Sudden Expansion Flow Research Articles

Asymmetry and transition to turbulence in a smooth axisymmetric constriction

The flow through a smooth axisymmetric constriction (a stenosis in medical applications) of 75% restriction in area is measured using stereoscopic and time-resolved particle image velocimetry (PIV) in the Reynolds number range Re ~ 100–1100. At low Reynolds numbers, steady flow results reveal an asymmetry of the flow downstream of the constriction. The jet emanating from the throat of the nozzle is deflected towards the wall causing the formation of a one-sided recirculation region. The asymmetry results from a Coanda-type wall attachment already observed in symmetric planar sudden expansion flows. When the Reynolds number is increased above the critical value of 400, the separation surface cannot remain attached and an unsteady flow regime begins. Low-frequency axial oscillations of the reattachment point are observed along with a slow swirling motion of the jet. The phenomenon is linked to a periodic discharge of the unstable recirculation region inducing alternating laminar and turbulent flow phases. The resulting flow is highly non-stationary and intermittent. Discrete wavelet transforms are used to discriminate between the large-scale motions of the mean flow and the vortical and turbulent fluctuations. Continuous wavelet transforms reveal the spectral structure of flow disturbances. Temporal measurements of the three velocity components in cross-sections are used with the Taylor hypothesis to qualitatively reconstruct the three-dimensional velocity vector fields, which are validated by comparing with two-dimensional PIV measurements in meridional planes. Visualizations of isosurfaces of the swirling strength criterion allow the identification of the topology of the vortices and highlight the formation and evolution of hairpin-like vortex structures in the flow. Finally, with further increase of the Reynolds number, the flow exhibits less intermittency and becomes stationary for Re ~ 900. Linear stochastic estimation identifies the predominance of vortex rings downstream of the stenosis before breakdown to turbulence.

Lagrangian simulation of deposition of CO2 gas-solid sudden expansion flow

Freezing and blockage resulting from the deposition of solid CO2 formed because of sudden expansion of the downstream pipe during the release of CO2 through safety valves, will endanger the protected equipment. To overcome this problem, the characteristics of the CO2 gas2solid sudden expansion flow are studied by using the disperse Lagrangian model. A comparison of the calculated deposition of the solid CO2 with the experimental results shows that they are in reasonable agreement. The simulation results show that the size of the solid CO2 formed should not be in the range of 0.04–0.07 mm (St number 3.2–9.8). This can be achieved by using an appropriate flow cross section of the safety valve.

Lattice Boltzmann modeling of Bingham plastics

A new lattice Boltzmann model within the framework of D2Q9 lattices for Bingham plastics is proposed. The essence of the present model lies in incorporation of the effect of local shear rate into the lattice equilibrium distribution function. With this arrangement, particle distribution functions are able to relax to the states containing proper local shear-rate information during collisions that makes the proposed scheme a more efficient and stable one. Macroscopically, consistency of the proposed lattice Boltzmann model with the equations of motion for Bingham plastics are demonstrated through the technique of Chapman–Enskog multi-scale expansion. The benchmark problem of a 2:1 sudden expansion flow in a planar channel for a wide range of Bingham numbers, 0 ≤ B n ≤ 2000 , and Reynolds numbers, 0.2 ≤ Re ≤ 200 , are executed to verify the applicability of the present model. It is shown that both the extent and shape for yielded/unyielded regions and for corner vortexes are accurately captured and their numerical values are also in good agreement with existing results.

Three-dimensional features of the turbulent flow through a planar sudden expansion

An experimental investigation of the turbulent flow downstream of a planar sudden expansion has been performed by means of a 2D particle image velocimetry (PIV) technique. Flow fields at the Reynolds number of 104 have been measured in several mutually perpendicular planes of a channel having an expansion ratio of 3 and an aspect ratio of 10. As usual for large expansion ratios, the separated flow exhibits a strong asymmetry about the expansion axis and, consequently, very different reattachment lengths on the two side walls of the channel. The mean flow turns out to be substantially symmetric about the midspan plane and strong three-dimensional effects are observed in wide portions of the separation bubbles adjacent to the upper and lower walls. The reattachment lengths exhibit significant spanwise variations that are particularly pronounced in the longer reattachment line. Measurements performed in a single flow plane at Re=4⋅104 show that the influence of the Reynolds number on the mean flow is not completely negligible in the considered variation range. Based on a careful analysis of the PIV data, a model of the three-dimensional mean flow structure in the separation bubbles has been conjectured and it is provided in the paper. The present investigation contributes to clarifying the controversial three-dimensional character of the turbulent flow in a planar sudden expansion and provides accurate and detailed reference data for numerical simulations.

Numerical computation of turbulent gas-particle flow in a 90 degree bend: comparison of two particle modelling approaches

A numerical study into the physical characteristics of dilute gas-particle flows over a square-sectioned $90^\circ$~bend is reported. Two approaches, namely the Lagrangian particle tracking model and Eulerian two fluid model are employed to predict the gas-particle flows. Renormalization Group based $k$-$\epsilon$ model is used as the turbulent closure for both the approaches; however, for the Eulerian model, additional transport equations are solved to account for the combined gas-particle interactions and the turbulence kinetic energy of the particulate phase. In comparison to both Eulerian-Eulerian and Eulerian-Lagrangian approaches the former was found to yield closer agreement with the measured values. The Eulerian-Lagrangian approach obtains finer details of the behaviour of particles, while Eulerian-Eulerian model can be used for industrial scale problems. All the simulated results are compared against the experimental finding of Kliafas and Holt (1987). References J. A. C. Humphrey, J. H. Whitelaw, and G. Yee. Turbulent flow in a square duct with strong curvature. J. Fluid Mech., 103:443--463, 1981. doi:10.1017/S0022112081001419. Y. Kliafas and M. Holt. Ldv measurements of a turbulent air-solid two-phase flow in a 90 degree bend. Exp. Fluids, 5:73--85, 1987. doi:10.1007/BF00776177. J. D. Kulick, J. R. Fessler, and J. K. Eaton. Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech., 277:109--134, 1994. doi:10.1017/S0022112094002703. Z. F. Tian, J. Y. Tu, and G. H Yeoh. Numerical simulation and validation of dilute gas- particle flow over a backward-facing step. Aerosol Sci. Technol., 39:319--332, 2005. doi:10.1080/027868290930961. J. Y Tu. Computational of turbulent two-phase flow on overlapped grids. Numer. Heat Transfer Part B Fundam, 32:175?195, 1997. doi:10.1080/10407799708915004. J. Y. Tu and C. A. J. Fletcher. An improved model for particulate turbulence modulation in confined two-phase flows. Int. Commun. Heat Mass Transfer, 21(6):775--783, 1994. doi:10.1016/0735-1933(94)90031-0. J. Y. Tu and C. A. J. Fletcher. Numerical computation of turbulent gas-solid particle flow in a 90 degree bend. AIChE Journal, 41(10):2187--2197, 1995. doi:10.1002/aic.690411003. A. Adeniji-Fashola and C. P. Chen. Modelling of confined turbulent fluid-particle flows using eulerian and lagrangian schemes. Int. J. Heat Mass Transfer, 3(4):691--701, 1990. doi:10.1016/S0307-904X(98)00007-9. F. Durst, D. Milojevic, and B. Schonung. Eulerian and lagrangian predictions of particulate two-phase flows :a numerical study. Appl. Math. Model, 8(2):101--115, 1984. doi:10.1016/0307-904X(84)90062-3. J. R. Fessler and J. K. Eaton. Particle response in a planar sudden expansion flow. Expl Thermal and Fluid Sci, 15:413--423, 1997. doi:10.1016/S0894-1777(97)00010-1. J. R. Fessler and J. K. Eaton. Turbulence modification by particles in a backward-facing step flow. J. Fluid Mech, 394:97--117, 1999. http://journals.cambridge.org/action/displayAbstract?aid=15369.

The influence of swirl on the reattachment length in an abrupt axisymmetric expansion

This paper presents a theoretical study on the influence of swirl on the reattachment length in an abrupt axisymmetric expansion. A scale analysis of the equations of motion reveals that this reattachment length decreases with increasing swirl. Moreover, it seems to suggest that there may be a singularity in the non-swirling sudden expansion flow, which disappears with increasing swirl beyond a critical value. This singularity is a possible explanation for the scatter of the data found in the literature at zero swirl. For the swirling flow, an analytical expression for the reattachment length is derived based on similarities found in experimental data between swirling and non-swirling flows. This expression shows that the reattachment length is a function of the swirl number and the expansion ratio and, to some extend, of the reattachment length at zero swirl. It is found that the local swirl number of the detaching streamline S D is a better parameter to characterise the reattachment length than the momentum flux averaged swirl number S. The theoretical model is validated based on values for the reattachment length found in the literature for expansion ratios h = R 2/ R 1 ranging from 1.5 to 2, Reynolds numbers Re from 10,000 to 100,000 and swirl numbers S from 0 to 1.23. Comparison with experiments shows a good agreement between the model and experimental data.

Numerical investigation of liquid metal flows in rectangular sudden expansions

Three-dimensional magnetohydrodynamic flows in sudden expansions of rectangular channels with walls of finite electric conductivity have been investigated. The used numerical tool, based on an extended version of the commercial code CFX, gives accurate results up to Hartmann numbers H a ≤ 1000 . For stronger magnetic fields an asymptotic-numeric approach has been used. The results of the study show that for moderate magnetic fields vortical recirculations form behind the expansion. They are, however, suppressed for sufficiently high Hartmann numbers. Moreover, regions with very small velocities may appear. The analysis highlights also that inertial effects become smaller with increasing the interaction parameter N, but even for large N an inertial influence is still present. The additional pressure drop caused by the three-dimensional flow at the expansion and the flow partitioning between cores, internal and side layers have been analyzed in detail. Some of the main outcomes are summarized in this paper.

Iterative solvers and inflow boundary conditions for plane sudden expansion flows

Incompressible laminar flow in a symmetric plane sudden expansion is studied numerically. The flow is known to exhibit a stable symmetric solution up to a critical Reynolds number above which symmetry-breaking bifurcation occurs. The aim of the present study is to investigate the effect of using different iterative solvers on the calculation of the bifurcation point. For this purpose, the governing equations for steady two-dimensional incompressible flow are written in terms of a stream function-vorticity formulation. A second order finite volume discretization is applied. Explicit and implicit solvers are used to solve the resulting system of algebraic equations. It is shown that the explicit solver recovers the stable asymmetric solution, while the implicit solver can recover both the unstable symmetric solution or the stable asymmetric solution, depending on whether the initial guess is symmetric or not. It is also found that the type of inflow velocity profile, whether uniform or parabolic, has a significant effect on the onset of bifurcation as uniform inflows tend to stabilize the symmetric solution by delaying the onset of bifurcation to a higher Reynolds number as compared to parabolic inflows.

Plane sudden expansion flows of viscoelastic liquids

We report a systematic numerical investigation of the creeping flow of three different viscoelastic models, the UCM, Oldroyd-B and the linear form of the PTT model, through a 1:3 planar sudden expansion. Although the effect of elasticity is to reduce both the length and intensity of the recirculation region downstream of the expansion, we show that this reduction is much lower than previous studies have suggested and that, at high Deborah number, a significant region of recirculation still exists for all of the models studied.

Bifurcation phenomena in viscoelastic flows through a symmetric 1:4 expansion

In this work we present an investigation of viscoelastic flow in a planar sudden expansion with expansion ratio D/ d = 4. We apply the modified FENE–CR constitutive model based on the non-linear finite extensibility dumbbells (FENE) model. The governing equations were solved using a finite volume method with the high-resolution CUBISTA scheme utilised for the discretisation of the convective terms in the stress and momentum equations. Our interest here is to investigate two-dimensional steady-state solutions where, above a critical Reynolds number, stable asymmetric flow states are known to occur. We report a systematic parametric investigation, clarifying the roles of Reynolds number (0.01 < Re < 100), Weissenberg number (0 < We < 100) and the solvent viscosity ratio (0.3 < β < 1). For most simulations the extensibility parameter of the FENE model was kept constant, at a value L 2 = 100, but some exploration of its effect in the range 100–500 shows a rather minor influence. The results given comprise flow patterns, streamlines and vortex sizes and intensities, and pressure and velocity distributions along the centreline (i.e. y = 0). For the Newtonian case, in agreement with previous studies, a bifurcation to asymmetric flow was observed for Reynolds numbers greater than about 36. In contrast viscoelasticity was found to stabilise the flow; setting β = 0.5 and We = 2 as typical values, resulted in symmetric flow up to a Reynolds number of about 46. We analyse these two cases in particular detail.

Alteration of Reynolds number and flow partition modify wall shear stresses at arterial branches in a way that can explain age- and species-dependent patterns of arterial disease

It is assumed that critical hemodynamic factors play an important role in the onset, localization and degree of post-operative complications, for example, thrombosis and restenosis. Of special interest are sudden expansion flows, which may occur in straight artery segments such as the common carotid after endarterectomy or end-to-end anastomoses. Sudden expansion geometries are possible origins of early post-operative emboli and significant myointimal hyperplasia resulting in early or late complications. Transient laminar axisymmetric and fully three-dimensional blood flows were simulated employing a validated finite volume code in conjunction with a Runge–Kutta particle tracking technique. Disturbed flow indicators, which may predict the onset of thrombosis and/or restenosis, were identified and employed to evaluate 90°-step and smooth expansion geometries.Smooth expansion geometries have weaker disturbed flow features than step expansion geometries. Specifically, the regions near the expansion wall and the reattachment point are susceptible to both atherosclerotic lesion and thrombi formations as indicated by non-uniform hemodynamic indicators such as near-zero wall shear stress and elevated wall shear stress gradients as well as blood particle accumulation and deposition. A new parameter, the wall shear stress angle deviation (WSSAD) has been introduced, which indicates areas of abnormal endothelial cell morphology and particle wall deposition. In turn, regions of low wall shear stress and high wall shear stress gradients are recognized as susceptible sites for arterial diseases. Thus, it is interesting to note that high WSSAD surface areas cover low wall shear stress, high wall shear stress gradient locations as well as high wall particle deposition.A gradual change in step expansion geometry provides better results in terms of WSSAD values and hence potentially reducing atherosclerosis as well as thrombi formation.

Effects of Entrance and Exit Shapes on a Uniform Flow in Regenerators

The flow loss in the regenerator mainly depends on fluid friction through the regenerator matrix, but it is also generated by sudden expansion and contraction flow at the regenerator ends. The entrance areas at the regenerator ends of typical Stirling cycle machines are smaller than the cross-sectional area of the regenerator matrix. So, the gas flow in the matrix becomes a flow field with non-uniform velocity distribution accompanying the expansion and contraction flow. In this paper, the geometry of a tapered flow passage between the regenerator ends and the matrix to produce more uniform flow in the matrix, is examined experimentally using steady single-blow equipment to model a regenerator with a narrow flow passage at the ends. Additionally, the effects of the flow passages are analyzed using CFD. The effect of the tapered flow passage, in producing more uniform flow, is greater than that of the gap.

Temporal gradients in shear, but not spatial gradients, stimulate ERK1/2 activation in human endothelial cells

We have previously demonstrated temporal gradients in shear stress stimulate endothelial cell proliferation, whereas spatial gradients do not. In the present study, the extracellular signal-regulated kinases 1 and 2 (ERK1/2) pathway was investigated as a possible mediator for the promitogenic effect of temporal gradients. The sudden expansion flow chamber (SEFC) model was used to differentiate the effect of temporal gradients in shear from that of spatial gradients on ERK1/2 activation in human umbilical vein endothelial cells (HUVEC). ERK1/2 activation in the SEFC was not significantly different from control when HUVEC were exposed to spatial gradients alone. When a single temporal impulse was superimposed on spatial gradients, ERK1/2 activation was stimulated 330% (relative to spatial alone) within the region of spatial gradients. Inhibition of the ERK1/2 pathway with U-0126 abolished all effects of temporal gradients. To further separate temporal and spatial gradients, a conventional parallel plate flow chamber was utilized. Acute exposure to oscillations in flow at a frequency of 1 Hz stimulated ERK1/2 activation 620 +/- 88% relative to control, whereas a single impulse of flow increased ERK1/2 activation 166 +/- 19%. Flow without the temporal component did not significantly activate ERK1/2. These results suggest that the ERK1/2 pathway directly mediates the promitogenic effects of temporal gradients in shear stress.

Normal and shear stresses influence the spatial distribution of intracellular adhesion molecule-1 expression in human umbilical vein endothelial cells exposed to sudden expansion flow

Patterns in cell adhesion molecule expression by endothelial cells may play a role in atherogenesis. Previous studies have shown dependence of intracellular adhesion molecule-1 (ICAM-1) expression in human umbilical vein endothelial cells (HUVEC) on shear stress and have indirectly linked ICAM-1 expression to spatial gradients in shear stress. The spatial distribution of ICAM-1 in HUVEC pre-exposed to flow for 8 h was determined using fluorescence microscopy and a sudden expansion flow chamber with a 2.66 expansion ratio to simulate gradients in wall shear stress found near arterial branches in vivo. When ICAM-1 expression in the disturbed flow region was compared to theoretical stress distributions obtained from a computational model of sudden expansion flow, a modest trend ( R 2 = 0.327 , p < 0.01 ) was observed between ICAM-1 and shear stress but the correlation between ICAM-1 and shear stress gradient was insignificant. In contrast, a moderately strong trend ( R 2 = 0.873 , p < 0.01 ) was evident between ICAM-1 expression and the component of normal stress induced by the expansion. Thus, in this in vitro model, normal stress arising from sudden expansion flow modulates the effect of shear stress on ICAM-1 expression.

Analysis of pressure distribution of turbulent asymmetric flow in a flat duct symmetric sudden expansion with small aspect ratio

This paper describes the pressure distribution of turbulent airflow through a flat duct containing one-dimensional symmetric sudden expansion in cross-sectional area encountered frequently in plate heat exchangers and other devices of practical importance. The pressure distributions of turbulent asymmetric airflow through constant width flat ducts having modest expansion ratios of 2, 2.5 and 3, aspect ratios of the expansion of 0.40, 0.26 and 0.20 and modest area ratios of the expansion of 1/3, 1/2.5 and 1/2 were investigated experimentally. The axial and vertical pressure distributions of the turbulent asymmetric flow with relatively small Reynolds numbers ( Re D h = uD h / ν = 12 000 , 4887 and 4125) in downstream cross section of the duct were analyzed. The variations of pressure coefficient with local Reynolds numbers were also investigated. Turbulent flow in flat ducts with symmetric sudden expansion has not sufficiently been studied contrary to axisymmetrical or two-dimensional case for which a large numbers of papers can be found in the literature. This experimental study fulfills this gap and shows that the flow is asymmetric as in a two-dimensional case. It also brings interesting data for numerical simulations for the presented flat duct configurations. These data concern the axial and vertical distribution of pressure coefficient, the axial velocity in the duct and Reynolds numbers based on the hydraulic diameter, the step height or the local axial distance of the duct. The results obtained complement and extend the previous results, and show that the expansion ratio and Reynolds number affect the flow field.

On the axisymmetric vortex breakdown of a swirling jet entering a sudden expansion pipe

This Brief Communication investigates the onset and bifurcation structure of vortex breakdown in a laminar sudden expansion flow. Bifurcation diagrams for variable inlet swirl levels are determined by integration of the time dependent, incompressible, axisymmetric, Navier–Stokes equations in a sudden expansion with expansion ratio λ=2.0 and for moderately large values of the Reynolds number. As in the case of swirling flows in pipes, vortex breakdown is seen to occur associated with the emergence of a stagnation point when the Reynolds number is sufficiently small (Re≲125 for λ=2), while for larger values it appears as a fold in the solution space. The standing wave analysis for the stream tube emerging from the inlet orifice rim indicates that the local criticality of the flow is a necessary condition for the appearance of the vortex breakdown. The axisymmetric computations also reveal the unsteadiness of the nonslender solutions above Re≳400.

Simulation of sudden expansion flows for power-law fluids

The goal of this work is the numerical solution of incompressible laminar flows through a channel with 3:1 sudden expansion for power-law fluids. For such flows, above the critical Reynolds value, three solutions can appear: a symmetric and two non-symmetric. The simulations are performed using a finite difference explicit Runge–Kutta three-stages scheme for second-order time and space approximations. Results show that bifurcations occur for the range of power-law index n ϵ (0, 2]; for shear-thinning the bifurcation appears after that of the Newtonian situation, while the opposite occurs for shear-thickening. Moreover, the solution becomes time dependent for higher Reynolds numbers depending on the value of the power law exponent n. These results build on earlier ones found for sudden expansions because here higher Reynolds numbers and non-Newtonian behavior are considered.

Generation of streamwise vortices in square sudden-expansion flows.

The intent of the present work is to investigate the nature of jet spreading and the process of evolution of the associated embedded streamwise vortices for the steady flow through a two-step square sudden expansion. Simulations are performed to review the flow physics within a square channel which undergoes a first expansion with an uniform step height 0.75h ( h being the inlet channel width); and at a streamwise distance 8h from the plane of first expansion the channel goes through another expansion with the second step height being half of the first step height. Unlike asymmetric jets, the square jet is observed to experience relatively faster nonuniform azimuthal perturbations during its streamwise evolution and at some downstream location the jet expands in such a way that it looks as if it has locally rotated by 45 degrees. The developed four pairs of outflow type streamwise vortices (with each pair occupying their position at the end of a jet diagonal), which dominated over the first expansion zone, seems to control the azimuthal jet deformation process through their induced outward velocity. Another important aspect of the present investigation is that here we have established a unique pressure analysis which efficiently predicts the presence of all the streamwise vortices in the setup and also their nature of dynamics without any ambiguity. Moreover, the presented pressure analysis suggests that nonuniform lateral flow acceleration within the channel, as induced by the developed transverse pressure gradient skewing, influences the generation of the streamwise vortices. The pressure analysis also successfully predicts every local change in the dynamics of the embedded streamwise vortices, during the downstream evolution of the jet.

スターリングエンジン性能に及ぼす再生器端部間隙の影響(再生熱交換器の基本特性(2))

The sudden expansion and contraction flow in the regenerator ends greatly influences the performance of the Stirling engines. The regenerator is installed between the heater and the cooler. The cross-sectional flow areas of regenerator ends of typical Stirling engines are smaller than the cross-sectional area of the regenerator matrix. So, the gas flow in the matrix becomes a flow field with non-uniform flow at end of the regenerator. The non-uniform flow causes increased pressure loss and decreased thermal performance. In this paper, the effects of gap in the regenerator ends on the engine performance have been examined experimentally and confirmed.

Parallelization of a Transient Method of Lines Navier–Stokes Code

Parallel implementation of a serial code, namely method of lines (MOL) solution for momentum equations (MOLS4ME), previously developed for the solution of transient Navier–Stokes equations for incompressible separated internal flows in regular and complex geometries, is described. *E-mail: ceme@metu.edu.tr The serial code was parallelized by using a domain decomposition strategy with overlapped boundary at the interfaces for information exchange between the sub-domains. A parallel virtual machine (PVM) and dual-processor personal computer (PC) connected over a switch are employed as the message passing software and the parallel computing platform, respectively. Performance of the parallelization strategy was first tested on a transient 1-D laminar pipe flow problem for MOL, explicit and implicit finite difference methods. Assessment of the performance of the parallel code (PARMOLS4ME) was then tested by applying it to two test cases; (i) laminar pipe flow with sudden expansion and (ii) turbulent flow in a gas turbine combustor simulator (GTCS) and comparing the results of serial and parallel codes. Comparisons show that the flow fields predicted by parallel codes agree well with those of serial codes at considerably lower execution times. Effects of load balancing are also investigated and it is seen that the load balancing has a significant effect on the execution time of the parallel code.