Session GC: Turbulence Simulations IV

Study of local isotropy in a turbulent pipe flow using longitudinal and transverse structure functions

The scaling exponents of the longitudinal $\left\langle \Delta u_z^n\right\rangle$ and the two transverse structure functions, $\left\langle \Delta u_r^n\right\rangle$ and $\left\langle \Delta u_{\theta}^n\right\rangle$ with $n \leq 7$ are studied in a fully developed incompressible turbulent pipe flow at $Re_D = 24580$ and $50000$ using direct numerical simulation flow fields. The scaling exponents for $\left\langle \Delta u_r^n\right\rangle$ and for $\left\langle \Delta u_{\theta} ^n\right\rangle$ increase with the turbulent Reynolds number $R_ {\lambda}$. However, the scaling exponents for $\left\langle \Delta u_z^n\right\rangle$ remain nearly unchanged. The Kolmogorov universal constants in both of the dissipative range and inertial range for the longitudinal structure functions show a smaller increase with $R_{\lambda}$ than those for the transverse structure functions. The present results are compared with previous experimental and DNS data for channel and duct flows (Antonia \textit{et al.} (1997). Phys. Fluids, 9 (11), 3465)   

Tensor-based Lagrangian time correlations in DNS of isotropic turbulence

We study Lagrangian statistics of dynamically important tensors, such as velocity- gradient tensor, together with its symmetric and antisymmetric parts, through fluid particle tracking. The data, a $1024^4$ space-time DNS of forced isotropic turbulence, are accessed using the web-services of the JHU public database (http://turbulence.pha.jhu.edu). A Tensor-based time-correlation function is defined by the tensor product between variables at different times along the Lagrangian trajectory. Analyses in the literature had shown slightly longer correlation times for the square rotation rate as compared to the square strain-rate magnitude. However, here we show that the difference is much larger when considering the dynamically more relevant tensor-based correlation function. The question whether these trends are due mostly to vortical coherent structures (worms) is addressed using conditional averaging. Even with the exclusion of worms, rotation-rate remains significantly more correlated over time than the strain-rate. The analysis is done for the pressure Hessian tensor and significant differences are obtained for its trace and deviatoric parts.   

Pressure, acceleration and velocity structure functions in DNS at high Reynolds number and/or improved small-scale resolution

Evidence from both numerical simulation and experiment in the literature suggest the second-order structure function of pressure fluctuations requires higher Reynolds number than the pressure spectrum for inertial range scaling. We use a direct numerical simulation database for isotropic turbulence at resolution up to $4096^3$ to directly calculate the pressure structure function and pressure gradient two-point correlation. We examine the relationships between those statistics and those same quantities calculated from fourth-order velocity structure functions. Our results suggest that the longitudinal, mixed and transverse fourth-order velocity structure functions, usually denoted by $D_{LLLL}(r)$, $D_{LLNN}(r)$ and $D_{NNNN}(r)$, obey, to a good approximation, the same scalings for scale size $r$ in the inertial range. While mutual cancellations limit the accuracy with which these can be used to evaluate the pressure structure function the ambiguities clearly become smaller at higher Reynolds number. We also use new datasets of improved small-scale resolution albeit at lower Reynolds number to re-examine the nature of pressure gradient and viscous force correlations at small scale separations, more definitively than possible before.   

Multi-particle Lagrangian statistics of turbulent dispersion from simulations of isotropic turbulence at $R_{\lambda}\approx 1100$

Numerical simulations at up to \(4096^3\) grid resolution have been conducted on machines with very large processor counts to obtain the statistics of Lagrangian particle pairs and tetrads in turbulent relative dispersion. Richardson-Obukhov scaling for mean-square pair separation adjusted for initial conditions is observed for intermediate initial separations, in support of prior estimates of about 0.6 for Richardson's constant. Simulations at \(R_{\lambda} \approx 650\) have also been conducted for sufficient duration to obtain fully converged exit time statistics for independently moving particles at very large scales. The fact that all particle pairs reach such large scales of separation means the inertial subrange of exit times is also captured accurately. The results show Kolmogorov scaling for positive moments of exit time, but a strong dependence on initial separations for inverse moments. Inertial-range estimates of tetrad shape factors are reinforced by simulations at Taylor-scale Reynolds numbers up to about 1100. Tetrad shape parameters conditioned on cluster size are also examined in order to understand geometric features of turbulent dispersion in more detail.   

DNS of the thermal effects of laser energy deposition in isotropic turbulence

Laser energy deposition in isotropic turbulence is studied using DNS. A spectral numerical method is combined with shock-capturing and numerical challenges faced are discussed. A model problem involving energy deposition near a single vortex is studied as a first step. For the turbulent problem, $Re_{\lambda} = 30$ and $M_t = 0.001$ and $0.3$ are considered. Evolution of the mean flow is divided into shock formation, shock propagation and core roll up stages. For $M_t = 0.3$, the turbulence slows down shock formation and propagation and prevents core roll up. This behavior is not observed for $M_t = 0.001$. The turbulence intensities are enhanced due to compression from the shock wave and suppressed due to expansion in the core. Turbulent kinetic energy budgets are computed to explain this behavior. Effect of mean vorticity production on the turbulence is also studied. As an application, laser energy deposition near a wall is studied. Orientation of the laser axis and distance of the focal volume from the wall are found to affect the evolution of the resulting flow field.   

Decomposition of Fluid Acceleration by Rotational and Irrotational Motion in Isotropic Turbulence

It is well known that fluid acceleration in turbulence is highly intermittent. Source of the intermittency was found to be closely related to the rotational motion of coherent vortical structures. From the Poisson equation for pressure, $\frac{1}{\rho} \nabla^2 P=\Omega -\frac{\epsilon}{2 \nu}$, acceleration, which is mostly the negative of pressure gradient, can be expressed as a sum of acceleration-like terms, $-\nabla (\nabla^2)^{-1} \Omega + \nabla (\nabla^2 )^{-1} \frac {\epsilon}{2 \nu}$, each of which is named as $a^{\Omega}$ and $a^{\epsilon}$ . They are acceleration due to rotational motion of eddy and acceleration due to irrotational strain field, respectively. We investigated the statistical characteristics of those accelerations by using direct numerical simulation of isotropic turbulence. Flatness of acceleration is of order of 10 but flatness of $a^{\Omega}$ and $a^{\epsilon}$ are $3 \sim 5$ which represents less intermittency in the range of $Re_{\lambda} = 47 \sim 130$. Based on the cylinder vortex model, we show that probability density function of acceleration must have -5/3 slope and pdf's of $a^{\Omega}$ and $a^{\epsilon}$ must have -3 slope in log- log scale when the Reynolds number is infinite. Numerical and experimental results do not show clear slope since the Reynolds number is relatively low, but an asymptotic behavior is observed.   

Evolution of Compressible Decaying Isotropic Turbulence with Multi-temperature Non-equilibrium

Understanding and predicting of transition and turbulence under non-thermodynamical-equilibrium (NTE) conditions are important for hypersonic flight and other industrial applications. In NTE turbulence, the Kolmogorov paradigm, which forms the basis of most equilibrium turbulence models, may be invalid. Furthermore, under the NTE conditions, multiple temperatures often take place in diatomic gases even at room temperature due to the insufficient particle collisions. Therefore, the effect due to the internal degrees of freedom interactions on turbulence physics is essential in non-equilibrium flows. Here, we apply gas kinetic scheme for DNS of compressible decaying isotropic turbulence with multi-temperature non-equilibrium. Our results show that the rotational collision number in the rotational energy relaxation model and the initial energy ratio of rotational and translational modes can significantly affect the evolution of the decaying turbulence.   

Large-eddy simulation of compressible flow over a backward-facing step using a spectral multidomain method

Analysis of compressibility effects on separated curved shear layers in practical configurations has received little attention in the turbulence community. In this work, we perform large-eddy simulation (LES) of cold flow in an asymmetric dump-combustor with a spectral multi-domain method. The LES method combines a high-order multi-domain approximation with a dynamic sub-grid model and explicit interpolant-projection filtering to facilitate simulation at high Reynolds numbers. The inflow turbulence is modeled using a novel stochastic model, which is both efficient and general. We investigate the impact of the important physical parameters, such as the state of the boundary layer at separation, Reynolds number and Mach number as well as the interplay between them. One of the principal findings is the different responses of the transitional and turbulent shear layers with increase in compressibility. Increase in compressibility for the transitional flow causes a larger production of turbulent kinetic energy resulting in a faster growth of the shear layer. While for the turbulent shear layer, the growth rate is inhibited with increase in compressibility as a result of higher pressure-dilatation.   

The scaling of polymer drag reduction with polymer and flow parameters in turbulent channel flow

The scaling of polymer drag reduction with polymer and flow parameters is investigated using results from direct numerical simulations (DNS) of dilute, homogeneous polymer solutions in a turbulent channel flow performed at a base Reynolds number of $Re_{\tau_b} \approx 230$. The full range of drag reduction from onset to maximum drag reduction (MDR) is reproduced in DNS with realistic polymer parameters, with results in good agreement with available experimental data. Onset of drag reduction is found to be a function of both the polymer concentration and the Weissenberg number ($We_\tau$), in agreement with the predictions of DeGennes (1986). Saturation of drag reduction is achieved at a viscosity ratio of $\beta \approx 0.98$ at all $We_\tau$, with the magnitude of drag reduction at saturation being a strong function of $We_\tau$. A $We_{\tau_b} \sim O(Re_{\tau_b}/2)$ is needed to reach MDR. The presence of the polymer results in attenuation of turbulence at certain turbulent scales, determined by the Weissenberg number and the concentration. At saturation concentrations, the size of the largest attenuated eddy conforms to the predictions of Lumley (1969), while at concentrations below saturation, it conforms to a modified form of DeGennes (1986) theory. A mechanism of polymer drag reduction consistent with these observations will be presented.   

Turbulent Channel Flow With $\Lambda$ Shape Turbulators on One Wall

tudy of turbulent heat or mass transport is of special interest in engineering, especially for heat exchangers. For instance, roughness elements (turbulators) are usually placed on the walls of the internal channels of a turbine blade to enhance the heat transfer. In the present paper, DNSs are carried out for passive heat transport in a turbulent channel flow with $\Lambda $ shape square ribs for w/k = 1, 3, 7, 15 (w being the pitch, k the height of the ribs turbulators. The angle of inclination of the lambda shape turbulators is 45 degrees. Numerical results show that $\Lambda $ shape square ribs are more efficient than square ribs in maximizing the heat transfer. The configuration with w/k=3 presents the largest heat flux. The increase in the heat transfer is due to a secondary motion which is generated by the $\Lambda $ shape turbulators. Two counter rotating vortices above the square ribs transport the heat out of the wall into the center of the channel. The distribution of the heat flux coefficient is not uniform in the channel and leads to temperature gradients at the wall. The total drag of the $\Lambda $ shape turbulators is larger than that over a smooth wall due to an increase of form drag.