Supersonic Mach Numbers Research Articles

Supersonic turbulence simulations with GPU-based high-order Discontinuous Galerkin hydrodynamics

ABSTRACT We investigate the numerical performance of a Discontinuous Galerkin (DG) hydrodynamics implementation when applied to the problem of driven, isothermal supersonic turbulence. While the high-order element-based spectral approach of DG is known to efficiently produce accurate results for smooth problems (exponential convergence with expansion order), physical discontinuities in solutions, like shocks, prove challenging and may significantly diminish DG’s applicability to practical astrophysical applications. We consider whether DG is able to retain its accuracy and stability for highly supersonic turbulence, characterized by a network of shocks. We find that our new implementation, which regularizes shocks at subcell resolution with artificial viscosity, still performs well compared to standard second-order schemes for moderately high-Mach number turbulence, provided we also employ an additional projection of the primitive variables on to the polynomial basis to regularize the extrapolated values at cell interfaces. However, the accuracy advantage of DG diminishes significantly in the highly supersonic regime. Nevertheless, in turbulence simulations with a wide dynamic range that start with supersonic Mach numbers and can resolve the sonic point, the low-numerical dissipation of DG schemes still proves advantageous in the subsonic regime. Our results thus support the practical applicability of DG schemes for demanding astrophysical problems that involve strong shocks and turbulence, such as star formation in the interstellar medium. We also discuss the substantial computational cost of DG when going to high order, which needs to be weighted against the resulting accuracy gain. For problems containing shocks, this favours the use of comparatively low DG order.

Numerical Analysis of Small Caliber Spinning Projectile with Variety Boattail Configurations

Range extension has received great interest in the field of artillery and spinning projectiles. Reducing base drag is an effective way for rang extension, because it is a major component in transonic and supersonic Mach numbers. Boattailing is considered as one of the most implemented techniques to reduce base drag. This work uses variety of passive drag reduction techniques over M33 .50cal projectile. Multiple design variations on projectile boattail are considered. This includes varying boattail angle, use of riblets, and use of arced boattail. Computations are conducted using computational fluid dynamics by solving RANS equations. Simulations are performed over Mach numbers from 0.6 to 2.5. The aim of the simulations is to calculate most affecting aerodynamic forces and moments which include drag force, lift force, Magnus force, Magnus moment, overturning moment, and spin damping moment. Then these coefficients are compared for all design variations. Results are validated by comparing with experimental and numerical results from the literature. Furthermore, a mesh independence study is done for verification. It was found that every configuration has good performance at a certain speed range with regard to zero yaw drag and significant yaw drag reduction for riblets boattail for low supersonic speeds.

Dynamically Linearized Time-Domain Approach for Limit-Cycle Oscillation Prediction for an Elastic Panel

A nonlinear aeroelastic model for a flexible panel is extended to consider the Euler equation as the aerodynamic model. A highly efficient method is presented to compute the generalized aerodynamic forces from a CFD simulation, and the results are compared to those results previously obtained using full potential flow aerodynamics and the linear piston theory. The flutter onset condition as well as limit cycle oscillation amplitudes are computed for a range of supersonic Mach numbers. Additionally, the effects of a shock wave and a viscous boundary layer (Reynolds-averaged Navier–Stokes) are considered in the computational fluid dynamics simulation and are implemented in the aeroelastic model via the generalized aerodynamic force obtained by the new approach. Conclusions are made based on the use and application of this more complete aerodynamic theory, including cases with shock impingement and near-transonic Mach numbers.

Linear stability analysis of compressible boundary layer over an insulated wall using compound matrix method: Existence of multiple unstable modes for Mach number beyond 3

The linear spatial stability of a parallel two-dimensional (2D) compressible boundary layer on an adiabatic plate is investigated by considering both 2D and three-dimensional (3D) disturbances. The compound matrix method is employed here, for the first time, for compressible flows, which, unlike other conventional techniques, can efficiently eliminate the stiffness of the equations governing the spectral amplitudes. The method is first validated with published results in the literature corresponding to spatial and temporal instability of flows ranging from low subsonic to high supersonic Mach numbers (M), which shows a good match depending upon the proper choice of free-stream temperature and the wall dispersion relation. Subsequently, flow compressibility effects and the spanwise variation of disturbances are also investigated for M ranging from low subsonic to high supersonic cases (from M = 0.1 to 6). Mack (AGARD Report No. 709, 1984) reported the existence of two unstable modes for M > 3 from viscous calculations (the so-called “second mode”) that subsequently fuse to create only one unstable zone when M increases. Our calculations show a series of higher-order unstable modes for M > 3 in addition to the findings of Ma and Zhong [“Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions,” J. Fluid Mech. 488, 31–78 (2003)], where such higher-order modes for supersonic boundary layers are all noted to be spatially stable. The number and the frequency extent of the corresponding unstable zones increase with an increase in M beyond 3 while propagating downstream at a higher speed than those corresponding to incompressible, subsonic, and low supersonic (M < 2) cases.

Reducing aerodynamic drag and heat generation in parabolic nose cones using single and double-disc tapered spikes

This numerical study investigates the use of aerospike designs on the noses of supersonic vehicles to reduce drag and heat loads. Various configurations, including single and double hemispherical spikes, as well as flat disk taper spikes, are analyzed at zero-degree attack angles. When attached to a parabolic nose cone, aerospikes significantly modify aerodynamic drag. The study examines supersonic Mach numbers (3–5.8) to identify geometries that minimize heating and drag. Velocity vectors show recirculation zones, while Mach number contours illustrate bow shock shapes for different spikes. Results reveal that double disk tapered spikes outperform single disk tapered spikes in reducing heating and drag. Specifically, the “double flat disks taper spike parabolic nose cone” configuration achieves the lowest surface heat flux and aerodynamic drag coefficient, demonstrating beneficial flow and shock features near the base. Compared to SHTA, using DFDTS reduces pressure and total drag by 25% and heat flux by 52%.

Off-design analysis of the inverted Brayton cycle engine

PurposeThe purpose of this study is to perform an off-design analysis of the inverted Brayton cycle engine.Design/methodology/approachThe off-design analysis equations of the inverted Brayton cycle engine were first derived in this study and the control parameters of the inverted Brayton cycle engine were first determined and investigated.FindingsIt is observed that by controlling the total temperature decrease in cooling section, it is possible to adapt the engine for low specific fuel consumption working conditions or high thrust working conditions. Specific fuel consumption is reduced by 27.1 % by stopping cooling in the cooling section and thrust is increased by 27.6 % by working with full load of the cooling section (500 K temperature decrease in cooling section). It is observed that thrust depending on the flight Mach number increases with an increase in flight Mach number and reaches a peak value at 5.21 flight Mach number and reduces by 80.8 % at 6 flight Mach number relative to the peak value. The specific fuel consumption increases rapidly as the Mach number increases, and the specific fuel consumption is 49.0 g/[kN.s] at Mach 1, reaches 70.4 g/[kN.s] at Mach 5 and increases to 412 g/[kN.s] at Mach 6. The specific fuel consumption increases from 68.1 to 73.0 g/(kN.s) and the thrust decreases from 16.5 to 13.3 kN as the total preburner exit temperature increases from 1,500 to 2,000 K. Specific fuel consumption decreases from 83.1 to 64.8 g/(kN.s) and thrust increases from 4.60 to 11.08 kN depending on afterburner exit total temperature increase from 1,800 to 2,500 K.Research limitations/implicationsThe cooling section reduces total temperature of the gas flow to lower values to increase the compressor total pressure ratio. The compressor increases the total pressure of the gas flow to the optimum total pressure ratios to increase the nozzle exit Mach number and gain more thrust. The afterburner increases the total temperature of the gas flow to increase the sound speed in the nozzle exit to increase thrust. The nozzle expands the gas flow to reduce the static pressure of the gas flow to near the optimum value, atmosphere pressure, to increase thrust and reduce specific fuel consumption.Practical implicationsHypersonic and supersonic air vehicles can use the current engine model for the its own propulsion systems.Social implicationsAfter first heavier than air flight, aero engines was designed for only used for aero vehicle. Internal combustion engines were used for propelled propeller aircraft at the first term of aircraft. However, propeller-propelled aircrafts are not sufficient to increase aircraft velocity to supersonic Mach numbers due to the shock losses of propeller, so the supersonic era was only introduced by revolution in propulsion systems with new concept. A jet engine was developed to be candidate for supersonic flight.Originality/valueOff-design analysis equations of an inverted Brayton cycle engine were first derived in this study. Furthermore, the control parameters of the inverted Brayton cycle engine were first determined and investigated in this paper.

PIV And Schlieren Measurements Of A Linear Plug Nozzle Jet Interacting With External Flow

Plug nozzles represent a promising concept as part of a propulsion system for space launchers. The ability to adapt the nozzle jet to the ambient pressure level improves thrust performance in overexpanded operating conditions compared to conventional bell nozzles. In this study, the dynamics of a jet flow of a cold air plug nozzle model are investigated by means of PIV and high-speed schlieren measurements. For a fixed nozzle pressure ratio, the jet flow is studied in an externalouter flow environment with sub-, trans-, and supersonic Mach numbers. The effect of plug truncation is analyzed as well. It is found that the outer Mach number strongly influences the flow pattern, local velocity magnitudes and aerodynamic modes. The frequency and dominance of vortex shedding and jet screeching modes are found to be highly dependent on the Mach number of the surrounding flow. A truncated plug introduces local accelerations in its base wake region, causing an increased shock strength in the jet structure. In addition,it causes severe periodic fluctuations in the flow that are transmitted to the shear layer and induce acoustic wave emissions. The impact of the plug length on the flow dynamics has been seen to decrease with increasing outer Mach number.

Influence of Sweep Angle on the Surface Pressure of Delta Wing Along Pivot Positions at Hypersonic Mach Numbers

Influence of Sweep Angle on the Surface Pressure of Delta Wing Along Pivot Positions at Hypersonic Mach Numbers

Nonlinear scaling of fluctuation kinetic energy for shock–vorticity wave interaction

Turbulent kinetic energy (TKE) is a quantity of primary importance in shock–turbulence interaction (STI). Linear interaction analysis (LIA) serves as a theoretical method to predict the amplification of TKE in STI. LIA is constrained by low-amplitude fluctuations and neglects nonlinear effects. In this paper, we explore the nonlinear amplification of the kinetic energy of fluctuations in the interaction between a vorticity wave and a shock wave that serves as a building block flow for STI. A weakly nonlinear framework (WNLF) is introduced to analyze nonlinear effects in fluctuation kinetic energy (FKE) and identify the dominant physical mechanisms driving its amplification. The theoretical framework is validated through high-accuracy numerical simulations of shock–vorticity wave interactions. The simulation results are compared with the predictions derived from the WNLF for a range of intensities and inclinations of shock-upstream vorticity fluctuations at different Mach numbers, and WNLF is found to successfully scale the numerical data for FKE, thus confirming the validity and applicability of the framework. According to WNLF findings, at lower supersonic Mach numbers, the intermodal interaction between vorticity–vorticity modes is important, whereas the interaction between vorticity and acoustic modes becomes dominant at higher Mach numbers. Using the intermodal interactions, a model based on WNLF is proposed to predict TKE amplification in STI. In comparison to direct numerical simulation, the WNLF based model predicts the TKE amplification for moderate turbulent Mach number and lower supersonic flow Mach numbers. This is a significant improvement over the LIA results available in the literature.

Simulation of supersonic axisymmetric base flow with a data-driven turbulence model

Axisymmetric base flow involves massive flow separation which is challenging for a typical Reynolds-averaged Navier-Stokes (RANS) turbulence model. Furthermore, a supersonic condition imposes additional difficulties to a turbulence model in predicting strong compressibility effects associated with the flow separation phenomena. A data-driven approach is pursued here to improve a turbulence model. The Spalart-Allmaras model is corrected from an optimization process, and then the model correction is mapped to local flow features through a machine learning process. For the optimization-combined machine learning method, the field inversion and machine learning framework is adapted here with three major modifications. First, a zonal-field inversion method is suggested to avoid the undesired modification of attached flow in the optimization process for the model correction. Second, the RANS model is modified by adjusting a net balance between the production and destruction terms in the RANS equation. Third, the local Mach number is included in the machine learning process to incorporate compressibility effects of the supersonic flow. The current study indicates that the improved RANS model reduces the eddy viscosity in the separated region, compared to the baseline RANS model. The reduction of the eddy viscosity helps to predict the base expansion of the supersonic flow and the size of the recirculation region. Current computations are compared with relevant literature data including wake velocity profiles and the base pressure in the wide range of the supersonic Mach number.

Aero-spike and aero-disk effects of on wave drag reduction of supersonic flow past over blunt body

PurposeThe purpose of this study is to explore the effects of aerospike and hemispherical aerodisks on flow characteristics and drag reduction in supersonic flow over a blunt body. Specifically, the study aims to analyze the impact of varying the length of the cylindrical rod in the aerospike (ranging from 0.5 to 2.0 times the diameter of the blunt body) and the diameter of the hemispherical disk (ranging from 0.25 to 0.75 times the blunt body diameter). CFD simulations were conducted at a supersonic Mach number of 2 and a Reynolds number of 2.79 × 106.Design/methodology/approachICEM CFD and ANSYS CFX solver were used to generate the three-dimensional flow along with its structures. The flow structure and drag coefficient were computed using Reynolds-averaged Navier–Stokes equation model. The drag reduction mechanism was also explained using the idea of dividing streamline and density contour. The performance of the aero spike length and the effect of aero disk size on the drag are investigated.FindingsThe separating shock is located in front of the blunt body, forming an effective conical shape that reduces the pressure drag acting on the blunt body. It was observed that extending the length of the spike beyond a specific critical point did not impact the flow field characteristics and had no further influence on the enhanced performance. The optimal combination of disk and spike length was determined, resulting in a substantial reduction in drag through the introduction of the aerospike and disk.Research limitations/implicationsTo predict the accurate results of drag and to reduce the simulation time, a hexa grid with finer mesh structure was adopted in the simulation.Practical implicationsThe blunt nose structures are primarily employed in the design of rockets, missiles, and re-entry capsules to withstand higher aerodynamic loads and aerodynamic heating.Originality/valueFor the optimized size of the aero spike, aero disk is also optimized to use the benefits of both.

Control of Nozzle Flow Using Rectangular Ribs at Sonic and Supersonic Mach Numbers

Control of Nozzle Flow Using Rectangular Ribs at Sonic and Supersonic Mach Numbers

Effect of Sweptback Angle of a Delta Wing on Surface Pressure Distribution at Supersonic Mach Numbers

Effect of Sweptback Angle of a Delta Wing on Surface Pressure Distribution at Supersonic Mach Numbers

Supersonic dusty gas flow past a cylinder in Eulerian–Lagrangian framework

The present study utilizes computational methods to analyze two-dimensional particle-laden flow over a circular cylinder. The effect of seeding of dust particles in the viscous flow of a compressible gas is analyzed. A new solver has been developed for the purpose of studying multi-phase flows in the supersonic regime. Most of the prior research has primarily focused on flows characterized by low Mach numbers and the absence of shock waves, and there have been very few studies dealing with supersonic dusty gas flows. This study considers a supersonic Mach number and investigates the effect of particle size and particle volume fraction on dusty-gas flow over a circular cylinder. The simulation results reveal that the seeding of particles in the flow creates perturbations. The present work also highlights the influence of particles on flow separation and the subsequent increase in the skin friction coefficient and coefficient of drag. The study shows that for supersonic flows, at the same volume fraction, larger particle size creates more instabilities in the flow, while smaller particles are responsible for increased drag on the cylinder, owing to a greater frequency of collisions.

Kinetic modeling of fluid-induced interactions in compressible, rarefied gas flows for aerodynamically interacting particles

In the study of gas-particulate multiphase systems, the flow of high-speed gas through a distribution of solid particulates is of utmost importance. While these aerodynamically interacting systems have been extensively studied for low-speed gas flows in the gas continuum regime, less attention has been given to high-speed systems where non-continuum effects are significant due to the high flow gradients. To address this, the flow of rarefied gas through an aerodynamically interacting monodisperse spherical particle system is studied using the Direct Simulation Monte Carlo (DSMC) gas-kinetic approach. Since the method provides the best resolution of shocks at supersonic Mach numbers it is used to classify the weak separated shocks and strong collective shocks in these systems based on particle spacing in a two-particulate system at different orientation angles. The study used the two-particle system to help analyze more complex particle distributions of volume fractions, 1%, 5%, and 15%, exposed to gas flows in the slip and transitional gas regime for a free-stream Mach number range of 0.2<Ma∞<2.0. We observe that the weak separated shocks in the 1% distribution allow a higher degree of gas penetration and shock-particle interactions or “hypersonic-surfing”, exposing a major fraction of the particulates to higher force magnitudes. In contrast, the strong collective shock in the 5% and 15% distributions only generates high particulate forces on the flow-facing particles. Finally, a simple stochastic model is proposed for use in large-scale Eulerian–Lagrangian simulations that captures the non-monotonic behavior of average drag and force variability generated by the complicated gas particulate interactions in the compressible gas regime.

Modelling the Wall Pressure Fluctuations on the VEGA-C Launcher in Supersonic Conditions

The prediction of pressure fluctuations generated over the external surface of aerospace launchers during the atmospheric flight remains a challenging task due to the complexity of the geometry and the effects of compressibility at high supersonic Mach numbers. An experimental database is here analysed to the scope of providing a procedure to model and predict the relevant statistics of the wall pressure fluctuations generated by a supersonic flow overflowing the VEGA-C Launcher Vehicle. Data have been obtained in an extensive Wind Tunnel test campaign carried out in the trisonic wind tunnel of the National Institute for Aerospace Research (INCAS) in Bucharest. Wall-mounted pressure transducers allowed for the computation of the pressure Auto- and Cross-spectra over the fourth (the payload region) and third stages of the launcher model. Coherence functions are modelled through exponential-like analytical functions following the approaches usually adopted in canonical boundary layer flows, whereas the auto-spectra models are based on polynomial fits. The approach adopted for the achievement of proper non-dimensional quantities as well as the procedure implemented for the full-scale extrapolation is presented and discussed.

Control of Base Pressure at Supersonic Mach Number in a Suddenly Expanded Flow

In improving the efficiency of applications for flow over a blunt body like missiles and rockets, passive and active control is used to increase the base pressure, hence reducing the base drag. It must be mentioned that this paper covers mainly a variety of passive control methods in the form of the cavity, rib, splitter plate, spike, and some others to regulate the base pressure and drag force. Later, this paper focuses on the control of base pressure in the form of the cavity at a Mach number of 2.2 and an area ratio of 4.84. In this experiment, Computational Fluid Dynamics (CFD) is used to model a convergent-divergent nozzle and a duct. The cavity’s dimensions and locations are studied to get the optimum cavity’s control of base pressure. Two sizes of the cavity are considered which are 3:3 and 6:3. The L/D is varied from 1, 2, 4, and 6 while the Nozzle Pressure Ratio (NPR) ranges from 3 to 16. The 2-D design of a convergent-divergent axisymmetric nozzle suddenly expanded into a duct with a diameter of 22 mm with and without annular rectangular cavities is sketched using ANSYS. The results show that the base pressure is greatly influenced by the cavity’s dimension and location as well as the NPR.

STAJe−: A Supersonic Flight Program STAJe− 1 Payload Design and System Study

The STAJe− flight program is the latest implementation of a university-based supersonic and hypersonic flight-test program. In the first flight, which is the subject of this study, the focus is on evaluating the suitability of commercial off-the-shelf electronic hardware, additively manufactured internal payload structures, and a long-range communications technique in the challenging environment presented by flight at high supersonic Mach numbers. These items can significantly reduce the cost of a flight experiment, and thus lower the threshold for flight experimentation. The scientific objectives of this flight are to collect pressure and temperature data on the whole trajectory to compare to numerical models, to optically measure the temperature of composite fins mounted on the payload, and to eject the flight module from the rocket assembly and track its location for subsequent recovery. Design calculations for the tracking system are presented alongside experimental results from ground tests demonstrating the suitability of the system. Furthermore, a one-dimensional calculation of the external wall temperatures over the trajectory is presented, which shows that internal systems are sufficiently protected from the harsh environment. Although the materials are shown to be appropriate for the flight, a layer of cork will be added to parts of the payload to further reduce the chance of structural failure. In addition, it is shown that a pneumatic ejection system is suited to overcoming the drag forces on the front of the rocket to initiate separation.

Drag Reduction of a Hemispherical Body Adopting Spike at Supersonic Speed

Use of spike on a hemispherical body changes the flow field and hence the aerodynamic drag. Experimental and computational studies have been made to obtain the flow field around a hemispherical body with spikes at a supersonic Mach number of 2. The effect of shape of spike tip and length has been studied. Experiments consisted of shadowgraph flow visualisation and measurement of drag. Computations have been made adopting structured grid and k-ω turbulence model using commercial software Fluent. It is observed that use of a sharp spike itself reduces the drag significantly. However the use of a hemispherical head spike further reduces the drag. Contribution of different components towards drag indicate that the increase in length of a spike do not change the spike contribution. However the flow field on main body is altered which leads to reduction in drag with change in length. Estimated drag generally found to be higher in comparison to measured value, however the trend is almost similar.

Experimental Evaluation of Isolated Intake for Hypersonic Air- Breathing Vehicle

Isolated intake of an air-breathing conceptual hypersonic demonstrator vehicle has been experimentally characterized simulating the entry Mach number and the entry flow direction. A 1:8 scale intake model having provision to vary the entry area of the internal compression portion by means of actuating the intake cowl has been tested in the supersonic freestream Mach numbers 3, 3.44 and 3.9. Tests were carried out in the 0.3 m x 0.3 m trisonic wind tunnel at National Aerospace Laboratories, Bangalore. The result pertaining to M¥ = 3.44 is discussed in this paper. The effect of cowl position on the intake starting characteristics and performance are analyzed using wall pressure measurements, schlieren and oil flow visualization. Intake unstart occurred before the cowl reaching to its fully open position with the original hinge location. Essentially the strength of cowl leading edge shock increases as the cowl opening angle increases. The strong shock-boundary layer interaction in the convergent portion of intake aids the growth of the separation bubble in the flow path and that cause the intake to unstart. Improvement of intake starting by means of shifting the cowl hinge location downstream was attempted. Shifting the cowl hinge location downstream has improved the intake starting characteristics. On the improved configuration, the effect of combustion induced back pressure and the effect of cowl opening speed on intake unstart have been analyzed and quantified.