Average Flow Direction Research Articles

Natural convective turbulent heat flow visualization around a vertical plate using low Reynolds number k-ϵ model

The authors of this present paper used the low Reynolds number (LRN) k-ϵ model to introduce the notion of turbulent heat function for visualization of average heat flow direction in a natural convective flow in the vicinity of the vertical plate. The explored problem is two-dimensional and incompressible. Governing equations such as continuity, momentum, energy, turbulent kinetic energy (TKE), dissipation rate of TKE, and also turbulent heat and stream functions are generated based on geometry and turbulent flow assumptions. Owing to the lack of analytical methods for solving the highly nonlinear set of partial differential equations, the Crank–Nicolson scheme (CNS) of finite difference approach is employed to find a numerical approximation of the governing turbulent equations. Further, this approach is unconditionally stable, and it helps in the discretization of governing equations, which are kept in the tridiagonal system of algebraic equations and solved using the Thomas algorithm. The obtained numerical results ensure convergence since the stability and compatibility holds good in CNS. The simulated results are examined using tables and graphs to determine how laminar flow differs from that of turbulent flow in terms of velocity, temperature, heat lines, and streamlines with the help of turbulent Prandtl () and Reynolds () numbers. Also, the authors demonstrated the behavior of average momentum and heat transfer rates of laminar and turbulent flows. Additionally, average velocity, kinetic energy, and dissipation rate contours are plotted and discussed including turbulent isotherms, heat lines, and streamlines. It has been noted that the average momentum rate decreased and the heat transfer rate increased with increasing in laminar flow. However, these rates decreased with increasing values in the turbulent flow. Furthermore, streamlines are denser in laminar and turbulent flow conditions at the top and the leading edge of the plate, respectively. Finally, as a particular instance, the outcomes obtained using the LRN k-ϵ model for turbulent flows are compared to the usual laminar flow and noted to be in excellent agreement.

Effects of the Yaw Angle on Air Drag Reduction for Various Riblet Surfaces.

Biomimetic riblet surfaces, such as blade, wavy, sinusoidal, and herringbone riblet surfaces, have widespread applications for drag reduction in the energy, transportation, and biomedicine industries. The drag reduction ability of a blade riblet surface is sensitive to the yaw angle, which is the angle between the design direction of the riblet surface and the average flow direction. In practical applications, the average flow direction is often misaligned with the design direction of riblet surfaces with different morphologies and arrangements. However, previous studies have not reported on the drag reduction characteristics and regularities related to the yaw angle for surfaces with complex riblet microstructures. For the first time, we systematically investigated the aerodynamic drag reduction characteristics of blade, wavy, sinusoidal, and herringbone riblet surfaces affected by different yaw angles. A precisely adjustable yaw angle measurement method was proposed based on a closed air channel. Our results revealed the aerodynamic behavior regularities of various riblet surfaces as affected by yaw angles and Reynolds numbers. Riblet surfaces with optimal air drag reduction were obtained in yaw angles ranging from 0 to 60° and Reynolds numbers ranging from 4000 to 7000. To evaluate the effects of the yaw angle, we proposed a criterion based on the actual spanwise spacing (d+) of microstructure surfaces with the same phase in a near-wall airflow field. Finally, we established conceptual models of aerodynamic behaviors for different riblet surfaces in response to changes in the airflow direction. Our research lays a foundation for practical various riblet surface applications influenced by yaw angles to reduce air drag.

Scale-dependent anisotropy of electric field fluctuations in solar wind turbulence

ABSTRACT We study the variation of average powers and spectral indices of electric field fluctuations with respect to the angle between average flow direction and the mean magnetic field in solar wind turbulence. Cluster spacecraft data from the years 2002 and 2007 are used for the present analysis. We perform a scale-dependent study with respect to the local mean magnetic field using wavelet analysis technique. Prominent anisotropies are found for both the spectral index and power levels of the electric power spectra. Similar to the magnetic field fluctuations, the parallel (or antiparallel) electric fluctuation spectrum is found to be steeper than the perpendicular spectrum. However, the parallel (or antiparallel) electric power is found to be greater than the perpendicular one. Below 0.1 Hz, the slope of the parallel electric power spectra deviates substantially from that of the total magnetic power spectra, supporting the existence of Alfvénic turbulence.

Effects of geological structures on rainfall‐runoff responses in headwater catchments in a sedimentary rock mountain

AbstractClarifying rainfall‐runoff responses in mountainous areas is essential for disaster prediction as well as water resource management. Although runoff is considered to be significantly affected by topography, some previous studies have reported that geological structures also have significant effects on rainfall‐runoff characteristics. Particularly in headwater catchments located in sedimentary rock mountains, dips and strikes may significantly affect rainwater discharge. In this study, the effects of geological structures on rainfall‐runoff characteristics were investigated based on observed discharge hydrographs from 12 catchments, which lie radially from the summit of a sedimentary rock mountain. The results obtained were as follows: (1) Even though the topographic wetness index (TWI) distributions of the 12 catchments were similar, there were significant differences in their runoff characteristics; (2) Catchments with average flow direction oriented towards the strike direction (strike‐oriented catchments) are characterized by large baseflows; (3) Catchments with average flow direction oriented towards the opposite dip direction (opposite dip‐oriented catchments) are steep, and this results in quick storm runoff generation; (4) Catchments with average flow direction oriented toward the dip direction (dip‐oriented catchments) are gentle, and this results in delayed storm runoff generation. It was presumed that in strike‐oriented catchments, large quantities of groundwater flowing along the bedding planes owing to hydraulic anisotropy, exfiltrate and sustain the large amount of the observed baseflow, that is, in strike‐oriented catchments, runoff is directly controlled by geological structures. Conversely, in opposite dip‐oriented and dip‐oriented catchments, runoff is indirectly controlled by geological structures, that is, geological structures affect slope gradients, which result in differences in storm runoff generation. Thus, this study clearly illustrates that geological structures significantly affect rainfall‐runoff responses in headwater catchments located in sedimentary rock mountains.

Enhanced Forest Microexpression Recognition Based on Optical Flow Direction Histogram and Deep Multiview Network

In order to recognize the instantaneous changes of facial microexpressions in natural environment, a method based on optical flow direction histogram and depth multiview network to enhance forest microexpression recognition was proposed. In the preprocessing stage, the histogram equalization of the acquired face image is performed, and then the dense key points of the face are detected. According to the coordinates of the key points and the face action coding system (FACS), the face region is divided into 15 regions of interest (ROI). In the feature extraction stage, the optical flow direction histogram feature between adjacent frames in ROI is extracted to detect the peak frame of microexpression sequence. Finally, the average optical flow direction histogram feature of the image sequence from the initial frame to the peak frame is extracted. In the classification stage, firstly, the head pose parameters under horizontal degrees of freedom are estimated to eliminate the influence of head pose motion, and a forest multiview conditional probability model based on deep multiview network is established. Conditional probability and neural connection function are introduced into the node splitting learning of random tree to improve the learning ability and distinguishing ability of the model on the limited training set. Finally, multiview-weighted voting is used to determine the categories of facial microexpressions. Experiments on CASME II microexpression dataset show that the proposed method can effectively describe the changes of microexpressions and improve the recognition accuracy compared with other new methods.

Flow-Area Relations in Immiscible Two-Phase Flow in Porous Media

We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two- and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.

Influence of ambient conditions on wind speed measurement: Impact on the annual energy production assessment

The Annual Energy Production (AEP) estimations are crucial to analyze the potential of wind energy projects. To calculate the AEP of a wind farm, it is necessary to accurately measure the wind speed, because small errors in these measures lead to significant deviations in the wind turbine power curve. In-field wind speed is usually measured by means of cup anemometers, which are calibrated within wind tunnels. In-field ambient conditions differ from those at the laboratory, which increases the uncertainty of the wind speed measures performed at the location of the turbine. The present work is focused on analyzing the effect of the following ambient parameters on the cup anemometer behavior: temperature, humidity and atmospheric pressure. In order to reach this target, experimental tests in a wind tunnel were performed, which allows minimizing the effect of the rest of influence parameters: turbulence, average flow inclination angle and flow direction. With this work it is determined how flow air viscous forces affect the cup anemometers, changing its rotation frequency. This explanation concludes that a variation on air temperature, humidity and/or pressure modifies moist air kinematic viscosity, which leads to change the friction between air and cups and, consequently, the cup anemometers rotational frequency. In most cases, the kinematic viscosity is inversely proportional to the air density and therefore, higher in-field densities, compared to those at the laboratory where the anemometer was calibrated, lead to underestimate the wind speed, and vice versa. The fact that this effect has been quantified during the calibration process is quite important, since it allows removing the influence of the environmental parameters studied; so that by modifying the calibration methodology, the accuracy of cup anemometers would be optimized. In order to clarify how the moist air kinematic viscosity influences the calibration curve, the calibration measurements of a real cup anemometer are mapped into a new dimensionless abacus, with the Tip Speed Ratio (TSR) and the Reynold’s number as coordinates. The key idea is that the rotation frequency of the cup anemometer is related to both wind speed and moist air kinematic viscosity. This relation is mathematically described by the equation of a hyperbolic paraboloid surface up to a value of wind speed of 15.3 m/s.

Comparison of Gaussian Plume Model and Lagrangian Particle Model for the Application of Coastal Air Quality Modelling

Incheon is one of the biggest cities located in coastal region where small to big size industries, Incheon sea port, Incheon airport, etc are in operation. The air pollution dispersion from those sources has been major concerns for Incheon coastal area where air emission, dispersion and deposition have been studied using different approaches of monitoring and modeling. Essential meteorological data were acquired by field monitoring and from the published data. GTOPO30 (global digital elevation model with a horizontal grid spacing of 30”) was used as terrain data for AERMOD and USGS 30” resolution terrain data was used in A2C flow/A2C t&d model. Steady state Gaussian plume dispersion based model, i.e. AERMOD, and Lagrangian puff dispersion based model, i.e. A2Cflow/A2Ct&d models, were accomplished by introducing the local meteorological and geographical information to test the performance of models around the unsteady air flow area. AERMOD simulation results showed that the pollutants from the source are transported and dispersed around the sources similar to the average wind flow direction. There was no significant difference in pollutants dispersion regardless of land breeze or sea breeze conditions. On the other hand, the results from Lagrangian puff model showed that the puffs transport, and dispersed around the coast area followed the sea/land breeze pattern. The comparative analysis of pollutants deposition estimated by steady state Gaussian plume model and Lagrangian puff model showed that the Gaussian plume model underestimate the pollution dispersion quantity at the onshore site during day time and overestimate during late night to early morning. Hence the Lagrangian based model is recommended for estimating pollutants dispersion and deposition around the unsteady air flow region.

Water flow across the interface of contrasting materials: Pressure discontinuity and its implications

Water flow along or across the interfaces of contrasting materials is ubiquitous in hydrology and how to solve them in macroscopic models derived from volumetric average of the pore-scale processes remains elusive. While the change in the average velocity and pressure at water-sediment interface has been well established for channel flow over porous beds, whether a volumetric average alerts the pressure continuity when water flows across the interface of two porous materials is poorly understood despite its imperative implications in hydrological modelling. The primary purpose of this paper is to provide evidences via pore-scale simulations that volumetrically averaging the pore-scale processes indeed yields a discontinuous pressure when water flows across a material interface. We simulated two columns numerically reconstructed by filling them with stratified media: One is an idealised two-layer system and the other one is a 3D column filled by fine glass beads over coarse glass beads with their pore geometry acquired using x-ray computed tomography. The pore-scale simulation is to mimic the column experiment by driving fluid to flow through the void space under an externally imposed pressure gradient. Once fluid flow reaches steady state, its velocity and pressure in all voxels are sampled and they are then spatially averaged over each section perpendicular to the average flow direction. The results show that the average pressure drops abruptly at the material interface no matter which direction the fluid flows. Compared with the effective permeability estimated from the homogenization methods well established in the literature, the emerged discontinuous pressure at the interface reduces the combined ability of the two strata to conduct water. It is also found that under certain circumstances fluid flow is direction-dependant, moving faster when flowing in the fine-coarse direction than in the coarse-to-fine direction under the same pressure gradient. Although significant efforts are needed to incorporate these findings into practical models, we do elicit the emergence of discontinuous pressure at material interface due to volumetric average as well as its consequent implications in modelling of flow in heterogeneous and stratified media.

Designing a Shock Control Bump Array for a Transonic Wing–Body Model

Research on three-dimensional shock control bumps has paid little attention to design methods for arrays on aircraft. This paper takes a first step, examining whether design rules for maximizing the on-design performance of swept infinite-wing bumps can be successfully used to build a finite array. A computational study using infinite-wing and aircraft models creates a design method tailoring bump location, ramp angle, and rotation to local flow conditions on the aircraft wing. Rules for rotation and ramp angle produce comparable performance trends on both models. The former correctly predicts the best rotation as a few degrees from the average local flow direction, whereas the optimal ramp angles were 0.625 times that of the initial distribution because the beneficial influence on lift of shorter arrays was stronger than that provided by infinite-wing shock control bumps. This final array performance was in good agreement with a ballpark prediction for its impact on local wave drag. However, the total aircraft drag change was larger than the local impact, due to an influence away from the immediate vicinity of the array, and the impact on lift. Consequently, when choosing preferred array designs, it is essential to consider the impact on the entire aircraft model at fixed-lift conditions.

Permeability prediction of an analytical pore-scale model for layered and isotropic fibrous porous media

In this study an existing analytical pore-scale model for flow parallel and perpendicular to 1D unidirectional fibres are used and adapted to propose permeability predictions for in-plane and through plane flow in layered 2D fibre arrangements as well as flow through 3D isotropic fibrous porous media. This is done by application of a weighted average equation in which different weights are assigned to flow parallel and perpendicular to 1D fibre arrangements, depending on the fibre orientation and average flow direction. Different arrays are considered, based on the degree of staggering of fibres with respect to the average flow direction. The effect of fibre orientation on permeability is investigated for flow through layered 2D fibre arrangements. It is illustrated how the permeability at low solid volume fractions reduces through the incorporation of the effect of developing flow. The effect of blocked pores at high solid volume fractions is also accounted for by introducing a percolation threshold solid volume fraction beyond which no more seepage takes place. A unimodal equivalent radius is furthermore introduced into the models in order to predict the permeability of bimodal fibrous media. The proposed permeability predictions are applicable over the entire range of solid volume fractions. Comparison with theoretical models from the literature as well as available experimental and numerical data proves satisfactory. The model characteristics that distinguish the proposed models from many other models in the literature are (i) being physically adaptable to extend its range of applicability, whilst at the same time (ii) balancing accuracy and simplicity (from an analytical point of view), and (iii) containing no empirical coefficients.

Numerical Simulation of Heat and Fluid Flow in Ammonothermal GaN Bulk Crystal Growth Process

A numerical simulation of an ammonothermal process for growing GaN bulk single crystals has been performed. The autoclave and growing crystal are assumed to be axisymmetric and the raw material is assumed to be a porous medium. Heat transfer by natural convection is discussed in terms of the open-space ratio of the baffle and the height of the crystals. Simulation results show that a larger open-space ratio, at least 30%, is better for the crystal growth from the viewpoints of average surface temperature and flow direction.

Geometry dependence of the clogging transition in tilted hoppers

We report the effects of system geometry on the clogging of granular material flowing out of flat-bottomed hoppers with variable aperture size D and with variable angle θ of tilt of the hopper away from horizontal. In general, larger tilt angles make the system more susceptible to clogging. To quantify this effect for a given θ, we measure the distribution of mass discharged between clogging events as a function of aperture size and extrapolate to the critical size at which the average mass diverges. By repeating for different angles, we map out a clogging phase diagram as a function of D and θ that demarcates the regimes of free flow (large D, small θ) and clogging (small D, large θ). We do this for both circular holes and long rectangular slits. Additionally, we measure four types of grain: smooth spheres (glass beads), compact angular grains (beach sand), disklike grains (lentils), and rodlike grains (rice). For circular apertures, the clogging phase diagram is found to be the same for all grain types. For narrow slit apertures and compact grains, the shape is also the same as for circular holes when expressed in terms of projected area of the aperture against the average flow direction. For lentils and rice discharged from slits, the behavior differs and may be due to alignment between grain and slit axes.

Model-Based Correction of Velocity Measurements in Navigated 3-D Ultrasound Imaging During Neurosurgical Interventions

In neurosurgery, information of blood flow is important to identify and avoid damage to important vessels. Three-dimensional intraoperative ultrasound color-Doppler imaging has proven useful in this respect. However, due to Doppler angle-dependencies and the complexity of the vascular architecture, clinical valuable 3-D information of flow direction and velocity is currently not available. In this work, we aim to correct for angle-dependencies in 3-D flow images based on a geometric model of the neurovascular tree generated on-the-fly from free-hand 2-D imaging and an accurate position sensor system. The 3-D vessel model acts as a priori information of vessel orientation used to angle-correct the Doppler measurements, as well as provide an estimate of the average flow direction. Based on the flow direction we were also able to do aliasing correction to approximately double the measurable velocity range. In vitro experiments revealed a high accuracy and robustness for estimating the mean direction of flow. Accurate angle-correction of axial velocities were possible given a sufficient beam-to-flow angle for at least parts of a vessel segment . In vitro experiments showed an absolute relative bias of 9.5% for a challenging low-flow scenario. The method also showed promising results in vivo, improving the depiction of flow in the distal branches of intracranial aneurysms and the feeding arteries of an arteriovenous malformation. Careful inspection by an experienced surgeon confirmed the correct flow direction for all in vivo examples.

Hot and cold ion outflow: Spatial distribution of ion heating

Ions apparently emanating from the same source, the ionospheric polar cap, can either end up as energized to keV energies in the high‐altitude cusp/mantle, or appear as cold ions in the magnetotail lobes. We use Cluster observations of ions and wave electric fields to study the spatial variation of ion heating in the cusp/mantle and polar cap. The average flow direction in a simplified cylindrical coordinate system is used to show approximate average ion flight trajectories, and discuss the temperatures, fluxes and wave activity along some typical trajectories. It is found that it is suitable to distinguish between cusp, central and nightside polar cap ion outflow trajectories, though O+ heating is mainly a function of altitude. Furthermore we use typical cold ion parallel velocities and the observed average perpendicular drift to obtain average cold ion flight trajectories. The data show that the cusp is the main source of oxygen ion outflow, whereas a polar cap source would be consistent with our average outflow paths for cold ions observed in the lobes. A majority of the cusp O+ flux is sufficiently accelerated to escape into interplanetary space. A scenario with significant oxygen ion heating in regions with strong magnetosheath origin ion fluxes, cold proton plasma dominating at altitudes below about 8 RE in the polar cap, and most of the cusp oxygen outflow overcoming gravity and flowing out in the cusp and mantle is consistent with our observations.

Permeability mapping in naturally heterogeneous sandstone cores by magnetization prepared centric-scan sprite

A time-efficient MRI method suitable for quantitative two-dimensional (2-D) mapping of permeability in sedimentary rock cores, and granular media samples is discussed. The images of porosity and mean axial velocity in the plane transverse to the average flow direction are essential to determine 2-D distribution of permeability in a core sample. The 2-D permeability mapping is particularly useful for discrimination of bedding and lamination layers, fractures and fault facies that occur in sedimentary rocks. The proposed method combines the 13-interval APGSTE scheme and centric-scan SPRITE. The APGSTE scheme is known to substantially reduce gradient-related errors in diffusion measurements. The SPRITE method provides quantitative information on fluid content within the core samples. The experiment time is critically reduced when only a few samples near the q-space origin are collected. The APGSTE-SPRITE method is illustrated through mapping of 2-D permeability and 3-D velocity field in naturally heterogeneous sandstone cores. © 2012 American Institute of Chemical Engineers AIChE J, 2012

Wind-Direction Effects on Urban-Type Flows

Practically all extant work on flows over obstacle arrays, whether laboratory experiments or numerical modelling, is for cases where the oncoming wind is normal to salient faces of the obstacles. In the field, however, this is rarely the case. Here, simulations of flows at various directions over arrays of cubes representing typical urban canopy regions are presented and discussed. The computations are of both direct numerical simulation and large-eddy simulation type. Attention is concentrated on the differences in the mean flow within the canopy region arising from the different wind directions and the consequent effects on global properties such as the total surface drag, which can change very significantly—by up to a factor of three in some circumstances. It is shown that for a given Reynolds number the typical viscous forces are generally a rather larger fraction of the pressure forces (principally the drag) for non-normal than for normal wind directions and that, dependent on the surface morphology, the average flow direction deep within the canopy can be largely independent of the oncoming wind direction. Even for regular arrays of regular obstacles, a wind direction not normal to the obstacle faces can in general generate a lateral lift force (in the direction normal to the oncoming flow). The results demonstrate this and it is shown how computations in a finite domain with the oncoming flow generated by an appropriate forcing term (e.g. a pressure gradient) then lead inevitably to an oncoming wind direction aloft that is not aligned with the forcing term vector.

Transient Heterogeneity in an Aquifer Undergoing Bioremediation of Hydrocarbons

Localized, transient heterogeneity was studied in a sand aquifer undergoing benzene, toluene, ethylbenzene, and xylene bioremediation using a novel array of multilevel, in situ point velocity probes (PVPs). The experiment was conducted within a sheet-pile alleyway to maintain a constant average flow direction through time. The PVPs measured changes in groundwater velocity direction and magnitude at the centimeter scale, making them ideal to monitor small-scale changes in hydraulic conductivity (K). Velocities were shown to vary nonuniformly by up to a factor of 3 when a source of oxygen was established down-gradient of the petroleum spill. In spite of these local variations, the average groundwater velocity within the 7 m × 20 m sheet-piled test area only varied within ± 25%. The nonuniform nature of the velocity variations across the gate indicated that the changes were not due solely to seasonal hydraulic gradient fluctuations. At the conclusion of the experiment, microbial biomass levels in the aquifer sediments was approximately 1 order of magnitude higher in the oxygen-amended portion of the aquifer than at the edge of the plume or in locations up-gradient of the source. These data suggest that the transient velocities resulted, at least in part, from enhanced biological activity that caused transient heterogeneities in the porous medium.

Transition in the propagation mechanism during flame acceleration in porous media

The combustion of stoichiometric hydrogen-air at various initial pressures was investigated in a 7.62 cm square cross-section channel filled with 1.27 cm diameter beads. The flame time-of-arrival and pressure time history along the channel were obtained by ionization probes and piezoelectric pressure transducers. Flame acceleration was found to be very rapid, e.g. at an initial pressure of 45 kPa the flame achieves a velocity of over 600 m/s in roughly 0.3 m. It was determined that at this high speed a well defined planar shock wave precedes a thick reaction zone. It was also shown that there is a transition in the flame propagation mechanism, similar to that observed in an obstacle laden channel [G. Ciccarelli and C. Johansen, The role of shock-flame interactions on flame acceleration in an obstacle laden channel, Proc. 22nd International Colloquium on the Dynamics of Explosions and Reactive Systems, Minsk, 2009]. By varying the initial pressure of the mixture, changes in the axial location of the transition between combustion propagation regimes was also observed. A soot foil technique was used to identify the transition in the propagation mechanism, as well as to provide information concerning the local flow field around the beads and the overall average flow direction.

Permeability mapping in porous media by magnetization prepared centric-scan SPRITE

The ability of porous media to transmit fluids is commonly referred to as permeability. The concept of permeability is central for hydrocarbon recovery from petroleum reservoirs and for studies of groundwater flow in aquifers. Spatially resolved measurements of permeability are of great significance for fluid dynamics studies. A convenient concept of local Darcy’s law is suggested for parallel flow systems. The product of porosity and mean velocity images in the plane across the average flow direction is directly proportional to permeability. Single Point Ramped Imaging with T 1 Enhancement (SPRITE) permits reliable quantification of local fluid content and flow in porous media. It is particularly advantageous for reservoir rocks characterized by fast magnetic relaxation of a saturating fluid. Velocity encoding using the Cotts pulsed field gradient scheme improves the accuracy of measured flow parameters. The method is illustrated through measurements of 2D permeability maps in a capillary bundle, glass bead packs and composite sandstone samples.