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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.

This work assesses the performance of two single-equation eddy viscosity transport models that are based on Menter’s transformation of the k-ε and the k-ω closures. The coefficients of both models are set exactly the same and follow directly from the constants of the standard k-ε closure. This in turn allows a cross-comparison of the effect of two different destruction terms on the performance of single-equation closures. Furthermore, some wall-free modifications to production and destruction terms are proposed and applied to both models. An assessment of the baseline models with and without the proposed modifications against experiments, and the Spalart-Allmaras turbulence model is provided via several boundary-layer computations. Better performance is indicated with the proposed modifications in wall-bounded nonequilibrium flows.

The purpose of this paper is to develop a second-moment closure with a near-wall turbulent pressure diffusion model for three-dimensional complex flows, and to evaluate the influence of the turbulent diffusion term on the prediction of detached and secondary flows. A complete turbulent diffusion model including a near-wall turbulent pressure diffusion closure for the slow part was developed based on the tensorial form of Lumley and included in a re-calibrated wall-normal-free Reynolds-stress model developed by Gerolymos and Vallet. The proposed model was validated against several one-, two, and three-dimensional complex flows.

One of the important research areas in the water-entry problem is the cavity dynamics. A theoretical analysis is presented to predict the dynamics of water-entry cavity up to the first cavity closure, which is generated by a solid body entering a semi-inifinite free surface of water at a wide range of entry speed. Two types of cavity closure, which are surface closure and the deep closure, depending on the magnitude of ambient atmosphere pressure and entry speed are described by the proposed theory. The time of surface closure at the relatively low-speed entry regime is estimated and compared with published experimental data. Currently no experimental data are available for the high-speed entry case.

A new multi-phase model for low speed gas/liquid mixtures is presented; it does not require ad-hoc closure models for the variation of mixture density with pressure and yields thermodynamically correct acoustic propagation for multi-phase mixtures. The solution procedure has an interface-capturing scheme that incorporates an additional scalar transport equation for the gas void fraction. Cavitation is modeled via a finite rate source term that initiates phase change when liquid pressure drops below its saturation value. The numerical procedure has been implemented within a multi-element unstructured framework CRUNCH that permits the grid to be locally refined in the interface region. The solution technique incorporates a parallel, domain decomposition strategy for efficient 3D computations. Detailed results are presented for sheet cavitation over a cylindrical head form and a NACA 66 hydrofoil.

The effect of axial tube rotation on the fully developed pipe flow is analyzed by a low-Reynolds-number turbulence closure and compared with experimental results. A flow which is initially turbulent is stabilized by the rotation leading to a laminarized mean axial velocity distribution. The applied second-moment closure reveals an encouraging ability to capture this phenomenon as well as other features of the mentioned flow configuration. The “rapid” part of the pressure-strain correlation model is found to have a significant influence on the numerical results and seems to be the key for further improvements concerning highly swirling flows.

In this paper we discuss a computational method focused on the prediction of unsteady aerodynamics, adequate for industrial turbomachinery. Here we focus on a single rotor device selected from a new family of large tunnel ventilation axial flow fans. The flow field in the fan was simulated using the open source code OpenFOAM, with a large-eddy simulation (LES) approach. The sub-grid scale (SGS) closure relied on a one-equation model, that requires us to solve a differential transport equation for the modeled SGS turbulent kinetic energy. The use of such closure was here considered as a remedial strategy in LES of high-Reynolds industrial flows, being able to tackle the otherwise insufficient resolution of turbulence spectrum. The results show that LES of the fan allows to predict the pressure rise capability of the fan and to reproduce the most relevant flow features, such as three-dimensional separation and secondary flows.

A nonorthogonal, collocated finite-volume scheme, based on a pressure-correction strategy and originally devised for general-geometry incompressible turbulent recirculating flow, has been extended to compressible transonic conditions. The key elements of the extension are a solution for flux variables and the introduction of streamwise-directed density-retardation which is controlled by Mach-number-dependent monitor functions, and which is applied to all transported flow properties. Advective fluxes are approximated using the quadratic scheme QUICK or the second-order TVD scheme MUSCL, the latter applied to all transport equations, including those for turbulence properties. The procedure incorporates a number of turbulence models including a new low-Re k–ε eddy-viscosity variant and a Reynolds-stress-transport closure. The predictive capabilities of the algorithm are illustrated by reference to a number of inviscid and turbulent transonic applications, among them a normal shock in a Laval nozzle, combined oblique-shock reflection and shock-shock interaction over a bump in a channel and shock-induced boundary-layer separation over channel bumps. The last-named application was computed both with eddy-viscosity models and Reynolds-stress closure, leading to the conclusion that the latter yields a much greater sensitivity of the boundary layer to the shock and, arising therefrom, a more pronounced λ-shock structure, earlier separation and more extensive recirculation. On the other hand, the stress closure is found to return an insufficient rate of wake recovery following reattachment.

The classic study of the water entry of a body has applications ranging from hydroballistics to behavior of basilisk lizards. The availability of Russian supercavitation theory in recent years has allowed for an even greater understanding, and was used to develop a model to predict the dynamic size, shape, and pressure of a naturally or artificially produced underwater cavity. This model combines supercavitation theory, rigid body dynamics, and hydrodynamic theory into a comprehensive model capable of determining the motional behavior of underwater objects. This model was used as the basis for modeling the vertical water entry of solid objects into a free water surface. Results from simulation of water entry of various-sized thin disks compared favorably with published experimental data from the technical literature. Additional simulated data support a disk radius dependence on a relative object depth at cavity closure that was not previously recognized. Cavity closure times are also presented.

The maximum pressure head resulting from one-speed closure of wide open valves is investigated. The dimensionless variables formulated in this study make the subtle effect of the initial valve head loss explicit and separate from that of the pipe frictional head loss. The maximum head is related to initial pipe frictional head loss, the initial valve head loss, the inherent flow characteristic of the valve, and the closure period by plots of dimensionless variables. The trends of the variation of the maximum pressure head are discussed. An example is used to illustrate the usage of the plots, and to show the advantage of having a global perspective of the phenomenon in the selection and sizing of valves from the water hammer point of view.

A new approach to the classical slug flow model is here proposed based on an original correlation for the minimum liquid level in the stratified regions of intermittent horizontal flows. This correlation is obtained by fitting experimental data obtained from a statistical analysis of void fraction signals from ring impedance probes. The new procedure improves the original model in terms of computing time reduction and algorithm simplification. In addition, it is demonstrated that the new closure relationship can be derived with more consistent experimental results, with respect to the slug length, which is employed in the original approach. The predictions of the main flow parameters are presented with reference to the classical and new approach, and all the results are critically compared with literature experimental data. It is demonstrated that the simplified procedure is able to predict the pressure drops and average void fraction values in good agreement with experimental measurements, while only the slug frequency and slug length predictions are affected by poor reliability.

A three-dimensional twisted hydrofoil with an attached cavitaty closely related to propellers was observed with a high-speed camera at the University of Delft Cavitation Tunnel. Reentrant flow coming from the sides of the cavity aimed at the center plane—termed side-entrant flow—collided in the closure region of the cavity, pinching off a part of the sheet resulting in a periodic shedding. The collapse of the remainder of the sheet appears to be a mixing layer at the location of the colliding reentrant flows. Collision of side-entrant jets in the closure region of a cavity is identified as a second shedding mechanism, in addition to reentrant flow impinging the sheet interface at the leading edge.

A Reynolds stress transport equation model and the k–ε turbulence model have been applied to the calculation of a confined, strongly swirling flow. A comparison of the results with measurement shows clearly the superiority of the transport equation model. It reproduces the major features of the flow including the strong stabilizing effects of the swirl on the shear stresses and the calculated axial and circumferential components of mean velocity are in reasonable agreement with measured profiles. The corresponding normal stresses are, however, overpredicted but previously suggested modifications to the ε-equation to account for rotation did not bring any improvement. The k–ε model does not contain any mechanism to describe the stabilizing effects of swirling motion and as a consequence it performs poorly; large discrepancies exist between the measured and calculated mean velocity field.

A procedure is presented for the generation of the optimal gate closure schedule for the case of full load rejection on an isolated hydroelectric system. Constraints are placed on turbine overspeed and penstock overpressure. The optimization is carried out on the basis of minimum integral square off speed and implemented digitally by the method of steepest descent. The computation indicates that a substantial performance improvement is achieved with optimal control as opposed to the conventional.