surface heat loads. Hence, for engineering applications the efficient numerical prediction of laminar-to-turbulent transition is a challenging and important task. Within the framework of the Reynolds averaged Navier-Stokes equations, Langtry/Menter [1] proposed the $γ$-$Re_{θ_t}$ transition model using two transport equations for the intermittency and $γ$-$Re_{θ_t}$ combined with the Shear Stress Transport turbulence model (SST) [2]. The transition mode…
The self-excited spanwise homogeneous perturbations arising in shock-wave/boundary-layer interaction (SWBLI) system formed in a hypersonic flow of molecular nitrogen over a double wedge are investigated using the kinetic Direct Simulation Monte Carlo (DSMC) method. The flow has transitional Knudsen and unit Reynolds numbers of 3.4 x 10$^{-3}$ and 5.2 x 10$^4$ m$^{-1}$, respectively. Strong thermal nonequilibrium exists downstream of the Mach 7 detached (bow) shock generated due to the upper wedge surface. A linear instability mechanism is expected to make the pre-computed 2-D base flow potenti…
The simulation of hypersonic flows is computationally demanding due to large gradients of the flow variables caused by strong shock waves and thick boundary or shear layers. The resolution of those gradients imposes the use of extremely small cells in the respective regions. Taking turbulence into account intensives the variation in scales even more. Furthermore, hypersonic flows have been shown to be extremely grid sensitive. For the simulation of three-dimensional configurations of engineering applications, this results in a huge amount of cells and prohibitive computational time. Therefore,…
The generation mechanism of wall heat flux is one of the fundamental problems in supersonic/hypersonic turbulent boundary layers. A novel heat decomposition formula under the curvilinear coordinate was proposed in this paper. The new formula has wider application scope and can be applied in the configurations with grid deformed. The wall heat flux of an interaction between shock wave and the turbulent boundary layer over a compression corner is analyzed by the new formula. The results indicated good performance of the formula in the complex interaction region. The contributions of different en…
The accurate prediction of aerothermal surface loading is of paramount importance for the design of high speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative of the inlet of an air-breathing flight vehicle, characterized by three-dimensional intersecting shock-wave/turbulent boundary-layer interaction at Mach 8.3. High Reynolds numbers ($Re_L \approx 11.6 \times 10^6$ based on free-stream conditions) and the presence of cold walls ($T_w/T_o \approx 0.27$) leading to large near-wall temperature gradients necessi…
The influence of high-enthalpy effects on hypersonic turbulent boundary layers is investigated by means of direct numerical simulations (DNS). A quasi-adiabatic flat-plate air flow at free-stream Mach number equal to 10 is simulated up to fully-developed turbulent conditions using a five-species, chemically-reacting model. A companion DNS based on a frozen-chemistry assumption is also carried out, in order to isolate the effect of finite-rate chemical reactions and assess their influence on turbulent quantities. In order to reduce uncertainties associated with turbulence generation at the inle…
A high-fidelity simulation of the shock/transitional boundary layer interaction caused by a 15-degrees axisymmetrical compression ramp is performed at a freestream Mach number of 5 and a transitional Reynolds number. The inlet of the computational domain is perturbed with a white noise in order to excite convective instabilities. Coherent structures are extracted using Spectral Proper Orthogonal Decomposition (SPOD), which gives a mathematically optimal decomposition of spatio-temporally correlated structures within the flow. The mean flow is used to perform a resolvent analysis in order to st…
Hypersonic leading-edge separation is studied towards understanding the varying shock-related unsteadiness with freestream Reynolds number ($1.66 \times 10^5 \leq Re_D \leq 5.85 \times 10^5$) in the newly constructed hypersonic Ludwieg tunnel (HLT) at a freestream design Mach number of $M_\infty=6.0$. An axisymmetric flat-face cylinder of base body diameter $D=35$ mm is fitted with protrusions of different fineness ($d/D=0.1,0.2,0.26,0.34$ at $L/D=1.4$) and slenderness ($L/D=0.7,1,1.4,1.9$ at $d/D=0.2$) ratio to induce a wide range of leading-edge separation intensities. Qualitative and quanti…
The paper gives experimental observations on the hypersonic flow past an axisymmetric flat-face cylinder with a protruding sharp-tip spike at a freestream Mach number of $M_\infty = 8.16$ at two different freestream Reynolds numbers based on the base body diameter ($Re_D = 0.76 \times 10^6$, and $3.05 \times 10^6$). Furthermore, modal analysis is done on schlieren images to understand the flow dynamics parallel with the unsteady pressure measurements. The protruding spike of length to base body diameter ratio of $[l/D]=1$ creates a familiar unsteady flowfield called 'pulsation.' Pressure loadi…
The dynamics of a shock wave impinging on a transitional high-enthalpy boundary layer out of thermochemical equilibrium is investigated for the first time by means of a direct numerical simulation. The freestream Mach number is equal to 9 and the oblique shock impinges with a cooled flat-plate boundary layer with an angle of 10°, generating a reversal flow region. In conjunction with freestream disturbances, the shock impingement triggers a transition to a fully turbulent regime shortly downstream of the interaction region. Accordingly, wall properties emphasize the presence of a laminar regio…
The BARC flow is studied via Direct Numerical Simulation at a relatively low turbulent Reynolds number, with focus on the geometrical representation of the leading-edge (LE) corners. The study contributes to further our understanding of the discrepancies between existing numerical and experimental BARC data. In a first part, rounded LE corners with small curvature radii are considered. Results show that a small amount of rounding does not lead to abrupt changes of the mean fields, but that the effects increase with the curvature radius. The shear layer separates from the rounded LE at a lower …
Linear global instability of the three-dimensional (3-D), spanwise-homogeneous laminar separation bubble (LSB) induced by shock-wave/boundary-layer interaction (SBLI) in a Mach 7 flow of nitrogen over a $30^{\circ}-55^{\circ}$ double wedge is studied. At these conditions corresponding to a freestream unit Reynolds number, $Re_1=5.2\times 10^{4}$ m$^{-1}$, the flow exhibits rarefaction effects and comparable shock-thicknesses to the size of the boundary-layer at separation. This, in turn, requires the use of the high-fidelity Direct Simulation Monte Carlo (DSMC) method to accurately resolve uns…
Finite-rate chemistry in a hypersonic wall model: heat-flux selection, non-monotone rate response and transport-closure effects
Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；School of Aeronautic Science and Engineering, Beihang University（北京航空航天大学航空科学与工程学院）
In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationally expensive, high-fidelity physics models. Such surrogate models are essential for many-query applications e.g., engineering design optimization and parameter estimation, where it is necessary to invoke the high-fidelity model sequentially, many times. Surrogate models are usually constructed for individual scalar quantities. However there are scenarios where a spatially varying field needs to be modeled as a funct…
Tall buildings are often subjected to steady and unsteady forces due to external wind flows. Measurement and mitigation of these forces becomes critical to structural design in engineering applications. Over the last few decades, many approaches such as modification of the external geometry of structures have been investigated to mitigate wind-induced load. One such proven geometric modification involved rounding of sharp corners. In this work, we systematically analyze the effects of rounded corner radii on the flow-induced loading for a square cylinder. We perform 3-Dimensional (3D) simulati…
Complex geometries can be easily treated using the well-known full-way and half-way bounce-back rules. However, the accuracy of the full-way bounce-back rule is one order lower than the half-way bounce-back rule. Moreover, when the walls are not aligned with the lattices, the errors increase. Including the collision operator on the walls with the full-way bounce-back rule leads to an improvement of the accuracy of the pressure-drop, but, a loss of momentum is observed on concave corners. We propose to improve the momentum conservation by adding an extrapolation of the density by the inverse di…
We study the turbulent square duct flow of dense suspensions of neutrally-buoyant spherical particles. Direct numerical simulations (DNS) are performed in the range of volume fractions $ϕ=0-0.2$, using the immersed boundary method (IBM) to account for the dispersed phase. Based on the hydraulic diameter a Reynolds number of $5600$ is considered. We report flow features and particle statistics specific to this geometry, and compare the results to the case of two-dimensional channel flows. In particular, we observe that for $ϕ=0.05$ and $0.1$, particles preferentially accumulate on the corner bi…
We use spectral analysis of Eulerian and Lagrangian dynamics to study the advective mixing in an incompressible 2D bounded cavity flow. A significant property of such a rotational flow at high Reynolds numbers is that mixing in its core is slower than wall-adjacent areas and corner eddies. We explain this property by considering the resonance between frequencies of unsteady motion -- captured by the Koopman spectral analysis of the velocity field -- and the circulation frequency of Lagrangian tracers in the mean flow. In high-Reynolds rotational 2D flows, the vorticity in the rotational core i…
The wake behind a cube with a face normal to the flow was investigated experimentally in a water tunnel using laser induced fluorescence visualisation (LIF) and particle image velocimetry (PIV) techniques. Measurements were carried out for moderate Reynolds numbers between 100 and 400 and in this range a sequence of two flow bifurcations was confirmed. Values for both onsets were determined in the framework of Landau`s instability model. The measured longitudinal vorticity was separated into three components corresponding to each of the identified regimes. It was shown that the vorticity assoc…
Wing-body junction flows occur when a boundary layer encounters an airfoil mounted on the surface. The corner flow near the trailing edge is challenging for the linear eddy viscosity Reynolds Averaged Navier-Stokes (RANS) models, due to the interaction of two perpendicular boundary layers which leads to highly anisotropic Reynolds stress at the near wall region. Recently, Xiao et al. proposed a physics-informed Bayesian framework to quantify and reduce the model-form uncertainties in RANS simulations by utilizing sparse observation data. In this work, we extend this framework to incorporate th…
We study the inertial migration of finite-size neutrally buoyant spherical particles in dilute and semi-dilute suspensions in laminar square duct flow. We perform several direct numerical simulations using an immersed boundary method to investigate the effects of the bulk Reynolds number $Re_b$, particle Reynolds number $Re_p$ and duct to particle size ratio $h/a$ at different solid volume fractions $ϕ$, from very dilute conditions to $20\%$. We show that the bulk Reynolds number $Re_b$ is the key parameter in inertial migration of particles in dilute suspensions. At low solid volume fraction …
In this paper, the TR-PIV method is used to study the internal flow field characteristics in U-shaped channels. The Reynolds number, based on the square cross section channel hydraulic diameter is 8888,13333 and 17777. Mean flow, Reynolds stress and POD are taken into consideration to investigate the flow characteristic with three different turning sections. Through analysis, a series of important conclusions have been drawn. For the main flow, the structure of turning sections has obvious influence on the characteristics of flow field. The size and number of vortices in the corner area are si…
For more than 150 years the Navier-Stokes equations for thermodynamically quasi-equilibrium flows have been the cornerstone of modern computational fluid dynamics that underpins new fluid technologies. However, the applicable regime of the Navier-Stokes model in terms of the level of thermodynamic non-equilibrium in the local flowfield is not clear especially for hypersonic and low-speed micro/nano flows. Here, we re-visit the Navier-Stokes model in the framework of Boltzmann statistics, and propose a new and more appropriate way of assessing non-equilibrium in the local flowfield, and the cor…
Cornerstone of this research is the examination of fluid flow around NACA0012 airfoil, with the aim of the numerical validation between the experimental results in the wind tunnel and the Lattice Boltzmann Method (LBM) analysis, for the medium Reynolds number (Re = 191000). The LBM-Large Eddy Simulation (LES) method described in this paper opens up opportunities for faster computational fluid dynamics (CFD) analysis, because of the LBM scalability on high performance computing architectures, more specifically general purpose graphics processing units (GPGPUs), pertaining at the same time the h…
The present experimental study addresses the flow of a Yield Stress Fluid with some elasticity (Carbopol gel) in a square duct. The behaviour of two fluids with lower and higher yield stress is investigated at multiple Reynolds numbers $Re^* \in$ (1, 200) and Bingham numbers $Bi \in$ (0.01, 0.35). A secondary flow consisting of eight vortices is observed to recirculate the fluid from the corners to the core. Their extent and intensity grows with increasing $Re^*$. The second objective of this study is to explore the change in flow in the presence of particles. Almost neutrally-buoyant finite-s…
Modelling hydrodynamic lubrication is crucial in the design of engineering components as well as for a fundamental understanding of friction mechanisms. The cornerstone of thin-film flow modelling is the Reynolds equation -- a lower-dimensional representation of the Stokes equation. However, the derivation of the Reynolds equation is based on assumptions and fixed form constitutive relations, that may not generally be valid, especially when studying systems under extreme conditions. Furthermore, these explicit assumptions about the constitutive behaviour of the fluid prohibit applications in a…
The work addresses 2D and 3D turbulent transonic flows past a wall with an expansion corner. A curved shock wave is formed upstream of a cylinder located above the corner. Numerical solutions of the Reynolds-averaged Navier-Stokes equations are obtained on fine meshes with a finite-volume solver of the second order accuracy. The solutions demonstrate the existence of adverse free-stream Mach numbers which admit abrupt changes of the shock position at small perturbations. This is explained by an instability of the closely spaced sonic surface and shock wave on the wall.
