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.

Evolution of enstrophy in shock/homogeneous turbulence interaction

2012 ◽  
Vol 707 ◽  
pp. 74-110 ◽  
Author(s):  
Krishnendu Sinha
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Interaction Analysis ◽  
Direct Numerical Simulations ◽  
Homogeneous Isotropic Turbulence ◽  
Mean Flow ◽  
Linear Interaction

AbstractInteraction of turbulent fluctuations with a shock wave plays an important role in many high-speed flow applications. This paper studies the amplification of enstrophy, defined as mean-square fluctuating vorticity, in homogeneous isotropic turbulence passing through a normal shock. Linearized Navier–Stokes equations written in a frame of reference attached to the unsteady shock wave are used to derive transport equations for the vorticity components. These are combined to obtain an equation that describes the evolution of enstrophy across a time-averaged shock wave. A budget of the enstrophy equation computed using results from linear interaction analysis and data from direct numerical simulations identifies the dominant physical mechanisms in the flow. Production due to mean flow compression and baroclinic torques are found to be the major contributors to the enstrophy amplification. Closure approximations are proposed for the unclosed correlations in the production and baroclinic source terms. The resulting model equation is integrated to obtain the enstrophy jump across a shock for a range of upstream Mach numbers. The model predictions are compared with linear theory results for varying levels of vortical and entropic fluctuations in the upstream flow. The enstrophy model is then cast in the form of$k$–$\epsilon $equations and used to compute the interaction of homogeneous isotropic turbulence with normal shocks. The results are compared with available data from direct numerical simulations. The equations are further used to propose a model for the amplification of turbulent viscosity across a shock, which is then applied to a canonical shock–boundary layer interaction. It is shown that the current model is a significant improvement over existing models, both for homogeneous isotropic turbulence and in the case of complex high-speed flows with shock waves.

Turbulent energy flux generated by shock/homogeneous-turbulence interaction

2016 ◽  
Vol 796 ◽  
pp. 113-157 ◽  
Author(s):  
Russell Quadros ◽  
Krishnendu Sinha ◽  
Johan Larsson
Keyword(s):  
Shock Wave ◽  
Turbulent Flows ◽  
Energy Flux ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Interaction Analysis ◽  
Turbulent Energy ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Linear Interaction

High-speed turbulent flows with shock waves are characterized by high localized surface heat transfer rates. Computational predictions are often inaccurate due to the limitations in modelling of the unclosed turbulent energy flux in the highly non-equilibrium regions of shock interaction. In this paper, we investigate the turbulent energy flux generated when homogeneous isotropic turbulence passes through a nominally normal shock wave. We use linear interaction analysis where the incoming turbulence is idealized as being composed of a collection of two-dimensional planar vorticity waves, and the shock wave is taken to be a discontinuity. The nature of the postshock turbulent energy flux is predicted to be strongly dependent on the angle of incidence of the incoming waves. The energy flux correlation is also decomposed into its vortical, entropy and acoustic contributions to understand its rapid non-monotonic variation behind the shock. Three-dimensional statistics, calculated by integrating two-dimensional results over a prescribed upstream energy spectrum, are compared with available data from direct numerical simulations. A detailed budget of the governing equation is also considered in order to gain insight into the underlying physics.

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.

Criterion Prediction of Changes of Shock-Wave Structure at Transonic Flow Around Airfoils with Local Impulse Energy

2014 ◽  
Vol 9 (1) ◽  
pp. 39-48
Author(s):  
Sergey Aulchenko ◽  
Vladimir Zamuraev ◽  
Anna Kalinina
Keyword(s):  
Shock Wave ◽  
Numerical Modeling ◽  
Mach Number ◽  
Pulse Energy ◽  
Transonic Flow ◽  
Energy Supply ◽  
Wave Structure ◽  
Shock Wave Structure ◽  
Wide Range ◽  
Comparison Of The Results

The results of numerical modeling of transonic streamline of profile with a local pulse energy supply were generalized in terms of criteria analysis for a wide range of parameters. Defined set of criteria allows predicting not only the degree, but the features of the flow transformation. A comparison of the results of the criteria analysis with numerical calculations of transonic streamline (Mach number M∞ = 0,85) of a symmetrical profile NASA-0012 were performed for energy supply in areas such as narrow and compact form

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.

Velocity and vorticity in weakly compressible isotropic turbulence under longitudinal expansive straining

2007 ◽  
Vol 584 ◽  
pp. 301-335 ◽  
Author(s):  
SAVVAS XANTHOS ◽  
MINWEI GONG ◽  
YIANNIS ANDREOPOULOS
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Pressure Gradient ◽  
Shock Tube ◽  
Isotropic Turbulence ◽  
Strain Tensor ◽  
Velocity Fluctuations ◽  
Total Enthalpy ◽  
Expansion Waves ◽  
Custom Made

The response of homogeneous and isotropic turbulence to streamwise straining action provided by planar expansion waves has been studied experimentally in the CCNY shock tube research facility at several Reynolds numbers. The reflection of a propagating shock wave at the open endwall of the shock tube generated an expansion fan travelling upstream and interacting with the induced flow behind the incident shock wave which has gone through a turbulence generating grid.A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three-dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed the computations of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of kinetic energy term and full rate-of-strain tensor. The longitudinal size of the straining zone was substantial so that measurements within it were possible. The flow accelerated from a Mach number of 0.23 to about 0.56, a value which is more than twice the initial one.Although the average value of the applied straining was only betweenS11= 130 s−1andS11= 240 s−1and the gradient Mach number was no more than 0.226, the amplitude of fluctuations of the strain rateS11were of the order of 4000 s−1before the application of straining and were reduced by about 2.5 times downstream of the interaction. This characteristic of high-amplitude bursts and the intermittent behaviour of the flow play a significant role in the dynamics of turbulence.One of the most remarkable features of the suppression of turbulence is that this process peaks shortly after the application of the straining where the pressure gradient is substantial. It was also found that the total enthalpy variation follows very closely the temporal gradient of pressure within the straining region and peaks at the same location as the pressure gradient.Attenuation of longitudinal velocity fluctuations has been observed in all experiments. It appears that this attenuation depends strongly on the characteristics of the incoming turbulence for a given straining strength and flow Mach number. The present results clearly show that in most of the cases, attenuation occurs at large times or distances from the turbulence generating grids where length scales of the incoming flow are high and turbulence intensities are low. Thus, large eddies with low-velocity fluctuations are affected the most by the interaction with the expansion waves. Spectral analysis has indicated that attenuation of fluctuations is not the same across all wavenumbers of the spectrum. The magnitude of attenuation appears to be higher in cases of finer mesh grids.

Linear interaction of two-dimensional free-stream disturbances with an oblique shock wave

2019 ◽  
Vol 873 ◽  
pp. 1179-1205 ◽  
Author(s):  
Zhangfeng Huang ◽  
Huilin Wang
Keyword(s):  
Shock Wave ◽  
Plane Wave ◽  
Transmission Coefficient ◽  
Acoustic Waves ◽  
Interaction Analysis ◽  
Oblique Shock Wave ◽  
Theoretical Problem ◽  
Linear Interaction ◽  
Incident Plane ◽  
Excited Wave

The problem of interaction between disturbances and shock waves was solved by a theoretical approach called linear interaction analysis in the mid-twentieth century. More recently, great progress has been made in analysing shock–turbulence interactions by direct numerical simulation. However, an unsolved theoretical problem remains: What happens when no acoustic waves are stimulated behind the shock wave? The concept of a damped wave is introduced, which is a type of excited plane wave. Based on this, the dispersion and amplitude relationships between any incident plane wave and resulting stimulated waves are constructed analytically, systematically and comprehensively. The physical essence of damped waves and the existence of critical angles are clarified. It is demonstrated that a damped wave is a complex number space solution to the acoustic dispersion relationship under certain conditions. It acts as a bridge connecting fast and slow acoustic waves at the position where the $x$ component of the group velocity is zero. There are two critical angles that can excite fast and slow acoustic waves, which determine the conditions that stimulate a damped wave. Our results show good agreement with theoretical and simulation results. The contribution of each excited wave to the transmission coefficient is evaluated, the distribution of the transmission coefficient is analysed and application to an engineering wedge model is performed.

scholarly journals Nematic Dispersive Shock Waves from Nonlocal to Local

2021 ◽  
Vol 11 (11) ◽  
pp. 4736
Author(s):  
Saleh Baqer ◽  
Dimitrios J. Frantzeskakis ◽  
Theodoros P. Horikis ◽  
Côme Houdeville ◽  
Timothy R. Marchant ◽  
...  
Keyword(s):  
Shock Wave ◽  
Liquid Crystals ◽  
Shock Waves ◽  
Numerical Solutions ◽  
Wave Structure ◽  
Beam Power ◽  
Input Beam ◽  
Shock Wave Structure ◽  
Wave Solutions ◽  
Modulation Theory

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

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