Shock Wave Boundary Research Articles

Assimilating mean velocity fields of a shockwave–boundary layer interaction from background-oriented schlieren measurements using physics-informed neural networks

We propose a novel method to reconstruct mean velocity fields of turbulent shockwave–boundary layer interactions (SBLIs) from background-oriented schlieren (BOS) measurement data using physics-informed neural networks (PINNs). By embedding the compressible Reynolds-Averaged Navier–Stokes equations into the PINN loss function, we recover a full set of physical variables from only the density gradient as training data. This technique has the potential to generate velocity fields similar to particle image velocimetry (PIV) results from usually simpler planar BOS measurements, at the cost of some computational resources. We analyze our method's capabilities on two oblique SBLI cases: a high-fidelity Mach 2.28 direct numerical simulation dataset for validation and a Mach 2.0 wind tunnel experiment. We demonstrate the positive impact of different wall boundary constraints such as the wall shear stress and pressure distribution for enhancing the PINN's convergence toward physically accurate solutions. The predicted fields are compared with experimental PIV and other point measurements, while we discuss the accuracy, limitations, and broader implications of our approach for SBLI research.

A study on shock-wave/boundary-layer interaction with varying flow deflection angle

Shockwave boundary layer interaction is studied for oblique shocks generated from a shock generator with a varying flow deflection angle. A two-dimensional shock generator with a wedge-shaped geometry is fixed inside the test section and mounted to the wind tunnel's top wall. The shock generator is made to pitch up and down so that the net flow deflection angle changes because of the pitch motion. As a result, the shock strength changes for a varying flow deflection angle of the shock generator with a fixed incoming Mach number of the flow. The imposed adverse pressure gradient on the boundary layer by this incident shock changes, which influences the shape and structure of the shockwave boundary layer interaction. Three different shockwave boundary layer interaction structures are observed with high-speed schlieren from the experiments conducted for the current study. Schematics for these structures' types are illustrated, and a model is presented to build the transition criteria for the flow deflection angles for which the transition would take place from one structure to the other. The two transition criteria, one for type 1 to type 2 transition and the other for type 2 to type 3 transition, are validated with the observed results from the experiments. Assumptions made for the transition criteria are also validated with experimental results.

Transonic buffet simulation using a partially-averaged Navier-Stokes approach

The present article assesses the capability of the partially averaged Navier-Stokes (PANS) method to reproduce accurately the self-sustained shock oscillations, also known as transonic buffet, occurring on airfoils and wings at transonic regime under certain conditions of Mach number and angle of attack. The test case under analysis is an OAT15A unswept wing at Mach number M∞=0.73 and Reynolds number Rec=3×106. The three-dimensional flow is studied by accounting for the wind tunnel walls adopted in the experiments of Jacquin et al. [1] in the simulations. The computations on a large-span, confined configuration reveal a strong three-dimensionality of the flow both before and after the buffet onset. Attention is paid to the comparison with unsteady Reynolds-averaged Navier Stokes (URANS) results, to show the benefits of PANS in resolving flow unsteadiness at different flow resolutions, especially on affordable CFD grids, at limited additional cost. In this context, the role of the mesh metrics and the local turbulence level in the formulation of the model is described, as well as the relation of this latter with the spatiotemporal discretization used for the numerical simulations. The aim is to extend the use of PANS and obtain accurate predictions of flow cases involving shock-wave boundary layer interactions without expensive approaches.

Effects of herringbone riblets on shock-wave/turbulent boundary-layer interactions

In the experiment reported in this paper, a spanwise array of herringbone riblets strips is applied upstream of the interaction region between an impinging shockwave and a turbulent boundary layer developing along a flat plate boundary layer at a freestream Mach number of 1.85. High-speed schlieren photography, surface oil flow visualization and PSP are used to examine the effect of herringbone riblets on the characteristics of the shockwave-boundary layer interactions. It shows that despite that the height of the riblets is less than 2 % of the local thickness of the undisturbed boundary layer, a profound modification to the shockwave-boundary layer interaction zone is observed, and the overall size of the separation bubble is decreased. The observed control effects are attributed to the large-scale secondary flow structures produced by the directional riblets. To the best knowledge of the author, this is the first study evaluating the control effect of herringbone riblets on shock wave and turbulent boundary layer interactions in supersonic flow using the experimental method.

Flow fields around asymmetrical micro vortex generators in supersonic flow

Motivated by the favorable effects of asymmetrical vortical structures on shock-wave boundary layer interactions, we performed implicit large-eddy simulations to analyze the ability of micro mechanical vortex generators (VGs) to generate such structures. For this purpose, we studied modified VG geometries, by skewing and varying the orientation of a microramp and introducing pairs of unevenly sized ramped-vanes. The modified VGs allow to study the effectiveness of these devices when operating in off-design conditions. The flow physics of all devices were investigated in a supersonic crossflow at Mach 2.5 and a momentum-thickness Reynolds number of 7000. The flow topology around each VG is very similar: the VG acts as an obstacle to the incoming flow and induces a complex system of shocks, recirculation regions, and vortical structures. We present a detailed study of the evolution of the dominant major counter-rotating vortex pair (CVP) to estimate the VGs' flow-control effectiveness. All modified configurations introduce asymmetry into the flow, yet to varying degree for different device types. The modifications made to the microramp have minimal impact on the boundary layer, while the uneven ramped-vane configurations have significant effect. Lateral spread of mechanical VG induced major CVP is not larger than the spanwise dimension of the VG. Consequently, the favorable effect of interactions between VGs arranged in arrays on flow-control effectiveness observed for air-jet VG arrays cannot be reproduced with mechanical VGs. Considering the large design offsets we introduced to the microramp and ramped-vane configurations, both device types are robust to off-design flight conditions.

Experimental and Numerical Investigations of Shock-Wave Boundary Layer Interactions in a Highly Loaded Transonic Compressor Cascade

Experimental and Numerical Investigations of Shock-Wave Boundary Layer Interactions in a Highly Loaded Transonic Compressor Cascade

Numerical investigation of wall-pressure fluctuations for Mach 2 turbulent shock-wave boundary layer interactions

Implicit large-eddy simulations of Mach 2.05 turbulent boundary layer interactions with oblique impinging shock-waves were carried out for shock generator angles of 8° and 9°. Both the streamwise extent of the separated region and the intensity of the velocity fluctuations are augmented when the strength of the impinging oblique shock-wave is increased from 8° to 9°. Temporal Fourier transforms of the spanwise-averaged wall-pressure coefficient indicate low-frequency unsteadiness at separation and mid-frequency content downstream of reattachment. The wall-pressure fluctuations were analyzed with the proper orthogonal decomposition. The modal analysis reveals pronounced 3D low-frequency wall-pressure fluctuations for the stronger interaction. Overall, the present findings provide advanced perspectives on low-frequency wall-pressure fluctuations in turbulent shock-wave boundary layer interactions that may lead to spanwise non-uniformity of the separation and shedding with possible implications for the design of structural panels on high-speed vehicles.

Sidewall effects in laminar ramp induced shockwave boundary layer interactions

Shock-wave boundary layer interactions (SWBLI) play a significant role in control surfaces and engine inlets. However, most simulations commonly assume span-periodic or 2D. Recent research conducted by Lusher and Sandham (2020) investigated the effects of sidewalls in impinging-type SWBLI (ISWBLI). This study’s focus is to numerically explore the influence of sidewalls in a three-dimensional context for ramp-induced SWBLI (RSWBLI). First a 2D ramp-induced separated boundary layer interaction with a ramp angle of 6.8° was identified. This configuration produced the same pressure rise and separation characteristics as those reported by Katzer (1989) at a Mach number of 2 and an impinging Reynolds number of 3×105. Subsequently, the sidewall was introduced for Aspect Ratio 1 and the results were analysed. From the analysis it was found out that the separation length for the 3D case is 14% greater than that observed in the 2D simulation. Upon comparison with the ISWBLI study of Lusher and Sandham (2020), it was found that (a) the sidewall and central separation are connected in RSWBLI, contrasting with ISWBLI, (b) the extent of sidewall separation in RSWBLI is very limited compared to the impingement interaction, and (c) RSWBLI displays characteristics closer to an owl-like separation of second kind, whereas in ISWBLI exhibits characteristics of the first kind of separation. Even though having identical shock-strength and separation length for both R & I SWBLI in 2D configuration, the introduction of sidewall resulted in a distinct topology and dynamics of interaction .

Shock impingement on a transitional hypersonic high-enthalpy boundary layer

Shock-wave boundary layer interactions are of utmost importance for both aeronautical and aerospace applications. The dynamics of high-speed compressible turbulent boundary layers becomes tightly coupled with strong gradients of thermodynamic properties, leading to an increase of thermomechanical loads. In the contextual presence of hypersonic and high-enthalpy regimes, thermochemical nonequilibrium effects must be considered as well. This work is a first step toward the fundamental understanding of this configuration.

Liquid jet injection in supersonic crossflow: Self-induced jet oscillations and its effects

Liquid jet injection into supersonic crossflow is one of the conceptually simple ways of fuel atomization in Scramjet engines. In the present work, we experimentally investigate the flow and spray formed due to the injection of a liquid jet in supersonic crossflow with free stream Mach number of M∞ = 2.5. The main focus of the work is on the unsteady aspects of the flow and spray, which are found to be self-induced and occur naturally in the flow. High speed shadowgraphy shows large variations in the windward spray edge and penetration with time. Unsteady pressure measurements in the liquid injection line show that in the presence of a supersonic crossflow, there exist significant self-generated mass flow fluctuations that occur in the injection line. The frequency of these oscillations is seen to be close to a Strouhal number, St = fδ /U∞ ≈ 0.007, close to the typical low frequencies seen in Shock-Wave Boundary Layer Interaction studies (δ = boundary layer thickness). The variations in mass flow rate within the injection line leads to significant fluctuations of the spray penetration and shocks. In particular, the variations in spray penetration with time is observed to lead to significant variations in both the droplet numbers and size at a given location in the generated spray, which can have significant implications for applications where such configurations are used.

Unsteady Motion of Shock Wave for a Supersonic Compression Ramp Flow Based on Large Eddy Simulation

A large eddy simulation (LES) is conducted to investigate shock wave/turbulent boundary layer interaction in a 24° compression ramp at a high inlet Mach number of Ma=2.9. The recycling/rescaling Method is used as the inflow turbulence generation technique. The shock wave structure and boundary layer flow in the interaction region are studied by flow visualization methods, such as vortex recognition and numerical schlieren. The distributions of turbulent kinetic energy and Reynolds normal stresses at different streamwise locations are analyzed. The results show that a strong anisotropy turbulent flow appears in the reattached boundary layer after the interaction of the shock wave. The large-scale unsteady motion of the separation shock wave is analyzed by using the intermittent factor and power spectrum. It is found that the shock moves around the averaged separation position, and the length scale is equal to 72% of the inlet boundary layer thickness. The power spectrum analysis reveals the existence of low-frequency instability in the separation region.

Numerical investigation of unswept and swept turbulent shock-wave boundary layer interactions

Hybrid turbulence model and large-eddy simulations of turbulent shock-wave boundary layer interactions at a freestream Mach number of 2.3 were carried out for sweep angles of 0 and 40 deg. The simulations for the unswept interaction reveal the shedding of spanwise coherent structures as well as intermittent spanwise deformations of the separation line. The frequencies associated with the spanwise deformations are in the low- to mid-frequency band. By adding a cross-flow component to the approach flow, a comparable turbulent interaction with 40 deg sweep was obtained. For the swept interaction, the overall level of the pressure fluctuations is higher than for the unswept case but the spanwise structures are absent. Instead, traveling oblique structures are observed downstream of the interaction.

Capsule aerodynamics and shock-wave boundary layer interaction (SBLI) in supersonic and transonic flow

Static force and moment measurements are performed on the MarcoPolo-R aero shape in the trisonic wind tunnel TMK. The static stability behaviour of the capsule is characterized in the Mach number range 0.5le Mle 3.5 reproducing the Mach and Reynolds conditions of the flight trajectory in the supersonic regime. An aerodynamic database is built based on the experimental results. The flow structure around the capsule is visualised in supersonic tests by means of schlieren imaging. Under certain conditions, development of a complex shock system on the leeward side of the inclined capsule is observed. Oil film technique is used to visualise boundary layer phenomena in connection to this shock system. Numerical simulations with the DLR TAU code are performed to support the interpretation of the flow phenomena under these conditions.Graphical abstractSchlieren imaging visualisation of density gradients in supersonic flow. Depending on the test conditions and angle of incidence, a complex shock system is observed on the leeward side of the inclined capsule. Analysis of the shock structure and its impact on aerodynamic coefficients is one subject of the present investigation.

Multi-scale study of the transitional shock-wave boundary layer interaction in hypersonic flow

A high-fidelity simulation of the massively separated shock/transitional boundary layer interaction caused by a 15-degrees axisymmetrical compression ramp is performed at a free stream Mach number of 6 and a transitional Reynolds number. The chosen configuration yields a strongly multiscale dynamics of the flow as the separated region oscillates at low-frequency, and high-frequency transitional instabilities are triggered by the injection of a generic noise at the inlet of the simulation. The simulation is post-processed using Proper Orthogonal Decomposition to extract the large scale low-frequency dynamics of the recirculation region. The bubble dynamics from the simulation is then compared to the results of a global linear stability analysis about the mean flow. A critical interpretation of the eigenspectrum of the linearized Navier–Stokes operator is presented. The recirculation region dynamics is found to be dominated by two coexisting modes, a quasi-steady one that expresses itself mainly in the reattachment region and that is caused by the interaction of two self-sustained instabilities, and an unsteady one linked with the separation shock-wave and the mixing layer. The unsteady mode is driven by a feedback loop in the recirculation region, which may also be relevant for other unsteady shock-motion already documented for shock-wave/turbulent boundary layer interaction. The impact of the large-scale dynamics on the transitional one is then assessed through the numerical filtering of those low wavenumber modes; they are found to have no impact on the transitional dynamics.

Characteristics of wall-shear stress fluctuations in shock wave and turbulent boundary layer interaction

The wall-shear stress (WSS) fluctuations in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer are investigated by means of direct numerical simulation (DNS) at Mach 2.25. The numerical results agree very well with previous experiments and DNS data in terms of turbulence statistics, wall pressure, and skin friction. The fluctuating WSS characteristics, including probability density function (PDF), frequency spectrum, space–time correlation, and convection velocity, are analysed systematically. It is found that the positively skewed PDF shape of the streamwise WSS fluctuations is significantly changed due to the presence of a separation bubble, while the PDF shape of the spanwise component is slightly affected, exhibiting a symmetric behaviour across the interaction. The weighted power-spectrum density map indicates that the low-frequency unsteadiness associated with the separated shock - exhibits little influence on the spectrum for either component, and no enhancement of the low-frequency energy is observed. A significant reduction in the spatial extent of the two-point correlation is observed, causing spanwise elongated coherence for the streamwise WSS fluctuations in the separation region. Moreover, the elliptic behaviour of the space–time correlations is essentially preserved throughout the interaction, and this is accompanied by a sudden reduction of the convection velocity in the separation bubble.

OpenSBLI: Automated code-generation for heterogeneous computing architectures applied to compressible fluid dynamics on structured grids

OpenSBLI is an open-source code-generation system for compressible fluid dynamics (CFD) on heterogeneous computing architectures. Written in Python, OpenSBLI is an explicit high-order finite-difference solver on structured curvilinear meshes. Shock-capturing is performed by a choice of high-order Weighted Essentially Non-Oscillatory (WENO) or Targeted Essentially Non-Oscillatory (TENO) schemes. OpenSBLI generates a complete CFD solver in the Oxford Parallel Structured (OPS) domain specific language. The OPS library is embedded in C code, enabling massively-parallel execution of the code on a variety of high-performance-computing architectures, including GPUs. The present paper presents a code base that has been completely rewritten from the earlier proof of concept Jacobs et al. (2017) [7], allowing shock capturing, coordinate transformations for complex geometries, and a wide range of boundary conditions, including solid walls with and without heat transfer. A suite of validation and verification cases are presented, plus demonstration of a large-scale Direct Numerical Simulation (DNS) of a transitional Shockwave Boundary Layer Interaction (SBLI). The code is shown to have good weak and strong scaling on multi-GPU clusters. We demonstrate that code-generation and domain specific languages are suitable for performing efficient large-scale simulations of complex fluid flows on emerging computing architectures. Program summaryProgram Title: OpenSBLI code-generation framework for compressible fluid dynamics on heterogeneous architecturesCPC Library link to program files:https://doi.org/10.17632/3sdb6hck2c.1Developer's repository link:https://github.com/opensbli/opensbliLicensing provisions: GPLv3Programming languages: Python, C/C++, OPS DSLNature of problem: The compressible 3D Navier-Stokes equations are solved via Implicit Large Eddy Simulation (ILES) or Direct Numerical Simulation (DNS).Solution method: OpenSBLI [1,2] is a Python-based code-generation system that uses symbolic algebra to generate a complete CFD solver in C/C++. The basic algorithm is a stencil-based finite-difference solver on structured curvilinear meshes. Shock-capturing is performed by a selection of high-order Weighted/Targeted Essentially Non-Oscillatory (WENO/TENO) schemes. Explicit low-storage Runge-Kutta schemes are used for time-advancement.Additional comments including restrictions and unusual features: The generated code is compliant with the Oxford Parallel Structured (OPS) [3] software library. OpenSBLI/OPS executables can be generated for the OpenMP, MPI, CUDA, OpenCL, and OpenACC parallel programming paradigms. Multi-GPU support is available via combinations of MPI with CUDA, OpenCL or OpenACC.

A Class of Shock Wave Solution to Singularly Perturbed Nonlinear Time-Delay Evolution Equations

Nonlinear singularly perturbed problem for time-delay evolution equation with two parameters is studied. Using the variables of the multiple scales method, homogeneous equilibrium method, and approximation expansion method from the singularly perturbed theories, the structure of the solution to the time-delay problem with two small parameters is discussed. Under suitable conditions, first, the outer solution to the time-delay initial boundary value problem is given. Second, the multiple scales variables are introduced to obtain the shock wave solution and boundary layer corrective terms for the solution. Then, the stretched variable is applied to get the initial layer correction terms. Finally, using the singularly perturbed theory and the fixed point theorem from functional analysis, the uniform validity of asymptotic expansion solution to the problem is proved. In addition, the proposed method possesses the advantages of being very convenient to use.

Failure mechanism of casing treatment in improving stability of a highly loaded two-stage axial compressor

Casing treatment is a powerful method for enhancing stability of certain aircraft compressors in which tip leakage vortex (TLV) triggers stall. An optimized slot-type casing treatment was installed on the first rotor of a highly loaded two-stage compressor. The experimental result showed that the casing treatment could not increase the compressor stability at three tested speeds. This study aims to understand the failure mechanism of the casing treatment for developing an effective method to depress stall. A “three-step method” is proposed to determine the stall-limiting location and understand the underlying stall mechanism. At 90% speed, there is a spike in the aerodynamic flow parameters in the tip region of the first rotor under the near stall condition compared with that under the design condition. The spike is induced by an interaction among the TLV, boundary layer at the blade suction surface, and passage shockwave. Both the TLV and the shockwave–boundary layer interaction contribute to the accumulation of tip blockage which triggers compressor stall. The TLV does not break down under the near stall condition, but unsteady forward spillage of the TLV at the blade tip leading edge can be detected, resulting in unsteady tip flow. When the casing treatment is installed on the first rotor, a typical flow circulation is established in the slots. The intensity of the TLV and the flow unsteadiness are greatly depressed, and the discharge capability in the tip region is remarkably improved. However, the flow circulation cannot manipulate the fierce boundary layer separation induced by the shockwave, which causes increased tip blockage and reduced compressor stability. A coupled casing treatment, which can bleed the shockwave induced blockage, is proposed and found to be very effective in improving compressor stability. Therefore, the technology for damping the compressor stall should be capable of manipulating both the TLV and the shockwave induced boundary layer separation. At 100% speed, a shedding vortex is initiated at the hub of the second stator. This vortex expands sharply in the stalling process and triggers compressor stall. Variation of the location at which the compressor stalls is the reason for the failure of the casing treatment at 100% speed.

Pedestrian Flow Characteristics at Upstream and Downstream of Bottleneck for Unidirectional Flow under Normal Conditions

The study of pedestrian flow characteristics at upstream and downstream of bottlenecks is important from level of service and evacuation perspective. Many controlled laboratory experiments have been conducted to study pedestrians’ behavior at bottlenecks. However, it is unclear whether experiments can reproduce real crowd flow characteristics. In this paper, real field data was collected at normal conditions for unidirectional pedestrian movement at Mahakaleshwar, a Hindu temple at Ujjain, India during Mahashivaratri, a festival day on which a large number of pilgrims visited the temple. Along the corridor there is a width reduction at a U-turn which creates a bottleneck. It is necessary to study pedestrian flow characteristics at bottlenecks to ensure desired level of service at temple premises during heavy flow. The speed-density relationships of upstream and downstream sections were compared and it was found that flow behavior at both the sections of bottleneck severely differ from each other. Pedestrians in the upstream are either at free flow speed for very low density values or moving slowly for intermediate to high range of density values. From the speed-density relationship, it can be concluded that pedestrians at upstream had visual clues of congestion ahead at bottleneck (pedestrian could also see the downstream flow through barricades). Therefore, pedestrians wait at their position, stay in their comfort zone and do not push each other. Thus, even at intermediate local density, pedestrians have such low speeds. This violates the general assumption that pedestrians change their speed only at the shockwave boundary. The movement of pedestrians at upstream is governed by local density and information of congestion status ahead, whereas pedestrian movement at downstream is governed by factors like density, side friction and pedestrians’ willingness to compensate for the delay at bottleneck. This study is expected to have application in planning and operation of pedestrian facilities.

Roles of bulk viscosity on transonic shock-wave/boundary layer interaction

Implicit large eddy simulations are carried out to investigate the influence of the molecular bulk viscosity on transonic shock-wave boundary layer interaction for flow past a natural laminar flow airfoil at a free-stream Mach number M∞ = 0.72 and an angle of attack α = 0.38°. To quantify the nonlinear interactions, we have discarded the putative assumption made by Stokes and used a mathematical model derived from acoustic attenuation measurements to compute bulk viscosity terms. Circumventing the Stokes’ assumption, the time-averaged Cp distributions reveal a much better agreement of the shock strength and location with the available experimental data. Furthermore, due to the additional dissipative term in the energy balance equation, the strength of the upstream propagating Kutta-waves also diminishes along with a decrement in the frequency of the unsteady shock oscillation. Finally, it is observed that the additional bulk viscosity in the fluid flow resulted in an overall increase in the aerodynamic efficiency (the lift-drag ratio).