Assumption Of Laminar Flow Research Articles

Development of Micro Channel Heat Exchanging

In order to investigate the performance of the micro channel heat exchanger, three-dimensional numerical simulations and experiments on heat transfer behavior and pressure loss were carried out. So far as the heat transfer phenomena is concerned, results obtained using a silicon chip micro channel model showed a very small thermal resistance, about 0.1 (Kcm2/W). And, measured pressure loss showed good agreement with that of analytical result obtained on the basis of fully developed laminar pipe flow assumption. Furthermore, a practical setup was made with a micro channel heat exchanger to clarify the possibility of using the micro channel heat exchanger in electrical equipment. As a result, it was confirmed that the performance of the micro channel heat exchanger system is sufficient to cool a silicon chip which generates a large amount of heat, and the scale of the system is compact compared to that of the whole setup of electrical equipment.

Development of Micro Channel Heat Exchanging.

The micro channel heat exchanger, which has many small channels (10∼100 μm order), is a promising device to cool an integrated circuit, which generates a large amount of heat. In order to investigate the performance of the micro channel heat exchanger, three-dimensional numerical simulations and experiments on heat transfer behavior and pressure loss were carried out. So far as the heat transfer phenomena is concerned, results obtained using a silicon chip micro channel model showed a very small thermal resistance, about 0.1 (Kcm2/W). And, in the designing of heat exchanger, the pressure loss phenomenon is of practical importance. In the present study, measured pressure loss showed good agreement with that of analytical result obtained on the basis of fully developed laminar pipe flow assumption. Furthermore, a practical setup was made with a micro channel heat exchanger to clarify the possibility of using the micro channel heat exchanger in electrical equipment. As a result, it was confirmed that the performance of the micro channel heat exchanger system is sufficient to cool a silicon chip which generates a large amount of heat, and the scale of the system is compact compared to that of the whole setup of electrical equipment.

A fluid--structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery.

A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.

DISCRIMINATING THE INFLUENCE OF SOIL TEXTURE AND MANAGEMENT-INDUCED CHANGES IN MACROPORE FLOW USING SOFT X-RAYS

Soft X-ray radiography, a nondestructive technique, was employed to examine macropore flow characteristics in soils of different management : paddy, upland field, and forest. A constant-head saturated hydraulic conductivity experiment was conducted using the soft X-ray apparatus. A contrast medium, CH 2 I 2 , was applied as a tracer to obtain contrast images of macropore flow. The visualization efficiency has been increased by the low-energy system that enables high-contrast images to be obtained as a result of a wider range of mass attenuation coefficients. CH 2 I 2 has a larger attenuation coefficient than bulk soil and has a kinematic viscosity similar to water. It was introduced dropwise to allow movement with the water flow. Macropore flow was captured using a soft X-ray TV camera, whereas flow paths were photographed on X-ray films. Light duralumin, was used for the sample holder instead of the conventionally used stainless steel in order not to cancel the efficiency induced by the contrast medium. We found that the highest resolution obtained was 42.3 μm. This corresponded well to the calculated value of 30 μm at an energy level of 60 to 70 keV. The resultant images showed that only about 30% of potentially available macropores conducted water flow. Macropore flow paths were affected by land management: straight isolated cylindrical paths in paddy field soils; a network of tortuous paths in upland field soils; and round cloudy interaggregate paths in forest soils. Macropore flow velocity was estimated from CH 2 I 2 movement. Because the flow area was restricted to a small number of macropores, the Reynolds number of flow ranged from 51.6 to 88.6. The flow was in a transition region from laminar to turbulent flow. Under actual conditions of macropore flow, the assumption of laminar flow was not realized. Both structural and dynamic analyses of macropore flow explained the flow characteristics successfully.

Flow control in a subcooled tube: an experimental investigation of the effects of crust formation

The flow control of molten liquids in tubes by manipulating the flow cross-sectional area using solidification has been investigated. Eicosane, because of its well characterised thermophysical properties, fixed melting point and known temperature dependent properties, was used as the test fluid. The eicosane data can be used to model the flow control of high temperature slag in the metallurgical industry and to verify the results of mathematical models of slag flow in tubes. Experimental results are presented in the form of pressure drop vs flow rate and dimensionless freezing parameter ( Tw ∗ ) vs flow rate. These are compared with a theoretical laminar flow model with solidification. The experimental results cover: 100 < Re < 1000, 0.3 < Tw ∗ < 5.4 and for cooled length to diameter ratios ( L D ) of 41.9, 27.6, 26.3 and 19.8. For Tw ∗ < 4 the agreement between experiment and theory is within 20%. For Tw ∗ > 4 it was clearly observed that the experimental pressure drop is significantly lower than the theoretical predictions and can be attributed to either the breakdown of the laminar flow assumption and/or the formation of an air gap between the tube and the solidified crust.

Wave-induced boundary layer flows above and in a permeable bed

In this paper, the oscillatory and steady streaming velocities over a permeable bed are studied both theoretically and experimentally. Three different sizes of glass beads are used to construct permeable beds in laboratory experiments: the diameters of the glass beads are 0.5 mm, 1.5 mm, and 3.0 mm, respectively. Several experiments are performed using different wave parameters. A one-component laser-doppler velocimeter (LDV) is used to measure the horizontal velocity component inside the Stokes boundary layer above the solid and permeable surfaces. It is observed that neither oscillatory nor steady velocity components vanish on the permeable surface. The ‘slip velocities’ increase with increasing permeability. Based on the laminar flow assumption and the order of magnitude of the parameters used in the experiments, a perturbation theory is developed for the oscillatory velocity and the steady wave-induced streaming in the boundary layers above and inside the permeable bed. The theory confirms many experimental observations. The theory also provides the damping rate and the phase changes caused by the permeable bed.

Chaotic motions of a rigid rotor in short journal bearings

In the present paper the conditions that give rise to chaotic motions in a rigid rotor on short journal bearings are investigated and determined. A suitable symmetry was given to the rotor, to the supporting system, to the acting system of forces and to the system of initial conditions, in order to restrict the motions of the rotor to translatory whirl. For an assigned distance between the supports, the ratio between the transverse and the polar mass moments of the rotor was selected conveniently small, with the aim of avoiding conical instability. Since the theoretical analysis of a system's chaotic motions can only be carried out by means of numerical investigation, the procedure here adopted by the authors consists of numerical integration of the rotor's equations of motion, with trial and error regarding the three parameters that characterise the theoretical model of the system: m, the half non-dimensional mass of the rotor, σ, the modified Sommerfeld number relating to the lubricated bearings, and ρ, the dimensionless value of rotor unbalance. In the rotor's equations of motion, the forces due to the lubricating film are written under the assumption of isothermal and laminar flow in short bearings. The number of numerical trials needed to find the system's chaotic responses has been greatly reduced by recognition of the fact that chaotic motions become possible when the value of the dimensionless static eccentricity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiabew7aLnaaBaaaleaacaWGZbaabeaaaaa!4046!\[\varepsilon _s \] is greater than 0.4. In these conditions, non-periodic motions can be obtained even when rotor unbalance values are not particularly high (ρ=0.05), whereas higher values (ρ>0.4) make the rotor motion periodic and synchronous with the driving rotation. The present investigation has also identified the route that leads an assigned rotor to chaos when its angular speed is varied with prefixed values of the dimensionless unbalance ρ. The theoretical results obtained have then been compared with experimental data. Both the theoretical and the experimental data have pointed out that in the circumstances investigated chaotic motions deserve more attention, from a technical point of view, than is normally ascribed to behaviours of this sort. This is mainly because such behaviours are usually considered of scarce practical significance owing to the typically bounded nature of chaotic evolution. The present analysis has shown that when the rotor exhibits chaotic motions, the centres of the journals describe orbits that alternate between small and large in an unpredictable and disordered manner. In these conditions the thickness of the lubricating film can assume values that are extremely low and such as to compromise the efficiency of the bearings, whereas the rotor is affected by inertia forces that are so high as to determine severe vibrations of the supports.

Experimental investigation on the heat transfer characteristics of an oscillatory pipe flow

Effects of oscillatory flow upon heat transfer characteristics have been studied experimentally for oscillating flow in a circular tube. The experimental apparatus was designed to simulate the heat exchangers of the Stirling or Vuilleumier cycle machines and the test section consists of heater and cooler. Measurements were presented of heat flux, axial wall temperature distribution, and radial temperature profile of the working fluid for several cases of oscillation frequency and swept distance ratio. The influences of two main parameters, frequency and tidal displacement of the oscillation were investigated. Then the heat transfer coefficient at the heater is obtained. The carried by the authors with a assumption of oscillatory laminar slug flow.

Investigation of flow and heat transfer in corrugated passages—II. Numerical simulations

An experimental and numerical study of flow and heat transfer was conducted for a crossed-corrugated geometry, representative of compact heat exchangers under transitional and weakly turbulent conditions. Three-dimensional numerical predictions were obtained by a finite volume method using a variety of approaches ranging from laminar flow assumptions to standard and low-Reynolds number k-ε turbulence models, direct simulation, and large-eddy simulation. In this paper, the various computational approaches are presented and their relative performance is discussed for various geometries and Reynolds numbers; results are compared with experimental measurements and literature data. Detailed experimental results are presented in Part I.

Computational model of flexible membrane wings in steady laminar flow

A computational procedure is presented that models the interaction of a two-dimensional flexible membrane wing and laminar, high-Reynolds-number fluid flow. The membrane wing model is derived by combining a spatial-coordinate-based finite difference formulation of the equilibrium statement for an elastic membrane with a pressure-based control volume formulation of the incompressible Navier-Stokes equations written in general curvilinear body-fitted coordinates. The model is applied to initially flat membrane wings of both vanishing and finite material stiffness as well as to flexible inextensible wings with excess length. Computational results are presented for Reynolds numbers between 2 x 10 3 and 10 4 . The results from the viscous-flow-based membrane wing model are compared with predictions using a potential-flow-based model as well as with experimental data for membrane wings in turbulent flow. Although the assumption of laminar flow precludes a quantitative comparison with the available experimental data, the solutions obtained capture many of the significant features of the aeroelastic interaction that are unaccounted for with a potential flow description of the fluid dynamics.

Computer modeling of enclosed inductively coupled plasma discharges

A mathematical model for an enclosed inductively coupled plasma (EICP) is developed for configurations important for spectrochemical analysis. The model, based on steady state, laminar flow, axial symmetry and local thermodynamic equilibrium assumptions, accounts for natural convection and radiative transfer effects. The computer simulations based in this model provide information about the temperature, flow, and electromagnetic fields for spherical and cylindrical discharge configurations.

The effect of shell side hydrodynamics on the performance of axial flow hollow fibre modules

Fluid flow and mass transfer experiments have been performed on axial flow hollow fibre modules of varying packing density (32 to 76%). Shell-side pressure drop was found to be proportional to (flowrate) n , where n varied from about 1.1 at high packing density to 1.5 at low packing density, for shellside Reynolds numbers < 350. Assuming an Ergun-type pressure drop relationship it was found that for packing densities < about 50% the inertial (turbulent) losses exceeded the viscous (laminar) losses. Inspection of cross-sections taken from the middle of modules revealed non-uniform fibre packing with regions of high and low packing density. The cross-sections also change along the length of the module. It is inferred that, in addition to axial flow along fibres, there is also a degree of stream splitting which provides transverse flow across fibres as fluid continuously seeks preferential paths through regions of lower packing density. The presence of transverse flow would explain the higher than expected velocity exponent. Mass transfer experiments involving the removal of oxygen from water flowing through the shell to a sweep gas in the fibre lumens produced higher than expected shell-side mass transfer coefficients. The results are correlated within ± 15% by Sh = (0.53 − 0.58φ) Re 0.53 Sc 0.33. The exponent on Re is consistent with entry region conditions, caused by repeated stream splitting and transverse flow. Compared with mass transfer predicted for axial flow through a uniformly packed shell the experimental results are up to 2× higher, with the most significant enhancement at the lower packing densities. The implication of this work is that module design requires a more sophisticated approach than the traditional assumption of laminar flow through parallel axial ducts.

Approximations in Hydrodynamic Lubrication

In this numerical study of the approximations that led Reynolds to the formulation of classical Lubrication Theory, we compare results from (1) the full Navier-Stokes equations, (2) a lubrication theory relative to the “natural,” i.e., bipolar, coordinate system of the geometry that neglects fluid inertia, and (3) the classical Reynolds Lubrication Theory that neglects both fluid inertia and film curvature. By applying parametric continuation techniques, we then estimate the Reynolds number range of validity of the laminar flow assumption of classical theory. The study demonstrates that both the Navier-Stokes and the “bipolar lubrication” solutions converge monotonically to results from classical Lubrication Theory, one from below and the other from above. Furthermore the oil-film force is shown to be invariant with Reynolds number in the range 0 &lt; R &lt; Rc for conventional journal bearing geometry, where Rc is the critical value of the Reynolds number at first bifurcation. A similar conclusion also holds for the off-diagonal components of the bearing stiffness matrix, while the diagonal components are linear in the Reynolds number, in accordance with the small perturbation theory of DiPrima and Stuart.

Photo‐sensor Methodology for Determining Residence Time Distributions of Particles in Continuous Flow Thermal Processing Systems

ABSTRACTA method applying photo‐sensors was developed to determine particle residence time distributions in the holding tube of aseptic processing systems. Multiple sensor pairs installed around a transparent glass tube (50.8 mm, i.d.) created a two‐dimensional “optical‐grid” for detecting particle movement. Detection of spherical particles (polystyrene, 19.1 mm diameter) could be achieved at particle velocities below 2.67 m/s to comply with sensor response time. A normal distribution of particle residence times was obtained from 75 replicated runs. The laminar flow assumption for the fastest fluid element was found to be conservative for public safety concerns in solid‐liquid two‐phase systems using the single particle basis for sizing holding sections.

Flow through isotropic granular porous media

A generalization of the Navier-Stokes equation is developed to include laminar flow through a rigid isotropic granular porous medium of spatially varying permeability. The model is based on a theory of interspersed continua and the mean geometrical properties of an idealized granular porous microstructure. The derived momentum transport equations are applicable to granular porous media over the entire porosity range from zero through unity. No restriction with respect to flow velocity is imposed, except for the assumption of laminar flow within the pores. The results provide useful and versatile equations and substantiate many of the empirical equations currently in use. One of the major advantages of the generalized momentum equation is its adaptability to numerical simulation.

A natural low-frequency oscillation of the flow over an airfoil near stalling conditions

An unusually low-frequency oscillation in the flow over an airfoil is studied experimentally as well as computationally. Wind-tunnel measurements are carried out with two-dimensional airfoil models in the chord Reynolds number (Rc) range of 0.15 × 105−3.0 × 105. During deep stall, at α [gsim ] 18°, the usual ‘bluff-body shedding’ occurs at a Strouhal number, Sts ≈ 0.2. But at the onset of static stall around α = 15°, a low-frequency periodic oscillation is observed, the corresponding Sts being an order of magnitude lower. The phenomenon apparently takes place only with a transitional state of the separating boundary layer. Thus, on the one hand, it is not readily observed with a smooth airfoil in a clean wind tunnel, while on the other, it is easily removed by appropriate ‘acoustic tripping’. Details of the flow field for a typical case are compared with a case of bluff-body shedding. The flow field is different in many ways from the latter case and does not involve a Kármán Vortex street. The origin of the flow fluctuations traces to the upper surface of the airfoil and is associated with a periodic switching between stalled and unstalled states. The mechanism of the frequency selection remains unresolved, but any connection to blower instabilities, acoustic standing waves or structural resonances has been ruled out.A similar result has been encountered computationally using a two-dimensional Navier–Stokes code. While with the assumption of laminar flow, wake oscillation akin to the bluff-body shedding has been observed previously, the Sts is found to drop to about 0.03 when a ‘turbulent’ boundary layer is assumed. Details of the flow field and unsteady forces, computed for the same conditions as in the experiment, compare reasonably well with the experimental data.The phenomenon produces intense flow fluctuations imparting much larger unsteady forces to the airfoil than that experienced in bluff-body shedding, and may represent the primary aerodynamics of stall flutter of blades and wings.

Isoaxial aerosol sampling: nondimensional representation of overall sampling efficiency

Accurate aerosol measurements of ambient and industrial air environments are essential for the protection of human health. In this study, the overall aerosol sampling efficiency of a tubular thin-walled inlet, sampling isoaxially from environmental airflows, has been determined by a dynamic evaluation technique for various values of particle size, wind and inlet velocities, and inlet size. With the assumption of laminar flow, models developed from the results discriminate the dominant mechanisms that modify the sample properties during sampling and evaluate quantitatively the possible sampling errors for relatively wide ranges of sampling conditions. For Stokes numbers less than 0.03, the sampling efficiencies are 100 f 20%, while for Stokes numbers larger than about 0.3 particle losses in the inlet become significant. On the basis of a large number of experimental data, the overall sampling efficiency of the inlet has been described accurately by a new nondimensional parameter consisting of Stokes number, gravitational deposition parameter, and Reynolds number.

On the Laminar Flow Characteristics of Conical Bearings. Part I—Analytical Approach

An analysis has been made of the characteristics of externally pressurized central recess conical bearings with nonconstant film thickness under the assumption of isothermal laminar flow of a viscous incompressible fluid. The flow in the narrow gaps that may be convergent, constant, or divergent has been approximately determined on the basis of the lubrication theory with convective inertia neglected except for that part which is due to rotation. The pressure distribution along the gap, the load capacity, and the torque of the bearings, were theoretically predicted. It was found that, while the gap is very narrow, both the load capacity and the torque for the convergent case decrease moderately, and for the divergent case increase significantly with respect to the constant gap bearing, provided with flow rate, rotational velocity and the film thickness at the outlet of the gap are the same.

Computation of the asymmetric vortex pattern for bodies of revolution

The three-dimensional flowfield surrounding a slender body of revolution at angle of attack was solved through numerical integration of the complete Navier-Stokes equations. The leeside vortex pattern was computed for two separate sets of conditions. First, a flowfield containing laterally symmetric vortices was computed for a three-caliber ogive cylinder at Mach number 1.98 and angle of attack of 20 deg. Second, a flowfield containing laterally asymmetric vortices was computed for a cone cylinder at Mach number 1.6 and angle of attack of 30 deg. Both cases used a laminar flow assumption. All results were obtained on a CRAY-1 computer utilizing MacCormack's algorithm as vectorized by Shang. The computed results compared favorably with the two sets of experimental data used, in that all the primary flow features were captured.

Magnetic particle capture and buildup on a current-carrying wire

Video studies of particle capture on a single current-carrying wire set in the axial and the cross-flow configurations show significant levels of particle accumulation at moderate levels of operating current and at practical values of flow rate. The buildup of particles in both the axial and the crossflow configurations are shown to follow theoretical predictions. Studies of trajectories in the axial flow configuration demonstrate that an assumption of laminar flow of the slurry past the wire provides a better theoretical model than one of ideal flow.