Search Results (6)

The mean dissipation rate of turbulent energy reaches a constant value at high Taylor–Reynolds numbers ($R_{\lambda }$). This value is associated with the well-scaling dissipation spectrum in Kolmogorov units, where the maximum corresponds to the bottleneck peak. Even the scalar dissipation rate at the high $R_{\lambda }$ considered in the present direct numerical simulations attains a constant value as $Sc$ increases. In this scenario, the maximum of the scalar dissipation spectra reaches its peak within the bottleneck, starting at $Sc>0.5$. A qualitative explanation for the formation of the two bottlenecks is related to the blockage of energy transfer from large to small scales in the inertial ranges. Within the bottleneck, the self-similar, ribbon-like structures transition into the rod-like structures characteristic of the exponential decay range. Investigating the viscous dependence of the bottleneck’s amplitude may be aided by examining the evolution of a passive scalar. As $Sc$ decreases, the scalar spectra undergo changes across the wave number k range. The bottleneck is dismantled, and at very low $Sc$ values, the spectrum tends towards Batchelor’s theoretical prediction, diminishing proportionally to $k^{-17/3}$. To comprehend the flow structures responsible for the bottleneck, visualizations of $\theta {\nabla }^2\theta$ and probability density functions at various $Sc$ values are presented and compared with those of $u_i{\nabla }^2{u}_i$. The numerical method employed for generating three-dimensional spectra and quantities such as energy and scalar variance dissipation in physical space must be accurate, particularly in resolving small scales. This paper additionally demonstrates that the second-order finite difference scheme conserving kinetic energy and scalar variance in the inviscid limit in viscous simulations accurately predicts the exponential decay range in one-dimensional and three-dimensional turbulent kinetic energy and scalar variance spectra. Full article

The internal flow in a vertical axial-flow pump is a complex unsteady three-dimensional viscous flow. An unstable flow often produces complex flow phenomena such as flow separation, vortices, and secondary reflux, which reduces the operating efficiency of the pump and can endanger safety and stability. In this paper, computational fluid dynamics is used to calculate the flow characteristics in an axial-flow pump using the shear stress transport and curvature correction (SST-CC) model for turbulence modified to account for the rotational curvature. Furthermore, the dependability of the numerical results was confirmed by a test with an actual model of a pump. The transient deviation angle at the impeller inlet of the pump, the stream field attributes in various spanwise parts of the impeller and guide vane, and the velocity distributions at the impeller inlet and outlet were analyzed. The omega method was utilized to recognize the vortex structure inside the guide vane. Moreover, the development of the transient vortex structure inside the guide vane was studied. As the flow rate increased, the scale and turbulent kinetic energy of the vortex structure gradually decreased. The time-domain graph for the impeller inlet is clearly periodic, with three peaks and three troughs in an impeller rotational period. The dominant frequency in the spectrum at each monitoring point was basically the blade frequency, and the secondary dominant frequency was twice the blade frequency. Full article

This study aims to review the physical theory and parametrizations associated to Turbulent Kinetic Energy Density Function (STKE). The bibliographic references bring a broad view of the physical problem, mathematical techniques and modeling of turbulent kinetic energy dynamics in the convective boundary layer. A simplified model based on the dynamical equation for the STKE, in an isotropic and homogeneous turbulent flow regime, is done by formulating and considering the isotropic inertial energy transfer and viscous dissipation terms. This model is described by the Cauchy Problem and solved employing the Method of Characteristics. Therefore, a discussion on Linear First Order Partial Differential Equation, its existence, and uniqueness of solution has been presented. The spectral function solution obtained from its associated characteristic curves and initial condition (Method of Characteristics) reproduces the main features of a modeled physical system. In addition, this modeling allows us to obtain the scaling parameters, which are frequently employed in parameterizations for turbulent dispersion. Full article

The flow fields over a simplified 3D hill covered by vegetation have been examined by many researchers. However, there is scarce research giving the three-dimensional characteristics of the flow fields over a rough 3D hill. In this study, large eddy simulations were performed to examine the coherent turbulence structures of the flow fields over a vegetation-covered 3D hill. The numerical simulations were validated by the comparison with the wind-tunnel experiments. Besides, the flow fields were systematically investigated, including the examinations of the mean velocities and root means square of the fluctuating velocities. The distributions of the parameters are shown in a three-dimensional way, i.e., plotting the parameters on a series of spanwise slices. Some noteworthy three-dimensional features were found, and the mechanisms were further revealed by assessing the turbulence kinetic energy budget and the spectrum energy. Subsequently, the instantaneous flow fields were illustrated, from which the coherent turbulence structures were clearly identified. Ejection-sweep motion was intensified just behind the hill crest, leading to a spanwise rotation. A group of vertical rotations were generated by the shedding of the vortex from the lateral sides of the hill. Full article

A numerical method is applied here to simulate the unstable flow and the vibration of a plane gate. A combination of the large eddy simulation (LES) method and the volume of fluid (VOF) model is used to predict the three-dimensional flow field in the vicinity of a plane gate with submerged discharge. The water surface profile, the streamline diagrams, the distribution of turbulent kinetic energy, the power spectrum density curve of the fluctuating pressure coefficient at typical points underneath the gate, and the complete vortex distribution around the gate are obtained by LES-VOF numerical calculation. The vibration parameters of the gate are calculated by the fluid-structure coupling interface transferring the hydrodynamic load. A simultaneous sampling experiment is performed to verify the validity of the algorithm. The calculated results are then compared with experimental data. The difference between the two is acceptable and the conclusions are consistent. In addition, the influence of the vortex in the slot on the flow field and the vibration of the gate are investigated. It is feasible to replace the experiment with the fluid-structure coupling computational method, which is useful for studying the flow-induced vibration mechanism of plane gates. Full article

The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES). The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES) approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier–Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor–Green Vortex (TGV) test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS) data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT). All combinations of numerical methods produce a $k^{-4}$ spectrum at $t^{*}=4$ , and near the dissipation peak, all methods were capable of predicting the $k^{-5/3}$ slope accurately when refining the mesh. Full article