Supersonic Regime Research Articles

Dynamical friction in a gas: The supersonic case

Any gravitating mass traversing a relatively sparse gas experiences a retarding force created by its disturbance of the surrounding medium. In a previous contribution (Lee & Stahler 2011), we determined this dynamical friction force when the object's velocity was subsonic. We now extend our analysis to the supersonic regime. As before, we consider small perturbations created in the gas far from the gravitating object, and thereby obtain the net influx of linear momentum over a large, bounding surface. Various terms in the perturbation series formally diverge, necessitating an approximate treatment of the flow streamlines. Nevertheless, we are able to derive exactly the force itself. As in the subsonic case, we find that F=Mdot*V, where Mdot is the rate of mass accretion onto the object and V its instantaneous velocity with respect to distant background gas. Our force law holds even when the object is porous (e.g., a galaxy) or is actually expelling mass in a wind. Quantitatively, the force in the supersonic regime is less than that derived analytically by previous researchers, and is also less than was found in numerical simulations through the mid 1990s. We urge simulators to revisit the problem using modern numerical techniques. Assuming our result to be correct, it is applicable to many fields of astrophysics, ranging from exoplanet studies to galactic dynamics.

Performance comparison of flux schemes for numerical simulation of high-speed inviscid flows

Numerical investigations to assess the performance of different flux schemes for the spatial discretisation of the Euler equations have been performed. The schemes employed in the study include flux vector and flux difference splitting schemes as well as hybrid schemes. The schemes are cast in an unstructured high-order finite volume framework and are studied on typical engineering problems in the supersonic and hypersonic regimes. While all the flux schemes perform well in the supersonic and low hypersonic range, their performance show a marked change in the high Mach number regimes. Numerical experiments suggest that the AUSM family of schemes is the most accurate while the Rusanov scheme is the most robust for the range of Mach numbers considered in the study. These studies indicate that a robust and accurate numerical solver for high-speed compressible flows necessitate the use of blended schemes that provide a right balance between accuracy and numerical dissipation.

Flow Field Investigation around Body Tail Projectile

The unsteady compressible flow around a 50 mm projectile governed by the Navier-Stocks (NS) equation is numerically solved with a Large Eddy Simulation (LES) method, with the Sub-Grid Scale (SGS) solved by Smagorinsky-Lilly model. The computed results are obtained in supersonic flow regime for a viscous fluid in order to determine the aerodynamic coefficients with different angles of attack. The flow around a body tail projectile was solved as a three-dimensional flow.

Spatial modeling of the nonstationary processes of boiling liquid outflows from high pressure vessels

The nonstationary processes of boiling liquid outflows following high-pressure vessel depressurization are studied. The two-phase model of a boiling vapour-liquid mixture is extended to solve spatial problems in the case of axial symmetry, where single velocity, single temperature and single pressure approximations are valid, using a wide range equation of state for water and steam in analytical form (R.I. Nigmatulin, R.Kh. Bolotnova). Numerical simulation of two-phase processes is implemented on moving (Lagrangian) meshes using the shock-capturing method. The peculiarities of formation of boiling liquid jets during the explosive outflow of water from high pressure vessels are studied for different initial state parameters of saturation close to the thermodynamic critical point. The calculated spatial distributions of volume vapour concentration and pressure and velocity fields are presented. It has been found that the jet has a conical form when the initial saturation temperature of water is below 480 K. A further increase in the initial saturation temperature up to the critical point leads to twisting of the jet against the flow direction and to its “sticking” to the sidewall, so that the cone opening angle increases to 180°. The values of supersonic and subsonic regimes of outflow are determined using the Mach numbers. Qualitative agreement between calculated and experimental data (A.V. Reshetnikov, N.A. Mazheiko, etc.) is obtained.

Formation of laser jet thrust in the supersonic regime

Basic methods for obtaining laser jet thrust in the supersonic regime corresponding to the supersonic flow in the jet nozzle are analyzed. It is shown that the method based on the interaction of a laser ablative jet with the supersonic flow is promising. In this case, laser thrust is formed due to additional acceleration of the flow behind the ablation region. Numerical simulation of the flow in a parabolic nozzle is employed to demonstrate the possibility of effective formation of laser thrust at a level of 3 × 10−3 N/W.

Global and Koopman modes analysis of sound generation in mixing layers

It is now well established that linear and nonlinear instability waves play a significant role in the noise generation process for a wide variety of shear flows such as jets or mixing layers. In that context, the problem of acoustic radiation generated by spatially growing instability waves of two-dimensional subsonic and supersonic mixing layers are revisited in a global point of view, i.e., without any assumption about the base flow, in both a linear and a nonlinear framework by using global and Koopman mode decompositions. In that respect, a timestepping technique based on disturbance equations is employed to extract the most dynamically relevant coherent structures for both linear and nonlinear regimes. The present analysis proposes thus a general strategy for analysing the near-field coherent structures which are responsible for the acoustic noise in these configurations. In particular, we illustrate the failure of linear global modes to describe the noise generation mechanism associated with the vortex pairing for the subsonic regime whereas they appropriately explain the Mach wave radiation of instability waves in the supersonic regime. By contrast, the Dynamic Mode Decomposition (DMD) analysis captures both the near-field dynamics and the far-field acoustics with a few number of modes for both configurations. In addition, the combination of DMD and linear global modes analyses provides new insight about the influence on the radiated noise of nonlinear interactions and saturation of instability waves as well as their interaction with the mean flow.

Aeroelastic analysis of versatile thermal insulation (VTI) panels with pinched boundary conditions

Launch vehicle design and analysis is a crucial problem in space engineering. The large range of external conditions and the complexity of space vehicles make the solution of the problem really challenging. The problem considered in the present work deals with the versatile thermal insulation (VTI) panel. This thermal protection system is designed to reduce heat fluxes on the LH2 tank during the long coasting phases. Because of the unconventional boundary conditions and the large-scale geometry of the panel, the aeroelastic behaviour of VTI is investigated in the present work. Known available results from literature related to similar problem, are reviewed by considering the effect of various Mach regimes, including boundary layer thickness effects, in-plane mechanical and thermal loads, non-linear effects and amplitude of limit cycle oscillations. A dedicated finite element model is developed for the supersonic regime. The models used for coupling the orthotropic layered structural model with Piston Theory aerodynamic models allow the calculations of flutter conditions in case of curved panels supported in a discrete number of points. An advanced computational aeroelasticity tool is developed using various dedicated commercial softwares (CFX, ZAERO, EDGE). A wind tunnel test campaign is carried out to assess the computational tool in the analysis of this type of problem.

Thin-film deposition with high pressure capillary micro-discharges under different supersonic flow and shock regimes

Hollow cathode microplasma jets operating under different supersonic flow regimes were investigated for spray deposition of nanostructured CuO thin films. A variety of supersonic flow phenomena (e.g., shock fronts, stagnation regions, flow instabilities, and turbulent mixing) were studied using fluorescence imaging of the jet afterglow, and were seen to have a dramatic effect on film deposition. Material growth with under-expanded flows was dominated by flux inhomogeneities related to standoff shocks and stagnation regions due to complex fluid interactions between the jet and substrate, resulting in dense, polycrystalline films with variable thickness. For a pressure-matched jet, film thickness was more uniform and morphology evolved from dense polycrystalline films to crystalline nanowires oriented perpendicularly to the substrate as source–substrate distance was increased. Overall, this work demonstrates that microplasma jet-based deposition is a scientifically rich and promising approach for nanostructured thin-film growth, which involves a unique combination of supersonic flow phenomena, plasma physics at high pressure, and mass transport processes.

A semi-implicit, second-order-accurate numerical model for multiphase underexpanded volcanic jets

Abstract. An improved version of the PDAC (Pyroclastic Dispersal Analysis Code, Esposti Ongaro et al., 2007) numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation of multiphase volcanic jets in supersonic regimes. The present version of PDAC includes second-order time- and space discretizations and fully multidimensional advection discretizations in order to reduce numerical diffusion and enhance the accuracy of the original model. The model is tested on the problem of jet decompression in both two and three dimensions. For homogeneous jets, numerical results are consistent with experimental results at the laboratory scale (Lewis and Carlson, 1964). For nonequilibrium gas–particle jets, we consider monodisperse and bidisperse mixtures, and we quantify nonequilibrium effects in terms of the ratio between the particle relaxation time and a characteristic jet timescale. For coarse particles and low particle load, numerical simulations well reproduce laboratory experiments and numerical simulations carried out with an Eulerian–Lagrangian model (Sommerfeld, 1993). At the volcanic scale, we consider steady-state conditions associated with the development of Vulcanian and sub-Plinian eruptions. For the finest particles produced in these regimes, we demonstrate that the solid phase is in mechanical and thermal equilibrium with the gas phase and that the jet decompression structure is well described by a pseudogas model (Ogden et al., 2008). Coarse particles, on the other hand, display significant nonequilibrium effects, which associated with their larger relaxation time. Deviations from the equilibrium regime, with maximum velocity and temperature differences on the order of 150 m s−1 and 80 K across shock waves, occur especially during the rapid acceleration phases, and are able to modify substantially the jet dynamics with respect to the homogeneous case.

Blade Tip Shape Optimization for Enhanced Turbine Aerothermal Performance

In high-speed, unshrouded turbines, tip leakage flows generate large aerodynamic losses and intense unsteady thermal loads over the rotor blade tip and casing. The stage-loading and rotational speeds are steadily increased to achieve higher turbine efficiency, and hence, the overtip leakage flow may exceed the transonic regime. However, conventional blade tip geometries are not designed to cope with supersonic tip flow velocities. A great potential lies in the modification and optimization of the blade tip shape as a means to control the tip leakage flow aerodynamics, limit the entropy production in the overtip gap, manage the heat-load distribution over the blade tip, and improve the turbine efficiency at high-stage loading coefficients. The present paper develops an optimization strategy to produce a set of blade tip profiles with enhanced aerothermal performance for a number of tip gap flow conditions. The tip clearance flow was numerically simulated through two-dimensional compressible Reynolds-averaged Navier–Stokes (RANS) calculations that reproduce an idealized overtip flow along streamlines. A multiobjective optimization tool, based on differential evolution combined with surrogate models (artificial neural networks), was used to obtain optimized 2D tip profiles with reduced aerodynamic losses and minimum heat transfer variations and mean levels over the blade tip and casing. Optimized tip shapes were obtained for relevant tip gap flow conditions in terms of blade thickness to tip gap height ratios (between 5 and 25) and blade pressure loads (from subsonic to supersonic tip leakage flow regimes), imposing fixed inlet conditions. We demonstrated that tip geometries that perform superior in subsonic conditions are not optimal for supersonic tip gap flows. Prime tip profiles exist, depending on the tip flow conditions. The numerical study yielded a deeper insight on the physics of tip leakage flows of unshrouded rotors with arbitrary tip shapes, providing the necessary knowledge to guide the design and optimization strategy of a full blade tip surface in a real 3D turbine environment.

A sub-parsec resolution simulation of the Milky Way: global structure of the interstellar medium and properties of molecular clouds

We present a self-consistent hydrodynamical simulation of a Milky Way-like galaxy, at the resolution of 0.05 pc. The model includes star formation and a new implementation of stellar feedback through photo-ionization, radiative pressure and supernovae. The simulation resolves the structure of the interstellar medium at subparsec resolution for a few cloud lifetimes, and at 0.05 pc for about a cloud crossing time. Turbulence cascade and gravitation from the kpc scales are de facto included in smaller structures like molecular clouds. We show that the formation of a bar influences the dynamics of the central ~100 pc by creating resonances. At larger radii, the spiral arms host the formation of regularly spaced clouds: beads on a string and spurs. These instabilities pump turbulent energy into the gas, generally in the supersonic regime. Because of asymmetric drift, the supernovae explode outside of their gaseous nursery, which diminishes the effect of feedback on the structure of clouds. The evolution of clouds is thus mostly due to fragmentation and gas consumption, regulated mainly by supersonic turbulence. The transition from turbulence supported to self-gravitating gas is detected in the gas density probability distribution function at ~2000 cm^-3. The power spectrum density suggests that gravitation governs the hierarchical organisation of structures from the galactic scale down to a few parsecs.

A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation

The explicit algebraic Reynolds stress model of Wallin and Johansson [J. Fluid Mech. 403, 89 (2000)] is extended to compressible and variable-density turbulent flows. This is achieved by correctly taking into account the influence of the mean dilatation on the rapid pressure-strain correlation. The resulting model is formally identical to the original model in the limit of constant density. For two-dimensional mean flows the model is analyzed and the physical root of the resulting quartic equation is identified. Using a fixed-point analysis of homogeneously sheared and strained compressible flows, we show that the new model is realizable, unlike the previous model. Application of the model together with a K − ω model to quasi one-dimensional plane nozzle flow, transcending from subsonic to supersonic regime, also demonstrates realizability. Negative “dilatational” production of turbulence kinetic energy competes with positive “incompressible” production, eventually making the total production negative during the spatial evolution of the nozzle flow. Finally, an approach to include the baroclinic effect into the dissipation equation is proposed and an algebraic model for density-velocity correlations is outlined to estimate the corrections associated with density fluctuations. All in all, the new model can become a significant tool for CFD (computational fluid dynamics) of compressible flows.

Effect of hot ion temperature on obliquely propagating ion-acoustic solitons and double layers in an auroral plasma

Properties of obliquely propagating ion-acoustic solitons and double layers in a magnetized auroral plasma composed of hot adiabatic ions and two types of, cool and hot Maxwellian electrons are studied using Sagdeev pseudo-potential technique and assuming the quasi-neutrality condition. The new and surprising result which emerges from the model is that in contrast to the case of cold ions where ion-acoustic solitons and double layers are found for subsonic Mach numbers only, the hot ions case allows these nonlinear structures to exist for both subsonic and supersonic Mach number regimes. The double layers exist at lower angle of propagation as hot ion temperature is increased. The soliton electric field amplitudes are increased but their width and pulse duration are decreased with the increase in hot ion temperature. For the auroral zone parameters, the maximum electric field amplitude, width, pulse duration and speed for the solitons come out to be in the range ∼ (0.3–15)mV/m, ∼ (195–455)m, (7–20)ms and (22–26)km/s, respectively. The results seem to be in agreement with the Viking satellite observations in the auroral zone.

Effects of blunt trailing edge flow discharge in supersonic regime

Flow discharge at the blunt trailing edge of bodies immersed into supersonic stream alters significantly the downstream aerodynamic characteristics. This paper studies the changes in the base region topology for a wide range of purge ejection, using Unsteady Reynolds Averaged Navier–Stokes solutions. At low purge rate the base pressure increases, resulting in a reduction of the trailing edge shock wave intensity. Supersonic purge flows diminishes the base pressure and thus strengthens the shock wave, a linear relationship between the base pressure and the shock strength was obtained for the investigated conditions. Furthermore, an auxiliary shock wave system was observed to form upstream of the main fish tail shock at certain discharge rates.

THE GRAVITATIONAL DRAG FORCE ON AN EXTENDED OBJECT MOVING IN A GAS

Using axisymmetrical numerical simulations, we revisit the gravitational drag felt by a gravitational Plummer sphere with mass M and core radius Rs, moving at constant velocity V0 through a background homogeneous medium of adiabatic gas. Since the potential is non-diverging, there is no gas removal due to accretion. When Rs is larger than the Bondi radius RB, the perturbation is linear at every point and the drag force is well fitted by the time-dependent Ostriker's formula with r_{min}= 2.25Rs, where r_{min} is the minimum impact parameter in the Coulomb logarithm. In the deep nonlinear supersonic regime (Rs<< RB), the minimum radius is no longer related with Rs but with RB. We find r_min=3.3mach^{-2.5}RB, for Mach numbers of the perturber between $1.5$ and $4$, although r_{min} = 2\mach^{-2}RB=2GM/V0^{2} also provides a good fit at mach>2. As a consequence, the drag force does not depend sensitively on the nonlinearity parameter RB/Rs, for RB/Rs-values larger than a certain critical value. We show that our generalized Ostriker's formula for the drag force is more accurate than the formula suggested by Kim & Kim (2009).

Numerical Investigation of Viscous Laminar Supersonic Flow Past an Asymmetric Biconvex Circular-Arc Aerofoil

A numerical investigation of two-dimensional unsteady, viscous and laminar compressible flow past an asymmetric biconvex circular-arc aerofoil in supersonic regime is carried out. The focus of the present work is to investigate the effects of variation of Mach number, at two different angles of attack, on the flow and force characteristics on NACA 2S-(50)(04)-(50)(20) aerofoil. The value of Reynolds number is taken as 5x105. The computations are carried out at Mach numbers of 1.25, 1.5 and 2.0 at an angle of attack of α=0° and α=10°. It is found that the aerofoil works well in the supersonic flow and, unlike the conventional symmetric biconvex aerofoil, generates finite lift at α=0° due to stronger shock waves at the lower surface. Moreover, the L/D ratio at α=10° is always found to be more than 2.5.

Energy cascade and scaling in supersonic isothermal turbulence

AbstractSupersonic turbulence plays an important role in a number of extreme astrophysical and terrestrial environments, yet its understanding remains rudimentary. We use data from a three-dimensional simulation of supersonic isothermal turbulence to reconstruct an exact fourth-order relation derived analytically from the Navier–Stokes equations (Galtier &amp; Banerjee, Phys. Rev. Lett., vol. 107, 2011, p. 134501). Our analysis supports a Kolmogorov-like inertial energy cascade in supersonic turbulence previously discussed on a phenomenological level. We show that two compressible analogues of the four-fifths law exist describing fifth- and fourth-order correlations, but only the fourth-order relation remains ‘universal’ in a wide range of Mach numbers from incompressible to highly compressible regimes. A new approximate relation valid in the strongly supersonic regime is derived and verified. We also briefly discuss the origin of bottleneck bumps in simulations of compressible turbulence.

Ship underwater noise assessment by the acoustic analogy. Part I: nonlinear analysis of a marine propeller in a uniform flow

The aim of this work is to analyze the hydroacoustic behavior of a marine propeller through the acoustic analogy and to test the versatility and effectiveness of this approach in dealing with the many (and relatively unexplored) issues concerning the underwater noise and its numerical prediction. In particular, a propeller in a noncavitating open water condition is examined here by coupling a Reynolds averaged Navier–Stokes hydrodynamic solver to a hydroacoustic code implementing different resolution forms of the Ffowcs Williams–Hawkings (FWH) equation. The numerical results suggest that unlike the analogous aeronautical problem, where the role played by the nonlinear quadrupole sources is known to be relevant just at high transonic or supersonic regime, the pressure field underwater seems to be significantly affected by the flow nonlinearities, while the contribution from the linear terms (the thickness and loading noise components) is dominant only in a spatially very limited region. Then, contrary to popular belief and regardless of the low blade rotational speed, a reliable hydroacoustic analysis of a marine propeller cannot put aside the contribution of the nonlinear noise sources represented by the turbulence and vorticity three-dimensional fields and requires the computation of the FWH quadrupole source terms.

A design of a two-dimensional, supersonic KH experiment on OMEGA-EP

An experiment meant to investigate the evolution of single mode Kelvin–Helmholtz (KH) instability in the supersonic regime is presented and theoretically analyzed. This experiment is intended to provide a direct measurement of the two-dimensional vortex evolution so that the high-Mach-number effects can be measured. The proposed design takes advantage of the ability of OMEGA-EP to drive experiments for up to 30 ns to produce steady conditions for KH that endure long enough to observe substantial growth. KH growth for the proposed design has been analyzed using two-dimensional numerical simulations. The results were compared to synthetic temporal KH numerical simulations using non-dimensional scaling in the low and high Mach number regime. The comparisons show that the growth in the high Mach number regime is expected to be suppressed by up to a factor of two. The effects of two-dimensional rarefactions from the lateral boundaries of the experimental system were also investigated. It was found that they introduce no major uncertainties or hazards to the experiment. We produced simulated radiographs, which show that the proposed experimental system will enable observation of the KH structures. An experiment of this kind has not yet been performed, and therefore would serve to validate numerical results and analytical models presented here and in the literature.

Modeling of Fuel Sloshing and its Physical Effects on Flutter

The sloshing effects of an internal fluid on the flutter envelope of an aeroelastic system have received little attention in the open literature. This issue is nevertheless relevant for many aircraft, especially high-performance fighter jets carrying stores. This paper addresses some aspects of this problem as well as related modeling and analysis issues. These include the importance or insignificance of accounting for the hydroelastic effect when modeling an internal fluid and its container as well as accounting for that container when modeling the aerodynamics of the overall aeroelastic system. The paper also reports on the findings of four independent sets of flutter analyses performed for a wing–store test configuration and various fuel fill levels in the subsonic, transonic, and early supersonic regimes. Two of these sets of numerica l experiments relied on a computational-fluid-dynamics-based computational technology, and two of them on the doublet-lattice method or a supersonic lifting-surface theory, where applicable. The geometry of the chosen test configuration is that of the AGARD Wing 445.6 with a blunt-nosed store. The obtained computational results show that, at least for the considered wing–store configuration, ignoring the aforementioned hydroelastic effect tends to overestimate the added-mass effect and underestimate the critical pressure and flutter speed. They also reveal that, whereas the aerodynamics of the store may be neglected in the subsonic regime, they cannot be ignored in supersonic air streams. Finally, the performed computational study suggests that, in general, the critical pressure and flutter speed decrease with an increasing fuel fill level.