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The present paper numerically investigates viscoelastic fluid flow in the developing flow regime through both straight and 90-degree curve ducts. The aim is to investigate the effects of the first and second normal-stress differences (N1 and N2) as well as the curvature ratio ( $$\kappa = D/R$$ , where R and D are the curvature radius and channel side, respectively) and Reynolds number on the secondary flow patterns. Simulations were carried out in developing flow conditions in curved ducts using the finite volume method. The Reynolds numbers were 10, 20, 30, 40, 50, and 100, and the curvature ratios were 0.05, 0.066, 0.1, and 0.2. The Giesekus constitutive equation was utilized to model the non-linear rheological behavior of a 5.0 wt.% solution of polyisobutylene (PIB) in tetradecane (C14H30). The results reveal that a secondary flow with eight corner vortices is generated in a fully developed flow of viscoelastic fluid through a straight duct. This behavior is attributed to the difference in the second normal stress in the flow field. The results of the current study confirm that the second normal stress difference and change in the sign of N2 around the cross section’s corners trigger these corner vortices. Furthermore, the effects of the curvature ratio on the distributions of first and second normal-stress differences in the developing Dean flow were studied for the first time. The vorticity vector method was used for mixing-enhancement assessment. The results show that the intensity of secondary flows was significantly higher in viscoelastic fluid at all curvature ratios and at all considered Reynolds numbers than in Newtonian fluid flow.

Shock/turbulent-boundary-layer interactions (STBLIs) are ubiquitous in high-speed flight and propulsion applications. Experimental and computational investigations of swept, three-dimensional (3-D) interactions, which exhibit quasi-conical mean-flow symmetry in the limit of infinite span, have demonstrated key differences in unsteadiness from their analogous, two-dimensional (2-D), spanwise-homogeneous counterparts. For swept interactions, represented by the swept–fin-on-plate and swept–compression–ramp-on-plate configurations, differences associated with the separated shear layers may be traced to the intermixing of 2-D (spanwise independent) and 3-D (spanwise dependent) scaling laws for the separated mean flow. This results in a broader spectrum of unsteadiness that includes relatively lower frequencies associated with the separated shear layers in 3-D interactions. However, lower frequency ranges associated with the global “breathing” of strongly separated 2-D interactions are significantly less prominent in these simple, swept 3-D interactions. A logical extension of 3-D interaction complexity is the compound interaction formed by the merging of two simple interactions. The first objective of this work is therefore to analyze the more complex picture of the dynamics of such interactions, by considering as an exemplar, wall-resolved simulations of the double-fin-on-plate configuration. We show that in the region of interaction merging, new flow scales, changes in separation topology, and the emergence of lower-frequency phenomena are observed, whereas the dynamics of the interaction near the fin leading edges are similar to those of the simple, swept interactions. The second objective is to evolve a unified understanding of the dynamics of STBLIs associated with complex configurations relevant to actual propulsion systems, which involve the coupling between multiple shock systems and multiple flow separation and attachment events. For this, we revisit the salient aspects of scaling phenomena in a manner that aids in assimilating the double-fin flow with simpler swept interactions. The emphasis is on the influence of the underlying structure of the separated flow on the dynamics. The distinct features of the compound interactions manifest in a centerline symmetry pattern that replaces the quasi-conical symmetry of simple interactions. The primary separation displays topological closure to reveal new length scales, associated unsteadiness bands, and secondary flow separation.

The two-stage ejector has been suggested to replace the single-stage ejector geometrical configuration better to utilize the discharge flow’s redundant momentum to induce secondary flow. In this study, the one-dimensional gas dynamic constant rate of momentum change theory has been utilized to model a two-stage ejector along with a single-stage ejector. The proposed theory has been utilized in the computation of geometry and flow parameters of both the ejectors. The commercial computational fluid dynamics tool ANSYS-Fluent 14.0 has been utilized to predict performance and visualize the flow. The performance in terms of entrainment ratio has been compared under on- design and off-design conditions. The result shows that the two-stage ejector configuration has improved (≈57%) entrainment capacity than the single-stage ejector under the on-design condition.

Effect of eccentricity on jets delivered from a primary nozzle surrounded by secondary flow is studied experimentally. The eccentricity is achieved by offsetting the annular spacing of the co-flow passage, surrounding the center nozzle generating the primary jet. This is achieved by making a base plate with its center which is offset by 2 mm in the downward direction with the center of inner nozzle. The studies have been carried out in possible flow regimes of jet exiting from a convergent nozzle like subsonic and correctly and underexpanded sonic conditions. The experiments were carried out for primary nozzle exit Mach numbers of 0.3, 0.5, 0.8 and 1.0 at correct expansion. The studies in underexpanded regime were conducted for nozzle pressure ratios (NPR) of 3 and 4. The eccentricity in the co-flow jet leads to 38% reduction in the supersonic core length at NPR 3 and 60% at NPR 4 in comparison with concentric co-flow configuration. The eccentricity also leads to early mixing of co-flowing jet.

In the present paper, the steady RANS (Reynolds-Averaged Navier-Stokes) simulations based on our independently developed CFD (Computational Fluid Dynamics) solver NUAA-Turbo 2.0, are carried out to investigate the shock wave/tip leakage vortex (SW/TLV) interaction in two representative transonic axial fan rotors, NASA Rotor 67 and NASA Rotor 37. The intent of this study is mainly to verify if an identification method derived from relevant theories is suitable for shock-induced vortex stability in the real engineering environment. As the additional findings, a universal tip vortex model is established and the characteristics of vortex breakdown or not are also summarized under different load levels. To ensure the prediction accuracy of all numerical methods selected in this research, detailed comparisons are made between computational and experimental results before flow analysis. The excellent agreement between the both indicates that the current code is capable of capturing the dominant secondary flow structures and aerodynamic phenomenon, especially the vortex system in tip region and SW/TLV interaction. It is found that three vortical structures such as tip leakage vortex (TLV), shock-induced vortex (SIV), tip separation vortex (TSV) in addition the tip leakage vortex-induced vortex (TLV-IV, which only occurs when the TLV strength increases to a certain extent) frequently exist near the blade tip and then abstracted as a tip vortex model. A stable TLV after passing through the passage shock is commonly characterized by tight rolling-up, slow deceleration and slight expansion. Conversely, the vortex behaves in a breakdown state. The final verification results show that the above two vortex states can be satisfactorily detected by the theoretical discriminant introduced in this work.

This contribution describes experimental and numerical research of an unsteady behaviour of a flow in an end-wall region of a linear nozzle cascade. Effects of compressibility ($$M_\mathrm {2,is}$$ M 2 , is ) and inlet flow angle ($$\alpha _1$$ α 1 ) were investigated. Reynolds number ($$Re_\mathrm {2,is}$$ R e 2 , is $$=8.5\times 10^5$$ = 8.5 × 10 5 ) was held constant for all tested cases. Unsteady pressure measurement was performed at the blade mid-span in the identical position $${\mathfrak {s}}$$ s to obtain reference data. Surface flow visualizations were performed as well as the steady pressure measurement to support conclusions obtained from the unsteady measurements. Comparison of the surface Mach number distributions obtained from the experiments and from the numerical simulations are presented. Flow visualizations are then compared with calculated limiting streamlines on the blade suction surface. It was shown, that the flow structures in the end-wall region were not affected by the primary flow at the blade mid-span, even when the shock wave formed. This conclusion was made from the experimental, numerical, steady as well as unsteady points of view. Three significant frequencies in the power spectra suggested that there was a periodical interaction between the vortex structures in the end-wall region. Based on the data analyses, anisotropic turbulence was observed in the cascade.

Abstract— The occurrence of turbulent pulsations in straight pipes of noncircular cross-section leads to the situation, when the average velocity field includes not only the longitudinal component but also transverse components that form a secondary flow. This hydrodynamic phenomenon discovered at the twenties of the last century (J. Nikuradse, L. Prandtl) has been the object of active research to the present day. The intensity of the turbulent secondary flows is not high; usually, it is not greater than 2–3% of the characteristic flow velocity. Nevertheless, their contribution to the processes of transverse transfer of momentum and heat is comparable to that of turbulent pulsations. In this paper, a review of experimental, theoretical, and numerical studies of secondary flows in straight pipes and channels is given. Emphasis is placed on the issues of revealing the physical mechanisms of secondary flow formation and developing the models of the apriori assessment of their forms. The specific features of the secondary flow development in open channels and channels with inhomogeneously rough walls are touched upon. The approaches of semiempirical simulation of turbulent flows in the presence of secondary flows are discussed.

By solving the three-dimensional incompressible Reynolds-averaged Navier-Stokes equations, numerical simulations of the viscous flow within a flush type intake duct of a waterjet under different motion conditions are carried out. Therein, the effects of the steering and reversing unit as well as the impeller shaft on the flow field are taken into account. The numerical results show that the static pressure under backward conditions with the reversing jet flow is the lowest, and the cavitations are most likely to occur within the intake duct. The flow field under forward conditions is less uniform because of the shaft, while the velocity uniformity under backward conditions is improved. The shaft rotation causes an asymmetric secondary flow above the shaft under all conditions. The pressure contours under backward conditions with the reversing jet flow are sensitive to the presence of the shaft. This study can provide some references for the design optimization of waterjet propulsion system.

Theoretical investigation on the interaction between conducting and non-conducting walls on hydromagnetic natural convection flow of viscous incompressible and electrically conducting fluid through a vertical micro-channel taking into account the effects of induced magnetic field in presence of Hall current is presented. Governing coupled equations responsible for the flow are obtained when either the micro-channel walls are electrically conducting or are electrically non-conducting. Using the method of undetermined coefficients, exact solution are obtained and presented in dimensionless form subject to relevant boundary conditions. Expressions for fluid velocity, induced magnetic field, skin friction, volume flow rate and induced current density in both primary and secondary flow directions are also obtained. Effects of some governing parameters like Hall current parameter, rarefaction parameter and Hartmann number on the different flow situations are given using the aid of line graphs and Tables. The main conclusion of the present analysis is that, in the existence of rarefaction parameter, primary fluid velocity could be enhanced with the increase in Hall parameter when the micro-channel walls are either insulated or when the left micro-channel wall is electrically conducting. Results obtained in this work are relevant in many magnetically controlled devices and could also be used as a benchmark in checking the accuracies of result obtained in some empirical experiments.

Fluid flow analysis through a bend pipe is extensively conducted in practical and cell separation operations. It is observed that flow behaviors in the bend pipe are influenced by some parameters such as curvature, aspect ratio, etc. As a result, various phenomena, steady solution branches, unsteady solutions, energy transfer are changed. In this paper, the acts of flows are performed together for fixed curvature, δ = 0.2, and Prandtl number, Pr = 7.0 (water). Here, for a wide variety of Dean numbers (100 ≤ Dn ≤ 1000) and three fixed Grashof numbers, Gr = 100, 500, and 1000; time-independent solutions with linear stabilities are investigated first where only the first steady branch exhibits linear stability out of two steady solution branches obtained. Then, different flow transitions between the required range of Dean numbers (Dn) and several Grashof numbers (Gr) are investigated using time-dependent solutions. Power spectrum density (PSD) is further revealed in order to gain a deeper understanding of periodic and multi-periodic flows. Flow velocity contours including axial flow (AF) and secondary flow (SF) and their temperature profiles (TP) are also exposed. The SFs reveal that two- to four-vortex flows are produced due to the turning of steady branch and the flow instabilities. Furthermore, the energy transfer between the cooled and heated sidewalls of the pipe is calculated. Finally, a link between centrifugal and body force with the energy transfer has been shown in this research which reveals that the fluid has merged that certainly rises the overall energy transfer.

In this study, the preferential concentration and clustering of inertial particles in fully developed turbulent square duct flows are studied using large eddy simulations combined with Lagrangian approach, where the Reynolds number is equal to Reτ = 600 (based on the mean friction velocity and duct full height), and the particle Stokes number ranges from 0.0007 to 1.16. The results obtained for duct flows are compared with those for channel flows under the same working conditions. Then, the effect of the secondary flow on the particle concentration in duct flows is investigated. The equation of particle motion is governed by the drag force, lift force, added mass force, pressure gradient force, and gravity. The inter-phase interaction that was considered includes one-way and two-way coupling. The simulations of a single phase are verified and in good agreement with the available literature data. For the discrete phase, particles in the duct flow are found to be more dispersed in the vertical direction compared with the channel flow. In near-wall regions, a small fraction of particles tends to accumulate in duct corners, forming stable particle streaks under the effect of the secondary flow. Meanwhile, most particles are likely to reside preferentially in the low-speed flow regions and form elongated particle streaks steadily in the middle region of duct or channel floors. The Voronoi diagram analysis shows that the near-wall secondary flows in the square duct could cause particle clusters to transfer from regions of high to low concentration, and this trend increases with particle size. In addition, two-way coupling is found to enhance the near-wall particle accumulation and to promote particles to form more elongated streaks than one-way coupling. Finally, the mechanism responsible for the particle preferential concentration in turbulent square duct flows is determined.

A spectral-based computational algorithm is presented, showing the effects of rotation and curvature on a fluid flow with natural and forced convective heat transfer (CHT) in a rotating curved rectangular channel with an aspect ratio of 3 and curvature ratio ranging from 0.001 to 0.5. The bottom wall of the channel is heated, with cooling from the ceiling; the vertical walls are thermally insulated. The system is rotated about the vertical axis in the positive and negative directions with the Taylor number $$-2500\le Tr \le 2500$$ due to a constant pressure gradient force applied in the stream-wise direction. With the numerical computation presented, five branches of asymmetric steady solution curves comprising single-pair to 11-pair vortices are found. The change in the flow state is then evaluated by means of time-evolution computation, and sketching of the phase space of the solutions enables good prediction of the flow transition. It is found that in the case of co-rotation, a chaotic flow turns into a steady-state flow via a periodic or multi-periodic flow. In the counter-rotation case, however, irregular oscillations change directly to a multi-periodic flow. The study shows appearance of maximum 6-pair vortices at a small curvature, 11-pair vortices at a moderate curvature, and maximum 2-pair vortices at strong curvature. It is also observed that the number of secondary vortices reduces as Tr increases. The vortex structure of secondary flows is also shown in bar diagrams for easy visualization of the effect of curvature on the flow evolution. The study shows that the CHT is significantly enhanced by the secondary flow and a chaotic flow boosts the heat transfer more effectively than other physically realizable solutions. Finally, a comparison between the simulated and experimental results is performed and reasonable matching between the two solutions is observed.

Achieving a unique solution for the 3D inverse design of a curved duct is a challenging problem in aerodynamic design. The centre-line curvature, and cross-sections’ area and shape of a 3D curved d...

We propose a new type of microfluidic flow sensor, where the velocity measurements are not done on the fluid sample itself but on a second, immiscible fluid in contact with the sample. This allows us to use a low-cost, straight-forward, and well-developed particle tracking velocimetry on samples otherwise unsuitable for tracer particles. Our proof-of-concept experimental setup consists of a microfluidic device with the main channel filled with the sample and rectangular side-cavities, adjacent and opened to the main channel, filled with immiscible fluid with tracer particles. The flow in the main channel induces a circular secondary flow of the cavity liquid. We observed and analyzed the side-cavity particle movement and found that its characteristic parameters show a good linear correlation with flow velocity in the main channel over the whole observed range, from approx. $600~\mu \text{m}$ /s (volumetric flow rate $\Phi _{v} \cong 200$ nl/min, Reynolds number $\textit {Re} \cong 10^{-3}$ ) to approx. $3500 ~\mu \text{m/s}\left ({\Phi _{v} \cong 1200~ \text{nl/min}, ~\text{Re} \cong 10^{-2}}\right)$ .

In modern high-load high-pressure turbine, the secondary flow in the blade channel is very strong and occupies a large spanwise region. Although high-quality experimental data at the stage interfaces have been obtained in previous research, the influence of the clocking position on the secondary flow patterns is not fully understood. This paper investigates the clocking effect in a 1.5-stage high-pressure turbine and focuses on the variations of secondary flow patterns and their effect on the turbine performance. The detailed flow fields of various clocking positions were obtained by carrying out unsteady flow simulations using an in-house code. Among the four clocking positions in this work, the highest entropy generation was observed when the wakes from stator 1 hit the leading edges of stator 2, which is opposite to the well-known conclusion for the turbine with high-aspect-ratio blades. Detailed flow analysis showed that the wakes and the near tip secondary vortices from stator 1 showed different traces when entering the stator 2 channel and the secondary vortices clearly have a more important influence in determining the performance. The different behaviors of the secondary vortices explained the performance variations due to the clocking effect.

In the ongoing exploration, a mathematical model is analyzed to study the combined effects of centrifugal and buoyancy forces on fluid flow and heat transfer through a curved square duct of fixed curvature, δ = 0.1 . The outer and bottom walls of the duct are heated while the inner and ceiling walls are in room temperature. Firstly, grid efficiency for different Grashof numbers is checked with evaluating percent relative errors and then the accuracy of the numerical investigation with numerous articles is also compared. After numerical calculation, the steady solution branches with their linear stability have been performed by adopting spectral method. As a result, two branches of asymmetric steady solutions are obtained comprising with two- to four-vortex solutions. Linear stability analysis shows that only the first branch is linearly stable while the other branch is linearly unstable. It is found that the flow is stable at small values of Dean (Dn) whatever the Grashof (Gr) number is, and the stability is delayed as the Grashof number is increased. A substantial interaction is observed between the steady solution branches and the secondary flow structure. A diagram has also been presented which describes the creation of vortex structure of secondary flows for various Dn and Gr. Time history analysis shows that for G r = 200 periodic flow turns into steady-state flow before turning into periodic or multi-periodic oscillation once. For Gr > 200, however, the flow undergoes "multi-periodic/periodic → steady-state'', if Dn is increased. Phase space and power spectrum are obtained to confirm the non-linear characteristics of the flow. Nusselt numbers are computed as an exponent of heat transfer and it is detected that convective heat transfers to periodic and multi-periodic flows have boosted significantly more than steady-state flows. Finally, A comparison among the numerical data and experimental results has been conferred which has shown that there is good consent between them.

The inspiration for this study is to explore the crucial impact of viscous dissipation (VISD) on magneto flow through a cross or secondary flow (CRF) in the way of streamwise. Utilizing the pertinent similarity method, the primary partial differential equations (PDEs) are changed into a highly nonlinear dimensional form of ordinary differential equations (ODEs). These dimensionless forms of ODEs are executed numerically by the aid of bvp4c solver. The impact of pertinent parameters such as the suction parameter, magnetic parameter, moving parameter, and viscous dissipation parameter is discussed with the help of plots. Dual solutions are obtained for certain values of a moving parameter. The velocities in the direction of streamwise, as well as cross-flow, decline in the upper branch solution, while the contrary impact is seen in the lower branch solution. However, the influence of suction on the velocities in both directions uplifts in the upper branch solution and shrinks in the lower branch solution. The analysis is also performed in terms of stability to inspect which solution is stable or unstable, and it is observed that the lower branch solution is unstable, whereas the upper branch one is stable.

In turbmachinery, splitters are used to control secondary flow and to improve the aerodynamic performance of outlet guide vane (OGV) of axial fan. However, there is few information in the open literature focusing on the effect of the splitter geometry on the secondary flow control. In this work, the numerical investigations were performed for NACA 65-010 profile with different splitters. The spacing ratio of the main blade was 1, the spacing between the splitters and the main blade was 30mm. Three different splitters were compared to investigate the effect of the splitter geometry on secondary flow control. The flow structures near the end-wall, the streamlines on the suction surface of blade and the distribution of the flow losses on the trailing edge of blade was shown and discussed. The results showed the splitters can control the secondary flow and reduce the area of the high flow losses at the junction of end-wall and blade. However, the flow separation of the splitters also causes flow losses in the wake behind the splitters. Therefore, only the specific configuration of splitters can reduce the flow losses of the blade.

As the core equipment of the power generation system, a gas turbine is an indispensable energy-converting device in the national industry. The flow inside a high-pressure turbine (HPT) is highly unsteady, which has a great influence on the aerothermal performance and structural strength. To better clarify the flow mechanism and guide the advanced design, the basic flow characteristics of transonic turbines are investigated in the paper by a modified scale-adaptive simulation (SAS) model based on the shear stress transport (SST) turbulence model. The numerical results reveal the formation and development of the secondary flow structures such as wake vortex, pressure wave, shock wave, and the interactions among them. The length and frequency characteristics of wake are in good agreement with the large eddy simulation (LES) and the experimental data. Based on the detailed flow information, the local loss analysis is performed using the entropy generation rate. In summary, the wake vortex-related flow is the main origin of unsteadiness and entropy loss in high-pressure turbine cascade.

The hydrodynamic instability of a system of vertical motions initiated by spatially periodic distributions of heat sources is investigated. The Galerkin method with three basis trigonometric functions is used to describe the perturbation dynamics. The nonlinear system of equations for finding the expansion coefficients is formulated. It is found that the vertical motions are unstable in the absence of dissipation if the Richardson number is less than one eighth. A weakly nonlinear model of inviscid instability is developed. It is shown that the loss of stability in the presence of dissipation can lead to formation of either steady-state or time-oscillating secondary flow with nontrivial streamline topology.

The influence of channel side slope on flow in strongly curved channel bends is studied numerically. The performances of five different turbulence models are investigated. Comparison to experimental measurements demonstrates that the fully 3D numerical model can reliably simulate a channel bend flow field. Among the tested turbulence models, the realizable k − e model performed best. The present study also demonstrates that the realizable k − e model can satisfactorily predict smaller flow features in bend flow, such as the outer-bank circulation cell. The validated model is employed to carry out additional computations for channel bends with different side slopes. It is found that the number, position, and strength of secondary flow cells varies with the channel side slope, with corresponding influence on flow distribution and flow vorticity.

Realization of the S-duct benefits requires scrutiny of certain phenomena such as swirls, secondary flows, and flow distortion creation which are related to the S-duct due to its physical curvature. The first phase of the study investigated the flow field inside the S-duct. NASA Glenn research center’s S-duct was adopted in this study. Geometry was created in SOLIDWORKS and mesh was done using ICEM CFD. Numerical analysis was carried out in ANSYS Fluent software. A turbulence model named kω-SST was incorporated. Boundary conditions were set so as to match the experimental test done by NASA Glenn research center. Computational results showed a significant agreement with the experiment. The results also affirmed the presence of the secondary flow and flow distortion at the aerodynamic interface plane. The second phase of the study investigated the ability to control the flow and reduce the flow distortion on the engine fan face. Results showed a 10% flow distortion reduction and the secondary flow severity decreased by 16.5% on the aerodynamic interface plane (AIP). Keywords: Active Flow Control (AFC), Aerodynamic Interface Plane (AIP), Flow Distortion, S-duct

Detailed experimental and numerical investigations were performed for an ultra-high-lift front-loaded low-pressure turbine cascade (Zw = 1.58) with periodic wakes. The interaction mechanisms between the incoming wakes and endwall secondary flow were carefully examined. Wakes were produced by moving upstream rods, and flow field downstream of the cascade was measured using a seven-hole probe. Experimental results revealed that incoming wakes influenced not only the boundary layer development of the blade suction surface but also the complex endwall secondary vortex structures. On the suction surface: Incoming wakes clearly suppressed the suction side separation bubble at a low Reynolds number of 25000. Nevertheless, the effects of different wake passing frequencies were not significantly different at Re = 100000, and the profile losses under wake passing were even greater than in the absence of wakes. At the endwalls: Incoming wakes more strongly suppressed secondary flow at Re = 100000 than at Re = 25000, because the low-momentum fluid inside the incoming wakes clearly increased the endwall cross-passage pressure gradient at Re = 25000. The experimental results indicated that periodic wakes decreased the passage vortex and counter vortex core strength by 25% and 30%, respectively, at Re = 100000. Instantaneous results also demonstrated that endwall secondary vortices decreased significantly near the position of wakes passing.

The general pressure equation (GPE) based method is fully explicit, and the method does not require either solving the pressure Poisson equation nor executing sub-iteration for incompressible flow simulation. However, few numerical validations of GPE method are available, especially under complex flows like turbulence. In this work, GPE is used to conduct direct numerical simulations of the turbulent lid-driven cavity (LDC) flow at $${\text {Re}}=3200$$ and fully developed turbulent flow through a square duct at $${\text {Re}}_{\tau }=360.$$ Predicted turbulence statistics are compared with existing numerical and experimental data, providing an excellent quantitative agreement. The intricate flow patterns such as the Taylor–Gortler-like vortices in LDC flow and the mean secondary flow at the cross-section in the square duct are captured, showing both qualitative and quantitative agreements with measurements. Results from the present study indicate the capability of the GPE method for accurate incompressible turbulent flow calculation.

Detailed experimental measurements were conducted to study the interactions between incoming wakes and endwall secondary flow in a high-lift Low-Pressure Turbine (LPT) cascade. All of the measurements were conducted in both the presence and absence of incoming wakes, and numerical analysis was performed to elucidate the flow mechanism. With increasing Reynolds number, the influence of the incoming wakes on suppressing the secondary flow gradually increased owing to the greater influence of incoming wakes on reducing the negative incidence angle at higher Reynolds numbers, leading to a lower blade loading near the leading edge and suppression of the Pressure Side (PS) leg of the horseshoe vortex. However, the effect of unsteady wakes on suppressing the profile losses gradually became weaker owing to the reduced size of the Suction Side (SS) separation bubble and increased mixing loss in the free-flow region at high Reynolds numbers. Incoming wakes clearly improved the aerodynamic performance of the low-pressure turbine cascade at low Reynolds numbers of 25,000 and 50,000. In contrast, at the high Reynolds number of 100,000, the profile loss at the midspan and mass-averaged total losses downstream of the cascade were higher in the presence of wakes than in the absence of wakes, and the unsteady wakes exerted a negative influence on the aerodynamic performance of the LPT cascade. Keywords: Experimental study, High-lift, Incoming wakes, Low-pressure turbine, Secondary flow

In granular flows, the particles not only move along the principal streamlines but can also circulate perpendicularly to streamlines slowly in a vortex-like manner. Such behaviours have both scientific and practical significances, e.g. in convective mixing of particles, but their mechanisms are still under study. Previous experimental observations have stimulated two explanations for them: centrifugal force and volumetric dilatancy. Here a theoretical model is constructed to test these conjectures, which is based on the frictional plasticity and accounts for both dynamic effect and strain-dependent dilatancy. The simulation results show that, under the influence of gravity, the centrifugal force can indeed give rise to vortices in a Couette cell. In the absence of centrifugal force, granular vortices can still be observed depending on the shape of the yield surface. If the yield surface is a von Mises circle in the deviatoric plane, i.e. of Drucker-Prager type, no vortex is observed in continuum modelling. But for noncircular yield surfaces, a clear secondary flow is generated at some boundary conditions and increases in magnitude with the non-circularity of yield surface. Large granular dilatancy occurs in some regimes of high gradients, but altogether its influence on secondary flow is not critical. The role of boundary conditions is also discussed.

By using the Stereo Particle Image Velocimetry (PIV) technique we observe the secondary flow of second kind in a corner of a channel of square cross-section. The boundary layer thickness is much lower than the channel size. Therefore, the flow is still developing, not filling the entire channel cross-section, which is the case more widely reported in literature studied in a very long channel. The non-linear secondary effects of interacting boundary layers are observed as a single stream-wise vortex close to the channel corner in case of laminar boundary layers. In the case of turbulent boundary layers, the secondary flow takes shape of a symmetric pair of counter-rotating vortices. This pattern is observable only in the average velocity field, while the instantaneous ones display large amount of vortices, whose spatial distribution close to the corner in dependence on their orientation leads to statistically emergent net vorticity. At the same time, this pattern is reproduced by using a numerical simulation.

A computational simulation related with the study of the influence of Hall Current of a viscous incompressible steady fluid flow through a rotating straight pipe of rectangular cross-section in the presence of magnetic field along the center line is investigated numerically. A cylindrical coordinate system has been employed to derive the steady two-dimensional momentum equations. By using the usual transformation, the steady two dimensional coupled nonlinear partial momentum equations are transferred into non-dimensional coupled nonlinear partial momentum equations. The simulated result of the non-linear dimensionless problem is solved numerically with Spectral Method as the main tool and Collocation Method, Chebyshev Polynomial and Newton-Raphson Method are also used as secondary tools. Also, Arc length Method is used to compute the critical zone results. The influence of magnetic parameter, hall parameter, pressure gradient parameter and rotating parameter, the nature of the total flow (flux) and streamline flow are investigated with different aspect ratios. For strong hall current, magnetic force and Coriolis force, all fluid particles strength is weak. The Compaq visual FORTRAN 6.6a, Tech plot and Gost Script as well as Gost View software’s are used for simulation as well as plotting. Finally, the axial flow and secondary flow have been shown in contour and streamlines format.

In this work, secondary convection regimes in a. fluid with a. viscosity linearly dependent on temperature, enclosed between two vertical parallel planes heated to different temperatures, are studied. The boundaries of the layer were considered hard and perfectly heat-conducting. The problem was solved numerically by the finite difference method. Calculations were carried out for Prandtl numbers equal to one and twenty. In the first case, in a. fluid with constant viscosity, the loss of stability of the main flow is related to the development of hydrodynamic perturbations, which comprise motionless vortices at the boundary of the counter flows. In the second case, the instability of the main flow is caused by oscillatory perturbations, which comprise thermal waves. Dependences of the Nus-selt number on the Grashof number and data on the structure of the secondary flows are obtained. It is found that, if the Prandtl number is equal to unity, the Nusselt number monotonically increases with the Grashof number and, near the instability threshold of the main flow, it increases according to the root law; i.e., the secondary flow arises softly. The secondary structures look like drifting vortices at the boundary of counter flows, which, after a. transient process, leads to the establishment of steady oscillations of the heat flux. At a. Prandtl number of twenty, the relationship of the Nusselt number with the Grashof number is nonmonotonic; the curve contains sections in which the Nusselt number is equal to unity and sections in which the Nusselt number increases/decreases with increasing Grashof number. This behavior is explained by the fact that, for the Prandtl number equal to twenty, there are two instability modes; oscillatory and monotonic, and the region of increasing oscillatory perturbations with a. fixed wavenumber is bounded both above and below.

We investigate turbulent flow with highly pulsating axial velocity passing through a duct with both first and second bends. The time-dependent velocity fields downstream of the bends were measured using time-resolved stereo particle image velocimetry for the steady case (Reynolds number Re = 36,700) and the pulsatile case (Re = 37,800 and Womersley number α = 59.1). Proper orthogonal decomposition (POD) of the in-plane velocity data isolates the energetic structures of the secondary flow. The modes downstream of the first bend have a Dean motion (mode 0), single swirl (mode 1), and double swirl (mode 2), which agree with those of previous studies on steady turbulent flow. Downstream of the second bend, additional vortices appear in the modes owing to the secondary flow originating in the first bend. The modal structure of the pulsatile case is virtually the same as that of the steady case. To our knowledge, we are the first to find swirl switching in pulsatile flow, whereas the switching has been reported only for steady cases. We further conduct a time-frequency analysis via wavelet transformation onto the POD time coefficient, showing intermittency in energy of the mode associated with swirl switching., This work was partially supported by a research grant from The Hiroshima University Education and Research Support Foundation.

The turbulent flow and interchannel mixing in rod bundles is a concerned issue in the thermal-hydraulic design of fuel assemblies. In this paper, a large eddy simulation was performed to study the turbulent flow of water in a 2 × 2 rod bundle. The diameter of each rod and the pitch-to-diameter ratio were set to 20 mm and 1.25, respectively. The grid resolutions were carefully studied by examining the two-point correlation of velocity components along the streamwise direction, and by comparing the power spectral density with Kolmogorov’s −5/3 law. The numerical results showed that the root-mean-square (RMS) velocity is highly anisotropic in the gap area. The secondary flow on the cross-section of the rod bundle was nonuniform, and the intensity is strong close to the wall where small eddies were generated. The distributions of Reynolds normal and shear stresses and the budget of primary normal stress were presented.

The flow in a 90° bend with Rc/D = 1.5 is studied at a Reynolds number of 34,800 to characterize the unsteady motions that may affect mass transfer in the latter part of the bend and downstream pipe where differences have been reported. Two-component, time-resolved measurements were performed on the axial symmetry plane and on cross sectional planes in the bend and up to 1D downstream of the bend using refractive index matched Particle Image Velocimetry. The unsteady flow structures were examined using the Snapshot Proper Orthogonal Decomposition (POD) technique. Frequency spectra of the POD coefficients and low-order reconstructions were used to characterize the time scales and dynamics of the motion. Unsteady variations in the secondary flow, consisting of two vortices, were found throughout much of the bend and the downstream pipe. The largest effect of the secondary motions within the bend occurred near the outer wall and side walls of the bend. Low to moderate frequency motions ( St ≤ 0.17 ) were prevalent at the 10° and 20° cross sectional planes. Moderate frequency motions (St of 0.17–0.35) played an increasing role in the latter part of the bend. The instantaneous longitudinal and swirling velocity near the inner centerline were small at 70° into the bend, but increased near the end of the bend as the unsteady motions on the side walls extended to the inner centerline. The unsteady secondary motions near the outer wall decreased at the beginning of the downstream pipe, while the role of the moderate and high frequency secondary motions near the inner wall (St of 0.35 and 0.4–0.6) increased. The secondary flow near the inner wall in the downstream pipe appears responsible for the unsteady recovery of the streamwise velocity observed near the inner wall. The unsteady interaction of the high-speed flow with the outer wall appears responsible for the streamwise velocity fluctuations near the outer wall in the downstream pipe.

A computational study is presented on cross-stream migration and focusing of deformable capsules in curved microchannels of square and rectangular sections under inertial and non-inertial regimes. The numerical methodology is based on immersed boundary methods for fluid–structure coupling, a finite-volume-based flow solver and finite-element method for capsule deformation. Different focusing behaviours in the two regimes are predicted that arise due to the interplay of inertia, deformation, altered shear gradient, streamline curvature effect and secondary flow. In the non-inertial regime, a single-point focusing occurs on the central plane, and at a radial location between the interior face (i.e. face with highest curvature) of the channel and the location of zero shear. The focusing position is nearly independent of capsule deformability (represented by the capillary number, $Ca$ ). A two-step migration is observed that is comprised of a faster radial migration, followed by a slower migration toward the centre plane. The focusing location progressively moves further toward the interior face with increasing curvature and width, but decreasing height. In the inertial regime, single-point focusing is observed near the interior face for channel Reynolds number $Re_{C}\sim {O}(1)$ , that is also highly sensitive to $Re_{C}$ and $Ca$ , and moves progressively toward the exterior face with increasing $Re_{C}$ but decreasing $Ca$ . As $Re_{C}$ increases by an order, secondary flow becomes stronger, and two focusing locations appear close to the centres of the Dean vortices. This location becomes practically independent of $Ca$ at even higher inertia. The inertial focusing positions move progressively toward the exterior face with increasing channel width and decreasing height. For wider channels, the equilibrium location is further toward the exterior face than the vortex centre.

The accumulation of particles in a turbulent flow of incompressible air with mono-dispersed solid particles inside a 90° pipe bend was simulated using ANSYS® Fluent (CFD), taking into account the effect of gravity, drag force and a bidirectional fluid-particle coupling. An analysis of the geometrical parameters and the structures of the secondary flow generated in a curved pipe (Dean vortices) was developed, thus determining the characteristic time scales of the flow. Four Stokes numbers (Stk) were formulated, whose values are calculated and studied from the numerical simulations performed. Two different particle sizes (d1 = 50 μm y d2 = 150 μm), at two different flow conditions (Re1 = 61,500 y Re2 = 173,972), and for three curvature ratios Rc/R = 1, 4 and 8 were studied. The flow was solved using a Eulerian–Lagrangian approach with a RNG k-ε turbulence model. Once the multiphase flow was solved and validated, the distribution and maximum particle concentration inside the 90° bend were presented. Additionally, the Stk numbers were calculated to estimate the possible particle concentration level for the different system configurations (dp, Re and Rc/R). It is concluded that, if all Stk numbers are less than one, relative concentration levels reach a minimum, while for Stk numbers larger than one, an increase in the maximum concentration inside the pipe bend was noticed.

Despite great developments in inertial microfluidics, there is still a lack of knowledge to precisely define the particles’ behavior in the microchannels. In the present study, as a prerequisite to experimental studies, numerical simulations have been used to study the capture efficiency of target particles in the contraction–expansion microchannel, aiming to provide an estimation of the conditions at which the channel performs best. Fluid analysis based on Navier–Stokes equations is conducted using the finite element method to determine the streamlines and vortices. The highest capture efficiency for 10, 15, and 19-micron particles occurs when the center of the vortex is approximately in the middle of the wide section (at the flow rate of 0.35 ml/min). In addition to investigating the effect of particle diameter and input flow rate, the effect of channel geometry parameters (channel height and initial length of the channel) on particle trapping has also been studied. Also, to consider great interest in separating different-sized bioparticles from a sample, a three-stage platform has been designed to separate four types of bone marrow cells and evaluate the possibility of using contraction–expansion channels in this application.

The high-Strouhal-number pulsatile flow in a curved pipe is studied numerically. A general force analysis is developed for the bend force, where the new contribution from flow acceleration is identified and analysed. The mechanisms of secondary flow production are studied by extending Hawthorne's (Proc. R. Soc. Lond. A, vol. 206, issue 1086, 1951, pp. 374–387) model to account for viscous effects and applied to assess the distinct contributions from an inviscid stretching and no-slip condition. A detailed comparison is made between the numerical simulations and models for a pipe flow characterised by a volume flux case, which is explained using a linear secondary flow model.

Gas turbines widely applied to power generation and aerospace propulsion systems are continuously enhanced in efficiency for the reduction of environmental load. The energy recovery efficiency from working fluid in a turbine component constituting gas turbines can be enhanced by the increase of turbine blade loading. However, the increase of turbine blade loading inevitably intensifies the secondary flows, and consequently increases the associated loss generation. The development of the passage vortex is strongly influenced by the pitchwise pressure gradient on the endwall in the cascade passage. In addition, a practical high pressure turbine stage is generally driven under transonic flow conditions where the shock wave strongly influences the pressure distribution on the endwall. Therefore, it becomes very important to clarify the effects of the shock wave formation on the secondary flow behavior in order to increase the turbine blade loading without the deterioration of efficiency. In this study, the two-dimensional and the three-dimensional transonic flows in the HS1A linear turbine cascade at the design incidence angle were analyzed numerically by using the commercial CFD code with the assumption of steady compressible flow. The isentropic exit Mach number was varied from the subsonic to the supersonic conditions in order to examine the effects of development of shock wave caused by the increase of exit Mach number on the secondary flow behavior. The increase of exit Mach number induced the shock across the passage and increased its obliqueness. The increase of obliqueness reduced the cross flow on the endwall by moving the local minimum point of static pressure along the suction surface toward the trailing edge. As a consequence, the increase of exit Mach number attenuated the passage vortex.

The rotating flash flow has rarely been studied, although its characteristics affect significantly the performance of the two-phase flow turbine. In this paper, through analyzing the flashing flow obtained by CFD methods, which is validated with the experimental data, the relationships of average flow parameters under various rotational speeds were studied theoretically and numerically using the flow equations established on the Frenet coordinate system. The ratio of the mass flow rate under various rotational speeds was formalized and found to be dependent on the rotational speed and thermophysical properties. The generation and development of vapour were revealed and correlated to the geometry of the channel. The secondary flow in the flashing rotating channel was discussed and found to rotate in opposite directions upstream/downstream of the throat. The flashing induced near the throat had the effect on flow homogenizing in the normal direction of the cross-section. The analysis could be further applied to the analogy of the secondary flow between the rotating single-phase flow and the rotating flashing flow.

Most 2D (two-dimensional) models either take vertical velocity profiles as uniform, or consider secondary flow in momentum equations with presupposed velocity profiles, which weakly reflect the spatio-temporal characteristics of meander flow. To tackle meander flow in a more accurate 3D (three-dimensional) way while avoiding low computational efficiency, a new 3D model based on spectral methods is established and verified in this paper. In the present model, the vertical water flow field is expanded into polynomials. Governing equations are transformed by the Galerkin method and then advection terms are tackled with a semi-Lagrangian method. The simulated flow structures of an open channel bend are then compared with experimental results. Although a zero-equation turbulence model is used in this new 3D model, it shows reasonable flow structures, and calculation efficiency is comparable to a depth-averaged 2D model.

Aerospike nozzles represent an interesting solution for Single-Stage-To-Orbit or clustered launchers owing to their self-adapting capability, which can lead to better performance compared to classical nozzles. Furthermore, they can provide thrust vectoring in several ways. A simple solution consists of applying differential throttling when multiple combustion chambers are used. An alternative solution is represented by fluidic thrust vectoring, which requires the injection of a secondary flow from a slot. In this work, the flow field in a linear aerospike nozzle was investigated numerically and both differential throttling and fluidic thrust vectoring were studied. The flow field was predicted by solving the Reynolds-averaged Navier–Stokes equations. The thrust vectoring performance was evaluated in terms of side force generation and axial force reduction. The effectiveness of fluidic thrust vectoring was investigated by changing the mass flow rate of secondary flow and injection location. The results show that the response of the system can be non-monotone with respect to the mass flow rate of the secondary injection. In contrast, differential throttling provides a linear behaviour but it can only be applied to configurations with multiple combustion chambers. Finally, the effects of different plug truncation levels are discussed.

When two converging flows of unequal velocities and different flow directions come into contact, large-scale coherent structures are generated. For shallow conditions and small angles between the incoming streams, the mixing layer (ML) forming downstream of the confluence apex contains quasi-two-dimensional, Kelvin–Helmholtz (KH) vortices. Due to flow shallowness (e.g. stabilizing effect of bed friction), these vortices gradually lose their coherence at large distances from the ML origin. For large angles between the incoming streams, the spatial development of the shallow ML is more complex as strongly coherent, streamwise-oriented-vortical (SOV) cells form in the vicinity of the shallow ML and helical cells of secondary flow are generated due to curvature effects. The present paper uses three-dimensional eddy-resolving numerical simulations to study the effects of varying the angles between the two incoming channels and the downstream channel, the velocity ratio (VR) of the incoming flows and the flow depth on flow, turbulence structure and sediment entrainment mechanisms inside the ML and its surroundings. The simulations are performed for highly idealized conditions in which the ML develops in a wide channel (no interactions with the channel banks), over a flat bed and the flow depth is constant. Simulation results show that the SOV cells play an important role in the redistribution of the streamwise momentum. Some of the SOV cells are subject to bimodal oscillations in the lateral direction which induce strong interactions between the SOV cells and the ML vortices and sharply increase mixing. As for the case of a shallow ML developing between parallel streams, vortex pairing ceases some distance from the ML origin, the KH vortices start losing their coherence and the ML assumes an undulatory shape. The paper describes the effects of VR, angle between the incoming streams (α = 0° and 60°), planform geometry (symmetric vs. asymmetric confluences with α = 60°) and flow shallowness on the transverse shift of the ML centreline, ML width, dynamics of the KH vortices and on the formation, position and circulation of the SOV cells. In most of the α = 60° cases, the largest bed shear stresses are induced beneath the SOV cells rather than beneath the high-speed stream and the SOV cells play a major role in enhancing mixing between the two streams.

Due to remarkable applications of the curved ducts in engineering fields, scientists have paid much attention to invent new characteristics of curved-duct flow in mechanical systems. In the ongoing study, a computational modeling of fluid flow and energy distribution through a curved rectangular duct of large aspect ratio is presented. Governing equations are enumerated by using a spectral-based numerical technique together with the function expansion and collocation method. The main purpose of the paper is to analyze the effect of centrifugal force in the flow transition as well as heat transfer in the fluid. The investigations are performed for the aspect ratio, Ar = 4; the curvature ratio, $$\delta = 0.5$$ δ = 0.5 ; the Grashof number, $${\text{Gr}} = 1000$$ Gr = 1000 ; and varying the Dean number, $$0 < {\text{Dn}} \le 1000.$$ 0 < Dn ≤ 1000 . It is found that various types of flow regimes including steady-state and irregular oscillations occur as Dn is increased. To well understand the characteristics of the flow phase spaces and power spectrum of the solutions are performed. Next, pattern variations of axial and secondary flow velocity with isotherms are illustrated for different Dn’s. It is revealed that the flow velocity and the isotherms are significantly influenced by the duct curvature and the aspect ratio. Convective heat transfer and temperature gradients are calculated which explores that the fluids are diversified due to centrifugal instability, and as a consequence the overall heat transfer is enhanced significantly in the curved duct.

Transient, steady and oscillatory flows in a $180^{\circ }$ curved pipe are investigated both numerically and experimentally to understand secondary flow vortex formation and interactions. The results of numerical simulations and particle image velocimetry experiments are highly correlated, with a low error. To enable simulations in a smaller domain with shorter inlet section, an analytical solution for the unsteady Navier–Stokes equation is obtained with non-zero initial conditions to provide physical velocity profiles for the simulations. The vorticity transport equation is studied and its terms are balanced to find the mechanism of vorticity transfer to structures in the curved pipe. Several vortices are identified via various vortex identification (ID) methods and their results are compared. Isosurfaces of the $\unicode[STIX]{x1D706}_{2}$ vortex ID are used to explain the temporal and spatial evolution of vortices in the curved pipe. Eigenvalues and eigenvectors of the velocity gradient tensor are calculated for the swirling strength vortex ID method, which also determines vortex axis orientation. The classical Lyne vortex in oscillatory flow with an inviscid core is also revisited and its results are compared with the transient and steady flows. These in-depth analyses provide a better understanding and characterization of vortical structures in the curved pipe flow. Our findings show that, although there are some visual similarities between cross-sectional views of steady/transient flows and oscillatory flows, the structure herein designated as Lyne-type vortex detected in the cross-sections (under steady, transient and pulsatile flows) is not the same as the classical Lyne vortex pair (in oscillatory flows).

In this work we extend the vorticity-flux approach, proposed by Brown and Roshko (2012) for the analysis of turbulent shear layers and wakes, to the study of secondary flows of Prandtl’s second kind. To this end, we assess direct numerical simulations (DNSs) of turbulent flow through sinusoidal channels (Vidal et al., 2018a) at bulk Reynolds numbers R e h = 2500 and 5000, and with various wall wave parameters, leading to a range of secondary flow intensities. We find that the fluctuating vorticity-flux difference w ′ ω y ′ ¯ + − v ′ ω z ′ ¯ + is closely connected to the in-plane cross-flow, in particular the large negative values present around the wall peak, which enhance the transport of near-wall momentum towards the channel core. The tilting of sweep events at the wall valley is also connected to the secondary flow magnitude, and is associated with positive values of the fluctuating vorticity-flux difference. Furthermore, conditionally averaged fields show that, unlike what is observed in channels with flat walls, the behavior in the vorticity-flux field at the peak is mostly due to Q 1 and Q 4 events, which essentially tilt momentum towards the peak.