In the tip clearance flow, the dominant vortex is the tip leakage vortex (TLV), which has a significant impact on the hydraulic and cavitation performance of axial flow machineries. In order to reveal the impact mechanism of the gap size on the TLV, gap flows with two gap sizes, i.e., τ = 0.2 (2 mm) and τ = 1.0 (10 mm), are numerically investigated. A NACA0009 hydrofoil is selected to create the gap flow, with an incoming velocity of 10 m/s and an attack angle of 10 deg . The results show that the two flow cases are significantly different in terms of vortex feature and the leakage flow distribution. In the small gap, a type of jet-pattern flow appears, whereas a type of rolling-pattern flow passes over the large gap. The vertical velocity gradient of the leakage flow has a decisive influence on the TLV trajectory. In addition, for the large gap, the axial velocity in the vortex center exceeds the incoming flow. This jet-like state of axial velocity can be maintained for a long distance, making the vortex more stable. However, the axial velocity in the case of τ = 0.2 cannot stay at the jet-like state and rapidly switches to a wake-like state.

Tip clearance results in the leakage flow from blade pressure side to suction side, which will further cause the tip leakage vortex (TLV). Moreover, the flow pattern in an impeller is seriously deteriorated due to the TLV and its interaction with the main stream. In this work, the TLV in a mixed flow pump is investigated by numerical simulation validated by experiment measurement. The primary tip leakage vortex (PTLV) trajectory is specially studied with consideration of the tip clearance size δ, the impeller blade number Z i , and the impeller rotational speed n. The results show that δ slightly shifts the separation point (SP) of the PTLV but rarely affects the separation angle α . The increase in Z i and the decrease in n both lead to the shift of the SP toward the blade trailing edge and the decrease in α . Furthermore, a theoretical prediction model is proposed to predict the PTLV trajectory, by which the axial position and radial position of PTLV trajectory versus the rotation angle can be predicted. The proposed model is verified to be accurate to predict the PTLV trajectory, especially for the PTLV trajectory in the main flow passage. The dynamic evolution of TLV under different tip clearance sizes can all be classified into the same three stages: splitting stage, developing stage, and merging stage. Meanwhile, the dynamic evolution frequency f e is the same as the impeller rotational frequency f i .

Tip clearance in pump induces tip leakage vortex (TLV), which interacts with the main flow and leads to instability of flow pattern and decrease of pump performance. In this work, the characteristics of TLV in a mixed-flow pump are investigated by the numerical simulation using shear stress transport (SST) k– ω turbulence model with experimental validation. The trajectory of the primary tip leakage vortex (PTLV) is determined, and a power function law is proposed to describe the intensity of the PTLV core along the trajectory. Spatial–temporal evolution of the TLV in an impeller revolution period T can be classified into three stages: splitting stage, developing stage, and merging stage. The TLV oscillation period T T is found as 19/160 T, corresponding to the frequency 8.4 f i (f i is impeller rotating frequency). Results reveal that the TLV oscillation is intensified by the sudden pressure variation at the junction of two adjacent blades. On analysis of the relative vorticity transport equation, it is revealed that the relative vortex stretching item in Z direction is the major source of the splitting and shedding of the PTLV. The dominant frequency of pressure and vorticity fluctuations on the PTLV trajectory is 8.4 f i , same as the TLV oscillation frequency. This result reveals that the flow instability in the PTLV trajectory is dominated by the oscillation of the TLV. The blade number has significant effect on pressure fluctuation in tip clearance and on blade pressure side, because the TLV oscillation period varies with the circumferential length of flow passage.

The effect of nonsinusoidal trajectory on the propulsive performances and the vortex shedding process behind a flapping airfoil is investigated in this study. A movement of a rigid NACA0012 airfoil undergoing a combined heaving and pitching motions at low Reynolds number (Re = 11,000) is considered. An elliptic function with an adjustable parameter S (flattening parameter) is used to realize various nonsinusoidal trajectories of both motions. The two-dimensional (2D) unsteady and incompressible Navier–Stokes equation governing the flow over the flapping airfoil are resolved using the commercial software star ccm +. It is shown that the nonsinusoidal flapping motion has a major effect on the propulsive performances of the flapping airfoil. Although the maximum propulsive efficiency is always achievable with sinusoidal trajectories, nonsinusoidal trajectories are found to considerably improve performance: a 110% increase of the thrust force was obtained in the best studied case. This improvement is mainly related to the modification of the heaving motion, more specifically the increase of the heaving speed at maximum pitching angle of the foil. The analysis of the flow vorticity and wake structure also enables to explain the drop of the propulsive efficiency for nonsinusoidal trajectories.

Centrifugal pumps operate below their nominal capacity when handling gas–liquid flows. This problem is sensitive to many variables, such as the impeller speed and the liquid flow rate. Several works evaluate the effect of operating conditions in the pump performance, but few bring information about the associated gas–liquid flow dynamics. Studying the gas phase behavior, however, can help understanding why the pump performance is degraded depending on the operating condition. In this context, this paper presents a numerical and experimental study of the motion of bubbles in a centrifugal pump impeller. The casing and the impeller of a commercial pump were replaced by transparent components to allow evaluating the bubbles' trajectories through high-speed photography. The bubble motion was also evaluated with a numerical particle-tracking method. A good agreement between both approaches was found. The numerical model is explored to evaluate how the bubble trajectories are affected by variables such as the bubble diameter and the liquid flow rate. Results show that the displacement of bubbles in the impeller is hindered by an increase of their diameter and impeller speed but facilitated by an increase of the liquid flow rate. A force analysis to support understanding the pattern of the bubble trajectories was provided. This analysis should enlighten the readers about the dynamics leading to bubble coalescence inside an impeller channel, which is the main reason behind the performance degradation that pumps experience when operating with gas–liquid flows.

The vertically launched underwater vehicle always suffers various hydrodynamic disturbances in its water-emerging process due to the uncertainty of the launch platform motion. Based on the nested sparse grid based stochastic collocation method (NSSCM) and nonintrusive polynomial chaos method, the effect of uncertainty of platform velocity and yaw angle on robustness of vehicle's trajectory and attitude is numerically studied. Results indicate that the uncertainty stemming from platform motion propagates along vehicle's water-emerging process. As the negative horizontal velocity of vehicle gradually changes to positive direction, the uncertainty bar of horizontal velocity presents contracting-expanding mode with an “hourglass” shape while the uncertainty bar of horizontal displacement experiences a “spindle-shaped” one (expanding-contracting-expanding), which is a half cycle later compared with the velocity. The uncertain motion of platform enlarges the uncertainty bar of bottom force via its impact on the gas-leakage process of trail bubble, resulting in the increasing of uncertainty of vertical velocity. Pitching angle (attitude of vehicle) and pitching angular velocity of vehicle persist getting worse driven by the pressure difference between vehicle's front and back sides especially on head part. And their continuous increasing uncertainty bars are formed mainly due to the condition that pressure uncertainty of front side is larger than that on back side, which also leads to the increasing of uncertainty of horizontal force.

Trajectory and penetration of elliptical liquid jets emerged into a low-speed crossflow of air are studied. The jets are introduced to the crossflow at different momentum ratios ranging from 1 to 300. The images are analyzed to obtain the trajectories of the outer boundary of the jets for two different aspect ratios. An empirical correlation is proposed for the present injector geometries and for the range of momentum ratio, Weber, and Reynolds numbers used in this study. Finally, a theoretical model for the trajectory of the liquid column for an initially elliptical liquid emerging into a crossflow is presented, and the associated drag coefficients are obtained for a precise trajectory prediction.

This study reports an experimental investigation of two planar jets in a crossflow in a tandem arrangement. Tests were conducted in an open-jet wind tunnel facility using two-dimensional (2D)-particle imaging velocimetry (PIV) measurement. Using the terminology in the dual jets in a quiescent ambient, the mean flow field of the crossflow arrangement was divided into a converging region, a merging region, and a combined region. An approach to determining the range of these three regions was proposed based on the mean characteristics of horizontal velocity profiles of the flow field, validated by the experimental data. The momentum-dominated near field (MDNF) for the rear jet in the dual-jet configuration was recognized using the horizontal offset of mean jet trajectory, which accordingly gives a quantitative definition of the MDNF range. Discussions were made on the effects of different parameters on the three regions and MDNF. Finally, snapshot proper orthogonal decomposition (POD) analysis was conducted, characterizing the coherent structures of the flow field, particularly the large-scale vortices. It was observed that the large-scale vortices mainly occur in the shear layers of the jets and their occurrence is affected by the parameters of the jets. In addition, compared with the single-jet configuration, the introduction of the front jet was found to contribute to the occurrence and development of the large-scale vortices.

Viscoelastic solution is encountered extensively in microfluidics. In this work, the particle movement of the viscoelastic flow in the contraction–expansion channel is demonstrated. The fluid is described by the Oldroyd-B model, and the particle is driven by dielectrophoretic (DEP) forces induced by the applied electric field. A time-dependent multiphysics numerical model with the thin electric double layer (EDL) assumption was developed, in which the Oldroyd-B viscoelastic fluid flow field, the electric field, and the movement of finite-size particles are solved simultaneously by an arbitrary Lagrangian–Eulerian (ALE) numerical method. By the numerically validated ALE method, the trajectories of particle with different sizes were obtained for the fluid with the Weissenberg number (Wi) of 1 and 0, which can be regarded as the Newtonian fluid. The trajectory in the Oldroyd-B flow with Wi = 1 is compared with that in the Newtonian fluid. Also, trajectories for different particles with different particle sizes moving in the flow with Wi = 1 are compared, which proves that the contraction–expansion channel can also be used for particle separation in the viscoelastic flow. The above results for this work provide the physical insight into the particle movement in the flow of viscous and elastic features.

Pressure-equalizing film is a slice of air film generated through exhausting and attached to the vehicle's exterior with nearly uniform inner pressure. Similar to ventilated cavity in composition, but of interest, here is the weakening of pitching moment and environment disturbance that the film offers, the film's forming speed and covering range upon vehicle determine the improvement effect of vehicle's trajectory stability as it emerges from water. This paper established a numerical approach to investigate the effect of single and double rows of venting holes on the evaluation of air film along vehicle's exterior, at the same time its influence on the trajectory stability of vehicle with three degrees-of-freedom (3DOF) motion is also analyzed. Results indicate that reverse flow forms between row-to-row spacing when exhausting with two rows of holes, which enhances the exhausting process with the film's size enlarged and axial length extended, meanwhile it brings about more complex vortices structure near venting holes compared to the single-row hole case. As for the 3DOF cases, the pressure difference between vehicle's front and back sides is dramatically reduced attributing to the existence of attached air film, consequently the rotation of vehicle is weaken, leaving a better attitude to vehicle after it piercing water surface. Besides, the rapid formation of air film in double-row hole cases is advantage for the timely inhibiting of vehicle's pitching motion compared to the single-row hole cases, and their weaker stagnation high pressure near film's closure region is also good for the reduction of vehicle's lateral load.

Planar laser-induced fluorescence (PLIF) with acetone seeding was applied to measure the scalar fields of an axisymmetric freejet and an inclined jet in crossflow as applicable to film cooling. From the scalar fields, jet-mixing and trajectory characteristics were obtained. In order to validate the technique, the canonical example of a nonreacting freejet of Reynolds numbers 900–9000 was investigated. Desired structural characteristics were observed and showed strong agreement with computational modeling. After validating the technique with the axisymmetric jet, the jet in crossflow was tested with various velocity ratios and jet injection angles. Results indicated the degree of wall separation for different injection angles and demonstrated both the time-averaged trajectories as well as select near-wall concentration results for varying jet momentum fluxes. Consistent with literature findings, the orthogonal jet trajectory for varying blowing ratios collapsed when scaled by the jet-to-freestream velocity ratio and hole diameter, rd . Similar collapsing was demonstrated in the cases of a nonorthogonal jets. Computational fluid dynamic (CFD) simulations using the openfoam software were used to compare predictions with select experimental cases and yielded reasonable agreement. Insight into the importance and structure of the counter-rotating vortex pair (CVP) and general flow field turbulence was highlighted by cross validation between CFD and experimental results.

During the transitional processes of load rejection in a pumped-storage station, the S-shaped characteristics of the pump-turbines can result in relatively large water-hammer and pulsating pressures. These pressures and the high runaway speed during transient processes may directly damage the penstocks and shorten the life of the turbine. In this study, different guide-vane closing schemes for reducing the maximum transient pressures, including the water-hammer and pulsating pressures, and runaway speed were investigated, and the principles for improving the closing schemes were theoretically analyzed based on the transient characteristics in the S-shaped region. First, an analytical expression for the rate of change of relative water head during the transitional processes was deduced based on a simplified mathematical model. It reveals the relationship between the slopes of the trajectory at the pump-turbine operating points (defined as trajectory slopes) and the rigid water-column pressure, which approximates the water-hammer pressure considering compressibility. Then, based on the characteristics of the rigid water-column pressure during the transient process and the effects of guide-vane closure on the trajectory slopes, the selection method for a two-phase guide-vane closing scheme was proposed. The method included the technique for choosing the coordinates of the turning point and the closing speed of the guide vane. Furthermore, the pulsating pressures of pump-turbines were discussed under different working regions and guide-vane openings (GVOs). Considering the characteristics of the pulsating pressures and the runaway speed during the transient processes, the advantage of three-phase valve-closing schemes in controlling the pulsating pressures and the runaway speed was clarified. Finally, a series of model tests were conducted on a pumped-storage station model and the measured data fully validated the correctness of our analyses in this work.

In this work we study the hydrodynamics of characteristic gas jets resulting from guillotine breaks of steam generator tube rupture sequences (SGTR) in pressurized nuclear power reactors. As an initial step towards describing an “in-bundle” gas jet, a hydrodynamic model of free gas jets emerging from a guillotine break under prototypical SGTR conditions has been developed. First we have studied the jet characteristic for an isolated tube; the analytical model estimates variables such as trajectories, centerline velocities, velocity distribution, and Reynolds stresses. We have performed model comparisons with experimental data for different experimental conditions with different mass flow rates, and we have found good agreement of the model with the experimental results. Additionally, an “ad hoc” expression has been derived for the centerline jet velocity, which has been experimentally confirmed. Consistently with the experimental data and the computational fluid dynamics (CFD) calculations the analytical model predicts no outflow near the jet center. As a complementary issue, we have performed CFD calculations for a guillotine tube rupture when the tube is surrounded by several rows of neighboring tubes, in this case the jet trajectories are affected by the Coanda effect near the tubes.

An investigation of the jet trajectories and mixing behavior of venturi-jet mixers, in which turbulent jet injects fluid at an arbitrary angle to mix incompressible fluids, is described in this paper. Numerical results of an incompressible cross flow-jet mixing in venturi-jet mixers are presented and validated against experimental results. Jet trajectories, concentration decay of tracer jet, spatial unmixedness, and mixing length are computed for a range of injection angles ( 45 deg ≤ θ o ≤ 135 deg ) . Twenty-five cases are studied with five different initial injection angles, each with five different jet momentum ratios. As an example of practical insights that can be gained from such detailed analysis, the resulting flow field is used to obtain an equation for trajectory and tracer concentration in the mixer. The penetration of jet scales with the third root of the jet-to-mainstream momentum ratio and that of with square root of downstream distance. The decay of mean concentration scales with the inverse of axial distance and with the negative root of injection angle. The results show a consistency in the experimental data and simulation has provided a good insight into the flow details and has paved the way in optimization of the geometry based on jet injection angle to get a good mixing efficiency.

In this paper, the structure of a wall jet deflected by a baffle along with the trajectory of particles has been studied. This baffle is used to produce a stable deflected surface jet, thereby deflecting the high-velocity supercritical stream away from the bed to the surface. An elliptic relaxation turbulence model ( ν 2 ¯ − f model) has been used to simulate this submerged flow. In recent years, the ν 2 ¯ − f turbulence model has become increasingly popular due to its ability to account for near-wall damping without use of damping functions. In addition, it has been proven that the ν 2 ¯ − f model is superior to other Reynolds-averaged Navier-Stokes (RANS) methods in many flows where complex flow features are present. In this study, we compare the results of the ν 2 ¯ − f model with available experimental data. Since erosion and deposition are coupled, the study of this problem should consider both of these phenomena using a proper approach. In addition to erosion over the bed, the trajectory of the particles is examined using a Lagrangian–Eulerian approach, the distribution of deposited particles over the bed is predicted for a two-phase test case based on a series of numerical simulations. Results show that the maximum erosion happens in a place in which no particle can be deposited, which causes the bed to deform very rapidly in that region. This should help prevent or reduce erosion over the bed. On the other hand, the study will help predict the trajectory of particles and the deposition rates at any section of the channel, and should thus provide useful information to control the erosion and deposition on the channel bed.

We have developed a numerical simulation scheme combining a vortex method and a particle trajectory tracking method, which is applicable to internal unsteady two-phase flows. It is a completely grid-free Lagrangian–Lagrangian simulation, which is able to simulate the primary effect of vortical flow on the unsteady particle motion and dispersion. It can handle unsteady high Reynolds number flows. So far, no one has applied this kind of method internal multiphase flows, though many industrial multiphase flows are internal. In this study, internal liquid-solid two-phase flows in a vertical channel and a mixing tee have been calculated by the new method, in which use of the vortex introduction model enables the simulation of the dynamic behavior of separation or reattachment. In the mixing tee, solid particle phenomena such as depositions or particle-wall collisions have been simulated and measured. Numerical results based on simple two-dimensional flow and one-way model show good agreement with the experimental data. The results show that turbulent vortices dominate particle motion. It has been shown that the present method can be useful in the design of industrial multiphase flows with particle mixing, dispersion, deposition, and particle-wall collision because it is possible to simulate the effect of turbulent vortices on the particle motion.

Jet-crossflow experiments were performed in a water channel to determine the Reynolds number effects on the plume trajectory and entrainment coefficient. The purpose was to establish a lower limit down to which small scale laboratory experiments are accurate models of large scale atmospheric scenarios. Two models of a turbulent vertical surface jet (diameters 3.175 mm and 12.7 mm ) were designed and tested over a range of jet exit Reynolds numbers up to 10 4 . The results show that from Reynolds number 200–4000 there is about a 40% increase in the entrainment coefficient, whereas from Reynolds number 4000–10,000, the increase in entrainment coefficient is only 2%. The conclusion is that Reynolds numbers significantly affect plume trajectories when the model Reynolds numbers are below 4000. Changing the initial turbulence in the exit flow from 12% to 2% without changing its mean velocity profile caused a less than one source diameter increase in the final plume rise.

Experiments have been performed on the low speed research compressor (LSRC) at General Electric Aircraft Engines to investigate the effects of flow coefficient, stagger angle, and tip clearance on tip vortex. Time resolved casing pressure distributions over the third stage rotor have been acquired with high-frequency-response pressure transducers. Also, tip vortex strength and trajectory have been estimated from the casing pressure fluctuations which have been obtained simultaneously from various axial locations. As flow coefficient decreases, tip vortex gets strengthened and migrates upstream. The stagger angle increase weakens the tip vortex and moves it downstream slightly because the blade loading is decreased. However, tip leakage vortex is influenced mainly by tip clearance, and there exists a “critical” tip clearance which determines the type of tip vortex trajectory (“straight” or “kinked”). As predicted by others, tip vortex gets strengthened with increasing tip clearance. However, unlike the predictions, the tip vortex trajectory moves upstream with increasing tip clearance. Furthermore, with tip clearance above a “critical” value, the tip vortex trajectory is no longer straight but shows a kink in the passage.

Impulsively started impinging jets were experimentally investigated in a water tank utilizing a fluorescent dye technique. The jets were examined prior to and subsequent to impingement. The impingement surfaces included a flat surface and a two-dimensional semicircular concave surface. The normalized jet-to-surface distance and the jet Reynolds number were varied in this study. Using digitized flow visualization images, the jet trajectories, front velocities, growth rates, and convective velocities of large-scale turbulent structures were quantified. A central conclusion of this investigation is that, for all cases studied, the jet-front velocity varies with the square root of time. These results are important to applications that might use starting or pulsed jets for heat transfer enhancement and in combustion processes.