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.

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.

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.

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.

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.

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.

SUPPRESSION OF THE SECONDARY FLOWS IN A BEND PIPE USING NAVIER-STOKES SOLVER AND EVOLUTIONARY ALGORITHMS

Hydrodynamic optimization design of the bend pipe from pump using theNavier-Stokes solver and evolutionary algorithms was conducted. The minimization of the totalpressure loss of the bend pipe was chosen as the design object in order to obtain the uniform exitflows through suppressing the secondary flows. The 3-D Navier-Stokes solver was applied to evaluatethe hydrodynamic performance of the bend-pipe flows. A 7th-order Bezier curve was used toparameterize the meridional section and elliptic representation was adopted to represent thecross-section profiles of the bend pipe. Evolutionary algorithms were applied in optimization. Theobtained results show that the designed bend pipe shape has much more uniform exit flows comparedwith the initial one and much weaker secondary flows, and that the evolutionary algorithms and CFDtechnique are the powerful optimization tools for the fluid machinery desiga

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 Effect of Secondary Flows on the Starting Pressure for a Second-throat Supersonic Ejector

The effect of the secondary flow on the starting pressure of a second-throat supersonic ejector has been investigated by adapting the height of the secondary flow inlet.The obtained results show that an optimum value of the secondary inlet height exists,and the starting pressure of the ejector becomes a minimum at that condition.Based on the results of the pressure measurements,a qualitative analysis has been made to clarify the flow behavior and the physical meaning of the performance diagram.It appears that the choking phenomenon of the secondary flow plays an important role in the starting process of the ejector.When the secondary inlet height is relatively small,the choked secondary flow and the supersonic primary flow could be employed to protect the static pressure in the suction chamber from being disturbed by the back pressure effect at a certain primary stagnation pressure,which is lower than the starting pressure for the case of the zero-secondary flow.However,as the secondary inlet height increases and exceeds a critical value,the static pressure in the suction chamber rapidly increases,and the starting pressure of the ejector increases accordingly.

A zero-flux principle for extracting secondary flows in arbitrary vertical planes of naturalrivers

The cross-sectional transverse flow field(represented by u_(con),)of rivers comprises a convective part(represented by ucon)and a circulatory part(represented by ueire),and a zero-flux principle of the ucire has been known for a long time.However,it is still difficult to separate the circulatory part from the convective part quantitatively in a 3-D velocity field,for an arbitrarily vertical plane in natura ivers of iregular shape this study,a ero-flux prineiple of the uis derived,o replace th old zero-fux principle of the ueire:.Based on the new principle,an all-purpose new method is proposed for extracting the circulations in arbitrary vertical planes of natural rivers of irregular shape.The calculation with the new method requires only the distribution of the horizontal velocities of a single vertical line(VL),and is simple.The calculation can be made based on either the velocity field simulated by a 3-D hydrodynamic model or the field measurements obtained by the acacoustic Doppler velocimetry(ADV).The new method is validated by using the field data of the lower Yangtze River.The extracted circulations are reasonable,while the results of the circulation extraction,respectively,based on the velocity field of a 3-D model and the field measurements of the ADV,are shown to be consistent.The capability of the method is also demonstrated,using the typical riverbends of the Yangtze River as examples.

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.

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 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.

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.

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.

LES for Turbulent Flows through Ducts of Regular-Polygon Cross-Sections

In this study,a large eddy simulation(LES)for fully-developed turbulent flows through a duct of regular-polygon cross-section using the immersed boundary(IB)method is performed.In case of the turbulent flow through the square duct,though there are some disagreements of the mean quantities related with the streamwise velocity among the present LES,the previous direct numerical simulation(DNS)and the LES without the IB method,and the present LES can reproduce the secondary flow of the DNS and LES.The LES result for ten types of regular-polygon duct shows that the secondary-flow speed decreases as the number of sides of the regular polygon n increases and that the secondary flow in case of the regular icosagon duct disappears like the turbulent pipe flow.In case of low n,the behavior of the turbulent structures near the side center is different from that near the vertex.