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.

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.

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.

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.

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.

Dynamic Characteristics Analysis on MHTGR Plant’s Secondary Side Fluid Flow Network

Multipe NSSS (Nuclear Steam Supply System) modules use the common feeding-water system to drive the common turbine power generation set. The SSFFN (secondary side fluid flow network) of MHTGR plant has features i.e. strong-coupling and nonlinearity. A wide range of power switching operation will cause unsteady flow, which may destroy the working elements and will be a threat for normal operation. To overcome those problems, a differential-algebraic model and PI controllers are designed for the SSFFN. In MATLAB\SIMULINK environment, a simulation platform is established and used to make a simulation of SSFFN of a MHTGR plant with two NSSS modules, which uses feedwater valves to control the mass flow rate in each module instead of feedwater pump. Results reflect good robustness of controllers.

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.

Influence of Tip Clearance on Unsteady Flow in Automobile Engine Pump

The automobile engine pump is an important part of the automobile cooling system,and has a direct influence on the engine performance.Based on the SST k-ωturbulence model,unsteady numerical simulation for an automobile engine pump with different tip clearances was carried out by Fluent.To study the flow field characteristics and pressure fluctuation,the characteristics of secondary flow distribution in volute are also analyzed.The result shows that the pressure fluctuation characteristics of the flow field show obvious periodic variation at different levels of tip clearances.The peak value of pressure fluctuation at each monitoring point is dependent on the blade frequency.At the same time,with the increase of the tip clearance,the pressure fluctuation in the blade and volute is gradually increased,while the pressure fluctuation at the tip is reduced clearance.The pressure gradient in the pump also varies periodically with the rotation of the impeller.With the increase of the tip clearance,the pressure of the impeller,volute and tip clearance is gradually decreased.There are secondary flow vortexes inside the impeller,volute outlet and volute section.With the increase of tip clearance,the vortex intensity in the impeller channel is weakened,and the vortex strength at the volute outlet is intensified.On the cross section of the volute,the morphology of most vortexes has insignificant changes,but the vortex intensity decreased.

THREE-DIMENSIONAL COUPLED IMPELLER-VOLUTE SIMULATION OF FLOW IN CENTRIFUGAL PUMP AND PERFORMANCE PREDICTION

A three-dimensional turbulent flow through an entire centrifugal pump is simulated using k-ε turbulence model modified by rotation and curvature, SIMPLEC method and body-fitted coordinate. The velocity and pressure fields are obtained for the pump under various working conditions, which is used to predict the head and hydraulic efficiency of the pump, and the results correspond well with the measured values. The calculation results indicate that the pressure is higher on the pressure side than that on the suction side of the blade; The relative velocity on the suction side gradually decreases from the impeller inlet to the outlet, while increases on the pressure side, it finally results in the lower relative velocity on the suction side and the higher one on the pressure side at the impeller outlet; The impeller flow field is asymmetric, i.e. the velocity and pressure fields arc totally different among all channels in the impeller; In the volute, the static pressure gradually increases with the flow route, and a large pressure gratitude occurs in the tongue; Secondary flow exists in the rear part of the spiral.

The dispersion of particles in turbulent semi-circular duct flows

The flow field in a semi-circular duct is simulated by Large Eddy Simulation(LES)and its particle field is simulated by Lagrange particle tracking method.Reynolds number Reb(based on bulk velocity and hydraulic diameter)is 80,000 and Ret(based on friction velocity and hydraulic diameter)is 3528.Particle diameter dpis chosen as 10,50,100,500 mm corresponding to St as 0.10,2.43,9.72,243.05.The results show that the intensity of the secondary flow near the ceiling is less than that near the floor because the ceiling is curved and able to inhibit the secondary flow.It is found that the difference between the semicircular duct and the square duct is that the secondary flow in a corner of the semi-circular duct is not symmetrical along the diagonal although they have the same generation mechanism.Regarding the particles,small particles(dp≤10 mm)are found to uniformly distribute in the duct,while large particles(dp≥50 mm)preferentially distribute in the corner and floor center.The maximum particles(dp=500mm)fall on the floor quickly and their dispersion mainly depends on the secondary flow near the floor.Particle deposition in the corner depends on particle size due to the effect of secondary flow and gravity.The effect of lift force on particles becomes more significant for 50 and 100 mm particles in comparison with other smaller particles.In the end,the effect of secondary flow is found to be more significant to dominate particle behavior than that of flow fluctuation.

Three-dimensional lattice Boltzmann method for simulating blood flow in aortic arch

The three-dimensional （3D） lattice Boltzmann models, 3DQ15, 3DQ19 and 3DQ27, under different wall boundary conditions and lattice resolutions have been investigated by simulating Poiseuille flow in a circular cylinder for a wide range of Reynolds numbers. The 3DQ19 model with improved Fillippova and Hanel （FH） curved boundary condition represents a good compromise between computational efficiency and reliability. Blood flow in an aortic arch is then simulated as a typical haemodynamic application. Axial and secondary fluid velocity and effective wall shear stress profiles in a 180° bend are obtained, and the results also demonstrate that the lattice Boltzmann method is suitable for simulating the flow in 3D large-curved vessels.

Prediction of velocity distribution in straight open-channel flow with partial vegetation by singular perturbation method

A numerical analysis model based on two-dimensional shallow water differential equations is presented for straight open-channel flow with partial vegetation across the channel. Both the drag force acting on vegetation and the momentum exchange between the vegetation and non-vegetation zones are considered. The depth-averaged streamwise velocity is solved by the singular perturbation method, while the Reynolds stress is calculated based on the results of the streamwise velocity. Comparisons with the experimental data indicate that the accuracy of prediction is significantly improved by introducing a term for the secondary current in the model. A sensitivity analysis shows that a sound choice of the secondary current intensity coefficient is important for an accurate prediction of the depth-averaged streamwise velocity near the vegetation and non-vegetation interfaces, and the drag force coefficient is crucial for predictions in the vegetation zone.

Effects of aspect ratio on unsteady solutions through curved duct flow

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.

Analysis of Flow Structure in Microturbine Operating at Low Reynolds Number

In this paper,three-dimensional flows in laminar subsonic cascades at relatively low Reynolds numbers(Re<2500)are presented,based on numerical calculations.The stator and rotor blade designs are those for a MEMS-based Rankine microturbine power-plant-on-a-chip with 109-micron chord blades.Blade passage calculations in 3D were done for different Reynolds numbers,tip clearances(from 0 to 20%)and incidences(0◦to 15◦)to determine the impact of aerodynamic conditions on the flow patterns.These conditions are applied to a blade passage for a stationary outer casing.The 3D blade passage without tip clearance indicates the presence of two large symmetric vortices due to the interaction between hub/casing boundary layers and the blade.Opening the tip clearance introduces the tip vortex,which tends to become dominant above a tip clearance of 10%.In addition to providing a description and understanding of the 3D flow in a MEMS microturbine,these results suggest the importance of considering 3D flows in the design of microturbomachinery,even though the geometry is dominantly 2D.