Flow Separation Angle Research Articles

Numerical study of energy consumption in spacer-filled feed channels through 3D inverse modeling and computational fluid dynamics

This project employs advanced Computational Fluid Dynamics (CFD) simulations to investigate the complex flow field dynamics within the channel of membrane module featuring a commercially available feed spacer. Utilizing Micro-CT scanning, the intricate three-dimensional (3D) structure of the spacer is accurately captured, enhancing the precision of the simulation models. The project focuses on the effects of varying Reynolds number (Re) and Aspect Ratio (AR) on the energy consumption within the feed channel of membrane module, analyzing streamline patterns, vorticity, and flow separation angles in detail. Findings indicate that the total enstrophy identification method effectively pinpoints areas of high energy consumption, especially at lower Re levels where flow separation significantly contributes to hydraulic losses. As Re increases, the separation vortex shifts rearward, resulting in a marked decrease in the energy consumption coefficient. Furthermore, the flow separation angle consistently declines with increasing Re, stabilizing at higher levels. Significantly, a reduction in AR from 1.015 to 0.725 more than doubles the decrease in flow separation angle, highlighting substantial potential energy savings through spacer design optimization. These insights are crucial for improving the design and efficiency of spiral wound membrane modules and for refining feed spacer configurations to enhance performance.

A multi-region analysis of unsteady Oseen's equation for accelerating flow past a circular cylinder

It is difficult to find a valid high-order (of Reynolds number) analytical approximation to the uniform viscous flow past an infinite circular cylinder by applying perturbation techniques. In this study, we show that by accelerating flow past a circular cylinder with taking unsteady Stokes' solution as an initial approximation, higher-order approximation solutions to unsteady Oseen's equation can be obtained by an iteration scheme of perturbation, which exactly satisfy the boundary conditions. As a matter of fact, the nonlinear (convective) term linearized by Oseen's approximation is overweighted especially near the body surface. To eliminate the overweight, a multi-region analysis is proposed in this study to improve analytical unsteady Oseen's solution so as to extend the valid range of Reynolds numbers. In other words, the flow region is hypothetically divided into several annular regions, and the linearized convective term in each region is modified by multiplying with a Carrier's coefficient c (0 < c ≤ 1). The results show that, when the accelerating parameter in the range of 0.5 ≤ a ≤ 4, the maximum effective Reynolds number Reeff of the fourth-order five-region solution is both much larger than that of Stokes' and Oseen's ones. For example, when a = 0.5, Reeff = 22.26 is roughly eight times that of Stokes' solution (Reeff = 2.67), and nine times that of Oseen's solution (Reeff = 2.41). Moreover, when the instantaneous Reynolds number Re(t) is smaller than the Reeff, the flow separation angle and the wake length are both consistent with the numerical results obtained by accurately solving the full Navier-Stokes equations. In addition, the flow properties, including the drag coefficients, streamline patterns, and the pressure coefficients, as well as the vorticity distributions also agree well with the numerical results. This study represents a significant extension of our previous study for unsteady Stokes' equation [Xu et al., Phys. Fluids 35, 033608 (2023)] to unsteady Oseen's equation and its generalization.

Semiempirical Model of the Drag Force Acting on an Obstacle in Downward Dense Particle Flows as per the Flow-Around Behavior

Determination of the flow-around drag force acting on an internal when particles downwardly flow around the internal is important for the safety of internals in the downward particle flow channel. In this study, the flow behaviors of particles downwardly flowing around different obstacles were investigated and a semiempirical drag force model was proposed based on the characteristics of the flow patterns. The proposed model was validated and key coefficients were correlated using the experimental data. The results indicate that there were three featured flow zones when particles downwardly flowed around an obstacle: the flow stagnant zone (disappear for triangular/conical obstacle), the slip-shear flow zone, and the flow separation zone. The stagnant zone angle and the flow separation angle were proposed to depict transition points of three flow zones when particles flowed around a cylindrical/spherical obstacle, and the two angles were found independent of the flow condition. A drag force model as per the flow patterns was proposed. The model decomposed the drag force into the compression force, the shear force, and the confinement force. The expressions of the compression stress, the shear stress, the effective area, and the confinement force were given. The mathematical form of the proposed model was validated and key coefficients in this model were also correlated using the experimental data. The average error of the drag force model was ±7.6% while the maximum error was within ±15%.

Steady flow of power-law fluids past a slotted circular cylinder at low Reynolds number

Steady laminar flow past a slotted circular cylinder was investigated for non-Newtonian power-law fluids at the low Reynolds number (Re) range (5 ⩽ Re ⩽ 40). Flow simulation was carried out for shear-thinning fluids with their power-law indices (n) varying from 0.2 to 1 (n = 0.2, 0.4, 0.6, 0.8, and 1). The normal (case A) and the slotted (case B) circular cylindrical geometries were considered, where the slit was placed between the front and the base pressure stagnation points. A finite volume method was used to calculate the flow field. The flow characteristics, such as flow separation angles, wake size, coefficients of pressure (Cp), and drag (CD), were studied for different Re and n values. For all n values, the slotted cylinder effectively delayed the flow separation. It showed much better pressure recovery than the normal cylinder due to the interaction between the self-bleed from the slit exit to the cylinder wake. The vorticity of this bleed influenced the wake's vorticity, and an increase of 3%–26.4% in higher maximum surface vorticity was reported for the slotted cylinder. An increase of 0.7%–6.5% in the bubble length was observed for the normal cylinder due to early flow separation. An enhanced pressure recovery across the slotted cylinder resulted in a significant drop in the pressure drag with 0.2%–4.56% reduction in the overall drag coefficient.

Effect of wall slip on laminar flow past a circular cylinder

A numerical study of two-dimensional flow past a confined circular cylinder with slip wall is performed. A dimensionless number, Knudsen number ($Kn$) is used to describe the slip length of cylinder wall. The Reynolds number ($Re$) and Knudsen number ($Kn$) ranges considered are $Re = [1, 180]$ and $Kn = [0, \infty)$, respectively. Time-averaged flow separation angle ($\bar{\theta_s}$), dimensionless recirculation length ($\bar{L_s}$) and the tangential velocity ($\bar{u_{\tau}}$) distributed on the cylinder's wall, drag coefficient ($\bar{C_d}$) and drag reduction ($DR$) are investigated. The time-averaged tangential velocity distribution on the cylinder's wall fit well with the formula $\bar{u_{\tau}} = [\frac{\alpha}{1+{\beta}e^{-{\gamma}({\pi}-{\theta})}}+{\delta}]sin(\theta) $, where the coefficients ($\alpha$, $\beta$, $\gamma$, $\delta$) are related with $Re$ and $Kn$. Several scaling-laws are found, $log(\bar{u_{{\tau}max}})\sim{log(Re)}$ and $\bar{u_{{\tau}max}}\sim{Kn}$ for low $Kn$, ($\bar{u_{{\tau}max}}$ is the maximum tangential velocity on the cylinder's wall), $log(DR)\sim{log(Re)}$ ($Re\leq45$ and $Kn\leq0.1$), $log(DR)\sim{log(Kn)}$ ($Kn\leq0.05$). At low $Re$, $DR_v$ (the friction drag reduction) is the main source of $DR$. However, $DR_p$ (the differential pressure drag reduction) contributes the most to $DR$ at high $Re$ ($Re>\sim60$) and $Kn$ over a critical number. $DR_v$ is found almost independent to $Re$.

Steady flow past elliptic cylinders with blockage effects

In the present work, steady two-dimensional flow past elliptic cylinders with different aspect ratios (Ar) have been investigated for Reynolds number (Re) up to 200. Main characteristics such as the bubble length, bubble width, separation Reynolds number, separation angle, drag coefficient, coefficients of the front and rear stagnation pressure, and the maximum vorticity on the cylinder surface have been obtained. Least squares fit equations for some of these quantities have also been presented. In the special case of a circular cylinder, results computed with the largest domain show that the bubble length, bubble width, maximum vorticity on the cylinder surface, coefficient of pressure drag, coefficient of total drag, and flow separation angle are linear functions of Re, Re0.5, Re0.35, Re−0.4, Re−0.5, and Re−0.1, respectively. As Ar changes, the trends in the growth, with respect to Ren (with the corresponding index), for the bubble length, bubble width, and the maximum surface vorticity deviate from their linear nature. The effect of blockage on the steady flow characteristics has been studied by changing the location of the side boundaries. In certain cases, the flow properties are found to vary in a non-monotonic fashion with the change in the blockage. An explanation based on the dual role of the side boundaries in promoting and suppressing the growth of the corresponding flow property is offered.

Vortex shedding, flow separation, and drag coefficient in the flow past an ellipsoid of different aspect ratios at moderate Reynolds number

Incompressible viscous flow past an ellipsoid of different aspect ratios (ARs, the ratio of the vertical to the horizontal axis of the ellipsoid, is ranged from 0.5 to 2) at a Reynolds number of 300 is investigated numerically by a finite volume method with adaptive mesh refinement, and the effects of different aspect ratios on vortex shedding, flow separation, and drag coefficient are analyzed in detail. The accuracy of the present results is ascertained by comparing the present drag coefficient and Strouhal number with other literature studies. The results show that the Strouhal frequency of vortex shedding decreases and the magnitude of vortex shedding becomes weaker with an increase in the aspect ratio. In particular, a secondary frequency will occur within a certain interval of 0.8 ≤ AR ≤ 1.2. The vortex shedding appears as a hairpin vortex at AR ∈ [0.5, 1.6], whereas it becomes a double-line vortex at AR ≥ 1.8. Both the upper flow separation angle and the length of the separation bubble increase with an increase in the aspect ratio. The flow separation is symmetrical about the (x, z)-plane only at 0.5 ≤ AR ≤ 0.7 and AR ≥ 1.8. Furthermore, the total drag coefficient and the pressure drag coefficient both increase gradually with an increase in the aspect ratio. Due to the trend of the contact area between the fluid and the surface of the ellipsoid, the friction drag coefficient decreases first (AR ≤ 1) and then increases (AR ≥1). The pressure drag coefficient reinforces the contribution to the total drag coefficient, and the contribution of the pressure drag coefficient grows with an increase in the aspect ratio.

The Symmetry and Stability of the Flow Separation around a Sphere at Low and Moderate Reynolds Numbers

The flow separation state reflects the symmetry and stability of flow around spheres. The three-dimensional structures of flow around a rigid sphere at moderate Reynolds number (Re) between 20 and 400 by using finite volume method with adaptive mesh refinement are presented, and the process of separation angles changing from stable to oscillating state with increasing of Re is analyzed. The results show that the flow is steady, and the separation angles are stable and axisymmetric at Re in less than 200. The flow is unsteady and time-periodic, and the flow separation becomes regular fluctuations and asymmetric at Re = 300, which leads to the nonzero value of lateral force and the phase difference between lift and lateral force. At Re = 400, the flow is unsteady, non-periodic, and asymmetric, as is the flow separation. It’s concluded that the flow separation angle increases when Re increases within a range between 40 and 200. With Re continues to increase, the flow separation state changes from stable to periodically regular until quasi-periodically irregular. The vortex structure changes from no shedding to asymmetric periodic shedding, and finally to asymmetric and intermittently periodic vortex shedding. These results have important implications for the stability of flow around spheres.

A sessile drop facing a shear flow: Surrounding flow dynamics during the deformation of the drop

When oil drops are recovered from surfaces by providing waterflow, the drop initially exhibits deformation. How the waterflow behaves during the deformation is examined experimentally and numerically. The flow observed from both approaches compares well. The drop exhibits deformation as the water shear flow velocity increases. The ranges of a deformation parameter, Di, and the Reynolds number (Re) varies from 0.02 to 0.28 and 1 to 97, respectively, for the oleophobic surface. Di and Re depend on each other. For oleophilic surfaces, Di and Re are found to be between 0.007 to 0.59 and 1 to 319, respectively. It is observed that when a drop continues to deform on an oleophobic surface due to the flow, four eddies are formed in the surrounding-however, the position of the eddies changes as the flow increases. For oleophilic surfaces, the number of eddies varies. The strength of the rear eddies increases, and the frontal eddies decrease with the Re. The reason for the initiation of early deformation on the oleophobic surface is found to be due to a higher pressure variation before and after the drop. A lower flow separation angle and higher strength of the eddies are the reason for the higher pressure difference. The pressure, viscous, and total drag coefficients on both surfaces, are observed to decrease with the flow. The pressure drag dominates over the viscous one for all Re on the oleophobic surface, while the viscous drag dominates at lower Re for drops on the oleophilic surface.

Direct numerical simulation of flow-induced vibrations of a wavy cable at a low Reynolds number

Previous studies have revealed that fluid induced forces and wake structure of a cylinder can be significantly modified by varying the cross-section size along its axis. However, the fluid dynamic characteristics behavior of a flexible cable with a sinusoidal wavy surface remains unclear. The current study endeavors to present a systematic investigation of flow-induced vibrations (FIV) of an infinitely long wavy cable with different wave amplitude (A=0.1D to 0.3D) and a constant spanwise wavelength λ=4π, by using a highly resolved direct numerical simulation employing a high-order spectral/hp element method at a Reynolds number of 100, corresponding to laminar flow state. A tensioned beam model with a tension value can trigger a single wave is selected to govern the dynamics of the wavy cables. In addition, the structural dynamics are initialized from a standing wave. The present study focuses on the effects of the wave amplitude on the cable wake and the structural dynamic response, including the transverse displacement, wake pattern, vortex formation length, energy transfer, vortex shedding frequency and flow separation angle. Two completely different vibration modes are identified from the numerical cases studied, and hence the wavy cable are divided into control failure (A<0.2D) and optimal wavy cable (0.2D⩽A⩽0.3D) classes, respectively. It is also revealed that the counter-rotating vortices observed in the optimal wavy cables play an important role in stabilizing the shear layer and elongating the vortex formation length. Furthermore, the three-dimensional wake patterns of the wavy cable are mainly caused by the variations of flow separation angle along its spanwise direction. For the optimal wavy cables, the separation point is almost fixed along its spanwise direction while is variable for the control failure cases.

Flow simulation around circular cylinder at low Reynolds numbers using vortex particle method

The algorithm of the Viscous Vortex Domain method implemented in the author’s code VM2D is investigated. This code allows simulating 2D viscous incompressible flows and solving fluid-structure interaction problems. The verification of the algorithm, namely, the correctness of taking into account the viscosity effect, is performed on well-studied test problems of the flow simulation around a circular cylinder for Reynolds numbers in the range 20 . 200: the problem of the impulse start of the circular cylinder is considered, and the dependency of the flow separation angle on the Reynolds number is investigated. The comparison shows that for low Reynolds numbers (up to 140), the flow separation angle obtained in numerical simulations by using the VM2D code is in good agreement with the results of other studies. For higher Reynolds numbers, the estimated separation angle is slightly overestimated.

Vortex structures and wake flow analysis from moving manikin models

Vortex shedding in the wake flow generated by moving bodies exerts considerable influence on pollutant dispersion. This study investigated the effects of different body shapes using scaled models 1/5th of realistic size, including thin and wide shapes, standing and walking poses. The airflow from moving bodies was simulated using computational fluid dynamics (CFD) with dynamic meshing to account for the manikin movement. Experimental data from a smoke visualisation technique provided validation data for computational simulations which included flow separation angle over the head computed through image processing. Vortex structures were visualised using an Omega vortex identification method and compared with experimental visualisations. The main objective of this study is to verify the CFD simulations with smoke visualisation in terms of predicting motion-induced vortex structures, thus helping identify contaminant transport around different shaped bodies during walking and when coming to a stop. The results showed matching locations and patterns of vortex structures between the smoke visualisation and CFD simulations. After the manikin came to a stop, the flow induced by the larger body was characterised by a longer residence time for airborne contaminants in the breathing region while a reduced flow residence time for the thinner bodied manikin.

ИССЛЕДОВАНИЕ СКОРОСТИ ДИСПЕРСНЫХ ЧАСТИЦ ПРИ РАЗЛИЧНЫХ УГЛАХ ДЕЛЕНИЯ ДВУХФАЗНОГО ПОТОКА

The aim of this work is to assess the influence of a t-shaped divider (α = 180°) on the speed of movement of spherical particles along the path of a two-nozzle lance in the air stream. Also, comparison with the results of flow separation experiments at smaller angles. The performed studies showed that in the t-shaped divider the reagent particles have a complex trajectory of motion. Part of the particles has an outflow velocity corresponding to other types of divider (7 – 14 m/sec), and the other equilibrium part of the particles is slowed down and has an outflow speed 4 – 5 times lower (1 – 3 m/sec). This is reflected by the bimodal nature of the distribution of the results. In this regard, the transition from single particles to a denser flow (in the case of an increase in the reagent supply intensity) will lead to instability of the injection process, to pulsations and even blocking of the lance. This under conditions of flow into the melt will lead to blockage of the nozzle. This is confirmed by individual attempts to inject granular magnesium through a t-shaped lance in cast iron desulfurization plants. In this case, magnesium was introduced with overestimated flow rates of the transporting gas and an intensity of no more than 5–6 kg/min, which is 5 times less than through a y-shaped two-nozzle lance. In addition, the injection was carried out through one nozzle, since the other in the first seconds of the release of magnesium was clogged. The process proceeded violently and was accompanied by splashes of cast iron from the ladle. It is established that, in comparison with the flow separation angles ( = 30, 60, 90), the t-shaped divider ( = 180) reduces the speed of magnesium and polystyrene particles to a greater extent (by 20 – 50%). In addition, the physical characteristics of the interacting materials, the shape of the particles, the flow rate of the transporting gas, and the length of the nozzle after the divider significantly affect the speed of movement of a solid particle along the path of a two-nozzle lance.

Design optimization and experimental study of coaxial powder-feeding nozzle in the laser cladding process

To improve the powder convergence and cladding layer quality, the three-dimensional axisymmetrical powder flow through a coaxial feeding nozzle was simulated by the Eulerian-Eulerian two-fluid model. With the composite design via the response surface method, the significance between the main geometric dimensions of nozzle and fluidization characteristics of powder flow was analyzed and regression-fitted. Moreover, a mathematical model was constructed to optimize the nozzle structure, and the optimal nozzle was used in laser cladding experiments. The results show that appropriate powder flow can be obtained in the condition of the carrier gas more than 9 l/min, and the powder sending rate less than 7.5 g/min. The structural parameters of the optimized nozzle are as follows: nozzle angle of 62.94°, outlet width of 1.0mm, exit radius of 5.83mm, and flow separation angle of 3.00°. With the optimized nozzle, the waist diameter and focus depth of the original powder flow decreased by 39.4 and 46.4%, respectively, and the discrepancy between the experimental and simulation results was less than 9%. With the appropriate technological parameters, a layer with good geometry morphology and appropriate dilution rate can be prepared in the laser cladding process with a coaxial feeding nozzle.

Jet amplification and cavity formation induced by penetrable fabrics in hydrophilic sphere entry

Studies of solid impact with fluid surfaces have traditionally considered splashing in the context of impactor shape and surface texture. However, it is not always possible to tune impactor properties for desired splash characteristics. In this experimental study, smooth, hydrophilic, free-falling spheres are allowed to impact a quiescent liquid surface for Weber numbers in the range of 400–1580. The liquid surface is modified by the inclusion of a thin fabric upon which a falling sphere strikes and penetrates at water entry. With respect to clean water, inclusion of a single layer of fabric on the surface increases the Worthington jet height across all entry speeds tested. As the sphere penetrates, the fabric is drawn inward, providing a fabric funnel through which a Worthington jet subsequently passes. We show that the presence of fabric increases the drag at entry and enables air-entraining cavities otherwise unattainable by hydrophilic spheres for the impact speeds tested. Such cavity formation is made possible by alteration of the flow separation angle, analogous to greater values of the advancing contact angle.

Kelvin-cell-based metal foam heat exchanger with elliptical struts for low energy consumption

Conventional Kelvin-cell-based metal foam (KMF) has triangular or circular struts. This study proposes a KMF with elliptical struts instead of such struts. Two schemes of transforming a circular strut into an elliptical strut are proposed: (1) maintaining the same circumference as the circular strut cross-section and (2) maintaining the same cross-section area as the circular strut cross-section. Five KMFs with different struts were designed. The fluid flow, heat transfer, and performance characteristics of the KMFs were numerically investigated. Two dimensionless diameters for the strut section are introduced to analyze the hydro-thermal characteristics of KMFs: λa, the major diameter ratio of the elliptical strut to the circular strut, and λb, the minor diameter ratio of the elliptical strut to the circular strut. The major axis of all struts was set parallel to the main flow direction. The pressure drop and heat transfer characteristics of KMFs are explained by the pressure drag and friction drag. As λb decreases from 1.000 to 0.556, the pressure drop of the KMF decreases by 44% because the pressure drag and blockage ratio decrease with λb. However, the decrease of λb results in decreases in the free stream velocity around the strut, which has a penalty on the heat transfer performance. This can be partially compensated by increasing λa by increasing the flow tortuosity, surface area, and separation angle. Therefore, using the scheme with the same cross-sectional area provides better performance than using the scheme with the same circumference. A KMF using the scheme with the same cross-section area scheme required 32% less pumping power than a KMF with circular struts and the same thermal resistance.

A comparative study on effect of plain- and wavy-wall confinement on wake characteristics of flow past circular cylinder

A first attempt is made for identifying the wake characteristics of circular cylinder confined by a wavy wall at laminar flow regime. Numerical study of flow characteristics past circular cylinder with wavy-wall confinement perpendicular to cylinder axis has been carried out in the range of Reynolds number 20–100. The finite volume-based CFD solver Ansys Fluent (Version 15.0) is used for computations. The results are presented in the form of streamline plots, mean drag co-efficient, flow separation angle and recirculation length. Wavy-wall confinement leads to highly significant changes in the cylinder wake such as the evolution of strong x-plane vortices, enhanced fluid mixing, wake suppression near the crest region and vortex stretching near the trough region on the downstream of the cylinder has been observed. Flow separation angle varies significantly along the axis of the cylinder. Increased wall shear stress on rear surface of the cylinder has also been observed. The part of vorticity magnitude as compared to strain rate has been distinguished and identified using vortex identification methods such as Q-criterion and Lambda-2 criterion.

Experimental study of flow around polygonal cylinders

The wake of polygonal cylinders with side number $N=2\sim \infty$ is systematically studied based on fluid force, hot-wire, particle image velocimetry and flow visualisation measurements. Each cylinder is examined for two orientations, with a flat surface or a corner leading and facing normally to the free stream. The Reynolds number $Re$ is $1.0\times 10^{4}\sim 1.0\times 10^{5}$, based on the longitudinally projected cylinder width. The time-averaged drag coefficient $C_{D}$ and fluctuating lift coefficient on these cylinders are documented, along with the characteristic properties including the Strouhal number $St$, flow separation point and angle $\unicode[STIX]{x1D703}_{s}$, wake width and critical Reynolds number $Re_{c}$ at which the transition from laminar to turbulent flow occurs. It is found that once $N$ exceeds 12, $Re_{c}$ depends on the difference between the inner diameter (tangent to the faces) and the outer diameter (connecting corners) of a polygon, the relationship being approximately given by the dependence of $Re_{c}$ on the height of the roughness elements for a circular cylinder. It is further found that $C_{D}$ versus $\unicode[STIX]{x1D709}$ or $St$ versus $\unicode[STIX]{x1D709}$ for all the tested cases collapse onto a single curve, where the angle $\unicode[STIX]{x1D709}$ is the corrected $\unicode[STIX]{x1D703}_{s}$ associated with the laterally widest point of the polygon and the separation point. Finally, the empirical correlation between $C_{D}$ and $St$ is discussed.

Effects of large spanwise wavelength on the wake of a sinusoidal wavy cylinder

The wake of a sinusoidal wavy cylinder with a large spanwise wavelength λ/Dm (=3.79–7.57) and a constant wave amplitude a/Dm=0.152, where Dm is the mean diameter of the cylinder, is investigated using three dimensional (3D) large eddy simulation (LES) at a subcritical Reynolds number Re=3×103, based on incoming free-stream velocity (U∞) and Dm. Attention is paid to assimilating the effects of λ/Dm on the cylinder wake, including vortex shedding frequency, spanwise vortex formation length, streamwise velocity distribution, flow separation angle, 3D vortex structure, and turbulent kinetic energy (TKE) distribution. Based on the predominant role of λ/Dm in the near wake modification, three regimes are identified, i.e., regime I at λ/Dm<6.0, regime II at λ/Dm≈6.0 and regime III at λ/Dm>6.0. A dramatic decrease in fluid forces is observed at λ/Dm=6.06, about 16% and 93% reduction in time-averaged drag and fluctuating lift, respectively, compared to those of a smooth cylinder. We identified, for the first time, an optimum λ/Dm (=6.06) for the wavy cylinder with relatively large λ/Dm (>3.5) in the subcritical flow regime. The underlying mechanisms of force reduction are discussed, including the flow characteristics at the three λ/Dm regimes. A comparison is also made between the results of λ/Dm effects on the near wakes of a circular and a square cylinder.

A Numerical Study on the Oscillating Flow Induced by an Acoustic Field around Coal Particles

In order to investigate the acoustically driven oscillating flow around coal particles in the power plant boiler, the two-dimensional, unsteady mass and momentum conservation equations for laminar flow in spherical coordinates are developed numerically. The velocity field, axial pressure gradient, shear stress, and flow separation angle on the particle surface are carefully analyzed with different values of acoustic Reynolds number and Strouhal number. The minimum frequency required for flow separation is also investigated with different SPL (sound pressure level). The axial pressure gradient, shear stress, and separation angle on the surface are proportional to the magnitude of the oscillating flow velocity at low frequency (~50 Hz). However, those physical quantities have different values at high frequency (~5000 Hz), due to the combined effect of curvature and the flow acceleration.