Flow regimes in a single dimple on the channel surface

The boundaries of the domains of existence of flow regimes past single dimples made as spherical segments on a flat plate are determined with the use of available experimental results. Regimes of a diffuser-confuser flow, a horseshoe vortex, and a tornado-like vortex in the dimple are considered. Neither a horseshoe vortex nor a tornado-like vortex is observed in dimples with the relative depth smaller than 0.1. Transformations from the diffuser–confuser flow regime to the horseshoe vortex regime and from the horseshoe vortex flow to the tornado-like vortex flow are found to depend not only on the Reynolds number, but also on the relative depth of the spherical segment. Dependences for determining the boundaries of the regime existence domains are proposed, and parameters at which the experimental results can be generalized are given.     

Flow stability in a channel with porous walls

We study the stability of the flow which forms in a plane channel with influx of an incompressible viscous fluid through its porous parallel walls. Under certain assumptions the study of the stability reduces to the solution of modified Orr-Sommerfeld equation accounting for the transverse component of the main-flow velocity. As a result of numerical integration of this equation we find the dependence of the local critical Reynolds number on the blowing Reynolds number R₀, which may be defined by two factors: the variation of the longitudinal velocity profile with R₀ and the presence of the transverse velocity component. A qualitative comparison is made of the computational results with experimental data on transition from laminar to turbulent flow regimes in channels with porous walls, which confirms that it is necessary to take into account the effect of the transverse component of the main-flow velocity on the main-flow stability in the problem in question.Flows in channels with porous walls are of interest for hydrodynamic stability theory in view of the fact that they can be described by the exact solutions of the Navier-Stokes equations by analogy with the known Poiseuille and Couette flows. However, in contrast with the latter, the flows in channels with porous walls (studies in [1], for example) will be nonparallel.The theory of hydrodynamic stability of parallel flows has frequently been applied to nonparallel flows (in the boundary layer, for example). In so doing the nonparallel nature of the flow has been taken into account only by varying the longitudinal velocity component profiles. A study was made in [2, 3] of the effect of the transverse component of the main flow on its stability. In the case of the boundary layer in a compressible gas, a considerable influence of the transverse velocity component on the critical Reynolds number was found in [2] and confirmed experimentally. A strong influence of the transverse velocity component on the instability region was also found in [3] in a study of the flow stability in a boundary layer with suction for an incompressible fluid.     

Lateral migration of a capsule in a plane Poiseuille flow in a channel

Three-dimensional numerical simulation is presented on the motion of a deformable capsule undergoing large deformation in a plane Poiseuille flow in a channel at small inertia. The capsule is modeled as a liquid drop surrounded by an elastic membrane which follows neo-Hookean law. The numerical methodology is based on a mixed finite-difference/Fourier transform method for the flow solver and a front-tracking method for the deformable interface. The methodology can address large deformation of a capsule over a wide range of capsule-to-medium viscosity ratio. An extensive validation of the methodology is presented on capsule deformation in linear shear flow and compared with the boundary-element/integral simulations. Motion of a capsule in wall-bounded parabolic flow is simulated over an extended period of time to consider both transient and steady-state motion. Lateral migration of the capsule towards the centerline of the channel is observed. Results are presented over a range of capillary number, viscosity ratio, capsule-to-channel size ratio, and lateral location. After an initial transient phase during which the capsule deforms very quickly, the flow of the capsule is observed to be a quasi-steady process irrespective of capillary number (Ca)$(\mathit{Ca})$, capsule-to-channel size ratio (a/H)$(a/H)$, and viscosity ratio (λ)$(\lambda )$. Migration velocity and capsule deformation are observed to increase with increasing Ca$\mathit{Ca}$ and a/H$a/H$, but decrease with increasing λ$\lambda$, and increasing distance from the wall. Numerical results on the capsule migration are compared with the analytical results for liquid drops, and capsules with Hookean membrane which are valid in the limit of small deformation. Unlike the prediction for liquid drops, capsules are observed to migrate toward the centerline for 0.2?λ?5$0.2?\lambda ?5$ range considered here. The migration velocity is observed to depend linearly on (a/H)³$(a/H{)}^3$, in agreement with the small-deformation theory, but non-linearly on Ca$\mathit{Ca}$ and the distance from the wall, in violation of the theory. Using the present numerical results and the analytical results, we present a correlation that can reasonably predict migration velocity of a capsule for moderate values of a/H$a/H$ and Ca$\mathit{Ca}$.     

Flow of a suspension in a flat channel with porous walls

In the flow of a suspension in a channel with porous walls, when the size of particles of a suspended phase is much less than the width of the channel but greatly exceeds the size of the pores (in particular, in the flow of blood in the plasma separator used in an artificial kidney system [1, 2]), phenomena are observed which apparently cannot be satisfactorily explained by means of the well-known solutions of problems on the motion of a Newtonian fluid [3]. For example, the flow rate of the liquid phase of the suspension through the walls depends on the velocity of the main flow and does not depend on the pressure drop on the wall at fairly high values of it [1, 2]. The present study gives below the formulation and an approximate solution, which explains this effect, of the problem of an incompressible two-phase suspension in a long slit with porous walls which are impermeable in relation to the suspended phase and through which the liquid phase is pumped. Certain effects are taken into account which are caused by the high volume concentration of the suspended phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 37–43, November–December, 1987.     

Flow through a diverging channel: instability and bifurcation

The flow of a viscous fluid along a diverging channel is important practically. The mechanics of the flow also poses many theoretical problems. Some of these problems were considered before the foundation of the Japan Society of Fluid Mechanics, so it is perhaps surprising that their solutions are still so poorly understood. Nonetheless, a revival of interest in the last 20 years has led to progress in our understanding of the early stages of transition to turbulence in a two-dimensional channel. The present paper is a review of this progress in the theory of instabilities and bifurcations as the flux driven steadily along the channel is increased.     

Flow in a symmetric channel with an expanded section

We consider the flow in a symmetric two-dimensional channel with an expanded section. By examining the effect of varying the ratio of the inlet and outlet channel widths, we are able to place the earlier results of Mizushima et al. (Phys. Fluids 8 (1996) 2933) within an entire spectrum of nonlinear phenomena. Laboratory experiments support predicted behaviour in two regions of parameter space and highlight the importance of imperfections in the experimental apparatus.     

Two-phase flow instabilities in a horizontal single boiling channel

A study of the stability of an electrically heated single channel, forced convection horizontal system was conducted by using Freon-11 as the test fluid. Two major modes of oscillations, namely, density-wave type (high frequency) and pressure-drop type (low frequency) oscillations have been observed. The steady-state operating characteristics and stable and unstable regions are determined as a function of heat flux, exit orifice diameter and mass flow rate. Different modes of oscillations and their characteristics have been investigated. The effect of the exit restriction on the system stability has also been studied.A mathematical model has been developed to predict the transient behavior of boiling two-phase systems. The model is based on homogenous flow assumption and thermodynamic equilibrium between the liquid and vapor phases. The transient characteristics of boiling two-phase flow horizontal system are obtained for various heat inputs, flow rates and exit orifice diameters by perturbing the governing equations around a steady state. Theoretical and experimental results have been compared.     

Experimental and numerical investigations on flashing-induced instabilities in a single channel

During the start-up phase, natural circulation BWRs (NC-BWRs) need to be operated at low pressure conditions. Such conditions favor flashing-induced instabilities due to the large hydrostatic pressure drop induced by the tall chimney. Moreover, in novel NC-BWR designs the steam separation is performed in the steam separators which create large pressure drops at the chimney outlet, which effect on stability has not been investigated yet.In this work, flashing-induced oscillations occurring in a tall, bottom heated channel are numerically investigated by using a simple linear model with three regions and an accurate implementation for estimating the water properties. The model is used to investigate flashing-induced instabilities in a channel for different values of the core inlet friction value. The results are compared with experiments obtained by using the CIRCUS facility at the same conditions, showing a good agreement. In addition, the experiments on flashing-induced instabilities are presented in a novel manner allowing visualizing new details of the phenomenon numerical stability investigations on the effect of the friction distribution are also done. It is found that by increasing the total restriction in the channel the system is destabilized. In addition, the chimney outlet restriction has a stronger destabilizing effect than the core inlet restriction. A stable two-phase region is observed prior to the instabilities in the experiments and the numerical simulations which may help to pressurize the vessel of NC-BWRs and thus reducing the effects of flashing instabilities during start-up.     

Stratification of boiling two-phase flow in a single horizontal channel

The objective of this study is to investigate experimentally the stratification phenomena of boiling two-phase flow in a uniformly heated horizontal channel. Two-phase flow stratification due to gravity effects, and consequently its thermal and hydrodynamic behavior, under steady state conditions, have been determined by measuring 16 top and 16 bottom wall temperatures. Six distinct wall temperature profiles are found, and the corresponding flow patterns are discussed. A dimensionless number has been formulated for the prediction of the occurrence of different flow patterns.     

Heat transfer of nanofluids considering nanoparticle migration and second-order slip velocity

The heat transfer of a magnetohydrodynamics nanofluid inside an annulus considering the second-order slip condition and nanoparticle migration is theoretically investigated.A second-order slip condition,which appropriately represents the non-equilibrium region near the interface,is prescribed rather than the no-slip condition and the linear Navier slip condition.To impose different temperature gradients,the outer wall is subjected to q2,the inner wall is subjected to q1,and q1 q2.A modified two-component four-equation non-homogeneous equilibrium model is employed for the nanofluid,which have been reduced to two-point ordinary boundary value differential equations in the consideration of the thermally and hydrodynamically fully developed flow.The homotopy analysis method(HAM) is employed to solve the equations,and the h-curves are plotted to verify the accuracy and efficiency of the solutions.Moreover,the effects of the physical factors on the flow and heat transfer are discussed in detail,and the semi-analytical relation between N uB and NBT is obtained.     

Flow of an Oldroyd-fluid in a contracting channel with a moving boundary

The industrial process of coating flat surfaces with polymeric substances is numerically simulated by solving the full equations of motion for a flow through a contraction with a moving boundary. The four-constant Oldroyd constitutive equation is used to represent the viscoelastic fluid. Some adjustments to existing finite-difference methods are made in such a way as to avoid singular iterative matrices during the solution process. Results are presented for flow situations with Weissenberg numbers up to about three times larger than any previously published results for this problem.     

Flow instability in baffled channel flow

Flow instability in baffled channel flow, where thin baffles are mounted on both channel walls periodically in the direction of the main flow, has been numerically investigated. The geometry considered here can be regarded as a simple model for finned heat exchangers. The aim of this investigation is to understand how baffle interval (L) and Reynolds number (Re) influence the flow instability. With a fixed baffle length of one quarter of channel height (H), ratios of baffle interval to channel height (R_B = L/H) between 1 and 4 are considered. The critical Reynolds number of the primary instability, a Hopf bifurcation from steady flow to time-periodic flow, turned out to be minimum when R_B = 3.08. The friction factor (f) is strongly correlated with the critical Reynolds number for R_B ⩽ 2.5. For the particular cases of R_B = 1.456 and R_B = 1.0, we performed Floquet stability analysis in order to study the secondary instability through which time-periodic two-dimensional flow bifurcates into three-dimensional flow. The results obtained in this investigation are in good agreement with those computed from full simulations, and shed light on understanding and controlling flow characteristics in a finned heat exchanger, quite beneficial to its design.     

Dynamic instabilities of boiling two-phase flow in a single horizontal channel

Dynamic instabilities of two-phase flow associated with refrigerant R-11 in a uniformly heated horizontal in-tube boiling system were experimentally investigated. An experimental setup was designed and built to work in a wide range of mass fluxes G [75–1050 kg/(m² s)], heat fluxes q (0–100 kW/m²), and fluid inlet temperatures T_inlet (2–24°C). Dynamic instability data were obtained under various working conditions. The dependence of oscillation amplitude and period on system parameters is discussed, and the boundaries of various oscillations are located on the steady-state characteristic curves.     

Flow past a thin profile in a channel with permeable working part

An exact solution is obtained to the problem of flow of an ideal incompressible fluid past a thin profile in a straight channel. The channel walls are continuous except for the working part, where they are permeable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 180–185, July–August, 1982.I thank Yu. B. Lifshitz for constant interest in the work.     

Numerical simulation of particle migration in asymmetric bifurcation channel

In this work we provide numerical validation of the particle migration during flow of concentrated suspension in asymmetric T-junction bifurcation channel observed in a recent experiment [1]. The mathematical models developed to explain particle migration phenomenon basically fall into two categories, namely, suspension balance model and diffusive flux model. These models have been successfully applied to explain migration behavior in several two-dimensional flows. However, many processes often involve flow in complex 3D geometries. In this work we have carried out numerical simulation of concentrated suspension flow in 3D bifurcation geometry using the diffusive flux model. The simulation method was validated with available experimental and theoretical results for channel flow. After validation of the method we have applied the simulation technique to study the flow of concentrated suspensions through an asymmetric T-junction bifurcation composed of rectangular channels. It is observed that in the span-wise direction inhomogeneous concentration distribution that develops upstream persists throughout the inlet and downstream channels. Due to the migration of particles near the bifurcation section there is almost equal partitioning of flow in the two downstream branches. The detailed comparison of numerical simulation results is made with the experimental data.