Spatial structure of the flow through an axisymmetric sudden expansion

Spatio-temporal velocity fields of an axisymmetric sudden expansion were measured using an ultrasonic velocity profiler and analyzed to investigate the transitional scheme of the spatial structure using two-dimensional Fourier transform and proper orthogonal decomposition techniques. The variation of the zero-crossing point, the fluctuation energy directed upstream and the eigenmode spectrum all have the same transitional scheme as a function of the Reynolds number. The transitional scheme can be classified Re _d<1,000 for the laminar regime, Re _d=1,000–3,000 for the transitional regime and Re _d>3,000 for the turbulent regime. Especially, in the transitional regime, we found large changes in the flow structure at Re _d=1,500 and 2,000. The jump at Re _d=2,000 is caused by the change in the flow condition upstream. The jump at Re _d=1,500 clearly shows a change in the spatial structure of the flow.     

Asymmetry in the turbulent flow of a viscoelastic liquid through an axisymmetric sudden expansion

This paper concerns the asymmetry in mean axial velocity distributions for the flow through an axisymmetric sudden expansion of a viscoelastic, shear-thinning aqueous solution of a polyacrylamide (PAA). The asymmetry manifests itself as an azimuthal variation in the length of the recirculation region of the separated flow downstream of the expansion inlet. For water, the flow is found to be axisymmetric. The asymmetry for the PAA flow, which remained unchanged despite alterations to the flow facility, is attributed to the high viscoelasticity of the polymer solution. The conclusion is drawn that the asymmetry is a purely physical feature of such a flow, and not the product of upstream or downstream flow conditions deriving from the flow facility, or the result of geometrical imperfections in the axisymmetric sudden expansion set-up.     

Aerodynamics and heat transfer in cyclones with particle-laden gas flow

Experiments were performed on a 204 mm diameter water-cooled cyclone to measure the pressure drop and heat transfer in different sections of the cyclone. Hot gas at 250°C entered the cyclone with and without suspended particles. Heat transfer and pressure drop in solids-free gas flow were compared with those measured for particle-laden gas flow of different solids.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Turbulent flow of Newtonian and shear-thinning liquids through a sudden axisymmetric expansion

 Measurements are reported for the turbulent flow through a sudden expansion of a moderately elastic shear-thinning liquid and also for two Newtonian liquids. The differences in the mean velocity fields for the two fluid types are relatively small, including the length of the recirculation region which is essentially unaffected by the fluid rheology. Although turbulent kinetic energy levels for the non-Newtonian fluids are always lower than for the Newtonian fluids, no significant difference is found in the relative contributions to the turbulent kinetic energy of the axial, radial and tangential normal stresses. Since the vorticity thicknesses are much the same for all flows, viscoelasticity appears to be responsible for the reduced levels of turbulent kinetic energy for the non-Newtonian fluids. Received: 6 November 1998/Accepted: 27 January 1999     

Comparison of the Eulerian and Lagrangian approaches in studying the flow pattern and heat transfer in a separated axisymmetric turbulent gas-droplet flow

The Eulerian and Lagrangian approaches are used to perform a numerical study of the disperse phase dynamics, turbulence, and heat transfer in a turbulent gas-droplet flow in a tube with sudden expansion with the following ranges of two-phase flow parameters: initial droplet size d ₁ = 0–200 µm and mass fraction of droplets M _L1 = 0–0.1. The main difference between the Eulerian and Lagrangian approaches is the difference in the predictions of the droplet mass fraction: the Eulerian approach predicts a smaller value of M _L both in the recirculation region and in the flow core (the difference reaches 15–20%). It is demonstrated that the disperse phase mass fraction calculated by the Lagrangian approach agrees better with measured data than the corresponding value predicted by the Eulerian approach.     

A PIV study of the laminar axisymmetric sudden expansion flow

The laminar flow through an axisymmetric sudden expansion was investigated experimentally using real-time digital particle image velocimetry. An expansion ratio (downstream-to-upstream pipe diameter ratio) of 2 was selected for the study. The measurements covered the regions of separation, reattachment and re-development. Two dimensional velocity maps were obtained on the vertical center plane for six Reynolds numbers between 20 and 211, based on the upstream pipe diameter and bulk velocity. The stream function distributions are calculated and presented from the streamwise and radial velocity maps. The dependence of reattachment length, redevelopment length and recirculating flow strength on the Reynolds number are determined. Results show that not only the reattachment length but also the redevelopment length downstream of reattachment is a linear function of the Reynolds number. The recirculation eddy strength, on the other hand, has a non-linear dependence on the Reynolds number which becomes weaker as the Reynolds number is increased. The results indicate no instability- or buoyancy-driven flow asymmetry in the range 20?Re? 211.     

Turbulent separated reattached flow in a two-dimensional curved-wall diffuser

A turbulent separation-reattachment flow in a two-dimensional asymmetrical curved-wall diffuser is studied by a two-dimensional laser doppler velocimeter. The turbulent boundary layer separates on the lower curved wall under strong pressure gradient and then reattaches on a parallel channel. At the inlet of the diffuser, Reynolds number based on the diffuser height is 1.2×10⁵ and the velocity is 25.2m/s. The results of experiments are presented and analyzed in new defined streamline-aligned coordinates. The experiment shows that after Transitory Detachment Reynolds shear stress is negative in the near-wall backflow region. Their characteristics are approximately the same as in simple turbulent shear layers near the maximum Reynolds shear stress. A scale is formed using the maximum Reynolds shear stresses. It is found that a Reynolds shear stress similarity exists from separation to reattachment and the Schofield-Perry velocity law exists in the forward shear flow. Both profiles are used in the experimental work that leads to the design of a new eddy-viscosity model. The length scale is taken from that developed by Schofield and Perry. The composite velocity scale is formed by the maximum Reynolds shear stress and the Schofield-Perry velocity scale as well as the edge velocity of the boundary layer. The results of these experiments are presented in this paper.     

Unsteady flow and heat transfer past an axisymmetric permeable shrinking sheet with radiation effect

In this paper, the problem of unsteady axisymmetric boundary layer flow and heat transfer induced by a permeable shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by an implicit finite‐difference scheme known as the Keller‐box method. The influence of radiation, unsteadiness and mass suction parameters on the reduced skin friction coefficient f′′(0) and the heat transfer coefficient ?θ′(0), as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and suction parameter delays the separation of boundary layer. Copyright © 2010 John Wiley & Sons, Ltd.     

Melting heat transfer in an axisymmetric stagnation-point flow of the Jeffrey fluid

This investigation explores the characteristics of melting heat transfer in a boundary layer flow of the Jeffrey fluid near the stagnation point on a stretching sheet subject to an applied magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by similarity transformations. Resulting nonlinear problems are solved analytically by the homotopy analysis method. It is noticed that an increase in the melting parameter decreases the dimensionless velocity and temperature, while an increase in the Deborah number increases the velocity and momentum boundary layer thickness.     

Instabilities in viscoelastic flow through an axisymmetric sudden contraction

Kinematics and dynamics of the viscoelastic flow in an axisymmetric 4 : 1 sudden contraction geometry are studied for a highly elastic polyisobutylene (PIB) based polymer solution (referred to as PIB-Boger fluid). The critical conditions for the onset of the elastic instabilities and the dynamics of the resulting secondary flows are measured for various flow rates. The spatio-temporal characteristics of the flow are determined by instantaneous pressure measurements and streakline photography. The nonlinear dynamics of the global flow field both upstream and downstream of the contraction plane are systematically examined. New dynamic flow behavior and elastic instabilities downstream of the contraction plane are reported. It is shown that the instantaneous pressure measurements along with flow visualization can be used as an effective tool to characterize viscoelastic flows in complex geometries.     

Aerodynamics of axisymmetric bodies in supersonic flow with local blowing

Journal of Applied Mechanics and Technical Physics -     

An experimental study of two flows through an axisymmetric sudden expansion

Two turbulent separated and reattaching flows produced by a sudden expansion in a pipe have been studied. The first was produced by a simple axisymmetric sudden enlargement from a nozzle of diameter 80 mm to a pipe of diameter 150 mm. The second was the flow at the same enlargement with the addition of a centerbody 90 mm downstream of the nozzle exit. Detailed measurements of velocity and skin friction (made primarily using pulsed wires) and of wall static pressure are presented. Without the centerbody the flow structure is similar to that observed in other sudden pipe expansions and over backward-facing steps. A turbulent free shear layer, bearing some similarity to that of a round jet, grows from separation and then reattaches to the pipe wall downstream. Reattachment is a comparatively gradual process, the shear layer approaching the wall at a glancing angle. The introduction of the centerbody causes the shear layer to curve towards the wall and reattach at a much steeper angle. Reattachment is much more rapid; gradients of skin friction and pressure along the wall are many times those without the centerbody. The high curvature of the shear layer strongly influences its turbulent structure, locally suppressing turbulence levels and reducing its growth rate.     

Calculation of the flow within the channel of an axisymmetric entrance diffuser

One of the possible flow schemes within the channel of a supersonic axisymmetric entrance diffuser is considered. The channel is formed by the surfaces of the central body of the diffuser and its outer surface and has an annular section. Axisymmetric flow in the channel of such a diffuser is calculated in the presence of an oblique shock in front of the separation region formed at the corner of the central body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 164–168, January–February, 1981.We thank É. A. Ashratov for valuable comments and assistance in preparing the program and discussing the results of the computer calculations.     

Numerical simulation of an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder

This article presents a numerical investigation of turbulent flow in an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder. The governing equations were discretized by the finite-volume method and SIMPLER method was applied to solve the equations on a staggered grid. The turbulent flow was numerically simulated using the standard k–ε, Abe–Kondoh–Nagano (AKN) and Shear Stress Transport (SST) turbulence models. The comparisons made between numerical results and experimental measurements showed that the SST model is superior to other models in the present calculation.Computations were performed for three different Reynolds numbers of 6000, 10 000 and 20 000 based on the cylinder diameter. To our knowledge, this study represents the first numerical investigation of the present flow configuration. The computational results were validated with the available experimental data of reattachment length, mean velocity distribution and wall static pressure coefficient in the turbulent blunt circular cylinder flows. Further, other characteristics of the flow, such as turbulent kinetic energy, pressure, streamlines, and the velocity vectors are discussed.The results show that the main characteristics of the turbulence flow in the separation region, such as reattachment length or velocity profiles, are nearly independent of the Reynolds number. The obtained results showed that a secondary separation bubble may appear in the main separation bubble near the leading edge. Furthermore, it was found that the turbulent kinetic energy has a large effect on the formation of the secondary bubble.     

MHD axisymmetric flow of third grade fluid between porous disks with heat transfer

The magnetohydrodynamic(MHD) flow of the third grade fluid between two permeable disks with heat transfer is investigated.The governing partial differential equations are converted into the ordinary differential equations by suitable transformations.The transformed equations are solved by the homotopy analysis method(HAM).The expressions for square residual errors are defined,and the optimal values of convergencecontrol parameters are selected.The dimensionless velocity and temperature fields are examined for various dimensionless parameters.The skin friction coefficient and the Nusselt number are tabulated to analyze the effects of dimensionless parameters.