The flow resulting from the rotation of a series of thin plates that initially separate two gases of different densities is analysed using Direct Numerical Simulations. The ninety degrees plates' rotation forms a vorticity shear layer and a density interface in between the tips of two neighbouring plates. Results of this study show that the shape of these layers strongly depends on the plate tip-based Reynolds number that can be varied thanks to a parametrisation of the plates' opening law. Different regimes are identified corresponding to single- or multi-mode initial interfaces, with or without the occurrence of starting vortices during the formation of the shear layer. The density interfaces resulting from this procedure are particularly well-suited to serve as initial conditions for the study of the Richtmyer-Meshkov instability-induced mixing. Results of this study also provide a description of vortex formation in stratified flows.

Perforated plates are commonly used for flow control in pressurized systems. In different industrial applications, these devices are also used in series (multistage perforated plates) to manage high pressure drop or reduce cavitation occurrence in industrial pipes and enhance efficiency of gas turbines in power plants. Based on analysis of literature and modeling considerations, a functional relationship that describes the dimensionless pressure loss for multistage perforated plates is proposed in this paper. Moreover, numerical investigation of the influence of the spacing between perforated plates for two identical-stage plates with aligned and misaligned holes is carried out by simulating a wide range of Reynolds number in turbulent flow regime. The obtained results include the trend of the pressure loss coefficient as the spacing between the two perforated plates varies for both cases of aligned and misaligned holes. The numerical achievements also show that for small spacing, the pressure loss coefficient is very different from that caused by two independent plates and is strongly influenced by the alignment between the holes of the two plates. By increasing the spacing, the behavior of the losses caused by the two-stage plates tends to that of two independent plates. A critical spacing between the plates has also been defined, beyond which the pressure losses are independent from the alignment of the holes.

A computational fluid dynamics model is developed to study the dynamics of meniscus formation and capillary flow between vertical parallel plates. An arbitrary Lagrangian–Eulerian approach is employed to predict and reconstruct the shape of the meniscus with no need to employ implicit interface tracking schemes. The developed model is validated by comparing the equilibrium capillary height and meniscus shape with those predicted by available theoretical models. The model was used to predict the capillary flow of water in hydrophilic (silver) and hydrophobic (Teflon) vertical channels with wall spacings ranging from 0.5 mm to 3 mm. It is shown that the computational model accurately predicts the capillary flow regardless of the channel width, whereas the theoretical models fail at relatively large wall spacings. The model captures several important hydrodynamic phenomena that cannot be accounted for in the theoretical models including the presence of developing flow in the entrance region, time-dependent formation of the meniscus, and the inertial effects of the liquid in the reservoir. The sharp interface tracking technique enables direct access to the flow variables and transport fluxes at the meniscus with no need to use averaging techniques.

A modified multiscale method without constitutive equation is proposed to investigate the microscopic information and macroscopic flow properties of polymeric fluid with the memory effect between parallel plates. In this method, the domain is entirely described by macromodel with isolated molecular dynamics simulations applied to calculate the necessary local stresses. The present method is first verified by the creep-recovery motion and pressure-driven flow, and all results are in excellent agreement with the available numerical solutions in literature. Then, the method is extended to simulate two typical problems of relatively large spatial scale in general beyond the capability of molecular dynamics simulations. In the planar Couette flow, the relationship between macroscopic properties and the time evolution of local molecular information is investigated in detail without long time averaging. All results that are consistent with nonequilibrium molecular dynamics and literature qualitatively or quantitatively demonstrate the validity of present multiscale method in simulating transient viscoelastic flows and the capacity to obtain the polymer information. In the pressure-driven flow, a general monotonically decreasing relationship between the maximum or average velocities and the polymer concentrations has been found regardless of the polymer chain length. Particularly, the reference concentration that satisfies a power law with chain length is closely related to the overlap concentration, and the reference velocity is exactly the relevant velocity of Newtonian fluid with corresponding zero shear rate viscosity.

The analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, “A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales,” J. Microscale Thermophys. Eng., 3, pp. 43–77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.

Enhancing mixing in heat exchangers for low Re regimes is vital. A better mixing may be achieved by using corrugated plates. In this work, the flow patterns between corrugated plates with a novel egg-carton geometry were studied. Three-dimensional (3D) numerical models were developed for the steady laminar flow between two corrugated plates having 180 deg or 0 deg phase angles. The Reynolds number (Re ≤ 600) was defined as a function of the average distance between the corrugated plates. The numerical models were strictly developed and corroborated to achieve global convergence, local convergence, and grid-size independence. For both phase angles, it was determined that “close recirculations” decrease in size downstream and finally disappear becoming “open recirculations” due to the flow developing characteristics; the secondary flow regions were found to grow downstream; interestingly, increments on the Reynolds number favor recirculation growth and early flow detachment; the behavior and geometry of the recirculation were in line with previous flow visualization results. The recirculations were determined to be z -symmetric with respect to the channel center only for the 180 deg model. The recirculations in the 0 deg model were smaller and became “open recirculations” earlier than in the 180 deg model. Convex geometries on the transversal direction were found to favor detachment, while concave geometries inhibit it. The capability of the numerical methods to track flow paths in any direction showed a complex three-dimensional flow causing 3D-interaction among secondary flows and the main flow not reported before for these channels and just hinted by previous flow visualization studies.

A computational study was carried out to investigate the effects of internal geometry changes on the likelihood of solids buildup within, and the efficiency of, an industrial dust collector. Combustible solids held up in the unit pose a safety risk. The dust collector serves multiple functions, so the design requires a delicate balance. Particles should be separated from the incoming mixture and collected in the bottom of the unit. This particulate material should freely flow into a high-speed ejector (Mach 0.4) underneath. Gas must also flow freely to the top outlet, but sufficient gas must flow down to the ejector so that its motive gas augments the transport of particles back to the reactor (recirculation). Computational design evaluations included: (1) rod spacing, (2) ledge removal, and (3) rod cover plates. Testing on particle size distribution and density was carried out in-house to provide inputs to the computational fluid dynamics (CFD) model. Rod spacing reduction had a mixed effect on flow distribution. Plates were found to induce a negative effect on recirculation and a mixed effect on combustible solids accumulation. Removal of the ledge, however, offered slightly more recirculation along with completely alleviating stagnant solids accumulation. It is shown that, without consideration of detailed fluid physics, general separator design principals might be misguiding.

The drag torque caused by the viscous shear in open multiplate wet clutches has been studied in most available literature whose focus is placed on low circumferential speed. However, the drag torque increases drastically in the high circumferential speed range. The underlying physical principles and the influencing factors of the drag torque at high speed are still indeterminate. The present study aims to experimentally investigate the characteristics of the wobbling vibrations of plates and to characterize the effects of average clearance, flow rate of lubricant, shifting condition, and the number of friction interfaces on the drag torque at high circumferential speed. The result of the experiment reveals that the friction plate (FP) starts to wobble periodically at low circumferential speed, though the effect is insignificant. The dominant frequency of plate wobbling movements increases with the input speed. When wobbling vibrations of plates become unstable, the wobble gradually becomes nonlinear. The experiments confirm that the mechanical contacts between plates during the unstable wobbling vibration result in the drag torque rise at high circumferential speed. At high speed, the supplying flow rate of the lubricant influences the drag torque values. The rotation of separator plates (SPs) brings forward the torque rise and makes the drag torque rise smoother. By reducing the number of interfaces, the drag torque rise is delayed and the magnitude becomes smaller. Finally, a four-stage drag torque characteristic curve is illustrated to show the dominant factors of drag torque at different stages.

The control of flow in the wake of a circular cylinder by an attached permeable plate having various porosity ratios was analyzed experimentally using both particle image velocimetry (PIV) and dye visualization techniques. The force measurements were also done in order to interpret the effect of control method on drag coefficient. The diameter of the cylinder and length to diameter ratio of the plate were kept constant as D = 50 mm and L/D = 1.0, respectively. The porosity ratio, β, which can be defined as the ratio of open surface area to the whole body surface area, was taken as β = 0.4, 0.5, 0.6, 0.7, and 0.8 (permeable plates). The study was performed considering deep water flow conditions with a constant Reynolds number of Re D = 5000 based on the cylinder diameter. Each permeable plate was attached on the separation point and the results were compared with the results of cylinder without permeable plate (plain cylinder) in order to understand the control effect. Both qualitative and quantitative results revealed that the permeable plates of 0.4 ≤ β ≤ 0.6 are effective on controlling the unsteady flow structure downstream of the cylinder, i.e., the vortex formation length was increased, turbulent statistics was reduced and vortex shedding frequency was diminished when the permeable plate attached normal to the cylinder surface from the lower separation point. However, the drag force acting on the cylinder was found to be increased due to the increased cross-sectional area.

Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates with nonuniform surface properties in the transverse direction are studied based on kinetic theory. We considered a simplified model in which one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary on which the accommodation coefficient varies periodically and smoothly in the transverse direction. The spatially two-dimensional (2D) problem in the cross section is studied numerically based on the linearized Bhatnagar–Gross–Krook–Welander (BGKW) model of the Boltzmann equation. The flow behavior, i.e., the macroscopic flow velocity and the mass flow rate of the gas as well as the velocity distribution function, is studied over a wide range of the mean free path of the gas and the parameters of the distribution of the accommodation coefficient. The mass flow rate of the gas is approximated by a simple formula consisting of the data of the spatially one-dimensional (1D) problems. When the mean free path is large, the distribution function assumes a wavy variation in the molecular velocity space due to the effect of a nonuniform surface property of the plate.

Fluid stiction may significantly influence the dynamic behavior when attempting to quickly separate two plates in close contact. The liquid fluid film, filling the gap between the plates, experiences a pressure drop resulting from an increasing distance, and cavitation may appear if sufficient separation speed and low plate distance are present. In the case of small initial plate separation, fluid tension is known to develop and the stiction force may exceed the maximum stiction force calculated by assuming strictly positive pressures in the fluid film. In this paper, a model for simulating the time dependent fluid stiction phenomenon, including a fluid tensile strength and cavitation effects, is proposed. The model is based on Reynolds theory, and the pressure distribution in the liquid zone is solved analytically for each time step, leading to a computationally efficient model without the need for finite element/volume methods. The considered geometry is two long parallel plates submerged in liquid, as present in many valve applications. The model is compared to experimental measurements, and it is found that the model is able to predict the stiction effect with reasonable accuracy given that proper selections of liquid tensile strength and initial plate distance are made.

Instabilities of a partial cavity developed on a hydrofoil, a converging-diverging step, or in an interblade channel have already been investigated in many previous works. The aim of this study is to evaluate a passive control method of the sheet cavity. According to operating conditions, cavitation can be described by two different regimes: an unstable regime with a cloud cavitation shedding and a stable regime with only a pulsating sheet cavity. Avoiding cloud cavitation can limit structure damage since this regime is less aggressive. The surface condition of a converging-diverging step is here studied as a solution to control the cavitation regime. This study discusses the effect of longitudinal grooves on the developed sheet cavity. Analyzes conducted with laser Doppler velocimetry, visualizations, and pressure measurements show that the grooves geometry, and especially the groove depth act on the sheet cavity dynamics and can even suppress the cloud cavitation shedding.

Stacks of parallel plates modeled as a standard fissure-type anisotropic porous medium are filled inside a rectangular channel up to half the cross section height. The interface slip coefficient α for the isothermal laminar incompressible flow exiting this partially filled porous-medium channel is then determined using particle image velocimetry (PIV) experiments and numerical simulations. Required measurements of the Darcy velocity uD on the porous-medium (PM) side, the local velocity uf, and its gradient ∂uf/∂y on the clear-fluid (CF) side are performed across different length scales. The fissure-type porous-medium parameters are systematically varied in the porosity range 0.2≤φ≤0.95 and flow direction permeability 10-6<K,m2<10-9. From the exit-velocity profile, the empirical slip coefficient α is determined using a generalized relationship. When the measurements across the PM-CF interface are performed across a length scale equal to the representative elemental length (REL) of the porous media considered (i.e., equal to the sum of plate thickness (a) and gap (b)), the determined α value is found to remain invariant.

This paper reports results of an experimental investigation of the loss coefficient and onset of cavitation caused by water flow through perforated plates of varying thickness and flow area to pipe area ratio at high speeds. The overall plate loss coefficient, point of cavitation inception, and point where critical cavitation occurs are functions of perforation hole size, number of holes, and plate thickness. Sixteen total plates were considered in the study with the total perforation hole area to pipe area ratio ranging from 0.11 and 0.6, the plate thickness to perforation hole diameter ranging from 0.25 to 3.3, and the number of perforation holes ranging from 4 to 1800. The plates were mounted in the test section of a closed water flow loop. The results reveal a complex dependency between the plate loss coefficient with total free-area ratio and the plate thickness to perforation hole diameter ratio. In general, the loss coefficient decreases with increasing free-area ratio and increasing thickness-to-hole diameter ratio. A model based on the data is presented that predicts the loss coefficient for multiholed perforated plates with nonrounded holes. Furthermore, the data show that the cavitation number at the points of cavitation inception and critical cavitation increases with increasing free-area ratio. However, with regard to the thickness-to-hole diameter ratio, the cavitation number at inception exhibits a local maximum at a ratio between 0.5 and 1.0. Empirical models to allow prediction of the point of cavitation inception and the point where critical cavitation begins are presented and compared to single hole orifice plate behavior.

Correlations predicting the pressure loss coefficient along with the laminar, transitional, and turbulent limiting Reynolds numbers with the β ratio are presented for short square-edged orifice plates. The knowledge of pressure losses across orifices is a very important industrial problem while predicting pressure losses in piping systems. Similarly, it is important to define stable operating regions for the application of a short orifice at lower Reynolds numbers. This work experimentally determined pressure loss coefficients for square-edged orifices for orifice-to-diameter ratios of β = 0.2, 0.3, 0.57, and 0.7 for Newtonian and non-Newtonian fluids in both laminar and turbulent flow regimes.

The determination of permeability K and form coefficient C, defined by the Hazen-Dupuit-Darcy (HDD) equation of flow through a porous medium, requires the measurement of the total pressure drop caused by the porous medium (i.e., inlet, core, and outlet) per unit of porous medium length. The inlet and outlet pressure-drop contributions, however, are not related to the porous medium length. Hence, for situations in which these pressure drops are not negligible, e.g., for short or very permeable porous media core, the definition of K and C via the HDD equation becomes ambiguous. This aspect is investigated analytically and numerically using the flow through a restriction in circular pipe and parallel plates channels. Results show that inlet and outlet pressure-drop effects become increasingly important when the inlet and outlet fluid surface-fraction φ decreases and the Reynolds number Re increases for both laminar and turbulent flow regimes. A conservative estimate of the minimum porous medium length beyond which the core pressure drop predominates over the inlet and outlet pressure drop is obtained by considering a least restrictive porous medium core. Finally, modified K and C are proposed and predictive equations, accurate to within 2.5%, are obtained for both channel configurations with Re ranging from 10 −2 to 10 2 and φ from 6% to 95%.

We have studied the phenomenon of squeeze film damping in a liquid with a microfabricated vibrating plate oscillating in its fundamental mode with out-of-plane motion. It is paramount that this phenomenon be understood so that proper choices can be made in terms of sensor design and packaging. The influences of plate-wall distance h , effective plate radius R , and fluid viscosity and density on squeeze film damping have been studied. We experimentally observe that the drag force is inertia dominated and scales as 1 / h 3 even when the plate is far away from the wall, a surprising but understandable result for a microfluidic device where the ratio of h to the viscous penetration depth is large. We observe as well that the drag force scales as R 3 , which is inconsistent with squeeze film damping in the lubrication limit. These two cubic power laws arise due to the role of inertia in the high frequency limit.

The present work investigates mass conservation equations in turbulent flow between parallel plates with variable mass diffusivity. Species conservation equations are relative to the average concentration, as well as to the concentration variance. The product of fluctuating mass diffusivity and space gradient of concentration fluctuation is appearing in the equation of mean and concentration variance. A physical interpretation is given to the different terms. The assumption of a relation between mass diffusivity and concentration allows writing expressions for average and fluctuating mass diffusivity, which can be simplified on the basis of theoretical considerations. The new mass flux is expressed as a function of mass diffusivity and a gradient of concentration variance. Further considerations make it possible to model the new terms appearing in the concentration variance equation. The mass conservation equation can be solved when coupled to the equation of concentration variance. The equations are solved numerically for flow between parallel plates in order to evaluate the influence of the new terms.

Flow over a circular cylinder with detached short splitter-plates is numerically simulated in order to assess the suppression of periodic vortex shedding. A finite-volume solver based on the Cartesian-staggered grid is implemented, and the ghost-cell method in conjunction with Great-Source-Term technique is employed in order to enforce directly the no-slip condition on the cylinder boundary. The accuracy of the solver is validated by simulation of the flow around a single circular cylinder. The results are in good agreement with the experimental data reported in the literature. Finally, the flows over a circular cylinder with splitter-plate in its downstream (off and on the centerline) are computed in Re = 40 as a nonvortex shedding case and in Re = 100 and 150 as cases with vortex shedding effects. The same simulations are also performed for the case where dual splitter-plates are in a parallel arrangement embedded in the downstream of the cylinder. The optimum location of the splitter-plate to achieve maximum reduction in the lift and drag forces is determined.

Microscale fluid dynamics has received intensive interest due to the emergence of micro-electro-mechanical systems (MEMS) technology. When the mean free path of the gas is comparable to the channel’s characteristic dimension, the continuum assumption is no longer valid and a velocity slip may occur at the duct walls. Noncircular cross sections are common channel shapes that can be produced by microfabrication. The noncircular microchannels have extensive practical applications in MEMS. The paper deals with issues of hydrodynamic flow development. Slip flow in the entrance of circular and parallel plate microchannels is first considered by solving a linearized momentum equation. It is found that slip flow is less sensitive to analytical linearized approximations than continuum flow and the linearization method is an accurate approximation for slip flow. Also, it is found that the entrance friction factor Reynolds product is of finite value and dependent on the Kn and tangential momentum accommodation coefficient but independent of the cross-sectional geometry. Slip flow and continuum flow in the hydrodynamic entrance of noncircular microchannels has been examined and a model is proposed to predict the friction factor and Reynolds product f Re for developing slip flow and continuum flow in most noncircular microchannels. It is shown that the complete problem may be easily analyzed by combining the asymptotic results for short and long ducts. Through the selection of a characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The proposed model has an approximate accuracy of 10% for most common duct shapes.