Tip leakage aerodynamics over stepped squealer tips in a turbine cascade

Tip gap flow physics and aerodynamic loss generations for two stepped squealer tips of a “Higher Pressure-side rim and Lower Suction-side rim” (HPLS) tip and a “Lower Pressure-side rim and Higher Suction-side rim” (LPHS) tip have been investigated in a turbine cascade. For a fixed tip gap height-to-chord ratio of h/c = 2.0%, oil film flow visualizations are performed on the casing wall as well as on the cavity floor, and three-dimensional flow fields downstream of the cascade are measured with a five-hole probe. For the HPLS tip, the leakage inflow over the pressure-side rim cannot reach the suction-side rim in the upstream region due to the presence of an inlet flow intrusion, and there exists a strong near-wall flow heading toward the trailing edge all over the cavity floor. On the other hand, the LPHS tip has a mid-chord leakage flow penetration into the blade flow passage, and also provides a downstream leakage flow penetration deeper than that for the HPLS tip. Its cavity floor can be divided into a backward flow region and a wide separation bubble. Aerodynamic loss for the HPLS tip, which is nearly identical to that for the cavity squealer tip, is lower than those for the LPHS and plane tips in a considerable degree.     

Three-dimensional flow in axial flow fans of non-free vortex design

Three-dimensional laser Doppler anemometer (LDA) measurements were carried out downstream of isolated axial fan rotors of non-free vortex design in order to investigate the role of radial velocity components in design. The structure of secondary flows due to non-free vortex operation was studied in detail. It is pointed out that the tangential gradient of radial velocity at midspan is nearly in direct proportion with the spanwise gradient of ideal total head rise prescribed in design. Design criteria have been established for the neglect of torsion of stream surface segments inside the blading. A linear relationship was proposed in order to estimate the pitch-averaged radial velocities at the rotor exit. Using this relationship, a proposal has been put forward for taking the radial velocity components into account in non-free vortex design with the assumption of conical stream surfaces through the blading.     

Characterization of the tip clearance flow in an axial compressor using 3-D digital PIV

The accurate characterization and simulation of rotor tip clearance flows has received much attention in recent years due to their impact on compressor performance and stability. At NASA Glenn the first known three dimensional digital particle image velocimetry (DPIV) measurements of the tip region of a low speed compressor rotor have been acquired to characterize the behavior of the rotor tip clearance flow. The measurements were acquired phase-locked to the rotor position so that changes in the tip clearance vortex position relative to the rotor blade can be seen. The DPIV technique allows the magnitude and relative contributions of both the asynchronous motions of a coherent structure and the temporal unsteadiness to be evaluated. Comparison of measurements taken at the peak efficiency and at near stall operating conditions characterizes the mean position of the clearance vortex and the changes in the unsteady behavior of the vortex with blade loading. Comparisons of the 3-D DPIV measurements at the compressor design point to a 3D steady N-S solution are also done to assess the fidelity of steady, single-passage simulations to model an unsteady flow field.     

Effect of upstream velocity profile and integral flow straighteners on turbine flowmeters

One of the most important factors determining the shape of the calibration curve for a given turbine meter is the change in the upstream velocity distribution with flowrate. A theoretical model is evolved which can be used to predict the effects of velocity profile, viscosity and swirl on the calibration curve. It has also been used to explain the calibration curve of a commercial meter having a geometry very different from that for which the theory was developed. The effect of different types of integral flow straighteners on turbine meters is also investigated and found to depend on both the number of vanes and their length. A correlation is suggested for radial-vaned flow-straighteners     

Lift enhancement of airfoil and tip flow control for wind turbine

Two techniques that improve the aerodynamic performance of wind turbine airfoils are described. The airfoil S809, designed specially for wind turbine blades, and the airfoil FX60-100, having a higher lift-drag ratio, are selected to verify the flow control techniques. The flow deflector, fixed at the leading edge, is employed to control the boundary layer separation on the airfoil at a high angle of attack. The multi-island genetic algorithm is used to optimize the parameters of the flow deflector. The results indicate that the flow deflector can suppress the flow separation, delay the stall, and enhance the lift. The characteristics of the blade tip vortex, the wake vortex, and the surface pressure distributions of the blades are analyzed. The vortex diffuser, set up at the blade tip, is employed to control the blade tip vortex. The results show that the vortex diffuser can increase the total pressure coefficient of the core of the vortex, decrease the strength of the blade tip vortex, lower the noise, and improve the efficiency of the blade.     

Experimental study on axial development of liquid film in vertical upward annular two-phase flow

Accurate measurements of the interfacial wave structure of upward annular two-phase flow in a vertical pipe were performed using a laser focus displacement meter (LFD). The purpose of this study was to clarify the effectiveness of the LFD for obtaining detailed information on the interfacial displacement of a liquid film in annular two-phase flow and to investigate the effect of axial distance from the air–water inlet on the phenomena. Adiabatic upward annular air–water flow experiments were conducted using a 3 m long, 11 mm ID pipe. Measurements of interfacial waves were conducted at 21 axial locations, spaced 110 mm apart in the pipe. The axial distances from the inlet (z) normalized by the pipe diameter (D) varied over z/D = 50–250. Data were collected for predetermined gas and liquid flow conditions and for Reynolds numbers ranging from Re_G = 31,800 to 98,300 for the gas phase and Re_L = 1050 to 9430 for the liquid phase. Using the LFD, we obtained such local properties as the minimum thickness, maximum thickness, and passing frequency of the waves. The maximum film thickness and passing frequency of disturbance waves decreased gradually, with some oscillations, as flow developed. The flow development, i.e., decreasing film thickness and passing frequency, persisted until the end of the pipe, which means that the flow might never reach the fully developed state. The minimum film thickness decreased with flow development and with increasing gas flow rate. These results are discussed, taking into account the buffer layer calculated from Karman’s three-layer model. A correlation is proposed between the minimum film thickness obtained in relation to the interfacial shear stress and the Reynolds number of the liquid.     

The dynamics of two-dimensional cantilevered plates with an additional spring support in axial flow

In this paper, the dynamics of two-dimensional cantilevered flexible plates in axial flow is investigated using a fluid–structure interaction model. An additional spring support of either linear or cubic type is installed at various locations on the plate; its presence qualitatively affects the dynamics of the fluid–structure system. Without the spring, the cantilevered plate loses stability by flutter when the flow velocity exceeds a critical value; as the flow velocity increases further, the system dynamics is qualitatively the same: the plate undergoes symmetric limit cycle oscillations with increasing amplitude. With a linear spring, a state of static buckling is added to the dynamics. Rich nonlinear dynamics can be observed when a cubic spring is considered; the plate may be stable and buckled, and it may undergo either symmetric or asymmetric limit cycle oscillations. Moreover, when the flow velocity is sufficiently high, the plate may exhibit chaotic motions via a period-doubling route.     

Experimental and numerical investigations on the pure material instability of an Oldroyd's 3-constant model

Received March 25, 2001 / Published online November 15, 2001     

On numerical errors and turbulence modeling in tip vortex flow prediction

The accuracy of tip vortex flow prediction in the near‐field region is investigated numerically by attempting to quantify the shortcomings of the turbulence models and the flow solver. In particular, some turbulence models can produce a ‘numerical diffusion’ that artificially smears the vortex core. Low‐order finite differencing techniques of the convective and pressure terms of the Navier–Stokes equations and inadequate grid density and distribution can also produce the same adverse effect. The flow over a wing and the near‐wake with the wind tunnel walls included was simulated using 2.5 million grid points. Two subset problems, one using a steady, three‐dimensional analytical vortex, and the other, a vortex obtained from experiment and propagated downstream, were also devised in order to make the study of vortex preservation more tractable. The method of artificial compressibility is used to solve the steady, three‐dimensional, incompressible Navier–Stokes equations. Two one‐equation turbulence models (Baldwin–Barth and Spalart–Allmaras turbulence models), have been used with the production term modified to account for the stabilizing effect of the nearly solid body rotation in the vortex core. Finally, a comparison between the computed results and experiment is presented. Published in 1999 by John Wiley & Sons, Ltd.     

Effect of casing separations and tip leakage jets on turbine efficiency

A single stage model turbine has been provided with a set of three special inlet sections which include backward facing steps to produce casing separations of varying size upstream of the stator blades. In addition each inlet section is equipped so as tc be able to emit a swirling jet which simulates the tip leakage jet from a preceeding stage. It is demonstrated that there is a substantial efficiency penalty associated with the stepped casing and its attendant separation and that a small mitigation is brought about by the tip leakage jet, by re-energising the fluid in the separation zone     

An investigation of the heat transfer and static pressure on the over-tip casing wall of an axial turbine operating at engine representative flow conditions. (I). Time-mean results

The over-tip casing of the high-pressure turbine in a modern gas turbine engine is subjected to strong convective heat transfer that can lead to thermally induced failure (burnout) of this component. However, the complicated flow physics in this region is dominated by the close proximity of the moving turbine blades, which gives rise to significant temporal variations at the blade-passing frequency. The understanding of the physical processes that control the casing metal temperature is still limited and this fact has significant implications for the turbine design strategy. A series of experiments has been performed that seeks to address some of these important issues. This article reports the measurements of time-mean heat transfer and time-mean static pressure that have been made on the over-tip casing of a transonic axial-flow turbine operating at flow conditions that are representative of those found in modern gas turbine engines. Time-resolved measurements of these flow variables (that reveal the details of the blade-tip/casing interaction physics) are presented in a companion paper. The nozzle guide vane exit flow conditions in these experiments were a Mach number of 0.93 and a Reynolds number of 2.7 × 10⁶ based on nozzle guide vane mid-height axial chord. The axial and circumferential distributions of heat transfer rate, adiabatic wall temperature, Nusselt number and static pressure are presented. The data reveal large axial variations in the wall heat flux and adiabatic wall temperature that are shown to be primarily associated with the reduction in flow stagnation temperature through the blade row. The heat flux falls by a factor of 6 (from 120 to 20 kW/m²). In contrast, the Nusselt number falls by just 36% between the rotor inlet plane and 80% rotor axial chord; additionally, this drop is near to linear from 20% to 80% rotor axial chord. The circumferential variations in heat transfer rate are small, implying that the nozzle guide vanes do not produce a strong variation in casing boundary layer properties in the region measured. The casing static pressure measurements follow trends that can be expected from the blade loading distribution, with maximum values immediately upstream of the rotor inlet plane, and then a decreasing trend with axial position as the flow is turned and accelerated in the relative frame of reference. The time-mean static pressure measurements on the casing wall also reveal distinct circumferential variations that are small in comparison to the large pressure gradient in the axial direction.     

An investigation of the heat transfer and static pressure on the over-tip casing wall of an axial turbine operating at engine representative flow conditions. (II). Time-resolved results

This article reports the measurements of time-resolved heat transfer rate and time-resolved static pressure that have been made on the over-tip casing of a transonic axial-flow turbine operating at flow conditions that are representative of those found in modern gas turbine engines. This data is discussed and analysed in the context of explaining the physical mechanisms that influence the casing heat flux. The physical size of the measurement domain was one nozzle guide vane-pitch and from −20% to +80% rotor axial chord. Additionally, measurements of the time-resolved adiabatic wall temperature are presented. The time-mean data from the same set of experiments is presented and discussed in Part I of this article. The nozzle guide vane exit flow conditions in these experiments were a Mach number of 0.93 and a Reynolds number of 2.7 × 10⁶ based on nozzle guide vane mid-height axial chord. The data reveal large temporal variations in heat transfer characteristics to the casing wall that are associated with blade-tip passing events and in particular the blade over-tip leakage flow. The highest instantaneous heat flux to the casing wall occurs within the blade-tip gap, and this has been found to be caused by a combination of increasing flow temperature and heat transfer coefficient. The time-resolved static pressure measurements have enabled a detailed understanding of the tip-leakage aerodynamics to be established, and the physical mechanisms influencing the casing heat load have been determined. In particular, this has focused on the role of the unsteady blade lift distribution that is produced by upstream vane effects. This has been seen to modulate the tip-leakage flow and cause subsequent variations in casing heat flux. The novel experimental techniques employed in these experiments have allowed the measurement of the time-resolved adiabatic wall temperature on the casing wall. These data clearly show the falling flow temperatures as work is extracted from the gas by the turbine. Additionally, these temperature measurements have revealed that the absolute stagnation temperature within the tip-gap flow can be above the turbine inlet total temperature, and indicates the presence of a work process that leads to high adiabatic wall temperatures as a blade-tip passes a point on the casing wall. It is shown that this phenomena can be explained by consideration of the flow vectors within the tip-gap, and that these in turn are related to the local blade loading distribution. The paper also assesses the relative importance of different time-varying phenomena to the casing heat load distribution. This analysis has indicated that up to half of the casing heat load is associated with the over-tip leakage flow. Finally, the implications of the experimental findings are discussed in relation to future shroudless turbine design, and in particular the importance of accounting for the high heat fluxes found within the tip-gap.     

A numerical study on flow through the spiral casing of a hydraulic turbine

Flow through the spiral casing of a hydraulic turbine was analyzed. Reynolds averaged Navier–Stokes equations were solved using a finite element method. The physical domain was divided into a number of hexahedral elements which are isoparametrically mapped onto standard cubic elements. Numerical integration for the unsteady momentum equation is performed over such hexahedral elements to obtain a provisional velocity field. Compliance with the mass conservation equation and determination of the pressure correction are accomplished through an iterative procedure. The velocity distribution inside the spiral casing corroborates the results available in literature. The static pressure at the midplane generally decreases from the outside wall towards the exit of the spiral casing. © 1998 John Wiley & Sons, Ltd.     

Stereoscopic PIV measurement of unsteady flows in an axial compressor stage

Stereoscopic particle-image velocimetry (SPIV) measurements are conducted in a Low-speed Large-scale Axial Compressor. During the experiment the two CCD cameras are placed at the different sides of the laser light sheet and it is proved that this configuration is more suitable for the investigation in multi-stage turbomachines. The measured results, including the overall performances of many typical flow structures near the rotor tip region and the phase locked unsteady flows inside the stator passage at both the design and near-stall conditions, are introduced. Some new features of the complicated flow structures, such as the breakdown of the tip leakage vortex, the formation of the compound corner vortex at the rotor suction tip corner, the interactions between the hub stall and the tip separation and the rotor wakes, and the evolutions of the tip corner anti-rotating streamwise vortices inside the stator passage, are revealed.     

Design optimization of axial flow hydraulic turbine runner: Part I—an improved Q3D inverse method

With the aim of constructing a comprehensive design optimization procedure of axial flow hydraulic turbine, an improved quasi‐three‐dimensional inverse method has been proposed from the viewpoint of system and a set of rotational flow governing equations as well as a blade geometry design equation has been derived. The computation domain is firstly taken from the inlet of guide vane to the far outlet of runner blade in the inverse method and flows in different regions are solved simultaneously. So the influence of wicket gate parameters on the runner blade design can be considered and the difficulty to define the flow condition at the runner blade inlet is surmounted. As a pre‐computation of initial blade design on S2m surface is newly adopted, the iteration of S1 and S2m surfaces has been reduced greatly and the convergence of inverse computation has been improved. The present model has been applied to the inverse computation of a Kaplan turbine runner. Experimental results and the direct flow analysis have proved the validation of inverse computation. Numerical investigations show that a proper enlargement of guide vane distribution diameter is advantageous to improve the performance of axial hydraulic turbine runner. Copyright © 2002 John Wiley & Sons, Ltd.     

Experimental and numerical investigations of pressure drop in a rectangular duct with modified power law fluids

Numerical solutions are presented for fully developed laminar flow for a modified power law fluid (MPL) in a rectangular duct. The solutions are applicable to pseudoplastic fluids over a wide shear rate range from Newtonian behavior at low shear rates, through a transition region, to power law behavior at higher shear rates. The analysis identified a dimensionless shear rate parameter which, for a given set of operating conditions, specifies where in the shear rate range a particular system is operating, i.e. in the Newtonian, transition, or power law regions. The numerical results of the friction factor times Reynolds number for the Newtonian and power law region are compared with previously published results showing agreement within 0.05% in the Newtonian region, and 0.9% and 5.1% in the power law region. Rheological flow curves were measured for three CMC-7H4 solutions and were found to be well represented by the MPL constitutive equation. The friction factor times Reynolds number values were measured in the transition region for which previous measurements were unavailable. Good agreement was found between experiment and calculation thus confirming the validity of the analysis.     

Laser Doppler anemometry measurements of laminar flow in helical pipes

Three-dimensional laser Doppler anemometry measurements are performed on developed laminar flow in three helical pipes. The experimental observations are compared to results of numerical calculations employing the fully elliptic numerical method. Good agreement is found between measured data and numerical results. The three helical pipes, with curvature ratios of 0.0734 and 0.1374 and non-dimensional pitches of 0.0793 and 0.193, are adopted to study the effects of curvature and pitch on laminar flow in the experimental approach. The range of Reynolds numbers is 500–2000 to ensure laminar flow in the entire helical pipe. Both the profile shapes of the normal components of the secondary flow and those of the axial flow along the same centerline present not only similar patterns but also similar change when pitch, curvature ratio, and Reynolds number vary. The results demonstrate comprehensive relationships between the axial flow and the secondary flow.     

Experimental and numerical investigations on PDE performance augmentation by means of an ejector

To improve the performance of pulse detonation engines, a 48 cm long cylindrical combustion chamber of 5cm internal diameter (i.d.) is fitted with an ejector of constant section. The role of the ejector is (i) to provide partial confinement of the detonation products escaping from the chamber and (ii) to suck in fresh air and then to increase the mass ejected compared to the ejection of burned gases alone.The combustion chamber is fully filled with a stoichiometric ethylene/oxygen mixture at ambient conditions. Three parameters of the ejector are varied: the i.d. D, the length L, and the position d relative to the thrust wall of the combustion chamber. For various configurations, the specific impulse (I _sp) is determined in single shot experiments. The maximum operating frequency (f _max) and the maximum thrust are then deduced. I _sp is measured by means of the ballistic pendulum method, and f _max is derived from the pressure signal recorded on the combustion chamber thrust wall.The addition of an ejector increases the specific impulse up to 60% in the best configuration tested, from 164s without ejector to 260s with ejector. The specific impulse can be represented by a single curve using suitable dimensionless parameters. The thrust results for the main ejector studied (D = 80mm) indicate an optimal (L, d) configuration that provides a 28% thrust gain. For the same ejector, f _max remains constant and equal to the frequency obtained without ejector in a large range of (L, d) values, before decreasing.Two-dimensional unsteady numerical computations agree reasonably with the experiments, slightly overestimating the experimental values. The results indicate that 80% of the I _sp gain comes from the action of the expanding detonation products on the annular end surface of the combustion chamber, governed by the tube wall thickness.This paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003 PACS 47.40.Rs     

Experimental and numerical investigations into flow features in an intake duct for the waterjet propulsion under mooring conditions

Acta Mechanica Sinica - The waterjet propulsion is widely applied in the marine vessels over 30 knots, and the intake duct is considered as an essential component that strongly relates to the...     

Large injection rates on unsteady compressible boundary layer flow over cones at angles of attack

Summary Three-dimensional unsteady laminar boundary layer near the planes of symmetry of sharp cones at angles of attack subject to large rates of injection is obtained numerically by using an implicit finite difference scheme in combination with the quasi-linearization technique. Several model gases are considered with Mach numbers, wall-to-total-enthalpy ratios, and cross-flow parameters spanning the ranges of main engineering interest. A detailed study has been made of the solutions in the symmetry plane, in order to increase the understanding of the problem. Various cases are considered, when the free-stream velocity and the surface mass transfer (injection) vary arbitrarily with time. The effects of viscous dissipation and the cross-flow parameter have also been discussed.This research has been partially supported by the Research and Development Centre for Iron and Steel, Steel Authority of India Ltd. The constructive comments of Professor G. Nath and Professor A. K. Lahiri are sincerely appreciated.