Supersonic Mach Numbers Research Articles

Breathing blunt-nose concept for drag reduction in supersonic flow

This paper presents the results and the physics behind the process which results in the reduction of pressure drag of blunt-nosed body by passive control in form of breathing nose at a supersonic Mach number. The drag of a blunt-nosed body with and without breathing nose at Mach 1.96 is compared. The breathing nose is found to reduce the drag on the body by manipulating the high pressure at the nose and the low pressure at the base simultaneously. The shock at the nose of the body becomes weaker when the hole at the nose is open. Direct measurement of drag and the pressure at the nose and at the surface downstream of the nose has been carried out. Flow field around the body with and without breathing nose has been visualized with shadowgraph. A maximum drag reduction of 21 per cent was obtained at NPR 2. This is because of the combined effect of the decrease of high pressure at the nose and increase of low pressure at the base, due to the breathing through the nose hole.

Characteristics of optimum power extraction in a MHD generator with subsonic and supersonic inlets

Analytical expressions for optimum power extracted in a MHD generator with constant channel width and constant electrical conductivity proposed by Neuringer was investigated for a range of subsonic and supersonic inlet Mach numbers. Characteristics of fluid-dynamical variables, optimum power extracted and the voltage drop in the external load were studied for a range of Mach numbers and interaction parameters. It was observed that the characteristics of voltage drop across the load with the interaction parameter differed significantly for subsonic and supersonic inlet Mach numbers. For each subsonic inlet Mach number, there exists a critical value of interaction parameter beyond which there is an abrupt change in terminal voltage, and fluid-dynamic variables. Also beyond this critical interaction parameter, the flow at the exit plane is choked. Supersonic inlets do not display the presence of such a critical interaction parameter or choking at the exit plane.

Single dielectric barrier discharge plasma enhanced aerodynamics: physics, modeling and applications

The term “plasma actuator” has been a part of the fluid dynamics flow control vernacular for more than a decade. A particular type of plasma actuator that has gained wide use is based on a single dielectric barrier discharge (SDBD) mechanism that has desirable features for use in air at atmospheric pressures. For these actuators, the mechanism of flow control is through a generated body force vector that couples with the momentum in the external flow. The body force can be derived from first principles and the plasma actuator effect can be easily incorporated into flow solvers so that their placement and operation can be optimized. They have been used in a wide range of applications that include bluff body wake control; lift augmentation and separation control on a variety of lifting surfaces ranging from fixed wings with various degrees of sweep, wind turbine rotors and pitching airfoils simulating helicopter rotors; flow separation and tip-casing clearance flow control to reduce losses in turbines, to control flow surge and stall in compressors; and in exciting instabilities in boundary layers at subsonic to supersonic Mach numbers for turbulent transition control. New applications continue to appear through programs in a growing number of US universities and government laboratories, as well as in Germany, France, England, Netherland, Russia, Japan and China. This paper provides an overview of the physics, design and modeling of SDBD plasma actuators. It then presents their use in a number of applications that includes both numerical flow simulations and experiments together.

Strong coupling strategy for fluid–structure interaction problems in supersonic regime via fixed point iteration

In this paper some results on the convergence of the Gauss–Seidel iteration when solving fluid/structure interaction problems with strong coupling via fixed point iteration are presented. The flow-induced vibration of a flat plate aligned with the flow direction at supersonic Mach number is studied. The precision of different predictor schemes and the influence of the partitioned strong coupling on stability is discussed.

Linear stability, transient energy growth, and the role of viscosity stratification in compressible plane Couette flow

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers (M). For a given M , the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, alpha ) of each mean flow belongs to different modes for a range of supersonic M . An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean flow to perturbations. It is shown that the energy transfer from mean flow occurs close to the moving top wall for "mode I" instability, whereas it occurs in the bulk of the flow domain for "mode II." For the nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, G(max), and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For alpha=0 , the linear stability operator can be partitioned into L ~ L+Re(2) L(p), and the Re-dependent operator L(p) is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t/Re) ~ Re(2). In contrast, the dominance of L(p) is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.

PKS B1545−321: bow shocks of a relativistic jet?

Sensitive, high resolution images of the double-double radio galaxy PKS B1545-321 reveal detailed structure, which we interpret in the light of previous work on the interaction of restarted jets with pre-existing relict cocoons. We have also examined the spectral and polarization properties of the source, the color distribution in the optical host and the environment of this galaxy in order to understand its physical evolution. We propose that the restarted jets generate narrow bow shocks and that the inner lobes are a mixture of cocoon plasma reaccelerated at the bow shock and new jet material reaccelerated at the termination shock. The dynamics of the restarted jets implies that their hot spots advance at mildly relativistic speeds with external Mach numbers of at least 5. The existence of supersonic hot spot Mach numbers and bright inner lobes is the result of entrainment causing a reduction in the sound speed of the pre-existing cocoon. The interruption to jet activity in PKS B1545-321 has been brief - lasting less than a few percent of the lifetime $\sim (0.3-2)\times 10^{8} yr$ of the giant radio source. The host galaxy is located at the boundary of a large scale filamentary structure, and shows blue patches in color distribution indicative of a recent merger, which may have triggered the Mpc-scale radio galaxy.

Preconditioner updates applied to CFD model problems

This paper deals with solving sequences of nonsymmetric linear systems with a block structure arising from compressible flow problems. The systems are solved by a preconditioned iterative method. We attempt to improve the overall solution process by sharing a part of the computational effort throughout the sequence. Our approach is fully algebraic and it is based on updating preconditioners by a block triangular update. A particular update is computed in a black-box fashion from the known preconditioner of some of the previous matrices, and from the difference of involved matrices. Results of our test compressible flow problems show, that the strategy speeds up the entire computation. The acceleration is particularly important in phases of instationary behavior where we saved about half of the computational time in the supersonic and moderate Mach number cases. In the low Mach number case the updated decompositions were similarly effective as the frozen preconditioners.

Supersonic scattering of a wing-induced incident shock by a slender body of revolution

The lift force acting on a slender body of revolution that separates from a thin wing in supersonic flow is analysed using Prandtl–Glauert linearized theory, scattering theory and asymptotic methods. It is shown that this lift is associated with multi-scattering of the wing-induced shock wave by the body surface. The local and global lift coefficients are obtained in simple analytical forms. It is shown that the total lift is mainly induced by the first scattering. Contributions from second, third and higher scatterings are zero in the leading-order approximation. This greatly simplifies calculations of the lift force. The theoretical solution for the flow field is compared with numerical solutions of three-dimensional Euler equations and experimental data at free-stream Mach number 2. There is agreement between the theory and the computations for a wide range of shock-wave strength, demonstrating high elasticity of the leading-order asymptotic approximation. Theoretical and experimental distributions of the cross-sectional normal force coefficient agree satisfactorily, showing robustness of the analytical solution. This solution can be applied to the moderate supersonic (Mach numbers from 1.2 to 3) multi-body interaction problem for crosschecking with other computational or engineering methods.

Acoustic properties associated with nozzle lip thickness in screeching jets

Imperfectly expanded supersonic jets generate discrete frequency sound known as screech tones. In the low supersonic Mach number, the screech phenomenon is axisymmetric. In this study the effect of nozzle lip thickness on the axisymmetric jet screech is investigated both by screech scattering computation and screeching jet simulation. The conservative form of the axisymmetric Euler equations in generalized coordinates are used to simulate a scattering problem and the Reynolds-Averaged Navier-Stokes equations with the modified Spalart-Allmaras turbulence model is employed for screeching jet simulation. Numerical results of scattered directivity pattern in scattering computation will be reported. Influence of the nozzle lip thickness on the momentum thickness, shock-cell spacing and screech tone wavelength is examined.

Dynamics of Supersonic Droplets of Volatile Liquids

T HE breakup and vaporization of liquid droplets in supersonic flow is an interesting research problem with potentially important implications for supersonic combustion ramjets (scramjets). Noncryogenic, liquid hydrocarbons have substantial benefits as scramjet fuel [1], including higher energy density, lower cost, and ease of handling compared to liquid hydrogen fuel. The complications and time associated with the atomization and vaporization of liquid hydrocarbon scramjet fuel can, in principle, be avoided by injecting the fuel in the vapor phase. In some situations, however, such as a “cold start” in which the fuel is not preheated, hydrocarbon fuel may necessarily be injected while still in liquid phase. In this case, the rates and physical mechanisms associated with the disruption and vaporization of liquid droplets under supersonic flow conditions become critical issues to scramjet combustor performance. One possible technique to increase the dispersion of liquid fuels is to exploit the accelerated vaporization made possible by superheating the liquid. Investigation of the vaporization of superheated droplets and sprays have to date been largely confined to incompressible flows [2,3], with the physics of superheated liquid droplet disruption and vaporization in supersonic flow not yet well established. Studies of droplet disruption in compressible flows that have been conducted [4–6] have generally not considered the effects of superheating. The numerical study of Joseph et al. [7] did suggest a flash vaporization mechanism in the disruption of liquid drops in steady, supersonic flow, arguing that superheating may occur over small regions of the droplet surface due to a local combination of low pressure and frictional heating. The disruption of droplets in high-speed flow has often been studied by the sudden application of aerodynamic loads though the use of shock tubes [4,6,8–10]. Though this technique can produce liquid droplets under locally supersonic conditions, this is accomplished only after the passage of a shock wave through the droplets. Other droplet disruption studies have been conducted at subsonic speeds [11,12], for example, by droplets falling across a high-speed gas jet [13], droplet-bearing jets in cross flow [14], and in drop tubes [15]. In any case, these techniques do not typically result in the droplets achieving a significant degree of superheating. The research presented here investigated the dynamics of droplets consisting of volatile fluid smoothly accelerated to supersonic Mach numbers without passage of shock waves through the droplet. This was accomplished over a range of liquid vapor pressures using a compact, underexpanded supersonic jet configuration. This is an extension of a previous study of superheated droplet disruption with compressible, but subsonic, flow relative to the droplets [16]. One challenging aspect in the study of liquid drops in high-speed airstreams is the measurement of the drop velocity and acceleration [17]. Double-pulsed, planar laser imaging was employed here to determine the velocity of the droplets for various test fluids.

Influence of Stores on the Transonic Flutter of a Delta Wing Configuration

Transonic and supersonic flutter characteristics of a delta wing configuration with external stores were computationally simulated, and the aerodynamic influence of the stores on the flutter characteristics was investigated. Delta wings with one and two external stores were considered. Unsteady aerodynamics of the wing with external stores were evaluated using Navier-Stokes equations, and equations of motion based on a modal approach were applied to the structural dynamics. These equations were coupled using a subiteration approach. The computational results showed that the flutter dynamic pressures were reduced for a wide range of Mach numbers when the external stores were attached. The flutter dynamic pressures also decreased as the number of external stores increased. In the case of one external store, the aerodynamic influence of the store could be divided into two regions according to the Mach number. It was found that neglecting the aerodynamic influence of the store led to an overestimation of the flutter dynamic pressures in the supersonic flow region. In the case of two external stores, the aerodynamic influence of the stores on the flutter boundary appeared only at one supersonic Mach number, unlike the case of one external store. Additional flutter analysis using a different store size and unsteady aerodynamic analysis with forced oscillations indicated that the interference position of the shock wave generated ahead of the external store on the lower surface was a key factor in determining the flutter boundary, and the shock wave oscillation may have acted as a negative damping on the wing motion.

Aerodynamic Analysis of Grid-Fin Configurations at Supersonic Speeds

An aerodynamic prediction method for the estimation of aerodynamic characteristics of grid-fin configurations at supersonic Mach numbers has been developed. The method is based on shock-expansion theory. The shock and expansion relations and the interactions between the shock and expansion waves are used to predict the pressure distribution inside each grid-fin cell. The effect of body is modeled using doublet in the crossflow plane. The effect of symmetric separated vortices from the leeward side of body is also modeled using empirical data for the strength and location of vortices. The present method has been validated with available experimental data for body grid-fin configurations at angles of attack without and with fin deflection. The comparison of normal force coefficient on the individual grid fins as well as the overall normal force, pitching moment, and axial force coefficient with experimental data is good. Effect of roll orientation on normal force, pitching moment, and induced out-of-plane force is also brought out.

Acoustic Pressure Waveforms Measured in High Speed Jet Noise Experiencing Nonlinear Propagation

An experimental study has been carried out in a controlled environment in a large anechoic chamber at Boeing to clarify certain features associated with the nonlinear distortion of acoustic waves. The test points were chosen to yield both subsonic and supersonic convective Mach numbers. Both spectral and time-domain analyses have been performed to elucidate nonlinear effects. The spectral analysis indicates that there is agglomeration of energy at the higher frequencies as the propagation distance increases. The time-domain analysis shows strong positive peaks in the pressure signals; the skewness values of the acoustic signals jump from ∼0.05 to ∼0.3, when the convective Mach number is increased from low subsonic values to just above unity. An examination of the Morfey-Howell nonlinear indicator reveals that energy is transferred from the spectral peak to the higher frequencies as a consequence of long-distance propagation. It is established that the convective Mach number is a critical parameter that may be used to identify the onset of nonlinear effects. When the value exceeds unity, there is a dramatic difference in the wave characteristics. In addition, a set of high-quality data has been generated that can be used to guide the development and the validation of prediction methods for nonlinear propagation.

Turbulence Model Studies to Investigate the Aerodynamic Performance of a NASA Dual Control Missile at Supersonic Mach Numbers

This paper contains an investigation of the ability of some of the current turbulence models to predict viscous effects in supersonic Mach number regimes. In most cases, these turbulence models have been derived and validated in traditional subsonic to transonic Mach number regimes and their application to supersonic and hypersonic regimes is assumed valid without a proper recourse to understanding the wider implications of the viscous flow field at high Mach numbers. In such flow regimes, such characteristics as the strong shock interactions with control surfaces and evolving vortices present in the flow, or other large entropy gradient effects brought about by the forebody or other fin surfaces, produce non-trivial challenges for the turbulence models. This study was aimed at interrogating the strength of the turbulence models to model such physics. The Applied Vehicle Technology Panel Group 082 of the Research Technology Organisation selected a dual control NASA missile to investigate the capabilities of Computational Fluid Dynamics (CFD) to predict the flow field and performance characteristics of complex-shaped projectiles at high Mach numbers. There are two types of difficulties that are encountered when computing such problems. The first type are geometry based, and are related to the shape of the nose and forebody, number and types of strakes or forward control mechanisms, fin geometry deployment, and shape and design of the cowls and intakes. The second type of difficulty deals with flow complexities such as the heat transfer (M > 4) implications; the vortices shed from the forebody and other control surfaces; the interaction of these vortices with the body structures, the free stream, and with each other; the base flow interaction with the free stream; the boundary-layer development; and, in the case of supersonic flows, the shock boundary-layer interactions. Air-breathing missiles with intakes or missiles with jet-controlled guidance systems add to the flow complexities. Various turbulence models employed in current CFD codes are tested for their ability to address these viscous issues.

Numerical Investigation of High Speed Free Shear Flow Instability and Mach Wave Radiation

The linear stability theory is used to investigate the emergence, in supersonic free shear flows such as mixing layers and fully expanded plane jets, of supersonically travelling instability waves, which do not vanish in the ambient space. It is shown that, at supersonic convective Mach numbers, the slow and fast supersonic modes in the mixing layer as well as the sinuous supersonic mode in the plane jet should lead to Mach wave radiation. Direct numerical simulations are further used to study nonlinear stages of instability development in high-speed mixing layers and jets. They have shown that the formation of oblique shock waves attached to large-scale structures is observed in free shear flows forced by modes with supersonic phase speeds. The relevance of this phenomenon to the noise generation by high-speed jets is discussed.

Experimental Investigation of the Effects of a Moving Shock Wave on Compressor Stator Flow

Linear cascade testing was performed to simulate the flow conditions experienced by stator blades in an axial compressor with supersonic relative Mach numbers at the inlet to the downstream embedded rotors. Experiments were conducted in a transonic blow-down wind tunnel with a nominal inlet Mach number of 0.65. A single moving normal shock introduced at the exit of the stator cascade simulated the bow shock from a downstream rotor. The shock was generated using a shock tube external to the wind tunnel. Pressure measurements indicated that the stator matched its design intent loading, turning, and loss under steady flow conditions. Effects of the passing shock on the stator flowfield were investigated using shadowgraph photography and digital particle image velocimetry (DPIV). Measurements were taken with three different shock strengths. In each case, the passing shock induced a vortex around the trailing edge of the stator. The size and strength of these vortices were directly related to the shock strength. A suction side separation on the trailing edge of the stator was observed and found to correlate with the vortex blockage.

Kinetic investigation of a collisionless scrape-off layer with a source of poloidal momentum

The influence of a source of poloidal momentum on the collisionless tokamak scrape-off layer (SOL) is investigated. The solutions of the kinetic equation for ion flow and the corresponding system of fluid equations assuming zero ion heat flux are compared. The two models agree quite well for small poloidal Mach numbers of the momentum source, and for larger Mach numbers near the target towards which the drift is directed. At the other target the agreement is poor because the kinetic heat flux dominates energy transport near the stagnation point. The kinetic model yields smooth solutions for any value of poloidal drift. The fluid model breaks down at a particular supersonic poloidal Mach number due to the appearance of a singularity on the domain. The failure of the fluid model does not represent a real detachment, but is simply a mathematical artefact caused by the truncation of the series of fluid moment equations.

Aeroacoustics of hot jets

A systematic study has been undertaken to quantify the effect of jet temperature on the noise radiated by subsonic jets. Nozzles of different diameters were tested to uncover the effects of Reynolds number. All the tests were carried out at Boeing's Low Speed Aeroacoustic Facility, with simultaneous measurement of thrust and noise. It is concluded that the change in spectral shape at high jet temperatures, normally attributed to the contribution from dipoles, is due to Reynolds number effects and not dipoles. This effect has not been identified before. A critical value of the Reynolds number that would need to be maintained to avoid the effects associated with low Reynolds number has been estimated to be 400 000. It is well-known that large-scale structures are the dominant generators of noise in the peak radiation direction for high-speed jets. Experimental evidence is presented that shows the spectral shape at angles close to the jet axis from unheated low subsonic jets to be the same as from heated supersonic jets. A possible mechanism for the observed trend is proposed. When a subsonic jet is heated with the Mach number held constant, there is a broadening of the angular sector in which peak radiation occurs. Furthermore, there is a broadening of the spectral peak. Similar trends have been observed at supersonic Mach numbers. The spectral shapes in the forward quadrant and in the near-normal angles from unheated and heated subsonic jets also conform to the universal shape obtained from supersonic jet data. Just as for unheated jets, the peak frequency at angles close to the jet axis is independent of jet velocity as long as the acoustic Mach number is less than unity. The extensive database generated in the current test programme is intended to provide test cases with high-quality data that could be used for the evaluation of theoretical/semi-theoretical jet noise prediction methodologies.

Computations of Interaction of an Incident Oblique Shock Wave with a Turbulent Boundary Layer on a Flat Plate

Results of numerical simulation of interaction between an oblique shock wave and a turbulent boundary layer formed in a supersonic (Mach number M =5) flow past a flat plate are presented. The computations are performed for three cases of interaction of different intensity, which result in an attached or detached flow. Numerical results are compared with experimental data. The effect of flow turbulence and shock‐wave unsteadiness on flow parameters is studied.

A Study of Advanced High-Loaded Transonic Turbine Airfoils

The development of high-performance turbine airfoils has been investigated under the condition of a supersonic exit Mach number. In order to obtain a new aerodynamic design concept for a high-loaded turbine rotor blade, we employed an evolutionary algorithm for numerical optimization. The target of the optimization method, which is called evolutionary strategy (ES), was the minimization of the total pressure loss and the deviation angle. The optimization process includes the representation of the airfoil geometry, the generation of the grid for a blade-to-blade computational fluid dynamics analysis, and a two-dimensional Navier-Stokes solver with a low-Re k-ε turbulence model in order to evaluate the performance. Some interesting aspects, for example, a double shock system, an early transition, and a redistribution of aerodynamic loading on blade surface, observed in the optimized airfoil, are discussed. The increased performance of the optimized blade has been confirmed by detailed experimental investigation, using conventional probes, hotfilms, and L2F system.