Search Results for « Gubser flow »

We examine the characteristics of mean flow and scalar concentration characteristics of a turbulent boundary layer flow impinging on a cluster of tall obstacles (which can also be interpreted as a porous obstruction). The cluster is created with a group of cylinders of diameter $d$ and height $h$ arranged in a circular patch of diameter $D$.The solidity of the patch/obstruction is defined by $φ$ (the total planar area covered by cylinders), which is systematically varied ($0.098 \leq φ\leq 1$) by increasing the number of cylinders in a patch ($N_c$). A point source is placed at ground level upstream of the patch and its transport around the patch is examined. Time-averaged velocity and scalar fields, obtained from simultaneous planar PIV-PLIF (particle image velocimetry-planar laser-induced fluorescence) measurements, reveal that the characteristics of wake and flow above porous patches are heavily influenced by $φ$. In particular, we observe that the horizontal and vertical extent of the wake and scalar concentration downstream of the patches decreases and increases with $φ$, respectively. Here, the recirculation bubble is shifted closer to the trailing edge of the patches as $φ$ increases, limiting the flow from convecting downstream, decreasing the scalar concentration and virtually `extending' the patch in streamwise direction. As the bubble forms in the trailing edge, vertical bleeding increases and hence the concentration increases above patch where the cylinders appear to be `extend' vertically towards the freestream.

The Boltzmann equation is solved in the relaxation time approximation using a hierarchy of angular moments of the distribution function. Our solution is obtained for an azimuthally symmetric radially expanding boost-invariant conformal system that is undergoing Gubser flow. The solution of moments that we get after truncating the infinite set of equations at various orders is compared to the exact kinetic solution. The dynamics of transition is described by the presence of fixed points which describes the evolution of the system from an early time collisionless free streaming to the hydrodynamic regime at intermediate times and back to free streaming at late times. The attractor solution is found for various orders of moments as an interpolation between these fixed points. The relation of moments to various approximations of relativistic viscous hydrodynamics is investigated.

Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical geometries is not established. We here quantitatively investigate the convergence of the phase-field method to the sharp-interface limit with simulations of two-phase pipe flow. We focus on core-annular flows, in which a highly viscous fluid is lubricated by a less viscous fluid, and validate our simulations with an analytic laminar solution, a formal linear stability analysis and also in the fully nonlinear regime. We demonstrate the ability of the phase-field method to accurately deal with non-rectangular geometry, strong advection, unsteady fluctuations and large viscosity contrast. We argue that phase-field methods are very promising for quantitatively studying moderately turbulent flows, especially at high concentrations of the disperse phase.

We derive the equations of motion for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse ``Gubser flow'' using leading-order anisotropic hydrodynamics. This is accomplished by assuming that the one-particle distribution function is ellipsoidally symmetric in the momenta conjugate to the de Sitter coordinates used to parametrize the Gubser flow. We then demonstrate that the $SO(3{)}_{q}$ symmetry in de Sitter space further constrains the anisotropy tensor to be of spheroidal form. The resulting system of two coupled ordinary differential equations for the de Sitter-space momentum scale and anisotropy parameter are solved numerically and compared to a recently obtained exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We show that anisotropic hydrodynamics describes the spatiotemporal evolution of the system better than all currently known dissipative hydrodynamics approaches. In addition, we prove that anisotropic hydrodynamics gives the exact solution of the relaxation-time approximation Boltzmann equation in the ideal, $\ensuremath{\eta}/s\ensuremath{\rightarrow}0$, and free-streaming, $\ensuremath{\eta}/s\ensuremath{\rightarrow}\ensuremath{\infty}$, limits.

Measurement techniques such as Magnetic Resonance Velocimety (MRV) and Magnetic Resonance Concentration (MRC) are useful for obtaining 3D time-averaged flow quantities in complex turbulent flows, but cannot measure turbulent correlations or near-wall data. In this work, we use highly resolved Large Eddy Simulations (LES) to complement the experiments and bypass those limitations. Coupling LES and magnetic resonance experimental techniques is especially advantageous in complex non-homogeneous flows because the 3D data allow for extensive validation, creating confidence that the simulation results portray a physically realistic flow. As such we can treat the simulation as data, which "enrich" the original MRI mean flow results. This approach is demonstrated using a cylindrical and inclined jet in crossflow with three distinct velocity ratios, $r=1$, $r=1.5$, and $r=2$. The numerical mesh is highly refined in order for the subgrid scale models to have negligible contribution, and a systematic, iterative procedure is described to set inlet conditions. The validation of the mean flow data shows excellent agreement between simulation and experiments, which creates confidence that the LES data can be used to enrich the experiments with near-wall results and turbulent statistics. We also discuss some mean flow features and how they vary with velocity ratio, including wall concentration, the counter rotating vortex pair, and the in-hole velocity.

This study experimentally investigated the influence of heat transfer from a heated hydrofoil on cavitating flow to understand the evaporation phenomenon under high-heat-flux and high-speed conditions. A temperature difference was generated between the hydrofoil and mainstream by installing an aluminum nitride heater in a NACA0015 hydrofoil fabricated from copper. A cavitation experiment was performed in a high-temperature water cavitation tunnel at the Institute of Fluid Science, Tohoku University. The effect of heating on cavitating flow was evaluated by changing the mainstream velocity and pressure, namely the cavitation number, at a fixed heater power of 860 W. Results showed that the heat transfer from the hydrofoil affected cavitating flow in terms of the cavity length, cavity aspect, and periodicity. The effect on the cavity length became stronger at a lower velocity owing to a higher hydrofoil temperature. The variation in periodicity implied that the heating effect reduced the unsteadiness of cavitation. A modified cavitation number was proposed by considering the heat transfer from the heated wall. A thermal correction term was derived by considering that the fluid temperature close to the heated hydrofoil was affected by the turbulent convective heat transfer between the mainstream and hydrofoil. The corrected cavitation number can be considered as a parameter that describes the cavity length in the isothermal and heated cases in a unified expression.

Exploring a variety of closing schemes to the infinite hierarchy of momentum moments of the exactly solvable Boltzmann equation for systems undergoing Gubser flow, we study the precision with which the resulting hydrodynamic equations reproduce the exact evolution of hydrodynamic moments of the distribution function. We find that anisotropic hydrodynamics, obtained by expanding the distribution function around a dynamically evolving locally anisotropic background whose evolution is matched to exactly reproduce the macroscopic pressure anisotropy caused by the different longitudinal and transverse expansion rates in Gubser flow, provides the most accurate macroscopic description of the microscopic kinetic evolution. This confirms a similar earlier finding for Bjorken flow [Moln\'ar et al., Phys. Rev. D 94, 125003 (2016)]. We explain the physics behind this optimal matching procedure and show that one can efficiently correct for a nonoptimized matching choice by adding a residual shear stress to the energy-momentum tensor whose evolution is again determined by the Boltzmann equation.

We have performed a direct numerical simulation of dilute turbulent particulate flow in a vertical plane channel, fully resolving the phase interfaces. The flow conditions are the same as those in the main case of "Uhlmann, M., Phys. Fluids, vol. 20, 2008, 053305", with the exception of the computational domain length which has been doubled in the present study. The statistics of flow and particle motion are not significantly altered by the elongation of the domain. The large-scale columnar-like structures which had previously been identified do persist and they are still only marginally decorrelated in the prolonged domain. Voronoi analysis of the spatial particle distribution shows that the state of the dispersed phase can be characterized as slightly more ordered than random tending towards a homogeneous spatial distribution. It is also found that the p.d.f.'s of Lagrangian particle accelerations for wall-normal and spanwise directions follow a lognormal distribution as observed in previous experiments of homogeneous flows. The streamwise component deviates from this law presenting significant skewness. Finally, a statistical analysis of the flow in the near field around the particles reveals that particle wakes present two regions, a near wake where the velocity deficit decays as 1/x and a far wake with a decay of approximately 1/(x*x).

This paper investigates systems far from equilibrium, which exhibit hydrodynamic behavior. The authors compare the usefulness of different approximation schemes, namely the gradient expansion and the ``slow roll'' approximation, when applied to Gubser" flow, which is more physical thanBjorken'' flow but is still mathematically tractable. The large order behavior of these perturbations is determined for the first time.