Vortex Cavity Research Articles

Numerical investigations on lifting and flow performance of finger seal with grooved pad

We investigate non-contact finger seal owing to its potential to reduce the specific fuel consumption of a gas turbine engine by 2–3%. The compliance features combined with the non-contact characteristic permits the position adjustment of the finger seal to the rotor excursions without destroying the stability of the rotor-seal system. The grooved structures on the lift pad of the three-layer finger seal are proposed with a view to improve the lifting and leakage capacities. Two-way fluid-structure interaction (FSI) methods are used, and the results show that the grooved structures positively affect the sealing performance. First, an uneven clearance occurs because of the seal deformation. Next, the sealing flow field is changed owing to the grooved structure. Finally, the grooved structure is proven to improve the seal's lifting capability, and the vortices in the grooves improve the sealing performance. The vortices in the groove cavities contribute significantly to the improvement in the lifting and leakage capacities. The grooved structure changes the pressure distribution under the lift pad, and a larger force is generated on the bottom surface of the lifting pad.

Effect of corrugated channel phase shifts on flow structures and heat transfer rate

The study of quantitative visualization of flow hydrodynamics, turbulent flow characteristics and time-dependent development and disappearance of vortices in cavities of corrugated channel regarding enhancements of heat transfer is limited in the literature. For this reason, the aim of the work is to search the effects of two different phase shifts, φ (i.e. 90°, 0°) of corrugated channels on flow hydrodynamics and the rate of heat transfer for Reynolds numbers varying from 3 × 103 to 6 × 103. The technique of particle image velocimetry (PIV) which has the capability of observing turbulent unsteady flows and provide instantaneous velocity vectors covering defined flow fields were employed. An effective fluid mixture occurs between the core and the separated flow regions due to the occurrence of a rapid vortex shedding downstream of the entrance of cavities. Along the lower and upper sides of hollow spaces, these shedding vortices spin either counterclockwise or clockwise to stimulate entrainment. In addition, the effects of turbulent flow hydrodynamics on convective heat transfer were also investigated numerically. Numerical results of flow hydrodynamic were found to be consistent with the experimental results. Heat transfer augmentation was reported as a conclusion of different parameters including different phase shifts, φ, aspect ratios, s/H and Reynolds numbers, Re.

Numerical study of guide vane effects on reacting flow characteristics in a trapped vortex combustor

ABSTRACTTrapped Vortex Combustor (TVC) is a simple and promising concept for flame stabilizations in aero-engines. In this concept, cavity trapped vortices are used to establish pilot flames for robust combustion performance. The main objective of this study is to numerically investigate the effects of guide vanes on the performance of a TVC installed in a small ramjet. Three dimensional steady and unsteady simulations are performed by solving the Reynolds-Averaged Navier-Stokes (RANS) equations with the commercial flow solver ANSYS FLUENT v16.1. The shear stress transport (SST) model is selected for the turbulence closure, and the eddy dissipation model (EDM) is used for the combustion modeling of gaseous propane (C3H8) fuel. In the current work, four cases are studied: (1) TVC without vanes, (2) TVC with a square-tip vane, (3) TVC with a sharp-tip vane, and (4) TVC with a sharp-tip vane and additional cavity fuel injection. Numerical results reveal that the introduction of guide vanes significantly changes the cavity vortex structure. Unlike the previous single cavity vortex, a counter-rotating dual-vortex structure is formed inside the cavity when the vane is implemented: one vortex is generated by the air jet guided by the vane and the other is the wake vortex downstream the vane. Because of the additional air introduced into the cavity by the guide vane, a fuel-lean mixture is obtained inside the cavity. This indicates fuel can be further injected inside to make full use of the air. Combustion results show that compared with the TVC without vanes, case 4 increases the combustion efficiency by 14% (to 99.3%) at the exit of combustor. Meanwhile, the combination of the sharp tip vane and cavity fuel injection only provides around 5% increase in aerodynamic drag and 3.9% in overall total pressure loss.

Moffatt eddies in the driven cavity: A quantification study by an HOC approach

In this paper, we establish Moffatt-likeness of the corner vortices in the lid-driven square cavity for Stokes flow and flow for moderate Reynolds numbers in the pre-asymptotic regime. The flow is computed by using an efficient transient Navier–Stokes (N–S) solver on compact non-uniform space grids. The quantification of the corner vortices in succession as Moffatt vortices follows from them following a fixed geometric ratio in sizes and intensities. In the process, we also provide more detailed benchmarking results for the corner vortices in the cavity flow. The accuracy of the scale resolution of the vortices has been verified by a novel approach to grid independence analysis. This approach utilizes the concept of adverse pressure gradients as a tool to validate that the separation zones in the neighborhood of the corners are consistent with the vortices obtained from our computed solution of the N–S equations.

A Semi-Empirical Prediction Method for Broadband Hull-Pressure Fluctuations and Underwater Radiated Noise by Propeller Tip Vortex Cavitation †

A semi-empirical method is presented that predicts broadband hull-pressure fluctuations and underwater radiated noise due to propeller tip vortex cavitation. The method uses a hump-shaped pattern for the spectrum and predicts the centre frequency and level of this hump. The principal parameter is the vortex cavity size, which is predicted by a combination of a boundary element method and a semi-empirical vortex model. It is shown that such a model is capable of representing the variation of cavity size with cavitation number well. Using a database of model- and full-scale measured hull-pressure data, an empirical formulation for the maximum level and centre frequency has been developed that is a function of, among other parameters, the cavity size. Acceptable results are obtained when comparing predicted and measured hull-pressure and radiated noise spectra for various cases. The comparison also shows differences that require adjustments of parameters that need to be further investigated.

Numerical study of the effect of the cavity depth on the leakage control in a cooled honeycomb-tip turbine cascade

The effect of the cavity depth on the leakage flow and tip cooling has been numerically investigated in a honeycomb-tip turbine cascade with cooling injection. Coolant is ejected through the center holes on the honeycomb cavity bottoms. Three dimensional flow fields were simulated using the Reynolds-averaged Navier-Stokes (RANS) method and the k-ω turbulence model. Then the tip configurations are evaluated according to several performance parameters, such as leakage mass flow rate, total pressure loss and film cooling effectiveness, in the upper passage, the gap and the honeycomb cavities. Furthermore, the secondary velocity streamlines are plotted at the cascade exit to characterize the upper passage vortices. The isothermal surface and contours of dimensional temperature are presented to explore the mixing between the coolant and the cavity vortices. The numerical results show that the aerodynamic and thermodynamic performance differs significantly with the cavity depth.

An analytical and semi-empirical model for the viscous flow around a vortex cavity

The minimum pressure in the core of a vortex, and therefore also the inception of cavitation, is considerably influenced by viscous effects. However, little information is available on the influence of viscous effects once the vortex cavity is fully developed. For that purpose an analytical solution for the azimuthal velocity distribution, including the boundary conditions, of a cavitating vortex in 2-D viscous flow is derived and investigated. The analytical solution, that can be designated as a cavitating Lamb–Oseen vortex, shows that with increasing cavity size the influence of viscosity decreases. For practical applications, the analytical model is extended to a second vortex model which allows for a region with vorticity roll-up. The resulting semi-empirical model for the azimuthal velocity distribution can be fitted well to experimental data for a wing-tip vortex for both non-cavitating and cavitating conditions. The vortex model has also been used to compare the relation between cavity size and cavitation number with experimental data. For the theoretical models, this relation can be presented such that it becomes independent of vortex strength and viscous core size.

Numerical study of non-reacting flowfields of a swirling trapped vortex ramjet combustor

In this work, 3D numerical investigations of a trapped vortex combustor operated in different swirling flow conditions are performed by solving Reynolds-averaged Navier–Stokes equations with Reynolds-stress model. Emphasis is placed on the non-reacting flowfield characteristics and the stability of the locked vortex. Validation is performed first by comparing the present results with experimental data available. It shows that the Reynolds-stress model can provide good predictions for flows with a swirl number up to 0.98. It is also found that the cavity vortex can be trapped well in flows with different swirl numbers. To further study the “locked” vortices, flow disturbances are introduced to the trapped vortex combustor via suddenly increasing swirl number from 0.6 to 0.98. The transient simulation results reveal that the cavity vortex is highly resistant to the flow disturbances and is still well trapped in the cavity, while vortex shedding of the conventional breakdown vortex is observed in the presence of the flow disturbances. Turbulence intensity and kinetic energy are found to be significantly increased by approximately 300%, which indicates that the fuel–air mixing can be dramatically improved. This study shows that the swirling trapped vortex combustor is an alternative promising robust and efficient combustor concept.

Study on tip leakage vortex cavitating flows using a visualization method

Experimental investigations of unsteady cavitating flows in a hydrofoil tip leakage region with different gap sizes are conducted to highlight the development of gap cavitation. The experiments were taken in a closed cavitation tunnel, during which high-speed camera had been used to capture the cavitation patterns. A new visualization method based on image processing was developed to capture time-dependent cavitation patterns. The results show that the visualization method can effectively capture the cavitation patterns in the tip region, including both the attached cavity in the gap and the tip leakage vortex (TLV) cavity near the trailing edge. Moreover, with the decrease of cavitation number, the TLV cavity develops from a rapid onset-growth-collapse process to a continuous process, and extends both upstream and downstream. The attached cavity in the gap develops gradually stretching beyond the gap and combines with the vortex cavity to form the triangle cavitating region. Furthermore, the influences of gap size on the cavitation are also discussed. The gap size has a great influence on the loss across the gap, and hence the locations of the inception attached cavity. Besides, inception locations and extending direction of the TLV cavity with different gap sizes also differ. The TLV in the case with [Formula: see text] = 0.061 is more likely to be jet-like compared with that in the case with [Formula: see text] = 0.024, and the gap size has a great influence on the TLV strength.

Experimental measurement of tip vortex flow field with/without cavitation in an elliptic hydrofoil

In this paper, recent measurements of tip vortex flow with and without cavitation carried out in Cavitation Mechanism Tunnel of China Ship Scientific Research Center (CSSRC) are presented. The elliptic hydrofoil with section NACA 662-415 was adopted as test model. High-speed video (HSV) camera was used to visualize the trajectory of tip vortex core and the form of tip vortex cavitation (TVC) in different cavitation situations. Laser Doppler velocimetry (LDV) was employed to measure the tip vortex flow field in some typical sections along the vortex trajectory with the case of cavitation free. Stereo particle image velocimetry (SPIV) system was used to measure the velocity and vorticity distributions with and without cavitation. Series measurement results such as velocity and vorticity distributions, the trajectory of tip vortex core, the vortex core radius, cavity size and cavitation inception number were obtained. The results demonstrated that the minimum pressure coefficient in the vortex core obtained by flow field measurement was quite coincident with the tip vortex cavitation inception number obtained under the condition of high incoming velocity and low air content. And TVC would decrease the vortex strength comparing with the case without cavitation.

Cavitation Compliance in 1D Part-load Vortex Models

When Francis turbines operate at partial load, residual swirl in the draft tube causes low-frequency pulsation of pressure and power output. Scale effects and system response may bias the prediction of prototype behavior based on laboratory tests, but could be overcome by means of a 1D analytical model. This paper deals with the two most important features of such a model, the compliance and the source of excitation. In a distributed-parameter version, compliance should be represented as an exponential function of local pressure. Lack of similarity due to different Froude number can thus be compensated. The normally unknown gas content in the vortex cavity has significant influence on the pulsation, and should therefore be measured and considered as a test parameter.

Propeller tip vortex cavitation control and induced noise suppression by water injection

As noise emission from ships garners increasing interest, control of propeller cavitation, which generates vibration and radiates noise, gains critical importance. In the case of full-scale propellers, the tip vortex cavitation typically incepts first, and noise levels rise dramatically thereafter. We propose the mass injection method to reduce noise induced from the tip vortex cavitation and increase the cavity inception speed. Water injected from the propeller tip decreases the rotational speed of the tip flow, and restrains the growth of the tip vortex cavity. For the preliminary test, we investigate the flow around an elliptic wing in a cavitation tunnel, and measured the induced noise levels. The results show a clear decrease in the noise levels in the case of water injection from the wing tip compared to that of without injection. On the basis of a successful preliminary study, we apply this method to the rotating model propeller. Experimental investigations of the model tests in a large cavitation tunnel show that we can control the tip vortex cavitation of the propeller, and hence, increase the cavitation inception speed of the ship using water injection from the propeller tip.

Tip gap size effects on thermal performance of cavity-winglet tips in transonic turbine cascade with endwall motion

AbstractThe thermal performance of two cavity-winglet tips with endwall motion is investigated in a transonic high pressure turbine cascade, which operates at an engine representative exit Mach number of 1.2 and an exit Reynolds number of 1.7 × 106. The numerical method is first validated with experimental data and then used to investigate blade heat transfer at three different tip clearances of 1.1, 2.1 and 3.1% chord. The effects of relative endwall motion are considered. The present results show that as the size of the tip gap increases, the heat transfer coefficient and heat load on the tip increases. The winglet geometries on the blade tip mainly affect the tip flow structure close to them. At a larger tip clearance, the size of the separation bubble above the pressure side winglet increases. The heat transfer coefficient is high on the pressure side winglet due to the flow reattachment at all tip clearances. Within the tip gap, when the size of the tip clearance increases, the size of the cavity vortex increases and the cavity scraping vortex due to relative endwall motion becomes smaller. The impingement of the both two vortexes can lead to high heat transfer coefficient on the cavity floor surface. On the blade suction surface, when the size of the tip clearance increases, the heat transfer coefficient of the cavity tip increases, but those of the winglet tips decreases. The heat transfer coefficient is high on the side surface of the suction side winglet at all tip clearances because of the tip leakage flow impingement.

Lattice Boltzmann Simulation of Steady Flow in a Semi-Elliptical Cavity

AbstractThe lattice Boltzmann method is employed to simulate the steady flow in a two-dimensional lid-driven semi-elliptical cavity. Reynolds number (Re) and vertical-to-horizontal semi-axis ratio (D) are in the range of 500-5000 and 0.1-4, respectively. The effects of Re and D on the vortex structure and pressure field are investigated, and the evolutionary features of the vortex structure with Re and D are analyzed in detail. Simulation results show that the vortex structure and its evolutionary features significantly depend on Re and D. The steady flow is characterized by one vortex in the semi-elliptical cavity when both Re and D are small. As Re increases, the appearance of the vortex structure becomes more complex. When D is less than 1, increasing D makes the large vortexes more round, and the evolution of the vortexes with D becomes more complex with increasing Re. When D is greater than 1, the steady flow consists of a series of large vortexes which superimpose on each other. As Re and D increase, the number of the large vortexes increases. Additionally, a small vortex in the upper-left corner of the semi-elliptical cavity appears at a large Re and its size increases slowly as Re increases. The highest pressures appear in the upper-right corner and the pressure changes drastically in the upper-right region of the cavity. The total pressure differences in the semi-elliptical cavity with a fixed D decrease with increasing Re. In the region of themain vortex, the pressure contours nearly coincide with the streamlines, especially for the cavity flow with a large Re.

Bubble-particle detachment in a turbulent vortex II—Computational methods

This is the second in a series of papers concerned with bubble-particle detachment in a turbulent vortex. Part I (Wang et al., 2016a, 2016b) explored, experimentally, the detachment of particles from bubbles due to centrifugal force generated in a rotating vortex in a wall cavity. Detachment was seen to be dependent on interactions between the turbulent vortex and the bubble-particle aggregate. Part II presents calculations of the flow field in the wall cavity, obtained using computational fluid dynamic (CFD) modelling. The probability of particle detachment from a bubble has been predicted using several different turbulence models.The traditional theory assumes that a bubble-particle aggregate is trapped inside an eddy and the attached particle is subjected to a centrifugal force as it rotates along with the eddy. When the centrifugal force on the particle exceeds the capillary force of attachment, the particle breaks away. The centrifugal force is a function of the energy dissipation rate, which requires an advanced turbulence model and high computational resources to achieve reliable predictions from the CFD calculations. To overcome the deficiencies of the current particle detachment model in the simulation of the flotation process, a new detachment model has been developed, relating the centrifugal acceleration to the vorticity in the flow field, where the vorticity calculation does not require the assumption of isotropic flow that is inherent in the dissipation method. Results from the Reynolds Stress Model (RSM) are compared with those from a Large Eddy Simulation (LES). The new vorticity model has advantages over the previous models which used the energy dissipation rate.

Cavitation Influence in 1D Part-load Vortex Models

Residual swirl in the draft tube of Francis turbines may cause annoying low- frequency pulsation of pressure and power output, in particular during part-load operation. A 1D analytical model for these dynamic phenomena would enable simulation by some conventional method for computing hydraulic transients. The proper structure of such a model has implications for the prediction of prototype behaviour based on laboratory tests.The source of excitation as well as the dynamic transmission behaviour of the draft tube flow may both be described either by lumped or distributed parameters. The distributed version contains more information and, due to limited possibilities of identification, some data must be estimated. The distributed cavitation compliance is an example for this dilemma. In recent publications, the customary assumption of a constant wave speed has produced dubious results. The paper presents a more realistic model for distributed compressibility. The measured influence of the Thoma number is applied with the local cavitation factor. This concept is less sensitive to modelling errors and explains both the Thoma and Froude number influence.The possible effect of the normally unknown non-condensable gas content in the vortex cavity is shortly commented. Its measurement in future tests is recommended. It is also recommended to check the available analytical vortex models for possible dispersion effects.

High load vortex oscillations developed in Francis turbines

Francis turbines operating at high load conditions produce a typical flow pattern in the draft tube cone characterized by the presence of an axisymmetric central vortex. This central cavity could become unstable, generating synchronic pressure pulsations, usually called self-excited oscillations, which propagate into the whole machine.The on-set and size of the central vortex cavity depend on the geometry of the runner and draft tube and on the operating point as well. Numerical flow simulations and model tests allow for the characterization of the different flow patterns induced by each particular Francis turbine design and, when studied in combination with the hydraulic system, including the intake and penstock, could predict the prototype hydraulic behavior for the complete operation zone.The present work focuses the CFD simulation on the development and dynamic behavior of the central axisymmetric vortex for a medium-head Francis turbine operating at high load conditions. The CFD simulations are based in two-phase transient calculations. Oscillation frequencies against its cavity volume development were obtained and good correlation was found with experimental results.

Heat Transfer of Winglet Tips in a Transonic Turbine Cascade

Understanding the heat transfer of winglet tips is crucial for their applications in high-pressure turbines. The current paper investigates the heat transfer performance of three different winglet-cavity tips in a transonic turbine cascade at a tip gap of 2.1% chord. A cavity tip is studied as the baseline case. The cascade operates at engine representative conditions of an exit Mach number of 1.2 and an exit Reynolds number of 1.7 × 106. Transient infrared thermography technique was used to obtain the tip distributions of heat transfer coefficient for different tips in the experiment. The CFD results were validated with the measured tip heat transfer coefficients, and then used to explain the flow physics related to heat transfer. It is found that on the pressure side winglet, the flow reattaches on the top winglet surface and results in high heat transfer coefficient. On the suction side winglet, the heat transfer coefficient is low near the blade leading edge but is higher from the midchord to the trailing edge. The suction side winglet pushes the tip leakage vortex further away from the blade suction surface and reduces the heat transfer coefficient from 85% to 96% span on the blade suction surface. However, the heat transfer coefficient is higher for the winglet tips from 96% span to the tip. This is because the tip leakage vortex attaches on the side surface of the suction side winglet and results in quite high heat transfer coefficient on the front protrusive part of the winglet. The effects of relative endwall motion between the blade tip and the casing were investigated by CFD method. The endwall motion has a significant effect on the flow physics within the tip gap and near-tip region in the blade passage, thus affects the heat transfer coefficient distributions. With relative endwall motion, a scraping vortex forms inside the tip gap and near the casing, and the cavity vortex gets closer to the pressure side squealer/winglet. The tip leakage vortex in the blade passage becomes closer to the blade suction surface, resulting in an increase of the heat transfer coefficient.

A global Stokes method of approximated particular solutions for unsteady two-dimensional Navier–Stokes system of equations

ABSTRACTThe unsteady two-dimensional Navier–Stokes system of equations, for viscous incompressible fluids are solved using a global method of approximated particular solutions (MAPS) in terms of a Stokes formulation, where the velocity and pressure fields are approximated from a linear superposition of particular solutions of a non-homogeneous Stokes system of equations, with a multiquadric (MQ) radial basis function (RBF) as non-homogeneous term. Steady-state solution of the flow problems considered in this work can be unstable at high Reynolds numbers (Re), corresponding to bifurcation of solutions that result in the appearance of new stable steady-state or periodic solutions. The main objective of this work is to present a global meshless numerical scheme able to predict these bifurcation points and concurrent new stable or periodic solutions. This is well known to be a very difficult task for any numerical scheme. An implicit first-order time-stepping scheme is used to approximate the transient term and the obtained nonlinear system of algebraic equations is solved by a Newton–Raphson method with variable step. Two steady-state and two transient problems are considered to validate the numerical scheme: the lid-driven cavity and backward-facing step (BFS) flows (steady-state problems) and the decaying Taylor–Green vortex and two-sided lid-driven cavity flows (transient problems). The first two problems are solved up to Re=10,000 and 2300, respectively. Results obtained are compared with corresponding benchmark numerical solutions, showing excellent agreement. Obtained numerical solutions for the decaying vortices at Re=100 shown excellent agreement with the corresponding analytical results. The transient problem of a rectangular two-sided lid-driven cavity flow is solved at Re=700. The influence of the cavity length, l, in determining the different structures of the flow pattern is studied for values of , showing that the scheme is able to reproduce the previously reported change in the flow pattern when l=2. Finally, the global Stokes MAPS are used to carry out nonlinear stability analyses of three steady-state problems: the sudden expansion, lid-driven cavity and BFS flows. Stable and unstable steady-state solutions at Re values greater than critical are predicted with the proposed numerical scheme. Our numerical results are consistent with previously stability analysis reported in the literature.

Experiments on the detachment of particles from bubbles in a turbulent vortex

In this paper we present a new method for studying the detachment of particles from bubbles in a rotating turbulent eddy. The eddy is formed in a wall cavity in a two-dimensional water tunnel with transparent walls. When water flows through the tunnel, a vortical flow field develops in the cavity. The properties of the eddy can be modulated by changing the free-stream velocity of the water in the tunnel. Bubbles are pre-loaded with one or more particles in a fluidized bed flotation device located beneath the vortex cavity. Loaded bubbles are released one at a time into the cavity, and the motion of the bubble-particle aggregate is studied using a high-speed video camera. The diameters of the particles and the bubbles, and the number of particles initially attached to the bubble, can be varied.The trajectories taken by the bubbles are quite complicated. In some cases, the bubble moves to the centre of the eddy, and particles rotate around its axis. If the rotational speed is sufficient, particles may detach due to centrifugal force. However, other modes were observed, including inertial detachment due to rapid changes in direction of the surface of the bubble, because of changes in trajectory of the bubble as a whole, or because of pulsations and oscillations of the bubble surface. Clusters of bubbles held together by particles were seen to form and reform.In the traditional explanation for the detachment of particles in flotation cells, it is assumed that particles detach from bubbles rotating in an eddy due to centrifugal force (Schulze, 1977) [1]. Although the conditions assumed in Schulze's theory may exist, it is only one of a range of phenomena that can lead to the detachment of particles from bubbles in a turbulent vortex. The interactions between bubbles and particles is stochastic in nature, and it is impossible to model precisely the series of events that take place when a particle and a bubble make contact with each other and move through the liquid. There can be no simple model for the recovery of hydrophobic particles in flotation machines.