Flow In Diverging Channel Research Articles

G803 自由運動する球を内部に有する拡大管流れ(2)(GS-8 管内流,混相流,粒子系,一般セッション)

G803 自由運動する球を内部に有する拡大管流れ(2)(GS-8 管内流,混相流,粒子系,一般セッション)

G803 自由運動する球を内部に有する拡大管流れ(1)(GS-8 管内流,混相流,粒子系,一般セッション)

G803 自由運動する球を内部に有する拡大管流れ(1)(GS-8 管内流,混相流,粒子系,一般セッション)

Steady nonlinear waves in diverging channel flow

An infinitely diverging channel with a line source of fluid at its vertex is a natural idealization of flow in a finite channel expansion. Motivated by numerical results obtained in an associated geometry (Tutty 1996), we show in this theoretical model that for certain channel semi-angles ? and Reynolds numbers Re := Q/2? (Q is the volume flux per unit length and ? the kinematic viscosity) a steady, spatially periodic, two-dimensional wave exists which appears spatially stable and hence plausibly realizable in the physical system. This spatial wave (or limit cycle) is born out of a heteroclinic bifurcation across the subcritical pitchfork arms which originate out of the well known Jeffery–Hamel bifurcation point at ? =?2(Re). These waves have been found over the range 5 ? Re ? 5000 and, significantly, exist for semi-angles ? beyond the point ?2 where Jeffery–Hamel theory has been shown to be mute. However, the limit of ??0 at finite Re is not reached and so these waves have no relevance to plane Poiseuille flow.

Excitation of Narrow‐Band Pulsations in a Short Portion of Transition from the Smaller Diameter of a Pipe to a Larger Diameter and Possibilities of Preventing Them

By using models of the portions of the circuit of main gas‐compressor stations, data on the frequencies of narrow‐band pressure pulsations have been obtained; these data demonstrate the jet character of flow in divergent channels with angles of opening on one side of 12°47′ and 23°50′. It has been shown that narrow‐band acoustic disturbances are generated in the internal flow with large‐scale hydrodynamic structures. Intense narrow‐band pulsations are prevented by a grid of internal divergent channels in the transition portion with small angles of opening in canals and in excitation of certain disturbances upstream of a short divergent channel.

Divergent channel flow of a liquid crystalline polymer solution

The flow of a `model' lyotropic liquid crystal polymer, (hydroxypropyl)cellulose in water, through a rectangular channel with a divergence in the channel width, is studied by in situ light microscopy. Microscopic texture observations are related to measurements of the flow velocity field, in order to characterize the shear and elongational aspects of the flow and to examine the effects of the divergence from a narrow channel to a wide channel. A strong dependence of flow-induced texture on position in the channel is observed and is related to the interplay of shear and elongational strain. The divergence generates both a perpendicular elongational strain due to the widening of the channel, and subsequently an elongational strain along the flow direction due to the change in flow pattern from quasi-radial to unidirectional down the wide channel. Additionally side wall structure is observed to be more complex than a simple strong alignment, displaying a fine birefringent texture. Finally there is a marked dependence of the macroscopic structure on the strain history of the fluid prior to entry into the channel, indicating that very different structures of, for instance, moulded parts, can result from differences in geometry and fluid treatment prior to entry into the mould itself.

Solutions for Classical Fluid Flow Problems in Porous Domains.

In this work exact solutions for different classical fluid flow problems in porous domains are presented. These problems include the transient Couette flow, Stokes' first and second problems in semi-infinite porous medium, pulsating flow in porous channels, steady flow in convergent and divergent porous channels, transient flow in porous annuli confined between two rotating cylinders and upward moving liquid film in porous domain.

Numerical investigation of free convective flow in divergent channels

Free convective flow for laminar, two-dimensional divergent channels with isothermal boundary conditions has been numerically analyzed. The study examines the effect of semi-vertical angles on the fluid flow and heat transfer rates for a Rayleigh number range of 10 to 4 × 10 4 considering water (Pr = 5.0) and air (Pr = 0.71) as working fluids. The results compare favourably with the existing experimental and numerical results for divergent channels. Comparison with plane channel results shows that there is a significant change in the flow pattern for the divergent channels for different Prandtl numbers and semi-vertical angles. However, the heat transfer results do not deviate much from the plane channel results.

Nonlinear development of flow in channels with non-parallel walls

In Jeffery–Hamel flow, the motion of a viscous incompressible fluid between rigid plane walls, unidirectional flow is impossible if the angle between the walls exceeds a critical value of 2α2 which depends on the Reynolds number. In this paper the nonlinear development of the flow near this critical value is studied through numerical solutions of the two-dimensional Navier–-Stokes equations for flow in divergent channels with piecewise straight walls. It is found that if the angle between the walls exceeds 2α2 then Jeffery–-Hamel flow does not occur, and the solution takes the form of a large-amplitude wave with eddies attached alternately to the upper and lower walls. When viewed in the appropriate coordinate system, far downstream the wave has constant wavelength and strength, although, physically, there is a linear increase in wavelength with distance downstream, i.e. the wavelength is proportional to the channel width. If the angle between the walls is less than 2α2, then the existence (or otherwise) of the wave depends on the conditions near the inlet, in particular the local geometry of the channel. Jeffery–-Hamel flow is obtained downstream of the inlet for angles well below 2α2, but close to but below the critical value, solutions have been obtained with the wave extending (infinitely) far downstream. The wavelengths obtained numerically were compared with those from linear theory with spatially developing steady modes. No agreement was found: the wavelengths from the steady Navier–-Stokes solutions are significantly larger than that predicted by the theory. However, in other important aspects the results of this study are consistent with those from previous studies of the development/existence of Jeffery–-Hamel flow, in particular as regards the importance of the upstream conditions and the subcritical nature of the spatial development of the flow near the critical boundary in the Reynolds number–wall angle parameter space.

Simulation of extraction of velocity from passive scalar data in a two-dimensional diverging channel flow

A technique for determining n-dimensional (n=2,3) velocity fields from measurement of n−1 passive or reactive scalars has recently been developed [Phys. Fluids 7, 754 (1995)]. The method utilizes n linear, first-order, uncoupled hyperbolic equations for n velocity components, derived from transport equations for n−1 scalars and conservation of mass. The velocity is determined by integration along the characteristic curves defined by the hyperbolic equations. Here we present the results of a computational proof-of-concept study for a steady, two-dimensional, diverging channel flow. We consider the effects of the resolution of the grid (and the shape of its elements) on which the scalar is known and its derivatives are approximated, the integration step size used to calculate the velocity components along characteristic curves, and the effects of multiplicative noise introduced into the scalar field. The results show that extraction of the velocity by integration of the equations along characteristics is stable, and that the techniques proposed for removal of singularities are effective. For steady flows, we show that noise in the scalar field measurements can be dealt with by extracting the velocity from the mean of several noisy scalar fields.

Dynamical flow characterization of transitional and chaotic regimes in converging–diverging channels

Numerical investigation of laminar, transitional and chaotic flows in converging–diverging channels are performed by direct numerical simulations in the Reynolds number range 10 < Re < 850. The temporal flow evolution and the onset of turbulence are investigated by combining classical fluid dynamics representations with dynamical system flow characterizations. Modern dynamical system techniques such as timedelay reconstructions of pseudophase spaces, autocorrelation functions, fractal dimensions and Eulerian Lyapunov exponents are used for the dynamical flow characterization of laminar, transitional and chaotic flow regimes. As a consequence of these flow characterizations, it is verified that the transitional flow evolves through intermediate states of periodicity, two-frequency quasi-periodicity, frequency-locking periodicity, and multiple-frequency quasi-periodicity before reaching a non-periodic unpredictable behaviour corresponding to low-dimensional deterministic chaos.Qualitative and quantitative differences in Eulerian dynamical flow parameters are identified to determine the predictability of transitional flows and to characterize chaotic, weak turbulent flows in converging–diverging channels. Autocorrelation functions, pseudophase space representations and Poincaré maps are used for the qualitative identification of chaotic flows, assertion of their unpredictable nature, and recognition of the topological structure of the attractors for different flow regimes. The predictability of transitional flows is determined by analysing the autocorrelation functions and by representing their attractors in the reconstructed pseudophase spaces. The transitional flow behaviour is examined by the geometric visualization of the evolution of the attractors and Poincaré maps until the appearance of a strange attractor at the onset of chaos. Eulerian Lyapunov exponents and fractal dimensions are quantitative parameters to establish the onset of chaos, the persistence of chaotic flow behaviour, and the long-term persistent unpredictability of chaotic Eulerian flow regimes. Lastly, three-dimensional simulations for converging–diverging channel flow are performed to determine the effect of the spanwise direction on the route of transition to chaos.

Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging–diverging channel flows

A study of Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging–diverging channel flows, using spectral element direct numerical simulations, is presented. The time-dependent, incompressible Navier–Stokes and continuity equations are solved for laminar, transitional, and chaotic flow regimes for 100≤Re≤850. Classical fluid dynamics representations and dynamical system techniques characterize Eulerian flows, whereas Lagrangian trajectories and finite-time Lagrangian Lyapunov exponents identify Lagrangian chaotic flow regimes and quantify mixing enhancement. Classical representations demonstrate that the flow evolution to an aperiodic chaotic regime occurs through a sequence of instabilities, leading to three successive supercritical Hopf bifurcations. Poincaré sections and Eulerian Lyapunov exponent evaluations verify the first Hopf bifurcation at 125<Re<150 and the onset of Eulerian chaos at Re≊550. Lagrangian trajectories and finite-time Lagrangian Lyapunov exponents reveal the onset of Lagrangian chaos, its relation with the appearance of the first Hopf bifurcation, the interplay between Lagrangian and Eulerian chaos, and the coexistence of Lagrangian chaotic flows with Eulerian nonchaotic velocity fields. Last, Lagrangian and Eulerian Lyapunov exponents are used to demonstrate that the onset of Eulerian chaos coincides with the spreading of a strong Lagrangian chaotic regime from the vortex region to the whole fluid domain.

An experimental investigation of interfacial instability in superposed flow of viscoelastic fluids in a converging/diverging channel geometry

The interfacial stability of superposed flow of polypropylene (PP) and high-density polyethylene (HDPE) in a converging-diverging channel geometry is experimentally investigated. Using the apparatus and procedures developed in our previous study [20], we have investigated the role of base flow kinematics on the interfacial stability of the HDPE/PP system. A comparison of experimentally determined neutral stability contours and disturbance growth rates in parallel, converging and diverging channel flows has revealed that channel convergence tends to stabilize interfacial disturbances while channel divergence has a destabilizing influence. Moreover, we have shown that the most dangerous wave number when made dimensionless with respect to the thickness of the more elastic and/or viscous component is of 0(1). In addition, based on a simple analysis, we have shown that the mechanism of interfacial instability in two-layer viscoelastic flows is due to the coupling between the perturbation velocity field and the polymeric stress gradient in the base flow.

Transition to chaos in converging–diverging channel flows: Ruelle–Takens–Newhouse scenario

Direct numerical simulations of the transition process from laminar to chaotic flow in converging–diverging channels are presented. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic self-sustained flow regimes. The numerical experiments reveal three distinct bifurcations as the Reynolds number is increased, each adding a new fundamental frequency to the velocity spectrum. In addition, frequency-locked periodic solutions with independent but synchronized periodic functions are obtained. A scenario similar to the Ruelle–Takens–Newhouse scenario of the onset of chaos is verified in this forced convective open system flow. The results are illustrated for different Reynolds numbers using time-velocity histories, Fourier power spectra, and phase space trajectories. The global structure of the self-sustained oscillatory flow for a periodic regime is also discussed.

Symmetry breaking in vortex-source and Jeffery—Hamel flows

The stability and bifurcations associated with the loss of azimuthal symmetry of planar flows of a viscous incompressible fluid, such as vortex-source and Jeffery–Hamel flows, are studied by employing linear, weakly nonlinear and fully nonlinear analyses, and features of new solutions are explained. We address here steady self-similar solutions of the Navier–Stokes equations and their stability to spatially developing disturbances. By considering bifurcations of a potential vortex-source flow, we find secondary solutions. They include asymmetric vortices which are generalizations of the classical point vortex to vortical flows with non-axisymmetric vorticity distributions. Another class of solutions we report relates to transition trajectories that connect new bifurcation-produced solutions with the primary ones. Such solutions provide far-field asymptotes for a number of jet-like flows. In particular, we consider a flow which is a combination of a jet and a sink, a tripolar jet, a jet emerging from a slit in a plane wall, a jet emerging from a plane channel and the reattachment phenomenon in the Jeffery–Hamel flow in divergent channels.

Temporal and spatial adaptive algorithm for reacting flows

A numerical integration scheme for quasi-one-dimensional unsteady flows with finite-rate chemistry is developed and demonstrated. The governing Euler and species-conservation equations are derived; the integration method and the spatial and temporal grid embedding techniques are explained; and results for sample problems involving stream-tube flow with one dissociating gas, shock-tube flow with one dissociating gas, and diverging-channel flow with multiple reactions are presented in extensive graphs and briefly characterized. Accuracy comparable to that of globally fine grid solutions is obtained with significant savings in CPU time.

Features of a reattaching turbulent shear layer in divergent channelflow

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.

Characteristics of Turbulent Flow and Mass Transfer in Divergent Channels of Rectangular Section

The characteristics of turbulent flow and mass transfer in divergent channels of rectangular cross-section were experinlentally investigated and the typical effects of main flow and the secondary flow on mass transfer were discussed. Sherwood number Shx, could be suitably expressed by Reynolds number Rex, and acceleration parameter K. Sherwood numbers Shx, in the entrance region of mass concentration were proportional to Rex, 0.83 for every diver-gent angle in the present experiment. The velocity profiles in the upper region were recognized as a composite structure consisting of those for the inner and outer layers. but it was difficult to predict the velocity profiles in the lower region with the plane jet profile.

Characteristics of Turbulent Flow and Mass Transfer in Divergent Channels of Rectangular Section

The characteristics of turbulent flow and mass transfer in divergent channels of rectangular section were experimentally investigated and the typical effects of main flow and the secondary flow on mass transfer were also discussed. Sherwood number Shx1 could successfully be expressed by Reynolds number Rex1 and acceleration parameter K. Sherwood numbers S__(hx1) in the entrance region of concentration were proportional to R__(ex1)0.83 for any divergent angle, which changed more intensively than R__(ex1)0.8 for the straight channel. The velocity profiles above the axis of divergent channels were recognized as a composite structure consisting of those in the inner and outer layers, but it was difficult to predict the velocity profiles below the axis by those of the plane jet.

Characteristics of Turbulent Flow in Divergent Channels of Rectangular Section

Characteristics of Turbulent Flow in Divergent Channels of Rectangular Section

Effects of separated flow on cotton dust sampling with a vertical elutriator.

The vertical elutriator used for cotton dust sampling was examined theoretically and experimentally to determine airflow patterns and particle transport. The theory of diverging channel flow predicts that a separated eddying flow will occur in the elutriator. This calculation disagrees with the laminar flow assumptions used to predict the size sampling characteristic or cutoff of the elutriator. Smoke injection tests verified random local velocity components and clearly showed that the flow is not uniformly upward and laminar. Particle transport tests indicated that unit density spheres as large as 27 micron can reach the sample on the elutriator filter.