Turbine Passage Secondary Flow Dynamics and Endwall Heat Transfer Under Different Inflow Turbulence

This study presents endwall hydrodynamics and heat transfer in a linear turbine cascade at Re 5×105 at low and high intensities of turbulence.Results are numerically predicted using the standard SST model and Reθ-γtransition model as well as using the high-resolution LES separately.The major secondary flow components,comprising the horseshoe,corner,and passage vortices are recognized and the impact on heat or mass transfer is investigated.The complicated behavior of turbine passage secondary flow generation and establishment are impacted by the perspective of boundary layer attributes and inflow turbulence.The passage vortex concerning the latest big leading-edge vane is generated by the enlargement of the circulation developed at the first instance adjacent to the pressure side becomes powerful and mixes with other vortex systems during its migration towards the suction side.The study conclusions reveal that substantial enhancements are attained on the endwall surface,for the entire spanwise blade extension on the pressure surface,and in the highly 3-D region close to the endwall on the suction surface.The forecasted suction surface thermal exchange depicts great conformity with the measurement values and precisely reproduces the enhanced thermal exchange owing to the development and lateral distribution of the secondary flows along the midspan of the blade passage downstream.The impacts of the different secondary flow structures on the endwall thermal exchange are described in depth.

Analysis of secondary flow in shell-side channel of trisection helix heat exchangers

The flow characteristics of shell-side fluid in the tube-and-shell heat exchangers with trisection helical baffles with 35° inclined angles are numerically analyzed. The secondary flow distribution of the fluid in the shell-side channel is focused on. The results on meridian planes indicate that in the shell-side channel, the center part of fluid has an outward tendency because of the centrifugal force, and the peripheral region fluid has an inward tendency under the centripetal force. So in a spiral cycle, the fluid is divided into the upper and lower beams of streamlines, at the same time the Dean vortices are formed near the left baffle, and then the fluid turns to centripetal flow near the right baffle. Finally the two beams of streamlines merge in the main flow. The results of a number of parallel slices between two parallel baffles with the same sector in a swirl cycle also show the existence of the secondary flow and some backward flows at the V-gaps of the adjacent baffles. The secondary flows have a positive effect on mixing fluid by promoting the momentum and mass exchange between fluid particles near the tube wall and in the main stream, and thus they will enhance the heat transfer of the helix heat exchanger.

Numerical Study of the Intensity Correlation between Secondary Flow and Heat Transfer of Circle Tube-Finned Heat Exchanger with Vortex Generators

The application of vortex generators in tube-finned heat exchangers is very universal.The vortex generators can generate secondary flow,and as we all know secondary flow can obviously strengthen heat transfer.To use vortex generators much more efficiently in the circle tube-finned heat exchangers,the intensity correlation study between secondary flow and heat transfer is needed.22 different structures of circle tube-finned heat exchangers were numerically studied,including the plain fin cases and the cases with vortex generators.In addition,the influence of fin spacing,transverse and longitudinal tube pitch,heights and attack angle of vortex generators,positions of vortex generators and shape of vortex generators on heat transfer and fluid flow are studied,too.The non-dimensional parameter Se is applied to quantify the secondary flow intensity.The results show that Se can describe the secondary flow intensity very well.There is very close corresponding relationship between overall averaged Nu and volumetrically averaged Se for all the researched cases and the relational expression is obtained.However,there is no one-to-one correlation not only between Re and f but also between volumetrically averaged Se and f for all the studied cases.

Effects of the computational domain on the secondary flow in turbulent plane Couette flow

A series of direct numerical simulations of the fully developed plane Couette flow at a Reynolds number of 6000（based on the relative wall speed and half the channel height h） with different streamwise and spanwise lengths are conducted to investigate the effects of the computational box sizes on the secondary flow（SF）. Our focuses are the number of counter-rotating vortex pairs and its relationship to the statistics of the mean flow and the SF in the small and moderate computational box sizes. Our results show that the number of vortex pairs is sensitive to the computational box size, and so are the slope parameter, the rate of the turbulent kinetic energy contributed by the SF, and the ratio of the kinetic energy of the SF to the total kinetic energy. However, the averaged spanwise width of each counter-rotating vortex pair in the plane Couette flow is found, for the first time, within 4（1 ± 0.25）h despite the domain sizes.

Multi-relaxation time lattice Boltzmann simulation of inertial secondary flow in a curved microchannel

The inertial secondary flow is particularly important tbr hydrodynamic lbcusing and particle manipulation m biomed- ical research. In this paper, the development of the inertial secondary flow structure in a curved microchannel was investi- gated by the multi relaxation time lattice Boltzmann equation model with a force term. The numerical results indicate that the viscous and inertial competition dominates the development of secondary flow structure development. The Reynolds number, Dean number, and the cross section aspect ratio influence significantly on the development of the secondary vor- texes. Both the intensity of secondary flow and the distance between the normalized vortex centers are functions of Dean numbers but independent of channel curvature radius. In addition, the competition mechanism between the viscous and inertial effects were discussed by performing the particle focusing experiments. The present investigation provides an improved understanding of the development of inertial secondary flows in curved microchannels.

Secondary flow coefficient of overbank flow

This paper presents a 2D analytical solution for the transverse velocity distribution in compound open channels based on the Shiono and Knight method （SKM）, in which the secondary flow coefficient （K-value） is introduced to take into account the effect of the secondary flow. The modeling results agree well with the experimental results from the Science and Engineering Research Council-Flood Channel Facility （SERC-FCF）. Based on the SERC-FCF, the effects of geography on the secondary flow coefficient and the reason for such effects are analyzed. The modeling results show that the intensity of the secondary flow is related to the geometry of the section of the compound channel, and the sign of the K-value is related to the rotating direction of the secondary flow cell. This study provides a scientific reference to the selection of theK-value.

Numerical Investigation on the Secondary Flow Control by Using Splitters at Different Positions with Respect to the Main Blade

In turbomachinery,strong secondary flow can produce significant losses of total pressure near the endwall and reduce the efficiency of the considered turbomachine.In this study,splitters located at different positions with respect to the main blade have been used to reduce such losses and improve the efficiency of the outlet guide vane(OGV).Three different relative positions have been considered assuming a NACA 65-010 profile for both the main blade and the splitter.The numerical results indicate that splitters can effectively reduce the total pressure loss by suppressing the secondary flow around the main blade,but the splitters themselves also produce flow losses,which are caused by flow separation effects.

Secondary flows in statistically unstable turbulent boundary layers with spanwise heterogeneous roughness

Large-scale secondary motions are known to occur in turbulent flows over surfaces with spanwise roughness heterogeneity.Numerical studies often use adjacent high-and low-roughness longitudinal strips to investigate these secondary rolls in boundary layers without any thermal stratification.In the present study,the effect of unstable thermal stratification on secondary rolls in a very high-Reynolds-number turbulent flow with spanwise-heterogeneous roughness is investigated by means of large-eddy simulation.The strength of the unstable stratification is systematically changed from L/h=−20 to L/h=−1,where L and h are Monin-Obukhov length and boundary-layer height,respectively.This range covers the transition from neutral stratification to unstable stratification.The results show that the positive buoyancy associated with the unstable thermal stratification acts against the roughness-induced secondary rolls.In the case of unstable stratification,secondary rolls are completely canceled out by buoyancy and replaced by new stronger convection-induced rolls rotating in opposite directions.

Controlling secondary flow in high-lift low-pressure turbine using boundary-layer slot suction

The design of high-lift Low-Pressure Turbines(LPTs)causes the separation of the boundary layer on the suction side of the blade and leads to a strong secondary flow.This present study aims to minimize secondary losses through endwall slot suction and incoming wakes in a front-loaded high-lift LPT cascade with Zweifel of 1.58 under low Reynolds number of 25000.Two slotted schemes for the boundary layer of the endwall were designed(Plan A and Plan B),and the effects of suction mass flow on secondary flow were studied.The underlying physics of the endwall boundary layer of the suction and secondary flow under unsteady wakes was discussed.The results show that slot suction at the endwall boundary layer can significantly suppress the secondary flow by removing low-momentum fluids.Plans A and B significantly reduced the secondary kinetic energy by 44.2%and 36.9%,respectively,compared with the baseline cascade at the suction mass flow ratios of 1%.With an increase in the mass flow ratio of suction,the secondary flow was gradually reduced in both Plans A and B.It is more beneficial to control the secondary flow to destroy the intersection of the pressure side and suction side of the horseshoe vortex before it develops into a passage vortex.Under unsteady wakes,the combined effects of incoming wakes and endwall boundary layer suction can further suppress the secondary flow at the suction mass flow ratios of 2%for Plan A,because the positive and negative vorticity inside upstream wakes accelerated the mixing of the main flow and secondary flow and thus increased the energy of secondary vortices.

Effect of Incoming Vortex on Secondary Flows in Turbine Cascades with Planar and Non-Axisymmetric Endwall

Non-Axisymmetric Endwall Profiling(NAEP) is commonly utilized in turbines to eliminate secondary flows.Nevertheless,most of the NAEP methods consider a single-blade row environment without incorporating the effect of the stage environment.This paper aims to investigate the influence mechanism of the incoming vortex on the endwall secondary flow structures of NAEP in a highly loaded turbine cascade.To model the incoming vortex in a stage environment,this study considers a half-delta wing as the vortex generator at the upstream of the turbine cascade.The NAEP is then carried out for a highly loaded turbine cascade with an in-house numerical optimization design platform subject to no incoming vortex.Numerical simulation is also carried out under the influence of the incoming vortex for the turbine cascades with both planar and non-axisymmetric endwall.This paper furthers investigated the pitchwise effect of the incoming vortex on the near endwall secondary flow.The results indicate that the NAEP effectively improves the endwall secondary flow of the turbine cascade,where the total pressure loss coefficient and the secondary kinetic energy(SKE) are reduced by 7.3%,and 45.7%,respectively.It is further seen that with the incoming vortex,the NAEP achieves a considerable control effect on the endwall secondary flow of the turbine cascade.With incoming vortex,the NAEP can still achieve considerable control effect on the endwall secondary flow of the turbine cascade;the averaged reductions of loss coefficient and SKE are 7.8% and 14.2%,respectively.Under some pitchwise locations,incoming vortex can suppress the convection of cross-passage flow toward the suction corner greatly and reduce the loss coefficient of the baseline cascade.The incoming vortex at 4/7 pitch impinged right at the blade leading edge,leading to the generation of low-momentum fluid,which increased the size and the strength of the horseshoe vortex.Under all the pitchwise locations,NAEP can suppress the secondary vortices,e.g.,the passage vortex and the counter vortex,considerably.

Numerical and experimental investigation of quantitative relationship between secondary flow intensity and inviscid blade force in axial compressors

The secondary flow attracts wide concerns in the aeroengine compressors since it has become one of the major loss sources in modern high-performance compressors.But the research about the quantitative relationship between secondary flow and inviscid blade force needs to be more detailed.In this paper,a database of 889 three-dimensional linear cascades was built.An indicator,called Secondary Flow Intensity(SFI),was used to express the loss caused by secondary flow.The quantitative relationship between the SFI and inviscid blade force deterioration was researched.Blade oil flow and Computation Fluid Dynamics(CFD)results of some cascades were also used to cross-validate.Results suggested that all numerical cascade cases can be divided into 3 clusters by the SFI,which are called Clusters A,B and C in the order of the increasing SFI indicator.The corner stall,known as the strong corner separation,only happens when the SFI is high.Both calculations and oil flow experiments show that the SFI would stay at a low level if the vortex core at the endwall surface does not appear.The strong interaction of Kutta condition and endwall cross-flow is considered the dominant mechanism of higher secondary flow losses,rather than the secondary flow penetration depth on the suction surface.In conclusion,the inviscid blade force spanwise deterioration is strongly related to the SFI.The correlation of the SFI and spanwise inviscid blade force deterioration is given in this paper.The correlation could provide a quantitative reference for estimating secondary flow losses in the design.

Relationship between the Intensity of Secondary Flow and Convection Heat Transfer in a Helically Coiled Circular Tube with Uniform Wall Temperature

Numerical method is used to investigate fully developed laminar flow in helically coiled circular tube in this paper.The non-dimensional parameter(secondary flow Reynolds number Se)based on absolute vorticity flux along the mainstream is used to indicate the intensity of secondary flow caused by the centrifugal effect in helically coiled circular tube.The relationship between the intensity of secondary flow and the intensity of laminar convective heat transfer is studied.The effects of curvature and torsion on the enhancement of heat transfer are also considered.The results reveal that the absolute vorticity flux along the mainstream can be used to indicate the local or averaged intensity of secondary flow;the non-dimensional parameter of the absolute vortex along the main flow determines the convective heat transfer and friction factor.The relationships of Nusselt number and friction factor with the Se are obtained.The effect of curvature on Nusselt number is obvious,but the effect of torsion on Nusselt number is less obvious.

Effect of aspect ratio of elliptical stirred vessel on mixing time and flow field characteristics in the absence of baffles

Elliptical tanks were used as an alternative to circular tanks in order to improve mixing efficiency and reduce mixing time in unbaffled stirred tanks(USTs). Five different aspect ratios of elliptical vessels were designed to compare their mixing time and flow field. Computational fluid dynamics(CFD) simulations were performed using the k–ε model to calculate the mixing time and simulate turbulent flow field features, such as streamline shape, velocity distribution, vortex core region distribution, and turbulent kinetic energy(TKE) transfer. Visualization was also carried out to track the tinctorial evolution of the liquid phase. Results reveal that elliptical stirred tanks can significantly improve mixing performance in USTs. Specifically, the mixing time at an aspect ratio of 2.00 is only 45.3% of the one of a circular stirred tank. Furthermore, the secondary flow is strengthened and the vortex core region increases with the increase of aspect ratio. The axial velocity is more sensitive to the aspect ratio than the circumferential and radial velocity. Additionally, the TKE transfer in elliptical vessels is altered. These findings suggest that elliptical vessels offer a promising alternative to circular vessels for enhancing mixing performance in USTs.

The influence of drag parameter on submerged vegetation flow simulation using a porous approach

In simulating vegetated flows using the porous approach,the reasonableness of the drag coefficient significantly impacts the calculation results.This study employs large eddy simulation(LES)to quantitatively investigate the effect of drag parameters on key flow characteristics in submerged vegetated flows.The results indicate that changes in the drag coefficient significantly alter the velocity in the middle of the vegetation layer and near the water surface in the free-flow layer.Compared with longitudinal velocity,the drag coefficient has a more pronounced effect on the vertical distribution of Reynolds stress,especially its peak at the top of the vegetation layer.The porous approach can accurately reproduce the vertical distribution of longitudinal velocity and Reynolds stress,consistent with experimental measurements,only when shear-scale flow dominates.Due to the high-intensity secondary flow under moderate vegetation density,fluctuations in the drag coefficient have a more significant impact on the numerical results than in very dense vegetation.Therefore,selecting the drag coefficient value should be done cautiously,especially in the absence of experimental measurements for validation.

A Novel Model for the Prediction of Liquid Film Thickness Distribution in Pipe Gas-Liquid Flows

A model is proposed for liquid film profile prediction in gas-liquid two-phase flow,which is able to provide the film thickness along the circumferential direction and the pressure gradient in the flow direction.A two-fluid model is used to calculate both gas and liquid phases’flow characteristics.The secondary flow occurring in the gas phase is taken into account and a sailing boat mechanism is introduced.Moreover,energy conservation is applied for obtaining the liquid film thickness distribution along the circumference.Liquid film thickness distribution is calculated accordingly for different cases;its values are compared with other models and available experimental data.As a result,the newly proposed model is tested and good performances are demonstrated.The liquid film thickness distribution in small pipes and inclined pipes is also studied,and regime transition is revealed by liquid film profile evolution.The observed inflection point demonstrates that the liquid film thickness decreases steeply along the circumference,when the circle angle ranges between 30°and 50°for gas-liquid stratified flow with small superficial velocities.

Secondary steady-state and time-periodic flows from a basic flow with square array of odd number of vortices

In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.

Numerical Investigation of Influence of Tip Leakage Flow on Secondary Flow in Transonic Centrifugal Compressor at Design Condition

In a centrifugal compressor, the leakage flow through the tip clearance generates the tip leakage vortex by the in- teraction with the main flow, and consequently makes the flow in the impeller passage more complex by the inte- raction with the passage vortex. In addition, the tip leakage vortex interacts with the shock wave on the suction surface near the blade tip in the transonic centrifugal compressor impeller. Therefore, the detailed examination for the influence of the tip leakage vortex becomes seriously important to improve the aerodynamic performance cs- pccia｜ly for the transonic centrifugal compressor. In this study, the flows in the transonic centrifugal compressor with and without the tip clearance at the design condition were analyzed numerically by using the commercial CFD code. The computed results revealed that the tip leakage vortex induced by the high loading at the blade tip around the leading edge affected the loss generation by the reduction or the suppression of the shock wave on the suction surface of the blade.

THREE-DIMENSIONAL NUMERICAL MODELING OF SECONDARY FLOWS IN A WIDE CURVED CHANNEL

Most natural rivers are curved channels, where the turbulent flows have a complex helical pattern, as has been extensively studied both numerically and experimentally. The helical flow structure in curved channels has an important bearing on sediment transport, riverbed evolution, and pollutant transport study. In this article, different turbulence closure schemes i.e., the mixing-length model and the k-ε model with different pressure solution techniques i. e., hydrostatic assumptions and dynamic pressure treatments are applied to study the helical secondary flows in an experiment curved channel. The agreements of vertically-averaged velocities between the simulated results obtained by using different turbulence models with different pressure solution techniques and the measured data are satisfactory. Their discrepancies with respect to surface elevations, superelevations and secondary flow patterns are discussed.

The characteristics of secondary flows in compound channels with vegetated floodplains

The experiments were conducted in compound channels with vegetated floodplains for investigating the influence of vegetation types on the characteristics of secondary flows. In terms of the streamwise and transverse velocities and the depth-averaged velocity, the secondary flow coefficient, M, is proposed, with good physical meanings, and it may characterize the rotational direction and the intensity of the secondary currents. The experimental results show that, for the cases without vegetation and with grass, the rotational directions of the secondary flows are all antielockwise while for the cases with shrubs, they are all changed to the clockwise direction in the whole cross-section. However, when trees are planted, the secondary flows rotate in the anticlockwise direction in the main channel and in the clockwise direction on the floodplain. In addition, for all cases, the intensities of the secondary currents on the floodplain are stronger than those in the main channel.

Experimental Studies on The Mechanism and Control of Secondary Flow Losses in Turbine Cascades

This paper summarizes the results of the authors' 4 year experimental studies on the secondary flow losses in turbine cascades. Cascade wind tunnel experiments were carried out concerning the influence of aspect ratios, incidence, turning angles and outer endwall divergent angles in order to unveil the evolution mechanism of secondary flow losses in turbine cascades without end clearance. Some methods for controlling the secondary flows are investigated including the blade leaning, blade cambering, endwall convergence and leading edge extension at two ends of the blade.