The study is dedicated to the peculiarities of implementing the flux limiter of the flow quantity gradient when solving 3D aerodynamic problems using the system of Navier–Stokes equations on unstructured meshes. The paper describes discretisation of the system of Navier–Stokes equations on a finite-volume method and a mathematical model including Spalart–Allmaras turbulence model and the Advection Upstream Splitting Method (AUSM+) computational scheme for convective fluxes that use a second-order approximation scheme for reconstruction of the solution on a facet. A solution of problems with shock wave structures is considered, where, to prevent oscillations at discontinuous solutions, the order of accuracy is reduced due to the implementation of the limiter function of the gradient. In particular, the Venkatakrishnan limiter was chosen. The study analyses this limiter as it impacts the accuracy of the results and monotonicity of the solution. It is shown that, when the limiter is used in a classical formulation, when the operation threshold is based on the characteristic size of the cell of the mesh, it facilitates suppression of non-physical oscillations in the solution and the upgrade of its monotonicity. However, when computing on unstructured meshes, the Venkatakrishnan limiter in this setup can result in the occurrence of the areas of its accidental activation, and that influences the accuracy of the produced result. The Venkatakrishnan limiter is proposed for unstructured meshes, where the formulation of the operation threshold is proposed based on the gas dynamics parameters of the flow. The proposed option of the function is characterized by the absence of parasite regions of accidental activation and ensures its operation only in the region of high gradients. Monotonicity properties, as compared to the classical formulation, are preserved. Constants of operation thresholds are compared for both options using the example of numerical solution of the problem with shock wave processes on different meshes. Recommendations regarding optimum values of these quantities are provided. Problems with a supersonic flow in a channel with a wedge and transonic flow over NACA0012 airfoil were selected for the examination of the limiter functions applicability. The computation was carried out using unstructured meshes consisting of tetrahedrons, truncated hexahedrons, and polyhedrons. The region of accidental activation of the Venkatakrishnan limiter in a classical formulation, and the absence of such regions in case a modified option of the limiter function, is implemented. The analysis of the flow field around a NACA0012 indicates that the proposed improved implementation of the Venkatakrishnan limiter enables an increase in the accuracy of the solution. Full article

This study aimed to explore the directional stability issues of a previously studied light box-wing aircraft model with a pusher propeller engine in the fuselage aft section. Earlier configurations have included the use of fuselage together with a lifting system consisting of two wings joined together at their wingtips with vertical stabilizers. However, these side vertical surfaces failed to provide the aircraft with sufficient directional stability, thus prompting the quest in this study for novel solutions that would exclude the need for a fuselage extension and a typical fin. Solutions included the use of a ducted propeller and few configurations of small “fishtail” vertical fins, which formed part of the aft fuselage itself and coupled with vortex generators on the fuselage surface to improve their interference and heal flow separation at the fuselage aft cone. The results of wind tunnel testing were supported with CFD simulations to explain the flow behavior of each of the studied solutions. Tuft visualization and computed flow patterns allowed identification of the sources of the observed low efficiency in terms of directional stability of the fishtail against a simple idle duct without a propeller. A final configuration with a duct and a modified version of the fuselage fins was achieved that provides enough yaw stability margins for a safe flight. Full article

This study focused on the development of the unsteady impact of a thermally stratified energy source on a supersonic flow around an aerodynamic (AD) body in a viscous heat-conducting gas (air). Research was based on the Navier-Stokes equations. The freestream Mach number was 2. A new multi-vortex mechanism of the impact of a time-limited stratified energy source on the aerodynamic characteristics of a body was described. Almost complete destruction of the bow shock wave in the density field, due to the multiple generation of Richtmyer-Meshkov instabilities in the region of a stratified energy source, was obtained. The dependences of the dynamics of frontal drag and lift forces of a streamlined body on temperature in the source layers were studied. It was determined that, by changing the temperature in the layers of a stratified energy source, it was possible to obtain more intense vortices accompanying the Richtmyer-Meshkov instabilities, causing a temporary decrease in the drag force of an AD body and ensuring the emergence and unsteady change in the magnitude of the lift (pitch) forces. The main principles of unsteady flow control using a stratified energy source were established. Full article

The supersonic wind tunnel facility SBR-50 at the University of Notre Dame was built in 2015 for experimental research related to shock wave (SW) interactions with obstacles and boundary layers (BL) as well as supersonic combustion and a plasma-based flow control. Currently, the facility provides the following range of flow parameters with a test section area at the nozzle exit of 76.2 × 76.2 mm: Mach number $M=2$ and 4, total pressure $p_0=$ 1–4 bar, stagnation temperature $T_0=$ 300–775 K, and typical duration of the steady-state flow $t=$ 0.5–2 s. One distinct feature of the facility is the Ohmic gas heater installed in a long plenum section. Objective of this study is to characterize flow in the SBR-50 facility, specifically the dynamics of the gas temperature. Two measuring methods were applied for collection of a detailed dataset: thermocouple measurements and schlieren-based thermal mark (laser spark) velocimetry. The experimental data are compared with 3D Navier–Stokes modelling of the gas parameters over the entire flowpath. Particularly, this study proves that the original facility schematics (the concept of a virtual piston in the plenum) allow for a longer operation with a constant stagnation temperature compared to a constant plenum volume with adiabatic cooling of the stored gas. Full article

The flooding of railway ballasts can cause extensive damage. This process has been the subject of several experimental investigations. In the present work, a relatively easy to implement approach to modelling this fluid flow is presented. It is shown that good agreement with the experimental results is obtained. The fluid flow is modelled by Darcy’s law, which we extend to the free fluid flowing above the ballast. The main complexity is in determining the free surface position, which is accomplished using an iterative procedure. The equations are solved using the finite element method. The method is illustrated by careful numerical calculations that are carefully compared with the experimental results reported in the literature. The method is then extended to realistic railway ballast, including the effects of ballast fouling. It is shown that when the flow begins to overtop the ballast, the free surface shifts to greatly increase the chance of ballast scouring. Full article

The recent revival of interest in developing new hypersonic vehicles brings attention to the need for accurate prediction of hypersonic flows by computational methods. One of the challenges is prediction of aerothermodynamic loading over the surface of the vehicles. Reynolds Average Navier-Stokes (RANS) methods have not shown consistent accuracy in prediction of such flows. Therefore, new methods including Large Eddy Simulations (LES) should be investigated. In this paper, the LES method is used for prediction of the boundary layer over a flat plate. A new recycling-rescaling method is tested. The method uses total enthalpy and static pressure along with the velocity components to produce the best results for the Law of the Wall, turbulent statistics and turbulent Prandtl number. Full article

The application of the Shock Vector Control (SVC) approach to an axysimmetric supersonic nozzle is studied numerically. SVC is a Fluidic Thrust Vectoring (FTV) strategy that is applied to fixed nozzles in order to realize jet-vectoring effects normally obtained by deflecting movable nozzles. In the SVC method, a secondary air flow injection close to the nozzle exit generates an asymmetry in the wall pressure distribution and side-loads on the nozzle, which are also lateral components of the thrust vector. SVC forcing of the axisymmetric nozzle generates fully three-dimensional flows with very complex structures that interact with the external flow. In the present work, the experimental data on a nozzle designed and tested for a supersonic cruise aircraft are used for validating the numerical tool at different flight Mach numbers and nozzle pressure ratios. Then, an optimal position for the slot is sought and the fully 3D flow at flight Mach number $M_{\infty }=0.9$ is investigated numerically for different values of the SVC forcing. Full article

This work explores several low-cost methods for the visualization and analysis of pulsed synthetic jets for cooling applications. The visualization methods tested include smoke, Schlieren imaging, and thermography. The images were analyzed using Proper Orthogonal Decomposition (POD) and numerical methods for videos. The results indicated that for the specific nozzle studied, the optimal cooling occurred at a frequency of 80 Hz, which also corresponded to the highest energy in the POD analysis. The combination of Schlieren photography and POD is a unique contribution as a method for the optimization of synthetic jets. Full article

One of the most important and complex effects associated with the presence of particles in the flow is the gas-dynamic interaction of particles with the shock layer. Of particular interest is the intensification of heat transfer by high inertia particles rebounding from the surface or by the products of erosion destruction, which reach the front of the bow shock wave and violate the gas-dynamic structure of the flow. In this case, according to experimental data, the increase in heat fluxes is much greater than it could be predicted based on the combined action of the kinetic energy of particles and a high-speed flow. The problem is related to the destruction of the flow structure. In this paper, the problem is studied with numerical simulation. We show that the key role in the intensification of heat transfer is played by the formation of an impact jet flowing onto the surface. An area of increased pressure and heat flux is formed in the zone of action of the impact jet. This effect is maintained over time by the successive action of particles. Full article

The paper is devoted to the experimental and CFD investigation of a plasma formation impact on the supersonic flow over a body “blunt cone-cylinder”. In the experiments, a series of schlieren pictures of bow shock wave–blast waves non-stationary interaction was obtained with the use of high speed shadowgraphy. The accompanying calculations are based on the system of Euler equations. The freestream Mach number is 3.1. The plasmoid is modeled by the instantaneous release of energy into a bounded volume of gas, increasing the pressure in the volume. The research of the dynamics of a shock wave structure caused by the bow shock wave and blast flow interaction has been conducted. The significant value of energy released to a supersonic flow (500J) allowed constructing a diagram of the generation and dynamics of the resulting shock waves and contact discontinuities, as well as obtaining a significant drop in the drag force and stagnation pressure (up to 80%). The dynamics of a low density and high gas temperature zone, which becomes the main factor reducing the frontal body drag force, was researched. The dynamics of the front surface drag forces have been studied for different values of the plasmoid energy as well. Qualitative agreement of the numerical flow patterns with the experiment ones has been obtained. Full article

The Mach stem height is an important parameter in the Mach reflection of steady supersonic flow. Various experimental, numerical, and theoretical works have been conducted to study this parameter in the past. However, much of the established work focuses around a single set of trailing edge heights. Here, we perform a study to show the dependence of Mach stem height on the trailing edge height for a wider range of geometry. Through numerical simulation for a set of trailing edge heights, we found that the normalized Mach stem height is almost linear with respect to the normalized wedge trailing edge height. The parameter used for normalization can be either the inlet height or the length of the lower wedge surface. The observation of this linear trend is justified through a simplified analysis, which leads to an expression of the Mach stem height that linearly depends on the trailing edge height. The present study extends our knowledge about how the geometry affects the Mach stem height, and provides a basis for future work to elaborate analytical models for Mach stem height. Full article

Studies of shock-vortex interactions in the past have predominantly been numerical, with a number of idealizations such as assuming an isolated vortex and a plane shock wave. In the present case the vortex is generated from flow separation at a corner. A shear layer results which wraps up into a spiral vortex. The flow is impulsively initiated by the diffraction of a shock wave over the edge. The strength of the shock determines the nature of the flow at the corner and that induced behind the diffracted wave. A wide variety of cases are considered using different experimental arrangements such as having two independent shock waves arriving at the corner at different times, to reflecting the diffracting wave off different surfaces back into the vortex, and to examining the flow around bends where the reflection off the far wall reflects back onto the vortex. The majority of studies have shown that the vortex normally retains its integrity after shock transit. Some studies with curved shock waves and numerous traverses have shown evidence of vortex breakup and the development of turbulent patches in the flow, as well as significant vortex stretching. Depending on the direction of approach of the shock wave it refracts through the shear layer thereby changing the strength and direction of both. Of particular note is that the two diffracted waves which emerge from the vortex as the incident wave passes through interact with each other resulting in a pressure spike of considerable magnitude. An additional spike is also identified. Full article

The influence of the expansion corner on pressure fluctuation is an important subject in supersonic flow around high-speed vehicles. Past studies have clarified how the expansion corner alters the root-mean-square of the fluctuating pressure coefficient ($C{p}_{rms}$) and the power spectral density (PSD) without considering how these fluctuating properties are related to compressible waves. In this paper, we use characteristics to determine the direction of wave propagation and identified three zones—U-zone, M-zone and D-zone—within which both $C{p}_{rms}$ and PSD are likely to display different behaviors across the boundary layer. The U-zone is upstream of the characteristic line of the second family and passing through the corner. The D-zone is downstream of the characteristic line of the first family and passing through the corner. The middle zone lies between the U-zone and D-zone. The results of $C{p}_{rms}$ and PSD at different layers within the boundary layer are obtained using numerical computation through a Detached Eddy Simulation (DES). It is found that in the U-zone and D-zone, both $C{p}_{rms}$ and PSD are the same in different layers within the boundary layer. In the M-zone, however, both $C{p}_{rms}$ and PSD may vary in different layers and this variation occurs in the high-frequency band upstream of the corner and mid-frequency band downstream of the corner. A feedback mechanism is tentatively used to explain the difference of spatial distribution of fluctuation properties inside the M-zone. Full article