Modified Reynolds Number Research Articles

Water Model and CFD Studies of Bubble Dispersion and Inclusions Removal in Continuous Casting Mold of Steel

A water model study was undertaken to investigate bubble dispersion and inclusions removal by bubble adhesion in continuous casting mold. The water flow rate was varied in the range of 37-74 L/min, which is equivalent to 1.0-2.0 m/min of the casting speed in continuous casting process. The gas flow rate was varied in the range of 0-2.5 L/min. Silver coated hollow glass beads (SCHG) and plastic particles were used to imitate the inclusions and to investigate the effect of wettability, i.e., contact angle of the inclusions with liquid, on inclusion removal by bubble adhesion. Effect of gas and water flow rates on bubble dispersion in the mold was systematically determined. Inclusion removal at different gas and water flow rates was quantitatively determined. It was identified that the wettability of inclusions with liquid was a decisive factor in inclusion removal: with low wettability, i.e., high contact angle, removal efficiency increased with increasing gas and liquid flow rates, whereas removal efficiency was hardly affected by gas flow rate with high wettability, i.e., low contact angle. To interpret the results of the water model experiments, various computational fluid dynamics (CFD) models which had been reported were applied. None of them was able to represent the experimental results within an acceptable discrepancy. Two new CFD models, which employed a modified Reynolds number and force field theory around the bubble, were developed to simulate bubble dispersion and inclusion removal, respectively. The results indicated that these models could simulate bubbles dispersion and inclusion removal and showed reasonable agreement with results of water model in continuous casting mold.

Characterizing heat transfer coefficients for heat exchangers in standing wave thermoacoustic coolers

The thermal performance of heat exchangers within a thermoacoustic cooler was investigated. Experimental procedures and calculation methods to evaluate the oscillating flow heat transfer coefficients were developed. Dimensionless heat transfer coefficients, or Colburn-j factors, were estimated based on the oscillating-flow variables and compared with results from steady-flow measurements. The results were also compared with heat transfer coefficients predicted from a boundary-layer conduction model, and methods that utilize steady-flow correlations with Reynolds numbers that characterize oscillating flow conditions. Although the boundary layer model is commonly employed for thermoacoustic calculations, it did not accurately predict heat transfer coefficients and the influence of Reynolds number on heat transfer performance. However, accurate predictions were obtained using a steady-flow correlation and a modified Reynolds number that accounts for the oscillating flow field, assuming a half-cycle Reynolds number correction value of 0.109.

Adsorption kinetics of cupric and cadmium ions on corncob particles

The effects of the pH, agitation speed, particle size, and concentration of corncob particle on the adsorption kinetics of cupric and cadmium ions were investigated in this study. It was found that the uptakes of cupric and cadmium ions on corncob particles increased with increasing the initial pH and agitation speed, and with decreasing the particle size. The amount of adsorbed ions also increased with increasing the concentration of corncob particles, but the amount of the adsorbed ions/unit mass of adsorbent diminished. Based on the elimination of the external and intraparticle diffusions, the intrinsic forward and backward rate constants in a reversible surface reaction model combined with an effectiveness factor were estimated for cadmium ions to be 2.88/(mmol min) and 0.184/min. The maximum adsorption capacity and the effectiveness factor in this model were determined for copper and cadmium ions as a function of the initial pH and particle size. Both values increased with increasing the initial pH, and decreasing the size and concentration of corncob particle. The simple external diffusion model can describe only the solute change in solution for initial 5 min, which suggested that adsorption of cadmium on corncob particles was controlled first by the external diffusion, and then by the intraparticle diffusion. The external mass transfer coefficients first increased with increasing the modified Reynolds number, and then reached a maximum value.

A reversible surface reaction model with an effectiveness factor and its application to sorption kinetics of cupric ions on corncob particles

A novel reversible surface reaction model with an effectiveness factor was developed. To avoid uncertainty of nonlinear regression, an experimental procedure was designed to determine the following four constants in the model: the effectiveness factor, the maximum sorption capacity, and the intrinsic forward and backward rates. In this procedure first the intrinsic forward and backward rate constants for copper sorption were estimated to be 1.082 l/(mmol min) and 0.472 min −1 based on the elimination of the effect of the intraparticle and external mass transfers, and then the other two constants, the effectiveness factor and the maximum sorption capacity, were regressed as a function of the corncob particle size. Their values increased with decreasing the particle size. The simple external mass transfer model can describe only the solute change in solution for an initial 5 min period of time, which suggests that sorption of copper on corncob particles is controlled first by the external mass transfer, and then by the intraparticle mass transfer. The external mass transfer coefficients increased with increasing the modified Reynolds number, and then reached a maximum at higher values of the number. Studying the effects of the agitation speed and size of corncob particle on the kinetics of cupric ions sorption, it was found that the uptake of cupric ions on corncob particles increased with decreasing particle size and with increasing the agitation speed.

Effects of non-Darcian on forced convection heat transfer over a flat plate in a porous medium-with temperature dependent viscosity

The non-Darcian effect on forced convection heat transfer over a flat plate in a porous medium is examined. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The effects of inertia forces and the distance from the leading edge of the plate on the velocity and temperature fields as well as on the skin friction and heat transfer coefficients in the boundary layer over a semi-infinite plate are studied. The nonlinear boundary layer equations, governing the problem under consideration, are solved numerically by applying an efficient numerical technique based on the Keller box method. The velocity profiles, temperature profiles and the skin friction components on the plate are computed and discussed in detail numerically for various values of the variable viscosity parameter, the modified Reynolds number, the stream wise coordinate and the Prandtl number.

Heat transfer and flow pattern in vertical liquid–solids flow

Wall-to-bed heat transfer in hydraulic transport of spherical glass particles of diameter 1.20, 1.94 and 2.98 mm and in single-phase flow regime was studied. Experiments were performed by transporting the spherical glass particles with water in a 25.4 mm I.D. copper tube equipped with a steam jacket. In the runs without particles, the tube Reynolds number varied between 2280 and 21,300, while in hydraulic transport runs, the tube Reynolds number varied between 3300 and 20,150. The loading ratio ( G p/ G f) was between 0.07 and 0.328, and the fluid superficial velocity was between 0.29· U t and 2.86· U t, where U t represents the single particle terminal velocity. For these ratios, the voidage ranged from 0.715 to 0.895. The data for the heat transfer factor ( j H) in single-phase flow are correlated using a general form j H= f( Re). The data for wall-to-bed heat transfer in the hydraulic transport of particles show that an analogy between heat and momentum transfer exists. The data were correlated by treating the flowing fluid–particle suspension as a pseudofluid, by introducing a modified suspension–wall friction coefficient ( f w) and a modified Reynolds number ( Re m).

Forced Convection Heat Transfer From a Low-Profile Block Simulating a Package of Electronic Equipment

Forced convection heat transfer from a low-profile block placed in a rectangular duct, simulating heat transfer in a compact packaged electronic device, is investigated experimentally. Local heat transfer from the block is measured by an infrared camera. A general correlation of the Nusselt number for the block is derived using a modified Reynolds number, ReL*=Um/β2L/ν, where Um is mean duct velocity, β is the opening ratio of the duct, and L is the block length. The correlation is shown to be applicable regardless of the configuration of the block and duct, under the conditions of laminar flow, a low-profile block (height/length<0.5), and a low blockage effect (β⩾0.5).

A spectral/finite‐difference approach for narrow‐channel flow with inertia

AbstractA hybrid spectral/finite‐difference scheme is proposed to determine the inertial flow inside narrow channels. The flow field is represented spectrally in the depthwise direction, which together with the Galerkin projection lead to a system of equations that are solved using a variable step finite difference discretization. The method is particularly effective for non‐linear flow, and its validity is here demonstrated for a flow with inertia. The problem is closely related to high‐speed lubrication flow. The validity of the spectral representation is assessed by examining the convergence of the method, and comparing with the fully two‐dimensional finite‐volume solution (FLUENT), and the widely used depth‐averaging method from shallow‐water theory. It is found that a low number of modes are usually sufficient to secure convergence and accuracy. Good agreement is obtained between the low‐order description and the finite‐volume solution at low to moderate modified Reynolds number. The depth‐averaging solution is unable to predict accurately (qualitatively and quantitatively) the high‐inertia flow. The influence of inertia is examined on the flow. Copyright © 2003 John Wiley & Sons, Ltd.

Rheology of non-Newtonian suspensions of fly ash: effect of concentration, yield stress and hydrodynamic interactions

Two different water-washed municipal solid waste (MSW) incinerator fly ashes were investigated. The rheological behaviour of these fly ashes in aqueous suspensions was studied using a parallel plate rheometer. Shear-thinning behaviour was observed in one sample whereas thixotropic behaviour was found in the other. Viscosity depends on both the volume fraction of solids in the suspension and on the yield stress. The data could be well correlated to a model we proposed which takes into account the volume fraction of solid and the shear rate. The comparison with various models of the literature is discussed. The hydrodynamic theory of particle movement in non-Newtonian fluids is discussed, focusing on inertia and viscous effects. Two modified Reynolds numbers involving respectively the shear rate and the yield stress, and with the shear rate and the volume fraction of solids, are proposed and discussed. The flow regime in the investigated experimental conditions is laminar and governed by hydrodynamic interactions. The results also show that inertia cannot be neglected.

Magnetohydrodynamic study of electromagnetic separation of nonmetallic inclusions from aluminum melt

Magnetohydrodynamic flow around the nonmetallic inclusions in aluminum melt and the force exerted on the inclusions were explored by dimensional analysis and numerical calculations. Dimensional analysis shows that the invariant \(A = {{JB\rho _f d_p^3 } \over {\mu _f^2 }}\) characterizes the force exerted on the inclusions and the flow intensity of the melt. The physical significance of A is represented as a modified particle Reynolds number that reflects the effects of electromagnetic force. The fluid flow around the particle becomes unstable when A>2×103. It is shown that the neglect of the inertial terms has little effect on the force exerted on the inclusions in the range of A≤1×106. However, the analytical solution of the maximum velocity inside the melt does not apply due to the appearance of turbulent flow in the case of A>2×103.

Effect of Fluid Film Inertia on Stability of Flexibly Supported Oil Journal Bearings: A Non-Linear Transient Analysis

In the analysis of hydrodynamic journal bearings the effect of fluid inertia is usually ignored in view of its negligible contribution compared to viscous force. However, the fluid inertia effect is to be taken in the analysis when modified Reynolds number is around one. Flexibly supported journal bearings are in general more stable when support design is proper. The aim of this paper is to see if there is any effect of fluid inertia on flexibly supported journal bearings. The mass parameters (measure of stability) are estimated for different support parameters and modified Reynolds numbers by adopting a non-linear time transient analysis.

Flow and Heat Transfer around a Square Block Simulating a Package of Electronic Equipment.

An experimental study was performed to investigate the flow and heat transfer around a square block, simulating a package of electronic equipment. The height and the side length of the block were H=2 mm and L=45 mm, respectively. The mean velocity of air in the rectangular duct, Um, ranged from 0.24 to 4 m/s, and the duct height, HD, ranged from 3.8 to 10mm. The thickness of laminar boundary layer was greater than the block height. It was found that the heat transfer distribution on the top face of the block was approximately correlated to the distribution based on the theory of laminar flat boundary layer. The average Nusselt number on the top face was correlated by Num=0.61Pr1/3(Re*L)0.5, where Re* is the modified Reynolds number considering the effect of the opening ratio. This correlation was confirmed by many previous researches, performed under the similar condition of flow field.

A generalized correlation for evaporation heat transfer of refrigerants in micro-fin tubes

A generalized correlation for flow boiling heat transfer in horizontal micro-fin tubes was developed by implementing non-dimensional parameters accounting for heat transfer enhancement over smooth tubes and physical phenomena into the basic form of a smooth tube correlation. The enhancement factor in nucleate boiling consists of surface tension and turbulence effects generated by the liquid flow. A modified Reynolds number having some similarities with the roughness Reynolds number is introduced into the model to estimate heat transfer enhancement in convective boiling. The ratio of the liquid film thickness to the fin height is also employed in the correlation. The database of the present correlation includes 749 data points for five different refrigerants. The present correlation has a relatively simpler form to employ and yields closer fit to the experimental data with a mean deviation of 20.5% as compared to the existing correlations in the literature.

Longitudinal Dispersion of the Continuous Phase in Spray Extraction Columns

Longitudinal dispersion of the continuous phase was studied in spray extractors operated in the loose, close, and turbulized drop packing modes. The Peclet number was found to depend on the Reynolds number modified to take into account the hydrodynamic conditions in the working zone of the column. When the continuous phase is pulsed, the Peclet number is also governed by the modified Reynolds number, which accounts for the effect of pulsation on the longitudinal dispersion.

Electrostatic charge generation during impeller mixing of used transformer oil

The purpose of this study was to examine the effects of varying conductivity and turbulent impeller mixing intensity on charge generation of used Shell Diala ® transformer oil. The oil was mechanically agitated by a pitched six-bladed impeller in a 1.5 quart fully baffled cylindrical vessel at impeller Reynolds numbers between 5 000 and 10 000. The electrical current generated from the mixing operation was measured on the wall of the mixing tank and also in the internal vapor space on a 1 cm 2 target disk positioned approximately 1.5″ above the free liquid surface. Fluid electrical conductivity was varied using different concentrations of two types of commercially available antistatic additives (Shell ASA-3 and DuPont Stadis 450). A generalized dimensional analysis performed by using the Buckingham Pi theorem showed that a dependent dimensionless group, π 1, which contains the measured wall current and other fluid dynamic and electrical variables was found to be dependent on six independent groups. Four of these groups were related to modified Reynolds numbers based on impeller diameter and width, and tank diameter and fluid depth or tank height. The two remaining independent groups were related to the mass transfer Schmidt number and the impeller rotational speed. The mean particle diameter from a Malvern ZetaSizer and π 1 were plotted versus fluid conductivity to investigate the functional dependence of these parameters. The dimensionless group π 1 was also plotted for different impeller Reynolds numbers. These different plots show results that appear to illustrate inverse dependencies. The current versus conductivity data for different impeller Reynolds numbers also show similar behavior to published data for both laminar and turbulent flow through capillaries (i.e., current first increases with increasing conductivity, hits a maximum and then decreases with further increases in conductivity). This apparently demonstrates that a single charge transport mechanism is responsible for the behavior in two different charge-generation situations for different geometrical conditions.

Effect of fluid inertia on the dynamic coefficients and stability of journal bearings

In the analysis of hydrodynamic journal bearings the effect of fluid inertia is generally neglected in view of its negligible contribution compared with viscous forces. However, there is a necessity to evaluate its effect at moderate values of the modified Reynolds number. An attempt is made to study the effect of fluid inertia on the stability of journal bearing for a flow in the laminar regime, i.e. for a value of the modified Reynolds number of the order of one. A linear perturbation technique is used to find the dynamic characteristics and stability of a finite journal bearing.

Speciation of Subsurface Contaminants by Cone Penetrometry Gas Chromatography/Mass Spectrometry

A thermal extraction cone penetrometry gas chroma tography/mass spectrometry system (TECP GC/MS) has been developed to detect subsurface contaminants in situ. The TECP can collect soil-bound organics up to depths of 30 m. In contrast to traditional cone penetrometer sample collectors, the TECP extracts organics from soil without bringing the soil to the surface or into a collection chamber. Results show that polychlorinated biphenyls, polycyclic aromatic hydrocarbons (PAHs), chlorinated pesticides, and explosives can be recovered (60−95%) from wet or dry soil, with extraction efficiency compound-specific. The data are in remarkable agreement with closed cell thermal desorption (TD) experiments, where no organics are lost to the environment during heating. TECP GC/MS results also compare favorably with solvent-extracted GC/MS analyses and can be used to delineate the presence and extent of contamination at hazardous waste sites. Data illustrating TECP dependence on probe temperature and soil moisture as well as carrier gas linear velocity and volume (modified Reynolds number) are shown along with sample analysis data from two hazardous waste sites. The total ion and reconstructed ion current chromatograms are shown for PAHs collected by TECP from a coal tar contaminated soil obtained at a manufactured gas plant in Massachusetts. TECP and TD results are within 15% for nonvolatile PAHs and within 50% of the solvent-extracted data.

Friction factors and rheological properties of orange juice

The rheological behavior of Brazilian orange juice with different water content (0.34–0.73 w/w) was studied at a wide range of temperatures (0.5–62 oC) using a concentric cylinder viscometer. The results indicated that the juices behave as pseudoplastic fluids with yield stress, being represented by the Herschel–Bulkley model. The rheological parameters were fitted as functions of both temperature and water content in the tested range. Based on dimensional analysis it was proposed a modified Reynolds number (Re M), which includes the Herschel–Bulkley parameters. Experimental data of friction factors during heating and cooling processes of orange juice in laminar flow through circular tubes could be well correlated as a function of Re M.

The hydromagnetic flow between eccentric cylinders with velocity slip at the cylinder walls

The hydrodynamic flow between two eccentric cylinders is examined for small values of modified Reynolds number, porosity parameter and the non-dimensional slip velocity parameter in the presence of a radial magnetic field.The stream function and the pressure distribution are calculated and the results are presented graphically.

Interaction of von Karman vortices and intersecting main streams in staggered tube bundles

Flow visualization, heat transfer and pressure drop characteristics in flow through staggered tube bundles have been regarded as classical, with results well-documented. However, the mechanism of producing such results has been left untouched. Applications of staggered tube bundles are abundant in industry, for example as heat exchange devices like the shell-and-tube type and fuel bundles in nuclear reactor cores. An experimental study is recorded in the present paper which investigates the interaction of von Karman vortices and intersecting main streams in staggered tube bundles. Flow visualization by means of the particle tracing method, laser Doppler velocimetry (LDV) and pressure drop measurements using a piezometer are conducted. A modified Reynolds number appropriate to flow through a staggered tube arrangement is defined together with a pressure drop coefficient. Auto-correlation and power spectrum analyses of signals obtained from LDV measurements yield an optimum spectrum frequency which is correlated against the Reynolds number. It is concluded that flow characteristics in staggered tube bundles are determined by the interaction between the von Karman vortex street and X-shaped interacting main streams.