Supersonic Regime Research Articles

Dense gas effects in inviscid homogeneous isotropic turbulence

A detailed numerical study of the influence of dense gas effects on the large-scale dynamics of decaying homogeneous isotropic turbulence is carried out by using the van der Waals gas model. More specifically, we focus on dense gases of the Bethe–Zel’dovich–Thompson type, which may exhibit non-classical nonlinearities in the transonic and supersonic flow regimes, under suitable thermodynamic conditions. The simulations are based on the inviscid conservation equations, solved by means of a ninth-order numerical scheme. The simulations rely on the numerical viscosity of the scheme to dissipate energy at the finest scales, while leaving the larger scales mostly unaffected. The results are systematically compared with those obtained for a perfect gas. Dense gas effects are found to have a significant influence on the time evolution of the average and root mean square (r.m.s.) of the thermodynamic properties for flows characterized by sufficiently high initial turbulent Mach numbers (above 0.5), whereas the influence on kinematic properties, such as the kinetic energy and the vorticity, are smaller. However, the flow dilatational behaviour is very different, due to the non-classical variation of the speed of sound in flow regions where the dense gas is characterized by a value of the fundamental derivative of the gas dynamics (a measure of the variation of the speed of sound in isentropic compressions) smaller than one or even negative. The most significant differences between the perfect and the dense gas case are found for the repartition of dilatation levels in the flow field. For the perfect gas, strong compressions occupy a much larger volume fraction than expansion regions, leading to probability distributions of the velocity divergence highly skewed toward negative values. For the dense gas, the volume fractions occupied by strong expansion and compression regions are much more balanced; moreover, strong expansion regions are characterized by sheet-like structures, unlike the perfect gas which exhibits tubular structures. In strong compression regions, where compression shocklets may occur, both the dense and the perfect gas exhibit sheet-like structures. This suggests the possibility that expansion eddy shocklets may appear in the dense gas. This hypothesis is also supported by the fact that, in dense gas, vorticity is created with equal probability in strong compression and expansion regions, whereas for a perfect gas, vorticity is more likely to be created in the strong compression ones.

Aerodynamic Flow Characteristics of Utilizing Delta Wing Configurations in Supersonic and Subsonic Flight Regimes

Computational fluid dynamic tests are performed on delta wing models at different heights and speeds in order to achieve lift and drag coefficient values. Primarily, testing was done at supersonic speeds to reveal the advantages of these wing configurations at supersonic flight regimes at a cruise speed and altitude. The low speed characteristics are also examined, important for take-off and landing regimes where the distinctive vortices become prominent. Throughout the two flight conditions tested, a simple delta wing model (with a straight swept wing) is compared to a delta wing model that exhibited a ‘LERX’ (leading edge root extension). Provided literature describes how the performance of delta wings can be improved through this inclusion. Results obtained from the tests show that the model with the LERX has a small, but significant, performance improvement over the simple delta model, in respect to the maximum achievable lift coefficient and maximum stall angle. Lift to drag ratio is not improved however, due to the large vortices creating pressure drag. Generally, the delta wing models produce relatively small amounts of drag, and slightly less lower lift, when at low angles of attack. This is primarily due to the geometry of the models that have thin leading edges and also low thickness to chord ratios.

Plasma torch for supersonic plasma spray at atmospheric pressure

This work presents a plasma torch able to operate at supersonic regime with axial injection of feedstock. In contrast to commonly used linear scheme, the principal axis of the plasma torch is perpendicular to feedstock injection direction, which is aligned with coming out plasma jet. The plasma torch has slightly ascending current voltage characteristics and fixed arc length. Electrical, thermal and kinetic characteristics outlined from comparison with conventional linear plasma spray torches are intermediate between APS, HVOF and VPS. The plasma torch developed in this work has an elevated arc voltage (370V) and low arc current (100A), which contribute to increase the electrode life and decrease the arc voltage relative fluctuation (10%). According to in-flight particle monitoring the CoNiCrAlY particles were sprayed at 500m/s and temperature of 2400°C, whereas the 7%YSZ at 491–683m/s and 2535–2636°C.

Mach number study of supersonic turbulence: the properties of the density field

We analyse the scaling properties of turbulent flows using a suite of three-dimensional numerical simulations. We model driven, compressible, isothermal, turbulence with Mach numbers ranging from the subsonic (⁠|$\mathcal {M} \approx 0.5$|⁠) to the highly supersonic regime (⁠|$\mathcal {M}\approx 16$|⁠). The forcing scheme consists of both solenoidal (transverse) and compressive (longitudinal) modes in equal parts. We confirm the relation |$\sigma _{s}^2 = \ln {(1+b^2\mathcal {M}^2)}$| between the Mach number and the standard deviation of the logarithmic density with b = 0.33. We find increasing deviations with higher Mach number from the predicted lognormal shape in the high-density wing of the density probability density function. The density spectra follow |$\mathcal {D}(k,\,\mathcal {M}) \propto k^{\zeta (\mathcal {M})}$| with scaling exponents depending on the Mach number. We find |$\zeta (\mathcal {M}) = \alpha \mathcal {M}^{\beta }$| with coefficients α = −2.1 and β = −0.33. The dependence of the scaling exponent on the Mach number implies a fractal dimension |$D=2+1.05 \mathcal {M}^{-0.33}$|⁠.

Neurofuzzy-Model-Based Unsteady Aerodynamic Computations Across Varying Freestream Conditions

This paper presents a reduced-order modeling approach based on recurrent local linear neurofuzzy models for predicting generalized aerodynamic forces in the time domain. Regarding aeroelastic applications, the unsteady aerodynamic loads are modeled as a nonlinear function of structural eigenmode-based disturbances. In contrast to established aerodynamic input/output model approaches trained by high-fidelity flow simulations, the Mach number is considered as an additional model input to account for varying freestream conditions. To train the relationship between the input parameters and the corresponding flow-induced forces, the local linear model tree algorithm is adopted in this work. The proposed method is tested exemplarily with respect to the AGARD 445.6 configuration in the subsonic, transonic, and supersonic flight regimes. It is shown that good conformity is obtained between the reduced-order model results and the respective full-order computational-fluid-dynamics solution. A further comparative analysis in the frequency domain in conjunction with a classical flutter analysis confirms the validity of the approach. Finally, the method’s potential for reducing the computational effort of aeroelastic analyses is demonstrated.

Numerical investigation of hypersonic flat-plate boundary layer transition mechanism induced by different roughness shapes

The roughness-induced laminar-turbulent boundary layer transition is significant for high-speed aerospace applications. The transition mechanism is closely related to the roughness shape. In this paper, high-order numerical method is used to investigate the effect of roughness shape on the flat-plate laminar-to-turbulent boundary layer transition. Computations are performed in both the supersonic and hypersonic regimes (free-stream Mach number from 3.37 up to 6.63) for the square, cylinder, diamond and hemisphere roughness elements. It is observed that the square and diamond roughness elements are more effective in inducing transition compared with the cylinder and hemisphere ones. The square roughness element has the longest separated region in which strong unsteadiness exists and the absolute instability is formed, thus resulting in the earliest transition. The diamond roughness element has a maximum width of the separated region leading to the widest turbulent wake region far downstream. Furthermore, transition location moves backward as the Mach number increases, which indicates that the compressibility significantly suppresses the roughness-induced boundary layer transition.

New longitudinal mode and compression of pair ions in plasma

Positive and negative ions forming the so-called pair plasma differing in sign of their charge but asymmetric in mass and temperature support a new acoustic-like mode. The condition for the excitation of ion sound wave through electron beam induced Cherenkov instability is also investigated. This beam can generate a perturbation in the pair ion plasmas in the presence of electrons when there is number density, temperature, and mass difference in the two species of ions. Basic emphasis is on the focusing of ion sound waves, and we show how, in the area of localization of wave energy, the density of pair particles increases while electrons are pushed away from that region. Further, this localization of wave is dependent on the shape of the pulse. Considering the example of pancake and bullet shaped pulses, we find that only the former leads to compression of pair ions in the supersonic regime of the focusing region. Here, possible existence of regions where pure pair particles can exist may also be speculated which is not only useful from academic point of view but also to mimic the situation of plasma (electron positron asymmetric and symmetric) observed in astrophysical environment.

Combined Turbine and Cycle Optimization for Organic Rankine Cycle Power Systems—Part B: Application on a Case Study

Organic Rankine cycle (ORC) power systems have recently emerged as promising solutions for waste heat recovery in low- and medium-size power plants. Their performance and economic feasibility strongly depend on the expander. The design process and efficiency estimation are particularly challenging due to the peculiar physical properties of the working fluid and the gas-dynamic phenomena occurring in the machine. Unlike steam Rankine and Brayton engines, organic Rankine cycle expanders combine small enthalpy drops with large expansion ratios. These features yield turbine designs with few highly-loaded stages in supersonic flow regimes. Part A of this two-part paper has presented the implementation and validation of the simulation tool TURAX, which provides the optimal preliminary design of single-stage axial-flow turbines. The authors have also presented a sensitivity analysis on the decision variables affecting the turbine design. Part B of this two-part paper presents the first application of a design method where the thermodynamic cycle optimization is combined with calculations of the maximum expander performance using the mean-line design tool described in part A. The high computational cost of the turbine optimization is tackled by building a model which gives the optimal preliminary design of an axial-flow turbine as a function of the cycle conditions. This allows for estimating the optimal expander performance for each operating condition of interest. The test case is the preliminary design of an organic Rankine cycle turbogenerator to increase the overall energy efficiency of an offshore platform. For an increase in expander pressure ratio from 10 to 35, the results indicate up to 10% point reduction in expander performance. This corresponds to a relative reduction in net power output of 8.3% compared to the case when the turbine efficiency is assumed to be 80%. This work also demonstrates that this approach can support the plant designer in the selection of the optimal size of the organic Rankine cycle unit when multiple exhaust gas streams are available.

Investigation on subsonic to supersonic flow around a sphere at low Reynolds number of between 50 and 300 by direct numerical simulation

In this study, analysis of flow properties around a sphere and its aerodynamic coefficients in the high-Mach-and-low-Reynolds-numbers conditions is carried out by direct numerical simulations solving the three-dimensional compressible Navier–Stokes equations. The calculation is performed on a boundary-fitted coordinate system with a high-order scheme of sufficient accuracy. The analysis is conducted by assuming a rigid sphere with a Reynolds number of between 50 and 300, based on the diameter of the sphere and the freestream velocity and a freestream Mach number of between 0.3 and 2.0, together with the adiabatic wall boundary condition. The calculation shows the following yields: (1) unsteady fluctuation of hydrodynamic forces become smaller as the Mach number increases under the same Reynolds number condition, (2) the drag coefficient increases with the Mach number due to an increase in the pressure drag by the shock wave, and (3) an accurate prediction of the drag coefficient in the supersonic regime using traditional models might be difficult.

APPLICATION OF GAS DYNAMICAL FRICTION FOR PLANETESIMALS. II. EVOLUTION OF BINARY PLANETESIMALS

ABSTRACT One of the first stages of planet formation is the growth of small planetesimals and their accumulation into large planetesimals and planetary embryos. This early stage occurs long before the dispersal of most of the gas from the protoplanetary disk. At this stage gas–planetesimal interactions play a key role in the dynamical evolution of single intermediate-mass planetesimals (m p ∼ 1021–1025 g) through gas dynamical friction (GDF). A significant fraction of all solar system planetesimals (asteroids and Kuiper-belt objects) are known to be binary planetesimals (BPs). Here, we explore the effects of GDF on the evolution of BPs embedded in a gaseous disk using an N-body code with a fiducial external force accounting for GDF. We find that GDF can induce binary mergers on timescales shorter than the disk lifetime for masses above m p ≳ 1022 g at 1 au, independent of the binary initial separation and eccentricity. Such mergers can affect the structure of merger-formed planetesimals, and the GDF-induced binary inspiral can play a role in the evolution of the planetesimal disk. In addition, binaries on eccentric orbits around the star may evolve in the supersonic regime, where the torque reverses and the binary expands, which would enhance the cross section for planetesimal encounters with the binary. Highly inclined binaries with small mass ratios, evolve due to the combined effects of Kozai–Lidov (KL) cycles with GDF which lead to chaotic evolution. Prograde binaries go through semi-regular KL evolution, while retrograde binaries frequently flip their inclination and ∼50% of them are destroyed.

Doppler effect induced spin relaxation boom.

We study an electron spin qubit confined in a moving quantum dot (QD), with our attention on both spin relaxation, and the product of spin relaxation, the emitted phonons. We find that Doppler effect leads to several interesting phenomena. In particular, spin relaxation rate peaks when the QD motion is in the transonic regime, which we term a spin relaxation boom in analogy to the classical sonic boom. This peak indicates that a moving spin qubit may have even lower relaxation rate than a static qubit, pointing at the possibility of coherence-preserving transport for a spin qubit. We also find that the emitted phonons become strongly directional and narrow in their frequency range as the qubit reaches the supersonic regime, similar to Cherenkov radiation. In other words, fast moving excited spin qubits can act as a source of non-classical phonons. Compared to classical Cherenkov radiation, we show that quantum dot confinement produces a small but important correction on the Cherenkov angle. Taking together, these results have important implications to both spin-based quantum information processing and coherent phonon dynamics in semiconductor nanostructures.

Nonlinear low frequency electrostatic structures in a magnetized two-component auroral plasma

Finite amplitude nonlinear ion-acoustic solitons, double layers, and supersolitons in a magnetized two-component plasma composed of adiabatic warm ions fluid and energetic nonthermal electrons are studied by employing the Sagdeev pseudopotential technique and assuming the charge neutrality condition at equilibrium. The model generates supersoliton structures at supersonic Mach numbers regime in addition to solitons and double layers, whereas in the unmagnetized two-component plasma case only, soliton and double layer solutions can be obtained. Further investigation revealed that wave obliqueness plays a critical role for the evolution of supersoliton structures in magnetized two-component plasmas. In addition, the effect of ion temperature and nonthermal energetic electron tends to decrease the speed of oscillation of the nonlinear electrostatic structures. The present theoretical results are compared with Viking satellite observations.

Features of primary damage by high energy displacement cascades in concentrated Ni-based alloys

Alloying of Ni with Fe or Co has been shown to reduce primary damage production under ion irradiation. Similar results have been obtained from classical molecular dynamics simulations of 1, 10, 20, and 40 keV collision cascades in Ni, NiFe, and NiCo. In all cases, a mix of imperfect stacking fault tetrahedra, faulted loops with a 1/3⟨111⟩ Burgers vector, and glissile interstitial loops with a 1/2⟨110⟩ Burgers vector were formed, along with small sessile point defect complexes and clusters. Primary damage reduction occurs by three mechanisms. First, Ni-Co, Ni-Fe, Co-Co, and Fe-Fe short-distance repulsive interactions are stiffer than Ni-Ni interactions, which lead to a decrease in damage formation during the transition from the supersonic ballistic regime to the sonic regime. This largely controls final defect production. Second, alloying decreases thermal conductivity, leading to a longer thermal spike lifetime. The associated annealing reduces final damage production. These two mechanisms are especially important at cascades energies less than 40 keV. Third, at the higher energies, the production of large defect clusters by subcascades is inhibited in the alloys. A number of challenges and limitations pertaining to predictive atomistic modeling of alloys under high-energy particle irradiation are discussed.

High-Speed Rarefied Flow Past a Rotating Cylinder: The Inverse Magnus Effect

In the present study, we investigate flow past a rotating cylinder over a wide range of flow rarefaction from the early slip through to the free-molecular regime using the direct simulation Monte Carlo method. We focus specifically on high-speed flow conditions and consider a wide range of Mach numbers near the high subsonic, transonic, and supersonic regimes. Various flow parameters such as the coefficients of lift and drag as well as the coefficients of pressure, skin friction, and wall heat transfer have been investigated as a function of both the Mach number and the Knudsen number to gain insight into the flow physics in the different regimes. The flow characteristics in the transonic regime have been found to be substantially different from those in the supersonic regime. In particular, an inverse Magnus effect involving a change in the direction of the lift force occurs in the supersonic regime. In contrast, subsonic flows in the early slip-flow regime experience the conventional direction for the Magnus lift force. This paper demonstrates that there is a subtle interplay between the Mach number and Knudsen number for the occurrence of the inverse Magnus effect.

Experimental and numerical investigations of the turbulent wake flow of a generic space launcher at $$M_\infty =3$$ M ∞ = 3 and $$M_\infty =6$$ M ∞ = 6

The turbulent wake of a generic space launcher wind tunnel model with an underexpanded nozzle jet is investigated experimentally and numerically to gain insight into the variation of intricate wake flow phenomena of space vehicles at higher stages of the flight trajectory with increasing Mach number. The experiments are carried out at $$M_\infty =3$$ and $$M_\infty =6$$ in the Ludwieg tube test facility at the Institute of Fluid Mechanics at the Technische Universitat Braunschweig, while the corresponding time-resolved computations are performed by the Institute of Aerodynamics at RWTH Aachen University using a zonal RANS–LES approach. A strong alteration of the wake topology with increasing Mach number due to the changing pressure ratio at the nozzle exit is found. At $$M_\infty =3$$ the moderate underexpansion rate of $$p_\mathrm{e}/p_\infty \approx 5$$ leads to a formation of a recirculation region with an elongated triangular cross-section reaching to the nozzle exit. At $$M_\infty =6$$ a substantially stronger afterexpansion of the jet plume ( $$p_\mathrm{e}/p_\infty \approx 100$$ ) causes the formation of a cavity region with a quadrangular cross-section. The stronger deflection towards the nozzle at $$M_\infty =3$$ results in lower mean and rms wall pressure ratios than at $$M_\infty =6$$ . However, due to the higher freestream pressure value at the lower Mach number the relation of absolute values is reciprocal, making the lower supersonic regime more critical with respect to dynamic structural loads. This observation is confirmed by an overall good agreement between numerical and experimental data at characteristic positions on the base and nozzle wall. Furthermore, it was shown that undesired effects of the strut support in the wake are present along the whole circumference. For $$M_\infty =3$$ the strut influence is found to be particularly intense. The spectral analysis of wall pressure fluctuations reveals fundamental differences in the dynamic behavior of the two investigated wake flow regimes. At $$M_\infty =3$$ , a dominant frequency range around $$Sr_\mathrm{D}\approx 0.2$$ associated with the inner dynamics of the recirculation bubble is found at the base, while on the nozzle a broad-band low-frequency content of substantially higher amplitudes is detected, which is a footprint of the graduate realignment of the turbulent shear layer along the nozzle wall. The spectra at $$M_\infty =6$$ are characterized by several high-frequency sharp peaks at $$Sr_\mathrm{D}\geqslant 0.8$$ . A strong correlation between the supported wind tunnel configuration and the axisymmetric free-flight case is found for the peaks at $$Sr_\mathrm{D}\approx 0.85$$ known to be caused by the radial flapping motion of the shear layer along the cavity.

Constructal design of the mixing zone inside a supersonic ejector

Supersonic ejectors can be used in heat powered chillers to transfer mechanical energy between the motive and the inverse cycle. Within the ejector, momentum is exchanged between a high speed flow produced by a primary nozzle and a slow current coming from the chiller evaporator. Due to the supersonic regime of the primary flow, the mixing of the two streams causes significant loss and impairs the system efficiency. Up to now, second law efficiency of ejector chillers is quite low and optimization is highly needed. The fluid dynamics of the whole ejector involves turbulent mixing, shock trains and complex wall flow, requiring CFD analyses for an adequate description. However, in order to attempt an optimization, mathematically workable models are advantageous. An analytical scheme that captures the basic features of the turbulent mixing zone is discussed here in view of a Constructal design of an ejector chiller.

A new approach to solve the problems of seismic vibrations for periodically nonuniform buried pipelines

The method proposed by E.A. Il’yushina is used to study the longitudinal vibrations of segmented buried pipelines. It is shown that the averaged wave velocity in a periodically nonuniform pipeline is specified by the effective static moduli of the periodicity cell and that, in the case of using a vibration damping material made of rubber or soft metal at joints between pipes, this velocity can be much less than the velocity of longitudinal waves in the main pipe. The last fact makes it reasonable to consider supersonic regimes in the problems of seismic vibrations when the wave velocity in a pipeline is less than the wave velocity in the soil.

Disk-Gap-Band パラシュートのための超音速領域における流体構造連成解析

The Mars landing system has been developed with a disk-gap-band (DGB) parachute in supersonic flow regime. The Mars' thin density creates a scaling challenge that is hard to overcome in windtunnel tests. Therefore, a computational analysis will require for parachute design. We use NURBS basis functions for spatial discretization in both structural and fluid mechanics computations. The parachute shape becomes smoother than what we get from a typical finite element discretization.

Numerical simulations in obtaining drag reduction for projectile with base bleed

An artillery projectile in flight produces a low pressure area immediately behind the projectile which creates a force called base drag which lessens the velocity of the projectile. It is known that theoretically this base resistance can be reduced or even eliminated by allowing a stream of hot gas to flow out of the base surface of the projectile in a suitable manner. The effect produced by this stream of hot gas is called base-bleed effect. The internal ballistic calculation of existing base bleed configuration is presented in the paper. A numerical simulation of axisymmetric body projectiles was obtained with the Reynolds Averaged Navier-Stokes (RANS) computational fluid dynamics software (CFD). Also, two turbulence models were tested and validated with the semi empirical prediction. The realizable k-ɛ turbulence model was chosen for calculation of aerodynamic drag of the projectile with and without base bleed effect. Computed result show a drag reduction with base bleed of about 12% in supersonic flow regime.

The study of the process of evolution of the jet under outflow of water from the supercritical state through a thin nozzle

The dynamics of the water outflow from the initial supercritical state through a thin nozzle is studied. To describe the initial stage of non-stationary process outflow the system of differential equations of conservation of mass, momentum and energy in a two-dimensional cylindrical coordinates with axial symmetry is used. The spatial distribution of pressure and velocity of jet formation was received. It was established that a supersonic regime of outflow at supercritical temperature of 650 K is formed, which have a qualitative agreement for the velocity compared with the Bernoulli analytical solution and the experimental data.