Prakash Vedula

SIMILARITY SCALING OF ACCELERATION AND PRESSURE STATISTICS IN NUMERICAL SIMULATIONS OF ISOTROPIC TURBULENCE

The scaling properties of one- and two-point statistics of the acceleration, pressure, and pressure gradient are studied in incompressible isotropic turbulence by direct numerical simulation. Ensemble-averaged Taylor-scale Reynolds numbers (Rλ) are up to about 230 on grids from 323 to 5123. From about Rλ 40 onwards the acceleration variance normalized by Kolmogorov variables is found to increase as Rλ1/2. This nonuniversal behavior is traced to the dominant irrotational pressure gradient contributions to the acceleration (whereas the much weaker solenoidal viscous part is universal). Longitudinal and transverse two-point correlations of the pressure gradient differ according to kinematic constraints, but both (especially the latter) extend over distances of intermediate scale size large compared to the Kolmogorov scale. These extended-range properties essentially provide the Eulerian mechanism whereby (as found in recent work) the accelerations of a pair of fluid particles can remain significantly correla...

Dynamics of scalar dissipation in isotropic turbulence: a numerical and modelling study

The physical mechanisms underlying the dynamics of the dissipation of passive scalar fluctuations with a uniform mean gradient in stationary isotropic turbulence are studied using data from direct numerical simulations (DNS), at grid resolutions up to 512 3 . The ensemble-averaged Taylor-scale Reynolds number is up to about 240 and the Schmidt number is from ⅛ to 1. Special attention is given to statistics conditioned upon the energy dissipation rate because of their important role in the Lagrangian spectral relaxation (LSR) model of turbulent mixing. In general, the dominant physical processes are those of nonlinear amplification by strain rate fluctuations, and destruction by molecular diffusivity. Scalar dissipation tends to form elongated structures in space, with only a limited overlap with zones of intense energy dissipation. Scalar gradient fluctuations are preferentially aligned with the direction of most compressive strain rate, especially in regions of high energy dissipation. Both the nature of this alignment and the timescale of the resulting scalar gradient amplification appear to be nearly universal in regard to Reynolds and Schmidt numbers. Most of the terms appearing in the budget equation for conditional scalar dissipation show neutral behaviour at low energy dissipation but increased magnitudes at high energy dissipation. Although homogeneity requires that transport terms have a zero unconditional average, conditional molecular transport is found to be significant, especially at lower Reynolds or Schmidt numbers within the simulation data range. The physical insights obtained from DNS are used for a priori testing and development of the LSR model. In particular, based on the DNS data, improved functional forms are introduced for several model coefficients which were previously taken as constants. Similar improvements including new closure schemes for specific terms are also achieved for the modelling of conditional scalar variance.

Conditional and unconditional acceleration statistics in turbulence

In this paper we study acceleration statistics from laboratory measurements and direct numerical simulations in three-dimensional turbulence at Taylor-scale Reynolds numbers ranging from 38 to 1000. Using existing data, we show that at present it is not possible to infer the precise behavior of the unconditional acceleration variance in the large Reynolds number limit, since empirical functions satisfying both the Kolmogorov and refined Kolmogorov theories appear to fit the data equally well. We also present entirely new data for the acceleration covariance conditioned on the velocity, showing that these conditional statistics are strong functions of velocity, but that when scaled by the unconditional variance they are only weakly dependent on Reynolds number. For large values of the magnitude u of the conditioning velocity we speculate that the conditional covariance behaves like u6 and show that this is qualitatively consistent with the stretched exponential tails of the unconditional acceleration proba...

Random Taylor hypothesis and the behavior of local and convective accelerations in isotropic turbulence

The properties of acceleration fluctuations in isotropic turbulence are studied in direct numerical simulations (DNS) by decomposing the acceleration as the sum of local and convective contributions (aL = ?u/?t and aC = u??u), or alternatively as the sum of irrotational and solenoidal contributions [aI = ??(p/?) and aS = ??2u]. The main emphasis is on the nature of the mutual cancellation between aL and aC which must occur in order for the acceleration (a) to be small as predicted by the “random Taylor hypothesis” [Tennekes, J. Fluid Mech. 67, 561 (1975)] of small eddies in turbulent flow being passively “swept” past a stationary Eulerian observer. Results at Taylor-scale Reynolds number up to 240 show that the random-Taylor scenario ?a2???aC2? ? ?aL2?, accompanied by strong antialignment between the vectors aL and aC, is indeed increasingly valid at higher Reynolds number. Mutual cancellation between aL and aC also leads to the solenoidal part of a being small compared to its irrotational part. Results for spectra in wave number space indicate that, at a given Reynolds number, the random Taylor hypothesis has greater validity at decreasing scale sizes. Finally, comparisons with DNS data in Gaussian random fields show that the mutual cancellation between aL and aC is essentially a kinematic effect, although the Reynolds number trends are made stronger by the dynamics implied in the Navier–Stokes equations.

Direct numerical simulation of differential diffusion with Schmidt numbers up to 4.0

Highly resolved direct numerical simulations are used to study the differential diffusion of passive scalars of above-unity Schmidt number in low Reynolds number turbulence. Both the coherency and the spectrum of the two-scalar difference obey Batchelor scaling based on the parameters of the less diffusive scalar. A reverse spectral transfer effect due to velocity modes in the far dissipation range is identified, which may be important at very high Schmidt numbers.

Theoretically based optimal large-eddy simulation

Large eddy simulation (LES), in which the large scales of turbulence are simulated while the effects of the small scales are modeled, is an attractive approach for predicting the behavior of turbulent flows. However, there are a number of modeling and formulation challenges that need to be addressed for LES to become a robust and reliable engineering analysis tool. Optimal LES is a LES modeling approach developed to address these challenges. It requires multipoint correlation data as input to the modeling, and to date these data have been obtained from direct numerical simulations (DNSs). If optimal LES is to be generally useful, this need for DNS statistical data must be overcome. In this paper, it is shown that the Kolmogorov inertial range theory, along with an assumption of small-scale isotropy, the application of the quasinormal approximation and a mild modeling assumption regarding the three-point third-order correlation are sufficient to determine all the correlation data required for optimal LES m...

Validity of quasinormal approximation in turbulent channel flow

The validity of the quasinormal approximation, which relates the fourth-order velocity correlations to second-order velocity correlations, is tested using data obtained from direct numerical simulation (DNS) of turbulent channel flow at Reτ≈590. Results indicate that the quasinormal approximation is accurate throughout the channel except for a thin layer near the wall (y+ 50 as it is for isotropic turbulence. This study is motivated by the need to model fourth-order correlations in optimal LES. To evaluate the impact of errors like those observ...

Influence of State-to-State Transport Coefficients on Surface Heat Transfer in Hypersonic Flows

A numerical study is performed to assess the influence of two state-to-state kinetic approaches on the prediction of surface heat transfer of Mach 7 hypersonic external flowfields. One approach consists of a simplified state-to-state kinetic model which utilizes Eucken’s relation for calculating thermal conductivity and a constant Lewis number assumption for calculating self-diffusion in the vibrational quantum levels. The other approach uses a rigorous kinetic theory based model for which collision integrals are used to determine transport coefficients related to thermal diffusion, heat conductivity, self-diffusion, and diffusion of vibrational energy. Inclusion of self-diffusion results in an increase in the surface heat flux of up to 6.5% upstream of a shoulder region. Thermal conductivity is found to be the primary contributor to surface heat flux. The differences in heat flux predictions between the two state kinetic models highlight the sensitivity of surface heat transfer rate to the thermal conductivity models used. As a starting point for future determination of transport coefficient model sensitivities, a probabilistic global sensitivity analysis is performed for a simplified set of hypersonic flow calculations involving the Sutherland viscosity model.

Nonlinear Stochastic Control Part II: Ascent Phase Control of Reusable Launch Vehicles

In designing a robust ascent phase control for reusable launch vehicles, uncertainties such as variations in aerodynamics, jet effects, hinge moments, mass property, and navigation processing, etc. have to be considered and normally time and labor intensive Monte Carlo simulations are used in order to achieve a desired tracking performance distribution. In this paper, a systematic stochastic control design method based upon a direct quadrature method of moments proposed in Part I [26] will be applied to the ascending phase attitude control problem. In conjunction with a nonlinear robust control and an offline optimization through nonlinear programming, any order of stationary statistical moments can be directly controlled. Two simulation scenarios of the X-33 ascent phase control have been used to demonstrate the capabilities of the proposed method and the results are validated by Monte Carlo runs.

Kinetic solution of the structure of a shock wave in a nonreactive gas mixture

The multispecies Boltzmann equation is numerically integrated to characterize the internal structure of a Mach 3 shock wave in a hard sphere gas. The collision integral is evaluated by the conservative discrete ordinate method [F. G. Tcheremissine, Comput. Math. Math. Phys. 46, 315 (2006)]. There was excellent agreement of macroscopic variables [Kosuge et al.., Eur. J. Mech. B/Fluids 20, 87 (2001)]. The effect of species concentration and mass ratio on the behavior of macroscopic variables and distribution functions in the structure of the shock wave is considered for both two- and three-species gas mixtures. In a binary mixture of gases with different masses and varying concentrations, the temperature overshoot of the parallel component of temperature near the center of the shock wave is highest for the heavy component when the concentration of the heavy component is the smallest. The rise in the parallel component of temperature is revealed by the behavior of the distribution function.