Secondary Flow Region Research Articles

Three-Dimensional Blade Boundary Layer and Endwall Flow Development in the Nozzle Passage of a Single Stage Turbine

The three-dimensional viscous flow field development in the nozzle passage of an axial flow turbine stage was measured using a “x” hot-wire probe. The measurements were carried out at two axial stations on the endwall and vane surfaces and at several spanwise and pitchwise locations. Static pressure measurements and flow visualization, using a fluorescent oil technique, were also performed to obtain the location of transition and the endwall limiting streamlines. The boundary layers on the vane surface were found to be very thin and mostly laminar, except on the suction surface downstream of 70 percent axial chord. Strong radial pressure gradient, especially close to the suction surface, induces strong radial flow velocities in the trailing edge regions of the blade. On the endwalls, the boundary layers were much thicker, especially near the suction corner of the casing surface, caused by the secondary flow. The secondary flow region near the suction surface-casing corner indicated the presence of the passage vortex detached from the vane surface. The boundary layer code accurately predicts the three-dimensional boundary layers on both vane surfaces and endwall in the regions where the influence of the secondary flow is small.

Secondary Flow Phenomena in an Axially Rotating FlowPassage with Sudden Expansion or Contraction

This paper investigates rotational effects on secondary flow in rotating flow passages with sudden expansion or contraction. Consideration is given to laminar flow. The governing boundary‐layer equations are discretized by means of a finite‐difference technique and numerically solved to determine the distributions of velocity vector under the appropriate boundary conditions. The Reynolds number (Re) and rotation rate are varied to determine their effects on the formation ofsecondary flows. It is disclosed from the study that: (i) when laminar flow is introduced into an axially rotating pipe with expansion, the stretch ofthe secondary flow zone is amplified with an increase in the rotation rate and Re, and (ii) in contrast, for axially rotating pipe flows with contraction, the secondary flow region is somewhat suppressed due to pipe rotation, and the change is slightly affected by the rotation rate and Re. Results may find applications in automotive and rotating hydraulic transmission lines.

Effects of secondary flow caused by a curved channel on plasma protein adsorption to artificial surfaces.

The effects of secondary flow induced by a curved channel on fibrinogen deposition and replacement on a glass surface were studied. Platelet adhesion to surface-bound fibrinogen was also studied to indicate how secondary flow may affect thrombogenesis on artificial surfaces. A saline pre-wetted channel with straight and curved sections was exposed to flowing plasma at a Reynolds number of 28.6. Results show that fibrinogen deposited on the surface at a shear rate of 175 s-1 was replaced faster in regions of secondary flow (Dean numbers from 11 to 19) than in adjacent regions of shear flow. Platelets adhered only to those surfaces where fibrinogen had been detected.

MIGRATORY BEHAVIOR OF JUVENILE AYU RELATED TO FLOW FIELDS IN DENIL AND STEEPPASS FISHWAYS

Portable Denil and steeppass fishways (0.3m wide, 0.3m deep) were experimentally installed on a divergent weir in Okitsu river. For ascended fishes to exit of the fishways, the number of fish in Denil were six times as many as ones in steeppass and the mean body size in steeppass were greater than ones in Denil. The fishes tend to choose the region of weak secondary flow and to ascend in upward secondary flow more than downward one in steeppass that contain much air bubble. The Denil fishways have the advantage of slower flow region without air bubbles for small fishes. It is pointed out for the juvenile ayu that flow directionality related to secondary flow and vortex scale have an effect on ascending behavior in the fishways.

Turbulent mixed-boundary flow in a corner formed by a solid wall and a free surface

Results from a joint numerical/experimental study of turbulent flow along a corner formed by a vertical wall and a horizontal free surface are presented. The objective of the investigation was to understand transport mechanisms in the corner. Numerical simulations were conducted at NRL to obtain data describing the dynamics of the near corner region. The Reynolds number for the simulations was Reθ ≈ 220. Flow visualization experiments conducted in the Rutgers free surface water tunnel were used to initially identify coherent structures and to determine the effect of these structures on the free surface. Time-resolved streamwise LDA measurements were made for Reθ ≈ 1150. The most significant results were the identification of inner and outer secondary flow regions in the corner. The inner secondary motion is characterized by a weak slowly evolving vortex with negative streamwise vorticity. The outer secondary motion is characterized by an upflow along the wall and outflow away from the wall at the free surface. Additional salient results included observations of surfactant transport away from the surface in cores of vortices connected to the free surface, intermittent energetic transport of fluid to the surface, and attenuation of streak motion by the free surface.

Investigation of three-dimensional flowfield at the exit of a turbine nozzle

The objective of the research reported in this article is to gain a detailed understanding of the flowfield at the exit of turbine nozzles. The flowfield was measured at two axial locations downstream of the nozzle of a single-stage turbine with a miniature five-hole probe. An area traverse was carried out to resolve the flowfield accurately, including the nozzle wake, secondary flow region, horseshoe vortex, and losses. All three components of the velocity, stagnation pressure, static pressure, and pitch and yaw angles have been resolved accurately. A distinct vortex core has been observed near the tip and at the hub. The indications are that the horseshoe vortex and the passage vortex have merged to produce a single-loss core region. Roughly, a third of the blade height passage near the tip and a third of the blade height near the hub is dominated by secondary flow phenomena. Only the middle third of the nozzle behaves according to design. The nozzle wake decay is compared to the wake decay of other blades. The nozzle wake decays much faster than a compressor cascade wake, an annular turbine nozzle cascade wake, or a turbine nozzle wake with a large rotor-stator spacing. This faster decay is attributed to effect of the downstream rotor at very small rotor-stator spacing (20% of nozzle axial chord). These and other data are presented, interpreted, and synthesized to understand the nozzle flowfield.

Flow Pattern and Pressure Drop in Viscoelastic Flow through Equidistant Multistage Slit

Viscoelastic flow patterns and pressure drop in single slit and equidistant multistage slit channels were investigated. In single slit channel, circularizer secondary flows were observed at the entrance, and abrupt expansion of streamlines (similar to die swell) was observed at the exit. In multistage slit channel, the circulating secondary flows at the first slit entrance were found to be the smallest compared with those at subsequent slits. These secondary flow regions depended on the first normal stress differences of the fluids. The pressure drop per slit, however, was the same through the channel. Relation between pressure drop and flow rate depended on the power law index.

Secondary Flow Measurements in a Turbine Cascade With High Inlet Turbulence

Measurements of the mean and turbulent flow field have been made in a cascade of high turning turbine rotor blades. The inlet turbulence was raised to 5 percent by a grid placed upstream of the cascade, and the secondary flow region was traversed within and downstream of the blades using a five-hole probe and crossed hot wires. Flow very close to the end wall was measured using a single wire placed at several orientations. Some frequency spectra of the turbulence were also obtained. The results show that the mean flow field is not affected greatly by the high inlet turbulence. The Reynolds stresses were found to be very high, particularly in the loss core. Assessment of the contributions to production of turbulence by the Reynolds stresses shows that the normal stresses have significant effects, as do the shear stresses. The calculation of eddy viscosity from two independent shear stresses shows it to be fairly isotropic in the loss core. Within the blade passage, the flow close to the end wall is highly skewed and exhibits generally high turbulence. The frequency spectra show no significant resonant peaks, except for one at very low frequency, attributable to an acoustic resonance.

等間隔スリット列流路内における粘弾性流体の流れ模様および圧力損失

Viscoelastic flow patterns and pressure drop in single slit and equidistant multistage slit channels were investigated. In single slit channel, circularizer secondary flows were observed at the entrance, and abrupt expansion of streamlines (similar to die swell) was observed at the exit. In multistage slit channel, the circulating secondary flows at the first slit entrance were found to be the smallest compared with those at subsequent slits. These secondary flow regions depended on the first normal stress differences of the fluids. The pressure drop per slit, however, was the same through the channel. Relation between pressure drop and flow rate depended on the power law index.

Ekman number dependence of the size of secondary flow regions generated by torsionally oscillating disks in stratified fluids

Measurements have been made of the size of the region of secondary flow in linearly stratified fluids (Brunt–Väisälä frequencies in the range 1.07–2.69 rad/sec that has been caused by torsionally oscillating disks, with radii of 3.0 cm≤r≤4.5 cm. Amplitudes of oscillation were held constant at approximately 1 rad and the frequency of oscillation varied from 0.69 rad/sec≤ω≤4.78 rad/sec. The fluid was bounded in a cylindrical container with a radius of 7.05 cm and the kinematic viscosity in the vicinity of the disk ν=1.08 cS, was approximately constant. Experiments were performed to extend the work of Folse et al. [Phys. Fluids 29, 667 (1986)] to include variations in the Ekman number, Ek=ν/ωr2. The size of the secondary flow region was measured from shadowgraphs and the flow field was mapped using a two-component laser-Doppler velocimeter. An empirical correlation of the data with the results of Folse et al. is presented.

Time-Dependent Laminar Backward-Facing Step Flow in a Two-Dimensional Duct

This paper presents results of numerical studies of the impulsively starting backward-facing step flow with the step being mounted in a plane, two-dimensional duct. Results are presented for Reynolds numbers of Re = 10; 368 and 648 and for the last two Reynolds numbers comparisons are given between experimental and numerical results obtained for the final steady state flow conditions. In the computational scheme, the convective terms in the momentum equations are approximated by a 13-point quadratic upstream weighted finite-difference scheme and a fully implicit first order forward differencing scheme is used to discretize the temporal derivatives. The computations show that for the higher Reynolds numbers, the flow starts to separate on the lower and upper corners of the step yielding two disconnected recirculating flow regions for some time after the flow has been impulsively started. As time progresses, these two separated flow regions connect up and a single recirculating flow region emerges. This separated flow region stays attached to the step, grows in size and approaches, for the time t → ∞, the dimensions measured and predicted for the separation region for steady laminar backward-facing flow. For the Reynolds number Re = 10 the separation starts at the bottom of the backward-facing step and the separation region enlarges with time until the steady state flow pattern is reached. At the channel wall opposite to the step and for Reynolds number Re = 368, a separated flow region is observed and it is shown to occur for some finite time period of the developing, impulsively started backward-facing step flow. Its dimensions change with time and reduce to zero before the steady state flow pattern is reached. For the higher Reynolds number Re = 648, the secondary separated flow region opposite to the wall is also present and it is shown to remain present for t → ∞. Two kinds of the inlet conditions were considered; the inlet mean flow was assumed to be constant in a first study and was assumed to increase with time in a second one. The predicted flow field for t → ∞ turned out to be identical for both cases. They were also identical to the flow field predicted for steady, backward-facing step flow using the same numerical grid as for the time-dependent predictions.

Behavior Analysis of Unmelted Layer in an Oval-Type Mixer for Polymeric Material

In order to perform a behavior analysis of polymeric material in a mixer with ovalor wing-type rotors, it was necessary to find a theoretical solution to the movement of an unmelted material layer. This layer, which appeared on to the rotor surface during the initial mixing period, was distinguished from the melt layer by a well-defined boundary. Photographs of material flow during various mixing stages of low-density polyethylene(LDPE) in a single-rotor mixer showed that the umelted layer moved along the rotor surface in the direction away from the tip region and finally broke at the end of the melt pool. This was previously referred to as the “breaking phenomenon.” The motion of the secondary flow boundary point, which is the separation point of the flow from the rotor surface, was analyzed using an assumed temperature distribution for the behavior model. The result agreed well with the actual movement of the unmelted layer. The result of model calculation indicates that the unmelted layer is the secondary flow region at the front face of the oval-type mixer. The breaking causes the undispersed, low-temperature material of the un-melted layer to flow into the melt layer and this gradually passes through the tip region of the rotor. During this passing period, the required torque increased even in the mixing of LDPE. Thus, it became more necessary to determine if this phenomenon corresponds to the second torque peak phenomenon which had been reported by many researchers for polymers containing large quantities of agglomerate particle additives such as carbon black.

Effects of blade boundary layer fences on secondary flow and losses in a turbine cascade.

This paper studies the effects of blade boundary fences on secondary flow and losses in a turbine cascade. Boundary layer fences were installed at the back of the cascade in parallel with the side walls. A wind tunnel test was conducted on the basis of different distances (Zf) between the fences and the endwalls. The fences effectively reduced secondary flow and loss. The total loss (the sum of net loss and secondary kinetic energy), net loss (average mass loss occurring between the upstream and downstream sides of the cascade), and secondary loss are minimized when Zf equals the inlet boundary layer thickness (d). The three losses decreased by 21, 12, and 32% respectively in comparison to the case of ordinary cascades. The passage vortex, trailing vortex, trailing secondary flow region thickness, and secondary kinetic energy were minimized when Zf = 2/3d. These values decreased by 30, 60, 40, and 50% respectively in comparison to the case of ordinary cascades. In the Zf range from 2/3d to 4/3d, fences shut up and trap the passage and trailing vortices. (14 figs, 2 tabs, 19 refs)

Turbulence models and their applications to the prediction of internal flows: A review

The paper presents a brief account of various turbulence models employed in the computation of turbulent flows, and evaluates the application of these models to internal flows by examining the predictions of various turbulence models in selected important flow configurations. The main conclusions of this analysis are: (a) The κ-ε model is used in a majority of all the 2-D flow calculations reported in the literature. (b) Modified forms of the κ-ε model improve the performance for flows with streamline curvature and heat transfer. (c) For flows with swirl, the κ-ε model performs rather poorly; the algebraic stress model performs better in this case. (d) For flows with regions of secondary flow (noncircular duct flows), the algebraic stress model performs fairly well. Two important factors in the numerical solution of the model equations, namely false diffusion and inlet boundary conditions, are discussed. The existence of countergradient transport and its implications in turbulence modeling are examined. Finally, some recommendations for improving the model performance are made. The need for detailed experimental data in flows with strong curvature is emphasized.

Pressure Flow of Non-Newtonian Fluids between Eccentric Double Cylinders with the Inner Cylinder Rotating

The authors experimentally observed the pressure flow of non-Newtonian fluids between eccentric double cylinders with the inner cylinder rotating. Experiments were carried out to measure the pressure gradient, the angle of the secondary flow region and the pressure distribution on the outer cylinder using aqueous solutions of hydroxy ethyl cellulose (HEC:). Results are summarized as follows:1) Axial flow rate was enhanced by the rotation of inner cylinder. Denote the axial flow rate Qs; and Qr; respectively with the inner cylinder stationary and rotating. Then the larger was the difference between Qs; and Qr; the larger was the effect of eccentricity.2) The angle of the secondary flow region increased with decreasing number of inner cylinder rotation and increasing axial pressure gradient.3) Distribution of pressure on outer cylinder was affected by the axial flow rate, radius ratio and eccentricity.4) Experimental results agreed well with numerical predictions. Thus the reliability of the numerical method used in the previous paper was confirmed.

Measurements of the size of the secondary flow regions generated by a torsionally oscillating disk in a linearly stratified fluid

Measurements have been made of the size of the region of secondary flow in a linearly stratified fluid, with Brunt–Väisälä frequencies in the range of 0.65–3.23 rad/sec, caused by a rotationally oscillating shearing stress. The stress was generated by the surfaces of a disk of radius r=5.078 cm undergoing torsional oscillations of angular frequency ω=1.50 rad/sec inside cylindrical boundaries with radii in the range 6.95–10.75 cm. The kinematic viscosity in the vicinity of the disk was approximately constant, ν=1.08 centistokes. Several features of the flow are similar to the secondary flow described by Scranton and Lindberg [Phys. Fluids 26, 1198 (1983)] as occurring in annular tank experiments to model geophysical turbulent mixing. For constant Ekman number Ek=ν/ωr2, the size of the secondary flow region depends on the Brunt–Väisälä frequency and the boundary radius; an empirical correlation of the data is presented.

強い二次流れを伴う倒立１８０°ベンド管内の流れの研究

Visualization studies of flow in vertically standing 180° bend rectangular section with strong curvature for Reynolds numbers (simplified Re) from 700 to 1500 reveal two regions of secondary flow. The secondary flow in such a strongly curved bends as curvature ratio 0.6 and 1.5 can be considered to have a forced vortex and a free vortex regions.When fluid particles exist in the former region, then fluid motion is rotational so that the dye-streak developes into a fine spiral line by the centrifugal force and primary flow, and besides dye-particles exist in the latter region, then fluid motion is irrotational, so that the streak developes into circular wavy thin belt by shear deformation and primary flow.A streak line which injecting dye to the center nozzle of the riser cross-section splits into two at θ=about 30° and secondary flow develop into rotation at θ=about 60° (θ=angular distance from the bend-starting point).Thus, twin counterrotating vortices come into the bend flow. The radius of gyration of a fluid particle in the barrier circle between forced and free vortex increases or decreases according to the strength of the free vortex.In this test, modiried Fround number exceeds far less than unity, the gravitation force will dominate than centrifugal force by bending. Further, the Coriolis force give rise to an additional acceleration to the centrifugal force.By this study was found that the secondary flow constitute a pair of counter-rotating streamwise vortices which is combined free vortex with forced vortex for Re from 800 to 1300. But above Re of 1300, the forced vortex strengthen than the free vortex as Re increase. Downward to Re of 800, the forced vortex weaken than the free vortex as the Reynolds number decrease.Numerical expressions for three typesof secondary flow patterns are given such as Vθ=αr +l, Vθ= αr1/2 and Vθ=αr-1 for the forced vortex, barrier and free vortex respectively, where Ve is peripheral velocity, r the radius of revolution and a constant.

Viscoelastic Flow in Y-Shaped Channel

A two-dimensional steady flow of viscoelastic and Newtonian liquids is investigated in Y-shaped channel. In the present paper a Maxwell model in which the viscosity term is due to Carreau is used for the viscoelastic liquid. It is the purpose of the present work to investigate the effects of elasticity and non-Newtonian viscosity on flow pattern.Numerical results agree qualitatively with experimental observations. With viscoelastic liquids a secondary flow appears upstream of the Y-shaped junction on its acute angle side. The region of secondary flow becomes larger with increasing Reynolds and Weissenberg numbers showing effects of elasticity and non-Newtonian viscosity. Whereas in the Newtonian flow no secondary flow appears at these Reynolds numbers, but when the Reynolds number becomes large a secondary flow appears downstream of the Y-shaped junction on its acute angle side.

Viscoelastic Flow in Y-Shaped Channel

A two-dimensional steady flow of viscoelastic and Newtonian liquids is investigated in Y-shaped channel. In the present paper a Maxwell model in which the viscosity term is due to Carreau is used for the viscoelastic liquid. It is the purpose of the present work to investigate the effects of elasticity and non-Newtonian viscosity on flow pattern.Numerical results agree qualitatively with experimental observations. With viscoelastic liquids a secondary flow appears upstream of the Y-shaped junction on its acute angle side. The region of secondary flow becomes larger with increasing Reynolds and Weissenberg numbers showing effects of elasticity and non-Newtonian viscosity. Whereas in the Newtonian flow no secondary flow appears at these Reynolds numbers, but when the Reynolds number becomes large a secondary flow appears downstream of the Y-shaped junction on its acute angle side.

Three-dimensional unsteady flow in an axial flow turbine

The results of an experimental program directed at understanding the unsteady mean and turbulent flow in a large-scale -l-Vi stage research turbine are presented. High response instrumentation and the phase-locked averaging data reduction technique were utilized to acquire data having high spatial and temporal resolution. These data included the unsteady three-dimensional distribution of mean and turbulent velocities and total and static pressures. The data between the guide vane and the rotor and downstream of the rotor are presented herein. The flow downstream of the vane was found to be essentially steady and was dominated by large Reynolds stresses in the wakes and secondary flow regions. In contrast, the flow downstream of the rotor was highly unsteady. Two different rotor exit flow regimes were identified, corresponding to maximum and minimum interaction of the rotor leading edges with the upstream vane wakes. During the maximum interaction, the vane wakes merged with the rotor wakes, the midchannel flow was fairly uniform, and two strong secondary flow vortices were present. During minimum interaction, the vane wakes entered the rotor passages between airfoils, the midchannel flow was nonuniform, and the secondary flow vortices were less well defined.