Takashi Masuoka

Stokes’ first problem for an Oldroyd-B fluid in a porous half space

Based on a modified Darcy’s law for a viscoelastic fluid, Stokes’ first problem was extended to that for an Oldroyd-B fluid in a porous half space. By using Fourier sine transform, an exact solution was obtained. In contrast to the classical Stokes’ first problem for a clear fluid, there is a y-dependent steady state solution for an Oldroyd-B fluid in the porous half space, which is a damping exponential function with respect to the distance from the flat plate. The thickness of the boundary layer, which tends to be a limited value, is also different from that of a clear fluid. The effect of viscoelasticity on the unsteady flow in porous media is investigated. It was found if α>1∕4[(αt∕Re)+Re]2, oscillations in velocity occur obviously and the system exhibits viscoelastic behaviors, where α and αt are nondimensional relaxation and retardation times, respectively, Re is Reynold number in porous media. Some previous solutions of Stokes’ first problem corresponding to Maxwell fluid and Newtonian fluid in por...

Unified theoretical prediction of fully developed nucleate boiling and critical heat flux based on a dynamic microlayer model

Abstract A new dynamic microlayer model has been proposed to predict theoretically the heat flux in fully developed nucleate boiling regions including critical heat flux (CHF). In this model, the heat transfer with boiling is mainly attributed to the evaporation of the microlayers which are periodically formed while the individual bubbles are forming. Since the initial microlayer thickness becomes thinner with the increase of wall superheat, both the local evaporation and the partial dryout speed of the microlayer increase. As a result, the time-averaged heat flux during the period of individual bubble has a maximum point, the CHF, at the predicted continuous boiling curve.

DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced. The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations. Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffler function. The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.

CHAOTIC BEHAVIOR AND TRANSITION TO TURBULENCE IN POROUS MEDIA

An experimental study has been made of the chaotic behavior in the transition to turbulence of flow through porous media consisting of a bank of tubes in a narrow gap. Judging from the examination of the correlation dimension and the maximum Lyapunov exponents, we can identify the chaotic behavior in porous media for Re > ∼60. Rapid increase in the maximum Lyapunov exponents was observed for Re > ∼300. Also, the spatial distribution of the Lyapunov exponents is discussed.

Theoretical studies on transient pool boiling based on microlayer model

Abstract An analytical model for transient pool boiling heat transfer was developed in this study. The boiling curves of the transient boiling were obtained based on the microlayer model proposed by the authors and the mechanism of transition from the non-boiling regime to film boiling, i.e., direct transition was theoretically examined. Since the nucleate boiling heat flux is mainly due to the evaporation of the microlayer and its initial thickness decreases rapidly with increasing superheat, the duration of nucleate boiling is markedly decreased as the incipient boiling superheat is increased. It is found that the direct transition is closely connected to the rapid dryout of the microlayer which occupies almost the whole surface at high wall superheat.

Investigation of Flooding Phenomena in PEMFC by Two-Phase Flow Numerical Simulation

Water Problem, which is represented by the flooding and the drying in PEMFC, is one of the critical issues relating to the recent trend of high current density operation of it. For spreading the practical use of PEMFC, we must grasp this problem exactly and resolve it. Two-phase flow numerical simulation is useful for this purpose. In this study, we numerically analyzed a unit-PEMFC two-dimensionally considering the two-phase flow based on the multiphase mixture model developed by Cheng and Wang, adding the authors’ equivalent electric circuit. We simulated not only steady state but also unsteady state. A slightly abrupt change in current density distribution appeared on the point where the interface between the one- and the two-phase zone in GDL was appeared. The distribution of water saturation after cell operation start changed with time passed: the liquid water tend to focus on the GDL after once it spread in both GDL and flow channel.Copyright

Response to “Comment on ‘Stokes’ first problem for an Oldroyd-B fluid in a porous half space’ ” [Phys. Fluids 21, 069101 (2009)]

In this comment, using Fourier sine transform to the governing equation, the authors get a so-called new subsidiary equation without considering the time domain, and claim that we made a mistake at the same stage of the solution process in our previous paper [W. Tan and T. Masuoka, “Stokes’ first problem for an Oldroyd-B fluid in a porous half space,” Phys. Fluids 17, 023101 (2005)]. In this response, we would like to clarify that there is no mistake in our solution and to point out the difference between our equation and their so-called new subsidiary equation.

BIFURCATION OF FLOW AND MASS TRANSPORT IN A CURVED BLOOD VESSEL

A numerical analysis of flow and concentration fields of macromolecules in a, slightly curved blood vessel was carried out. Based on these results, the effect of the bifurcation of a flow on the mass transport in a curved blood vessel was discussed. The macromolecules turned out to be easier to deposit in the inner part of the curved blood vessel near the critical Dean number. Once the Dean number is higher than the critical number, the bifurcation of the flow appears. This bifurcation can prevent macromolecules from concentrating in the inner part of the curved blood vessel. This result is helpful for understanding the possible correlations between the blood dynamics and atherosclerosis.

Transition Process to Turbulent Flow in Porous Media

Turbulence in porous media has attracted much interest recently, and many turbulence models have been proposed [1-12]. However, the mathematical treatments in some turbulence models have been developed without reference to the unique structure of vortices in porous media. The further development of the turbulence model and the theoretical argument in the transition flow regime need the experimental verification of the microscopic flow field in porous media, but the geometric complexity of porous media brings about technical difficulties of the measurement and the visualization. Therefore, we adopt the flow through a bank of cylinders in a narrow gap as a model for the flow through porous media, and perform the PIV (Particle Image Velocimetry) and LIF (Laser Induced Fluorescence) techniques to examine the microscopic flow field in porous media. We have confirmed that the solid matrix in porous media plays an important role in the vortex diffusion. The large vorticity at the throat produces such vortex as the swirl flow. On the other hand, the obstruction due to the solid matrix forces such large vortex as a Karman vortex to be dissipative. Furthermore, the present experimental results are in agreement with our model [2] for the production and dissipation of turbulence.Copyright

Natural Convection Heat Transfer in Vertical Fluid Layers of High Aspect Ratio

A two-dimensional numerical analysis is made on the effect of aspect ratio on flow and heat transfer characteristics of natural convection in a slender fluid layer enclosed between two vertical plates of different temperatures. It is shown that the boundary layer instability induces the hook-shaped flows and that its growth disrupts the large-scale circulatory flow into cellular flows of smaller scales, which in part include the renewed boundary layers. Then it is suggested that there exists a transition region where the average heat transfer coefficient increases with the increase of the height of a vertical fluid layer, as is seen in the transition region from laminar to turbulent natural convection along a single vertical plate. Discussion is also made on the nature of instability to yield cellular flows of smaller scales.Copyright