Convective Inertia Research Articles

Convective inertia effects in wall-bounded thin film flows

We apply the boundary layer equations to inertial flow in wall bounded films that might be characterized as ‘thin’, say ɛ ≤ 0.1 where ɛ is the ratio of the characteristic lengths, yet to which the lubrication approximation of Reynolds no longer applies. Two particular flow geometries are investigated, nominally parallel plates and nominally inclined plates, both with and without spatially periodic perturbation of the stationary plate. A Galerkin-B spline formulation of the governing equations is employed, and we rely on parametric continuation to obtain solutions at higher values of the Reynolds number. In particular, we are able to demonstrate that the boundary layer equations yield accurate results for a wide range of Reynolds numbers when the aspect ratio is less than 1/10. We also find that in both nominally parallel and nominally inclined geometries the sign of the inertial force correction is determined by the film contour in the neighborhood of the exit, this result might have implications in the design of MEMS devices.

Numerical procedure for fluid flow in a pipe performing transverse oscillations

AbstractNumerical procedure for the analysis of fluid flow in a tube performing transverse oscillations is developed. The formulation of the problem is presented in differential equation form and a finite element model is developed leading to the first‐order matrix differential equation. The fluid flow model incorporates transverse oscillation of the boundary through the convective inertia terms. Modal decomposition of the solution is performed and a technique for numerical solution of the finite element problem incorporating parametric vibrations is developed. Numerical results provide insight into the problem of fluid flow control by transverse vibrations of the tube. Copyright © 2006 John Wiley & Sons, Ltd.

Numerical Study on Mass Transport Enhancement in Oscillatory Flow of Avian Lung Model

It is well known that the airflow in the gas exchange bronchi in avian lung has a unidirectional nature. Since the direction of the flow is against the blood flow, the gas exchange efficiency of avian respiration is higher than that of mammalian counterpart. To clarify flow phenomena in avian lungs, oscillatory flow fields and concentration fields in a right angle branched tube, model bifurcation of avian trachea, were numerically studied. The three-dimensional incompressible Navier-Stokes equations were solved by SIMPLE method, while the convection equation of concentration was solved by CIP method based on the results of flow simulation. The results showed that separation vortex observed at the entrance of a side-daughter tube during inspiration drove the unidirectional net flow from the side-daughter tube to the daughter tube. Due to the convective inertia, unidirectional net flow persisted even in the expiration. It was clearly shown that the unidirectional net flow strongly enhanced axial mass transport. The effect of constriction just upstream of the bifurcation was also studied and increase in the magnitude of unidirectional net flow was observed in the case with constriction.

Frequency Dependency of Measured and Predicted Rotordynamic Coefficients for a Load-On-Pad Flexible-Pivot Tilting-Pad Bearing

Experimental dynamic-stiffness-coefficient results are presented for a high-speed, lightly loaded, load-on-pad, flexible-pivot tilting-pad (FPTP) bearing. Results show that the real parts of the direct dynamic-stiffness are quadratic functions of the excitation frequency. Frequency independent [M], [K], and [C] matrices can be used in place of frequency dependent [K] and [C] matrices to model the FPTP bearing for the conditions tested. The model reduction that results in moving from twelve degrees of freedom (three degrees of freedom for each of four pads) to two degrees of freedom in the bearing reaction model seems to account for most of the observed and predicted frequency dependency. Predictions indicate that pad and fluid inertia have a secondary impact for excitation frequencies out to synchronous frequency. Experimental results are compared to numerical predictions from models based on: (i) The Reynolds equation, and (ii) a Navier-Stokes (NS) equations bulk-flow model that retains the temporal and convective fluid inertia terms. The NS bulk-flow model results correlate better with experimental dynamic stiffness results, including added-mass terms. Both models underestimate the measured added-mass coefficients for the full excitation range; however, they do an adequate job for excitation frequencies up to synchronous frequency. The advantage of using a frequency-independent [M]-[K]-[C] model is that rotordynamic stability calculations become noniterative and much quicker than for a frequency dependent [K]-[C] model. However, these results only apply to this bearing at the conditions tested. Conventional tilting pad and/or FPTP bearings with different geometry and operating conditions (or even this FPTP bearing at higher loads) may require a frequency-dependent [K]-[C] model.

Modified log-wake law for zero-pressure-gradient turbulent boundary layers

This paper shows that the turbulent velocity profile for zero-pressure-gradient boundary layers is affected by the wall shear stress and convective inertia. The effect of the wall shear stress is dominant in the so-called overlap region and can be described by a logarithmic law in which the von Karman constant is about 0.4 while the additive constant depends on a Reynolds number. The effect of the convective inertia can be described by the Coles wake law with a constant wake strength about 0.76. A cubic correction term is introduced to satisfy the zero velocity gradient requirement at the boundary layer edge. Combining the logarithmic law, the wake law and the cubic correction produces a modified log-wake law, which is in excellent agreement with experimental profiles. The proposed velocity profile law is independent of Reynolds number in terms of its defect form, while it is Reynolds number dependent in terms of the inner variables. The modified log-wake law can also provide an accurate equation for skin friction in terms of the momentum thickness. Finally, by replacing the logarithmic law with van Driest's mixing-length model in which the damping factor varies with Reynolds number, the modified log-wake law can be extended to the entire boundary layer flow.

Effects of fluid inertia in magneto-hydrodynamic annular squeeze films

The effects of fluid inertia on the squeeze film behaviors between two parallel annular disks with an electrically conducting fluid in the presence of a transverse magnetic field are analyzed. The local inertia and the convective inertia of the magneto-hydrodynamic fluid flow are considered in the study. Analytical expressions for the magneto-hydrodynamic squeeze film characteristics are obtained using the momentum approximation method. The results are compared with those based upon the assumption of non-inertial flow. It is found that the inertia correction factor in the magneto-hydrodynamic load-carrying capacity is more pronounced with large Hartmann numbers.

Oscillatory Flow Structure and Unidirectional Flow in Model Avian Bifurcation

In the circular channel of avian lungs, there exists unidirectional flow, which is thought to be induced by the mechanism of 'aerodynamic valves'. To clarify flow phenomena in the avian lung, oscillatory flow in a right angle branched tube was experimentally studied. Periodical variation of flow rate was measured with Particle-Imaging velocimetry (PIV). Velocity fields near the bifurcation were visualized with illuminated tracers and measured by PIV technique. The main concern was focused on the separation vortex near the bifurcation and convective inertia, which were found to cause unidirectional net flow from a side-daughter tube to a daughter tube. Based on the experimental observation, a flow model was proposed. It was suggested that the periodical variation of pressure drop induced by the separation vortex near the bifurcation in the inspiratory phase should work as the 'aerodynamic valves', and cause the unidirectional flow. Due to convective inertia, the unidirectional flow persisted even in the expiratory phase, in which no vortex existed near the bifurcation.

On probability density function equations for particle dispersion in a uniform shear flow

The paper examines a fundamental discrepancy between two probability density function (PDF) models, the kinetic model (KM) and generalized Langevin model (GLM), currently used to model the dispersion of particles in turbulent flows. This discrepancy is manifest in particle dispersion in an unbounded simple shear flow where model predictions for the values of the streamwise fluid-particle diffusion coefficients are not only different but are of opposite sign. It is shown that this discrepancy arises through a neglect of the inertial convection term in the GLM equation for the mean carrier flow velocity local to a particle which eventually leads to algebraic forms for the particle-fluid diffusion coefficients. Evaluating this term for a Gaussian process leads to identical results for both PDF formulations. This also resolves a fundamental long-standing discrepancy in previous forms reported for the passive scalar diffusion coefficients in a simple shear flow where similar assumptions were made. Avoiding this assumption, the exact solutions are given for the dispersion of particles in this simple shear flow case derived from the solution of the GLM PDF equation which show explicitly the dependence on the particle response time and the strain rate, both normalized on the integral timescale of the turbulence. The analysis shows that the particle diffusion coefficient in the streamwise direction is negative when the strain rate a certain value. The origin of negative diffusion coefficients is explained and their influence is shown in the way in which the mean concentration and mean velocity flow fields of the particle and carrier flow (seen by the particle) evolve with time for particles released from the centre of the shear.

Direct Numerical Simulations of Micro-Bubble Expansion in Gas Embolotherapy

We are currently developing a novel gas embolotherapy technique that involves the selective, acoustic vaporization of liquid perfluorocarbon droplets in or near a tumor as a possible treatment for cancer The resulting bubbles can then stick within the tumor vasculature to occlude blood flow and "starve" the tumor The potential development of high stresses during droplet vaporization is a major concern for safe implementation of this technique. No prior study, either experimentally or theoretically, addresses this important issue. In this work, the acoustic vaporization procedure of the therapy is investigated by direct numerical simulations. The nonlinear, multiphase, computational model is comprised of an ideal gas bubble surrounded by liquid inside a long tube. Convective and unsteady inertia, viscosity, and surface tension affect the bubble dynamics and are included in this model, which is solved by a novel fixed-grid, sharp-interface, moving boundary method. We assess the potential for flow-induced wall stresses to rupture the vessel or damage the endothelium during vaporization under a range of operating conditions by varying dimensionless parameters--Reynolds, Weber, and Strouhal numbers, inertial energy and initial droplet size. It is found that the wall pressure is typically highest at the start of the bubble expansion, but the maximum wall shear stress occurs at a later time. Smaller initial bubble diameters, relative to the vessel diameter, result in lower wall stresses.

Effects of couple stresses and convective inertia forces in parallel circular squeeze‐film plates

A theoretical study of the combined effects of non‐Newtonian couple stresses and fluid inertia forces on the squeeze‐film behaviors for parallel circular plates is presented in this paper. Based upon the micro‐continuum theory, the Stokes constitutive equations are used to account for the couple stress effects resulting from the lubricant blended with various additives. The convective inertia forces included in the momentum equation are approximated by the mean value averaged across the fluid film thickness. Numerical solutions for the squeezing film characteristics are presented for various values of couple stress parameter and Reynolds number. Comparing with the classical Newtonian non‐inertia flow, the combined effects of couple stresses and convective inertia forces result in a larger load‐carrying capacity and therefore, increase the response time of the squeezing film plates.

A Study on Squeeze Films Between Porous Rubber Surface and Rigid Surface: Analysis Based on the Viscoelastic Continuum Model

The squeeze-film effect between a porous rubber surface and a rigid surface has been investigated as a problem of viscoelastic hydrodynamic lubrication (VEHL). An axisymmetric continuum model is introduced to estimate the surface deformation of a cylindrical porous rubber block based on a three-element viscoelastic model. The coefficients in the viscoelastic constitutive equation are experimentally determined and then the deformation of the porous rubber block is calculated by the FEM technique. The approximate solutions for the fluid pressures in the squeeze film are obtained from the equation of motion, which includes both local and convective inertia terms, and the continuity equation, using the perturbation method. Experimental data on the squeeze-film pressures and forces are also obtained under the sinusoidal squeezing motion of a rigid plate facing a cylindrical porous rubber block. It is found that the difference between the VEHL solutions and the EHL (elastohydrodynamic lubrication) solutions becomes more marked for a higher frequency of squeeze oscillation due to the effect of viscoelasticity of the porous rubber. The VEHL solutions hence correspond better to the measured results and yield a smaller surface deformation of the porous rubber block than the EHL solutions as the frequency of squeeze oscillation increases. The results also show that the fluid inertia effect due to the flow in the squeeze film becomes noticeable for a higher frequency of the squeezing motion as the effect of viscoelasticity of the porous rubber.

Maps of precipitation by source region, binned by IMF, with inertial convection streamlines

We present maps of ionospheric precipitation regions, based on 11 years of DMSP particle data, binned by the interplanetary magnetic field (IMF), with superposed SuperDARN convection streamlines gathered under similar conditions. The convection patterns are transformed into an inertial coordinate system. The maps, which include both the nightside and dayside, are created in a fully automated fashion, with, for example, the cusp centered at its centroid latitude for each half hour bin of MLT, with a latitudinal width equal to the statistical difference between the poleward and equatorward edges. The mantle asymmetry about noon does not fit the pattern expected from simple theoretical considerations (namely, that the mantle should be thicker postnoon for positive By in the Northern Hemisphere). The mantle is appreciably thicker prenoon than postnoon, especially for positive By but also even for negative By. This asymmetry matches the SuperDARN convection flows, in which, irrespective of the sign of By, most of the conversion of closed field lines to open occurs prenoon. Quantitatively expressed, for southward IMF, the potential encompassed by flux crossing the open‐closed boundary prenoon (0600–1200 MLT) exceeds that for postnoon (1200–1800 MLT) by 30 kV to 15 kV for By > 3 nT and by 30 kV to 20 kV for By < −3 nT. The mantle shape thus matches convection pattern variations. Only ∼25–35% of the dayside open‐closed field line conversion occurs within the particle cusp, with the lower number appropriate to northward IMF. Most closed‐to‐open field line conversion occurs away from noon. Merging is thus active throughout the frontside magnetosphere. Field lines that merge well away from noon do not experience enough particle inflow against the solar wind velocity to produce anything more than a weak, deenergized (mantle) precipitation. The boundary between the dusk cell and dawn cells consistently coincides with one edge of the cusp. IMF By also controls where most of the nightside reconnection occurs. For positive Bz and By > 3 nT, 31 kV reconnects from 1800 to 2400 MLT, but only 14 kV reconnects from 0000 to 06000 MLT. The convection reversal boundary (CRB) consistently coincides with the nightside open‐closed particle boundary (OCB). On the dayside, the CRB lies equatorward (poleward) of the OCB in the postnoon (prenoon) sector for By < 0 (By > 0). This shift is consistent with the effects of an interhemispheric current produced by the partial penetration of the IMF By into the frontside magnetosphere.

Shallow Water Wave Propagation in Convectively Accelerating Open-Channel Flow Induced by the Tailwater Effect

Propagation of shallow water waves in viscous open-channel flows that are convectively accelerating or decelerating under gradually varying water surface profiles is theoretically investigated. Issues related to the hydrodynamics of wave propagation in a rectangular open channel are studied: the effect of viscosity in terms of the Manning coefficient; the effect of gravity in terms of the Froude number; wave translation and attenuation characteristics; nonlinearity and wave shock; the role of tailwater in wave propagation; and free surface instability. A uniformly valid nonlinear solution to describe the unsteady gradually varying flow throughout the complete wave propagation domain at and away from the kinematic wave shock as well as near the downstream boundary that exhibits the tailwater effect is derived by employing the matched asymptotic method. Different scenarios of hydraulically spatially varying surface profiles such as M1, M2, and S1 type profiles are discussed. Results from the nonlinear wave analysis are further interpreted and the influence of the tailwater effect is identified. In addition to the nonlinear wave analysis, a linear stability analysis is introduced to quantify the impact from such water surface profiles on the free surface instability. It is shown that the asymptotic flow structure is composed of three distinct regions: an outer region that is driven by gravity and channel resistance; a near wave shock region dominated by the convective inertia, pressure gradient, gravity and channel resistance; and a downstream boundary impact region where the convective inertia, pressure gradient, gravity and channel resistance terms are of importance. The tailwater effect is demonstrated influential to the flow structure, free surface stability, wave transmission mechanism, and hydrostatic pressure gradient in flow.

Inertial convection in rotating fluid spheres

The onset of convection in the form of inertial waves in a rotating fluid sphere is studied through a perturbation analysis in an extension of earlier work by Zhang (1994). Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived and new results for the case of a nearly thermally insulating boundary are obtained.

直角分岐管内振動流の数値解析(G02-6 流体,G02 バイオエンジニアリング部門)

To clarify flow phenomena in avian lung, oscillatory flow in a right angle branch was numerically studied in the range of dimensionless tidal volume, v_γ/a^3, of 10 to 80, and dimensionless frequency, α^2, of 8 to 40. The results show that the pressure drop caused by separation vortex at the entrance of side-daughter tube in the inspiratory phase drives unidirectional (circular) flow from the side-daughter tube to the daughter tube. Due to convective inertia, the unidirectional flow persists even in the expiratory phase, in which no vortex exists at the entrance of the side-daughter tube. By visualizing the streaming of fresh gas inspired from the mother tube, it is also shown that the unidirectional flow strongly enhances axial gas transportation in the process of avian respiration.

Effects of surface waves on a turbulent current over a smooth or rough seabed

Laboratory experiments by earlier authors have shown that the near-surface velocity of an otherwise uniform current is reduced by following waves, but is increased by opposing waves. By a boundary-layer analysis with depth-dependent eddy viscosities, we show analytically that this is the consequence of second-order effects of wave-current interaction. Physical effects of waves on the current profile due to the moving free surface, wave attenuation and convective inertia are discussed. Comparisons with available experiments for smooth and rough seabeds are discussed. New predictions of the longitudinal variations along the current are made.

Many-body Oseen hydrodynamic interactions

We consider the many-sphere hydrodynamic interactions in the incompressible, viscous fluid, under small Reynolds number Re conditions. The interactions are analysed in the framework of the Oseen equation of motion, with the aid of the respective Green tensor, accounting for the convective inertia of the fluid. The hydrodynamic forces, exerted by the fluid on the spheres, are described by means of the multiple scattering series. The properties of the Oseen velocity field of the fluid, generated by the many-sphere hydrodynamic interactions, are contrasted with the features of the respective Stokes velocity field.

Theoretical Analysis of the Incompressible Laminar Flow in a Macro-Roughness Cell

The present work deals with the analysis of the incompressible laminar shear driven flow in a channel of which one of the walls carries a macro roughness pattern while the opposite one has a parallel velocity. The problem is discussed from the standpoint of lubrication theory and it is shown that the usual simplified models as the Reynolds or the Stokes equations are not applicable. Numerical results are presented for three types of two dimensional macro-roughness and two versions of a three dimensional one. It is shown that a pressure generation effect occurs with increasing the relative importance of convective inertia. Previous analyses found in the literature discussed only the increase of the shear stress due to the presence of the macro roughness but the lift effect due to the pressure generation has never been enlightened up to now. It is further discussed that, extrapolated to a very large number of macro roughness characterizing a textured surface, this new effect could be added to the other lift generating mechanisms of the lubrication theory. It could thus bring a different light on inertia effects stemming from the use of textured surfaces.

Forced Convective Heat Transfer in Metallic Fibrous Materials

A numerical study is reported for high Reynolds number forced convection in a channel filled with rigid metallic fibrous materials of high porosity. The effects of convective and form inertia, viscous shear, and thermal dispersion are all considered together. Inertia and thermal dispersion are modeled. The numerical results suggest that heat transfer rate increases with increasing Reynolds number within a range, but not significantly beyond that range. The heat transfer rate also increases with stagnant thermal conductivity, and decreases with Darcy number. The fiber thickness was found to have significant influence on thermal dispersion. The range of applicability of the local volume averaging in terms of the significant parameters is discussed.

Forced heat convection in a reciprocating duct fitted with 45 degree crossed ribs

This experimental study investigated heat-transfer physics of forced convection in a reciprocating square duct fitted with 45° crossed ribs on two opposite walls. The parametric conditions involved several Reynolds, pulsating and buoyancy numbers, respectively, in the ranges of 600–10 000, 0–10, and 0–0.14 with five different reciprocating frequencies tested, namely, 0.67, 1, 1.33, 1.67 and 2 Hz. The rib-induced flows in the static duct produced an augmentation of heat transfer in the range of 260–300% compared to the smooth-walled situation. The reciprocating heat-transfer data reconfirmed the appearance of large-scale wavy-like axial heat transfer distribution that differed significantly from the stationary results. The manner in which the pulsating force and convective inertia, with and without buoyancy interaction, interactively affected the local heat transfer along the rib-roughened surface was illustrated using a number of experimentally based observations and extrapolations. The buoyancy interaction in the reciprocating duct reduced heat transfer, which effect was enhanced by increasing the pulsating number, but appeared to be a weak function of Reynolds number. When the Reynolds and pulsating numbers were relatively low, a range of heat transfer impediments, that could lead the spatial-time averaged heat-transfer to levels about 71% of nonreciprocating values, was observed. A further increase of pulsating number resulted in a subsequent heat-transfer recovery, which tendency could lead to heat-transfer improvement from the nonreciprocating level. An empirical correlation to evaluate the spatial-time averaged heat transfer over the reciprocating ribbed duct was developed to assist the design activity. The possibility to further enhance heat-transfer via the use of angled ribs in a reciprocating duct is confirmed, but it is important to ensure that the range of reciprocating flow parameters produced does not create heat-transfer impediment in order to avoid overheating situations.