Flow Boundary Conditions Research Articles

The structure and stabilization by boundary conditions of an annular flow of Kolmogorov type

Abstract A system of Navier-Stokes equations with a right-hand side is considered in the case when the system approximately describes the motion of a thin layer of a viscous incompressible fluid in an annular domain under the action of external electromagnetic force. The problem possesses an unstable two-stream nonstationary main flow and a set of quasistationary solutions of vortex type for the tested range of parameters. A method of study of the general dynamic pattern is proposed in the paper. The method is based on the construction of control boundary conditions specified on the internal boundary of the annulus and providing the stabilization of considered unstable modes. The problem of boundary stabilization of the main and secondary flows is also solved numerically and we obtained that it is sufficient to take into account only a part of unstable modes in the construction of stabilizing conditions for the main flow. The method based on the partial stabilization of the main flow is first proposed for stabilization of secondary flows, which essentially simplifies the implementation of the algorithm. Formulations of the problems and numerical algorithms are presented.

Hydro-dynamic Solute Transport under Two-Phase Flow Conditions

There are abundant examples of natural, engineering and industrial applications, in which “solute transport” and “mixing” in porous media occur under multiphase flow conditions. Current state-of-the-art understanding and modelling of such processes are established based on flawed and non-representative models. Moreover, there is no direct experimental result to show the true hydrodynamics of transport and mixing under multiphase flow conditions while the saturation topology is being kept constant for a number of flow rates. With the use of a custom-made microscope, and under well-controlled flow boundary conditions, we visualized directly the transport of a tracer in a Reservoir-on-Chip (RoC) micromodel filled with two immiscible fluids. This study provides novel insights into the saturation-dependency of transport and mixing in porous media. To our knowledge, this is the first reported pore-scale experiment in which the saturation topology, relative permeability, and tortuosity were kept constant and transport was studied under different dynamic conditions in a wide range of saturation. The critical role of two-phase hydrodynamic properties on non-Fickian transport and saturation-dependency of dispersion are discussed, which highlight the major flaws in parametrization of existing models.

Predictions of first passage times in sparse discrete fracture networks using graph-based reductions.

We present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We derive graph representations of generic three-dimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the k shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. Accurate estimates of first passage times are obtained with an order of magnitude reduction of CPU time and mesh size using the proposed method.

Extended kinetic theory applied to inclined granular flows: role of boundaries

We compare the predictions of extended kinetic theory (EKT), where the roles of surface friction and correlation in fluctuation velocities are taken into account, with discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls. We show that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of excluded volume and shielding associated with collisions of particles with the boundary itself. We also note that currently available boundary conditions for flows over bumpy planes in kinetic theory underestimate the energy dissipation. These two observations explain the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady, fully-developed flows are possible. That is, for some high angles of inclination, EKT does not have solutions, while steady flows are predicted in DEM. However, whenever a solution to the system of differential equations of EKT does exist, the predicted distributions of velocity, solid volume fraction and granular temperature satisfactorily match the numerical measurements. The incompressible, algebraic approximation of EKT, which ignores the conduction of energy in the energy balance, admits solutions for a wider range of angles of inclination, as in the simulations, but fails to reproduce the quantitative and qualitative behaviour of solid volume fraction and granular temperature in the two conductive layers at the top and bottom of the flow. When frictional sidewalls are added to the domain, we show that the spanwise ratio of shear stress to pressure is linearly distributed in the dense core region of the flow, confirming that the sidewalls exert, on average, a Coulomb-like resistance to the flow with an effective friction coefficient which is less than half the actual particle-wall friction.

Numerical simulations of flow pattern and particle trajectories in feline aorta for hypertrophic cardiomyopathy heart conditions

ABSTRACTNumerical simulations of pulsatile flow in a feline aorta for hypertrophic cardiomyopathy (HCM) heart conditions are performed to predict flow details and to evaluate possible thrombus trajectory patterns. The study demonstrates that average flow rate boundary conditions (QBC) at artery outlets act as a resistance-type boundary condition for pulsatile flow. For simulations when the exact artery outflows are not known, specification of estimated values from physiological conditions is a plausible approach. This boundary condition is further improved using an iterative method (I-QBC) to accurately satisfy outflow conditions when expected outflow is known. The approach is validated against experimental data for the prediction of iliac artery flow and wall stresses in a human abdominal aorta. The feline aorta simulations including Lagrangian particle transport are performed on grids with up to 11M cells for a generalized feline aorta. It is found that LES on larger grids performs significantly better than URANS for the prediction of vortical structures. Simulations for both healthy and HCM conditions show similar flow patterns in the upper abdominal aorta. However, the HCM condition shows the presence of large recirculation regions in the thoracic aorta resulting in 50% lower flow through the iliac arteries and increased entrapment of fluid-borne particles near the trifurcation region compared to the healthy condition.

Prediction of Groundwater Quality Trends Resulting from Anthropogenic Changes in Southeast Florida.

The effects of surface water flow system changes caused by constructing water-conservation areas and canals in southeast Florida on groundwater quality under the Atlantic Coastal Ridge was investigated with numerical modeling. Water quality data were used to delineate a zone of groundwater with low total dissolved solids (TDS) within the Biscayne aquifer under the ridge. The delineated zone has the following characteristics. Its location generally coincides with an area where the Biscayne aquifer has high transmissivities, corresponds to a high recharge area of the ridge, and underlies a part of the groundwater mound formed under the ridge prior to completion of the canals. This low TDS groundwater appears to be the result of pre-development conditions rather than seepage from the canals constructed after the 1950s. Numerical simulation results indicate that the time for low TDS groundwater under the ridge to reach equilibrium with high TDS surface water in the water-conservation areas and Everglades National Park are approximately 70 and 60 years, respectively. The high TDS groundwater would be restricted to the water-conservation areas and the park due to its slow eastward movement caused by small hydraulic gradients in Rocky Glades and its mixing with the low TDS groundwater under the high-recharge area of the ridge. The flow or physical boundary conditions such as high recharge rates or low hydraulic conductivity layers may affect how the spatial distribution of groundwater quality in an aquifer will change when a groundwater flow system reaches equilibrium with an associated surface water flow system.

A comparative study of boundary conditions for lattice Boltzmann simulations of high Reynolds number flows

Four commonly-used boundary conditions in lattice Boltzmann simulation, i.e. the bounce-back, non-equilibrium bounce-back, non-equilibrium extrapolation, and the kinetic boundary condition, have been systematically investigated to assess their accuracy, stability and efficiency in simulating high Reynolds number flows. For the classical lid-driven cavity flow problem, it is found that the bounce-back scheme does not influence the simulation accuracy in the bulk region if the boundary condition is properly implemented to avoid generating non-physical slip velocity. Although the kinetic boundary condition naturally produces physical slip velocity at the wall, it gives overall satisfactory predictions of the center-line velocity profile and the vortex center locations for the Reynolds numbers considered. For the cavity flow problem, all four boundary conditions show minimal difference in the computing time needed to reach a steady state. This is surprising because the kinetic boundary condition is significantly different from the other three schemes which are designed specifically for no-slip boundary conditions. The bounce-back scheme is the most computationally efficient in updating boundary points, which is particularly attractive if there are a large number of solid bodies in the flow field. For the numerical stability, we further test the pressure-driven channel flow with or without a enclosed square cylinder. Overall, the kinetic boundary condition is the most stable of the four schemes. The non-equilibrium extrapolation scheme presents excellent stability second to the kinetic boundary condition for the lid-driven cavity flow. In comparison with other threes schemes, the stability of non-equilibrium bounce-back scheme appears to be less satisfactory for both flows.

Network modeling of liquid flow in Yanchang shale

The pore geometry and slip conditions are two principal characteristics of liquid flow in shale noncircular nanopores. We have considered the pore shape and liquid slippage on the pore interior wall in pore-network models of the Yanchang shale in China. Multiple scanning electron microscopy (SEM) images of the Yanchang shale samples were analyzed to document and summarize various pore shapes and sizes. Fluid-flow behavior in noncircular pores significantly deviates from the flow behavior in circular pores used in many current models. In addition, liquid flow simulations in conventional reservoir systems assume a no-slip flow boundary condition, which is unacceptable in nanoscale pores associated with the Yanchang shale. We studied liquid permeability in the Yanchang shale by developing realistic pore-network models based on nitrogen sorption data and SEM image analysis. The input data to the developed pore-network models include pore-size distribution, total organic carbon, porosity, surface area, pore geometry, and liquid slip length. We found that the effective permeability based on the realistic multigeometry model is significantly higher than the predicted Darcy permeability. The apparent permeability discrepancy between Darcy’s law and the realistic slip-corrected multigeometry model is higher for shale samples with an increasing number of noncircular pores. We also found that neglecting the liquid slip and noncircularity of pores significantly underestimates apparent permeability in Yanchang shale samples.

Experimental validation of heat/mass transfer analogy for two-dimensional laminar and turbulent boundary layers

Heat and mass transfer from a solid surface into a fluid stream are both diffusion driven processes. Their constant property mathematical model equations are identical for identical flow and equivalent boundary conditions, when Lewis number is equal to unity. Problems with engineering applications can be transformed from one domain to the other for practical and economic advantages. Mass transfer measurement using naphthalene sublimation can be faster, of higher resolution, economical, and more accurate than a direct heat transfer measurement. The diffusion rates by heat in air and naphthalene in air are quantitatively different. Hence, the advantages of naphthalene sublimation measurement are justified when the heat/mass transfer analogy is experimentally and/or analytically verified and an analogy factor (F=Nu/Sh) is determined.Heat/mass transfer analogy is experimentally verified in this study for two dimensional laminar and turbulent boundary layer flows over a flat plate. A thermal boundary layer technique is used to measure local heat transfer coefficient (Nu) and a naphthalene sublimation measurement is used to evaluate local mass transfer coefficient (Sh) for two similar plates subjected to the same boundary layer flow. The heat/mass transfer analogy factor is calculated using the measured Nu and Sh. It is found to agree with the analytical prediction of 0.677 within 2% for the laminar case and is found to be constant at 0.667 for the turbulent flow.

Meshfree Multiquadric Solution for Real Field Large Heterogeneous Aquifer System

Meshfree methods are often tested in literature for the rectangular domain with uniform aquifer properties (e.g. transmissivity or hydraulic conductivity) and constant groundwater head boundary conditions. In this paper, a multiquadric meshfree (Mfree) groundwater model is developed for a real field irregular domain aquifer system which is capable of incorporating variability like heterogeneity, temporally and spatially varied groundwater head and flow boundary conditions. The developed model is free from the inadequacy of meshing which eventually saves the time on computing resources by calculating the groundwater head-derivatives at different nodes sprinkled over the entire flow domain. Initially, two synthetic problems with pre- existing analytical and grid based results are tested against the presented model. Sensitivity analysis of different parameters like time step size, nodal density and support size of basis function are also investigated. Subsequently Mfree solutions are obtained for a large Mahi Right Bank Canal (MRBC) unconfined aquifer located in Gujarat India. The Mfree solution performance on two synthetic and one real field large aquifer problem revealed that the projected method is advantageous over other grid based simulator in terms of computational time consideration. Such a simulation is preferable in groundwater management models where flow models are coupled with the optimization problem.

Advanced turbulence models and boundary conditions for flows around different configurations of ground-mounted buildings

When dealing with Atmospheric Boundary Layer (ABL) simulations, commercial computational fluid dynamics (CFD) acquires a strategic resonance. Thanks to its good compromise between accuracy of results and calculation time, RANS still represents a valid alternative to more resource-demanding methods. However, focusing on the models’ performances in urban studies, LES generally outmatches RANS results, even if the former is at least one order of magnitude more expensive. Consequently, the present work aims to propose a variety of approaches meant to solve some of the major problems linked to RANS simulations and to further improve its accuracy in typical urban contexts. All of these models are capable of switching from an undisturbed flux formulation to a disturbed one through a local deviation or a marker function. For undisturbed flows, a comprehensive approach is adopted, solving the issue of the erroneous stream-wise gradients affecting the turbulent profiles. Around obstacles, Non-Linear Eddy-Viscosity closures are adopted, due to their prominent capability in capturing the anisotropy of turbulence. The purpose of this work is then to propose a new Building Influence Area concept and to offer more affordable alternatives to LES simulations without sacrificing a good grade of accuracy.

Derivation of the Navier slip and slip length for viscous flows over a rough boundary

In this paper, we derive the Navier slip boundary condition for flows over a rough surface, by combining homogenization methods and boundary layer techniques. The Navier slip condition is derived as the effective boundary condition, in the limit as the roughness becomes small; it is the first order corrector to the no-slip condition on the limiting smooth surface. Using this method, we are simultaneously able to provide a formula for computing the slip length for various geometries. The paper provides a theoretical justification for the observed slip in micro- or nanofluidics, as well as a computational tool. Computations done using FreeFem++ agree with experimental data.

Numerical simulation of plasma waves in a quasi-2D electron gas based on the Boltzmann transport equation

The calculation of plasma waves in a homogeneous quasi-2D electron gas is usually based on the Euler equation. It yields a dispersion relation with two branches, which are often referred to as Vlasov modes. Dyakonov and Shur were able to show that under certain boundary conditions for a constant current flow in a high electron mobility transistor these two modes can lead to a plasma instability and generation of THz waves. If, on the other hand, the more physics-based Boltzmann transport equation is solved for plasma waves, a multitude of modes is obtained in addition to the two Vlasov modes. In the case of nonequilibrium and high frequencies, it is no longer possible to identify the two Vlasov modes by simple means. This phenomenon is discussed in detail, and a method for the identification of the Vlasov modes is proposed. In addition, it is shown that for strong nonequilibrium the Dyakonov---Shur instability can be evaluated numerically using a method based on the Boltzmann transport equation.

Electrostatically driven helical plasma state

A novel plasma state has been found in the presence of a uniformly applied axial magnetic field in periodic cylindrical geometry. This state is driven electrostatically by helical electrodes, providing a driving field that depends on the radius and mθ−nζ, where θ is the poloidal angle and ζ=z/R is the toroidal angle. We focus on m=n=1. The radial magnetic field at the wall is taken to be zero. With weak driving, the resulting distortion is very small, but for stronger driving, the mean field of the state has field line safety factor q0(r) just above the pitch of the electrodes m∕n = 1 except near the edge, where q0 increases monotonically. This state is characterized as a single helicity Ohmic equilibrium with the helical symmetry of the applied field. The plasma appears to be close to force-free in the interior, but current density crosses the magnetic flux surfaces near the edge, where current must enter and exit through the helical electrodes. This perpendicular current density drives large helical plasma flows. The sensitivity of this state to flow boundary conditions, plasma resistivity profile, the strength of electrostatic driving, and parameters such as the loop voltage and the Lundquist number is explored. The magnetic helicity is calculated for both the transient period and time-asymptotic state. Possible applications to current drive in toroidal confinement devices and to electrical transformers are discussed.

Spectral element simulations of three dimensional convective heat transfer

This paper presents new formulation for simulating three-dimensional convective heat transfer by incorporating the complete viscous dissipation function in the energy equation to account for viscous heating and adopting the Boussinesq approximation for the thermal buoyancy term in the Navier-Stokes equations. In addition, new implementation of fourth order Stiffly Stable Schemes was achieved and tested for time integration. In order to provide dual-level mesh refinement, the hp-refinement, for flexible spatial resolutions, a modal spectral element method was used to solve these equations in three dimensions. Simulation results were compared with exact solutions or higher order solutions and good agreement were accomplished. This demonstrates that the new formulation and implementation are accurate enough for investigating convective heat transfer with viscous heating subject to complex thermal and flow boundary conditions in three dimensional irregular domains using the high order version of finite element method.

A multiphase MPS solver for modeling multi-fluid interaction with free surface and its application in oil spill

Numerical simulation of free surface multi-fluid flow is a challenging problem owning to the interaction between deformed interface and free surface. In this paper, a multiphase particle solver (free surface multiphase moving particle semi-implicit method, FS-MMPS) is developed to predict the early spreading flow of spilled oil where exist the oil–water interface and air–oil/air–water free surface. First, a multiphase virtual particle model is proposed to substitute the inaccurate free surface boundary condition for multiphase flow in conventional MPS methods. Specifically, virtual particles of different liquid phases are compensated outside free surface so that the pressure of free surface particles can be solved from pressure Poisson equation, thereby improving the accuracy of multi-fluid interaction at free surface. Meanwhile, a pressure gradient model based on the coupling of Taylor series expansion and dynamic specification of particle stabilizing term (PST) is proposed to simultaneously enhance accuracy and depress instability caused by multiphase virtual particles. Experiments of early spreading of thick oil slicks and continuous oil spill from a damaged tank are conducted for validation and demonstration of the accuracy and stability enhancements in 2D. Finally, the effects of traveling wave and continuous spilling on oil spreading are investigated to show the capability of the proposed method. The spreading of thick oil slicks is accelerated when wave height increases or wave length decreases, and the largest increase of spreading rate accelerated by traveling wave is 14%.

Passive flow control for aerodynamic performance enhancement of airfoil with its application in Wells turbine – Under oscillating flow condition

In this work, the passive flow control method was applied to improve the performance of symmetrical airfoil section in the stall regime. In addition to the commonly used first law analysis, the present study utilized an entropy generation minimization method to examine the impact of the flow control method on the entropy generation characteristics around the turbine blade. This work is performed using a time-dependent CFD model of isolated NACA airfoil, which refers to the turbine blade, under sinusoidal flow boundary conditions, which emulates the actual operating conditions. Wells turbine is one of the most proper applications that can be applied by passive flow control method because it is subjected to early stall. Additionally, it consists of a number of blades that have a symmetrical airfoil section subject to the wave condition. It is deduced that with the use of passive flow control, torque coefficient of blade increases by more than 40% within stall regime and by more than 17% before the stall happens. A significantly delayed stall is also observed.

Transient evolution of suspended and benthic algae in a riverine ecosystem: A numerical study

It is a well-established fact that there is no direct resource competition between pelagic and benthic primary producers when their habitats are located in physically separate areas. However, the benthic habitat located at the bottom of the water column is affected by the light rays that gets attenuated as it passes through the pelagic zone and is obstructed by the algal cells and suspended material present in the water column. Therefore, benthic primary production is very much influenced by the conditions and concentrations in the pelagic zone. Another level of complexity is added to the system while considering the impact of flowing water in a riverine environment. In the research presented here a numerical model is developed to examine the impact of flow and nutrients on pelagic and benthic primary producers. The aforementioned numerical model solves advection diffusion and reaction (ADR) equation through TVD (total variation diminishing) − MacCormack scheme. The diffusion term is solved through central difference scheme. The model results are first validated by comparing the results with analytical solutions for the simplified case. The validated model is then applied to a 30kms stretch of the Bode River and simulations are conducted for multiple flow conditions. Impact of transient flow and nutrient boundary conditions on the evolution of algal trait is examined. Our simulation exercise highlights the importance of residence time in the temporal evolution of algae in pelagic and benthic zone and further identifies the most sensitive parameter influencing the evolution of the algal community modelled. Our research also reveals that largest uncertainty in the modelling stems from the wide range of entrainment rate that could be used for modelling resuspension of benthic algae in pelagic zone. The use of higher entrainment rate increased the algal concentration in the water column by 48% for identical flow conditions.

Robust boundary treatment for open-channel flows in divergence-free incompressible SPH

A robust Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed to simulate specified inflow and outflow boundary conditions for open-channel flow. Being purely divergence-free, the framework offers smoothed and structured pressure distribution. An implicit treatment of Pressure Poison Equation and Dirichlet boundary condition is applied on free-surface to minimize error in velocity-divergence. Beyond inflow and outflow threshold, multiple layers of dummy particles are created according to specified boundary condition. Inflow boundary acts as a soluble wave-maker. Fluid particles beyond outflow threshold are removed and replaced with dummy particles with specified boundary velocity. The framework is validated against different cases of open channel flow with different boundary conditions. The model can efficiently capture flow evolution and vortex generation for random geometry and variable boundary conditions.

CFD-RANS prediction of the dispersion of a hazardous airborne material released during a real accident in an industrial environment

This work presents the Computational Fluid Dynamics (CFD) – Reynolds-Averaged Navier Stokes (RANS) simulation and results of the dispersion of a hazardous airborne material which was released during a real accident in an industrial facility. During the event the material was released as flashing liquid from a point located inside a building, partially opened to the outside. According to estimations, after having evaporated, a total material mass in the order of 900 kg escaped to the atmosphere with a time-varying rate from five main openings of the building. The CFD simulations presented here concern the dispersion of the gaseous substance outside the building from where it was released but inside the complex industrial site. The few meteorological measurements that were available in the area have been used for the construction of inlet flow boundary conditions for the model. To take into account the uncertainty due to the scarcity of the available in situ meteorological data, and the temporal variability of the wind direction, three different incident wind directions have been considered in the computations. In each case, the CFD-RANS results for concentration have been compared with the real measurements recorded by the sensors during the accident, paired in space and time. The performance of the model depends on the incident wind direction and it varies depending on the position of the sensors. However, the overall agreement with the observations is considered as satisfactory taking into account the complexity of the problem and the uncertainties associated with the emission rate and the meteorological conditions. The maximum measured concentrations near the sources are predicted very well by the model.