Tip Cavity Research Articles

Effects of the inclination angle of oval film holes on the aero-thermal performance of a squealer blade tip

The investigation and study on the characteristics of the flow and wall heat transfer on the squealer tip is of vital importance to the safe and durable operation of a turbine rotor. The numerical model of the blade squealer tip with discrete film cooling holes (round and oval holes) was constructed and validated in this paper. The effects of the radial and axial inclination of oval-holes on aero-thermal performance were systematically investigated, which received little attentions in previous studies. The result shows that the streamline deflection produced by negative inclination structures significantly improves the coverage of film, but the development of the jet vortex leads to an enhancement in leakage flow. The lift-off of film is effectively restrained by positive inclination structures, however, the jet outflow contraction limits the expansion of film coverage. Besides, the scraping between tip cavity flow and leakage flow is also an important factor to the leakage flow control, which can reduce the momentum of leakage flow. Overall, the negative radial inclination structure achieves the optimal performance of film cooling, whose tip average cooling effectiveness at 0.5 blowing ratio is even 132% higher than that in the round hole reference at 1.5 blowing ratio. The highest relative reduction of leakage flow is obtained by the positive axial inclination structure with 62.79% at the blowing ratio of 1.5.

What causes the persistent seismicity below the eastern flank of Piton de la Fournaise (la Réunion Island)? Elasto-plastic models of magma inflation

Identifying the causes of flank destabilization of active volcanic edifices is key to prevent catastrophic events. The persistent seismicity recorded below the eastern flank of Piton de la Fournaise shield volcano (la Réunion Island), both in between and during eruptive events, may give indications on the mechanical stability of this edifice. Whether this asymmetric “cup” shaped seismicity is linked to magma injections and whether it sparks a gravitational flank slide motivates this study. Here we model the elasto-plastic behavior of this volcanic edifice at crustal scale, with the 3D finite-element code Adeli. First, we test the influence of tensile failure, recently implemented in combination to a Drucker-Prager shear failure criterion; a pressurized cavity below a flat top surface triggers shear failure in general, with tensile failure restricted to the surface and cavity tip. Then we include the topography of Piton de la Fournaise in the gravity field. Considering first only elasticity, deviatoric stresses attain about 35 MPa below the volcanic edifice and displacements are maximum in the horizontal east–west direction, reaching 30 m near sea-level. Introducing plastic behavior produces a rather symmetric cup shape plastic domain around the volcano’s summit, that extends at depth with reducing bedrock effective friction (which acts is a proxy for reduced standard friction due to pore fluid pressurization). An asymmetric listric shear zone develops down to −3 km (bsl) only if the tensile strength, cohesion and friction angle are set as low as 1.5 MPa, 3 MPa and 3°, respectively; these values hence provide a lower bound for the edifice’s effective strength. The second part of this study explores the influence of an internal overpressure, which is either applied as a vertical inflation source located about 500 m below the surface of the eastern flank, simulating a distal dike, or from a deeper ellipsoid simulating the magma reservoir located at depth ca. 0 km (near sea level) below the summit. The resulting strain pattern forms a cup-shaped shear zone dipping down below the eastern flanks of the edifice, reaching depth −2 km (bsl) if effective friction angle is ⩽5°. Whereas the deep base of the dike and the eastern edge of the magma reservoir coincide geometrically in the models, the inflating dike produces a shear zone 1 km shallower than does the inflating magma reservoir, the latter coinciding better with the shape of the observed seismic cup. Hence, we propose that this structure is a mechanical consequence of continuous magma supply in the reservoir, coherent with previous interpretations. This means that at least originally it did not need to form as a pre-existing weak zone or a magma-filled structure. However, this shear zone delimits an underlying domain in dilatation relative to a constricted hanging-wall; it may thus promote magma sills. It also branches to the surface with planar radial shear zones comparable to some observed eruptive fissures. The 3D kinematics of this shear zone does not rule out the possibility of a giant flank slide, although it does not appear today as imminent.

Effects of the multicavity tip coolant injection on the blade tip and the over tip casing aerothermal performance in a high-pressure turbine cascade

In high performance gas turbine engines, the over tip leakage flow driven by the lateral pressure gradient is inevitably induced inside the blade tip gap in the high-pressure stage turbine due to the freestanding airfoil design methodology. To obtain an increasing level of thermal efficiency, the turbine inlet temperature is gradually increased in terms of the Brayton cycle. Hence, the blade tip and the over tip casing are subjected to high thermal load. In real turbine blade, cavity tips are widely used to decrease the over tip leakage flow and the thermal load on the blade tip and over tip casing. In the present study, the numerical simulations were conducted to investigate the effects of the multicavity coolant injection on the blade tip and the over tip casing aerothermal performance. Three-dimensional (3-D) Reynolds-averaged Navier–Stokes (RANS) equations and standard turbulence model were solved together in the simulations. The results indicate the ribs inside the tip cavity alter the distribution of film cooling efficiency by changing flow structure within the tip gap. Most of the coolant is limited in each little cavity owing to the blockage of ribs. Here, the swirling action of each cavity vortex results in the coolant providing a wider film cooling coverage. Therefore, the increase in film cooling effectiveness on the blade tip surface is more efficient than that of over-tip casing. The blade with four tip cavities film cooling (4CFC) obtains the largest area-averaged film cooling effectiveness, which is augmented by 14.3% in comparison with the case with a single tip cavity film cooling (1CFC).

Effects of inclined squealer rims on tip leakage vortex and loss in a transonic axial turbine

In this paper, to investigate the effects of inclined squealer rims on tip leakage flow and loss, numerical simulations have been performed on a transonic high-pressure turbine. Based on the geometry of prototype with conventional cavity tip, six modifications with different inclined rims are constructed. The effects of inclined suction side squealer rim (SSSR) on tip leakage flow (TLF) is analyzed emphatically. The results show that it is advantageous to control the TLF and loss if the internal and external surface of SSSR are inclined in a proper direction. When the internal surface of SSSR is inclined toward the cavity, the scraping vortex and its pneumatic labyrinth sealing effect are enhanced, which is beneficial to blocking the TLF and reducing the mixing loss. As the external surface of SSSR is inclined toward the passage, the pressure gradient near the tip changes and the intensity of adverse pressure gradient decreases, which is conducive to suppressing the breakdown of tip leakage vortex (TLV). In addition, the inclined external surface could make the TLV away from the blade and reduce the viscous dissipation. Regarding the aerodynamic performance of the turbine, the inclined pressure side squealer rim (PSSR) could improve the stage efficiency of the turbine by 0.08% relative to the prototype, while the proper inclined SSSR could further improve that by 0.18%.

Investigation into the film cooling performance of multi-cavity tips with different cavity depths

In modern gas turbines, sufficient cooling is required for preventing the blade tip region from being ablated due to the increasing of operating temperature. In this work, an experiment was conducted focusing on the film cooling performance of the multi-cavity tips (one cavity, two cavities, three cavities and four cavities) with two different cavity depths. The distributions of film cooling effectiveness on these multi-cavity tips were measured by the pressure sensitive paint (PSP) technique under five coolant blowing ratios. In addition, a validated computational method was performed to make further insight into the coolant flow pattern near the tip and the aerodynamic loss. Results showed that performance of superiority in film cooling is achieved on the central portion of the multi-cavity tips, compared to the conventional cavity tip. The uniformity of effectiveness values in film cooling is improved by a deeper cavity depth. The effectiveness values of the tip surface increase first and then decrease with an increase of blowing ratio. The aerodynamic performance of these multi-cavity tips was assessed as well.

Efficient Uncertainty Quantification and Sensitivity Analysis on the Aerothermal Performance of Turbine Blade Squealer Tip

Abstract It is important to accurately estimate the impact of flow and geometric variations for engineering design and manufacture. In this paper, an efficient uncertainty quantification analysis framework based on the combination of Universal Kriging (UK) metamodels and sparse Polynomial Chaos Expansion (PCE) is proposed. A challenging analytical test function and an engineering test are considered to investigate the response performance of the UK-PCE method. Then, this method was applied to the uncertainty quantification on the aerodynamic and heat transfer performance of GE-E3 rotor blade squealer tip. Meanwhile, a global parameter sensitivity analysis using the Sobol Indice method is carried out to identify the key parameters for the aerothermal performance of the squealer tip. Wherein, the inlet total temperature is considered as flow condition uncertainty parameters and tip clearance and cavity depth are considered as geometrical uncertainty parameters. The results show that the UK-PCE method reduces the computational cost by more than 70% in comparison to the typical PCE method. Under the influence of the uncertain geometry and operating conditions, the heat flux of the squealer tip basically conforms to the normal distribution and the statistical mean value of it increased by 5.32% relative to the design value and the probability of it deviating from the design value by 5% is as high as 44.62%. The result of sensitivity analysis reveals that the uncertainty of the aerodynamic characteristics of the squealer tip is almost entirely caused by the tip clearance which accounts for 90.31% and 98.77% of the variance of the leakage flow rate and total pressure loss coefficient. And it is also a key variable for the uncertainty of the heat transfer performance considering that its variance indexes for tip heat flux and blade heat flux are 31.23% and 73.14%, respectively. Finally, the influence mechanisms of the uncertainty parameters on the aerothermal performance of the squealer tip are investigated by detailed flow and thermal field analysis.

Effect of blade squealer tips on aerodynamic performance and stall margin in a transonic centrifugal compressor with vaned diffuser

In order to enhance the aerodynamic performance of a centrifugal compressor with a vaned diffuser while also improving its stall margin, squealer tip cavities were applied to the tips of the impeller blades. Computational analysis was carried out by solving the compressible three-dimensional Reynolds-averaged Navier-Stokes equations. The numerical approach was validated by comparing the results from the flat tip reference case with experimental measurements. Various squealer tips with different cavity depths were applied to both the main and splitter blades and were numerically tested to investigate the influence of cavity depth on the performance and stall margin of the compressor. The results show that squealer tips with a proper cavity depth were effective in enhancing compressor efficiency by 0.32% at the design point, in addition, they were able to improve the stall margin by 1.02%. It was found that the squealer tips reduce tip leakage flow and circumferential velocity near the impeller shroud compared to using flat tips due to the generation of vortical structure within the cavity, which blocks leakage flow in a similar way to labyrinth seals. However, it was observed that by increasing the cavity depth, the size of this vortex becomes larger and the entropy production is increased inside the cavity. Moreover, it was found that the proper cavity depth decreases the mixing tip loss by about 4% compared to flat tips, this plays an important role in the stall margin improvement.

Control strategies for tip leakage vortex using inclined squealer rim in axial turbines

In a typical gas turbine, due to its complicated blade geometry, complex vortex structures appear and cause significant aerodynamic loss. Vortex systems dominated by a tip leakage vortex near the tip region are the primary source of this loss. In this paper, to improve the aerodynamic performance of the turbine, two novel control strategies for tip leakage vortex and the tip leakage flow of the cavity tip are proposed, and their coupling control effects are numerically investigated. The first control strategy is intended to control the loss caused by the breakdown of tip leakage vortex. By inclining the external wall of the suction side rim toward the passage, the emergence of a trailing edge pressure spike is delayed. This significantly reduces the adverse pressure gradient, suppressing the breakdown of tip leakage vortex and reducing tip leakage loss. The second control strategy controls tip leakage flow using the inclined inner wall of the suction side rim, which enhances the separation bubble on the top of the rim of the suction side and reduces the leakage rate by 7.7%. In this way, the formation and development of tip leakage vortex are indirectly manipulated, inhibiting the tip leakage loss. The coupling of the two strategies reduces the blocking effect on tip leakage flow slightly compared to the second strategy. However, the stage efficiency of the turbine is still improved by 0.24% because of the effective suppression of tip leakage vortex breakdown.

Effects of the casing step size on the tip leakage flow pattern and heat transfer characteristic of turbine blade squealer tip

In this paper, under the GE-E3 turbine stage condition, the effect of the casing step on the heat transfer performance is obtained by solving three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations. The heat transfer characteristics predicted by standard k-ω model are consistent with the experimental data. The simulation results reveal that, the tip heat transfer coefficient decreases and the area of the high heat transfer region is reduced by introducing the casing step structure. Compare to the baseline case, when the casing step height is 1%, 2% and 3% of the blade height, the area-average heat transfer coefficient at the blade tip decreases by 6.1%, 6.7% and 7.0%, respectively. The introduction of casing step structure can eliminate the swirling strength of Scraping Vortex (SV), thus weaken the reattachment of tip leakage flow on the cavity bottom. Under the step vortex effect, the mainstream from the tip pressure side entering the tip cavity is reduced and replaced by entering from the tip suction side. Because of the lower pressure difference between the tip suction side and the tip clearance, the swirling strength of SV is decreased. Arranging a casing step with the same size as the tip clearance upstream the blade can reduce the tip heat transfer performance to the greatest level. The introduction of casing step structure also has a negative effect on the output power and efficiency of the turbine, it is necessary to balance the aerodynamic and heat transfer of the turbine in order to achieve the optimal results.

Unsteady flow phenomena in turbine shroud cavities

This paper presents those flow parameters at which coherent structures appear in the blade tip cavities of shrouded turbine blades. To the authors’ knowledge, this is reported for the first time in the open literature. The unsteady flow in a shroud cavity is analysed based on experimental data recorded in a labyrinth seal test rig. The unsteady static wall pressure in the shroud cavity inlet and outlet is measured using time-resolving pressure sensors. Sensors are located at staggered circumferential positions to allow cross-correlation between signals. The unsteady pressure signals are reduced using Fourier analysis and cross-correlation in combination with digital filters. Based on the data, a theory is formulated explaining the phenomena reflected in the measurements. The results suggest that pressure fluctuations with distinct numbers of nodes are rotating in the shroud cavity outlet. Moreover, modes with different node numbers appear to be superimposed, rotating at a common speed in circumferential direction. The pressure fluctuations are not found at all operating points. Further analysis indicates that the pressure fluctuations are present at operating points matching distinct parameters correlating with the cavity flow coefficient. Unsteady RANS simulations predict similar flow structures for the design operating point of the test rig.

Endodontic Treatment of a Traumatic Tusk Fracture With Exposed Pulp in an Asian Elephant (Elephas maximus).

Tusk fracture in elephants is a common incident often resulting in pulp exposure and pulpitis. Extensive lavage, endodontic therapy, direct pulp capping, or extraction are treatment options. In this report, the successful management of a broken tusk of a juvenile male Asian elephant (Elephas maximus) including morphological analysis of the tusk tip 2 years after surgery are presented. Treatment was carried out under barn conditions and included antimicrobial photodynamic therapy and partial pulpotomy with direct pulp capping. Immediate pain relief was reached. The fractured tusk was preserved and continued to grow. The therapeutic filling material remained intact for over 1 year but was absent 2 years after treatment. The former pulp cavity of the tusk tip was filled with reparative dentin, osteodentin, and bone, but the seal between these hard tissues and pulp chamber dentin was incomplete. Radiographs obtained 3 years after treatment showed no differences in pulp shape, pulp width, and secondary dentin formation between the treated right and the healthy left tusk. It can be concluded that in case of an emergency, the endodontic therapy of a broken elephant tusk can be attempted under improvised conditions with adequate success. Photodynamic therapy might contribute to prevent infection and inflammation of the pulp. The decision tree published by Steenkamp (2019) provides a valuable tool to make quick decisions regarding a suitable therapy of broken tusks.

Investigation on film cooling and aerodynamic performance of blade tip with tangential jet cooling scheme at transonic flow

An innovative blade tip cooling system is proposed in the current paper. The aerothermal characteristics of the blade tip with the tangential jet cooling scheme are investigated using the Pressure Sensitive Paint (PSP) technique under transonic flow conditions. The experiment is carried out at tip clearance gaps of 0.7% and 1.5% and four mass flow ratios. The cascade inlet Reynolds number and cascade exit Mach number are 370000 and 1.05, respectively. The computational fluid dynamics method was used to analyze the flow characteristics of the blade tip. The bottom wall of the tip cavity downstream of the tangential jet cooling scheme is completely covered by the secondary flow. With the mass flow ratio (MFR) increasing, the film cooling effectiveness (η) of the whole blade tip surface is improved. The small tip clearance gap shrinks the low η region in the mid-chord cavity near the suction-side.

Near Tip Loss Control With a Winglet Baffle Cavity Tip in a Turbine Cascade

Abstract The aerodynamic performance of a winglet baffle cavity tip is investigated at different inlet incidences from −12.5 to +12.5 deg. This blade tip shows a geometry feature with a pressure side winglet and a baffle within the tip cavity. The experimental studies were carried out in a large-scale linear cascade. Numerical methods were also used to obtain the detail flow physics. The baffle on the tip divides the cavity vortex into two main parts, and enhances flow mixing over the tip. As the tip leakage flow exits the tip near the baffle and the cavity corner, flow separation occurs over the suction side and its blockage effect reduces the local tip leakage mass flow rate. The additional pressure side winglet reduces the contraction coefficient on the pressure side squealer. Compared with the squealer tip, the winglet baffle cavity tip reduces the tip leakage mass flow by 12.1% and the near tip loss by 4.2%. Removing the baffle on the tip also results in an increase of the loss. As the incidence of the incoming flow decreases, the loss near the tip reduces mainly due to a reduction of the strength of the passage vortex, which develops from the casing endwall. At all incidences studied, the winglet baffle cavity tip shows better aerodynamic performance than the squealer tip.

Application of Large Eddy Simulation to Predict Underwater Noise of Marine Propulsors. Part 1: Cavitation Dynamics

Marine propulsors are identified as the main contributor to a vessel’s underwater radiated noise as a result of tonal propeller noise and broadband emissions caused by its induced cavitation. To reduce a vessel’s signature, spectral limits are set for the propulsion industry, which can be experimentally obtained for a complete vessel at the full-scale; however, the prediction capability of the sound sources is still rudimentary at best. To adhere to the regulatory demands, more accurate numerical methods for combined turbulence and two-phase modeling for a high-quality prediction of acoustic sources of a propeller are required. Several studies have suggested implicit LES as a capable tool for propeller cavitation simulation. In the presented study, the main objective was the evaluation of the tip and hub vortex cavitating flows with implicit LES focusing on probable sound source representation. Cavitation structures for free-running propeller test cases were compared with experimental measurements. To resolve the structure of the tip vortex accurately, a priory mesh refinement was employed during the simulation in regions of high vorticity. Good visual agreement with the experiments and a fundamental investigation of the tip cavity structure confirmed the capability of the implicit LES for resolving detailed turbulent flow and cavitation structures for free-running propellers.

Aerothermal Effect of Cavity Welding Beads on a Transonic Squealer Tip

Abstract High-pressure turbine blade tips are critical for gas turbine performance and are sensitive to small geometric variations. For this reason, it is increasingly important for experiments and simulations to consider real geometry features. One commonly absent detail is the presence of welding beads on the cavity of the blade tip, which are an inherent by-product of the blade manufacturing process. This paper therefore investigates how such welds affect the Nusselt number, film cooling effectiveness and aerodynamic performance. Measurements are performed on a linear cascade of high-pressure turbine blades at engine realistic Mach and Reynolds numbers. Two cooled blade tip geometries were tested: a baseline squealer geometry without welding beads, and a case with representative welding beads added to the tip cavity. Combinations of two tip gaps and several coolant mass flow rates were analyzed. Pressure sensitive paint was used to measure the adiabatic film cooling effectiveness on the tip, which is supplemented by heat transfer coefficient measurements obtained via infrared thermography. Drawing from all of this data, it is shown that the weld beads have a generally detrimental impact on thermal performance, but with local variations. Aerodynamic loss measured downstream of the cascade is shown to be largely insensitive to the weld beads.

Unsteady Steam Turbine Optimization Using High-Fidelity Computational Fluid Dynamics

Abstract This paper presents the computational methodology and experimental investigations accomplished to enhance the efficiency of a turbine stage by applying non-axisymmetric profiling on the rotor hub wall. The experimental setup was a two-stage axial turbine, which was tested at “LISA” test facility at ETH Zurich. The first stage was considered to create the flow history for the second stage, which was the target of the optimization. The hub cavity of the second stage was designed with large dimensions as a requirement of a steam turbine. The goal was to optimize the interaction of the cavity leakage flow with the rotor passage flow to reduce the losses and increase efficiency. The computational optimization was completed using a genetic algorithm coupled with an artificial neural network on the second stage of the test turbine. Unsteady time-accurate simulations were performed using in-house developed “MULTI3” solver. Besides implementing all geometrical details (such as hub and tip cavities and fully 3D blade geometries) from the experimental setup into the computational model, it was learned that the unsteady upstream effect could not be neglected. A novel approach was introduced using unsteady inlet boundary conditions to consider the multistage effect while reducing the computational cost to half. The importance of this implementation was tested by performing a steady simulation on the optimized geometry. The predicted efficiency gain from steady simulations was 4.5 times smaller (and negligible) compared to the unsteady approach. Excluding the cavity geometry was also assessed in a different simulation setup showing 3.9% over-prediction in the absolute efficiency value. Comprehensive steady and unsteady measurements were performed utilizing pneumatic, fast response aerodynamic probe (FRAP), and fast response entropy probe (FENT) on the baseline and profiled test cases. The end wall profiling was found to be successful in weakening the strength of the hub passage vortex by a 19% reduction in the under-over turning. As a result, the blockage was reduced near the hub region leading to more uniform mass flow distribution along the span. The flow angle deviations at the higher span position were also corrected due to better control of the flow angles. Furthermore, the improvements were confirmed by reductions in entropy, secondary kinetic energy, and pressure unsteadiness. The accurate computational implementations led to an excellent agreement between the predicted and measured efficiency gain.

Effect of in-service burnout effect on the transonic leakage flows over cavity tip model

Increasing the gas temperature at the inlet to the high pressure turbine of gas turbine engines is known as a proven method to increase the efficiency of these engines. However, this will expose the blades’ surface to very high heat load and thermal damages. In the case of the un-shrouded turbine blades, the blade tip will be exposed to a significant thermal load due to the developed leakage flows in the tip gap, this leads to in-service burnout which degrades the blade tip and shortens its operational life. This paper studies the in-service burnout effect of the transonic tip flows over a cavity tip which is a configuration commonly used to reduce the tip leakage flows. This investigation is carried out experimentally within a transonic wind tunnel and computationally using steady and unsteady Reynolds Averaged Navier Stokes approaches. Various flow measurements are established and different flow behaviour including separation bubbles, shockwave development and distinct flow interactions are captured and discussed. It is found that when the tip is exposed to the in-service burnout, leakage flow behaves in a significantly different way. In addition, the effective tip gap becomes much larger and allows higher leakage mass flow rate in comparison to the sharp-edge tip (i.e. a tip at the beginning of its operational life). The tip leakage losses are found much higher for the round-edge cavity tip (i.e. a tip exposed to burn-out effect). Experimental and computational flow visualisations, surface pressure measurements and discharge coefficient variation are given and analysed for several pressure ratios across the tip gap.

Aerodynamic Effects of an Incoming Vortex on Turbines With Different Tip Geometries

Abstract Experimental and numerical methods were used to investigate the aerodynamic effects of a near-casing streamwise incoming vortex flow on the tip leakage flow of different tip geometries in an unshrouded high-pressure turbine. A flat tip, a cavity tip, and a suction side winglet tip were investigated with the quasi-steady method first. A swirl generator was used to produce the incoming vortex in a linear cascade. In the flat tip case, the incoming vortex interacts with the tip leakage flow and the two vortices gradually mix together. The tip leakage loss is reduced due to the streamwise momentum supplement within the tip leakage vortex core. For the cavity tip, the tip leakage vortex appears at a location relatively downstream in the blade passage compared with the flat tip and no evident vortex interaction is observed. The incoming vortex causes extra viscous dissipation within the blade passage and increases the aerodynamic loss for the cavity tip. For the winglet tip, the extension of the suction side winglet tends to push the incoming vortex and the tip leakage vortex move and mix together, thus reducing the loss. Then, the effects of periodic unsteady vortex transportations were investigated by conducting unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations. The incoming vortex is stretched as it transports downstream. The unsteady incoming vortex is easier to interact with the tip leakage vortex for the winglet tip. As a result, the winglet tip is the most efficient tip design with unsteady incoming flow among the three tips and achieves a 3.7% reduction of mixed-out loss coefficient compared with the flat tip, larger than 2.8% reduction in the uniform inlet condition. The detailed loss mechanism is discussed in this paper.

Influence of tip clearance and cavity depth on heat transfer in a cutback squealer tip

Numerical simulations are conducted to present the aerothermal performance of a turbine blade tip with cutback squealer rim. Two different tip clearance heights (0.5%, 1.0% of the blade span) and three different cavity depths (2.0%, 3.0%, and 6.0% of the blade span) are investigated. The results show that a high heat transfer coefficient (HTC) strip on the cavity floor appears near the suction side. It extends with the increase of tip clearance height and moves towards the suction side with the increase of cavity depth. The cutback region near the trailing edge has a high HTC value due to the flush of over-tip leakage flow. High HTC region shrinks to the trailing edge with the increase of cavity depth since there is more accumulated flow in the cavity for larger cavity depth. For small tip clearance cases, high HTC distribution appears on the pressure side rim. However, high HTC distribution is observed on suction side rim for large tip clearance height. This is mainly caused by the flow separation and reattachment on the squealer rims.

Numerical Simulations of Air Cavities in Inclined Plunging Jets

The dynamic process of circular water jets plunging into a quiescent pool was analyzed in this study based on the RNG k∼ε turbulence model and VOF method. The effects of jet velocity and inclination angles relative to horizontal on the cavity shapes and sizes were analyzed. The simulation successfully captured the formation, development, pinch-off, and disintegration phenomena of cavities. The shape of the cavity is mainly affected by the impact angle, while the impact velocity mainly affects the size of the cavity. The cavity pinch-off initially appears at a certain point in any direction for vertical jets, while the cavity in the opposite direction of flow pinch-off appears before the cavity in the direction of flow for inclined jets. Before cavity pinch-off, the maximum radial and axial sizes of the cavity generally increase with the impact velocity and the time after impingement. The axial penetration velocity of the cavity tip is approximately half of the impact velocity, which is consistent with previous research. Finally, based on the statistics of the cavity sizes, empirical formulas for predicting the maximum radial and axial sizes of the cavity were established.