Supersonic Flow Regimes Research Articles

Advanced Numerical Techniques for Supersonic Flow Analysis: From Euler Equations to Practical Applications in Aerospace and Turbomachinery Engineering

This paper explores advanced numerical techniques for analyzing supersonic flow, with a particular focus on the application of Euler equations in aerospace and turbomachinery engineering. Theoretical foundations such as boundary conditions, error evaluation, grid partitioning, and the Successive Over-Relaxation (SOR) method are thoroughly examined. Rigorous numerical simulations are conducted to investigate the final velocity field distribution and convergence characteristics under various conditions. The research underscores the precision and efficiency of these numerical methods, highlighting their practical applications in the aerodynamic design of aircraft and potential use in turbomachinery design. The findings contribute significantly to the advancement of computational fluid dynamics in supersonic flow regimes, providing valuable insights for engineers and researchers engaged in this specialized area. The study not only enhances understanding of complex flow dynamics but also supports the development of more effective engineering solutions in high-speed applications.

Research and Analysis of the Small Disturbance Equation in Subsonic, Transonic, and Supersonic Regimes

This paper explores the application of the Small Disturbance Equation (SDE) across subsonic, transonic, and supersonic flow regimes. Derived from the Euler and Navier-Stokes equations, the SDE offers an efficient framework for analyzing aerodynamic behaviors, particularly through the utilization of discretization techniques and iterative solving methods executed in Python. The study assesses the accuracy and limitations of the SDE in detailing essential flow characteristics, revealing that while the equation performs effectively in subsonic and transonic flows, it encounters challenges in supersonic regimes. Nonlinear effects such as shock waves significantly hinder its performance at high speeds. Compared with conventional computational fluid dynamics (CFD) methods, the SDE stands out in scenarios where computational efficiency is paramount. However, its limitations in handling high-speed flows must be carefully considered, highlighting the need for further refinement in its application to supersonic dynamics. This analysis suggests that while the SDE is beneficial for certain aerodynamic studies, its scope and utility are constrained by the inherent complexities of high-speed fluid dynamics.

Comparative Study on the Application Efficacy of Small Disturbance Equation versus One-Dimensional Euler Equation in Nozzle Flow Analysis

This paper presents a numerical simulation study of subsonic and supersonic nozzle flow regimes utilizing the Small Disturbance Equation (SDE), implemented through Python to analyze flow stability under various boundary conditions. The SDE, extensively applied in aerospace, meteorology, and fluid mechanics, offers a critical framework for examining aircraft stability and maneuverability, essential for ensuring flight safety. Additionally, its application extends to spacecraft stability and control in aerospace science. The findings from this study reveal that subsonic flows, characterized by their stability and smoothness, respond more predictably under varying boundary conditions compared to their supersonic counterparts. Conversely, supersonic flows demonstrate increased sensitivity to changes in boundary conditions, resulting in more complex flow patterns. This sensitivity underscores the need for precise control mechanisms in supersonic applications to maintain flow stability and ensure the safety and efficiency of aerospace operations. The simulations underscore the practical importance of the SDE in advancing the understanding of dynamic flow problems across different scientific and engineering disciplines.

The effects of Gurney flap on the aerodynamic characteristics of two airfoils in non-continuum regimes

Gurney flap is a simple and effective high-lift device that has the potential to reduce the takeoff-and-landing distance for transport aircraft. It is also a good option for enhancing the airfoil cruising characteristics. However, its effectiveness in non-continuum regimes has rarely been studied. The Unified Gas Kinetic Scheme algorithm, which is valid for all flow regimes, is further developed and used to simulate the flow field around a cambered airfoil and a high-speed quadrilateral airfoil with and without the Gurney flap in the supersonic non-continuum flow regimes. The distribution function shapes at different spatial locations are provided and analyzed. The effects of angle of attack, free-stream Knudsen number, free-stream Mach number, Gurney flap height, and Gurney flap mounting angle on the aerodynamic characteristics of the two airfoils are studied. The results show that the lift and drag of the airfoil with the attached Gurney flap are increased. The pressure rise on the lower surface of the airfoil is the primary factor contributing to the increase in lift. The overall increase in drag mainly comes from the Gurney flap, which also generates a small amount of negative lift. When the angle of attack is less than the critical angle of attack, the Gurney flap can increase the lift-to-drag ratio of the airfoil and improve its aerodynamic performance. The critical angle of attack decreases with the increase in the free-stream Knudsen number and the free-stream Mach number. It decreases with increasing Gurney flap height and increases with increasing Gurney flap mounting angle.

Aeroelastic analysis of a lightweight topology-optimized sandwich panel

Sandwich structures with lattice cores are novel, lightweight composite structures and are widely used in the aerospace industry. Besides, the aeroelastic behavior of sandwich panels in a supersonic flow regime still needs to be thoroughly studied. This work investigates the supersonic flutter of a sandwich panel whose core is topology-optimized. A finite element model of a sandwich panel based on the layerwise theory, coupled with the first-order piston theory, is presented. The sandwich panel core is assessed using a topology optimization approach with flutter loading constraints. The subsequent analytical homogenization scheme is developed to provide the equivalent mechanical properties of the topology-optimized panel. The modeling approach is fully validated, and the results demonstrate that the sandwich panel is capable of enlarging the flutter-free operational flight range when compared with other conventional panel designs. A parametric analysis of the topology-optimized sandwich panel regarding the critical flutter conditions is performed.

Influence of the shape of the anode assembly inner channel on plasma flow velocity

This article considers how the shape of the inner channel in the anode assembly affects plasma flow velocity in a plasma torch. Three different shapes of the anode assembly were analyzed, all with a conical confusor part of 50 mm in length: with a diameter transition from 12 to 6 mm, from 12 to 8 mm, and from 12 to 10 mm. A computer experiment was performed using the finite element method and then validated by the subsequent full-scale experiment on a laboratory plasma unit. The obtained results were verified. The verification outcomes showed a satisfactory convergence and were consistent with the published data. A review of the existing plasma unit designs for powder production, application of functional coatings, and surface modification was carried out. The software packages implementing the finite element method to solve these problems were examined. The study yielded practical recommendations for consumers and developers of plasma equipment and identified the shapes of the anode assembly enabling both supersonic and subsonic plasma flow regimes.

Experimental and numerical investigation of porous bleed control for supersonic/subsonic flows, and shock-wave/boundary-layer interactions

This paper presents a comprehensive experimental and numerical investigation into the control of boundary layers using porous bleed systems. The study focuses on both supersonic and subsonic flow regimes, as well as on the control of shock-wave/boundary-layer interactions. By simplifying this complex problem into two separate scenarios, the research establishes the necessity of individually characterizing bleed systems for both supersonic and subsonic flow regimes due to variations in the flow topology within the bleed holes. In supersonic conditions, a strong agreement between experimental and numerical results validates the effectiveness of porous bleed in controlling boundary layers. Notably, three-dimensional effects are experimentally demonstrated, and variations of the boundary-layer profiles along the span are the first time experimentally proven. The study extends its scope to subsonic flows, revealing that while boundary-layer bleeding enhances flow momentum near the wall, mass removal induces a decrease in momentum in the outer boundary layer and external flow. The research also explores shock-wave/boundary-layer interaction control, achieving a remarkable alignment between simulations and experiments. The findings endorse the use of Reynolds-Averaged Navier-Stokes simulations for studying porous bleed systems in various flow conditions, providing valuable insights to enhance bleed models, especially in the context of shock-wave/boundary-layer interaction control.

Overview of Computational Methods to Predict Flutter in Aircraft

Abstract Aeroelastic flutter is a dynamically complex phenomenon that has adverse and unstable effects on elastic structures. It is crucial to better predict the phenomenon of flutter within the scope of aircraft structures to improve the design of their wings. This review aims to establish fundamental guidelines for flutter analysis across subsonic, transonic, supersonic, and hypersonic flow regimes, providing a thorough overview of established analytical, numerical, and reduced-order models as applicable to each flow regime. The review will shed light on the limitations and missing components within the previous literature on these flow regimes by highlighting the challenges involved in simulating flutter. In addition, popular methods that employ the aforementioned analyses for optimizing wing structures under the effects of flutter—a subject currently garnering significant research attention—are also discussed. Our discussion offers new perspectives that encourage collaborative effort in the area of computational methods for flutter prediction and optimization.

Influence of the hydrogen transverse injection mode in a scramjet combustor performance

This paper focuses on the numerical investigation of the transverse hydrogen injection technique in the supersonic airflow on the combustor performance of a scramjet technological demonstrator developed at Universidade Federal do Rio Grande do Norte (UFRN). The UFRN's scramjet vehicle was designed to be fully operational at a hypersonic velocity of 2050 m/s (Mach number 6.8), at 30 km of altitude, which provided a temperature of 1156.95 K and supersonic velocity of 1414.39 m/s (Mach number 2.1), at the combustion chamber entrance. Hydrogen was transversally injected into supersonic airflow at a sonic speed of 1318.46 m/s. A set of 2D-RANS simulations of the reactive flow was performed in combination with a simplified chemical kinetics approach based on the finite-rate chemistry model, defined by a one-step global reaction based on Arrhenius expression to combustion modeling. The turbulence was modeled by the k-kl-ω transition model. Different transverse fuel injections with different dimensions and positioning of injectors were evaluated keeping the same inlet conditions: single-injection versus dual-injection modes. A detailed visualization of several flow phenomena, such as the formation of shock waves, and the performance combustion parameters on the combustor surface were discussed. The analyses indicated hydrogen combustion with a predominantly supersonic flow regime. The transversal injection caused the detachment of the boundary layer as indicated by the recirculation flow structures in the neighboring region next to the injectors. Flow analyses indicate that the purely oblique shock trains were established tending to redirect the airflow over the mixing layer and accelerate the hydrogen burning. Nevertheless, the results showed that this was a local effect since the downstream both mixing and combustion efficiency increased. The dual-injection mode proved to be a promising injection method due to the higher global fuel penetration, elevated from 27,9% to 33,8%, and higher combustion efficiency, increased from 10,33% to 21,99%, with reduced addition of total pressure loss, concerning the single-injection case. Additionally, the growth behavior of performance curves showed that an extension of the combustor downstream length can be indicated to maximize combustor performance.

Predicting wing-pylon-nacelle configuration flutter characteristics using adaptive continuation method

In this study, the aeroelastic response of a wing-pylon-nacelle system in subsonic and low supersonic flow regimes is analyzed using the continuation method in conjunction with an adaptive step size control algorithm. Idealizing the pylon and nacelle as a point mass, the computed effects of a standard structural analysis of the wing together with the pylon and nacelle are compared with those of a clean wing to build a reduced-order model for analysis. The aerodynamic forces relating to different reduced frequencies are assessed using the Doublet Lattice Method (DLM) in the subsonic flow regime and supersonic lifting surface theory relying on the unsteady linearized small-disturbance potential flow model in the low supersonic flow regime. The Rational Function Approximation (RFA) method is then utilized for the state-space formulation of the system equations, appended with the continuation method for flutter prediction. Thereafter, the linearized aeroelastic equations are resolved using the continuation method with adaptive step size, the results of which are matched with those obtained from the traditional p-k method to emphasize that the continuation method exhibits a distinct advantage in achieving better accuracy in estimating the flutter speed and identifying the “mode switching” phenomenon.

A GPU-Accelerated Particle Advection Methodology for 3D Lagrangian Coherent Structures in High-Speed Turbulent Boundary Layers

In this work, we introduce a scalable and efficient GPU-accelerated methodology for volumetric particle advection and finite-time Lyapunov exponent (FTLE) calculation, focusing on the analysis of Lagrangian coherent structures (LCS) in large-scale direct numerical simulation (DNS) datasets across incompressible, supersonic, and hypersonic flow regimes. LCS play a significant role in turbulent boundary layer analysis, and our proposed methodology offers valuable insights into their behavior in various flow conditions. Our novel owning-cell locator method enables efficient constant-time cell search, and the algorithm draws inspiration from classical search algorithms and modern multi-level approaches in numerical linear algebra. The proposed method is implemented for both multi-core CPUs and Nvidia GPUs, demonstrating strong scaling up to 32,768 CPU cores and up to 62 Nvidia V100 GPUs. By decoupling particle advection from other problems, we achieve modularity and extensibility, resulting in consistent parallel efficiency across different architectures. Our methodology was applied to calculate and visualize the FTLE on four turbulent boundary layers at different Reynolds and Mach numbers, revealing that coherent structures grow more isotropic proportional to the Mach number, and their inclination angle varies along the streamwise direction. We also observed increased anisotropy and FTLE organization at lower Reynolds numbers, with structures retaining coherency along both spanwise and streamwise directions. Additionally, we demonstrated the impact of lower temporal frequency sampling by upscaling with an efficient linear upsampler, preserving general trends with only 10% of the required storage. In summary, we present a particle search scheme for particle advection workloads in the context of visualizing LCS via FTLE that exhibits strong scaling performance and efficiency at scale. Our proposed algorithm is applicable across various domains, requiring efficient search algorithms in large, structured domains. While this article focuses on the methodology and its application to LCS, an in-depth study of the physics and compressibility effects in LCS candidates will be explored in a future publication.

Verification of a High-Order FEM-based CFD Code using the Method of Manufactured Solutions

A high-order computational fluid dynamics (CFD) code capable of solving compressible turbulent flow problems was developed. The CFD code employs the Flowfield Dependent Variation (FDV) scheme implemented in a Finite Element Method (FEM) framework. The FDV scheme is basically derived from the Lax-Wendroff Scheme (LWS) involving the replacement of LWS’s explicit time derivatives with a weighted combination of explicit and implicit time derivatives. The code utilizes linear, quadratic and cubic isoparametric quadrilateral and hexahedral Lagrange finite elements with corresponding piecewise shape functions that have formal spatial accuracy of second-order, third-order and fourth-order, respectively. In this paper, the results of observed order-of-accuracy of the implemented FDV FEM-based CFD code involving grid and polynomial order refinements on uniform Cartesian grids are reported. The Method of Manufactured Solutions (MMS) is applied to governing 2-D Euler and Navier-Stokes equations for flow cases spanning both subsonic and supersonic flow regimes. Global discretization error analyses using discrete 𝐿2 norm show that the spatial order-of-accuracy of the FDV FEM-based CFD code converges to the shape function polynomial order plus one, in excellent agreement with theory. Uniquely, this procedure establishes the wider applicability of MMS in verifying the spatial accuracy of a high-order CFD code.

Sulfur hexafluoride pulsed jet visualization by the Resonant Schlieren method

Resonant Schlieren technique combines the variation of the refractive index of the medium with the absorption of seeded particles, thus producing high contrast images. It presents low cost and a relatively easy implementation and operation, and allows visualization of low and high-density flows. This paper describes the application of the Resonant Schlieren method to visualize a pulsed free jet of sulfur hexafluoride. A piezoelectric valve with a duty cycle of 10 Hz and pulse width of 2 ms was used to control the flow through a nozzle with 1 mm diameter. Pressures in a vacuum chamber with optical windows were varied from 20 mbar to 1 bar and the flow was seeded with iodine molecules in order to increase the gas refractive index. The Schlieren images of the expanded flows presented a high contrast and the measured pulsed jet front velocities varied from 3 to 166 m/s, from subsonic to supersonic flow regimes. Numerical simulations were performed using the lattice Boltzmann method and the theoretical results showed a good agreement with experimental data.

Computational Analysis of Surface Pressure Distribution over a 2D Wedge in the Supersonic and Hypersonic Flow Regimes

The complex fluid-dynamic instabilities and shock waves occurring along the surface of a two-dimensional wedge at high values of the Mach number are studied here through numerical solution of the governing equations. Moreover, a regression model is implemented to determine the pressure distribution for various Mach numbers and angles of incidence. The Mach number spans the interval from 1.5 to 12. The wedge angles (θ) are from 5° to 25°. The pressure ratio (P2/P1) is reported at various locations (x/L) along the 2D wedge. The results of the numerical simulations are compared with the regression model showing good agreement.

Geometric Optimization of Blunt Bodies with Aerodisk and Opposing Jet for Wave Drag and Heat Reduction

The use of passive, active, or hybrid flow control techniques is often investigated to reduce the acoustic signature, wave drag, and aerodynamic heating associated with the supersonic flow regime. This research explores passive and hybrid flow control techniques to achieve an optimal reduction in wave drag and aerodynamic heating on a blunt body using an aerodisk. While passive techniques use one or two aerospikes, hybrid techniques employ opposing jets and aerospikes. Numerical analysis is performed using Reynolds-Averaged Navier–Stokes (RANS) equations to analyze the bodies’ flow field. The statistical technique, Design of Experiments (DOE), is combined with Response Surface Method (RSM) to find the optimal configuration for four cases by generating design space. Two cases were considered for the optimization: single aerospike with and without opposing jet and double aerospike with and without opposing jet. Variables used for the design of the aerodisks were spike length and diameter, while the response variables were wave drag and normalized heat flux. The current study has established an optimum relationship between spike length and aerospike diameter located in front of the main blunt body for both single and double aerospikes. The study’s results suggest that a double aerodisk configuration is more beneficial for reducing drag and heat flux at supersonic speed than a single aerodisk. By incorporating an opposing jet at a pressure ratio of 0.8 from the frontal aerodisk to the spiked blunt body, it can reduce drag and heat flux by 86% and 95%, respectively. Finally, numerical verification is performed for statistically optimized designs.

A Unified Asymptotic Theory of Supersonic, Transonic, and Hypersonic Far Fields

The problems of steady, inviscid, isentropic, irrotational supersonic plane flow passing a body with a small thickness ratio was solved by the linearized theory, which is a first approximation at and near the surface but fails at far fields from the body. Such a problem with far fields was solved by W.D. Hayes’ “pseudo-transonic” nonlinear theory in 1954. This far field small disturbance theory is reexamined in this study first by using asymptotic expansion theory. A systematic approach is adopted to obtain the nonlinear Burgers’ equation for supersonic far fields. We also use the similarity method to solve this boundary value problem (BVP) of the inviscid Burgers’ equation and obtain the nonlinear flow patterns, including the jump condition for the shock wave. Secondly, the transonic and hypersonic far field equations were obtained from the supersonic Burgers’ equation by stretching the coordinate in the y direction and considering an expansion of the freestream Mach number in terms of the transonic and hypersonic similarity parameters. The mathematical structures of the far fields of the supersonic, transonic, and hypersonic flows are unified to be the same. The similar far field flow patterns including the shock positions of a parabolic airfoil for the supersonic, transonic, and hypersonic flow regimes are exemplified and discussed.

ADAPTATIONS OF RESULTS OF EXPERIMENTAL QUALIFICATION OF PASSIVE SAFETY SYSTEMS OF NUCLEAR POWER PLANTS

Problems. An urgent issue of ensuring the safety of nuclear power plants is the adaptation of the results of experimental qualification of the fittings of passive safety systems in a single-phase environment to emergency conditions of two-phase flows. For most of the equipment of systems important for the safety of nuclear power plants, there is no principled possibility of qualification through direct tests in emergency conditions. The experience of operating nuclear power plants, as well as the results of simulations after design accidents, determined the possible inconsistency of the operating conditions of the fittings in emergency situations and in the modes of operational tests with a single-phase steam-gas environment.Thus, it is necessary to adapt the results of the experimental qualification of the fittings of the emergency steam and gas removal systems in a single-phase environment to the emergency conditions of two-phase flows. The aim of the study. The purpose of this article is sufficient justification of the adaptation of test results on a single-phase environment to the conditions of emergency processes with a two-phase environment. Methodology of implementation. To achieve the goals of the study, deterministic modeling of the conditions and criteria of operation/testing of valves of emergency steam and gas removal systems was used. Research results. T An analysis of the validity of the results of the experimental qualification was performed for the dynamic pressure pressure on the closing device in the test mode (single-phase flow mode) and the dynamic pressure pressure on the closing device in the emergency mode (two-phase flow mode). The adaptation of the results of the experimental qualification for closing the valves of the emergency steam and gas removal systems in a single-phase environment to the emergency conditions of two-phase flows was carried out under the conditions of subsonic and supersonic flow regimes. Conclusions. The conditions for adapting the results of the experimental qualification for closing the valves of the emergency vapor gas removal systems to the emergency conditions of subsonic and transonic flows of two-phase flow in the flow part of the valves have been determined. The dynamic pressure on the closing device of the valve in single-phase flows of operational tests and the dynamic pressure in two-phase flows of emergency modes are considered qualification criteria.

Fan Stability With Leading Edge Damage: Blind Prediction and Validation

Abstract This paper considers the impact of a damaged leading edge (LE) on the stall margin and stall inception mechanisms of a transonic, low-pressure ratio fan. The damage takes the form of a squared-off leading edge over the upper half of the blade. Full-annulus, unsteady CFD simulations are used to explain the stall inception mechanisms for the fan at low- and high-speed operating points. A combination of steady and unsteady simulations shows that the fan is predicted to be sensitive to leading edge damage at low-speed, but insensitive at high-speed. This blind prediction aligns well with rig test data. The difference in response is shown to be caused by the change between subsonic and supersonic flow regimes at the leading edge. Where the inlet relative flow is subsonic, rotating stall is initiated by the growth and propagation of a subsonic leading edge flow separation. This separation is shown to be triggered at higher mass flow rates when the leading edge is damaged, reducing the stable flow range. Where the inlet relative flow is supersonic, the flow undergoes a supersonic expansion around the leading edge, creating a supersonic flow patch terminated by a shock on the suction surface. Rotating stall is triggered by the growth of this separation, which is insensitive to the leading edge shape. This creates a considerable difference in sensitivity to damage at low- and high-speed operating points.

Dynamic stability analysis in sandwich composite laminated face structure with partially treated magnetorheological fluid-filled core

Sandwich composites with controllable cores have wide applications in aerospace structures. This paper presents a dynamic modeling and stability analysis of sandwich beams with a partially filled magneto-rheological (MR) fluid core covered by laminated composite face sheets in the supersonic flow regime. The equations of motion of the resulting system are formulated using energy expressions and the Hamilton principle. Finite element modeling is employed to solve the equations with different boundary conditions. Initially, free vibration analysis is performed and the effect of the magnetic field on the natural frequencies of the beam is reported. In order to minimize the weight, the magnetorheological fluid is filled at selected cells in the core layer. The locations and sizes of these cells affect the modal characteristics and flutter stability of the beam. Also, the impact of core layer thickness under different boundary conditions is studied. Furthermore, the influence of magnetic field on the critical pressure in supersonic flow regime is investigated using first-order piston theory to identify the unstable regions. The results revealed that the size and position of the MR section in the beam and the applied magnetic field strength drastically influence the natural frequencies of partially treated magnetorheological laminated sandwich beams. The influencing variables are identified from main-effect plots using analysis of variance study.

Nonlinear aeroelastic analysis of sandwich composite cylindrical panel with auxetic core subjected to the thermal environment

In this study, nonlinear aeroelastic instability of a composite sandwich panel subjected to a supersonic airflow and thermal loading is investigated. The sandwich panel is composed of three-phase composites with polymer/Graphene platelet/fiber skins at the top and bottom surfaces and an auxetic honeycombs core layer with a negative Poisson’s ratio. The motion equations of the panel within the framework of higher-order shear deformation theory (HSDT) and von Kármán nonlinearity are driven. In addition to Krumhaar’s modified supersonic piston, unsteady aerodynamic pressure in the supersonic flow regime is considered. The governing equations of the sandwich panel are derived by implementing Hamilton’s principle and solved by the generalized differential quadrature method (GDQM). Validation of the present formulation is assessed by comparing the numerical results with those available in the open literature. Then, the effects of several parameters such as geometric parameters, volume fraction, Mach number, different boundary conditions, yaw angle, and different inclined angles on the nonlinear aeroelastic stability of sandwich panels are examined. Finally, it was found that the ratio of core thickness, inclined angle, and Mach number have significant effects on aerodynamic pressure.