Tip gap height effects on the aerodynamic performance of a cavity squealer tip in a turbine cascade in comparison with plane tip results: part 2—aerodynamic losses

Tip gap height effects on aerodynamic losses downstream of a cavity squealer tip have been investigated in a linear turbine cascade for power generation, in comparison with plane tip results. Three-dimensional flow fields are measured with a five-hole probe for tip gap height-to-chord ratios of h/c = 0.5, 1.0, 1.5 and 2.0%. The cavity squealer tip has a full length squealer with its rim height-to-chord ratio of 5.51%. For a fixed value of h/c, the tip leakage vortex for the cavity squealer tip is always weaker than that for the plane tip, and the flow field in the passage vortex region for the cavity squealer tip is less influenced by the tip leakage flow than that for the plane tip. For the cavity squealer tip, there is no appreciable change in local aerodynamic loss with h/c in the passage vortex region, but local aerodynamic loss in the tip leakage vortex region increases with h/c. The roles of the cavity squealer tip in reducing aerodynamic loss in comparison with the plane tip case are twofold: (1) the cavity squealer tip decreases the leakage flow discharge in the region from the leading edge to the mid-chord, which leads to an aerodynamic loss reduction in the passage vortex region and (2) it also decreases the leakage flow discharge downstream of the mid-chord, which results in an aerodynamic loss reduction in the tip leakage vortex region.     

Tip gap height effects on the aerodynamic performance of a cavity squealer tip in a turbine cascade in comparison with plane tip results: part 1—tip gap flow structure

Tip gap height effects on the flow structure over a cavity squealer tip have been investigated in a linear turbine cascade for power generation, in comparison with the corresponding plane tip results. Oil film flow visualizations are conducted on the tip surface and casing wall for tip gap height-to-chord ratios of h/c = 1.0, 2.0, and 3.0%. The squealer tip has a recessed cavity enclosed by a full length squealer with its rim height-to-chord ratio of 5.51%. The results show that most of in-coming fluid entering the tip gap inlet for the cavity squealer tip is entrapped by the suction-side squealer rim, and the cavity fluid is discharged into the blade flow passage over the suction-side squealer rim in the region from the mid-chord to the trailing edge. Regardless of h/c, the cavity squealer tip makes the leakage flow zone narrower than the plane tip, and is superior to the plane tip in reducing the tip leakage mass flow rate. A qualitative flow model describing full flow features over the cavity squealer tip is suggested. In this flow model, the tip gap exit area is classified into four different regions, and the tip gap height effects on the discharge characteristics in each region are discussed in detail.     

Over-tip leakage flow and loss in a turbine cascade equipped with suction-side partial squealers

Over-tip leakage flow and loss in a turbine cascade equipped with suction-side partial squealer rims have been investigated for the squealer rim height-to-span ratios (h_st/s) of 0.94%, 1.88%. 3.75%, and 5.63% in the case of a tip gap height-to-span ratio of h/s = 1.36%. The casing wall and tip surface visualizations for h_st/s = 3.75% show that most of the incoming tip leakage flow tends to accelerate through a convergent (nozzle-like) tip gap flow channel and penetrates into the neighboring blade flow passage even upstream of the mid-chord in the form of a wall jet, whereas the rest of it is entrapped by the suction-side squealer rim, flows backward, and is separated from the tip surface along a backward flow separation line. Therefore, the tip surface can be divided into a separation bubble and a backward flow area by the backward flow separation line. A qualitative tip gap flow model for the suction-side squealer tip is suggested in this study. For the present suction-side squealer tip, the total pressure loss coefficient mass-averaged throughout the present measurement plane decreases consistently with increasing h_st/s and is higher than that for the cavity squealer tip or the pressure-side squealer tip regardless of h_st/s.     

Tip gap flow characteristics in a turbine cascade equipped with pressure-side partial squealer rims

Tip gap flow characteristics and aerodynamic loss generations in a turbine cascade equipped with pressure-side partial squealer rims have been investigated with the variation of its rim height-to-span ratio (h_p/s) for a tip gap height of h/s = 1.36%. The results show that the tip gap flow is characterized not only by the incoming leakage flow over the pressure-side squealer rim but also by the upstream flow intrusion behind the rim. The incoming leakage flow tends to decelerate through the divergent tip gap flow channel and can hardly reach the blade suction side upstream of the mid-chord, due to the interaction with the upstream flow intrusion as well as due to the flow deceleration. A tip gap flow model has been proposed for h_p/s = 3.75%, and the effect of h_p/s on the tip surface flow is discussed in detail. With increasing h_p/s, the total-pressure loss coefficient mass-averaged all over the present measurement plane decreases steeply, has a minimum value for h_p/s = 1.88%, and then increases gradually. Its maximum reduction with respect to the plane tip result is evaluated to be 11.6%, which is found not better than that in the cavity squealer tip case.     

The sliding interface crack with friction between elastic and rigid bodies

The paper analyzes the frictional sliding crack at the interface between a semi-infinite elastic body and a rigid one. It gives solutions in complex form for non-homogeneous loading at infinity and explicit solutions for polynomial loading at the interface. It is found that the singularities at the crack tips are different and that they are related to distinct kinematics at the crack tips. Firstly, we postulate that the geometry of the equilibrium crack with crack-tip positions b and a is determined by the conditions of square integrable stresses and continuous displacement at both crack tips. The crack geometry solution is not unique and is defined by any compatible pair (b,a) belonging to a quasi-elliptical curve. Then we prove that, for an equilibrium crack under given applied load, the “energy release rate” G_tip, defined at each crack tip by the J_ε-integral along a semi-circular path, centered at the crack tip, with vanishing radius ε, vanishes. For arbitrarily shaped paths embracing the whole crack, with end points on the unbroken zone, the J-integral is path-independent and has the significance of the rate, with respect to the crack length, of energy dissipated by friction on the crack.     

Study on electroelastic field concentration around the electrode tip in multilayer ferroelectric actuators of two designs and their optimizations

Distribution of electromechanical field near electrode tips is closely related to the reliability of ferroelectric multilayer actuators. In this paper, the deformation and stress concentrations around the electrode tip in two multilayer actuator designs, partially and fully cofired, are investigated by means of experimental measurement and numerical simulations. The digital speckle correlation method (DSCM) is used to measure the full displacement field near the electrode tip with the high spatial resolution. The paths of electric breakdown and cracks initiated from the edge of electrodes were observed. With the proposed Double Gibbs free energy criterion, a fully coupled nonlinear electromechanical finite element method based on domain-switching mechanisms is developed and the simulation results agree well with the experiments. It is found that the crack-like “defects” in the partially cofired layered actuators, i.e. the interlayer gaps filled with soft insulating wax, can significantly reduce the maximum tensile stress level compared with that in “perfect” fully cofired actuators, which implies that the partially cofired design is more reliable than the fully cofired one. Further optimization on geometrical dimension of actuators is also carried out.     

Comparative analyses of phase-detective intrusive probes in high-velocity air–water flows

A comparative analysis of a wide range of air–water flow properties was conducted for two types of phase-detection intrusive probes including fiber-optical and conductivity probes. Experiments were conducted on a stepped spillway model for a skimming flow discharge q = 0.478 m²/s and for Re = 4.7 10⁵ in a flow region just downstream of the inception point of free-surface aeration and in the fully developed flow region. The comparison of a large number of key air–water flow properties showed a very close agreement for the two sensor types including void fraction, interfacial velocity and equivalent clear water flow depth enabling a direct comparison of past and future data collected with either phase-detection probe type. Minor differences were observed in terms of chord sizes, clustered properties and interparticle arrival times linked with the slightly smaller sensor size of the fiber-optical probe. The in-line positioning of the leading and trailing tips of the fiber-optical probe affected the trailing tip properties resulting in elevated turbulence intensities. An optimum dual-tip phase-detection probe design should consist of small probe tips positioned side-by-side.     

Frequency and development of slugs in a horizontal pipe at large liquid flows

The generation of slugs was studied for air–water flow in horizontal 0.0763 m and 0.095 m pipes. The emphasis was on high liquid rates (u_LS ? 0.5 m/s) for which slugs are formed close to the entry and the time intervals between slugs are stochastic. A “fully developed” slug flow is defined as consisting of slugs with different sizes interspersed in a stratified flow with a height slightly larger than the height, h₀, needed for a slug to be stable. Properties of this “fully developed” pattern are discussed. A correlation for the frequency of slugging is suggested, which describes our data as well as the data from other laboratories for a wide range of conditions. The possibility is explored that there is a further increase of slug length beyond the “fully developed” condition because slugs slowly overtake one another.     

Experimental and numerical investigations of tip injection on tip clearance flow in an axial turbine cascade

This investigation presents detailed experimental measurements of an active tip-clearance control method based on tip injection in a high-turning axial turbine cascade. Besides that, numerical investigations are also conducted to study phenomena which are not easily measured in the experiments. It aims to study the influence of tip injection on tip clearance flow, with emphasis on the effects of injection locations. Detailed flow field measurements were made downstream of the cascade using a three-hole probe. Static pressure distributions were also measured on the blade surface at 50% and 97.5% span, respectively. The results suggest that tip injection can weaken tip clearance flow, reducing the tip clearance mass flow and its associated losses. Meanwhile, the heat transfer condition on the blade tip surface can be also improved significantly. It also can be found that injection chordwise location plays an important role in the redistribution of secondary flow within the cascade passage. When the same number of injection holes and injection mass flow are applied, holes located in the aft part of blade can perform much better than that in the front part.     

Steady flow around a plane cascade by an ideal gas

The steady separation-free flow around a flat cascade by an ideal gas is discussed. Most of the attention is devoted to blocking regimes with a supersonic velocity in the entire flow and its subsonic component normal to the front of the cascade. A directing action of the cascade (the direction of the velocity and the Mach number of the advancing flow turn out to be related) is exhibited in these regimes which is a consequence of an independence of the flow in front of the cascade of the conditions behind it [1–5]. The most widespread method of their calculation [3, 4, 6] is based on the method of characteristics with establishment of the flow outside the cascade in a timelike coordinate. Although the integrated conservation laws also permit finding the parameters at infinity, the numerical construction of as long-range fields as desired with periodic sequences of attenuating discontinuities is practically impossible. The approximation of nonlinear acoustics (ANA) [7, 8] is justified here, as it is very effective in such problems [8–12]. A combination of ANA, the integrated conservation laws, and establishment in a calculation according to [13, 14] with isolation of the discontinuities has been realized in [5] for the construction of a solution on the entrance section of a cascade and everywhere in front of it. Below the method of [5] is extended to the entire flow and simplified even more. The flow on the entrance section of the cascade is, just as in [3], found in the approximation of a simple wave, in the rest of it and in a finite strip behind it-the flow is found with the help of the straight-through version of the scheme of [13, 14], and in the long-range field-in the ANA. A simpler version is proposed. In it ANA is applied outside the cascade and the linear theory is applied inside the cascade. Examples of the calculations are given. Similarity laws are formulated for all the regimes of streamline flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 35–43, November–December, 1984.     

A Thickened-Hole Model for Large Eddy Simulations over Multiperforated Liners

Flow instabilities such as Rotating Stall and Surge limit the operating range of centrifugal compressors at low mass-flow rates. Employing compressible Large Eddy Simulations (LES), their generation mechanisms are exposed. Toward low mass-flow rate operating conditions, flow reversal over the blade tips (generated by the back pressure) causes an inflection point of the inlet flow profile. There, a shear-layer induces vortical structures circulating at the compressor inlet. Traces of these flow structures are observed until far downstream in the radial diffuser. The tip leakage flow exhibits angular momentum imparted by the impeller, which deteriorates the incidence angles at the blade tips through an over imposed swirling component to the incoming flow. We show that the impeller is incapable to maintain constant efficiency at surge operating conditions due to the extreme alteration of the incidence angle. This induces unsteady flow momentum transfer downstream, which is reflected as compression wave at the compressor outlet traveling toward the impeller. There, the pressure oscillations govern the tip leakage flow and hence, the incidence angles at the impeller. When these individual self-exited processes occurs in-phase, a surge limit-cycle establishes.     

High-frequency cell vibrations and spatial skin effect in thick cascade junction with heavy concentrated masses

We study the asymptotic behavior of eigenvalues and eigenfunctions of the Laplacian in a 2D thick cascade junction with heavy concentrated masses. We present two-term asymptotic approximations, as ε→0$\epsilon \to 0$, for the eigenelements in the case of “slightly heavy”, “moderate heavy”, and “super heavy” concentrated masses. Asymptotics of high-frequency cell-vibrations are found as well.     

A three-velocity-component laser-Doppler velocimeter for measurements inside the linear compressor cascade

A 24′′ (610 mm) access laser-Doppler velocimeter (LDV) system was developed to make simultaneous three-velocity-component measurements in a low speed linear cascade wind tunnel with moving wall simulation. The probe has a 610 mm access length and achieves a measurement spatial resolution of 100 μm by using off-axis optical heads. With the relatively large access length, the LDV probe allows for measurements from the side of a wind tunnel instead of through the tunnel floor, while the high spatial resolution allows for quality near-wall measurements. The probe has been tested in a zero-pressure gradient 2D turbulent boundary layer and the test results agree well with the experimental data measured with different LDV systems and hot-wire anemometery for the boundary layer flows. The energy spectral density was estimated using a slot correlation, and Von Kármán’s model for the energy-spectrum function was used to analyze the measured spectral data to estimate the turbulent kinetic energy dissipation rate, which compares favorably with the measured production values in the log-layer region of the turbulent boundary layer. Measurements are presented for the moving endwall boundary layer at the inlet of the linear compressor cascade facility to validate the capability of this LDV for tip leakage flow measurements. These results indicate that the moving endwall reduces velocity gradients in the near-wall region and results in less production of Reynolds stresses and turbulent kinetic energy compared to the stationary endwall case.     

Air–water flow properties in step cavity down a stepped chute

For the last three decades, the research into skimming flows down stepped chutes was driven by needs for better design guidelines. The skimming flow is characterised by some momentum transfer from the main stream to the recirculation zones in the shear layer developing downstream of each step edge. In the present study some physical modelling was conducted in a relatively large facility and detailed air–water flow measurements were conducted at several locations along a triangular cavity. The data implied some self-similarity of the main flow properties in the upper flow region, at step edges as well as at all locations along the step cavity. In the developing shear layer and cavity region (i.e. y/h < 0.3), the air–water flow properties presented some specific features highlighting the development of the mixing layer downstream of the step edge and the strong interactions between cavity recirculation and mainstream skimming flows. Both void fraction and bubble count rate data showed a local maximum in the developing shear layer, although the local maximum void fraction was always located below the local maximum bubble count rate. The velocity profiles had the same shape as the classical mono-phase flow data. The air–water flow properties highlighted some intense turbulence in the mixing layer that would be associated with large shear stresses and bubble–turbulence interactions.     

A review of turbomachinery tip gap effects: Part 2: Rotating machinery

This two part review covers experiments examining the effects of blade tip gaps encountered in turbomachines and the methods by which the synthesised data are currentl used in turbomachine design and analysis. Data gained since the 1930's are subdivided for convenience into cascade (Part 1) and rotating machinery (Part 2) data, with a further subdivision into diffusing, or compressor type flows and accelerating, or turbine type flows. The overall trend is that an increasing tip gap, whose effect can reach over most or all of the blade height, reduces turbomachine performance. There is some evidence among the compressor and compressor cascade data that an optimum gap exists when the opposing effects of secondary flows and tip leakage with rotor/wall relative movement tend to balance. Turbine data are, in general, more regular than the body of compressor data, possibly because of the enhanced effect of, usually, undefined boundary layers in diffusing flow in the latter. Comment is made in Part 2 on the predictive and design models reported in the liturature     

Nano-ductile crack propagation in glasses under stress corrosion: spatiotemporal evolution of damage in the vicinity of the crack tip

Recent experiments have evidenced the existence of a ductile fracture mode at the nanometer scale in Aluminosilicate glass. The present study is designed to check whether such a ductile mode is inherent to the amorphous nature of glass. Therefore, the slow crack advance is observed in real time via an Atomic Force Microscope in a minimal glass, amorphous Silica, under stress corrosion. In this case, the Crack propagation proceeds by the nucleation, growth and coalescence of damage cavities as in the Aluminosilicate glass, but the cavity size is significantly larger. We focus here on the kinematics of crack propagation by looking at the spatio-temporal evolution of both the tip of the main crack and the cavity ahead. It is shown that the velocity of the main crack tip is significantly lower than the one of the cavity edge toward the main crack tip, like in metallic alloys. Moreover, the velocities of the different fronts (main crack, frontward and backward cavity tips) at these nanometric scales is one order of magnitude smaller than the crack tip velocity at the continuum scale. This has important consequences for the modelling of stress corrosion, especially at ultra-slow crack propagation.     

A mixer design for the pigtail braid

The stirring of a body of viscous fluid using multiple stirring rods is known to be particularly effective when the rods trace out a path corresponding to a nontrivial mathematical braid. The optimal braid is the so-called “pigtail braid”, in which three stirring rods execute the usual “over-under” motion associated with braiding (plaiting) hair. We show how to achieve this optimal braiding motion straightforwardly: one stirring rod is driven in a figure-of-eight motion, while the other two rods are baffles, which rotate episodically about their common centre. We also explore the extent to which the physical baffles may be replaced by flow structures (such as periodic islands).     

Experimental investigations on steady wake effects in a high-lift turbine cascade

This paper reports on the investigation of steady wake effects in cascades. An annular cascade rig, where two stators having the same blade pitch can be circumferentially traversed relatively to each other, is used to analyse the profile losses and the boundary layer development of the downstream stator for different circumferential positions of the upstream stator (clocking positions). Different measurement techniques are used such as three-hole pressure probes, and hot wire- and surface-mounted hot-film probes. The results show a varying pressure loss coefficient of the downstream cascade (S2) for different clocking positions of the upstream cascade (S1_SP).     

On the use of genetic algorithm for finding the neutral instability curve in plane Poiseuille flow

A novel method based on genetic algorithm (GA) is proposed, to the best of our knowledge for the first time, for finding the neutral instability curve of the Orr-Sommerfeld equation in (nearly) parallel flows. New concepts such as “proximity of parents” and “gender discrimination” are added to the conventional GA in order for this algorithm to find the neutral instability curve. Certain GA operators such as “crossover” and “mutation” will also be modified in such a way that this algorithm can meet this purpose. To check the applicability of the modified genetic algorithm (MGA) developed in this work in finding the neutral instability curve, the case of plane Poiseuille flow will be used as a benchmark. It will be shown that the modified genetic algorithm developed in this work is well capable of determining the neutral instability curve for this particular flow geometry.     

Stability of crystalline solids—I: Continuum and atomic lattice considerations

Many crystalline materials exhibit solid-to-solid martensitic phase transformations in response to certain changes in temperature or applied load. These martensitic transformations result from a change in the stability of the material's crystal structure. It is, therefore, desirable to have a detailed understanding of the possible modes through which a crystal structure may become unstable. The current work establishes the connections between three crystalline stability criteria: phonon-stability, homogenized-continuum-stability, and the presently introduced Cauchy-Born-stability criterion. Stability with respect to phonon perturbations, which probe all bounded perturbations of a uniformly deformed specimen under “hard-device” loading (i.e., all around displacement type boundary conditions) is hereby called “constrained material stability”. A more general “material stability” criterion, motivated by considering “soft” loading devices, is also introduced. This criterion considers, in addition to all bounded perturbations, all “quasi-uniform” perturbations (i.e., uniform deformations and internal atomic shifts) of a uniformly deformed specimen, and it is recommend as the relevant crystal stability criterion.