Session P15: Turbulence: Compressible (3:10pm - 3:55pm CST)

Turbulence generation with piston-driven synthetic jets

An apparatus for generating compressible turbulence in a closed chamber is developed with high-speed synthetic jet actuators driven by pistons, which are connected to electronic motors. Each actuator repeatedly suctions and injects fluid via four orifice holes on the top of the cylinder. Totally eight actuators are placed on two opposing surfaces of a rectangular parallelepiped chamber. By driving the actuators at 150 Hz, jets with the maximum Mach number of about 1.2 are repeatedly ejected from each actuator into the chamber. The interaction of the opposed synthetic jets generates turbulence with density variations in the chamber. The characteristics of the generated turbulent flow field are investigated with particle image velocimetry (PIV) and shadowgraph method. Large density fluctuations are observed in the turbulent flow by the shadowgraph visualization. Tracer particles for PIV are seeded into the chamber by oil evaporation and condensation inside the cylinder due to significant pressure variations. Root-mean-squared velocity fluctuations are similar for the direction of the jet ejection and its normal direction at the center of the chamber, where the mean velocity is also small compared with the velocity fluctuations. The turbulence at the center is shown to be nearly isotropic and homogeneous compared with the regions strongly influenced by the jets. The probability density function of velocity fluctuations is well approximated by the Gaussian distribution at the center of the chamber.   

Temporal evolution of flow features in isotropic turbulence and shock-turbulence interaction

We present a numerical study of the temporal evolution of flow structures in compressible turbulent mixing of passive scalars. To elucidate the effect of shock waves on the geometry of the scalar structures and mixing enhancement, we compare temporally decaying homogeneous isotropic turbulence, and the statistically stationary interaction of a nominally planar shock wave with spatially decaying isotropic turbulence ($Re_{\lambda}=40$; $M_t=0.2$; $M=1.5,3.0$). The passive scalar fields are initialized as collections of uniformly spaced spheres and ellipsoids of varying scales, commensurate to the Taylor microscale, $\lambda$, of the underlying turbulence. Isosurfaces of the passive scalars and the Q-criterion field are individually tracked in time. We analyze how changes in the evolving geometry relate to changes in physical quantities relevant to mixing, such as the alignments between the scalar gradient, the strain eigendirections and the vorticity, mapped on each isosurface. The interaction between passive scalar structures and the shock increases the scalar gradient magnitude, and hence the scalar dissipation, on the structures and induces an increased number of splitting structures which further enhances the mixing. Larger scalar gradients correlate with flat surface regions   

Cascade of internal energy fluctuations in compressible isotropic turbulence with thermal nonequilibrium

Inter-scale transfer of the internal energy fluctuations are investigated by numerical simulations of stationary compressible isotropic turbulence in vibrational nonequilibrium with large-scale thermal forcing. The attentions are mainly focused on statistical properties of turbulence, and inter-scale transfer of the translational-rotational and the vibrational energy fluctuations, with impacts of large-scale thermal forcing, compressibility and vibrational relaxation. Based on the Helmholtz decomposition, it is found that the solenoidal velocity component predominates over the dilatational component; fluctuations of the solenoidal velocity and pressure components are insensitive to the turbulence Mach number and the vibrational relaxation, while fluctuations of the dilatational velocity and pressure components depend closely on them. It is revealed that cascades of the translational-rotational and the vibrational energy fluctuations are mainly dominated by the solenoidal mode of filtered velocity. SGS fluxes of the translational-rotational and the vibrational energy fluctuations due to the solenoidal component of filtered velocity are insensitive to the local compressibility; SGS fluxes due to the dilatational component of filtered velocity are positive in the compression region, balanced by the reverse SGS fluxes in the expansion region.   

Symmetry Analysis of Probability Density Function Hierarchy in Compressible Turbulence

We perform symmetry analysis on the multi-point probability density function (PDF) hierarchy that governs the statistics of compressible turbulence. To this end, we utilize the PDF equations and side conditions derived from compressible flow equations that satisfy ideal gas law in the recent work of Praturi \emph{et al.} (Phys. Fluids, \textbf{32}, 066102, 2020). The PDF equations (i) are integro-differential in nature; (ii) account for the statistics of density, temperature and pressure, in addition to that of the velocity field and do not make assumptions regarding the strength of fluctuations; and (iii) indicate a closure problem: the $n$-point statistics behavior is influenced by $(n+1)$- and $(n+2)$-point statistics. It is seen that the PDF equations and the side conditions, when viscosity and heat conductivity are zero, satisfy all the symmetries of compressible Euler equations including three scaling groups and kinematic symmetries. We also plan to derive all the Lie symmetries and corresponding invariant solutions, typically known as turbulent scaling laws. This approach is of great importance for compressible turbulence as there are very few works in the literature that undertake a similar approach.   

Extreme events in compressible turbulence

Compressible turbulence appears in many engineered and natural settings, such as in scramjet engines and astrophysical jets. Even at subsonic speeds, however, turbulent fluctuations can be fast enough relative to the speed of sound that regions of local strong compression and expansion appear in the flow. Experiments are needed to further develop models that quantify the influence of compressibility on turbulence. In our laboratory, we used in-house hot-wire probes and state-of-the-art nanofabricated hot-wire anemometers [Vallikivi et al., Exp. Fluids (2011)] which resolve inertial range statistics, and measured turbulence in a specialized pressure vessel filled with sulfur hexafluoride (SF6). The flow was driven by a fan which produced a turbulent jet. Since SF6 gas has a low speed of sound compared to air we attained jet Mach numbers up to 0.7 at speeds low enough to enable high resolution measurements. The Taylor Reynolds number was modulated independently between 200 and 3700 with pressure adjustments. We report on the scaling of extreme events in probability distributions of velocity increments consistent with the appearance of shocklets with increasing Mach numbers, and we compare our data with DNS as well as with previous experiments.   

Thermodynamic fluctuations in compressible homogeneous turbulence

At its core, in incompressible turbulence, the velocity field is divergence-free, i.e., solenoidal, whereas it has both solenoidal and dilatational components in compressible turbulence. In incompressible turbulence, the pressure field has no impact on the density and temperature fields. On the other hand, in compressible turbulence, pressure fluctuations are coupled with the density and temperature fields through the energy equation and the equation of state. In this work, we explore these phenomena through numerical simulations of forced compressible subsonic turbulence (i.e, at turbulent Mach numbers less than unity). First, we derive how turbulence should be forced in compressible simulations. Using the proposed framework, we then analyze how compressibility effects arise when a compressible simulation is initialized with an incompressible turbulent field. We observe a non-isentropic transient behavior in which density fluctuations are small and temperature fluctuations are large, after which the isentropic behavior is recovered. Finally, we compare the solenoidal and dilatational components of the pressure fields, by looking at their respective magnitude and probability density functions as a function of the Mach number.   

Compressible homogeneous turbulence: universality classes and scaling

A critical element in studying complex systems such as turbulence is the concept of universal scaling laws which provide fundamental as well as practical information about their spatio-temporal behavior. Universality in compressible flows, however, has proven to be elusive as no unifying set of parameters have been found to yield universal scaling laws. This severely limits our understanding of these flows and the successful development of theoretically sound models. Using a massive new DNS database of compressible isotropic turbulence with different driving mechanisms along with more than 15 studies of homogeneous flows in the literature, we show that universality is indeed observed when the parameter space is extended to include dilatational motions. Collapse of a number of statistics is observed across flows with solenoidal, dilatational and/or thermal forcing as well as shear flows, resolving some discrepancies in the literature. We postulate the existence of universality classes which bundle the evolution of flows in the new parameter space. An ultimate asymptotic regime predicted by renormalization group theories and statistical mechanics is also assessed with available data.