Development Of Secondary Flows Research Articles

Computational fluid dynamics and the physical modelling of an upland urban river

This paper describes the application of a commercially available, three-dimensional computational fluid dynamic (CFD) model to simulate the flow structure in an upland river that is prone to flooding. Simulations use a rectangular channel geometry, smooth sidewalls and a bed topography obtained from the field site that contains a subdued pool–riffle sequence. The CFD model uses the RNG κ– ε turbulence closure scheme of Yakhot and Orszag (J. Sci. Comput. 1 (1986) 1), as implemented in FLUENT 4.4.4, with a free surface. Results are shown for numerical runs simulating a 1:100 year return interval flood. Output from the numerical model is compared to a physical model experiment that uses a 1:35 scale fibreglass mould of the field study reach and measures velocity using ultrasonic Doppler velocity profiling (UDVP). Results are presented from the numerical and flume models for the water surface and streamwise velocity pattern and for the secondary flows simulated in the numerical model. A good agreement is achieved between the CFD model output and the physical model results for the downstream velocities. Results suggest that the streamwise velocity is the main influence on the flow structure at the discharge and channel configuration studied. Secondary flows are, in general, very weak being below the resolution of measurement in the physical model and less than 10% of the streamwise velocity in the numerical model. Consequently, there is no evidence for a ‘velocity dip’. It is suggested that the subdued topography or inlet morphology may inhibit the development of secondary flows that have been recorded in previous flat-bed, rectangular open channel flows. A significant corollary of these results is that the morphological evolution of the pool–riffle sequence at high discharges may be controlled primarily by the downstream distribution of velocity and sediment transport with little role for lateral sorting and sediment routing by secondary flows. This paper also raises a number of issues that may be of use in future CFD modelling of three-dimensional flow in open channels within the geomorphological community.

Mainstream Aerodynamic Effects Due to Wheelspace Coolant Injection in a High-Pressure Turbine Stage: Part I—Aerodynamic Measurements in the Stationary Frame

The relative aerodynamic and performance effects associated with rotor–NGV gap coolant injections were investigated in the Axial Flow Turbine Research Facility (AFTRF) of the Pennsylvania State University. This study quantifies the effects of the coolant injection on the aerodynamic performance of the turbine for radial cooling, impingement cooling in the wheelspace cavity and root injection. Overall, it was found that even a small quantity (1 percent) of cooling air can have significant effects on the performance character and exit conditions of the high pressure stage. Parameters such as the total-to-total efficiency, total pressure loss coefficient, and three-dimensional velocity field show local changes in excess of 5, 2, and 15 percent, respectively. It is clear that the cooling air disturbs the inlet end-wall boundary layer to the rotor and modifies secondary flow development, thereby resulting in large changes in turbine exit conditions.

Mainstream Aerodynamic Effects Due to Wheelspace Coolant Injection in a High-Pressure Turbine Stage: Part II—Aerodynamic Measurements in the Rotational Frame

The current paper deals with the aerodynamic measurements in the rotational frame of reference of the Axial Flow Turbine Research Facility (AFTRF) at the Pennsylvania State University. Stationary frame measurements of “Mainstream Aerodynamic Effects Due to Wheelspace Coolant Injection in a High Pressure Turbine Stage” were presented in Part I of this paper. The relative aerodynamic effects associated with rotor–nozzle guide vane (NGV) gap coolant injections were investigated in the rotating frame. Three-dimensional velocity vectors including exit flow angles were measured at the rotor exit. This study quantifies the secondary effects of the coolant injection on the aerodynamic and performance character of the stage main stream flow for root injection, radial cooling, and impingement cooling. Current measurements show that even a small quantity (1 percent) of cooling air can have significant effects on the performance and exit conditions of the high-pressure turbine stage. Parameters such as the total pressure coefficient, wake width, and three-dimensional velocity field show significant local changes. It is clear that the cooling air disturbs the inlet end-wall boundary layer to the rotor and modifies secondary flow development thereby resulting in large changes in turbine exit conditions. Effects are the strongest from the hub to midspan. Negligible effect of the cooling flow can be seen in the tip region.

Mechanics of the Flow in the Small and Middle Human Airways

Steady divergent flow (inspiration directed) is measured using Laser Doppler Velocimetry in a large-scale model carefully mimicing the morphometry of small human airways. The anatomical features, which induced vorticity in the flow from vorticity free entrance flow, are evaluated under conditions of convective similitude. The flow pattern in the daughter tubes is typical of laminar flow within the entrance to sharp bends (Dean number >500) with rapid development of strong secondary flows (maximum secondary velocity is 45 percent of mean axial velocity). The secondary flow consists of two main vortices, with two smaller and weaker secondary vortex activities toward the inner wall of curvature. There appears to be time dependent interaction with these vortices causing warbling at specific flow conditions. The calculated vorticity transport along the flow axis showed interaction between the viscous force at the new boundary layer development along the carinal wall and centrifugal force of curvature, with a significant influence by the upstream flow prior to entering the actual flow division. This interplay results in an overshoot of the calculated vorticity transport comparable to flow entering curved bends and suppression for the tendency to separate at the inner wall of these tight bends. The maximum primary flow velocities are skewed toward the carinal side (outer wall of curvature) and development of a second peak occurred with convection of the high velocity elements toward the inner wall of curvature by the strong secondary flow. [S0098-2202(00)01903-9]

Three-Dimensional Flowfield Downstream of an Axial-Flow Turbine Rotor

A systematic and comprehensive investigation was performed to provide detailed data on the threedimensional viscous flow phenomena downstream of a modern turbine rotor and to understand the flow physics such as the origin, nature, development of wakes, secondary flow, and leakage flow. The experiment was carried out in the Axial Flow Turbine Research Facility (AFTRF) at The Pennsylvania State University, with velocity measurements taken with a 3-D LDV System. Two radial traverses at 1% and 10% of chord downstream of the rotor were performed. Sufficient spatial resolution was maintained to resolve blade wake, secondary flow, and tip leakage flow. The wake deficit is found to be substantial, especially at 1% of chord downstream of the rotor. At this location, negative axial velocity occurs near the tip, suggesting flow separation in the tip clearance region. Cross-correlations are mainly associated with the velocity gradient of the wake deficit. The radial velocities, both in the wake and in the endwall region, are found to be substantial. Two counter-rotating secondary flows are identified in the blade passage, with one occupying the half span close to the casing and the other occupying the half span close to the hub. The tip leakage flow is restricted to 10% immersion from the blade tip. There are strong vorticity distributions associated with these secondary flows and tip leakage flow. The passage averaged data are in good agreement with design values.

A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus

A numerical and experimental study of buoyancy-driven flow in the annulus between two horizontal coaxial cylinders at Rayleigh numbers approaching and exceeding the critical values is presented. The stability of the flow is investigated using linear theory and the energy method. Theoretical predictions of the critical Rayleigh number for onset of secondary flows are obtained for a wide range of radius ratio R and are verified by comparison with results of previous experimental studies. A subcritical Rayleigh number which provides a necessary condition for global flow stability is also determined. The three-dimensional transient equations of fluid flow and heat transfer are solved to study the manifestation of instabilities within annuli having impermeable endwalls, which are encountered in various applications. For the first time, a thorough examination of the development of spiral vortex secondary flow within a moderate gap annulus and its interaction with the primary flow is performed for air. Simulations are conducted to investigate factors influencing the size and number of post-transitional vortex cells. The evolution of stable three-dimensional flow and temperature fields with increasing Rayleigh number in a large gap annulus is also studied. The distinct flow structures which coexist in the large gap annulus at high Rayleigh numbers preceding transition to oscillatory flow, including transverse vortices at the end walls which have not been previously identified, are established numerically and experimentally. The solutions for the large-gap annulus are compared to those for the moderate-gap case to clarify fundamental differences in behaviour. Heat transfer results in the form of local Nusselt number distributions are presented for both the moderate- and large-gap cases. Results from a series of experiments performed with air to obtain data for validation of the numerical scheme and further information on the flow stability are presented. Additionally, the change from a crescent-shaped flow pattern to a unicellular pattern with centre of rotation at the top of the annulus is investigated numerically and experimentally for a Prandtl number of 100. Excellent agreement between the numerical and experimental results is shown for both Prandtl numbers studied. The present work provides, for the first time, quantitative three-dimensional descriptions of spiral convection within a moderate-gap annulus containing air, flow structures preceding oscillation in a large-gap annulus for air, and unicellular flow development in a large-gap annulus for large Prandtl number fluids.

Development of secondary flow and convective heat transfer in isothermal⧹iso-flux rectangular ducts rotating about a parallel axis

The present study investigates rotation-induced secondary flow and mixed convection heat transfer in the entrance region of rectangular ducts rotating about a parallel axis. Boussinesq approximation is invoked to take into account the centrifugal buoyancy. Mechanisms of the secondary vortex development in ducts of isothermal or iso-flux walls are explored by a vorticity transport analysis. Numerical solutions of the parabolized velocity–vorticity formulation of Navier–Stokes⧹Boussinesq systems are used to corroborate the above theoretical analysis and provide evidence for the relevance of axial variation of transport rates to the evolution of the secondary vortices. The present results also reveal that the rotational effect in an iso-flux duct is more significant than that in an isothermal flux. In a fully developed flow region, the iso-flux case can still retain a secondary vortex effect, while the effect vanishes in isothermal ducts.

The influence of the wall temperature on the development of heat transfer and secondary flow in a coiled heat exchanger

In the present study the development of mixed convective flow is studied in a helically coiled heat exchanger with an axially varying wall temperature for Re = 500, Pr = 5 and δ = 1 14 and compared to the constant wall temperature boundary condition. In the method used the parabolized equations are solved using a finite difference discretization scheme. The influence of buoyancy forces is analyzed on heat transfer and secondary flow. For all Grashof numbers studied it appears that both heat transfer, quantified by the Nusselt number, and secondary flow, quantified by the relative kinetic energy, exhibit a wavy behaviour in axial direction. For higher Grashof numbers, however, this phenomenon diminishes for the case with an axially varying wall temperature due to stabilizing stratification effects.

Model Experiment on Physiologically Intermittent Flow in an Aortic Arch.

The aortic blood flow is characterized by the intermittent entry flow in a strongly curved tube because of the presence of stationary diastolic period. In this study we measured the axial and secondary velocity of intermittent flow in a strongly curved tube simulating the blood flow in an aortic arch (the ratio of the tube radius to the radius of curvature=1 / 3, Dean number=79l) by Laser Doppler Velocimeter. In order to reveal the effect of diastolic period (td) on the flow development, td ranges from 0.4 to 2.0 sec, whereas the systolic period remains constant (0.4 sec). During the deceleration phase of the systolic period, reversed axial flow starts to appear near the inner wall. This reversed axial flow becomes significant at the end of systolic phase and causes to induce the new secondary flow development. For td=0.4 sec flow does not diminish completely until the end of the diastolic period and affects the flow development in the following systolic period. This secondary flow augmentation in the beginning of diastolic phase is remarkable in the entry region of curved tube.

Experimental study of turbulent flow in a U-bend of circular cross-section

Hot-wire measurement of the longitudinal and radial velocity components and Reynolds stresses are reported for developing turbulent flow in a strongly curved 180 deg. pipe and its tangents. Slanted wire is rotated to 6 directions and the voltage outputs of them are combined to obtain the mean velocities and Reynolds stresses. Significant double maxima in the longitudinal velocity component appear in the bend. V-profiles reveal the development of a strong secondary flow. This secondary flow is induced by the transverse pressure gradient set up between the outer(ro/) and inner(ri/) wall region of the bend. Another second cross-stream flow develops after .theta.=135 deg. and its direction is opposed to that of main second flow.

Fully developed intermittent flow in a curved tube

Fully developed intermittent flow in a strongly curved tube was numerically simulated using a numerical scheme based on the simpler method. Physiological pulsatile flow in the aorta was simulated as intermittent flow, with a waveform consisting of a pulse-like systolic flow period followed by a stationary diastolic period. Numerical simulations were carried out for the following conditions: Dean number κ=393, frequency parameter α=4–27, curvature ratio δ=1/2, 1/3 and 1/7, and intermittency parameter η=0–1/2, where η is the ratio of a systolic time to the cycle period. For α=18 and 27 the axial-flow profile in a systolic period becomes close to that of a sinusoidally oscillatory flow. At the end of the systole, a region of reversed axial velocity appears in the vicinity of the tube wall, which is caused by the blocking of the flow, similar to blocked flow in a straight tube. This area is enlarged near the inner wall of the bend by the curvature effect. Circumferential flow accelerated in a systole streams into the inner corner and collides at the symmetry line, which creates a jet-like secondary flow towards the outer wall. The region of reversed axial velocity is extended to the tube centre by the secondary flow. The development of the flow continues during the diastolic period for α higher than 8, and the flow does not completely dissipate, so that a residual secondary vortex persists until the next systole. Accordingly, the development of secondary flow in the following systolic phase is strongly affected by the residual vortex at the end of the previous diastolic phase, especially by stationary diastolic periods. Therefore, intermittent flow in a curved tube is strongly affected by the stationary diastolic period. For η=0 and 1/5, the induced secondary flow in a systole forms additional vortices near the inner wall, whereas for η=1/3 and 1/2 additional vortices do not appear. The characteristics of intermittent flow in a curved tube are also strongly affected by the length of the diastolic period, which represents a period of zero flow.

Three-dimensional finite element model to simulate secondary flows: development and validation

This paper presents the formulation of a 3-D finite element hydrodynamic model to simulate secondary flows and their damping in channel bends and flow around obstacles. An emphasis has been focused on the formulation of viscous terms that are responsible for the secondary flow development. Basic equations and associated hypothesis are also presented in this paper. Validation of the model was performed based on a complex case. The model has correctly reproduced the development and the damping of secondary currents generated by river meanders. The comparison between experimental and numerical results confirms the validity of the formulation and the reliability of the approach.

Flow visualization and the three-dimensional flow in an axial-flow pump

Surface flow visualization on an axial-flow pump results in patterns of the skin-friction lines on various surfaces and these patterns provide important insight into the topology of the three-dimensional flowfield. In particular, critical points and lines within the patterns give characteristics of three-dimensi onal separation and the formation of vortical structures. Here, oil-paint tests show the topology for the formation of horseshoe vortices, the structure of three-dimensional corner separation, the initial development of a rotor tip leakage vortex, and the development of other important secondary flows. Surface flow visualization can also provide information concerning boundary-layer transition. In summary, the surface flow visualization experiment presented in this article allows one to give a fairly detailed description of the complex flow within an axial-flow pump.

Secondary flows through an impeller of centrifugal compressor at design and off-design conditions

The flow through a centrifugal compressor impeller was calculated using the 3-dimensional Navier-Stokes solution method. A control volume method based on a rotating curvilinear coordinate system was used to solve the time-averaged Navier-Stokes equations, and a standard k-.epsilon. model was used to obtain eddy viscosity. Numerical results and experimental data were compared for the overall performance of the impeller, the pressure distributions along the shroud wall and the detailed flowfields at the design and off-design conditions, which showed good coincidence. The flow through the impeller is complex with the curvature of the streamlines and rotation. The development of secondary flows and the jet-wake flow characteristics, which is the main source of flow loss, was discussed. Calculation results show quite different patterns as the flow rate changes.

Measurements of the Flow Field Within a Compressor Outlet Guide Vane Passage

A series of tests have been carried out to investigate the flow in a Compressor Outlet Guide Vane (OGV) blade row downstream of a single-stage rotor. The subsequent flow field that developed within an OGV passage was measured, at intervals of 10 percent axial chord, using a novel design of miniature five-hole pressure probe. In addition to indicating overall pressure levels and the growth of regions containing low-energy fluid, secondary flow features were identified from calculated axial vorticity contours and flow vectors. Close to each casing the development of classical secondary flow was observed, but toward the center of the annulus large well-defined regions of opposite rotation were measured. These latter flows were due to the streamwise vorticity at inlet to the blade row associated with the skewed inlet profile. Surface static pressures were also measured and used to obtain the blade pressure force at three spanwise locations. These values were compared with the local changes in flow momentum calculated from the measured velocity distributions. With the exception of the flow close to the outer casing, which is affected by rotor tip leakage, good agreement was found between these quantities indicating relatively weak radial mixing.

Three-Dimensional Flow Structure at Open-Channel Diversions

The authors correctly highlight the three-dimensional nature of flow in open channels and its important role in channel diversion dynamics. This discussion questions some of the ideas presented by the authors and suggest additional contributory sources for the development of secondary flow at channel divergences.

On necessary conditions for the secondary flow of non-Newtonian fluids in straight tubes

In this paper, we provide a necessary condition for the development of steady secondary flow of non-Newtonian fluids in straight tubes of arbitrary bounded cross-section under constant body force potential, without making any specific constitutive assumption. Speziale [11] showed, that for certain models involving quadratic terms in the kinematical tensors, axial flow is possible in straight tubes. However, his claim that secondary flows are not possible is only true under the additional assumption that the equations have unique solutions.

Aeroloads and Secondary Flows in a Transonic Mixed-Flow Turbine Stage

A numerical simulation of a transonic mixed-flow turbine stage has been carried out using an average passage Navier–Stokes analysis. The mixed-flow turbine stage considered here consists of a transonic nozzle vane and a highly loaded rotor. The simulation was run at the design pressure ratio and is assessed by comparing results with those of an established throughflow design system. The three-dimensional aerodynamic loads are studied as well as the development and migration of secondary flows and their contribution to the total pressure loss. The numerical results indicate that strong passage vortices develop in the nozzle vane, mix out quickly, and have little impact on the rotor flow. The rotor is highly loaded near the leading edge. Within the rotor passage, strong spanwise flows and other secondary flows exist along with the tip leakage vortex. The rotor exit loss distribution is similar in character to that found in radial inflow turbines. The secondary flows and nonuniform work extraction also tend to redistribute a nonuniform inlet total temperature profile significantly by the exit of the stage.

A model for phase lag of secondary flow in river meanders

The phase lag in a meandering channel is the phase difference between the development (growth and decay) of secondary flow and the channel curvature. The secondary flow is predominantly driven by the channel curvature; its phase lag behind (downstream of) the channel pattern is an important feature in the mechanics of flow and the migration pattern of meander bends. This paper presents an analytical solution for the phase lag derived based on the mechanics of secondary flow. The physical process for this approach is the growth and decay of secondary flow which has a basis different from flow instability used in previous approaches. The analytical approach employs simplifying assumptions to focus on the role of secondary flow; its limitations in application are described. Major variables affecting the phase lag are identified to be channel roughness, suspended sediment concentration, flow depth, and meander arc length. It is very interesting to note that similar variables for the phase lag have been identified based on different physical processes. The results of this study are compared with previous studies as well as laboratory and field data; they suggest that phase lags in tight meandering channels are pronounced.

Study on vortex flow control of inlet distortion

The present study demonstrates that the reduced Navier-Stokes code (RNS3D) can be used very effectively to develop a vortex generator installation for the purpose of minimizing the engine-face circumferential distortion by controlling the development of secondary flow. The computing times required are small enough that studies such as this are feasible within a design environment with all its constraints of time and costs. A series of design observations were made concerning the importance of various vortex generator design parameters in minimizing engine-face circumferential distortion. The study showed that vortex strength, generator scale, and secondary flowfield structure have a complicated and interrelated influence on the engine-face distortion, over and above the initial geometry and arrangement of the generators. Overall, the installed vortex generator performance was found to be a function of three categories of variables: 1) the inflow conditions, i.e., throat Mach number (inlet mass flow), Reynolds number, etc.; 2) the aerodynamic characteristics associated with the inlet duct; and 3) the design parameters related to the geometry, arrangement, and placement of the vortex generators within the inlet duct itself.