Swirling flows in horizontally vibrated beds of dense granular materials

In a series of experiments, a granular material in a rectangular container with two hollow cylinders was studied as it underwent horizontal vibrations. At the peak values of acceleration, novel swirling granular flows were observed in the cylinders while the grains cascaded down the outer surface of the piles that formed outside the cylinders. Computer simulations were performed that supported our interpretation of the behaviour observed in the experiments.     

Non equilibrium gas-liquid flows in variable cross section ducts

The behaviour of two-phase high velocity flows in variable cross section ducts was investigated using a one-dimensional numerical model developed for the study of the annular flow configuration. Heat, mass, and momentum transfer between the phases during the flow were considered. The validation of the calculation procedure was made with some experimental data for the air-water couple, while the main application concerned the evaluation of momentum transfer from an expanding gas to an entrained liquid stream in droplet form. A liquid metal-gas flow was considered to simulate the process taking place in a plant where electrical power is generated by a liquid metal flowing in a magnetic field (MHD). The effectiveness of energy and momentum transfer between the liquid and the gas phase during the expansion was evaluated and the influence of nozzles with different convergence angles was investigated.     

Freezing in forced convection flows inside ducts: A review

The present work gives an overview about the recent developments in research on freezing phenomena in forced convection flows inside ducts. Emphasis is given to the fundamental aspects of the phenomena observed in the solidification processes as well as on the analytical and numerical modelling aspects for this kind of problems. The paper deals with solidification problems inside tubes, parallel plate channels, curved rectangular channels and in diverging rectangular channels. Additionally, some new experimental and numerical results on solidification in duct flows are shown from the current research program in Darmstadt on freezing phenomena.     

Effects of the side walls on starting flows in ducts

This article considers the effects of the side walls on the unsteady flow of an incompressible viscous fluid in a duct of uniform cross-section. In order to show the effects of the side walls, three illustrative examples are given. They are: the starting flow in a duct of semicircular cross-section, the starting flow in a duct of rectangular cross-section and the starting flow in a duct of circular cross-section. The velocity distributions and the volume fluxes obtained for these flows are compared and it is shown that the flow in a duct of semicircular cross-section reaches steady state earlier than those for the flow in a duct of circular cross-section and for the flow in a duct of square cross-section. It is found that there are remarkable effects of the side walls of a duct on the required time to attain the asymptotic values of flow properties.     

Shock-fitting method for two-dimensional inviscid,steady supersonic flows in ducts

Summary A numerical technique to solve the Euler equations for two-dimensional, steady, inviscid, supersonic flows in ducts is presented. The technique is second-order accurate and is based on the-scheme plus shock-fitting method. Many cases have been tested. The method used and the results obtained demonstrate the versatility of the technique specially if confronted with analogous methods that use shock-capturing techniques.

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Sommario Viene presentato un metodo numerico per l'integrazione delle equazioni di Eulero per flussi supersonici, bidimensionali, stazionari, non-viscosi in condotti. La tecnica, che possiede una accuratezza del secondo ordine, è basata sui metodi del-scheme e dello shock-fitting. Molti sono stati i casi provati. Il metodo usato ed i risultati ottenuti dimostrano la versatilità della tecnica, specialmente se confrontata con metodi analoghi che fanno uso di tecniche shock-capturing.

     

Numerical simulation for rotating internal weakly viscoelastic flows in rectangular ducts

The present work develops a numerical method for the solution of rotating internal weakly viscoelastic flows in rectangular ducts for dimensionless parameters such as the Reynolds, Rossby and Weissenberg numbers, taken respectively in the intervals between 171 and 12000, 0.047 and 1/12 and up to 1/10000. It is shown that the usual counter‐rotating double‐vortex configuration of secondary flow breaks down with the increase of the Reynolds number (over the threshold of 171). For higher Reynolds numbers such as 7500 and 12000 the secondary flow diffuses to the interior of the duct where it assumes a fully developed configuration and the transition to the turbulence structure is observed. The Sobolev norms increase almost proportionally to the increase of the Reynolds number, and play an essential role for more complex problems involving transition to turbulence modelling. Copyright © 2002 John Wiley & Sons, Ltd.     

Analytical solutions for laminar fully developed flows in double-sine shaped ducts

Fully developed, constant property, laminar flows in double-sine shaped ducts are considered. This cross section represents a limiting inter-plate channel geometry in plate heat exchangers. Accurate analytical solutions based on the Galerkin integral method are presented. Heat transfer with both T and H1 thermal boundary conditions is analyzed; they simulate the most fundamental practical heating/cooling applications. Velocity and temperature distributions, along withfRe, Nu _T , andNu _H1 results for flows in double-sine ducts of different aspect ratios (1/8 ≤γ ≤ 8) are presented. Effects of the relative cross-sectional geometry and thermal boundary conditions are delineated. A comparison of the thermal-hydraulic performance with that of other compact channel geometries is made. The results suggest an optimum (Nu/fRe) performance in a double-sine duct of aspect ratio near unity.     

Predicting transition in two- and three-dimensional separated flows

This paper is concerned with the numerical prediction of two- and three-dimensional transitional separated flows of turbomachinery interest. The recently proposed single-point transition model based on the use of a laminar kinetic energy transport equation is considered, insofar as it does not require to evaluate any integral parameter, such as boundary-layer thickness, and is thus directly applicable to three-dimensional flows. A well established model, combining a transition-onset correlation with an intermittency transport equation, is also used for comparison. Both models are implemented within a Reynolds-averaged Navier–Stokes solver employing a low-Reynolds-number k–ω turbulence model. The performance of the transition models have been evaluated and tested versus well-documented incompressible flows past a flat plate with semi-circular leading edge, namely: tests T3L2, T3L3, T3L5, and T3LA1 of ERCOFTAC, with different Reynolds numbers and free-stream conditions, the last one being characterized by a non-zero pressure gradient. In all computations, the first model has proven as adequate as or superior to the second one and has been then applied with success to two more complex test cases, for which detailed experimental data are available in the literature, namely: the two- and three-dimensional flows through the T106 linear turbine cascade.     

On stress distribution in flows of viscoelastic fluids through ducts with porous walls

Summary In continuation of an earlier investigation, the present paper discusses the stress distribution in the inertialess flow of a viscoelastic fluid confined between two plane parallel walls, in which the upper wall moves with a constant velocity while the lower is held at rest with a uniform constant suction applied on its surface. However, the stress field is discussed in detail for the case when the upper wall is also held at rest and the effects arising due to application of suction are pointed out. The most important difference in the behaviour of viscoelastic fluid, compared with that ofNewtonian fluid, lies in the fact that the gradient of the normal stress component in the horizontal direction depends on the distance from the walls.A short discussion has also been provided for the flow in a cylindrical tube with uniform constant suction applied on its surface. Though not evident from general considerations, it is seen that the situation here also is quite similar to that of plane flow.

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Zusammenfassung In Fortsetzung einer früheren Untersuchung wird in der vorliegenden Arbeit die Spannungsverteilung in einer viskoelastischen Flüssigkeit diskutiert, die trägheitslos zwischen zwei parallelen Wänden strömt, wenn die obere Wand mit konstanter Geschwindigkeit bewegt wird und an der unteren, in Ruhe befindlichen eine gleichförmige konstante Absaugung erfolgt. Das Spannungsfeld wird indessen im einzelnen nur für den Spezialfall diskutiert, daß auch die obere Wand ruht, und die infolge der Absaugung entstehenden Effekte werden aufgezeigt. Der wichtigste Unterschied im Verhalten einer viskoelastischen Flüssigkeit, verglichen mit einerNewtonschen Flüssigkeit, besteht darin, daß der Gradient der Normalspannungskomponente in horizontaler Richtung vom Wandabstand abhängt.Abschließend wird noch die Strömung durch ein zylindrisches Rohr mit gleichmäßiger konstanter Absaugung kurz diskutiert. Man findet, daß die Situation hier ganz ähnlich ist wie bei der ebenen Strömung, wenngleich dies nicht aus allgemeinen Betrachtungen gefolgert werden kann.

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Paper presented at the annual meeting of German Rheologists held in Berlin, May 11–13, 1970.     

Development of secondary flows in viscoelastic curved ducts and the influence of outlet region

This paper presents numerical simulations of Newtonian and viscoelastic flows through a 180° curved duct of square cross section with a long straight outlet region. A particular attention is paid to the development of the flow in the output rectangular region after the curved part. The viscoelastic fluid is modeled using the constitutive equation proposed by Phan–Thien–Tanner (PTT). The numerical results, obtained with a finite-volume method, are shown for three different Dean numbers (125,137,150)$(125,137,150)$ and for three Deborah numbers (0.1,0.2,0.3)$(0.1,0.2,0.3)$. The necessary outlet length to impose boundary conditions is presented and discussed for these cases. Streamlines and vortex formation are shown to illustrate and analyze the evolution of the secondary flow in this region.     

Bypass transition through interactions of localized disturbances in wall-bounded flows

A new mechanism bypass in a wall-bounded internal flow is proposed and the proposal is checked by direct numerical simulations of high temporal and spatial resolution. The mechanism is based on the interactions of the localized perturbations, rather than the effect of a single perturbation investigated so far in the classical bypass transition process. It is first shown by theoretical considerations that two pairs of quasistreamwise vortices can interact near the wall in such a manner that the compression (stretching) of the existing wall-normal vorticity induced by one of the pairs can enhance a new streamwise vorticity zone that can lead to new coherent structures and enhance considerably the transition process. Direct numerical simulations confirm this hypothesis.     

Flow pattern transition in liquid-liquid flows with a transverse cylinder

The effect of a cylindrical bluff body on the interface characteristics of stratified two-phase, oil-water, pipe flows is experimentally investigated with high speed Particle Image Velocimetry (PIV). The motivation was to study the feasibility of flow pattern map actuation by using a transverse cylinder immersed in water in the stratified pattern, and particularly the transition from separated to dispersed flows. The cylinder has a diameter of 5 mm and is located at 6.75 mm from the bottom of the pipe in a 37 mm ID acrylic test section. Velocity profiles were obtained in the middle plane of the pipe. For reference, single phase flows were also investigated for Reynolds numbers from 1550 to 3488. It was found that the flow behind the cylinder was similar to the two dimensional cases, while the presence of the lower pipe wall diverted the vorticity layers towards the top. In two-phase flows, the Froude number (from 1.4 to 1.8) and the depth of the cylinder submergence below the interface affected the generation of waves. For high Froude numbers and low depths of submergence the counter rotating von Karman vortices generated by the cylinder interacted with the interface. In this case, the vorticity clusters from the top of the cylinder were seen to attach at the wave crests. At high depths of submergence, a jet like flow appeared between the top of the cylinder and the interface. High speed imaging revealed that the presence of the cylinder reduced to lower mixture velocities the transition from separated to dual continuous flows where drops of one phase appear into the other.     

VITA measurements of transition in transitional hypersonic boundary layer flows

The variable interval time-averaging (VITA) technique is applied to the hot-wire measurements made in three axisymmetric, transitional hypersonic boundary layers. The average duration of conditionally sampled events is used to detect the transition region. It is found that the stability Reynolds number at the peak in the average duration of conditionally sampled events correlates well with the stability Reynolds number that is intermediate to the onset of transition and peak heating. This VITA-identified location of transition moves upstream under the effects of both an adverse pressure gradient and wall cooling; this agrees with previous experimental and computational studies. The VITA technique, therefore, offers an alternative method to obtain details of the location of transition in hypersonic stability experiments, in which hot-wire measurements of the transitioning boundary layers are made.     

Universal threshold of the transition to localized turbulence in shear flows

Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows. By scaling analysis of a disturbed-flow model, this paper proposes a local Reynolds number Re_M to characterize the threshold of transition triggered by finite-amplitude disturbances. The Re_M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion. The lower critical Re_M observed in experiments of plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow are all close to 323, indicating the uniformity of mechanism governing the transition to localized turbulence.