scholarly journals Density effects on post-shock turbulence structure and dynamics

2019 ◽  
Vol 880 ◽  
pp. 935-968 ◽  
Author(s):  
Yifeng Tian ◽  
Farhad A. Jaberi ◽  
Daniel Livescu
Keyword(s):  
Shock Wave ◽  
Isotropic Turbulence ◽  
Joint Probability ◽  
Variable Density ◽  
Particle Methods ◽  
Turbulence Structure ◽  
Differential Distribution ◽  
Flow Topology ◽  
Turbulent Statistics ◽  
Post Shock

Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles that density plays in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic VGT, PDF$(Q^{\ast },R^{\ast })$, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-species case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetric PDF$(Q^{\ast },R^{\ast })$ in heavy-fluid regions, while the light-fluid regions retain the characteristic tear-drop shape. To understand this behaviour and the return to ‘standard’ turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants is studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multi-fluid case, making them critically important to the flow dynamics and turbulence structure.

scholarly journals Numerical study of variable density turbulence interaction with a normal shock wave

2017 ◽  
Vol 829 ◽  
pp. 551-588 ◽  
Author(s):  
Yifeng Tian ◽  
Farhad A. Jaberi ◽  
Zhaorui Li ◽  
Daniel Livescu
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
Numerical Study ◽  
Variable Density ◽  
Computational Method ◽  
Normal Shock ◽  
Turbulence Structure ◽  
Linear Interaction ◽  
Normal Shock Wave ◽  
Turbulent Statistics

Accurate numerical simulations of shock–turbulence interaction (STI) are conducted with a hybrid monotonicity-preserving–compact-finite-difference scheme for a detailed study of STI in variable density flows. Theoretical and numerical assessments of data confirm that all turbulence scales as well as the STI are well captured by the computational method. Linear interaction approximation (LIA) convergence tests conducted with the shock-capturing simulations exhibit a similar trend of converging to LIA predictions to shock-resolving direct numerical simulations (DNS). The effects of density variations on STI are studied by comparing the results corresponding to an upstream multi-fluid mixture with the single-fluid case. The results show that for the current parameter ranges, the turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations exist. Turbulent mixing enhancement by the shock is also increased and stronger mixing asymmetry in the postshock region is observed when there is significant density variation. The turbulence structure is strongly modified by the shock wave, with a differential distribution of turbulent statistics in regions having different densities. The dominant mechanisms behind the variable density STI are identified by analysing the transport equations for the Reynolds stresses, vorticity, normalized mass flux and density specific volume covariance.

Turbulence structure behind the shock in canonical shock–vortical turbulence interaction

2014 ◽  
Vol 756 ◽  
Author(s):  
Jaiyoung Ryu ◽  
Daniel Livescu
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Isotropic Turbulence ◽  
Interaction Analysis ◽  
Longitudinal Velocity ◽  
Wave Structure ◽  
Turbulence Structure ◽  
Turbulent Structures ◽  
Linear Interaction ◽  
Third Invariant

AbstractThe interaction between vortical isotropic turbulence (IT) and a normal shock wave is studied using direct numerical simulation (DNS) and linear interaction analysis (LIA). In previous studies, agreement between the simulation results and the LIA predictions has been limited and, thus, the significance of LIA has been underestimated. In this paper, we present high-resolution simulations which accurately solve all flow scales (including the shock-wave structure) and extensively cover the parameter space (the shock Mach number, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_s$, ranges from 1.1 to 2.2 and the Taylor Reynolds number, ${\mathit{Re}}_{\lambda }$, ranges from 10 to 45). The results show, for the first time, that the turbulence quantities from DNS converge to the LIA solutions as the turbulent Mach number, $M_t$, becomes small, even at low upstream Reynolds numbers. The classical LIA formulae are extended to compute the complete post-shock flow fields using an IT database. The solutions, consistent with the DNS results, show that the shock wave significantly changes the topology of the turbulent structures, with a symmetrization of the third invariant of the velocity gradient tensor and ($M_s$-mediated) of the probability density function (PDF) of the longitudinal velocity derivatives, and an $M_s$-dependent increase in the correlation between strain and rotation.

Reynolds- and Mach-number effects in canonical shock–turbulence interaction

2013 ◽  
Vol 717 ◽  
pp. 293-321 ◽  
Author(s):  
Johan Larsson ◽  
Ivan Bermejo-Moreno ◽  
Sanjiva K. Lele
Keyword(s):  
Shock Wave ◽  
Numerical Scheme ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Linear Analysis ◽  
Direct Numerical Simulations ◽  
High Reynolds Numbers ◽  
Grid Convergence ◽  
Post Shock ◽  
High Reynolds

AbstractThe interaction between isotropic turbulence and a normal shock wave is investigated through a series of direct numerical simulations at different Reynolds numbers and mean and turbulent Mach numbers. The computed data are compared to experiments and linear theory, showing that the amplification of turbulence kinetic energy across a shock wave is described well using linearized dynamics. The post-shock anisotropy of the turbulence, however, is qualitatively different from that predicted by linear analysis. The jumps in mean density and pressure are lower than the non-turbulent Rankine–Hugoniot results by a factor of the square of the turbulence intensity. It is shown that the dissipative scales of turbulence return to isotropy within about 10 convected Kolmogorov time scales, a distance that becomes very small at high Reynolds numbers. Special attention is paid to the ‘broken shock’ regime of intense turbulence, where the shock can be locally replaced by smooth compressions. Grid convergence of the probability density function of the shock jumps proves that this effect is physical, and not an artefact of the numerical scheme.

scholarly journals Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 157
Author(s):  
Duane Rosenberg ◽  
Annick Pouquet ◽  
Raffaele Marino
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Potential Vorticity ◽  
Isotropic Turbulence ◽  
Joint Probability ◽  
Buoyancy Flux ◽  
Turbulent Regime ◽  
Stratified Turbulence ◽  
Low Dissipation ◽  
Linear And Nonlinear

We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

Computational investigation of turbulent jet impinging onto rotating disk

2007 ◽  
Vol 17 (3) ◽  
pp. 284-301 ◽  
Author(s):  
A.C. Benim ◽  
K. Ozkan ◽  
M. Cagan ◽  
D. Gunes
Keyword(s):  
Boundary Conditions ◽  
Isotropic Turbulence ◽  
Domain Size ◽  
Rotating Disk ◽  
Turbulent Jet ◽  
Turbulence Structure ◽  
Computational Domain ◽  
Convergence Criteria ◽  
Computational Investigation ◽  
Content Type

PurposeThe main purpose of the paper is the validation of a broad range of RANS turbulence models, for the prediction of flow and heat transfer, for a broad range of boundary conditions and geometrical configurations, for this class of problems.Design/methodology/approachTwo‐ and three‐dimensional computations are performed using a general‐purpose CFD code based on a finite volume method and a pressure‐correction formulation. Special attention is paid to achieve a high numerical accuracy by applying second order discretization schemes and stringent convergence criteria, as well as performing sensitivity studies with respect to the grid resolution, computational domain size and boundary conditions. Results are assessed by comparing the predictions with the measurements available in the literature.FindingsA rather unsatisfactory performance of the Reynolds stress model is observed, in general, although the contrary has been expected in this rotating flow, exhibiting a predominantly non‐isotropic turbulence structure. The best overall agreement with the experiments is obtained by the k‐ω model, where the SST model is also observed to provide a quite good performance, which is close to that of the k‐ω model, for most of the investigated cases.Originality/valueTo date, computational investigation of turbulent jet impinging on to “rotating” disk has not received much attention. To the best of the authors' knowledge, a thorough numerical analysis of the generic problem comparable with present study has not yet been attempted.

scholarly journals Estimate of Plasma Temperatures Across a CME-Driven Shock from a Comparison Between EUV and Radio Data

Solar Physics ◽  
2020 ◽  
Vol 295 (9) ◽  
Author(s):  
Federica Frassati ◽  
Salvatore Mancuso ◽  
Alessandro Bemporad
Keyword(s):  
Shock Wave ◽  
Compression Ratio ◽  
Emission Measure ◽  
Type Ii ◽  
Solar Dynamics Observatory ◽  
Radio Data ◽  
Shock Temperature ◽  
Post Shock ◽  
Dem Analysis ◽  
Solar Dynamics

Abstract In this work, we analyze the evolution of an EUV wave front associated with a solar eruption that occurred on 30 October 2014, with the aim of investigating, through differential emission measure (DEM) analysis, the physical properties of the plasma compressed and heated by the accompanying shock wave. The EUV wave was observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and was accompanied by the detection of a metric Type II burst observed by ground-based radio spectrographs. The EUV signature of the shock wave was also detected in two of the AIA channels centered at 193 Å and 211 Å as an EUV intensity enhancement propagating ahead of the associated CME. The density compression ratio $X$ X of the shock as inferred from the analysis of the EUV data is $X \approx 1.23$ X ≈ 1.23 , in agreement with independent estimates obtained from the analysis of the Type II band-splitting of the radio data and inferred by adopting the upstream–downstream interpretation. By applying the Rankine–Hugoniot jump conditions under the hypothesis of a perpendicular shock, we also estimate the temperature ratio as $T_{\mathrm{D}}/T_{\mathrm{U}} \approx 1.55$ T D / T U ≈ 1.55 and the post-shock temperature as $T_{\mathrm{D}}\approx 2.75$ T D ≈ 2.75 MK. The modest compression ratio and temperature jump derived from the EUV analysis at the shock passage are typical of weak coronal shocks.

scholarly journals A Self-Similar Flow behind a Magnetogasdynamic Shock Wave Generated by a Moving Piston in a Gravitating Gas with Variable Density: Isothermal Flow

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
G. Nath ◽  
A. K. Sinha
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Ambient Medium ◽  
Initial Density ◽  
Power Laws ◽  
Variable Density ◽  
Ideal Gas ◽  
Piston Velocity ◽  
Azimuthal Magnetic Field ◽  
Initial Magnetic Field

The propagation of a cylindrical (or spherical) shock wave in an ideal gas with azimuthal magnetic field and with or without self-gravitational effects is investigated. The shock wave is driven out by a piston moving with time according to power law. The initial density and the initial magnetic field of the ambient medium are assumed to be varying and obeying power laws. Solutions are obtained, when the flow between the shock and the piston is isothermal. The gas is assumed to have infinite electrical conductivity. The shock wave moves with variable velocity, and the total energy of the wave is nonconstant. The effects of variation of the piston velocity exponent (i.e., variation of the initial density exponent), the initial magnetic field exponent, the gravitational parameter, and the Alfven-Mach number on the flow field are obtained. It is investigated that the self-gravitation reduces the effects of the magnetic field. A comparison is also made between gravitating and nongravitating cases.

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