Range Of Mach Numbers Research Articles

Local non-equilibrium phase density reconstruction with Grad and Chapman-Enskog methods

The study of the non-equilibrium velocity gas distribution function reconstruction was carried out due to extended gas dynamics methods. The bimodal Mott-Smith solution for a plane shock wave was used as a reference distribution function. The shock-wave solutions were considered in the range of Mach numbers from Ma = 2.0 to Ma = 8.0. The reconstruction of the original function was carried out using the Navier-Stokes-Fourier, 13-moment, regularized 13-moment and 26-moment approximating functions.

A multiplicity of regimes of transonic flow in channels with branching

The flow in 2D channel with a flat plate located along the plane of symmetry of the channel at a certain distance from the inlet was numerically studied. Straight segments formed the channel walls. At the inlet and the outlet of the channel, a supersonic flow was set. The first and third parts of the channel diverged. The middle part converged. Solutions to the Euler equations were obtained using the Ansys CFX finite volume solver. Four solutions were found that differed in the position of the shock waves. The hysteresis in the shock wave position versus Mach number given at the inlet was found. In a certain range of the inlet Mach number, there were asymmetric solutions of the equations.

Scaling behavior of density gradient accelerated mixing rate in shock bubble interaction

Variable-density mixing in shock bubble interaction, a canonical flow of Richtermyer-Meshkov instability, is studied by the high-resolution simulation. While the dissipation mainly controls the passive scalar mixing rate, an objective definition of variable-density mixing rate characterizing the macroscopic mixing formation is still lacking, and the fundamental behavior of mixing rate evolution is not yet well understood. Here, we first show that the variable-density mixing of shock bubble interaction is distinctly different from the previous observations in the passive scalar mixing. The widely-accepted hyperbolic conservation of the first moment of concentration in the scalar mixing, i.e., the conservation of the mean concentration, is violated in variable-density flows. We further combine the compositional transport equation and the divergence relation for the miscible flows to provide the evidence that the existence of density gradient accelerated mixing rate, decomposed by the accelerated dissipation term and redistributed diffusion term, contributes to the anomalous decrease or increase of the mean concentration depending on Atwood number. Further analyzing a number of simulations for the cylindrical or spherical bubbles under a broad range of shock Mach numbers, Reynolds numbers, and Peclet numbers, the density gradient accelerated mixing rate exhibits weak dependent on Peclet numbers, and identifies an Atwood number range with high mixing rate, which can be theoretically predicted based on the mode of hyperbolic conservation violation behavior.

Estimation of Aerodynamic Heating on Scramjet Inlets and Validation With Measurements

Abstract Aerodynamic heating levels on a typical inlet configuration of a scramjet engine are estimated using both standard design correlations and numerical flow simulations. The stagnation point heat flux is estimated using the Fay and Riddell formula. Aerodynamic heating over the inclined ramps is estimated using Van Driest method. Numerical flow simulations are carried out using a Reynolds averaged Navier–Stokes (RANS) solver coupled with energy equations and the Shear Stress Transport (SST) k–ω turbulence model. The aerodynamic heat flux estimates are validated with in-house measurements in a shock tunnel and for a scramjet flight experiment in the Mach number range 1.59 to 7.92. The emergence of a good agreement between them confirms the appropriateness of design correlations for heat flux estimation in scramjet inlets. The choice of simplification and appropriateness of design correlations to complex geometries demand critical assessment. Numerical flow simulations capture flow features and enable the identification of potential augmented heating zones, which will be critical for long-duration scramjet missions.

Ion Acceleration Efficiency at the Earth’s Bow Shock: Observations and Simulation Results

Abstract Collisionless shocks are some of the most efficient particle accelerators in heliospheric and astrophysical plasmas. Here we study and quantify ion acceleration at Earth’s bow shock with observations from NASA’s Magnetospheric Multiscale (MMS) satellites and in a global hybrid-Vlasov simulation. From the MMS observations, we find that quasiparallel shocks are more efficient at accelerating ions. There, up to 15% of the available energy goes into accelerating ions above 10 times their initial energy. Above a shock-normal angle of ∼50°, essentially no energetic ions are observed downstream of the shock. We find that ion acceleration efficiency is significantly lower when the shock has a low Mach number (M A < 6) while there is little Mach number dependence for higher values. We also find that ion acceleration is lower on the flanks of the bow shock than at the subsolar point regardless of the Mach number. The observations show that a higher connection time of an upstream field line leads to somewhat higher acceleration efficiency. To complement the observations, we perform a global hybrid-Vlasov simulation with realistic solar-wind parameters with the shape and size of the bow shock. We find that the ion acceleration efficiency in the simulation shows good quantitative agreement with the MMS observations. With the combined approach of direct spacecraft observations, we quantify ion acceleration in a wide range of shock angles and Mach numbers.

Parametric Study of Separation and Reattachment in Transonic Airfoil Flows

Shock and boundary-layer interactions in transonic airfoils are investigated by means of wall-modeled large-eddy simulation. A distinctive flow model, organized and chaotic, occurs in this regime driven by the transition from laminar to turbulent flow, and therefore the appearance of coherent structures such as the Kelvin–Helmholtz instability. This phenomenon is crucial for designing transonic airfoils because it leads to a high rise in drag. Experimental observations show that the main variables of transonic airfoil flow are the freestream Mach number, the Reynolds number, and boundary-layer thickness. Simulations are performed to investigate the relation of various components of the shock/boundary-layer interaction, that is, the pressure rise to shock-induced separation, the length of the separation bubble, and the rear separation to the unit Reynolds number and the boundary-layer condition upstream of the shock. Flow around NACA0012 is investigated in a range of transonic Mach numbers at various unit Reynolds numbers. It is found that the bubble length on the airfoil changes rapidly with relatively small changes in the freestream Mach number. Simulation results show that the separation length decreases with increasing of the unit Reynolds number; however, increasing the boundary-layer thickness results in an increase in the bubble’s extent. Evaluation of the rear-separation region shows that, as the Reynolds number increases, the length of the rear separation declines at a given Mach number.

Magnetized decaying turbulence in the weakly compressible Taylor-Green vortex

Magnetohydrodynamic (MHD) turbulence affects both terrestrial and astrophysical plasmas. The properties of magnetized turbulence must be better understood to more accurately characterize these systems. This work presents ideal MHD simulations of the compressible Taylor-Green vortex under a range of initial subsonic Mach numbers and magnetic field strengths. We find that regardless of the initial field strength, the magnetic energy becomes dominant over the kinetic energy on all scales after at most several dynamical times. The spectral indices of the kinetic and magnetic energy spectra become shallower than k^{-5/3} over time and generally fluctuate. Using a shell-to-shell energy transfer analysis framework, we find that the magnetic fields facilitate a significant amount of the energy flux and that the kinetic energy cascade is suppressed. Moreover, we observe nonlocal energy transfer from the large-scale kinetic energy to intermediate and small-scale magnetic energy via magnetic tension. We conclude that even in intermittently or singularly driven weakly magnetized systems, the dynamical effects of magnetic fields cannot be neglected.

Vortex-Generating Shock Control Bumps for Robust Drag Reduction at Transonic Speeds

The 3D contour bump has been integrated with vane-type vortex generators to weaken the shock wave and suppress potential flow separation at higher transonic speeds. The integrated vortex-generating shock control bump is parameterized as a whole, in a manner that the contour bump is designed for shock control and the vortex-generating fins are integrated to the contour bump for separation control. This allows the balance between the two factors affecting the total wing drag. The optimization studies based on the Reynolds-averaged Navier–Stokes equations have been carried out to find the optimal vortex-generating bump designs at the given design conditions. Single-point and multipoint global optimizations are carried out to search the optimum parameters at the corresponding design points. It is found that the vortex-generating bump can further reduce the total drag at the higher transonic Mach numbers due to the alleviation of after-bump streamwise separation by a pair of counter-rotating vortices generated. The inclusion of the vortex generators in the bump design allows for a better balance of the design in controlling both the shock strength and the flow separation after the bump at higher Mach numbers. A multipoint optimization leads to a robust vortex-generating bump design for a range of Mach numbers. The distinctive vortical flow structures induced by the vortex-generating bump are highlighted and discussed.

Compromising with corrector step of SIMPLE Algorithm

Abstaining from a corrector step of SIMPLE-like algorithms, a coupled pressure-based algorithm is designed using a cell-centered finite-volume Δ-approximation on a collocated grid to predict all-speed fluid flows. A consistently formulated cell-face dissipation scheme is invoked to unravel the occurrence of pressure–velocity decoupling. Modified Rusanov, Roe and Lax–Wendroff flux-difference schemes accompanied by a newly devised differentiable slope limiter function are used to compute inviscid fluxes over the entire spectrum of subsonic to hypersonic flow. Numerical experiments in reference to incompressible and compressible flows demonstrate that the proposed algorithm maintains an excellent consistency with analytic solutions and available literature data. The method is anticipated to be stable for an extensive range of Mach numbers with an avoidance of under-relaxation (UR) factors.

Role of solution reconstruction in hypersonic viscous computations using a sharp interface immersed boundary method.

This work discusses the development of a sharp interface immersed boundary (IB) method for viscous compressible flows and its assessment for accurate computations of wall shear and heat fluxes in hypersonic flows. The IB method is implemented in an unstructured Cartesian finite-volume (FV) framework and resolves the geometric interface sharply on the nonconformal mesh through direct imposition of boundary conditions employing a local reconstruction approach. The efficacy of the IB-FV solver is investigated for canonical high-speed viscous flows over a range of Mach numbers. The numerical results indicate that the surface pressure and shear stress distributions are computed with reasonable accuracy, whereas surface heat fluxes for aerodynamically blunt configurations are underpredicted. Employing a set of carefully designed experiments and simple diagnostic tools, we probe the possible causes for the underprediction in heat flux. We show that there exist two sources of error-one due to grid resolution and the other due to solution reconstruction, with the latter being more prominent and responsible for the observed underprediction in heat fluxes. Studies reveal that the heat flux estimates are sensitive to the choice of temperature reconstruction and linear interpolations could lead to poor estimates of heat flux. Our investigations conclusively point out the fact that existing polynomial-based reconstruction approaches for sharp interface IB techniques are not necessarily adequate for heat transfer predictions in high Reynolds number hypersonic flows.

ANALYTIC SOLUTIONS FOR TRUNCATED PLASMONS

We present a new plasmon model for a cometary clump moving supersonically in an environment with a non-zero gas pressure. We find that the environmental pressure produces a cutoff in the wings of the cometary clump, therefore resulting in quite "stubby" plasmons for a large range of flow Mach numbers. We derive a relation between the length-to-width ratio of the plasmon and the Mach number M of the flow, which could be used to directly derive M from observations of (appropriate) cometary clumps.

Coagulation of inertial particles in supersonic turbulence

Coagulation driven by supersonic turbulence is primarily an astrophysical problem because coagulation processes on Earth are normally associated with incompressible fluid flows at low Mach numbers, while dust aggregation in the interstellar medium for instance is an example of the opposite regime. We study coagulation of inertial particles in compressible turbulence using high-resolution direct and shock-capturing numerical simulations with a wide range of Mach numbers from nearly incompressible to moderately supersonic. The particle dynamics is simulated by representative particles and the effects on the size distribution and coagulation rate due to increasing Mach number is explored. We show that the time evolution of particle size distribution mainly depends on the compressibility (Mach number). We find that the average coagulation kernel ⟨Cij⟩ scales linearly with the average Mach number ℳrms multiplied by the combined size of the colliding particles, that is, 〈Cij〉∼〈(ai+aj)3〉 ℳrmsτη−1, which is qualitatively consistent with expectations from analytical estimates. A quantitative correction 〈Cij〉∼〈(ai+aj)3〉(vp,rms/cs)τη−1 is proposed and can serve as a benchmark for future studies. We argue that the coagulation rate ⟨Rc⟩ is also enhanced by compressibility-induced compaction of particles.

Rapid airfoil design optimization via neural networks-based parameterization and surrogate modeling

Aerodynamic optimization based on computational fluid dynamics (CFD) is a powerful design approach because it significantly reduces the design time compared with the human manual design. However, CFD-based optimization can still take hours to converge because it requires repeatedly running computationally expensive flow simulations. To further shorten the design optimization time, we propose a fast, interactive design framework that allows us to complete an airfoil aerodynamic optimization within a few seconds. This framework is made efficient through a B-spline-based generative adversarial network model for shape parameterization, which filters out unrealistic airfoils for a reduced design space that contains all relevant airfoil shapes. Moreover, we use a combination of multilayer perceptron, recurrent neural networks, and mixture of experts for surrogate modeling to enable both scalar (drag and lift) and vector (pressure distribution) response predictions for a wide range of Mach numbers (0.3 to 0.7) and Reynolds numbers (104 to 1010). To verify our proposed framework, we compare the optimization results with the ones computed by direct CFD-based optimization for subsonic and transonic conditions. The results show that the optimal designs and the aerodynamic quantities (lift, drag, and pressure distribution) obtained by our proposed framework agree well with the ones computed by direct CFD-based optimizations and evaluations. The proposed framework is being integrated into a web-based interactive aerodynamic design framework that allows users to predict drag, lift, moment, pressure distribution, and optimal airfoil shapes for a wide range of flow conditions within seconds.

Cycle and turbine optimisation for an ORC operating with two-phase expansion

• Novel ORC system operating with two-phase expansion and radial-inflow turbine. • Single- and multi-objective cycle optimisation for 150, 200 and 250 °C heat sources. • MM and MDM are optimal fluids producing up to 28% more power than single-phase ORC. • Mean-line turbine optimisation completed for two-phase radial-inflow turbine. • Feasible subsonic rotor geometries obtained, and candidate turbines designs proposed. Previous investigations suggest the power output from waste-heat recovery organic Rankine cycle (ORC) systems could be enhanced by up to 30% by operating with two-phase expansion, which could reduce cost and aid in the more widespread deployment of ORC technology. However, there are limited expander technologies suitable for such operation. The aim of this research is to investigate a novel ORC system that operates with wet-to-dry expansion permitting the use of a radial-inflow turbine. Specifically, through the exploitation of molecularly complex fluids the wet-to-dry expansion could be achieved across a single turbine stage, whilst the two-phase region is confined to the stator vane. Thermodynamic system optimisation is completed for potential fluids in which the degree of reaction is used to differentiate between the stator and rotor expansion processes. The results reveal that siloxanes are optimal fluids, and that for heat-source temperatures of 150, 200 and 250 ° C the two-phase systems could generate up to 28%, 14% and 3% more power than single-phase systems, respectively. Following this, existing mean-line turbine methods are extended to two-phase turbines under the assumption of a two-phase homogeneous fluid under thermal equilibrium, which is supported with numerical simulations of a two-phase stator vane. The mean-line turbine optimisation for the 200 ° C heat source is then conducted, with the optimal system corresponding to a turbine inlet vapour quality of 0.1 and degree of reaction of 0.4, with lower reaction leading to lower turbine efficiencies. More generally, feasible rotor geometries can be obtained, and conditions with the rotor are expected to remain subsonic. Whilst stator outlet Mach numbers range between 1.5 and 2.1, and stator throat widths below 1 mm are required, the CFD simulations indicate that wet-to-dry expansion can be successfully realised within the stator. In summary, these results provide the first positive demonstration that a 30% improvement in power output could be achieved with a two-phase ORC system operating with molecularly complex working fluids and a radial-inflow turbine.

A simple method for drag estimation for wedge-like fairings in hypersonic flow

ABSTRACTThe addition of wedge-like fairings onto the side of missiles and space launch vehicles, to shield devices such as cameras and reaction jet nozzles, creates additional drag, particularly when in supersonic and hypersonic freestream flow. An experimental and computational study was performed to obtain aerodynamic data on simple representative configurations to test the accuracy of simple theories for the drag increment due to these types of fairings. A semi-empirical method to estimate drag on wedge-shaped projections is presented, which may be used by missile designers to provide predictions of the drag increment due to wedge-like fairings. The method is shown to be valid where the wedge width is much smaller than body diameter, and across the Mach number range 4–8.2 but is likely to be valid for higher Mach numbers. Drag coefficient is found to increase with increasing wedge angle and reducing wedge slenderness, although increasing slenderness tends to increase skin friction drag.

Computational evaluation of geometric effects on aerodynamic performance of circulation control airfoils

The geometric effects of Coanda trailing edges on the aerodynamic performance of an airfoil are numerically evaluated for a range of different freestream Mach numbers and momentum coefficients. A Circulation control (CC) airfoil with a circular trailing edge (ACTE) proves to have better control effectiveness at low subsonic freestream speeds (Mach = 0.1). A CC airfoil having an elliptic trailing edge (AETE) outperforms the ACTE at high subsonic flow conditions. The occurrence of C μ-stall for the AETE is greatly postponed, and meanwhile the maximum net lift coefficient increment achieved for the AETE (Δ C L = 0.51) is slightly higher than that of the ACTE (Δ C L = 0.50) at Mach 0.6. Compared to the ACTE, the AETE is found to have better control consistency at different operating velocities and better control stability when the Coanda jet is supersonic. Through careful consideration of the aerodynamic performance and the control effects, the most appropriate axial ratio for an AETE ellipse is within the interval from 1.5 to 2. Finally, the flow field instability phenomenon and the jet detachment induced by the supersonic Coanda jet are investigated. A self-sustained shock-wave instability phenomenon without jet detachment is first observed in this paper.

An integration method based on a novel combined flow for aerodynamic configuration of strutjet engine

In this paper a novel design method of aerodynamic configuration is proposed to integrate forebody, strut and inlet for strutjet engine, and a model at design point of Mach number 6 is generated to investigate the aerodynamic performance by both simulations and experiments. The basic flow field employed by proposed method is a combined flow named IBB, which is combined by Internal Conical Flow A (ICFA), truncated Busemann flow I (BI) for external section, and truncated Busemann flow II (BII) for internal section. The model configuration is generated by streamline tracing method from basic flow field, in which the forebody section is traced from ICFA and BI flows, and the inlet as well as strut section is traced from BII flow. The simulations in Mach number 4, 5, and 6 demonstrate uniform starting flow fields with relatively high total pressure recovery, which agree well with experiments in wind tunnel. Additionally, in low Mach number cases, this inlet could start at Mach number 3 while it is unstarted at Mach number 2.7; in high Mach number cases, a uniform flow could still exist in Mach number 6.5 while a relatively strong shock wave boundary layer interaction is found in cowl area of Mach number 7 case, indicating the inlet designed by proposed method works in a relatively wide Mach number range.

Higher Order Sliding Mode-Based Guidance for Controlling Statically Unstable Missiles

A surface to air missile (SAM) typically operates at a wide range of Mach numbers, angles of attack and altitudes. This leads to an inevitable significant variation in center of pressure (CP) location. In addition, the propulsion burning changes the Center of Gravity (CG) location. The variation in CP and CG locations results in high variation in aerodynamic static stability in the flight envelope. The high variation of static stability makes operating at statically unstable regions inevitable and needs to be tackled through the missile on-board algorithm. The control design poses a requirement of high autopilot bandwidth to tackle the static instability, which leads to unrealistic actuator bandwidth requirements. Here, we propose a novel technique to handle the high static instability outside the purview of control design without burdening the control requirements. In this paper, the highly unstable operating conditions are avoided through judicious design of mid-course guidance. This paper also presents design of this guidance scheme through higher order sliding mode technique.

High subsonic flow of an organic vapor past a circular cylinder

A circular cylinder was tested in the cross-flow of an organic vapor (Novec™ 649) and of air over the subsonic (M < 0.4) and high subsonic (0.4 < M < 0.8) speed range in a continuously running pressurized closed-loop wind tunnel test facility. Time-averaged pressure measurements gave information on surface pressure distributions, and the corresponding drag and base pressure drag coefficients were obtained. Due to the charging of the wind tunnel, different values of the compressibility factor (0.876 < Z < 0.999) could be achieved for the organic vapor flow. This enabled in combination with the results for air an assessment of the impact of non-ideal gas dynamics on the form drag of a cylinder in the considered highly subsonic flow regime. The new experimental data were compared with available literature results. Changes in surface pressure distribution at higher subsonic velocities were identified and discussed. It was found that non-ideal gas effects did not strongly affect the overall drag. The variation of drag coefficient over the Mach number range was comparable with literature data for ideal-gas compressible flow, including shock-less and intermittent shock wave, and permanent shock wave flows regimes. At Mach 0.4, the flow of Novec™ 649 was in the shock-less regime and exhibited a pronounced dependency on the Reynolds number. An increase in drag was observed at Mach 0.6 which was attributed to the commencement of vortex shedding. Non-ideal thermodynamics only affected the flow locally and a reduction of the critical pressure coefficient in the high subsonic flow regime was observed in the surface pressure distribution. However, this mechanism did not alter significantly the overall drag behavior.Graphic abstractDrag coefficient CD against Re for several Mach numbers M and comparison with available literature results obtained for air (colored symbols indicate different Mach number clusters)

Impacts of grid turbulence on the side projection of planar shock waves

In this study, the characteristics of side-projected planar shock waves propagating through grid turbulence were investigated using a counter-driver shock tube. At the location of visualization of the shock–turbulence interactions, the range of the shock Mach numbers was $$M_{\mathrm {s}} = 1.01{-}1.15$$ and the representative values of the turbulent Mach numbers $$\widetilde{M_{\mathrm {t}}}$$ were $$ 0.005{-}0.014$$ . The interaction length between the shock wave and grid turbulence was in the range approximately from $$-50$$ to $$300$$ times the integral length scale of the turbulence. For the interaction involving the strongest turbulence with $$\widetilde{M_{\mathrm {t}}} = 0.014$$ , the weakest planar shock wave with $$M_{\mathrm {s}} = 1.01$$ was largely deformed and could not be detected on the projected shadowgraph and schlieren images. The density changes on the grayscale in the projected images of the shock waves weakened and expanded multidimensionally. This undetectable profile of the shock wave could indicate that the shock wave locally lost discontinuous property change profile. The shock waves with $$M_{\mathrm {s}} \ge 1.05$$ did not show the undetectable profile in the projected image. In these cases, the projected thickness of the shock wave increased with an increase in the interaction length. The increase in the projected thickness became larger as the turbulent Mach number increased, and the shock Mach number decreased.