Interaction Of Isotropic Turbulence Research Articles

On the accuracy of Lagrangian point-mass models for heavy non-spherical particles in isotropic turbulence

The interaction of isotropic turbulence with heavy particles, the size of which is on the order of the smallest turbulent eddies, is considered. Although this case is relevant to pulverized coal and biomass combustion, there is an apparent lack of reliable numerical models for the particle dynamics and the response of the turbulent flow field. By conducting particle resolving direct numerical simulations, we generate accurate results for the dynamics of spherical and non-spherical particles and the associated turbulence modulation effects. Subsequently, we verify the ability of two different two-way coupled Lagrangian models, one derived for spherical and one for ellipsoidal particles, to reproduce the reference results. It is found that the velocities of prolate ellipsoids are significantly reduced compared to spherical particles of the same volume. This behavior is captured by neither of the Lagrangian models since the spherical model does not account for the particle shape and the ellipsoidal model does not account for particle inertia. Additionally, the spectra of fluid kinetic energy indicate that the models fail to resolve the interaction in the high wave number regime, i.e., the interaction of the particle boundary layers and wakes with the smallest flow scales. This is reflected by the vast underprediction of the overall viscous dissipation by both models. As a consequence, the attenuation of kinetic energy contained in large-scale flow structures is underpredicted by the Lagrangian models. In summary, for the slightly non-spherical particles, accounting for inertia effects appears to be more important than inclusion of non-spherical effects for the kinetic energy balance of both phases. However, the ellipsoidal particle model reproduces the preferential alignment of the non-spherical particles within the turbulent flow which becomes more important in highly anisotropic turbulent flows such as in industrial furnaces.

SHOCK-TURBULENCE INTERACTION

The interaction of isotropic turbulence with a shock wave is investigated. The searching and analyzing of works has been prepared. The focus of the present study in this sphere is the instantaneous picture of shock-turbulence interaction. Own results of computational method are represented and compared with results of other scientists. The assumption that shock wave is non-stationary has corroborated in both cases. The assumption of sound propagation due to the interaction of turbulence with shock wave is investigated.

Shock-turbulence interaction: What we know and what we can learn from peta-scale simulations

Many applications in engineering and physical sciences involve turbulent flows interacting with shock waves. High-speed flows around aerodynamic bodies and through propulsion systems for high-speed flight abound with interactions of shear driven turbulence with complex shock waves. Supernova explosions and implosion of a cryogenic fuel pellet for inertial confinement fusion also involve the interaction of shockwaves with turbulence and strong density variations. Numerical simulations of such physical phenomena impose conflicting demands on the numerical algorithms. Capturing broadband spatial and temporal variations in a turbulent flow suggests the use of high-bandwidth schemes with minimal dissipation and dispersion, while capturing the flow discontinuity at a shock wave requires numerical dissipation.Results from three promising shock-capturing schemes a) high order WENO, b) nonlinear artificial diffusivity with compact finite differences, and c) a hybrid approach combining high-order central differencing with WENO near the shocks are compared using the Taylor-Green problem and compressible isotropic turbulence with eddy-shocklets. The performance of each scheme is characterized in terms of an effective bandwidth. The comparison highlights the damaging effect of numerical dissipation when the WENO scheme is applied everywhere. The hybrid approach is found to be best suited for studying shock-turbulence interactions.Results from previous DNS and LES studies of the canonical shock-turbulence interaction problem, i.e. the interaction of isotropic turbulence with a (nominally) normal shock and comparison with available theory and experimental data are recalled. The principal physical effects include the amplification of turbulent kinetic energy across the shock and its anisotropy, change in turbulence length scales across the shock, departure from the common assumption of strong Reynolds analogy (used in modeling turbulence in high-speed flows), and the distortion of the shock due to its interaction with the incident turbulence. In this context new results from our SciDAC sponsored project are shown and open issues are mentioned. New DNS results achieve a significantly larger turbulence Reynolds number and allow an exploration of the nonlinear effects. While the linear interaction theory of Ribner provides useful estimates of the amplification of vorticity fluctuations across the shock, it misses the strong nonlinear dynamics of the energized and highly anisotropic vorticity downstream of the shock. It is found that previous DNS studies also underestimated this effect. The simulations show that turbulent self-stretching and tilting mechanisms bring about a relatively rapid return to isotropy in the turbulent vorticity field. The turbulent velocity field, however, does not show any appreciable tendency towards isotropy. It is further observed that when the turbulence interacting with the shock is sufficiently energetic the instantaneous shock structure is significantly modified; local regions of significant over-compression are found as well as regions where the mean shock compression is nearly isentropic. Estimates for the computational resources necessary for studying this fundamental shock-turbulence interaction problem at higher Reynolds number on peta-scale computing systems are given.

Interaction of isotropic turbulence with shock waves: effect of shock strength

As an extension of the authors' work on isotropic vortical turbulence interacting with a shock wave (Lee, Lele & Moin 1993), direct numerical simulation and linear analysis are performed for stronger shock waves to investigate the effects of the upstream shock-normal Mach number (M1). A shock-capturing scheme is developed to accurately simulate the unsteady interaction of turbulence with shock waves. Turbulence kinetic energy is amplified across the shock wave, and this amplification tends to saturate beyond M1 = 3.0. An existing controversy between experiments and theoretical predictions on length scale change is thoroughly investigated through the shock-capturing simulation: most turbulence length scales decrease across the shock, while the dissipation length scale (ρq3/ε) increases slightly for shock waves with M1<1.65. Fluctuations in thermodynamic variables behind the shock wave are nearly isentropic for M1<1.2, and deviate significantly from isentropy for the stronger shock waves, due to the entropy fluctuation generated through the interaction.

Interaction of isotropic turbulence with a normal shock wave

Interaction of isotropic turbulence with a normal shock wave