Supersonic Regime Research Articles

HF-plasmatron experiment and numerical simulation of heat transfer in underexpanded dissociated-nitrogen jets

Experiments on heat transfer in underexpanded supersonic jets of high-enthalpy nitrogen are performed on the VGU-4 induction high-frequency plasmatron at a pressure of 10.4 GPa in a compression chamber. At gas flow rates of 2.4 and 3.6 g/s and HF generator powers of 45 and 64 kW the heat fluxes to the copper, stainless steel, MPG-7 graphite, and quartz surfaces are measured at the stagnation point of a water-cooled cylindrical, flat-ended model, 20 mm in diameter. In the same regimes the stagnation pressures are measured. The effect of the surface catalyticity with respect to nitrogen atom recombination on the heat flux is demonstrated and the qualitative catalyticity scale of the studied materials is established. In the supersonic regimes nonequilibrium nitrogen plasma flow in the discharge channel of the plasmatron and the underexpanded jet flow past the model are numerically simulated for the experimental conditions. The experimental and calculated data on the stagnation pressures and the heat fluxes to cooled surfaces of the metals, graphite, and quartz are compared.

Instability wave-streak interactions in a supersonic boundary layer.

Optimal initial conditions for transient growth in a two-dimensional boundary layer flow correspond to stationary, counter-rotating vortices that subsequently develop into streamwise elongated streaks, which are characterized by an alternating pattern of low and high streamwise velocity. For incompressible flows, previous studies have shown that boundary layer modulation due to streaks below a threshold amplitude level can stabilize the Tollmien-Schlichting instability waves, resulting in a delay in the onset of laminar-turbulent transition. In the supersonic regime, the linearly, most-amplified waves become three-dimensional, corresponding to oblique, first-mode waves. This change in the character of dominant instabilities leads to an important change in the transition process, which is now dominated by oblique breakdown via nonlinear interactions between pairs of first-mode waves that propagate at equal but opposite angles with respect to the free stream. Because the oblique breakdown process is characterized by a rapid amplification of stationary streamwise streaks, artificial excitation of such streaks may be expected to promote transition in a supersonic boundary layer. Indeed, suppression of those streaks has been shown to delay the onset of transition in prior literature. Consistent with those findings, the present study shows that optimally growing stationary streaks indeed destabilize the first-mode waves, but only when the spanwise wavelength of the instability waves is equal to or smaller than twice the streak spacing. Transition in a benign disturbance environment typically involves first-mode waves with significantly longer spanwise wavelengths, and hence, these waves are stabilized by the optimal growth streaks. Thus, as long as the amplification factors for the destabilized, short wavelength instability waves remain below the threshold level for transition, a significant net stabilization is achieved, yielding a transition delay that is comparable to the length of the laminar region in the uncontrolled case.

An efficient algorithm for the retarded time equation for noise from rotating sources

This study concerns modelling of noise emanating from rotating sources such as helicopter rotors. We present an accurate and efficient algorithm for the solution of the retarded time equation, which can be used both in subsonic and supersonic flow regimes. A novel approach for the search of the roots of the retarded time function was developed based on considerations of the kinematics of rotating sources and of the bifurcation analysis of the retarded time function. It is shown that the proposed algorithm is faster than the classical Newton and Brent methods, especially in the presence of sources rotating supersonically.

Nonlinear finite element aeroelastic analysis of multibay panels in supersonic flow regime

Aircraft wing and fuselage panels are often built in multibay configurations. Aeroelastic studies on multibay panels in supersonic flight were addressed by many authors in the past century under the assumption of linear structural behavior, therefore unable to assess the amplitude of the limit cycle oscillations. This work contributes to the study of multibay panel flutter by extending the model to account for geometrical non-linearities, and also by using direct time integration without any sort of linearization or eigenvalue assessment procedure. Results generated for two- and three-bay panels reveal that the single-panel model can drastically underestimate the maximum displacements at the structure, which is critical for structural design and fatigue-life estimation. Also, for the first time, the existence of discontinuous bifurcations has been observed in the limit cycle amplitude diagrams for different multibay arrangements. Such bifurcations have been proven to be directly related to the nonlinear coupling between adjacent bays and the coexistence of different stable limit cycles sensitive to initial disturbance.

The stress-velocity relationship of twinning partial dislocations and the phonon-based physical interpretation

The dependence of dislocation mobility on stress is the fundamental ingredient for the deformation in crystalline materials. Strength and ductility, the two most important properties characterizing mechanical behavior of crystalline metals, are in general governed by dislocation motion. Recording the position of a moving dislocation in a short time window is still challenging, and direct observations which enable us to deduce the speed-stress relationship of dislocations are still missing. Using large-scale molecular dynamics simulations, we obtain the motion of an obstacle-free twinning partial dislocation in face centred cubic crystals with spatial resolution at the angstrom scale and picosecond temporal information. The dislocation exhibits two limiting speeds: the first is subsonic and occurs when the resolved shear stress is on the order of hundreds of megapascal. While the stress is raised to gigapascal level, an abrupt jump of dislocation velocity occurs, from subsonic to supersonic regime. The two speed limits are governed respectively by the local transverse and longitudinal phonons associated with the stressed dislocation, as the two types of phonons facilitate dislocation gliding at different stress levels.

Optical investigations of multicomponent plasma of capillary discharge. Supersonic outflow regime

We present the results of spectroscopic investigations of the plasma of an impulse discharge in a capillary with an ablation wall made of carbon-containing polymer, within the discharge pulse parameters providing the supersonic flow regime of a plasma jet. Based on a 2D-matrix high resolution spectra containing Hα, Cu I, Cu II, C I, C II, and CN and the Swan molecular bands, we obtain spatiotemporal distributions of the electron number density and the plasma temperature in the capillary and the supersonic plasma jet. We reveal the peculiarities of the spatial distribution of the electron number density and of the spectral component intensity within both above stated zones, conditioned, in particular, by achievement, in the hot central zone, of an electron temperature above the “normal” temperature, as well as by essential nonisobaricity of the initial section of the plasma jet. The emission properties of the high-temperature jet core–the intensities and the profiles of the Hα and Hβ Balmer lines, relative intensities of the C II and O II ion lines–registered with high temporal (10 μs) and spatial (20–30 μm) resolution make it possible to discover the main regularities in the spatiotemporal distributions of pressure, temperature, and ionization degree in the capillary and in the supersonic heterogeneous jet of the erosion discharge. Due to the presence in the flow of the molecular components displaying their emission properties at the jet periphery, we manage to obtain information on the plasma parameters within the zone of formation of the “intercepting” shocks in the supersonic jet.

Shock-conforming mesh generation for aerodynamic analyses at supersonic regimes

A shock estimation approach is proposed in the context of the generation of shock-conforming meshes for the numerical analysis of inviscid, steady, supersonic and hypersonic flows. For given flow conditions and vehicle’s geometry, the method provides a fast estimation of the shock waves pattern such that grid points can be clustered along the shock waves in a judicious manner. In this way, the uncertainty on mesh generation for shock-dominated flows is reduced and the use of adaptive mesh refinement could be made more efficient or, in some cases, even considered not necessary. The approach is verified against two- and three-dimensional supersonic flows for conceptual exemplary geometries like wedges and revolution bodies and more real-world vehicles configurations like rockets and hypersonic aircraft. Qualitative and quantitative assessment of the solution-mesh pair quality is proposed to evaluate the quality of the resulting shock-conforming meshes.

Energy transfer in compressible magnetohydrodynamic turbulence

Magnetic fields, compressibility, and turbulence are important factors in many terrestrial and astrophysical processes. While energy dynamics, i.e., how energy is transferred within and between kinetic and magnetic reservoirs, has been previously studied in the context of incompressible magnetohydrodynamic (MHD) turbulence, we extend shell-to-shell energy transfer analysis to the compressible regime. We derive four new transfer functions specifically capturing compressibility effects in the kinetic and magnetic cascade, and capturing energy exchange via magnetic pressure. To illustrate their viability, we perform and analyze four simulations of driven isothermal MHD turbulence in the sub- and supersonic regime with two different codes. On the one hand, our analysis reveals robust characteristics across regime and numerical method. For example, energy transfer between individual scales is local and forward for both cascades with the magnetic cascade being stronger than the kinetic one. Magnetic tension and magnetic pressure related transfers are less local and weaker than the cascades. We find no evidence for significant nonlocal transfer. On the other hand, we show that certain functions, e.g., the compressive component of the magnetic energy cascade, exhibit a more complex behavior that varies both with regime and numerical method. Having established a basis for the analysis in the compressible regime, the method can now be applied to study a broader parameter space.

Experimental Investigation of Shock Waves Formation and Development Process in Transonic Flow

An extensive experimental investigation was performed to explore the shock waves formation and development process in transonic flow. Shadowgraph visualization technique was employed to provide visual description of the flowfield features. Based on the visualization, the formation process was categorized into two intrinsically different phases, subsonic and supersonic. The characteristics of subsonic phase are well known; however, those of the supersonic ones are far less studied. The supersonic phase itself is made up of two consecutive phases, namely approaching and sweeping. The effects of each phase on the flowfield characteristics and on shaping the supersonic regime have been studied in details. In order to generalize the results, three different models were tested. Moreover, a special terminology is suggested by authors to ease the process description and to pave a way for future studies. Above all, as the transition from transonic regime to supersonic one is a vague concept in terms of physical reasoning, a new explanation was proposed that could be used as a criterion for distinguishing between transonic and supersonic regimes.

Nonlinear finite element post-flutter analysis of multibay composite panels in supersonic regime

This study consists of a numerical investigation on the nonlinear flutter oscillations of composite panels on multiple supports (multibay panels) in high supersonic flow. In contrast to what is done in the majority of studies, direct time-domain integration is used here instead of linearized updated mode approximations or modal decomposition techniques. The main goal is to study the interaction between adjacent bays in the nonlinear regime in order to identify aeroelastic phenomena that are not predicted by the usual single-panel approach. Multiple lamination schemes and multibay arrangements are considered, and new important results have been found. In nearly all cases simulated, severe jump discontinuities have been detected in the limit cycle oscillation amplitudes when the dynamic pressure reaches certain values. Such jumps, observed here for the first time, occur due to the nonlinear coupling between neighboring bays and consist of very abrupt amplitude elevations that happen when there are inversions in the motion phase of one or more bays. Furthermore, this study has been able to show that single-panel analysis may be unsafe for structural design as it drastically underestimates the maximum displacements of the bays located in rear (downwind) positions.

Aerodynamic optimisation of the rocket plane in subsonic and supersonic flight conditions

This paper presents the results of a numerical study of the aerodynamic shape of the Rocket Plane LEX. The Rocket Plane is a main part of the Modular Airplane System – MAS; a special vehicle devoted to suborbital tourist flights. The Rocket Plane was designed for subsonic and supersonic flight conditions. Therefore, the impact of the Mach number should be considered during the aerodynamic design of the Rocket Plane. The main goal of the investigation was to determine the sensitivity of the Rocket Plane aerodynamic characteristics to the Mach number during the optimisation of the LEX geometry. The paper includes results of the optimisation process for Mach number from the range Ma = 0.5 to Ma = 2.5. These results reveal that the aerodynamic characteristics of models optimised for the subsonic and transonic regime of Mach numbers (up to Ma = 1) were also improved for the supersonic speed regime. However, in the case of models optimised for the supersonic flight regime the aerodynamic characteristics in subsonic flight regime, are inferior compared to the model before the optimisation process.

Nondimensional Parameter for Characterization of Wall Shear Stress From Underexpanded Axisymmetric Impinging Jets

Wall shear stress is characterized for underexpanded axisymmetric impinging jets for the application of aerodynamic particle resuspension from a surface. Analysis of the flow field resulting from normally impinging axisymmetric jets is conducted using computational fluid dynamics (CFD). A normally impinging jet is modeled with a constant area nozzle while varying the height to diameter ratio (H/D) and the inlet pressures. Schlieren photography is used to visualize the density gradient of the flow field for validation of the CFD. A dimensionless jet parameter (DJP) is developed to describe flow regimes and characterize shear stress. The DJP is defined as being proportional to the jet pressure ratio divided by the H/D ratio squared. Maximum wall shear stress is examined as a function of DJP with three distinct regimes: (i) subsonic impingement (DJP < 1), (ii) transitional (1 < DJP < 2), and (iii) supersonic impingement (DJP > 2). It is observed that wall shear stress is limited to a finite value due to jet energy dissipation in shock structures, which become a dominant dissipation mechanism in the supersonic impingement regime. Additionally, the formation of shock structures in the wall flow was observed for DJP > 2, resulting in difficulties with dimensionless analysis. In subsonic impingement and transitional regimes, equations as a function of the DJP are obtained for the maximum wall shear stress magnitude, maximum shear stress location, and shear stress decay. Using these relationships, wall shear stress can be predicted at all locations along the impingement surface.

How a dissimilar-chain system is splitting: Quasi-static, subsonic and supersonic regimes

We consider parallel splitting of a strip composed of two different chains. As a waveguide, the dissimilar-chain structure radically differs from the well-studied identical-chain system. It is characterized by three speeds of the long waves, c1 and c2 for the separate chains, and c+=(c12+c22)/2 for the intact strip where the chains are connected. Accordingly, there exist three ranges, the subsonic for both chains (0, c2) (we assume that c2 < c1), the intersonic (c2,c+) and the supersonic, (c+,c1). The speed in the latter range is supersonic for the intact strip and at the same time, it is subsonic for the separate higher-speed chain. This fact allows the splitting wave to propagate in the strip supersonically.We derive steady-state analytical solutions and find that the splitting can propagate steadily only in two of these speed ranges, the subsonic and the supersonic, whereas the intersonic regime is forbidden. In the case of considerable difference in the chain stiffness, the lowest dynamic threshold corresponds to the supersonic regime. The peculiarity of the supersonic mode is that the supersonic energy delivery channel, being initially absent, is opening with the moving splitting point.Based on the discrete and related continuous models we find which regime can be implemented depending on the structure parameters and loading conditions. The analysis allows us to represent the characteristics of such processes and to demonstrate strengths and weaknesses of different formulations, quasi-static, dynamic, discrete or continuous.Analytical solutions for steady-state regimes are obtained and analyzed in detail. We find the force-speed relations and show the difference between the static and dynamic thresholds. The parameters and energy of waves radiated by the propagating splitting are determined. We calculate the strain distribution ahead of the transition point and check whether the steady-state solutions are admissible.

Super-soliton dust-acoustic waves in four-component dusty plasma using non-extensive electrons and ions distributions

Based on Sagdeev pseudo-potential and phase-portrait, the dynamics of four-component dust plasma with non-extensively distributed electrons and ions are investigated. Three distinct types of nonlinear waves, namely, soliton, double layer, and super-soliton, have been found. The basic features of such waves are high sensitivity to Mach number, non-extensive parameter, and dust temperature ratio. It is found that the multi-component plasma is a necessary condition for super-soliton's existence, having a wider amplitude and a larger width than the regular soliton. Super-solitons may also exist when the Sagdeev pseudo-potential curves admit at least four extrema and two roots. In our multi-component plasma system, the super-solitons can be found by increasing the Mach number and the non-extensive parameter beyond those of double-layers. On the contrary, the super-soliton can be produced by decreasing the dust temperature ratio. The conditions of the onset of such nonlinear waves and its merging to regular solitons have been studied. This work shows that the obtained nonlinear waves are found to exist only in the super-sonic Mach number regime. The obtained results may be of wide relevance in the field of space plasma and may also be helpful to better understand the nonlinear fluctuations in the Auroral-zone of the Earth's magnetosphere.

Fully-coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries

A generalized finite-volume framework for the solution of fluid flows at all speeds in complex geometries and on unstructured meshes is presented. Starting from an existing pressure-based and fully-coupled formulation for the solution of incompressible flow equations, the additional implementation of pressure–density–energy coupling as well as shock-capturing leads to a novel solver framework which is capable of handling flows at all speeds, including quasi-incompressible, subsonic, transonic and supersonic flows. The proposed numerical framework features an implicit coupling of pressure and velocity, which improves the numerical stability in the presence of complex sources and/or equations of state, as well as an energy equation discretized in conservative form that ensures an accurate prediction of temperature and Mach number across strong shocks. The framework is verified and validated by a large number of test cases, demonstrating the accurate and robust prediction of steady-state and transient flows in the quasi-incompressible as well as subsonic, transonic and supersonic speed regimes on structured and unstructured meshes as well as in complex domains.

Numerical studies of static aeroelastic effects on grid fin aerodynamic performances

The grid fin is an unconventional control surface used on missiles and rockets. Although aerodynamics of grid fin has been studied by many researchers, few considers the aeroelastic effects. In this paper, the static aeroelastic simulations are performed by the coupled viscous computational fluid dynamics with structural flexibility method in transonic and supersonic regimes. The developed coupling strategy including fluid–structure interpolation and volume mesh motion schemes is based on radial basis functions. Results are presented for a vertical and a horizontal grid fin mounted on a body. Horizontal fin results show that the deformed fin is swept backward and the axial force is increased. The deformations also induce the movement of center of pressure, causing the reduction and reversal in hinge moment for the transonic flow and the supersonic flow, respectively. For the vertical fin, the local effective incidences are increased due to the deformations so that the deformed normal force is greater than the original one. At high angles of attack, both the deformed and original normal forces experience a sudden reduction due to the interference of leeward separated vortices on the fin. Additionally, the increment in axial force is shown to correlate strongly with the increment in the square of normal force.

Influence of Mach number and static pressure on plasma flow control of supersonic and rarefied flows around a sharp flat plate

This paper presents an experimental investigation, carried out at the Icare Laboratory by the FAST team, focusing on plasma flow control in supersonic and rarefied regime. The study analyzes how the Mach number as well as the ambient pressure modify the repercussions of the plasma actuator on the shock wave. It follows previous experiments performed in the MARHy (ex–SR3) wind tunnel with a Mach 2 flow interacting with a sharp flat plate, where modifications induced by a plasma actuator were observed. The flat plate was equipped with a plasma actuator composed of two aluminum electrodes. The upstream one was biased with a negative DC potential and thus, created a glow discharge type plasma. Experimental measurements showed that the boundary layer thickness and the shock wave angle increased when the discharge was ignited. The current work was performed with two nozzles generating Mach 4 flows but at two different static pressures: 8 and 71 Pa. These nozzles were chosen to study independently the impact of the Mach number and the impact of the pressure on the flow behavior. In the range of the discharge current considered in this experimental work, it was observed that the shock wave angle increased with the discharge current of $$+15\%$$ for the Mach 2 flow but the increase rate doubled to $$+28\%$$ for the Mach 4 flow at the same static pressure, showing that the discharge effect is even more significant when boosting the flow speed. When studying the effect of the discharge on the Mach 4 flow at higher static pressure, it was observed that the topology of the plasma changed drastically and the increase in the shock wave angle with the discharge current of $$+21 \%$$ .

Supersonic Plasma Spray Deposition of CoNiCrAlY Coatings on Ti-6Al-4V Alloy

Plasma spray is a versatile technology used for production of environmental and thermal barrier coatings, mainly in the aerospace, gas turbine, and automotive industries, with potential application in the renewable energy industry. New plasma spray technologies have been developed recently to produce high-quality coatings as an alternative to the costly low-pressure plasma-spray process. In this work, we studied the properties of as-sprayed CoNiCrAlY coatings deposited on Ti-6Al-4V substrate with smooth surface (R a = 0.8 μm) by means of a plasma torch operating in supersonic regime at atmospheric pressure. The CoNiCrAlY coatings were evaluated in terms of their surface roughness, microstructure, instrumented indentation, and phase content. Static and dynamic depositions were investigated to examine their effect on coating characteristics. Results show that the substrate surface velocity has a major influence on the coating properties. The sprayed CoNiCrAlY coatings exhibit low roughness (R a of 5.7 μm), low porosity (0.8%), excellent mechanical properties (H it = 6.1 GPa, E it = 155 GPa), and elevated interface toughness (2.4 MPa m1/2).

Wake potential in 2-D magnetized complex plasma

Analytical expression for wake potential is obtained in a 2-D magnetized complex plasma using Linear Response Theory. The dynamics of the system is explored at moderate to relatively high magnetic field limit. A 2-D expression for wake potential is obtained and the variation in the strength of the wake potential is explored at different magnetic fields in moderate regime and for ion flow speed in supersonic regime. The theory also facilitates the understanding on the nature of wake potential in relatively high magnetic field limit. Molecular Dynamics simulation is performed to see the role of wake potential developed in this paper on governing the structural property of strongly coupled dusty plasma in presence of moderate to relatively strong magnetic field.

A systematic comparison of two-equation Reynolds-averaged Navier–Stokes turbulence models applied to shock–cloud interactions

Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-Averaged Navier-Stokes (RANS) turbulence models, and we implement six models in the Athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.