Supersonic Regime Research Articles

Crack Branching Characteristics at Different Propagation Speeds: From Quasi-Static to Supersonic Regime

Classical dynamic fracture mechanics predicts that the crack branching occurs when crack propagation speed exceeds a subsonic critical velocity. In this paper, we performed simulations on the dynamic fracture behaviors of idealized discrete mass–spring systems. It is interesting to note that a crack does not branch when traveling at supersonic speed, which is consistent with others' experimental observations. The mechanism for the characteristics of crack branching at different propagation speeds is studied by numerical and theoretical analysis. It is found that for all different speed regimes, the maximum circumferential stress near the crack tip determines the crack branching behaviors.

Aerodynamic criterion of weak blowing in optimal control of laminar boundary layer in supersonic flows on permeable surfaces

The purpose of the paper is to obtain a criterion for the optimal blowing intensity on the permeable surface at supersonic flow regime, which makes it possible to use the boundary layer equations for friction and heat flows computation.

Gas flow transition over sound speed in a thermal jet

Monograph [1] represents the generalities of choosing such parameters and conditions of a one-dimensional gas flow in a channel, which make it possible, without compression shock, to transfer gas from the subsonic regime to the supersonic regime; the known relation of actions inversion from which, in particular, follows the possibility of flow transition over the sound speed in a cylindrical jet via changing the sign of the heat flux through the channel wall. However, creation of such a thermal jet (Vulis jet) is hampered by the influence of friction forces on the flow, which leads to acceleration of the subsonic flow and deceleration of the supersonic flow. Here we analyzed the possibility of transition of a stationary flow to supersonic regime in the case of combined action of friction forces and heat flux, found the condition of the change of sign of the latter, and also proposed and numerically analyzed several schemes of transition to a supersonic flow.

Reduced-Order Modeling of Unsteady Aerodynamics Across Multiple Mach Regimes

A reduced-order model for unsteady aerodynamic calculations across a range of Mach regimes based on linear convolution and a nonlinear correction factor is developed. Separate investigations are conducted for the sub-, trans-, and supersonic Mach regimes, and overall good results are seen when reduced-order model results are compared with full-order computational-fluid-dynamics solutions, though the reduced-order model errors tend to decrease as the Mach number increases. To assist reduced-order model construction, the method-of-segments simplified model has been created and tested throughout these same Mach regimes. Finally, a practical example of the reduced-order model’s applicability is presented by following a single test case from subsonic up through supersonic flight.

Numerical Prediction of Pitch Damping Stability Derivatives for Finned Projectiles

Reynolds-averaged Navier–Stokes computational fluid dynamics and linear flight mechanics theory were used to compute the pitch damping dynamic stability derivatives for two basic finned projectiles using two numerical methods, namely, the transient planar pitching method and the steady lunar coning method. Numerical results were compared with free-flight and wind-tunnel experimental data for Mach numbers in the range of 0.5–4.5. The accuracy, efficiency, and dependence of these methods on various aerodynamic and numerical modeling parameters were investigated. The numerical methods generally showed good agreement with each other, except at some transonic Mach numbers. Both methods showed good to excellent agreement with experimental data in the high transonic and supersonic Mach regimes. In the subsonic and low transonic regimes, agreement between numerical and experimental data was less favorable. The accuracy of the free-flight test data in these regimes was uncertain due to instances of large scatter, large standard deviation errors, and different data sources showing significantly different results.

Ion acoustic solitons and supersolitons in a magnetized plasma with nonthermal hot electrons and Boltzmann cool electrons

Arbitrary amplitude, ion acoustic solitons, and supersolitons are studied in a magnetized plasma with two distinct groups of electrons at different temperatures. The plasma consists of a cold ion fluid, cool Boltzmann electrons, and nonthermal energetic hot electrons. Using the Sagdeev pseudo-potential technique, the effect of nonthermal hot electrons on soliton structures with other plasma parameters is studied. Our numerical computation shows that negative potential ion-acoustic solitons and double layers can exist both in the subsonic and supersonic Mach number regimes, unlike the case of an unmagnetized plasma where they can only exist in the supersonic Mach number regime. For the first time, it is reported here that in addition to solitions and double layers, the ion-acoustic supersoliton solutions are also obtained for certain range of parameters in a magnetized three-component plasma model. The results show good agreement with Viking satellite observations of the solitary structures with density depletions in the auroral region of the Earth's magnetosphere.

Investigation of Broadband Shock Noise from a Jet Near a Planar Surface

Many current and future aircraft designs rely on the wing or other aircraft surfaces to shield observers on the ground from the engine noise. However, the available data showing how surfaces interact with a jet to shield and/or enhance the jet noise are currently limited. Therefore, far-field noise data and background-oriented schlieren images were acquired for a round jet, operating in the overexpanded, ideally expanded, and underexpanded supersonic flow regimes, near a planar surface to investigate how airframe surfaces might affect the shock-cell structure in the jet plume and the broadband shock noise produced. These data show that broadband shock noise is produced by the relatively weak shocks far downstream of the nozzle exit; consequently, a surface will be effective at reducing broadband shock noise only if it is long enough to shield the noise produced by shocks. Furthermore, the presence of a surface very near the edge of an underexpanded jet increases the shock-cell spacing, pushing the shock cells farther downstream. Conversely, the surface has a minimal affect on the shock cells in an overexpanded jet.

Brittle fracture in a periodic structure with internal potential energy. Spontaneous crack propagation

Spontaneous brittle fracture is studied based on the model of a body, recently introduced by two of the authors, where only the prospective crack path is specified as a discrete set of alternating initially stretched and compressed bonds. In such a structure, a bridged crack destroying initially stretched bonds may propagate under a certain level of the internal energy without external sources. The general analytical solution with the crack speed–energy relation is presented in terms of the crack-related dynamic Green's function. For anisotropic chains and lattices considered earlier in quasi-statics, the dynamic problems are examined and discussed in detail. The crack speed is found to grow unboundedly as the energy approaches its upper limit. The steady-state sub- and supersonic regimes found analytically are confirmed by numerical simulations. In addition, irregular growth, clustering and crack speed oscillation modes are detected at a lower bound of the internal energy. It is observed, in numerical simulations, that the spontaneous fracture can occur in the form of a pure bridged, partially bridged or fully open crack depending on the internal energy level.

Interaction mechanisms between dust grains in the presence of asymmetric ion flow and an external magnetic field in complex plasma

We have reported a theoretical study on the interaction mechanism between dust particles in the presence of asymmetric ion flow and an external magnetic field in complex plasma. The recent experimental and numerical results on the particle-wake interaction ensures the dominance of the wake effect in the subsonic regime of plasma flow using the cold ion approximation. The recent developments in dusty plasma research and its growing interest towards more realistic magnetized dusty plasma scenarios also demand serious attention to study the wake effect both in the sub and supersonic regimes in the presence of a magnetic field. It is a challenging task to develop a correct, quantitative theory of wake potential for different regimes of magnetic field and ion flow velocity. Analytic expressions for the wake potential have been reported in this paper for both subsonic and supersonic regimes in the presence of an external magnetic field along with Debye-Huckel type potentials. The results show that the wake potential plays a dominant role in the subsonic regime and its strength increases with an increase in magnetic field. The behaviour of the wake potential is found to have an interesting effect on the Coulomb crystallization of dust grains and is studied with the help of molecular dynamic (MD) simulation.

Suborbital Reentry Demonstration of Inflatable Flare-Type Thin-Membrane Aeroshell Using a Sounding Rocket

An inflatable decelerator is promising as a next-generation atmospheric-entry system owing to its reduced aerodynamic heating and high packing efficiency. In this study, a suborbital reentry demonstration of a flare-type thin-membrane aeroshell sustained by a single inflatable torus using an S-310-41 sounding rocket was carried out. An experimental vehicle was specially developed for this reentry demonstration; it was equipped with a 1.2-m-diam flare-type thin-membrane aeroshell and had a total mass of 15.6 kg. In the flight test, the aeroshell with an inflatable torus was deployed at an altitude of 100 km during a suborbital flight under the conditions of zero-gravity and near vacuum. The experimental vehicle reentered Earth’s atmosphere from an altitude of 150 km. During free fall, it accelerated to a Mach number of 4.5 () because of gravity force. After that, it started decelerating because of aerodynamic force at an altitude of 70 km. According to the flight data, the vehicle remained intact during the reentry and the aeroshell achieved the expected decelerating performance. This reentry demonstration proves that the flare-type thin-membrane aeroshell sustained by the inflatable torus works well as a decelerator for atmospheric-entry vehicles. Further, the drag coefficient of the experimental vehicle in the supersonic, transonic, and subsonic regimes under free-flight conditions was estimated from the flight trajectory.

Scattering, Tracking and Seeding Characteristics of TiO2 using Particle Image Velocimetry in Supersonic Flows

Abstract In this work, the particle image velocimetry (PIV) technique was applied to study the compressible supersonic flow regimes in the multi-Mach number high-speed (MMH) wind tunnel. To generate sufficient light scattering and flow across shock waves, tracer particles and the seeding technique were used, as well as scattering and tracking of particles were investigated using experimental observations and theoretical analysis. It was determined that the actual particle diameter should be around 200 nm to guarantee an adequate aerodynamic response to velocity gradients in the flow. It was further shown by the PIV measurements over a sharp cone that the uniformity of seeding particles dispersion was very important for the operations of the seeding facility. The present study indicated that the PIV technique could be an efficient method for monitoring the flow field of shock wave and subsonic flow regimes.

Thrust Enhancement Through Bubble Injection Into an Expanding-Contracting Nozzle With a Throat

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle with a throat. The presence of a throat in an expanding-contracting nozzle can result in flow transition from the subsonic regime to the supersonic regime (choked conditions) for a bubbly mixture flow, which may result in a substantial increase in jet thrust. This increase would primarily arise from the fact that the injected gas bubbles expand drastically in the supersonic region of the flow. In the current work, an analytical 1D model is developed to capture choked bubbly flow in an expanding-contracting nozzle with a throat. The study provides analytical and numerical support to analytical observations and serves as a design tool for nozzle geometries that can achieve efficient choked bubbly flows through nozzles. Starting from the 1D mixture continuity and momentum equations, along with an equation of state for the bubbly mixture, expressions for mixture velocity and gas volume fraction were derived. Starting with a fixed geometry and an imposed upstream pressure for a choked flow in the nozzle, the derived expressions were iteratively solved to obtain the exit pressures and velocities for different injected gas volume fractions. The variation of thrust enhancement with the injected gas volume fraction was also studied. Additionally, the geometric parameters were varied (area of the exit, area of the throat) to understand the influence of the nozzle geometry on the thrust enhancement and on the flow conditions at the inlet. This parametric study provides a performance map that can be used to design a bubble augmented waterjet propulsor, which can achieve and exploit supersonic flow. It was found that the optimum geometry for choked flows, unlike the optimum geometry under purely subsonic flows, had a dependence on the injected gas volume fraction. Furthermore, for the same injected gas volume fraction the optimum geometry for choked flows resulted in greater thrust enhancement compared to the optimum geometry for purely subsonic flows.

Stellar dynamics in gas: the role of gas damping

In this paper, we consider how gas damping affects the dynamical evolution of gas-embedded star clusters. Using a simple three-component (i.e. one gas and two stellar components) model, we compare the rates of mass segregation due to two-body relaxation, accretion from the interstellar medium, and gas dynamical friction in both the supersonic and subsonic regimes. Using observational data in the literature, we apply our analytic predictions to two different astrophysical environments, namely galactic nuclei and young open star clusters. Our analytic results are then tested using numerical simulations performed with the NBSymple code, modified by an additional deceleration term to model the damping effects of the gas. The results of our simulations are in reasonable agreement with our analytic predictions, and demonstrate that gas damping can significantly accelerate the rate of mass segregation. A stable state of approximate energy equilibrium cannot be achieved in our model if gas damping is present, even if Spitzer's Criterion is satisfied. This instability drives the continued dynamical decoupling and subsequent ejection (and/or collisions) of the more massive population. Unlike two-body relaxation, gas damping causes overall cluster contraction, reducing both the core and half-mass radii. If the cluster is mass segregated (and/or the gas density is highest at the cluster centre), the latter contracts faster than the former, accelerating the rate of core collapse.

Investigation of aerodynamic characteristics of rarefied flow around NACA 0012 airfoil using DSMC and NS solvers

In this study, rarefied supersonic and subsonic gas flow around a NACA 0012 airfoil is simulated using both continuum and particle approaches. Navier–Stokes equations subject to the first order slip/jump boundary conditions are solved under the framework of OpenFOAM package. The DSMC solver of the package, i.e., dsmcFoam, has been improved to include a newly presented “simplified Bernoulli trial (SBT)” scheme for inter-molecular collision modeling. The use of SBT collision model permits to obtain accurate results using a much lower number of simulator particles. We considered flow at different angles of attacks and Knudsen numbers at both the subsonic and supersonic regimes. The computed density and surface pressure distributions are compared with the experimental and numerical data and suitable accuracy was observed. We investigate variations of the lift and drag coefficients with the Knudsen number and angle of attack. At low Kn number in supersonic regime, our results for lift coefficient agree well with the linearized theory; however, the deviation starts as soon as the angle of attack goes beyond 15° or shock wave forms above the airfoil. Along with this, we have observed that drag coefficient increases with the Kn number increasing. We also investigated the effect of Kn number on the leading edge shock position and structure, drag polar (CL/CD), and slip velocity over the airfoil.

Statistical Entry, Descent, and Landing Performance Reconstruction of the Mars Science Laboratory

The Mars Science Laboratory spacecraft landed an approximately 900 kg rover on Mars on 5 August 2012. Similar to past Mars missions, the spacecraft recorded inertial measurement unit data and radar altimeter measurements, but its aeroshell was also instrumented with flush atmospheric data system sensors that captured the pressure distribution on the vehicle during hypersonic and supersonic flight regimes. The rich data set enables a comprehensive postflight analysis of the vehicle’s trajectory, atmosphere, and aerodynamics. This paper demonstrates a comprehensive statistical estimation methodology and applies it to the large but disparate data set to reconstruct the vehicle’s entry performance, while using several statistical estimation methods, specifically the extended Kalman filter, unscented Kalman filter, and adaptive filter, which concurrently estimate both the state and the uncertainties. The results of the analysis shows good agreement between the estimated states, preflight predictions, and independent reconstructions, while also demonstrating the efficacy of the comprehensive statistical estimation method for Mars entry, descent, and landing reconstruction.

Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion

This paper presents the development of a discontinuous Galerkin (DG) method for application to chemically reacting flows in subsonic and supersonic regimes under the consideration of variable thermo-viscous-diffusive transport properties, detailed and stiff reaction chemistry, and shock capturing. A hybrid-flux formulation is developed for treatment of the convective fluxes, combining a conservative Riemann-solver and an extended double-flux scheme. A computationally efficient splitting scheme is proposed, in which advection and diffusion operators are solved in the weak form, and the chemically stiff substep is advanced in the strong form using a time-implicit scheme. The discretization of the viscous-diffusive transport terms follows the second form of Bassi and Rebay, and the WENO-based limiter due to Zhong and Shu is extended to multicomponent systems. Boundary conditions are developed for subsonic and supersonic flow conditions, and the algorithm is coupled to thermochemical libraries to account for detailed reaction chemistry and complex transport. The resulting DG method is applied to a series of test cases of increasing physico-chemical complexity. Beginning with one- and two-dimensional multispecies advection and shock–fluid interaction problems, computational efficiency, convergence, and conservation properties are demonstrated. This study is followed by considering a series of detonation and supersonic combustion problems to investigate the convergence-rate and the shock-capturing capability in the presence of one- and multistep reaction chemistry. The DG algorithm is then applied to diffusion-controlled deflagration problems. By examining convergence properties for polynomial order and spatial resolution, and comparing these with second-order finite-volume solutions, it is shown that optimal convergence is achieved and that polynomial refinement provides advantages in better resolving the localized flame structure and complex flow-field features associated with multidimensional and hydrodynamic/thermo-diffusive instabilities in deflagration and detonation systems. Comparisons with standard third- and fifth-order WENO schemes are presented to illustrate the benefit of the DG scheme for application to detonation and multispecies flow/shock-interaction problems.

Numerical investigation of supersonic flow breakdown at the inlet duct throttling

The work presents the results of investigating the process of supersonic flow deceleration in a duct of the two-dimensional inlet throttled by variation of the outlet cross-sectional area. An inlet with three external compression shock waves designed for the freestream Mach number Md = 7 was considered as an example for the investigation. A one-dimensional analysis of the conditions for realization of the supersonic flow deceleration regimes in the inlet duct with two throats — in the inlet entrance and at the inlet duct outlet, has been carried out. The parametric numerical computations of two-dimensional inviscid or turbulent flows in the inlet were performed with the use of the Euler and Navier—Stokes codes of the program package FLUENT. The critical conditions for the nonuniform flow in the outlet throat bringing to choking the inlet duct were determined.

COMPUTATIONAL STUDY OF THE EFFECT OF GEOMETRIC PARAMETERS ON THE PERFORMANCE OF SINGLE EXPANSION RAMP NOZZLE FLOWS

The present work deals with the computational study of the single expansion ramp nozzle (SERN) flows for the supersonic regime. Theoretical calculations are carried out for different geometries with certain assumptions. Based on the initial calculation and with the help of Method of Characteristics, nozzle configuration with similar axisymmetric convergent portion and distinct non-axisymmetric divergent portions are drafted. Commercial CFD software ANSYS 12 with Navier Stokes code is used for the computational studies. The study begins with a simple upper flat ramp at different angles with a very small lower cowl at fixed angles. The divergent section of a conventional three-dimensional nozzle is used as the upper ramp of the SERN. The study includes the variation of the ramp at different angles ranging from 16 deg. to 24 deg. with 2 deg. intervals, the cowl angle ranging from 0 deg. to 6 deg. with 2 deg. intervals and the length of the cowl varying from 0.2, 0.4, 0.6, 0.8 and 1.0 times the length of the ramp. The performance parameters like Thrust, Normal force and Mach Variation for these different contours are analyzed and compared. The various parameters used are nozzle length, cowl length, cowl angle, ramp-angle, and ramp length. The shape of the SERN is optimized for the design parameters. The grid sensitivity computational analysis is also performed before finalizing the grid for study.

A Fully Coupled Navier-Stokes Solver for Fluid Flow at All Speeds

This article deals with the formulation and testing of a newly developed, fully coupled, pressure-based algorithm for the solution of fluid flow at all speeds. The new algorithm is an extension into compressible flows of a fully coupled algorithm developed by the authors for laminar incompressible flows. The implicit velocity–pressure–density coupling is resolved by deriving a pressure equation following a procedure similar to a segregated SIMPLE algorithm using the Rhie-Chow interpolation technique. The coefficients of the momentum and continuity equations are assembled into one matrix and solved simultaneously, with their convergence accelerated via an algebraic multigrid method. The performance of the coupled solver is assessed by solving a number of two-dimensional problems in the subsonic, transsonic, supersonic, and hypersonic regimes over several grid systems of increasing sizes. For a desired level of convergence, results for each problem are presented in the form of convergence history plots, tabulated values of the maximum number of required iterations, the total CPU time, and the CPU time per control volume.

On the role of a balancing load in the problem of aerodynamic drag minimization in the supersonic flight regime

The problem of reducing the aerodynamic losses through balancing in the supersonic flight regime is considered. An analysis and a comparison of the drag components due to the aerodynamic surface deformation and the balancing weigh distribution is made with reference to the examples of a zero-thickness airfoil and a three-dimensional configuration of an aircraft with a wing of complicated planform. It is shown that minimum values of the aerodynamic drag are achieved as a result of complex optimization including the dead load mass as a varied parameter.