High Speed Flows

High speed gas flows occur during the movement of aircrafts, rockets, and descent vehicles, as well as in combustion chambers, nozzles, and many other technological applications. High speed flows are characterized by a complex shock–vortex structure and the presence of large gradients of gas parameters due to the emerging shock waves, areas of shear deformations and the possible development of gas-dynamic instabilities. This Special Issue of Fluids, entitled “High Speed Flows”, is focused on recent advances in the numerical and experimental modeling of high speed flows. The topics considered by the Issue include the following areas: aircraft concepts, developing new hypersonic vehicles, flows around high speed vehicles, supersonic/hypersonic flows, flow control, supersonic nozzles, synthetic jets, shock waves, vortices and vortex structures, turbulence, and boundary layers. Together with these topics devoted to modeling the problems of application, attention has been paid to the construction of numerical methods and the application of the apparatus of solid and fluid media to new technological problems.

Topics concerning aircraft concepts, developing new hypersonic vehicles, and investigation of high speed flows around vehicles are considered in [1,2,3,4]. The development of hypersonic aircraft requires the simulation of hypersonic flows using new computational methods. In particular, this concerns the modeling of heat fluxes to the boundary of a streamlined body. The Reynolds-averaged Navier–Stokes (RANS) method proved to be insufficiently accurate for solving such problems. Therefore, new methods were explored, including large eddy simulation (LES). In [1], Knight and Kianvashrad proposed a new LES method for predicting the dynamics of a boundary layer over a flat plate, using a new recirculation-scaling approach. The method is based on the calculation of total enthalpy and static pressure, along with velocity components, to obtain the best results for hard wall and the parameters of turbulence. The results of the Law of the Wall, Reynolds Analogy Factor, turbulent stresses, and energy spectrum were compared with the previous methods. It was shown that the new recycling–rescaling method improves the prediction of the Strong Reynolds Analogy and turbulent Prandtl number.

The development of new CFD approaches for simulating high speed flows is presented by Struchkov et al. in [2], where the features of the implementation of a flow limiter in solving 3D aerodynamic problems using the system of Navier–Stokes equations on unstructured grids are presented. The paper describes the discretization of the system of Navier–Stokes equations by the finite volume method, a mathematical model which includes the Spalart–Allmaras turbulence model, and the calculation scheme of the splitting method using a second-order approximation scheme. To monotonize the method, the Venkatakrishnan limiter function was chosen by the authors. It was shown that when calculating on unstructured grids, the Venkatakrishnan limiter can lead to the appearance of areas of its accidental operation, which affects the accuracy of the result. A modified variant of the Venkatakrishnan limiter for unstructured grids was proposed, which was free from this shortcoming. To study the applicability of the limiting function, the problems with supersonic flow in a channel with a wedge and a transonic flow around the NACA0012 airfoil were simulated on an unstructured grid. The analysis of the flow field around the NACA0012 airfoil revealed the absence of areas of accidental triggering in the case of using the modified version of the limiter function.

In [3], Zhang and Wu simulated the expansion problem and used the characteristic directions of wave propagation and determined three zones—the U-zone, the M-zone, and the D-zone—within which the characteristics of pressure fluctuations exhibit different behavior in the boundary layer. The D-zone was defined as being located downstream of the first family characteristic line passing through the corner. The U-zone was defined as being located upstream of the second family characteristic line passing through the corner. The middle zone (M-zone) was defined as the zone between the U-zone and D-zone. The results of numerical analysis through the Detached Eddy Simulation (DES) made it possible to reveal this difference in behavior of pressure fluctuations. In addition, it was found that in the M-zone, the spatial distributions of fluctuation properties can differ at different levels, which, in the opinion of the authors, is explained by the action of the feedback mechanism.

The study by Gueraiche et al. [4] aimed to research the flight stability of an aircraft with a light box wing and a pusher propeller in the rear fuselage. New solutions were proposed, which included the use of a propeller in a fairing and several configurations of small vertical stabilizers in combination with vortex generators on the surface of the fuselage. Experiments were carried out in a wind tunnel, the results of which were confirmed by CFD modeling. Thus, the dynamics of the flow were explained for each of the proposed solutions. It was shown that effect of the expansion angle on pressure fluctuations is an important issue in supersonic flow around high speed vehicles.

Currently, non-mechanical control of highspeed flows is a widely studied research topic, both experimentally and numerically. The studies in [5,6] are devoted to this topic. The research in [5] by Azarova and Kravchenko focuses on the investigation, based on the Navier–Stokes equations, of the effect of the thermally stratified energy deposition in front of the bow shock wave (SW) in the supersonic flow created by an aerodynamic (AD) body in air. A new multi-vortex mechanism for the impact of a stratified energy source on a supersonic flow/flight is described, which is due to the multiple manifestation of the Richtmyer–Meshkov instabilities. Flow regimes are obtained for which almost complete destruction of the bow SW in the density field occurs due to the multiple generation of this instability. It is also shown that, by changing the temperature in the layers of a stratified energy source, it is possible to influence the drag forces of the AD body and ensure the emergence and change in the magnitude of the lift (pitch) force. Thus, the basic principles for controlling non-stationary high speed flows using stratified energy sources were established.

The research in [6] by Znamenskaya et al. is devoted to the experimental and numerical investigation of the influence of a high-energy plasma formation (plasmoid) on the supersonic flow past a blunt body. The experimentally obtained series of Schlieren patterns of the unsteady interaction of the bow SW with explosive waves is compared with the results of modeling the flow dynamics based on the Euler equations. A qualitative agreement between the calculated flow patterns and the experimental ones is shown. Based on this comparison, the dynamics of the shock-wave structure caused by the interaction of the bow SW and the blast flow were studied, and a scheme was constructed for the initiation and dynamics of the generated SWs and contact discontinuities. A significant drop in drag force and stagnation pressure (up to 80%) was obtained, and the dynamics of the zone of low density and high gas temperature was studied. The dynamics of the drag forces of the front surface were also considered for various values of the plasmoid energy.

The construction of a supersonic wind tunnel facility, as well as the development of supersonic nozzles and synthetic jets are studied in [7,8,9]. The aim of the study in [7] by Andrews et al. is to characterize the flow in the SBR-50 facility (University of Notre Dame, Notre Dame, IN, USA) containing a supersonic shock tube to study the dynamics of gas temperature. Using thermocouple measurements and laser spark velocimetry, a detailed set of gas parameters along the entire length of the pipe was obtained, which was compared with 3D modeling based on the Navier–Stokes equations. This study proved that the original scheme of the experimental setup allows longer operation with a constant stagnation temperature.

The application of the Shock Vector Control (SVC) approach to an axisymmetric supersonic nozzle was numerically investigated by Resta et al. [8]. In the SVC method, the injection of a secondary air stream creates an asymmetrical pressure distribution on the wall. Forcing the SVC axisymmetric nozzle created fully three-dimensional flows that interact with the external flow. Experimental data on a nozzle designed and tested for a passenger supersonic aircraft were used to validate numerical software at various flight Mach numbers and nozzle pressures. Then, as a result of the fully 3D flow simulations, the optimal position of the slot was found at the Mach number M = 0.9 for various values of SVC forcing.

In [9], Pellessier et al. investigated several methods for visualization of pulsed synthetic jets for cooling applications. The visualization techniques under consideration include smoke, Schlieren imaging, and thermography. The Schlieren images were analyzed using Proper Orthogonal Decomposition (POD) and numerical methods for processing the videos. The results showed that for the particular nozzle under study, the optimal cooling occurs at a frequency of 80 Hz. It was shown that the combination of Schlieren visualization and POD is a unique method for optimizing synthetic jets.

For a long time, a particularly wide research area in the study of high speed flows has been the dynamics of the interaction of SWs with other SWs, barriers, boundary layers, and inhomogeneities of the medium (vortices, simple waves, and rarefaction waves). In this Special Issue, this topic is touched upon in [10,11], where the Mach reflection of SWs and shock–vortex interactions are studied. The Mach stem arises as an additional SW in the SW reflection of the Mach type in a steady supersonic flow. In [10], Bai and Wu showed that the normalized length of a Mach stem is almost linear with respect to the normalized wedge trailing edge height, which was justified by the theoretical analysis. This result gives the possibility to obtain analytical models for expression of the length of a Mach stem through the flow parameters.

In [11], Skews presented the results of experimental studies of shock-vortex interactions accompanied by the numerical simulations. In the experiments, the vortex is formed due to flow separation from the corner and is accompanied by the appearance of a shear layer; next, the SW is diffracted at the edge. A review of the results of various experiments is presented, in which two independent SW reach the corner at different times, the diffracting SW is reflected from different surfaces back into the vortex, and the flow around bends is studied, where the SW is reflected from the far wall back into the vortex. In most cases it was obtained that the vortex retained its integrity after passing through a SW. Some studies with curved SWs showed signs of the decay of a vortex and development of turbulent spots, as well as a significant change in the vortex shape.

The papers [12,13] are devoted to new directions of using the concept of solid media and fluid description for modeling the gas dynamics of solid and fluid substances. A paper [12] by Sposobin and Reviznikov is devoted to numerical simulation of the gas-dynamic interaction of solid particles with the shock layer; in particular, the heat transfer by high-inertia particles. The particles rebound from the surface and destroy the bow SW front, which changes the structure of the whole flow. It is shown that by the successive action of particles, the impact jet flowing onto the surface is generated. In the impact jet, the values of pressure and heat flux are increased, which is the reason for the effect obtained.

The flooding of railway ballasts has been the subject of several experimental investigations. In [13], Alrdadi and Meylan presented the results of numerical simulation of two experiments on the flooding of railway ballast. The fluid flow is modelled by Darcy’s law, which the authors extend to the free fluid flowing above the ballast. The equations are solved using the finite element method. The results of numerical calculations were compared with the experimental ones reported in the literature and a good agreement was demonstrated. The method was then extended, taking into account the realistic railway ballast.

Thus, the Special Issue “High Speed Flows” of the Fluids journal covers a wide variety of modern areas of experimental and numerical research into high speed flows of a solid medium, arising both in problems of internal and external gas dynamics as well as in some new practical problems.