Supersonic Turbulent Flow Research Articles

Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls – ERRATUM

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Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls

Abstract

Numerical investigation on the extrusive and intrusive subcavity types and their location on the primary recirculation zone for the supersonic turbulent flow through cavity type flameholders

Supersonic turbulent non-reacting flow through a cavity-type flameholder employed in scramjet engines with and without subcavities is numerically investigated. The governing equations describing the flow are solved by employing a density-based solver i.e., rhoCentralFoam which is an open-source computational fluid dynamics (CFD) code in OpenFOAM. The turbulence is modeled using the two-equation k-ω SST (shear stress transport) turbulence model. In the present study implication of subcavity types (i.e., extrusive and intrusive) on recirculation patterns and their strength at different subcavity aspect ratios (l/d) and subcavity locations at different inflow Mach numbers is investigated. A significant increase in the strength of the primary recirculation zone is observed for modified rectangle cavity 2 (MRC2) compared to the base rectangle cavity (BRC) and modified rectangle cavity 1 (MRC1). Results show a significant decrease in the size of the secondary recirculation zone for modified angle cavity 2 (MAC2) for all the subcavity aspect ratios and subcavity leading-edge distances (SLDs) at Mach 2. Results also indicate that at a fixed Mach number, the strength of the primary recirculation decreases with the increase in base cavity aspect ratio (L/D) for all the cavity types. Results show a substantial decrease in the velocity magnitude of cavity fluid with the decrease in cavity aft wall angle from 90° to 30°, which shows that the strength of the primary recirculation zone for BRC and MRC2 is higher compared to base angle cavity (BAC) and MAC2. Results show a 20.4776 % and 7.3822 % increase in the peak values of streamwise and normal velocities for MRC2 compared to BRC and MRC1 at Mach 2, and the corresponding increase in velocities for Mach 3 are 14.7979% and 5.6693% respectively for all the aspect rations and SLDs. Present results are validated with the experimental results available in the literature.

Investigation of the Impact of Flow of Vented Gas on Propagation of Thermal Runaway in a Li-Ion Battery Pack

The venting of hot gases due to rupture of a Li-ion cell during thermal runaway may rapidly transfer thermal energy to neighboring cells in a battery pack and cause propagation of thermal runaway. While thermal runaway has been studied extensively through both measurements and simulations, there is a relative lack of research on the impact of the venting process on thermal runaway propagation. This work presents a non-linear thermal-fluidic simulation of supersonic turbulent flow of hot gases ejecting from a trigger cell and spreading to neighboring cells. Assuming isentropic flow, temperature and speed of the gas flow as functions of time are estimated based on past measurements. These data are used in simulations to determine the thermal impact of the venting process on neighboring cells. The impact of various geometrical parameters of the battery pack on the spreading of venting gases is investigated. Results indicate that cell-to-cell gap, overhead gap and the location of the vent hole on the cell body strongly influence the nature of propagation of thermal runaway to neighboring cells. This work develops a fundamental understanding of an important process during thermal runaway, and may help in the design and optimization of safe Li-ion battery packs for energy conversion and storage.

A multishock model for the density variance of anisotropic, highly magnetized, supersonic turbulence

ABSTRACT Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma ^2_{\rho /\rho _0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parametrizes the star formation (SF) rate of a cloud. However, models for $\sigma ^2_{\rho /\rho _0}$ all share a common feature – the variance is assumed to be isotropic. This assumption does not hold when a trans-/sub-Alfvénic mean magnetic field, ${B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $\sigma _{\rho /\rho _0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $\sigma _{\rho /\rho _0}^2$ in the high Mach number $(\mathcal {M})$ limit as small-scale density fluctuations become suppressed by the strong ${B}_0$. The model reduces to the isotropic $\sigma _{\rho /\rho _0}^2\!-\!\mathcal {M}$ relation in the hydrodynamical limit. To validate our model, we calculate $\sigma _{\rho /\rho _0}^2$ from 12 high-resolution, three-dimensional, supersonic, sub-Alfvénic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented overdensities observed in some MCs and the implications for SF theory in the presence of a sub-Alfvénic ${B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.

Effect of Mach number and plate thickness on the flow field and heat transfer characteristics of supersonic turbulent flow over a flat plate at different thermal boundary conditions

Conjugate heat transfer analysis of supersonic turbulent flow over a finite thickness flat plate is studied numerically. The flow field is modeled by employing the Favre averaged Navier–Stokes (FANS) equations. Turbulence is modeled with the Menter’s shear-stress-transport (SST) k−ω model. The comparison of NCHT (non-conjugate heat transfer) and CHT (conjugate heat transfer) analysis shows that the interface temperature and fluid temperature variation for the CHT analysis are lower compared to the NCHT analysis. The results indicate that the interface temperature is significantly increased for the low thermal conductivity plate material, due to the reduced rate of heat transfer. The effect of plate thickness on the flow field temperature variation is negligible. However, it is observed that the maximum interface temperature Ti,max increases with the increase in plate thickness. The values of maximum interface temperature difference between the 5 mm and 2 mm thick Steel-1006 plates at Mach numbers 2, 4, and 5 in non-dimensional (non-dimensionalized with free-stream temperature) form are 0.05594, 0.129, and 0.1816 respectively for the isothermal boundary condition. Results indicate that for Mach 2, the heated wall thermal boundary conditions acts like heat source, leading to the higher interface temperature, whereas for Mach 4, and 5 the heated wall thermal boundary conditions acts like heat sink, thus lowering the interface temperature. The results show that for NCHT analysis the leading edge shock strength, and mean pressure along the wall increases with an increase in Mach number. The non-conjugate results (flow and heat transfer characteristics) of the present numerical study is validated with the direct numerical simulation (DNS) results available in the literature.

Acoustic pulsation for heat transfer abatement in supersonic channel flow

The impact of periodic pulsation normal to the flow passage on the heat and momentum transport is studied using direct numerical simulations. The selected test case is the fully developed supersonic turbulent flow at Reynolds numbers Reb=ρ¯bU¯bδ/μ¯wall=3000 and 6000 and Mach number Mcl=U¯cl/c¯cl≈1.5, bounded by isothermal walls. The pulsation is introduced by imposing a time-periodic uniform body-force in the spanwise directions, mimicking two acoustic drivers placed on the side-walls that are operating with a 180° phase difference. Results indicate that the spanwise pulsation at a moderate forcing amplitude, with the spanwise velocity oscillation amplitude W̃cl≈12% of bulk streamwise velocity or W̃cl+=W̃cl/uτ≈2, can create about 8% reduction in the Nusselt number (Nu), as well as in the skin friction coefficient (Cf), if applied at the optimal pulsation period T+=Tuτ2/ν¯wall within [173, 346], where T=2π/ωf. The excitation outside this band fails to achieve such high levels of modulations in heat and momentum transport processes near the walls. Visualizing the instantaneous temperature field reveals a periodic tilting of the near-wall turbulent structures that is translated into a decay in the energy of the streamwise vortices and an increase in the mean spanwise distance of such structures. The effect of the excitation on reducing the turbulent heat flux and Reynolds shear stress is studied, and the resulting streaming temperature and velocity profiles are discussed.

Experimental investigation of supersonic turbulent flow over cylinders with various heights

The unsteady flow structures and pressure fluctuations of the cylinder-induced shock wave/boundary layer interactions (SBLIs) were investigated at Mach 3.4 and 3.8. The cylinders were mounted on the test section floor with a turbulent boundary layer, and six cylinders with various heights have been tested. The nanoparticle-based planar laser scattering (NPLS) flow visualization tests were performed, and the different features of shock systems as well as the "breath" effects of the separation bubble, have been validated by NPLS images. Dynamic pressure transducers were used to characterize the pressure fluctuations, and a remarkable spectra change was noticed around the cylinder foot. With increasing height, the PSD curve of x/D = − 1 ahead of the cylinder shaped from one-peak pattern to two-peaks pattern, while the second frequency peak showed a typical frequency of f ≈32 kHz. It was inferred that the first peak was more influenced by the free end of the cylinder and the detached shock. The second peak pattern of f ≈32 kHz was presumed to be affected by the vortex breakdown near the cylinder foot through analysis of flow visualization. Low frequency around 0 ~ 3 kHz was found to have an obvious rise at x/D = − 2, close to the typical frequency of SBLIs.

Numerical Investigation of Supersonic Turbulent Flow Over Open Cavities

The study of cavity flow is one of the most important research topics of unsteady aerodynamics. Supersonic turbulent flows over a cavity are mostly encountered in missiles, turbomachinery, and high-speed aircraft. The turbulence inside the cavity gives rise to excess drag, acoustic waves, pressure fluctuations, and vibrations which may lead to numerous problems like excess fuel consumption, failure of missile trajectory or mechanical parts, and aerodynamic heating. We conduct numerical simulations to investigate the flow and compare our results to existing experimental data to show quantitative validation. We then investigate the effect of the Mach number of the turbulent supersonic flow on the pressure contours and the vortical structures inside the cavity and the subsequent effect on other flow parameters like acoustic waves. Thereafter, we propose two modifications of the cavity geometry, a) slanted edges and b) smoothened corners with slanted edges, to improve the aerodynamic performance. ANSYS ICEM tool has been used for the fine mesh generation of our cavity geometry and all the simulation was run on ANSYS fluent software. The K omega SST turbulence model was used for the simulation as it can capture the near wall property with reasonable accuracy and a grid independence study was carried out to find the correct solution of the Navier Stokes equation was proceeding by the solver. The parameters like pressure contours, streamline pattern, coefficient of pressure distribution and sound pressure level (SPL) has been found and compared for both modified and unmodified open cavity at different Mach number. The modifications suggested show a significant improvement over the open cavity designs in the mean pressure distribution and sound pressure level distributions.

Influence of Jet-to-Freestream Momentum Ratio and Gas Molecular Weight on Mixing at the Injection of Jets into a Supersonic Crossflow

A computational study of turbulent supersonic flows in a channel with a backward-facing step under the counter injection of argon and hydrogen jets is presented. The calculations are performed at the Mach number of 4 at the channel entrance for conditions close to flight ones, which are realized at the tests in a short-duration aerodynamic facility. Comparing the flowfields is carried out for the jet-to-crossflow momentum flux ratio range 1–6. It is shown that the mixing degree increases with a jet-to-crossflow momentum flux ratio and the molecular weight of the injected gas.

Aero-optical suppression for supersonic turbulent boundary layer

Aero-optical reduction in flat-plate turbulent boundary layer has been widely concerned due to critical application for high-speed target-seeking vehicles. From the perspective of disciplinary intersection between aerodynamic and optical engineering, the turbulence-aberrated optical behaviour, in high-Reynolds-number supersonic freestream, is numerically investigated using the in-house code High-Order SimulaTor for Aerodynamics (HOSTA) and ray-tracing scheme. To evaluate the efficiency of wall cooling strategy to reduce the detrimental aero-optical distortions, the authors leverage the theoretical equation deduced from Sutton statistic model for mutual verification with the simulative results. Additionally, based on the beneficial wall cooling effects on turbulent aero-optical reduction, comparison suggests that refrigeration directly towards the turbulence section is the most effective rather than cooling the laminar or transitional region. In further discussion, wall blowing, suction and combinational blowing and suction schemes are issued. Results reveal the rationality of employing proper suction amplitude to modify the flow into laminar state, and sufficiently high suction intensity is also promising in turbulent aero-optical reduction despite the fact of low efficiency currently. The current study puts an eye on the simulation concerning three-dimensional supersonic turbulent flow in high-Reynolds-number freestream and the application of statistic model, and future investigation is suggested for higher effectiveness of aero-optical suppression.

Влияние динамического напора и молекулярного веса газа на смешение при инжекции струй в поперечный сверхзвуковой поток

The results of a computational study of turbulent supersonic flows in a channel with a backward-facing step are presented, taking into account crossflow injection of argon and hydrogen jets. The calculations are performed at Mach number M = 4 at the channel entrance under the real flight conditions, which were realized in experiments in a hot-shot aerodynamic facility. The comparison of the flowfields is carried out for jet-to-freestream momentum ratio range J = 1 ÷ 6. It is shown that the degree of mixing, estimated from the uniformity index, increases with J increasing and with an increase in the molecular weight of the injected gas at the same J.

The Cloud Factory II: gravoturbulent kinematics of resolved molecular clouds in a galactic potential

ABSTRACTWe present a statistical analysis of the gravoturbulent velocity fluctuations in molecular cloud complexes extracted from our ‘Cloud Factory’ Galactic-scale interstellar medium (ISM) simulation suite. For this purpose, we produce non-local thermodynamic equilibrium 12CO J = 1 − 0 synthetic observations and apply the principal component analysis (PCA) reduction technique on a representative sample of cloud complexes. The velocity fluctuations are self-consistently generated by different physical mechanisms at play in our simulations, which include Galactic-scale forces, gas self-gravity, and supernova feedback. The statistical analysis suggests that, even though purely gravitational effects are necessary to reproduce standard observational laws, they are not sufficient in most cases. We show that the extra injection of energy from supernova explosions plays a key role in establishing the global turbulent field and the local dynamics and morphology of molecular clouds. Additionally, we characterize structure function scaling parameters as a result of cloud environmental conditions: some of the complexes are immersed in diffuse (interarm) or dense (spiral-arm) environments, and others are influenced by embedded or external supernovae. In quiescent regions, we obtain time-evolving trajectories of scaling parameters driven by gravitational collapse and supersonic turbulent flows. Our findings suggest that a PCA-based statistical study is a robust method to diagnose the physical mechanisms that drive the gravoturbulent properties of molecular clouds. Also, we present a new open source module, the pcafactory, which smartly performs PCA to extract velocity structure functions from simulated or real data of the ISM in a user-friendly way.

On Recirculation Region Length of Suddenly Expanded Supersonic Flows, Using CFD and Fuzzy Logic

This paper aims to introduce the core features of the Fuzzy Logic (FL) approach in simulations of turbulent Supersonic flows as a cost-effective methodology. Computational Fluid Dynamic (CFD) analysis is conducted to study the effect of Mach number (M e ), nozzle pressure ratio (NPR) and expansion corners (EC) on primary recirculation region length (Xr1). An Open FOAM numerical solver was used for this purpose. The CFD results developed were focused on developing relationships between input and output using the Mamdani-based fuzzy logic approach. This approach used membership functions viz. Triangular, Generalized bell shape and Gaussian membership functions. The models developed were matched with confirmatory test cases which differ from the training data. The flow field contours showed that the flow field generated numerous intrinsic features in the corner vortex. Also, the Triangular membership function made better predictions than the other two functions as it had a least absolute percentage error of 9.0705%.

The formulation of the RANS equations for supersonic and hypersonic turbulent flows

AbstractAccurate prediction of supersonic and hypersonic turbulent flows is essential to the design of high-speed aerospace vehicles. Such flows are mainly predicted using the Reynolds-Averaged Navier–Stokes (RANS) approach in general, and in particular turbulence models using the effective viscosity approximation. Several terms involving the turbulent kinetic energy (k) appear explicitly in the RANS equations through the modelling of the Reynolds stresses in such approach, and similar terms appear in the mean total energy equation. Some of these terms are often ignored in low, or even supersonic, speed simulations with zero-equation models, as well as some one- or two-equation models. The omission of these terms may not be appropriate under hypersonic conditions. Nevertheless, this is a widespread practice, even for very high-speed turbulent flow simulations, because many software packages still make such approximations. To quantify the impact of ignoring these terms in the RANS equations, two linear two-equation models and one non-linear two-equation model are applied to the computation of five supersonic and hypersonic benchmark cases, one 2D zero-pressure gradient hypersonic flat plate case and four shock wave boundary layer interaction (SWBLI) cases. The surface friction coefficients and velocity profiles predicted with different combinations of the turbulent kinetic energy terms present in the transport equations show little sensitivity to the presence of these terms in the zero-pressure gradient case. In the SWBLI cases, however, comparisons show that inclusion of k in the mean flow equations can have a strong effect on the prediction of flow separation. Therefore, it is highly recommended to include all the turbulent kinetic energy terms in the mean flow equations when dealing with simulations of supersonic and hypersonic turbulent flows, especially for flows with SWBLIs. As a further consequence, since k may not be obtained explicitly in zero-equation, or certain one-equation, models, it is debatable whether these models are suitable for simulations of supersonic and hypersonic turbulent flows with SWBLIs.

On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high‐speed compressible flows

SummaryHigh‐speed compressible turbulent flows typically contain discontinuities and have been widely modeled using Weighted Essentially Non‐Oscillatory (WENO) schemes due to their high‐order accuracy and sharp shock capturing capability. However, such schemes may damp the small scales of turbulence and result in inaccurate solutions in the context of turbulence‐resolving simulations. In this connection, the recently developed Targeted Essentially Non‐Oscillatory (TENO) schemes, including adaptive variants, may offer significant improvements. The present study aims to quantify the potential of these new schemes for a fully turbulent supersonic flow. Specifically, DNS of a compressible turbulent channel flow with M = 1.5 and Reτ = 222 is conducted using OpenSBLI, a high‐order finite difference computational fluid dynamics framework. This flow configuration is chosen to decouple the effect of flow discontinuities and turbulence and focus on the capability of the aforementioned high‐order schemes to resolve turbulent structures. The effect of the spatial resolution in different directions and coarse grid implicit LES are also evaluated against the WALE LES model. The TENO schemes are found to exhibit significant performance improvements over the WENO schemes in terms of the accuracy of the statistics and the resolution of the three‐dimensional vortical structures. The sixth‐order adaptive TENO scheme is found to produce comparable results to those obtained with nondissipative fourth‐ and sixth‐order central schemes and reference data obtained with spectral methods. Although the most computationally expensive scheme, it is shown that this adaptive scheme can produce satisfactory results if used as an implicit LES model.

Improvements to the Quadratic Constitutive Relation Based on NASA Juncture Flow Data

Modifications to the quadratic constitutive relations (QCRs) of Spalart (“Strategies for Turbulence Modelling and Simulation,” International Journal of Heat and Fluid Flow, Vol. 21, 2000, pp. 252–263) and Mani et al. (“Predictions of a Supersonic Turbulent Flow in a Square Duct,” AIAA Paper 2013-0860, Jan. 2013) are proposed. These modifications result from computational fluid dynamics (CFD) studies in the FUN3D and OVERFLOW solvers of the flowfield in the body boundary layer and near-corner region of the NASA Juncture Flow model. When used in conjunction with the Spalart–Allmaras turbulence model with rotation/curvature correction, the new relations improve the CFD Reynolds normal stress predictions, as compared with the experiment. This improvement leads to better predictions of separated corner flow behavior across a wide range of angles of attack that were measured, somewhat beyond the original QCR effect. The model’s performance in a square duct, driven by turbulence-induced vortices, is slightly improved. The QCR remains fairly simple to program and compatible with other eddy-viscosity models.

Application of flux vector splitting methods with SST turbulence model to wall-bounded flows

An explicit 3D Reynolds Averaged Navier-Stokes solver SURFS3D has been developed and run on a structured grid. A 4-stage Runge-Kutta (RK) method is used for the time integration and OpenMP is used to parallelize the solver. This is used as a platform to compare Van Leer’s Flux Vector Splitting Method (VLFVSM) to a variant of Liou’s Advection Upstream Splitting with velocity and pressure diffusion (AUSM+-up2). The code results are validated for wall bounded flows. Menter’s k−ω Shear Stress Transport (SST) turbulence model is employed and validated for turbulent flows. The SST turbulence model is selected due to its capability to predict the shock location and separation location in adverse pressure gradient accurately. The validation cases are laminar and turbulent incompressible flows and turbulent supersonic flow over flat plate, transonic flow over an axisymmetric bump, and supersonic flow over a blunt bi-conic configuration. It is observed that VLFVSM+SST lacks accurate viscous prediction capability for the wall-bounded flows at low speeds compared to AUSM +-up2+SST, which works well at low speed. In transonic flow conditions, both schemes perform well. AUSM +-up2 scheme exhibits mild carbuncle problem for Mach 3.0 flow over a blunt biconic configuration, whereas, VLFVSM is free from this problem. Overall, the SST turbulence model performance is good for all the validation cases studied.

HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

In this study, the open-source Hypersonics Task-based Research (HTR) solver for hypersonic aerothermodynamics is described. The physical formulation of the code includes thermochemical effects induced by high temperatures (vibrational excitation and chemical dissociation). The HTR solver uses high-order TENO-based spatial discretization on structured grids and efficient time integrators for stiff systems, is highly scalable in GPU-based supercomputers as a result of its implementation in the Regent/Legion stack, and is designed for direct numerical simulations of canonical hypersonic flows at high Reynolds numbers. The performance of the HTR solver is tested with benchmark cases including inviscid vortex advection, low- and high-speed laminar boundary layers, inviscid one-dimensional compressible flows in shock tubes, supersonic turbulent channel flows, and hypersonic transitional boundary layers of both calorically perfect gases and dissociating air. Program summaryProgram Title: Hypersonics Task-based Research solverProgram Files doi:http://dx.doi.org/10.17632/9zsxjtzfr7.1Licensing provisions: BSD 2-clauseProgramming language: RegentNature of problem: This code solves the Navier–Stokes equations at hypersonic Mach numbers including finite-rate chemistry for air dissociation along with multicomponent transport. The solver is designed for direct numerical simulations (DNS) of transitional and turbulent hypersonic turbulent flows at high enthalpies, and accounts for thermochemical effects such as vibrational excitation and chemical dissociation.Solution method: This code uses a low-dissipation sixth-order targeted essentially non-oscillatory (TENO) scheme for the spatial discretization of the conservation equations on Cartesian stretched grids. The time advancement is performed either with an explicit method, when the chemistry is slow and therefore does not introduce additional stiffness in the integration, or with an operator-splitting method that integrates the chemical production rates with an implicit discretization.Additional comments: The HTR solver builds on the runtime Legion [1] and is written in the programming language Regent [2] developed at Stanford University. Instructions for the installation of the components are provided in the README file enclosed with the HTR solver and in the Legion repository [1].

Dynamic mode decomposition of supersonic turbulent pipe flow with and without shock train

ABSTRACTLow frequency dynamics of shock–turbulence interactions in constant area pipe flow with centre-line Mach number of 1.7 and friction Reynolds number of 245 is analysed using dynamic mode decomposition (DMD) of well-resolved large eddy simulation (LES) data. Two flow cases – one with a shock train and the other without shocks – are analysed. The dominant DMD modes show the near-wall sweep-ejection activity especially for the flow without shocks and also show the influence of the shocks on the near-wall organisation of the flow. The DMD modes also demonstrate a reasonable correlation between the near-wall coherent structures and the shock train for some of the modes.