Steady-state Flow Pattern Research Articles

Steady-State Transitions in Ordered Porous Media

Previously performed experiments on flow through an ordered porous media cell with tomographic particle image velocimetry reveal a complex three-dimensional steady-state flow pattern. This flow pattern emerge in the region where inertial structures have been previously reported for a wide range of packings. The onset of these steady-state inertial flow structures is here scrutinized for three different types of packing using a finite difference method. It is concluded that the onset of the flow structure coincides with a symmetry break in the flow field and discontinuities in the pressure drop, volume averaged body forces and heat transfer. A quantity for identifying the transition is proposed, namely the pressure integral across the solid surfaces. It is also shown that the transition can both increase and decrease the heat transfer dependent on the actual geometry of the porous medium.

Influence of the corner radii on the flow characteristics of three square-like cylinders in an equilateral-triangular arrangement using IB-LBM

A two-dimensional momentum exchange-based immersed boundary–lattice Boltzmann method (IB-LBM) is used to scrutinize the influence of the corner radii on the characteristics of laminar flow around square-like cylinders arranged in an equilateral-triangular configuration, with each cylinder represented by 300 discrete elements. Numerical simulations were carried out in Newtonian flow with viscous, incompressible, and constant properties, by simultaneously changing the corner ratio λ from 0.0 (square) to 1.0 (circular), Reynolds number Re from 40 to 160, and gap ratio δ from 0.5 to 5.0. The wake flow patterns, force coefficients, and Strouhal number St were calculated and discussed. The numerical outcomes demonstrate that the corner ratio, Re, and gap ratio have a prominent influence on the flow characteristics. The wake flow patterns in the λ-Re plane can be divided into steady-state, flip-flopping, anti-phase, and in-phase modes for δ = 3.0. The drag Cd and lift Cl coefficients exhibit a decreasing trend with increasing corner radius except for Clc1; as δ is increased, the Cl of all three cylinders for λ ranging from 0 to 1.0 gradually approached zero. The St of the steady state flow pattern is significantly lower than that of other flow states, the relationship between St and λ is complex and irregular; as δ increases, the St and λ show a positive correlation.

Transient electrohydrodynamics of a liquid drop: The interplay of fluid flow evolution and dynamic response, and the density ratio effects

Computer simulations are performed to study some of the less explored aspects of the transient electrohydrodynamics of a liquid drop in uniform DC electric fields. The governing equationsof the problem are solved using a parallelized front tracking/finite difference method in the framework of Taylor-Melcher's leaky dielectric theory. For density- and viscosity-matched fluid systems, the evolution of the flow field at a high Ohnesorge-squared number Oh^{2}=μ^{2}/γρa is studied. It is shown that the instantaneous flow pattern is the result of superposition of deformation- and hydrodynamic shear-driven vortices, and that depending on the placement of the fluid systems on the deformation-circulation map, there exists two different paths for the development of the velocity field toward steady state. Examination of the steady-state flow patterns shows that the location of the maximum velocity can shift from the (classically known) drop surface to inside the drop along the poles. The effect of Oh^{2} on the dynamic response of the drop and the kinetic energy of the fluid is studied. For high Oh^{2} number flows, the dynamic response is monotonic while the kinetic energy evolves in a nonmonotonic way, achieving a distinct peak before settling to steady state. However, for low Oh^{2} number flows, both the dynamic response and kinetic energy are oscillatory. Inspection of the results show a two-way coupling between the deformation rate and the fluid flow. The effect of the density ratio ρ[over ̃]=ρ_{i}/ρ_{o} (drop to ambient) on the dynamic response and fluid flow strength shows that for high Oh^{2} number flows both parameters remain essentially intact at steady state, while their evolution modes transition from a monotonic response to an oscillatory one at high density ratio. However, for low Oh^{2} number flows, with an increase in ρ[over ̃], the oscillation frequency of both parameters remain intact, while their oscillation amplitudes increase.

A Preliminary Study of Oxygen Transport from Capillary to Tissue using Finite Difference Method

In this study, Finite Difference Method is used to examine oxygen transport from blood capillary to tissue. Tissue is modelled as porous media and oxygen rich blood is transported throughout the tissue from the blood vessel by advection and diffusion. Uniform consumption by tissue is considered for simplicity. Steady state flow patterns and concentration contours are discussed. A simplistic 2-D model was created after reviewing the literature. The model considers interlinkage of capillaries. Stream Function-Vorticity formulation coupled with advection-diffusion equation are solved simultaneously to evaluate velocities and concentration values in the domain. This report focuses on the how various parameters affect flow and mass transfer inside a porous media. Effect of various non dimensional parameters like Darcy number and non-dimensional absorption coefficient are discussed.

Development of an Algebraic Model of Empirical Parameterization of Near Wakes around a Vehicle

In this paper, we describe and evaluate an algebraic model that has been adopted in a diagnostic wind flow model. Our numerical model is based on the Röckle’s wind modelling approach and we intend to reproduce the steady-state flow patterns of recirculation vortices that are generated in the near-wake region behind a vehicle. The evaluation of the practicality of our proposed model is performed by comparing the wind tunnel experiments of the flow around a vehicle conducted by the Loughborough University. We also compare the numerical results of our model with the CFD model. The proposed model reproduces the flow patterns behind a vehicle and it has significant advantages, such as low numerical costs. We expect that further improvements in the algebraic model when considering the vehicle’s shape will improve its practicality for the numerical analysis of flow fields around a vehicle.

Hysteresis effect of propeller jet flows in viscoelastic fluids: Steady state flow patterns

Contrary to existing knowledge, the flow field showed a hysteresis effect when the rotational speed varied. The speed up operation in hysteresis range generates a semi-radial flow field, whereas the slow down operation causes an axial flow filed. Therefore, two stable flow fields can be formed at the same rotational speed and which one prevails depends on the flow history. The flow fields were measured using PIV and UVP, to explore the hysteresis range of four different xanthan gum solutions. The hysteresis range shifts toward higher rotational speed with increasing concentrations. The Reynolds number was failed to characterize the flow within hysteresis range but can be used for rotational speeds exceeding hysteresis range. The aim of this work was to introduce this phenomenon and to provide the first comparison between the two flow patterns and the fundamental for further researches dealing with the hysteresis effect in flow fields.

A neural-network enhanced modeling method for real-time evaluation of the temperature distribution in a data center

The thermal predicting/evaluating model of data centers is pivotal in designing their thermal control systems. The existing modeling methods are based on the computational fluid dynamics (CFD) simulations, which is accurate in modeling for a steady-state flow pattern but considerably time-consuming. Besides, the corresponding parameters of CFD have to be re-identified with the deviation of the flow field, which makes it extremely inefficient in real-time thermal control system design of data centers. This paper proposed a machine learning method to derive the fast-temperature evaluation model with a constructed artificial neural network. It learns the relationship between the flow patterns and model parameters based on the system thermal–physical analysis, which replaces the time-consuming CFD-based parameter identifying process. Then, the temperature evaluation is implemented under different flow patterns with the proposed neural-network enhanced modeling method. In the learning process, multi-type of neural networks, i.e., backpropagation network, radial basis function network and extreme learning machine, are considered and compared. The accuracy of the proposed model is validated by comparing with the pure CFD results as the satisfactory standard. With the efficiency and accuracy, the proposed modeling method is more suitable to design real-time controllers for data centers with changing flow fields.

Buoyancy-driven natural ventilation in one storey connected with an atrium

A macroscopic zone model is used to analyze buoyancy-driven natural ventilation in one storey connected with an atrium. The height ratio between the storey and atrium can be variable as well as the heat ratio between the two heat sources, one in storey and the other in atrium. Both the steady-state and time-dependent flow rate through the storey and atrium are investigated. The transient process from different initial conditions to different steady-state flow patterns are numerically performed by means of Euler method, especially the detailed investigation of time evolution of flow rate between different flow patterns from ‘zero’ initial conditions. Seven classical cases of time development flow rate are given to explain flow pattern can evolve from one to another and the implications of natural ventilation driven by the two opposing buoyancy forces in atrium building are discussed. Furthermore, small-scale experiments were conducted to evaluate switch of flow pattern in transient flow. Stability analysis and bifurcation point of multiple flow patterns are also considered on the basis of fundamental nonlinear dynamics.

Enhancement of the Drift-Flux Model for gas-liquid slug flow in a long vertical pipe

The paper presents an Averaged Drift-Flux Model (ADFM) facilitating consideration of the internal structure of the gas-liquid slug flow in a vertical pipe. Modulation equations are used for flow parameter averaging. The allowable domain of the ADFM has been determined and its difference from the conventional model has been demonstrated. The specific features of the developed model for frictional and frictionless steady state flow patterns have been considered. The averaged model has been verified by comparing the calculation results and the results of three experimental studies. The proposed paper is aimed at expanding the capabilities of the Drift-Flux Model class. The model is oriented on advanced hydrodynamic calculations in oil and gas wells and risers.

Evaluation of high-resolution GRAMM–GRAL (v15.12/v14.8) NO<sub><i>x</i></sub> simulations over the city of Zürich, Switzerland

Abstract. Hourly NOx concentrations were simulated for the city of Zürich, Switzerland, at 10 m resolution for the years 2013–2014. The simulations were generated with the nested mesoscale meteorology and micro-scale dispersion model system GRAMM–GRAL (versions v15.12 and v14.8) by applying a catalogue-based approach. This approach was specifically designed to enable long-term city-wide building-resolving simulations with affordable computation costs. It relies on a discrete set of possible weather situations and corresponding steady-state flow and dispersion patterns that are pre-computed and then matched hourly with actual meteorological observations. The modelling system was comprehensively evaluated using eight sites continuously monitoring NOx concentrations and 65 passive samplers measuring NO2 concentrations on a 2-weekly basis all over the city. The system was demonstrated to fulfil the European Commission standards for air pollution modelling at nearly all sites. The average spatial distribution was very well represented, despite a general tendency to overestimate the observed concentrations, possibly due to a crude representation of traffic-induced turbulence and to underestimated dispersion in the vicinity of buildings. The temporal variability of concentrations explained by varying emissions and weather situations was accurately reproduced on different timescales. The seasonal cycle of concentrations, mostly driven by stronger vertical dispersion in summer than in winter, was very well captured in the 2-year simulation period. Short-term events, such as episodes of particularly high and low concentrations, were detected in most cases by the system, although some unrealistic pollution peaks were occasionally generated, pointing at some limitations of the steady-state approximation. The different patterns of the diurnal cycle of concentrations observed in the city were generally well captured as well. The evaluation confirmed the adequacy of the catalogue-based approach in the context of city-scale air pollution modelling. The ability to reproduce not only the spatial gradients but also the hourly temporal variability over multiple years makes the model system particularly suitable for investigating individualized air pollution exposure in the city.

Cycle flows and multistability in oscillatory networks.

We study multistability in phase locked states in networks of phase oscillators under both Kuramoto dynamics and swing equation dynamics-a popular model for studying coarse-scale dynamics of an electrical AC power grid. We first establish the existence of geometrically frustrated states in such systems-where although a steady state flow pattern exists, no fixed point exists in the dynamical variables of phases due to geometrical constraints. We then describe the stable fixed points of the system with phase differences along each edge not exceeding π/2 in terms of cycle flows-constant flows along each simple cycle-as opposed to phase angles or flows. The cycle flow formalism allows us to compute tight upper and lower bounds to the number of fixed points in ring networks. We show that long elementary cycles, strong edge weights, and spatially homogeneous distribution of natural frequencies (for the Kuramoto model) or power injections (for the oscillator model for power grids) cause such networks to have more fixed points. We generalize some of these bounds to arbitrary planar topologies and derive scaling relations in the limit of large capacity and large cycle lengths, which we show to be quite accurate by numerical computation. Finally, we present an algorithm to compute all phase locked states-both stable and unstable-for planar networks.

A cost-effective method for simulating city-wide air flow and pollutant dispersion at building resolving scale

A cost-effective method is presented allowing to simulate the air flow and pollutant dispersion in a whole city over multiple years at the building-resolving scale with hourly time resolution. This combination of high resolution and long time span is critically needed for epidemiological studies and for air pollution control, but still poses a great challenge for current state-of-the-art modelling techniques. The presented method relies on the pre-computation of a discrete set of possible weather situations and corresponding steady-state flow and dispersion patterns. The most suitable situation for any given hour is then selected by matching the simulated wind patterns to meteorological observations in and around the city. The catalogue of pre-computed situations corresponds to different large-scale forcings in terms of wind speed, wind direction and stability. A meteorological model converts these forcings into realistic mesoscale flow patterns accounting for the effects of topography and land-use contrasts in a domain covering the city and its surroundings. These mesoscale patterns serve as boundary conditions for a microscale urban flow model which finally drives a Lagrangian air pollutant dispersion model. The method is demonstrated with the modelling system GRAMM/GRAL v14.8 for two Swiss cities in complex terrain, Zurich and Lausanne. The mesoscale flow patterns in the two regions of interest, dominated by land-lake breezes and driven by the partly steep topography, are well reproduced in the simulations matched to in situ observations. In particular, the combination of wind measurements at different locations around the city appeared to be a robust approach to deduce the stability class for the boundary layer within the city. This information is critical for predicting the temporal variability of pollution concentration within the city, regarding their relationship with the intensity of horizontal and vertical dispersion and of turbulence. In the vicinity of sources, the 5 m resolution chosen in our set-up is not always sufficient to reproduce the very steep concentration gradients, pointing at additional cost optimisations in the method required to make higher resolutions affordable. Nevertheless, the catalogue-based methodology allows reproducing concentration variability very consistently further away from emission sources, hence for most parts of the city.

Study of transient heat transfer at different proton beam energy in ADS windowless spallation target

Accelerator driven system (ADS) is a promising technique for reducing the amount of long-lived fission products in a safe manner. It consists of a subcritical core coupled with an accelerator by means of a spallation target arrangement. Thermal hydraulics of a spallation target is of great complexity due to the multiphase flow, the cavitation, and the coupling with the spallation reaction. In this paper, we firstly obtain the steady-state flow pattern of lead-bismuth eutectic (LBE) in the target, and then based on the flow pattern, the heat deposition with different proton beam energy is calculated via nuclear physics simulation. After that, the heat deposition is imported into CFD calculation to study the process of heat transfer. The transient temperature distributions with different proton beam energy are calculated. It is observed that the shape of temperature distribution varies with proton beam energy although the beam intensity is kept the same. The results also show that the temperature of recirculation zone is very effectively limited by adopting the annulus shaped proton beam. Above all, the temperature distribution depends on the heat deposition, the velocity and the flow pattern. The results are of great value and can be applied to the future design and optimization of the ADS windowless spallation target in China.

Effect of Roughness and Contact Coefficients on the Dynamic Behavior of Droplet Impact onto a Solid Surface

In this paper, a lattice Boltzmann model (LBM) is applied to simulate the dynamic behavior of liquid droplets on a solid substrate with variable wettabilities and different micro-topographical patterns. The relationship among fluid/solid interaction parameter, contact angle and surface wettability is obtained by the linear fitting of the pre-simulation results. In the case of 0.314 < |Gt| < 0.563, 0.149 < |Gt| < 0.314 and 0.066 < |Gt| < 0.149, the contact angle will be θ < 90°, 90° < θ < 150° and 150° < θ < 180°, namely the material is the hydrophilic, hydrophobic and superhydrophobic, respectively. Flowing state of droplets on different surfaces are presented. For the hydrophilic rough surface, the droplet fills up the grooves among roughness bumps, while for the hydrophobic one, liquid drop suspends and sits on the tops of the posts with pockets of air beneath it. Most of all, the effects of roughness on droplet behavior are studied and some comprehensive results have been obtained. When the surface is hydrophilic and super hydrophobic, changing the structure of rough units has less impact on the steady-state flow pattern of droplet. And for hydrophobic surface, the effect of surface roughness on the impact characteristics is significant. Only when the structures of rough units meet that the height of the rough unit is greater than the depth the droplets dipping into grooves, droplets can suspend on the top of the rough units with no contact with the bottom wall of the groove.

Stokesian spherical swimmers and active particles.

The net steady state flow pattern of a distorting sphere is studied in the framework of the bilinear theory of swimming at low Reynolds number. It is argued that the starting point of a theory of interacting active particles should be based on such a calculation, since any arbitrarily chosen steady state flow pattern is not necessarily the result of a swimming motion. Furthermore, it is stressed that as a rule the phase of stroke is relevant in hydrodynamic interactions, so that the net flow pattern must be used with caution.

The Effect of Beam Intensity on Temperature Distribution in ADS Windowless Lead-Bismuth Eutectic Spallation Target

The spallation target is the component coupling the accelerator and the reactor and is regarded as the “heart” of the accelerator driven system (ADS). Heavy liquid metal lead-bismuth eutectic (LBE) is served as core coolant and spallation material to carry away heat deposition of spallation reaction and produce high flux neutron. So it is very important to study the heat transfer process in the target. In this paper, the steady-state flow pattern has been numerically obtained and taken as the input for the nuclear physics calculation, and then the distribution of the extreme large power density of the heat load is imported back to the computational fluid dynamics as the source term in the energy equation. Through the coupling, the transient and steady-state temperature distribution in the windowless spallation target is obtained and analyzed based on the flow process and heat transfer. Comparison of the temperature distribution with the different beam intensity shows that its shape is the same as broken wing of the butterfly. Nevertheless, the maximum temperature as well as the temperature gradient is different. The results play an important role and can be applied to the further design and optimization of the ADS windowless spallation target.

Flow patterns and deformation modes of coaxial liquid columns in transverse electric fields

Steady-state flow patterns and deformation modes of coaxial liquid columns in transverse electric fields are studied analytically. The governing creeping flow equations are solved for Newtonian and (mutually) immiscible fluids in the framework of leaky dielectric theory. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the columns, in terms of the direction of the external flow (top-to-sides/bottom-to-sides vs. sides-to-top/sides-to-bottom) and the number of vortices (single vortex vs. double vortices) in the shell, and that the senses of the net electric shear stresses at the inner and the outer interfaces and their relative importance are the key parameters in setting these patterns. Equilibrium shapes of the interfaces are also found and it is shown that there are four distinct modes of deformation, depending on the governing nondimensional parameters of the problem. The instability of the jet is also examined qualitatively using the observations pertaining the instability of single-phase drops and jets and the scaling arguments based on the present solution.

Coefficients of Local Head Losses in Steady-State Flow of Throttled Surge Tanks with Standpipe by CFD

This study investigates the steady-state flow pattern of throttled surge tanks with standpipe, especially the coefficients of local head losses. The experiments were carried out, and FLUENT, which solves the Reynolds-averaged Navier-Stokes equations, was applied to experimental data for solving flow fields. The results show the computed and measured local head losses agree closely. The coefficients of the local head losses are linearly proportional to diameter ratio with the slope of 0.037. The anticlockwise backflow region occurs in the standpipe, and it induces inflow into and outflow from the standpipe. For hydraulic engineering projects, the discharge into and out from standpipe does not change with velocity and diameter of main conduit, but are linearly proportional to diameter ratio with the slope of 0.0378.

The steady-state flow pattern past gravitating bodies

Gravitating bodies significantly alter the flow pattern (density and velocity) of the gas that attempts to stream past. Still, small protoplanets in the Mars--super-Earth range can only bind limited amounts of nebular gas; until the so-called critical core mass has been reached (~1-10 Earth masses) this gas is in near hydrostatic equilibrium with the nebula. Here we aim for a general description of the flow pattern surrounding these low-mass, embedded planets. Using various simplifying assumptions (subsonic, 2D, inviscid flow, etc), we reduce the problem to a partial differential equation that we solve numerically as well as approximate analytically. It is found that the boundary between the atmosphere and the nebula gas strongly depends on the value of the disc headwind (deviation from Keplerian rotation). With increasing headwind the atmosphere decreases in size and also becomes more asymmetrical. Using the derived flow pattern for the gas, trajectories of small solid particles, which experience both gas drag and gravitational forces, are integrated numerically. Accretion rates for small particles (dust) are found to be low, as they closely follow the streamlines, which curl away from the planet. However, pebble-size particles achieve large accretion rates, in agreement with previous numerical and analytical works.

Experimental and numerical studies on periodic convection flow and heat transfer in a lid-driven arc-shape cavity

This paper presents experimental and numerical studies on periodic convection flow and heat transfer in a lid-driven arc-shape cavity with temperature differential. Three cases were considered: Gr=2×105, 5×105 and 1.2×106 at Re=100 (Gr = Grashof number; Re = Reynolds number). The mathematical model was proposed in our previous study. The current study performs an experiment to validate this model, to corroborate the existence of the periodic flow, and to more deeply probe the internal flow and temperature characteristics. The experimental setup primarily comprised an arc-shape cavity, a moving lid, a thermo-system, a smoke generator and an image acquisition system. The periodic convection flow in the cavity was visualized using kerosene smoke. The numerical and experimental results consistently reveal that the periodic flow pattern was observed in the case with Gr=5×105, whereas the steady-state flow pattern took place in the other two cases (Gr=2×105 and Gr=1.2×106). The numerical simulation produced reasonable and satisfactory agreement with the experiment for the periodic flow pattern and period. The difference between the predicted and measured periods is less than 5%. The transport properties, such as average kinetic energy, overall Nusselt number, stream function, phase space trajectory, local kinetic energy, velocity history and temperature distribution, were further analyzed and discussed in this paper. The proposed numerical simulation not only confirms the experimental observation, but also enhances the understanding of periodic convection in an arc-shape cavity subjected to a moving lid and temperature differential.