Wide Range Of Mach Numbers Research Articles

Development of three-dimensional rotated lattice Boltzmann flux solver for the simulation of high-speed compressible flows

A three-dimensional (3D) Rotated Lattice Boltzmann Flux Solver (RLBFS) is proposed and analyzed with matrix-based linear stability theory for simulating compressible flows in a wide range of Mach numbers. The 3D RLBFS applies the finite volume method to discrete the Navier-Stokes equations and evaluates its fluxes at each cell interface. To improve numerical stability, the convective fluxes are obtained in a hybrid way by using the D1Q4 lattice Boltzmann model in two perpendicular directions decomposed by the outer normal vector of each cell interface. The viscous fluxes are computed in a conventional way using the second-order central scheme. The stability performance and order accuracy of the proposed 3D RLBFS are examined by using the matrix-based stability theory and L2 errors on different meshes respectively. It is shown that the 3D RLBFS is stable even at high Mach number and has the second-order accuracy in space. The reliability and capability of the proposed method is further evaluated by simulating several challenging compressible flow problems, including subsonic flow over the DLR-F4, transonic flow over the ONERA M6 wing, supersonic flow around NACA0012 wing, hypersonic flow over the Viking lander capsule, hypersonic flow over a hemisphere and hypersonic flow around a blunt nose double cone. The obtained numerical results are in good agreement with experimental and/or numerical data published in the literature, indicating that the present method provides a reliable and effective tool for simulating practical three-dimensional compressible flow problems in aeronautics and astronautics.

Flow Coefficient and Starting Performance Prediction of Variable Geometry Curved Axisymmetric Inlet

With the development of combined cycle engines, it is urgent to estimate more quickly and accurately the flow capture capacity and starting performance of variable geometry inlets over a wide Mach number range. Based on the flow field and parameter fitting, two prediction methods for the curved axisymmetric inlet with lip translation scheme have been proposed. The method based on the flow field of the reference inlet is more efficient than the parameters-based prediction method, as it can accurately predict the lip translation distance and the corresponding flow coefficient over the entire working range of the inlet without additional numerical calculations. Moreover, the starting Mach number is accurately predicted by the fitting method based on the throat Mach number of the reference inlet, with a relative error of only 0.95% compared to the numerical simulation. The flow coefficient-based method is simple and accurate for predicting lip translation distances with a known starting Mach number, with a relative error of only 1.65% compared to numerical simulations. The prediction approaches can overcome the drawbacks of the standard iterative algorithms and significantly enhance computational accuracy and efficiency.

Benchmarking the face-centred finite volume method for compressible laminar flows

Purpose This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks. Design/methodology/approach The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software. Findings The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%. Originality/value The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

Aerodynamic Coefficients of a Microspoiler for Spin-Stabilized Projectiles

In this paper, the aerodynamic coefficients of a microspoiler for a spin-stabilized projectile are studied using a computational fluid dynamics (CFD) simulation. To guarantee an effective study, the CFD simulation methodology is validated by the current literature and a wind-tunnel test. As a result, the additional axial force coefficient, additional normal force coefficient, and normal moment coefficient are obtained and varied with a wide range of Mach numbers (from 0.6 to 2.0), angles of attack (from 0 to 30°), and aerodynamic roll angles (from 0 to 180°). The numerical simulation results show that, in addition to the freestream Mach number and the angle of attack, the effect of the aerodynamic roll angle on the additional axial force and normal force coefficients cannot be negligible. By observing and analyzing a series of pressure field plots around the uncontrolled and controlled projectiles, some important phenomena are reasonably discussed. It was found that the complicated variation in the aerodynamic coefficients of the microspoiler is induced by flow modifications, such as the pressure distribution around the projectile. The results of this research are expected to be supplementary to those concerning the aerodynamic characteristics of spin-stabilized projectiles with microspoilers, as concluded in the current literature.

Surrogate-based aerodynamic shape optimization of a sliding shear variable sweep wing over a wide Mach-number range with plasma constraint relaxation

Surrogate-based aerodynamic shape optimization of a sliding shear variable sweep wing over a wide Mach-number range with plasma constraint relaxation

Assessment of a new hybrid-SSOR implicit temporal scheme for turbulent flows across a wide range of Mach numbers

Assessment of a new hybrid-SSOR implicit temporal scheme for turbulent flows across a wide range of Mach numbers

Vane–Probe Interactions in Transonic Flows

AbstractIn this article, a numerical investigation of the effect of a miniaturized five-hole probe downstream of a transonic low-pressure turbine vane row is presented. First, a numerical calibration of the probe was performed in uniform flow conditions, as is the case for any traditional calibration, for a wide range of Mach number, yaw angle, and pitch angle conditions. The effect of the probe on the general flow field throughout the turbine vane segments was then evaluated by performing a comparison between a setup with vanes only (no probe) and with vanes and probes. It was found that, as the probe traverses downstream the vane, the probe impact on the vane isentropic Mach number depends on the probe circumferential position. The highest impact was observed when the probe is located at the upper mid-passage (θ = 0.5), consisting of a relatively small reduction of the isentropic Mach number on the vane suction side of just 0.02. To assess the accuracy of the quantities “measured” by the probe, the probe-determined flow field was compared to the flow field of the vanes-only setup. A nonnegligible modification of the probe-determined local distributions of Mach number, yaw angle, and pitch angle is revealed with respect to the undisturbed flow. Further investigation involving stagnation point tracking showed that the artificial high circumferential variation of the yaw angle is not caused by a modification of the vane outlet flow angle, but is induced by nonuniform flow conditions downstream of the vanes. With knowledge of the above, a two-step correction is used to account for the effects of the nonuniformity of the flow, and its impact is evaluated on 2D and 3D flow regions. A significative effect of the correction was found on the probe-determined yaw angle, in which the difference from the vanes-only data was reduced to below 1 deg, except near the endwalls where larger discrepancies remain due to probe–endwall interactions. A shortfall of the correction was instead observed on the probe-determined Mach numbers. Finally, the pitch-wise averaged quantities were evaluated. It was observed that the highest differences between probe-determined and undisturbed data occur where radial gradients of total pressure are stronger and that the two-step correction had almost negligible impact on the pitch-wise averaged quantities.

Pasivna modifikacija protoka preko supersoničnog i hipersoničnog sistema za usisavanje vazduha pomoću odvoda

The air intake should be operated at design conditions to achieve a high total pressure recovery and optimum mass capture ratio. The current research focuses on the numerical simulation of the supersonic and hypersonic air inlet and its starting and unstarting characteristics. 2D RANS equation for supersonic and hypersonic intake has been solved using the k-oSST turbulence model. The in-house code and the algorithm based on the RANS equation have also been validated in due process and used for subsequent simulations. The sudden drop in mass capture ratio indicates the unstart condition of the intake. The presence of a bleed section has a commendable effect on the performance parameter of the air intake. A separation bubble was observed at the intake's entrance during the off-design conditions, resulting in performance losses. Four different bleed sections ranging in size from 1.6mm to 8.6mm were used, and simulations with bleed were run for different Mach numbers ranging from 3 to 8. The optimum bleed size of 3mm has been found quite effective in modifying Total pressure recovery within the optimum mass flow rate over the wide range of Mach numbers.

The outflow of gas mixture into vacuum, periodically interrupted by bodies moving towards the jet

The problem about the unsteady outflow of a mixture of gases into a vacuum, periodically interrupted by bodies moving toward the jet, was studied. This problem was considered as a possible gas separation technique. The unsteady flow of the gas mixture was simulated using the event-driven molecular dynamics (EDMD) approach under the following conditions: (1) moving boundaries, (2) a wide range of Knudsen number, (3) a wide range of Mach number, (4) violation of equilibrium between rotational and translational degrees of freedom. The problem of periodically interrupted flow was solved as close to reality as possible, taking into account the finite gap between the stator and the moving runner blades. The dependences of the molar fraction and flow rate of the resulting mixture on the system parameters were obtained. As a result, a number of practically important recommendations for the design of such systems have been formulated.

An extension of the all-Mach number pressure-based solution framework for numerical modelling of two-phase flows with interface

In this paper, we present the extension of the pressure-based solver designed for the simulation of compressible and/or incompressible two-phase flows of viscous fluids. The core of the numerical scheme is based on the hybrid Kurganov — Noele — Petrova/PIMPLE algorithm. The governing equations are discretized in the conservative form and solved for velocity and pressure, with the density evaluated by an equation of state. The acoustic-conservative interface discretization technique helps to prevent the unphysical instabilities on the interface. The solver was validated on various cases in wide range of Mach number, both for single-phase and two-phase flows. The numerical algorithm was implemented on the basis of the well-known open-source Computational Fluid Dynamics library OpenFOAM in the solver called interTwoPhaseCentralFoam. The source code and the pack of test cases are available on GitHub: https://github.com/unicfdlab/hybridCentralSolvers The research was supported by Russian Science Foundation (proj. 17-79-20445).

Performance analysis of the hypersonic vehicle with dorsal and ventral intake

The integrated design of the airframe and inlet is the favorite choice for the aerodynamic configuration design of the air-breathing hypersonic vehicle. To better understand the integrated configurations with a dorsal intake, this paper utilizes the computational fluid dynamics (CFD) method to comprehensively compare the performance of integrated configurations with the dorsal and traditionally used ventral intake. The performance indexes include aerodynamic performance, such as lift-to-drag ratio, the inlet performance, and thrust-to-drag balance performance. First, under the same geometric constraints, two integrated aerodynamic configurations with dorsal and ventral intake are designed based on a truncated Busemann inlet. Second, the CFD numerical simulation method based on multi-GPU parallel computing is developed and verified. Then, the flow-field characteristics, the aerodynamic, inlet, and thrust-to-drag balance performance of the two types of configurations in a wide range of Mach numbers are comprehensively compared using the GPU-based efficient numerical simulation method. The advantages and disadvantages of the two types of configurations are then analyzed to provide a meaningful reference for the aerodynamic configuration design of air-breathing hypersonic vehicles.

A parallel discrete unified gas kinetic scheme on unstructured grid for inviscid high-speed compressible flow simulation

The discrete unified gas kinetic scheme (DUGKS) is a recently devised approach to simulate multiscale flows based on the kinetic models, which also shows distinct features for continuum flows. Most of the existing DUGKS are sequential or based on structured grids, thus limiting their scope of application in engineering. In this paper, a parallel DUGKS for inviscid high-speed compressible flows on unstructured grids is proposed. In the framework of the DUGKS, the gradients of the distribution functions are calculated by a least-square method. To parallelize the method, a graph-based partitioning method is employed to guarantee the load balancing and minimize the communication among processors. The method is validated by several benchmark problems, i.e., a two-dimensional (2D) Riemann problem, 2D subsonic flows passing two benchmark airfoils, a 2D regular shock reflection problem, 2D supersonic flows (Mach numbers are 3 and 5) around a cylinder, an explosion in a three-dimensional (3D) box, a 3D subsonic flow around the Office National d'Etudes et de Recherches Aérospatiales M6 wing, a 3D hypersonic flow (Mach number is 10) around a hemisphere, and a supersonic flow over the Northrop YF-17 fighter model. The numerical results show good agreement with the published results, and the present method is robust for a wide range of Mach numbers, from subsonic to hypersonic. The parallel performance results show that the proposed method is highly parallel scalable, where an almost linear scalability with 93% parallel efficiency is achieved for a 3D problem with over 55 × 106 tetrahedrons on a supercomputer with up to 4800 processors.

Non-equilibrium condensation

The condensation process today requires more accurate, efficient and well-tested modeling approaches. In this article the numerical simulations of monatomic vapor condensation on its liquid phase have been carried out by applying the S-model kinetic equation, the Molecular Dynamics approach and the Moment Method. A good agreement is found between the results obtained by these three methods for monatomic gases. The Moment Method has great potential for efficient estimation of condensation fluxes by respecting the conservation of mass, momentum and energy through the Knudsen layer. This method has no analytical solution in the case of condensation, unlike the evaporation process, and the three conservation equations must be solved numerically (the Python tool is provided in Supplementary). Similar to evaporation, the nonlinear form of Schrage’s analytic expression requires information about the third parameter, additionally to two needed in the case of condensation, while linear Schrage’s formula overestimates the condensation rate for small condensation velocities and underestimates it for higher ones. We have tested our approaches by comparison with experimental data for the condensation of mercury for a wide range of Mach numbers, up to 0.85. The existence of an inverted temperature gradient has been showed numerically as well as the reason of its appearance and its evolution for different experimental conditions. The methodology for extracting the condensation coefficient based on the results of the Moment method is proposed. Obtained by this way condensation coefficients were found to be close to unity and decreasing with increasing vapor pressure and temperature.

Principles of Magnetohydrodynamical Control of Internal and External Supersonic Flows

This paper demonstrates the possibility of active magnetohydrodynamic (MHD) control of supersonic flows containing shock waves. The shock wave configurations that occur at the inlet to a supersonic diffuser and in front of a streamlined semicylindrical model are used for the purpose of investigation. The impact is carried out by organizing local gas discharge regions when applying a magnetic field transverse to gas discharge currents. It has been shown that by changing the local region of application, the intensity and the direction of the gas discharge currents, it is possible to change the intensity and direction of the ponderomotive force acting on the gas flow during MHD interaction. The ponderomotive force control allows for acting locally on the shape and position of shock waves, the speed and direction of the flow, and the increase or reduction of pressure near the surface of the streamlined body. The experiments were carried out on a gas dynamic setup based on a shock tube in a gas dynamic path, capable of creating supersonic flows in a wide range of Mach numbers at M = 4–7. There was a possibility of organizing the electric and pulsed magnetic fields with an intensity of up to 1.5 T. The given experimental Schlieren flow patterns and the analysis of the obtained data demonstrate the MHD effect on: the change in the angle of inclination of the attached shocks, both into increase and decrease; the bow shock wave approaching the body or the removal from it; and the change in the aerodynamic drag and lift force of the streamlined bodies.

Implicit Solar Coronal Magnetohydrodynamic (MHD) Modeling with a Low-dissipation Hybridized AUSM-HLL Riemann Solver

In this paper, we develop a 3D implicit single-fluid magnetohydrodynamic (MHD) model to simulate the steady-state solar corona with a wide range of Mach numbers and low plasma β. We employ a low-dissipation advection upstream splitting method (AUSM) to calculate the convective flux in the regions of low Mach numbers for a high resolution, and hybridize the AUSM with Harten-Lax-van Leer Riemann solver in the regions of high Mach numbers to improve the solver’s robustness. The inner boundary condition of no backflow is implemented by numerical flux. A reconstruction method based on the divergence-free radial basis function is adopted to enhance the divergence-free constraint of magnetic field. Also, an anisotropic thermal conduction term is considered; the positivity-preserving reconstruction method is used to prevent the presence of negative thermal pressure and plasma density, and the implicit lower-upper symmetric Gauss Seidel method is implemented for a better convergence rate. After establishing the implicit solar wind MHD model, we employ it to simulate steady-state solar coronal structures in Carrington rotations 2177 and 2212. The simulations demonstrate that the MHD model’s computational efficiency is desirable, and the modeled results are basically in agreement with the solar coronal observations and the mapped in situ measurements from the OMNI archive. Consequently, this implicit MHD model is promising to simulate a complex plasma environment with high-intensity magnetic field and wide-ranging Mach numbers.

Surrogate-based aerodynamic shape optimization of a morphing wing considering a wide Mach-number range

Aerodynamic shape design considering both subsonic and hypersonic performance is a challenge in the field of aerospace. Many studies have shown that morphing wing is a promising technology to address this challenge. In this article, a new morphing mechanism which changes both the plane shape (such as span and sweep angle) and the profile (such as chord length and relative thickness) of the wing is proposed and a multi-objective optimization design for this new morphing mechanism is conducted based on surrogate-based optimization (SBO) algorithm. In the optimization design, three different configurations of the morphing wing which are the 36-, 45- and 70-degree sweep angle state, respectively and four different flow conditions which are subsonic flow (0.25 Ma), transonic flow (0.85 Ma), supersonic flow (1.2 Ma) and hypersonic flow (6 Ma) are considered. 36-degree sweep angle state is used for subsonic flow, 45-degree sweep angle state is used for transonic flow and supersonic flow and 70-degree sweep angle state is used for hypersonic flow. Subsonic lift and transonic, supersonic, hypersonic lift-to-drag ratios are objectives of this optimization design which has up to 64 design variables. To reduce computational cost of high-fidelity CFD (computational fluid dynamics) simulations and find the global optimum, Kriging surrogate model combined with a parallel infill-sampling method and a multi-round strategy are employed in this study. At last, the optimized morphing wing is evaluated and compared with the baseline and a fixed wing which is a moderate sweep wing. Results show that the optimized morphing wing features a very good aerodynamic performance improvement over the flow regimes from subsonic to hypersonic flow conditions.

HALO3D: An All-Mach Approach to Hypersonic Flows Simulation

This paper presents HALO3D, a CFD code simulating the wide range of Mach numbers a hypervelocity vehicle experiences. HALO3D is composed of (a) a RANS edge-based Finite Element (FE) solver modelling high-velocity thermo-chemical non-equilibrium flows, (b) an electromagnetic interactions solver, (c) an ablation module, (d) a Direct Simulation Monte Carlo (DSMC) solver for the rarefied regime, seamlessly linked to the continuum one, and (e) a powerful automatic mesh optimiser finely capturing the many singular hypersonic flow phenomena. Verification and validation simulations for two- and three-dimensional hypersonic flows over a flat plate, a cylinder, a blunt conical body, re-entry capsules, and a waverider geometry demonstrate accurate aerothermodynamic predictions in a wide range of Knudsen numbers, complex geometries and multiphysics.

Research on Flow Characteristics of a Variable Mach Number Aerodynamic Test Device by a Rotating Profile

In the development process of aircraft, it needs to be tested in different incoming flow environments. Therefore, the test equipment that can provide a wide Mach number range and a fast-response flow field has always been a research hotspot. In this paper, a variable Mach number aerodynamic test device by a rotating profile is constructed with a divergent nozzle. The flow field parameters of the device are calculated by numerical simulation. The influence of the initial divergent half-angle of the cubic curve profile and the profile rotation mode on the test area is analyzed by using the flow quality evaluation method. The results show that when the incoming flow Mach number is 1.5 to 3.0, by adjusting the incoming flow Mach number and the expansion ratio of the test device, the Mach number in the test area can change continuously from 3 to 5 and the atmospheric environment at an altitude of 11 km to 20 km can be simulated. The test device composed of the cubic curve profile with the same initial divergent half-angle as the original straight line has a better flow quality. The both-side rotation mode can ensure the symmetry of the flow direction better than the one-side rotation mode.

Anti-dissipation pressure correction under low Mach numbers for Godunov-type schemes

An effective and unified framework, termed anti-dissipation pressure correction, is established to overcome the deterioration in the accuracy observed in Godunov-type schemes in low-speed scenarios. Based on the scale analysis of the nonlinear characteristic line relation, the deteriorated-accuracy source term is associated with the speed of sound and velocity difference term. Subsequently, the anti-dissipation pressure correction term is constructed by using the scaling Mach number function to rescale the error source term to be of the magnitude of the convective velocity and ensure a satisfactory accuracy. This scaling function is a polynomial of the local Mach number and restrained by the shock indicator. Results of the asymptotic analysis demonstrate that the anti-dissipation pressure correction helps recover the correct Ma2 scaling of the pressure fluctuations and damps the checkerboard modes, and this aspect is verified considering low Mach number flows over the NACA0012 airfoil. This novel framework can remarkably enhance the low Mach number performance and is also applicable to scenarios involving moderate or high Mach numbers. The performance of the approach is validated through numerical investigations across a wide range of Mach numbers.

Comparison of hot-wire and particle image velocimetry measurements in the zone of interaction of a shock wave with a boundary layer at Mach number of 1.43

The interaction of a shock wave with a laminar boundary layer was studied at the low supersonic Mach number M = 1.43. The measurements were carried out by particle image velocimetry and hot-wire anemometry. The wide range of Mach numbers in the shear layer occurring in the interaction zone made the analysis of hot-wire anemometer data much more difficult. The paper proposes the method of processing of the hot-wire anemometer data involving the simplified sensor calibration and the data obtained by the particle image velocimetry measurements. Good agreement of the results obtained by two experimental techniques is demonstrated. The data gathered in this work permit simplifying essentially the usage of the hot-wire anemometer technique applied for the study of transonic shear flows.