In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes its prediction very crucial in industry. Providing that wall-based quantities can be measured, we know today how to obtain good predictions for two and three-dimensional steady and periodic flows. In these flows, the separation is defined on a fixed line attached to a material surface. The last case to elucidate is the one where this line is no longer attached to the wall but on the contrary is contained within the flow. This moving separation is probably, however, the most common case of separation in natural flows and industrial applications. Since this case has received less attention during the past few years, we propose in this study to examine some properties of moving separation in two-dimensional, unsteady flows where the separation does not leave a signature on the wall. Since in this framework separation can be extracted by using a Lagrangian frame where the separation profile can be viewed as a hyperbolic unstable manifold, we propose a method to extract the separation point defined by the Lagrangian saddle point that belongs to this unstable manifold. In practice, the separation point and profile are initially extracted by detecting the most attracting Lagrangian coherent structure near the wall, and can then be advected in time for following instants. It is found that saddle points, which initially act as separation points in the viscous wall flow region, remarkably preserve their hyperbolicity even if they are ejected from the wall toward the inviscid region. Two test cases are studied, the creeping flow of a rotating and translating cylinder close to a wall, and the unsteady separation in the boundary layer generated by a planar jet impinging onto a plane wall.
We propose here a method to experimentally quantify unsteady leading-edge flow separation on aerofoils with finite thickness. The methodology relies on the computation of a leading-edge suction parameter based on measured values of the partial circulation around the leading-edge and the stagnation point location. We validate the computation of the leading-edge suction parameter for both numerical and experimental data under steady and unsteady flow conditions. The leading-order approximation of the definition of the leading-edge suction parameter is proven to be sufficiently accurate for the a…
A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is constituted by the convolutional neural network (CNN), improved convolutional Long-Short Term Memory neural network (ConvLSTM) and deconvolutional neural network (DeCNN). Flow fields at future time step can be predicted through flow fields by previous time steps and boundary positions at those steps by the novel hybrid deep neural network. Unsteady wake flows ar…
Unified Gas-Kinetic Scheme for Unsteady Multiscale Flows with Moving Boundaries
Hong Kong University of Science and Technology（香港科技大学）；Department of Mathematics, Hong Kong University of Science and Technology（香港科技大学数学系）；Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology（香港科技大学机械与航空航天工程系）；Shenzhen Research Institute, Hong Kong University of Science and Technology（香港科技大学深圳研究院）
Landing-gear noise is an increasing issue for transport aircraft. A key determinant of the phenomenon is the surface pressure field. Previous studies have described this field when the oncoming flow is perfectly aligned with the gear. In practice, there may be a cross-flow component; here its influence is investigated experimentally for a generic, two-wheel, landing-gear model. It is found that yaw angles as small as 5° cause significant changes in both overall flow topology and unsteady surface pressures. Most notably, on the outboard face of the leeward wheel, large-scale separation replaces…
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…
We apply the recent frame-invariant theory of separation spike formation to complex unsteady flows including a turbulent separation bubble, an impinging jet, and flows around a freely moving cylinder and a freely rotating ellipse. We show how the theory captures the onset of material spike formation, without any assumption on the flow type (steady, periodic, unsteady) or separation type (on- or off-wall, fixed or moving boundaries). We uncover new phenomena, such as the transition from on-wall to off-wall separation, the merger of initially distinct spikes, and the presence of severe material …
We experimentally investigate a partially shrouded sonic jet (a sonic free-jet shielded by a solid wall-extension on one side) exiting from a planar nozzle at two different nozzle pressure ratio ($ζ=4$ and $5$). We experimentally show that the inherent jet unsteadiness from the shock-induced flow separation on the wall and the emitted noise in the far-field is strongly coupled through a series of experiments like high-speed schlieren, wall-static pressure, unsteady pressure spectra, and microphone measurements. The partially shrouded jet's lateral free expansion is also identified to be compli…
Unsteady inviscid flow models of wings and airfoils have been developed to study the aerodynamics of natural and man-made flyers. Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the strength and distribution of the vortices in the wake. In such modeling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from sharp edges. To determine the formation of the trailing-edge vortex sheet, the classical Kutta condition can be extended to unsteady situations by rea…
The unsteady response of a water free surface to a localized pressure source moving at constant speed $U$ in the range $0.95c_\mathrm{min} \lesssim U \leq 1.02 c_\mathrm{min}$, where $c_\mathrm{min}$ is the minimum phase speed of linear gravity-capillary waves in deep water, is investigated through experiments and numerical simulations. This unsteady response state, which consists of a V-shaped pattern behind the source and features periodic shedding of pairs of depressions from the tips of the V, was first observed qualitatively by Diorio et al. (Phys. Rev. Let., 103, 214502, 2009) and called…
In this article, we propose a passive boundary layer control method to control the vortex structure of the cavity on the suction side and wake region of the CAV2003 benchmark hydrofoil. This method may be used in different applications such as marine, turbomachinery and hydraulic machinery. First, we used a hybrid URANS model for turbulence to simulate the 3D unsteady cloud cavitating flow and validated it based on experimental data. We performed the numerical simulations using open source code OpenFOAM and an Euler-Euler cavitation model. Second, we studied the effect of passive boundary laye…
A delayed detached eddy simulation (DDES) of an overexpanded nozzle flow with shock-induced separation is carried out at a Reynolds number equal to 1.7 10^7. The flow unsteadiness, characterised by self-sustained shock oscillations, induces local unsteady loads on the nozzle wall as well as global off-axis forces. A clear physical understanding of the driving factors of the unsteadiness is still lacking. Under the current conditions, the nozzle operates in a highly-overexpanded regime and comprises a conical separation shock within the nozzle contour, merging into a Mach disk in the nozzle cen…
The transition between the Regular Reflection (RR) and Mach Reflection (MR) phenomenon impacts the design of the supersonic and hypersonic air-breathing vehicles. The aim of this paper is to numerically investigate the dynamic transition from RR to MR of unsteady supersonic flow over a two-dimensional wedge, whose trailing edge moves along the $x$-direction upstream with a velocity, $V(t)$ at a free-stream Mach number of $M_{\infty}=3$. The simulation is conducted using the unsteady compressible inviscid flow solver, which is implemented in OpenFOAM\textsuperscript{\textregistered}, the open-s…
The design of supersonic and hypersonic air-breathing vehicles is influenced by the transition between the Mach Reflection (MR) and Regular Reflection (RR) phenomena. The purpose of this study is to investigate the dynamic transition of unsteady supersonic flow from MR to RR over a two-dimensional wedge numerically. The trailing edge of the wedge moves downstream along the $x$-direction with a velocity, $V(t)$ at a free-stream Mach number of $3$. An unsteady compressible inviscid flow solver is used to simulate the phenomenon. Further, the Arbitrary Lagrangian-Eulerian (ALE) technique is appli…
We investigate the behaviour of accelerating contact lines in an unsteady quasi-capillary channel flow. The configuration consists of a liquid column that moves along a vertical 2D channel, open to the atmosphere and driven by a controlled pressure head. Both advancing and receding contact lines were analyzed to test the validity of classic models for dynamic wetting and to study the flow field near the interface. The operating conditions are characterized by a large acceleration, thus dominated by inertia. The shape of the moving meniscus was retrieved using Laser-Induced Fluorescence (LIF)-b…
Two spherical bubbles with changing radii are considered to be moving in ideal fluid along their center-line. The exact expression for the fluid kinetic energy is obtained. The Stokes stream function is expanded in Gegenbauer polynomials in bispherical coordinates. This expansion is used to obtain the exact series for the fluid kinetic energy quadratic form coefficients. The new series are confirmed to be correct by comparison with the known ones. The main advantage of the new kinetic energy form is the possibility to obtain asymptotic expansions at small separation distance between the bubble…
Flapping animal flight is often modeled as a combined pitching and heaving motion in order to investigate the unsteady flow structures and resulting forces that could augment the animal's lift and propulsive capabilities. This work isolates the heaving motion of flapping flight in order to numerically investigate the flow physics at a Reynolds number of 40,000, a regime typical for large birds and bats and challenging to simulate due to the added complexity of laminar to turbulent transition in which boundary layer separation and reattachment are traditionally more difficult to predict. Period…
The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the tube. Prediction and understanding of the complex fluid dynamics is of theoretical and practical importance. It is also an extremely challenging problem for numerical simulation, especially at relatively high Reynolds numbers. Daru & Tenaud (Daru, V. & Tenaud, C. 2001 Evaluation of TVD high resolution schemes for unsteady viscous shocked flows. Computers & …
Sequential learning based PINNs to overcome temporal domain complexities in unsteady flow past flapping wings
Department of Aerospace Engineering, Indian Institute of Technology Madras（航空航天工程系，印度理工学院马德拉斯分校）；Laboratoire Interdisciplinaire des Sciences du Numérique LISN-CNRS（跨学科数字科学实验室（LISN-CNRS））
High-fidelity wall-resolved large-eddy simulations (LES) are utilized to investigate the flow-physics of small-amplitude pitch oscillations of an airfoil at Re = 100,000. The investigation of the unsteady phenomenon is done in the context of natural laminar flow airfoils, which can display sensitive dependence of the aerodynamic forces on the angle of attack in certain "off-design" conditions. The dynamic range of the pitch oscillations is chosen to be in this sensitive region. Large variations of the transition point on the suction-side of the airfoil are observed throughout the pitch cycle r…
Deep reinforcement learning (DRL) algorithms are rapidly making inroads into fluid mechanics, following the remarkable achievements of these techniques in a wide range of science and engineering applications. In this paper, a deep reinforcement learning (DRL) agent has been employed to train an artificial neural network (ANN) using computational fluid dynamics (CFD) data to perform active flow control (AFC) around a 2-D circular cylinder. Flow control strategies are investigated at a diameter-based Reynolds number Re_D = 100 using advantage actor-critic (A2C) algorithm by means of two symmetri…
We describe a novel mathematical method to supplant the classic approach and properly treat the spatiotemporal scale disparities present between the acoustics and remaining fluid dynamics. The method is applied in this work to well-known problems of semi-infinite extent defined by the Navier-Stokes equations, and preserves unsteady fluid behavior driven by the acoustic wave. The separation of the governing equations between the fast (acoustic) and slow (hydrodynamic) spatiotemporal scales are shown to naturally arise from the intrinsic properties of the fluid under forcing, not by arbitrary as…
In this work, using a unified framework consisting of third-order accurate discontinuous Galerkin schemes, we perform a comparison between five different numerical approaches to the free-surface shallow flow simulation on bottom steps. Together with the study of the overall impact that such techniques have on the numerical models, we highlight the role that the treatment of bottom discontinuities plays in the preservation of specific asymptotic conditions. In particular, we consider three widespread approaches that perform well if the motionless steady state has to be preserved and two approac…
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…
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…
The paper addresses the hydrodynamic behavior of a sphere close to a micro-patterned superhydrophobic surface described in terms of alternated no-slip and perfect-slip stripes. Physically, the perfect-slip stripes model the parallel grooves where a large gas cushion forms between fluid and solid wall, giving rise to slippage at the gas-liquid interface. The potential of the boundary element method (BEM) in dealing with mixed no-slip/perfect-slip boundary conditions is exploited to systematically calculate the mobility tensor for different particle-to-wall relative positions and for different p…
We present a hybrid partitioned deep learning framework for the reduced-order modeling of fluid-structure interaction. Using the discretized Navier-Stokes in the arbitrary Lagrangian-Eulerian reference frame, we generate the full-order flow snapshots and point cloud displacements as target data for the learning and inference of fluid-structure dynamics. The hybrid operation of this methodology comes by combining two data-driven models for fluid and solid subdomains via deep learning-based reduced-order models (DL-ROMs). The proposed framework comprises the partitioned data-driven drivers for u…
Turbulent resuspension, a process of lifting solid particles from the bottom by turbulent flow, is ubiquitous in environmental and industrial applications. The process is a sequence of events that start with an incipient motion of the particle being dislodged from its place, continue as sliding or rolling on the surface, ending with the particle being detached from the surface and lifted up into the flow. In this study the focus is on the resuspension of solid spherical particles with the density comparable to that of the fluid and the diameter comparable with the Kolmogorov length scale. We t…
The dynamics of shock-induced unsteady separated flow past a three-dimensional square-faced protuberance is investigated through wind tunnel experiments. Time-resolved schlieren imaging and unsteady surface pressure measurements are the diagnostics employed. Dynamic Mode Decomposition (DMD) of schlieren snapshots, and analysis of spectrum and correlations in pressure data are used to characterize and resolve the flow physics. The mean shock foot in the centreline is found to exhibit a Strouhal number of around 0.01, which is also the order of magnitude of the Strouhal numbers reported in the l…
We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in three-dimensional flows with arbitrary time dependence. Based on the exact evolution of the largest principal curvature on near-wall material surfaces, our theory identifies fixed and moving separation. Our approach is effective over short time intervals and admits an instantaneous limit. As a byproduct, we derive explicit formulas for the evolution of the Weingarten map and the principal curvatures of any surface advected by general three-dimensional flows. The material backbone w…
We combine three-dimensional (3D) large-eddy simulations (LES) and resolvent analysis to design active separation control techniques on a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of $23,000$ and a free-stream Mach number of $0.3$ are considered at two post-stall angles of attack of $6^\circ$ and $9^\circ$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. For the most successful control case that achieves full reattachmen…
An analysis of calibration for reduced-order models (ROMs) is presented in this work. The Galerkin and least-squares Petrov-Galerkin (LSPG) methods are tested on compressible flows involving a disparity of temporal scales. A novel calibration strategy is proposed for the LSPG method and two test cases are analyzed. The first consists of a subsonic airfoil flow where boundary layer instabilities are responsible for trailing-edge noise generation and the second comprises a supersonic airfoil flow with a transient period where a detached shock wave propagates upstream at the same time that shock-…
The lift and drag forces acting on a small spherical particle moving with a finite slip in single-wall-bounded flows are investigated via direct numerical simulations. The effect of slip velocity on the particle force is analysed as a function of separation distance for low slip and shear Reynolds numbers ($10^{-3} \leq Re_γ, Re_{\text{slip}} \leq 10^{-1}$) in both quiescent and linear shear flows. A generalised lift model valid for arbitrary particle-wall separation distances and $Re_γ, Re_{\text{slip}} \leq 10^{-1}$ is developed based on the results of the simulations. The proposed model can…
