Secondary Flow Behavior Research Articles

Secondary flow behavior in a double bifurcation

Secondary flows in the form of multivortex structures can occur in bifurcation models as the result of upstream influence. Results from numerical modeling of steady inspiratory flows indicate that, for the case of a symmetric planar double bifurcation, four counter-rotating vortices develop in each of the grand daughter branches. In this paper, experimental visualization and verification is provided by particle image velocimetry measurements on a modified single bifurcation model. A splitter plate was positioned in the mother tube so that secondary vorticity was introduced into the fluid core. The axial velocity profile before the bifurcation junction resembles the M-shaped velocity profile commonly observed in bifurcated tube flows. The result of this manipulation is the development of a physically observable four-vortex configuration in the cross sections of the daughter branches, thus demonstrating the strong influence of upstream secondary vorticity. Through numerical visualization of vortex lines, it is shown that secondary vorticity is amplified by the extension of vortex lines due to secondary flow within the daughter tube. Order-of-magnitude arguments have been applied to the vorticity transport equation; and key dimensionless parameters have been obtained, accounting for curvature effects. Results indicate that the secondary vorticity goes through a maximum with increasing downstream distance, as a result of the interplay between vortex stretching and viscous effects.

J0501-1-1 小弦節比翼列ディフューザにおける二次流れの挙動解析(流体機械の研究開発におけるEFD/CFD(1))

A low-solidity cascade diffuser was proposed for achieving a wide operating range as well as a high pressure ratio. However, noise increased by means of LSD due to vortex shedding from the LSD blade surface. The objectives of the present study are to show that the noise can be reduced effectively by means of a small tip-groove located at the shroud side alone without deterioration of the LSD performance, and to clarify the mechanism of high blade loading of the LSD blade with the shroud side tip-groove limited near the LSD blade leading edge. The effect of a small groove on the stagnation area, the vortex generated in the tip groove and the secondary flow behavior on the suction surface of the LSD blade and the diffuser walls as well are analyzed numerically. It is found that the formation of the recirculating secondary flow generated additionally and significantly by the shroud tip-groove is a key point of the high LSD performance.

Experimental Investigation of Turbine Leakage Flows on the Three-Dimensional Flow Field and Endwall Heat Transfer

Within a European research project, the tip endwall region of low pressure turbine guide vanes with leakage ejection was investigated at DLR in Göttingen. For this purpose a new cascade wind tunnel with three large profiles in the test section and a contoured endwall was designed and built, representing 50% height of a real low pressure turbine stator and simulating the casing flow field of shrouded vanes. The effect of tip leakage flow was simulated by blowing air through a small leakage gap in the endwall just upstream of the vane leading edges. Engine relevant turbulence intensities were adjusted by an active turbulence generator mounted in the test section inlet plane. The experiments were performed with tangential and perpendicular leakage ejection and varying leakage mass flow rates up to 2%. Aerodynamic and thermodynamic measurement techniques were employed. Pressure distribution measurements provided information about the endwall and vane surface pressure field and its variation with leakage flow. Additionally streamline patterns (local shear stress directions) on the walls were detected by oil flow visualization. Downstream traverses with five-hole pyramid type probes allow a survey of the secondary flow behavior in the cascade exit plane. The flow field in the near endwall area downstream of the leakage gap and around the vane leading edges was investigated using a 2D particle image velocimetry system. In order to determine endwall heat transfer distributions, the wall temperatures were measured by an infrared camera system, while heat fluxes at the surfaces were generated with electric operating heating foils. It turned out from the experiments that distinct changes in the secondary flow behavior and endwall heat transfer occur mainly when the leakage mass flow rate is increased from 1% to 2%. Leakage ejection perpendicular to the main flow direction amplifies the secondary flow, in particular the horseshoe vortex, whereas tangential leakage ejection causes a significant reduction of this vortex system. For high leakage mass flow rates the boundary layer flow at the endwall is strongly affected and seems to be highly turbulent, resulting in entirely different heat transfer distributions.

Biosimulation and visualization: effect of cerebrovascular geometry on hemodynamics.

Hemodynamics plays an important role in cardiovascular disorders, and the authors are applying numerical and experimental studies of cerebrovascular blood flow to the creation and rupture of cerebral aneurysms. In particular, this study aims to investigate the effects of cerebrovascular geometry on hemodynamics, such as flow pattern, wall shear stress distribution, and pressure. This report consists mainly of two parts: numerical study of blood flow in the artery extracted from computer tomography data, and numerical and experimental studies of a curved pipe model. The simulation was conducted by using a finite element method; the experiment was conducted by particle imaging velocimetry. Numerical and experimental results are compared and both show similar secondary flow behavior.

Hydrodynamic Design of Pump Diffuser Using Inverse Design Method and CFD

A new approach to optimizing a pump diffuser is presented, based on a three-dimensional inverse design method and a Computational Fluid Dynamics (CFD) technique. The blade shape of the diffuser was designed for a specified distribution of circulation and a given meridional geometry at a low specific speed of 0.109 (non-dimensional) or 280 (m3/min, m, rpm). To optimize the three-dimensional pressure fields and the secondary flow behavior inside the flow passage, the diffuser blade was more fore-loaded at the hub side as compared with the casing side. Numerical calculations, using a stage version of Dawes three-dimensional Navier-Stokes code, showed that such a loading distribution can suppress flow separation at the corner region between the hub and the blade suction surface, which was commonly observed with conventional designs having a compact bowl size (small outer diameter). The improvements in stage efficiency were confirmed experimentally over the corresponding conventional pump stage. The application of multi-color oil-film flow visualization confirmed that the large area of the corner separation was completely eliminated in the inverse design diffuser.

Modeling of flows between two consecutive reverse curves

The objective of this paper is to model the behavior of secondary flows between two successive and reverse curves. The influence of different hydraulic and geometric parameters on the secondary current damping was also analysed. A three-dimensional finite element model has been developed based on Navier-Stokes equations assuming fluid incompressibility and hydrostatic pressure. An eddy viscosity formulation based on the mixing length concept has been introduced to correctly reproduce velocity profiles of turbulent flows. To validate the numerical model, velocity measurements have been conducted in the laboratory using two identical 90° curves separated by a straight reach. The predicted velocities have been compared with the experimental velocities measured at different channel sections. The validity of the numerical model formulation was confirmed by the laboratory work.

Behavior of Secondary Flow in a Turbulent Boundary Layer through Gaps between Roughness Elements.

In a turbulent boundary layer through gaps between roughness elements, behavior of secondary flow and streamwise vortices generated due to the three-dimensional roughness has been studied experimentally. Measurement was made on four different gap sizes, G=δ0/8, δ0/4, δ0/2 and δ0. Qualitative feature of secondary flow is similar in the four gap sizes. Positive and negative streamwise vortices exist behind the roughness and decay in a spanwise divergent flow field. In the decay process, strength of these vortices keeps the largest value at the smallest gap size, G=δ0/8. Streamwise vorticity has influence on magnitude of main rate of strain ∂U/∂y associated with the gap size and suppresses the mixing length scale. A ratio of the transverse and spanwise mixing length scales qualitatively depends on a corresponding deformation rate ratio.

Diffusion rate influences on inter-turbine diffusers

Inter-turbine diffusers are becoming of increasing importance to the aero gas turbine designer to diffuse the flow between the HP (high-pressure) or IP (intermediate-pressure) turbine and the LP (low-pressure) turbine. Diffusing the flow upstream of the LP turbine and raising the mean passage radius increases stage efficiency. These inter-turbine diffusers, which have high curvature, S-shaped geometry and low-energy wakes created by the upstream turbine, together give rise to secondary flows, making the flow fully three-dimensional. Using both experimental measurements and CFD (computational fluid dynamics) predictions, this paper demonstrates how the secondary flow behaviour is controlled by both the duct diffusion rate and upstream wake intensity.

B231 同軸回転するマルチディスク間の流れの可視化と数値解析

Flows between corotating flat multidisks were studied with two methods, flow visualization and numerical simulation. Flow visualization was performed for Reynolds number from 600 to 2000 and dimensionless spacing H/R of two disks from 0.1 to 0.4. When angular velocities of multidisks were changed to faster, slower or reverse rotation, streaklines of flow fields were observed in the laser light sheet. For the reverse of rotation, unsteady behavior of secondary flows in the meridian plane of two disks showed that tornado effects appeared on the disk in a short time, and then steady secondary flows of constant rotation were formed. Incompressible axisymmetric viscous flows between the multidisks were analyzed through the finite element method-the SMAC method. Growth process of the tornado effects in flow fields was numerically represented in detail. Results from numerical simulation corresponded to that of flow visualization.

Behavior of Secondary Flow in Turbulent Boundary Layer along Rows of Streamwise Square Ribs on Plane Surface.

This paper presents an experimental investigation of the turbulent boundary layer flow along rows of streamwise square ribs on a plane surface for various spacings of rows. The spacing between the centers of two adjoining square ribs was varied at S/D=2, 3, 4, 5, 7 and ∞, i.e., a single square rib. The time-mean velocity was measured by the Pitot and static pressure tubes. The turbulence intensities and auto-correlation were obtained using the data processing system and the F.F.T. analyzer connected to a hot wire anemometer. The Velocity vectors of secondary flow were measured by LDV. As a main result, the secondary flow becomes offset as the spacing between two ribs becomes small, since the directions of the secondary flow near the edges between the marked rib and the adjoining rib are opposite

Fluid Flow Behavior in the Curved Annular Sector Duct

A numerical analysis of the axial and secondary flow behavior in a curved annular sector duct is presented in the paper. The flow is considered to be fully developed laminar flow with constant physical properties. Five parameters have been identified as major variables in controlling the flow behavior. The study indicates that with a moderate Dean number and when the sector angle is smaller than π/2, only two vortices will appear in the cross section of the curved annular sector duct. When the sector angle is larger than π/2, the vortex structure can be very complex, and is often determined by other parameters, especially by the angle between the annular sector duct centerline and the curvature radius direction. The friction coefficient of the curved annular sector duct is affected mainly by the radius ratio, curvature, and axial pressure gradient. The radius ratio of the inner/outer walls can affect the vortex structure only when the radius ratio is very small. When the radius ratio is larger than 0.6, the friction coefficient is only slightly higher than that of a straight annular sector duct. Nevertheless, for the small radius ratio duct, the friction coefficient can be tripled, as compared with a straight annular sector duct. Although the holding pipe curvature and the axial pressure gradient cannot significantly change the vortex structure of the secondary flow, they can however, remarkably increase the friction coefficient by increasing the velocity gradient near the solid boundary.

Behavior of secondary flows in a rotating pipe

The later stages of laminar-turbulent transition are studied by direct numerical integration of the Navier-Stokes equations. A sequence of flow regimes which replace each other as the Reynolds number increases is obtained. In the coordinate system moving with the traveling wave this sequence includes steady, periodic, quasiperiodic and chaotic motions. The chaotic motion is preceded by synchronization of the frequencies of the quasiperiodic regime.

Some flow visualization and laser-Doppler-velocity measurements in a true-to-scale elastic model of a human aortic arch--a new model technique.

Flow studies were done in an elastic true-to-scale silicone rubber model of an aortic arch to study further hemodynamic influences on atherosclerosis. The model was prepared from a cast of a young woman. A revised model technique was used. The model had a compliance similar to that of the human aortic arch. Velocity measurements were done in the model with a two component laser-Doppler-anemometer in steady and pulsatile flow using a calcium chloride solution with a viscosity of eta = 3.18 mPas and density of rho = 1.28 kg/m3 at 20 degrees C. The time average Reynolds numbers over a whole cycle in the ascending aorta was Re = 1350. The Womersley parameter for pulsatile flow was a = 20. The pulse wave velocity in the ascending aorta was about c = 5.4 m/sec. The secondary flow behavior was discussed for steady and pulsatile flow. Reverse flows were found, especially along the inner radius of the aortic arch in the descending aorta in steady and pulsatile flow and also in small areas of the ascending aorta and at the branches of the aortic arch. The formation of atherosclerotic plaques at preferred local flow regions is discussed.

Calculation of three-dimensional transonic turbine cascade flow

A computer code has been applied to inviscid and viscous flows through a linear turbine cascade operating in the transonic flow regime. The Euler and Navier-Stokes equations are solved by an explicit finite-volume time-stepping procedure based on the method of Jameson et al. for the integration of the Euler equations and extended to Navier-Stokes equations by Schwamborn. The inviscid and viscous results in two-dimensions represent the profile characteristics at midspan position and the three-dimensional, viscous results include sidewall effects. A particular consideration of the flow losses gives detailed information about secondary flow behavior. The computational results are compared to experimental data for the MTU-T5.1 profile at isentropic outflow Mach numbers of 0.7, 0.9, and 1.1.

TURBULENT MOMENTUM AND HEAT TRANSPORT IN SQUARE-SECTIONED DUCTS ROTATING IN ORTHOGONAL MODE

Finite-volume computations are reported for the fully developed turbulent flow through a square-sectioned duct rotating about an axis perpendicular to that of the duct at a Reynolds number of 5 × 104. Two turbulence models are used to represent the turbulent stresses and heat fluxes in the main part of the flow: the standard k-∊ eddy-viscosity model (EVM) and an algebraic second-moment closure(ASM). In the semiviscous sublayer adjacent to the wall a generalization of Van Driest's version of the mixing-length hypothesis is adopted. Quadratic upstream discretization of momentum and energy convection is used with grid densities up to 65 × 127. The computed behavior is in close agreement with experimental data at low spin rates. At a Rossby number of 0.2, for which no data are available, the predictions show a complex secondary flow behavior with two counterrotating secondary eddies present. At this spin rate the mean level of Nusselt number is some 40% higher than in a nonrotating passage at the same Reynolds number, while there is a 2:1 variation in level circumferentially.

Turbulent Momentum and Heat Transport in Square-Sectioned Ducts Rotating in Orthogonal Mode

Finite-volume computations are reported for the fully developed turbulent flow through a square-sectioned duct rotating about an axis perpendicular to that of the duct at a Reynolds number of 5 x 10/sup 4/. Two turbulence models are used to represent the turbulent stresses and heat fluxes in the main part of the flow: the standard kappa-epsilon eddy-viscosity model (EVM) and an algebraic second-moment closure (ASM). In the semiviscous sublayer adjacent to the wall a generalization of Van Driest's version of the mixing-length hypothesis is adopted. Quadratic upstream discretization of momentum and energy convection is used with grid densities up to 65 x 127. The computed behavior is in close agreement with experimental data at low spin rates. At a Rossby number of 0.2, for which no data are available, the predictions show a complex secondary flow behavior with two counterrotating secondary eddies present. At this spin rate the mean level of Nusselt number is some 40% higher than in a nonrotating passage at the same Reynolds number, while there is a 2:1 variation in level circumferentially.

The effect of primary pump coastdown characteristics on loss-of-flow transients without scram in EBR-II

A series of loss-of-flow (LOF) tests without scram (unprotected) is planned for the Experimental Breeder Reactor II (EBR-II) to demonstrate the inherent shutdown capability of the reactor during an LOF event. The purpose of this paper is to discuss in detail the unprotected LOF transient analysis, the validation of the EBR-II reactivity feedback modeling, and the significance of pump coastdown characteristics on peak reactor temperatures. The tests as designed are limited by the fuel-cladding eutectic temperature of the fuel elements, and in order to meet the required temperature limit, the initial power and flow of all the tests are 16.7 and 20% of their rated values, respectively. To further reduce peak temperature, the primary tank temperature is to be decreased to 338°C from the nominal 371°C. The results show that primary flow coastdown rate and the capacity of the auxiliary pump have dramatic effects on the reactor temperatures. The impact of secondary flow depends somewhat on test conditions. When the auxiliary pump is in operation, the effect of secondary flow behavior on the reactor temperature becomes less significant during an unprotected LOF event.

Secondary Flows and Losses Downstream of a Turbine Cascade

The loss mechanisms and the behavior of secondary flows downstream of a large scale, linear turbine cascade have been investigated experimentally. A five-blade replica of the cascade used by Langston et al. at United Technologies Research Center was used for the present tests. Detailed flow measurements, using five-hole and three-hole probes, were made at four different planes, one just upstream of the trailing edge and the rest downstream. The secondary flow field at each measurement plane was found to be dominated by a single large passage vortex, which decayed in strength because of the mixing occurring in the flow. More than one-third of the losses were found to occur downstream of the trailing edge. This rise in total pressure loss in the present tests was almost entirely explained by a corresponding dissipation of the secondary kinetic energy of the flow. A mixing analysis of the flow was done to predict the additional losses due to “mixing” until the flow became completely uniform.

A new approach for solving the three-dimensional steady Euler equations. I. General theory

The present iterative procedure combines the Clebsch potentials and the Munk-Prim (1947) substitution principle with an extension of a semidirect Cauchy-Riemann solver to three dimensions, in order to solve steady, inviscid three-dimensional rotational flow problems in either subsonic or incompressible flow regimes. This solution procedure can be used, upon discretization, to obtain inviscid subsonic flow solutions in a 180-deg turning channel. In addition to accurately predicting the behavior of weak secondary flows, the algorithm can generate solutions for strong secondary flows and will yield acceptable flow solutions after only 10-20 outer loop iterations.

A new approach for solving the three-dimensional steady Euler equations. II. Application to secondary flows in a turning channel

The solution procedure developed in Part I (S.-C. Chang and J. J. Adamczyj, J. Comput. Phys. 59 (1985), 000-000) is discretized and used to obtain inviscid solutions for subsonic flows in a 180° turning channel. It is shown that the current algorithm can accurately predict the behavior of weak secondary flows and is capable of generating solutions for strong secondary flows. Moreover, it is shown that acceptable flow solutions may be contained after only 10–20 outer looop interactions.