3D-PTV measurements were conducted on the wake of a sphere. The Reynolds number is 1130 with diameter d = 30 mm. The measurement system consisted of three CCD cameras, an image grabber, an Ar-ion laser and a host computer. Structural analysis was adopted for the analysis on the wake using the obtained velocity profiles. Statistical turbulent properties were quantitatively clarified using the time-consecutive instantaneous three-dimensional vectors obtained by the 3D-PTV system. The spatial velocity profiles of the sphere wake seemed to have a strong relationship with the spiral motion of the vortices that were shed from the surface of the sphere.

http://iopscience.iop.org/article/10.1088/0957-0233/15/6/004/pdf

3D-PTV measurements of the wake of a sphere

This paper introduces the results of numerical simulations on flow fields and relevant heat transfer in the pebble bed reactor (PBR) core. In the core, since the coolant passes a highly complicated random flow path with a high Reynolds number, an appropriate treatment of the turbulence is required. A set of simple experiments for the flow over a circular cylinder with heat transfer was conducted to finally select the large eddy simulation (LES) and k-ω model among the considering Reynolds-averaged Navier-Stokes (RANS) models for PBR application. Using these models, the PBR cores, whose geometries were simplified to the body-centered cubical (BCC) and face-centered cubical (FCC) structures, were simulated. A larger pressure drop, a more random flow field, a higher vorticity magnitude and a higher temperature at the local hot spots on the pebble surface were found in the results of the LES than in those of RANS for both geometries. In cases of the LES, the flow structures were resolved up to the grid scales...

https://www.tandfonline.com/doi/pdf/10.1080/18811248.2007.9711338

Turbulence-induced Heat Transfer in PBMR Core Using LES and RANS

Numerical study of the flow interference between tandem cylinders employing non-linear hybrid URANS–LES methods

A discrete mathematical model of hydrobiology of coastal zone is constructed and analyzed. The model takes into account the transport and transformation of polluting biogenic elements in water basins. The propagation and transformation of biogenic elements is affected by such physical factors as three-dimensional motion of water taking into account the advective transport and microturbulent diffusion, spatially inhomogeneous distribution of temperature, salinity, and oxygen. Biogenic pollutants typically arrive into the water basin with river flow, which depends on the weather and climate of the geographic region, or with drainage of insufficiently purified domestic and industrial waste or other kinds of anthropogenic impact. Biogenic pollutants can also appear due to secondary pollution processes, such as stirring up and transport of bed silt, shore abrasion, etc. Stoichiometric relations between biogenic nutrients for phytoplankton algae that can be used to determine the limiting nutrient for each species are obtained. Observation models describing the consumption, accumulation of nutrients, and growth of phytoplankton are considered. A three-dimensional mathematical model of transformation of forms of phosphorus, nitrogen, and silicon in the plankton dynamics problem in coastal systems is constructed and analyzed. This model takes into account the convective and diffusive transport, absorption, and release of nutrients by phytoplankton as well as transformation cycles of phosphorus, nitrogen, and silicon forms. Numerical methods for solving the problem that are based on high-order weighted finite difference schemes and take into account the degree of fill of the computation domain control cells are developed. These methods are implemented on a multiprocessing system. They make it possible to improve the accuracy of the numerical solution and decrease the computation time by several fold. Based on the numerical implementation, dangerous phenomena in coastal systems related to the propagation of pollutants, including oil spill, eutrophication, and algae bloom, which causes suffocation phenomena in water basins, are reconstructed.

A Model of Transport and Transformation of Biogenic Elements in the Coastal System and Its Numerical Implementation

A moving-domain computational fluid dynamics (CFD) solver is designed by deploying the Arbitrary Lagrangian Eulerian Variational Multi-scale Formulation (ALE-VMS) enhanced with weak enforcement of essential boundary conditions (weak BC) into the open-source finite element automation software FEniCS. The mathematical formulation of ALE-VMS, which is working as a Large Eddy Simulation (LES) model for turbulent flows, and weak BC, which is acting as a wall model, are presented with the implementation details in FEniCS. To validate the CFD solver, simulations of flow past a stationary sphere are performed with moving meshes first. Refinement study shows the results quickly converge to the reference results with fixed grids. Then, the solver is utilized to simulate a tidal turbine rotor with uniform and turbulent inflow conditions. Good agreement is achieved between the computational results and experimental measurements in terms of thrust and power coefficients for the uniform inflow case. The effect of the inflow turbulence intensity on the tidal turbine performance is quantified.

A moving-domain CFD solver in FEniCS with applications to tidal turbine simulations in turbulent flows

Direct numerical simulation of the transitional separated fluid flows around a sphere and a circular cylinder

For the detailed investigation of the 3D unsteady incompressible viscous separated fluid flows around a sphere (for 200 ≤ Re ≤ 700) and a circular cylinder (for 200 ≤ Re ≤ 400) the direct numerical simulation and 3D visualization are used. For 3D visualization of the fluid flows around a sphere the definition of vortex core as a connected region containing two negative eigenvalues of the S^2 + Ω^2 tensor is used (where S_{i,j} and Ω_{i,j} are the rate of strain and the rate of rotation tensors). The formation mechanism of vortices in the sphere wake for Re = 500 is described in detail. For 3D visualization of the fluid flows around a circular cylinder the 3D isosurfaces of the streamwise component of vorticity ω_x are used.

3D Visualization of the Separated Fluid Flows

Based on numerical simulation and visualization, the vortex structure of the flow past a sphere moving uniformly and horizontally in a linearly (density) stratified viscous fluid with an increasing degree of stratification (with the internal Froude number Fr decreasing from infinity to 0.005) at Re = 100 is analyzed in detail for the first time. The classification of the flow regimes is refined. The direct numerical simulation is based on the method of splitting with respect to physical factors (MERANZH) with an explicit hybrid finite-difference scheme, which is second-order accurate in space, monotone, and has a minimal numerical viscosity and dispersion.

Numerical simulation and visualization of vortical structure transformation in the flow past a sphere at an increasing degree of stratification

The flows past a sphere and a square cylinder of diameter d moving horizontally at the velocity U in a linearly density-stratified viscous incompressible fluid are studied. The flows are described by the Navier–Stokes equations in the Boussinesq approximation. Variations in the spatial vortex structure of the flows are analyzed in detail in a wide range of dimensionless parameters (such as the Reynolds number Re = Ud/ν and the internal Froude number Fr = U/(Nd), where ν is the kinematic viscosity and N is the buoyancy frequency) by applying mathematical simulation (on supercomputers of Joint Supercomputer Center of the Russian Academy of Sciences) and three-dimensional flow visualization. At 0.005 < Fr < 100, the classification of flow regimes for the sphere (for 1 < Re < 500) and for the cylinder (for 1 < Re < 200) is improved. At Fr = 0 (i.e., at U = 0), the problem of diffusion-induced flow past a sphere leading to the formation of horizontal density layers near the sphere’s upper and lower poles is considered. At Fr = 0.1 and Re = 50, the formation of a steady flow past a square cylinder with wavy hanging density layers in the wake is studied in detail.

Simulation and study of stratified flows around finite bodies

The 3D separated, density stratified viscous fluid flows around a sphere are investigated by means of the direct numerical simulation (DNS) on the basis of the Navier-Stokes equations in the Boussinesq approximation on the supercomputers at the wide range of internal Froude (Fr) and Reynolds (Re) numbers. For DNS the Splitting on physical factors Method for Incompressible Fluid flows (SMIF) with the hybrid explicit finite difference scheme (second-order accuracy in space, minimum scheme viscosity and dispersion, monotonous) has been used. At Fr > 10 with increasing of Re we observed the flow regimes of the homogeneous viscous fluid (including the laminar-turbulent transition in the boundary layer on the sphere). With decreasing of Fr at Re < 500 the strong transformation of vortex structures in the sphere wake is demonstrated by means of the β – visualization. Thus the refined classification of the flow regimes around a sphere moving in the viscous stratified fluid is presented.

P. V. Matyushin

Papers

Direct numerical simulation of the transitional separated fluid flows around a sphere and a circular cylinder

3D Visualization of the Separated Fluid Flows

Numerical simulation and visualization of vortical structure transformation in the flow past a sphere at an increasing degree of stratification

Simulation and study of stratified flows around finite bodies

Transformation of vortex structures in the wake of a sphere moving in the stratified fluid with decreasing of internal Froude number