Numerical simulation of non-Newtonian Carreau fluid in a lid-driven cavity

In this work, the 2D lid-driven cavity flow of non-Newtonian Carreau fluids has been studied by finite difference method on a staggered grid. A finite-difference algorithm on staggered grid based on projection method is adopted to solve the lid-driven cavity flow, which includes a second-order central difference scheme for the non-Newtonian viscous stress term. This study has been conducted for the certain pertinent parameters of Reynolds number (Re=100-1000), power-law index (n=0.6-1.4). The results show that as the Reynolds number increases, the influence of the power-law index on the flow increases. As the power-law index decreases, the flow field becomes more complicated.

Dynamical modelling of disc vertical structure in superthin galaxy ‘UGC 7321’ in braneworld gravity: an MCMC study

ABSTRACT Low surface brightness (LSBs) superthins constitute classic examples of very late-type galaxies, with their disc dynamics strongly regulated by their dark matter haloes. In this work, we consider a gravitational origin of dark matter in the braneworld scenario, where the higher dimensional Weyl stress term projected on to the three-brane acts as the source of dark matter. In the context of the braneworld model, this dark matter is referred to as the ‘dark mass’. This model has been successful in reproducing the rotation curves of several LSB and high surface brightness galaxies. Therefore, it is interesting to study the prospect of this model in explaining the vertical structure of galaxies which has not been explored in the literature so far. Using our two-component model of gravitationally coupled stars and gas in the external force field of this dark mass, we fit the observed scale heights of stellar and atomic hydrogen (H i) gas of superthin galaxy ‘UGC7321’ using the Markov Chain Monte Carlo approach. We find that the observed scale heights of ‘UGC7321’ can be successfully modelled in the context of the braneworld scenario. In addition, the model predicted rotation curve also matches the observed one. The implications on the model parameters are discussed.

Study of intrinsic rotation by the Gyrokinetic Electromagnetic Numerical Experiment code in the Joint Texas Experimental Tokamak

The core toroidal plasma intrinsic rotation has been studied by experiments and simulations in the Joint Texas Experimental Tokamak (J-TEXT). The direction of core intrinsic rotation in the J-TEXT plasma is counter-current. As the plasma density ramps up, the rotation velocity increases in the counter-current direction. By comparing four different electron densities, linear local gyrokinetic simulations have been performed by the Gyrokinetic Electromagnetic Numerical Experiment code for the first time on J-TEXT. It is found that the most dominant turbulence is the ion temperature gradient at $0.2a$ , where $a$ is the minor radius of the plasma and this is unchanged during the plasma density ramp up. By scanning the radial wave vectors, it is found that the residual stress term reverses from negative to positive when the plasma density exceeds a certain threshold. The pinch term is larger than the residual stress term at all four electron densities, which means that the pinch term is always dominant in the core of a J-TEXT plasma.

Distributed LES-based drag parameterisation for heterogeneous urban neighbourhoods

<p><span>The form and density of buildings modify the air flow and momentum exchange within cities, and therefore strongly affect local wind, temperature, humidity and pollution. Numerical weather prediction (NWP) models currently do not account for heterogeneity in their surface layer parameterisation. Regional models represent buildings, if at all, based on quantities such as plan and frontal area indices, and parameterise their impact at the lowest grid level, even though buildings can protrude a significant height into the atmospheric boundary layer.</span></p><p><span>To investigate how to parameterise urban roughness in NWP, we analysed high-resolution building-resolving large eddy simulations (LES) with the uDALES model over a range of heterogeneous urban neighbourhoods. The simulation setups have a similar building density and frontal aspect ratio, but vary in complexity with different building heights, plan areas and street geometries. Using the LES data we developed a parameterisation model that describes the vertical distribution of building drag inside a heterogeneous urban canopy. The drag force exerted on the atmosphere represents the momentum loss in the urban canopy due to buildings and can be incorporated as additional stress term in the momentum equations. The parameterisation represents the spatial heterogeneity effects in a one-dimensional vertical function, and links the building drag force to the heterogeneity of building layouts. A characterisation of the vertical and horizontal heterogeneity of built-up neighbourhoods is used as model input.</span></p>

2D Numerical Modeling on the Transformation Mechanism of the Braided Channel

This paper investigates the transformation mechanism between different channel patterns. A developed 2D depth-averaged numerical model is improved to take into account a bank vegetation stress term in the momentum conservation equation of flow. Then, the extended 2D model is applied to duplicate the evolution of channel pattern with variations in flow discharge, sediment supply and bank vegetation. Complex interaction among the flow discharge, sediment supply and bank vegetation leads to a transition from the braided pattern to the meandering one. Analysis of the simulation process indicates that (1) a decrease in the flow discharge and sediment supply can lead to the transition and (2) the riparian vegetation helps stabilize the cut bank and bar surface, but is not a key in the transition. The results are in agreement with the criterion proposed in the previous research, confirming the 2D numerical model’s potential in predicting the transition between different channel patterns and improving understanding of the fluvial process.

An unexpected balance between outer Rayleigh streaming sources

Acoustic streaming generated by a plane standing wave between two infinite plates or inside a cylindrical tube is considered, under the isentropic flow assumption. A two-dimensional analysis is performed in the linear case of slow streaming motion, based on analytical formal solutions of separate problems, each associated with a specific source term (Reynolds stress term). In order to obtain these analytical solutions, a necessary geometrical hypothesis is that $(R/L)^{2}\ll 1$, where $R$ and $L$ are the guide half-width (or radius) and length. The effect of the two source terms classically taken into account is quantified in order to derive the dependence of the maximum axial streaming velocity on the axis as a function of the ratio $R/\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$, where $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$ is the acoustic boundary layer thickness. The effect of two other source terms that are usually neglected, is then analysed. It is found that one of these terms can generate a counter-rotating streaming flow. While negligible for very narrow guides, this term can become important for some values of the aspect ratio $L/R$.

INTERACTIONS OF WAVES WITH IDEALIZED HIGH-RELIEF BOTTOM ROUGHNESS

Interactions between waves and high-relief bottom roughness were investigated using Large Eddy Simulations of oscillatory flow over an infinite array of regularly spaced hemispheres. Simulation results were analyzed using a spatially- and phase-averaged momentum balance to provide insight into how flow-topography interactions affect wave-driven oscillating flows. Phase-averaging was applied first, and then spatial averaging was applied over volumes with horizontal length scales greater than the size of a single solid obstacle but fine enough in the vertical direction that the vertical structure of the dynamics was resolved. Spatial averaging of the momentum equation results in terms that represent drag and inertial forces, and a dispersive stress term that represents a vertical momentum flux induced by the spatial heterogeneity of the phase-averaged flow. These new terms require parameterization in coastal ocean wave and circulation models.

POD Analysis of Entropy Generation in a Laminar Separation Boundary Layer

Separation of laminar boundary layer is a great source of loss in energy and power machinery. This paper investigates the entropy generation of the boundary layer on the flat plate with pressure gradient. The velocity of the flow field is measured by a high resolution and time related particle image velocimetry (PIV) system. A method to estimate the entropy generation of each mode extracted by proper orthogonal decomposition (POD) is introduced. The entropy generation of each POD mode caused by mean viscous, Reynolds normal stress, Reynolds sheer stress, and energy flux is analyzed. The first order mode of the mean viscous term contributes almost 100% of the total entropy generation. The first three order modes of the Reynolds sheer stress term contribute less than 10% of the total entropy generation in the fore part of the separation bubble, while it reaches to more than 95% in the rear part of the separation bubble. It indicates that the more unsteady that the flow is, the higher contribution rate of the Reynolds sheer stress term makes. The energy flux term plays an important role in the turbulent kinetic energy balance in the transition region.

Numerical Study of the Wake Flow of a Wind Turbine with Consideration of the Inflow Turbulence

Considering the fact that wind turbines operate at the bottom of the atmospheric boundary layer (ABL) where the turbulence is at a high level, and the difficulty of mesh generation in the fully modeled numerical simulation, it is necessary to carry out researches to study the wake flow of wind turbines with consideration of the inflow turbulence. Therefore, a numerical method generating turbulence was proposed and the results show good agreement with those in experiments, based on which the flow fields in the wake of a wind turbine at two tip speed ratios are examined in detail through three actuator methods, namely, ADM, ADM-R and ALM. The performances of these methods were studied and the error sources for each method are clarified. Moreover, the computational efficiency were revealed and the influencing factor for the efficiency is concluded. Besides, the equilibrium relation of the N-S equation in the wake is revealed, which provides a theoretical basis for the optimal arrangement of the wind turbine. It shows that the mean velocity and fluctuating velocity vary greatly near the wind turbine, and become stable gradually away from the wind turbine. The results of ALM method shows the best agreement with the experiment. At near wake region, the turbulent stress term, pressure gradient term and convection term mainly contribute to the equation equilibrium, and convection term is in equilibrium with the turbulent stress term at the far wake.

Numerical Modeling of Wave-Current Flow around Cylinders Using an Enhanced Equilibrium Bhatnagar-Gross-Krook Scheme

Flow around cylinders is a classic issue of fluid mechanics and it has great significance in engineering fields. In this study, a two-dimensional hydrodynamic lattice Boltzmann numerical model is proposed, coupling wave radiation stress, bed shear stress, and wind shear stress, which is able to simulate wave propagation of flow around cylinders. It is based on shallow water equations and a weight factor is applied for the force term. An enhanced equilibrium Bhatnagar-Gross-Krook (BGK) scheme is developed to treat the wave radiation stress term in collision step. This model is tested and verified by two cases: the first case is the flow around a single circular cylinder, where the flow is driven by current, wave, or both wave and current, respectively, and the second case is the solitary waves moving around cylinders. The results illustrate the correctness of this model, which could be used to analyze the detailed flow pattern around a cylinder.