Secondary Flow Effects Research Articles

Predictions of solute transport in a compound channel using turbulence models

Prediction of solute distributions in an asymmetric compound channel is carried out using two turbulence models. Results of the numerical models are compared with turbulence data recently obtained using laser Doppler anemometer (LDA) and laser induced fluorescence (LIF) in a small laboratory flume. The predicted distributions of solute and Reynolds flux using a k-s model and an algebraic stress model for various injection points near the water surface are used to identify different mixing mechanisms. A skewed distribution of solute on the floodplain observed in the experimental data is well predicted by the algebraic stress model but not by the k-ε model. The cause of the skewed distribution is examined through the variations of secondary flow and eddy diffusivity. The predicted eddy viscosity and diffusivity and the turbulent Schmidt number are discussed with the experimental data. As a result, solute concentration distribution can be well predicted by adjusting the turbulent Schmidt number even if the eddy viscosity was not correctly calculated by any particular model. An effect of secondary flow on peak concentration in the shear layer along the channel is also demonstrated.

Turbulence Measurements of Dye Concentration and Effects of Secondary Flow on Distribution in Open Channel Flows

This paper presents simultaneous turbulence measurements of velocity and tracer concentration using a combination of laser Doppler anemometer (LDA) and laser induced fluorescence (LIF) in rectangular and compound channels. Secondary flow, Reynolds stresses, Reynolds fluxes, and dye concentration distributions were measured near the water surface in both channels. An investigation of the effect of secondary flow on passive contaminant diffusion processes was carried out with relatively weak secondary flow in the rectangular channel and relatively strong secondary flow in the compound channel. The results show that the secondary flow clearly influences the spreading of the tracer concentration and the location of concentration peak, being different from the injection location. The transport rate of solute due to the secondary flow is not significant in the rectangular channel case but significant in the compound channel case. The transverse eddy viscosity is demonstrated to be equal to the transverse eddy diffusivity. The transverse eddy diffusivity near the water surface is larger than the vertical one. The Fickian law is valid in most regions investigated, but there are some regions where the Reynolds flux and concentration gradients are locally of the same sign due to the influence of secondary flow on the concentration distribution.

Combustor Turbine Interface Studies—Part 1: Endwall Effectiveness Measurements

Improved durability of gas turbine engines is an objective for both military and commercial aeroengines as well as for power generation engines. One region susceptible to degradation in an engine is the junction between the combustor and first vane given that the main gas path temperatures at this location are the highest. The platform at this junction is quite complex in that secondary flow effects, such as the leading edge vortex, are dominant. Past computational studies have shown that the total pressure profile exiting the combustor dictates the development of the secondary flows that are formed. This study examines the effect of varying the combustor liner film-cooling and junction slot flows on the adiabatic wall temperatures measured on the platform of the first vane. The experiments were performed using large-scale models of a combustor and nozzle guide vane in a wind tunnel facility. The results show that varying the coolant injection from the upstream combustor liner leads to differing total pressure profiles entering the turbine vane passage. Endwall adiabatic effectiveness measurements indicate that the coolant does not exit the upstream combustor slot uniformly, but instead accumulates along the suction side of the vane and endwall. Increasing the liner cooling continued to reduce endwall temperatures, which was not found to be true with increasing the film-cooling from the liner.

Effects of Rib-Induced Secondary Flow on Heat Transfer Augmentation Inside a Circular Tube

Effects of Rib-Induced Secondary Flow on Heat Transfer Augmentation Inside a Circular Tube

Influence of secondary flow on diffusion with heterogeneous reaction

The concentration distribution in a Newtonian fluid for the secondary flow in a curved tube with bulk/wall reaction is obtained for a range of parameter values using an axially marching spectral finite difference scheme. The results predominantly illustrate that for fixed extent of secondary flows there is an improvement in the performance of the reactor as the effect of bulk and wall reaction mechanisms intensify in the system. For the same magnitude (moderate effects) of bulk and wall reaction mechanisms, there appears to be an increased conversion/performance in the homogeneous case. For small values of the reaction parameters, the improvement in the performance (3%) is more due to the wall reaction than bulk reaction. But, for moderate values of the non-dimensional reaction parameters (around 10), the enhanced performance (28%) is more due to the bulk reaction than wall reaction. As the effects of secondary flow dominate, there is an improvement in the performance of the reactor irrespective of the reactivity of the solute and the results agree with those of Mashelkar and Venkatasubramanian [AIChE J. 313 (1985) 440] for the case of non-absorbing walls. It is also observed that the approach of isoconcentration profile to the stream line pattern occurs at a lower value of the curvature parameter in the presence of wall reaction. The study is extended to examine the modifications in the tracer response measurements due to the power law rheology of the flowing fluid. The salient observation, irrespective of the reactivity of the solute, is that the performance of the reactor is improved in the case of pseudoplastic fluids compared to dilatant fluids. This improvement is further enhanced due to the presence of mild wall reaction.

Liquid–solid separation phenomena of two-phase turbulent flow in curved pipes

The present study is to contribute some knowledge of phase separation phenomena of liquid–solid two-phase turbulent flow in curved pipes and provide a basis for the invention and development of a new type of curved pipe separator. Firstly, the solid–liquid two-phase flows in two-dimensional (2D) curved channels were numerically simulated using a two-way coupling Euler–Lagrangian scheme. Phase distribution characteristics of 2D curved channel two-phase flow were examined under conditions of different particle size, liquid flowrate and coil curvature. Based on the numerical results, the dynamic effects and contributions to phase separation of particle-subjected forces, including centrifugal force, drag force, pressure gradient force, gravity force, buoyancy force, virtual mass force and lift force, were exposed by kinematic and dynamic analysis along particle trajectories. Secondly, measurement of particle size and concentration profiles in helically coiled tube two-phase flow was conducted using a nonintrusive Malvern 2600 particle sizer based on laser diffraction. Particle size and concentration distribution characteristics of helically coiled tube two-phase flow and the effect of secondary flow on phase separation were analyzed based on experimental data.

PTV measurement on interaction between two immiscible droplets and turbulent uniform shear flow of carrier fluid

A flow visualization and a particle-tracking-velocimetry measurement have been conducted for a turbulent water plane Couette flow with two oil droplets in the central region in order to elucidate the effect of secondary flow induced by the droplets on the modification of shear-dominant turbulence. The diameters of these droplets are about 80 times larger than the micro scale of turbulence. The tracer particles coated with fluorescence color and the optical filter for the video camera is found to be effective for diminishing the reflected light from the interface and the moving wall. The experimental results show that zero-velocity regions exist near the interface around the axis because the direction of the wall-normal secondary flow is opposite to that of water moving with the rotating droplets. It is also found that the turbulence intensities in the region between the two droplets and in the small regions for the confluence and stagnation are attenuated due to the weakening of the wall-normal secondary flow particularly in the case where the distance between the centers of the two droplets is twice as long as the droplet diameter.

Effects of Secondary Flow on the Electromagnetic Separation of Inclusions from Aluminum Melt in a Square Channel by a Solenoid.

Effects of secondary flow of the melt on the separation of inclusions from molten aluminum flowing in a square channel by a solenoid were investigated theoretically and experimentally. Numerical methods were used to calculate the secondary flow, the separation efficiency of inclusions, and the particle motion. It is found that there appear two recirculating loop flows in a quarter cross section of the channel and the separation efficiency of inclusions is significantly improved by the secondary flow mainly owing to the mixing effect. The separation efficiency increases with the increase of the effective magnetic flux density and the frequency of magnetic field, and decreases significantly with the increase of the size of the separator channel for a constant value of a/δ. However, it is possible to achieve high separation efficiency by using largesized square channels and high frequency magnetic field with the help of the mixing effect of secondary flow. The computed results of particle trajectories show that the secondary flow accelerates the transportation of the particles from the inner region to the vicinity of the wall and greatly shortens the separation time of those particles. The effects of secondary flow on the separation efficiency were confirmed by comparing the measured separation efficiency with the computed results.

The use of dean vortices for crossflow microfiltration: basic principles and further investigation

Abstract The effect of Dean vortices on the filtration flux and efficiency of crossflow microfiltration processes in sinusoidal curved and helically coiled tubular membranes was investigated by several research groups. Experimental results are presented showing an enhanced filtrate flux and efficiency of the filtration process. CFD simulations were performed, revealing two important effects of secondary flow: an increased wall shear stress causing a reduced particle deposition and an enhanced mass transfer between the boundary layer and the bulk phase.

Dispersion visualization of model fluids in a transparent Couette flow cell

Dispersion mechanisms in model fluid systems of different viscosity ratios were studied in a transparent Couette flow cell. The counter-rotating concentric cylinders were driven by two independent dc motors. Drops of the minor phase were then maintained at a constant position by fixing the inner and outer cylinders’ rotational speeds. The advantage of this new setup is that visualization can be made at high shear rates without any secondary flow effects, usually observed with cone-plate or parallel plates geometry. Constant viscosity viscoelastic drops (Boger fluid) and Newtonian drops [high viscosity polydimethylsiloxane, (PDMS)], deformed at low shear rates in a Newtonian matrix (low viscosity PDMS), oriented along the flow field and drop deformation increased with shear rate, as expected. However, when a critical shear rate (characteristic of the fluid system used) was reached, the deformed drops began to contract in the flow direction. When increasing the shear rate over this critical value, drop contraction was followed by elongation perpendicular to the flow direction, i.e., parallel to the vorticity axis. This elongation increased with shear rate until the final breakup occurred. These deformation and breakup mechanisms were attributed to elastic normal forces present at high deformation rates.

SECONDARY FLOW EFFECT TO HEAT TRANSFER OF A DUCT WITH DISCRETE RIB TURBULATORS

In the present study, three-dimensional numerical simulation is carried out for discrete rib arrays to investigate the local fluid and heat transfer characteristics. Rib pitch and gap width were varied in several steps. Furthermore, two kinds of rib arrays were studied, i.e. an array of ribs having the gaps at both spanwise ends and a staggered array of ribs with gaps at both spanwise ends and with gaps in the middle. Eventually, the staggered arrayed ribs is suggested to be best in performance of heat transfer.

Effects of temperature-dependent viscosity on fully developed laminar forced convection in a curved duct

For most liquids the specific heat and thermal conductivity are almost independent from temperature, but the viscosity decreases significantly. A fully developed laminar water flow in a curved duct with temperature-dependent viscosity is analyzed in this work. The mass, momentum and energy conservation equations are numerically solved by the finite element method. Both heating and cooling of the water flow is studied. The secondary flow induced by the curvature effects increases the heat transfer rate in comparison with the straight ducts but the velocity and temperature profiles are distorted when the effects of temperature-varying viscosity are included. The Nusselt number obtained when the fluid is cooled with variable viscosity assumption are lower than the constant properties results due to the increase of the viscosity values at the inner points of the curved tube that reduces the secondary flow effect. The friction factor results also show a marked dependence on the viscosity variations in the coil tube cross-section.

A computer-aided parametric analysis of mixed convection in ducts

This study develops a novel technique of computer-aided parametric analysis (CAPA) to formulate simple correlations for thermal flow characteristics in a complex convective flow system. To demonstrate the validity of the technique, fully developed mixed convection in uniformly heated horizontal ducts of square and circular cross-sections are employed as illustrative examples. The effects of secondary flow generated by the thermal buoyancy force are included. The CAPA technique employs characteristic quantities, constant factors and multi-term relationships to convert the governing equations into a set of algebraic equations. Relatively, this technique generates more extensive results than the conventional order-of-magnitude and scaling analyses. With the aid of limited data from numerical results (or measurements), formulas for evaluating the cross-sectional averages of axial velocity and temperature, the strength of secondary vortices, friction factors and the heat transfer rates at various Pr and ReRa can be derived. Comparisons of the present results and the direct numerical solutions manifest quite satisfactory performance of the CAPA technique. Merits of the CAPA technique are: (1) less effort required in the developing procedure, (2) clear parameter-dependence of the thermal flow characteristics, and (3) convenience in using the resultant correlations of algebraic form.

Formation and dispersion of ropes in pneumatic conveying

In this study, the solid flow nonuniformities which develop in lean phase upward flow in a vertical pneumatic conveying line following a horizontal-to-vertical elbow were investigated. Laboratory experiments were conducted in 154 and 203 mm I.D. test sections using pulverized-coal particles (90% less than 75 μm) for two different 90° circular elbows having pipe bend radius to pipe diameter ratios of 1.5 and 3.0. The experiments covered a range of conveying air velocities and solids mass loadings. Experimental measurements of time-average local particle velocities, concentrations, and mass fluxes were obtained using a fiber-optic probe which was traversed over the cross-section of the pipe. The measurements indicate a continuous rope-like structure forms within the elbow. The rope maintains its continuous structure until it disintegrates into large discontinuous clusters at downstream locations. Comparisons of the results of CFD simulations of turbulent gas-particle flow and time-average experimental data were used to explain rope formation and dispersion. The CFD simulations, based on the Lagrangian particle-source-in-cell method, predict a denser particle rope as the nondimensional radius of curvature ( R/D) is increased, agreeing with trends in experimental data. The individual effects of secondary flows and turbulence on axial dispersion of the rope were studied computationally and the results show both mechanisms are important.

Experiments on bar formation in a straight flume: 1. Uniform sediment

Laboratory experiments have been carried out in a large laboratory flume using a nearly uniform sand and under controlled steady flow conditions such as to ensure the development of alternate bars on a ripple and/or dune‐covered bed. The interaction between small‐scale and large‐scale bed forms is found to enhance a modulation in time and in space of the bar pattern. Moreover, the flow depth decrease experienced by the flow field when approaching bar fronts, leading to a progressive reduction of the dimensions of small‐scale bed forms, may influence appreciably the overall flow resistance. Experimental values of bar wavelength and of bar celerity are compared with the theoretical estimates obtained from a model developed within the classical framework of linear stability analysis. In particular, the model accounts for the local variability of friction coefficient and water level, for the secondary helical flow effects, and for the influence of longitudinal slope on sediment transport. Quantitatively satisfactory predictions of bar wavelength appear to be possible in spite of the fact that in various runs a correct estimation of flow resistance and flow discharge appears to be relatively difficult.

Oscillatory Flow and Gas Transport Through a Symmetrical Bifurcation

Axial gas transport due to the interaction between radial mixing and radially nonuniform axial velocities is responsible for gas transport in thick airways during High-frequency oscillatory ventilation (HFO). Because the airways can be characterized by a bifurcating tube network, the secondary flow in the curved portion of a bifurcating tube contributes to cross-stream mixing. In this study the oscillatory flow and concentration fields through a single symmetrical airway bifurcating tube model were numerically analyzed by solving three-dimensional Navier-Stokes and mass concentration equations with the SIMPLER algorithm. The simulation conditions were for a Womersley number, alpha = 9.1 and Reynolds numbers in the parent tube between 200 and 1000, corresponding to Dn2/alpha 4 in the curved portion between 2 and 80, where Dn is Dean number. For comparison with the results from the bifurcating tube, we calculated the velocity and concentration fields for fully developed oscillatory flow through a curved tube with a curvature rate of 1/10, which is identical to the curved portion of the bifurcating tube. For Dn2/alpha 4 < or = 10 in the curved portion of the bifurcating tube, the flow divider and area changes dominate the axial gas transport, because the effective diffusivity is greater than in either a straight or curved tube, in spite of low secondary velocities. However, for Dn2/alpha 4 > or = 20, the gas transport characteristics in a bifurcation are similar to a curved tube because of the significant effect of secondary flow.

Numerical study on the effect of secondary flow in the human aorta on local shear stresses in abdominal aortic branches

Flow in the aortic arch is characterized primarily by the presence of a strong secondary flow superimposed over the axial flow, skewed axial velocity profiles and diastolic flow reversals. A significant amount of helical flow has also been observed in the descending aorta of humans and in models. In this study a computational model of the abdominal aorta complete with two sets of outflow arteries was adapted for three-dimensional steady flow simulations. The flow through the model was predicted using the Navier–Stokes equations to study the effect that a rotational component of flow has on the general flow dynamics in this vascular segment. The helical velocity profile introduced at the inlet was developed from magnetic resonance velocity mappings taken from a plane transaxial to the aortic arch. Results showed that flow division ratios increased in the first set of branches and decreased in the second set with the addition of rotational flow. Shear stress varied in magnitude with the addition of rotational flow, but the shear stress distribution did not change. No regions of flow separation were observed in the iliac arteries for either case. Helical flow may have a stabilizing effect on the flow patterns in branches in general, as evidenced by the decreased difference in shear stress between the inner and outer walls in the iliac arteries.

Viscous-Flow Two-Dimensional Analysis Including Secondary Flow Effects

During the last few decades extremely powerful Quasi-three-dimensional (3D) codes and fully 3D Navier-Stokes solvers have been developed and successfully utilized in the design process and optimization of multistage axial-flow compressors. However, most of these methods proved to be difficult in handling and extremely time consuming. Due to these disadvantages, the primary stage design and stage matching as well as the off-design analysis is nowadays still based on fast 2D methods incorporating loss-, deviation- and end wall modeling. Only the detailed 3D optimization is normally performed by means of advanced 3D methods. In this paper a fast and efficient 2D calculation method is presented, which already in the initial design phase of multistage axial flow compressors, considers the influence of hub leakage flows, tip clearance effects, and other end wall flow phenomena. The method is generally based on the fundamental approach by Howard and Gallimore (1992). In order to allow a more accurate prediction of skewed and nondeveloped boundary layers in turbomachines, an improved theoretical approach was implemented. Particularly the splitting of the boundary layers into an axial and tangential component proved to be necessary in order to account for the change between rotating and stationary end walls. Additionally, a new approach is used for the prediction of the viscous end wall zones including hub leakage effects and strongly skewed boundary layers. As a result, empirical correlations for secondary flow effects are no longer required. The results of the improved method are compared with conventional 2D results including 3D loss- and deviation-models, with experimental data of a three-stage research compressor of the Institute for Jet Propulsion and Turbomachinery of the Technical University of Aachen and with 3D Navier-Stokes solutions of the V84.3A compressor and of a multistage Siemens research compressor. The results obtained using the new method show a remarkable improvement in comparison with conventional 2D methods. Due to the high quality and the extremely short computation time, the new method allows an overall viscous design of multistage compressors for heavy duty gas turbines and aeroengine applications.

Heat transfer behavior of temperature -dependent viscoelastic non-Newtonian fluid with buoyancy effect in 2:1 rectangular duct

This numerical study investigates the flow characteristics and heat transfer mechanism of a viscoelastic non-Newtonian fluid in a 2:1 rectangular duct. The combined effect of temperature-dependent viscosity, buoyancy, and secondary flow caused by a second normal-stress difference is considered. The Reiner-Rivlin constitutive equation was adopted to model the viscoelastic fluid characteristics. An axially constant heat flux on the bottom wall and peripherally adiabatic boundary condition (H2) were both used. The numerical results for a polyacrylamide (Separan AP-273) solution showed a significant heat transfer enhancement compared to those of a constant property fluid, and exhibited a good consistency with experimental results for both thermal developing and thermally developed regions. In a bottom-wall-heated 2:1 rectangular duct, the main cause of the heat transfer enhancement of the viscoelastic fluid was viscoelastic-driven secondary flow, with temperature-dependent viscosity and buoyancy-induced secondary flow playing supporting roles.

Application of the wavelet transform in the laminar turbulent transition for a flow in a mixed convection phenomenon

The aim of this paper is to show the effect of secondary flows caused by natural convection on the laminar-turbulent hydrodynamic transition. It is not a question of measuring a critical threshold value of Reynolds number of transition but only to estimate the degree of turbulence in the transition regime, i.e. weak turbulence in the case of superposition (mixed convection) or not (forced convection) of secondary flows on the forced flow. This is possible thanks to the application of the wavelet transform. The calculation of the Holder exponent, associated with the maximum value of the singularity spectrum for two configurations, vertical (forced convection) and horizontal (mixed convection) allows the degree of turbulence to be measured in both cases. The variation of the Holder exponent versus the Reynolds number has enabled it to be shown that the secondary flows stabilise the main flow and stifle the beginnings of the turbulence during the regime of transition to turbulence; these kinds of results have also been shown in literature. Generally, large-sized secondary flows (for example Dean's flows) stabilise the turbulence. Our work confirms this, through an experiment carried out in identical conditions for mixed convection (horizontal flow) and forced convection (vertical flow).