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Computational procedures and results of an upwash jet arising from two opposing plane wall jets based on the Reynolds averaged Navier‐Stokes equations are discussed. For the calculation of the flow, a steady and an unsteady numerical approach were taken. For the steady computation, we adopted various eddy viscosity models(the standard k‐ε model, the RNG k‐ε model and the Bardina’s model) and the Reynolds stress transport model with various diffusion term closures. Results of the steady computation indicated that the jet half‐width was very much underpredicted, and hence the velocity profiles of the upwash jet were in very poor agreement with the experimental data. We found, however, that the velocity profiles nondimensionalized by the jet half width and the maximum velocity appeared to be in good agreement with the experimental data, which could be misleading. When an unsteady approach with an unsteady version of the standard k‐ε eddy viscosity model was taken, a periodic oscillation of the jet was observed. The jet half‐width distribution obtained by taking the time average of the periodic velocity profiles was found to be in much better agreement with the experimental data.

The purpose of this paper is to describe how the hydraulic performance and pressure fluctuations in the entire flow passage of a Francis turbine were predicted numerically for the highest head. The calculations are used to partition the turbine operating regions and to clarify the unsteady flow behavior in the entire flow passage including the blade channel vortex in the runner and vortex rope in the draft tube.

Three‐dimensional unsteady numerical simulations were performed for a number of operating conditions at the highest head. The unsteady Reynolds‐averaged Navier‐Stokes equations with the k‐ω based SST turbulence model were solved to model the unsteady flow within the entire flow passage of a Francis turbine.

The predicted pressure fluctuations in the draft tube agree well with the experimental results at low heads. However the peak‐to‐peak amplitudes in the spiral case are not as well predicted so the calculation domain and the inlet boundary conditions need to be improved. The unsteady simulation results are better than the steady‐state results. At the most unstable operating condition of case a0.5h1.26, the pulse in the flow passage is due to the rotor‐stator interference between the runner and the guide vanes, the blade channel vortex in the runner blade passage and the vortex rope in the draft tube.

This study investigates the characteristics of the dominant unsteady flow frequencies in different parts of the turbine for various guide vane openings at the highest head. The unsteady flow patterns in the turbine, including the blade channel vortex in the runner and the helical vortex rope in the draft tube, are classified numerically, and the turbine operating regions are partitioned to identify safe operating regions.

The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy.

In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence.

In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod’s shock-tube problem, Stokes’ second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient.

The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations.

This paper aims to simulate unsteady flows with surfaces in relative motion using a multi-block structured flow solver.

A procedure for simulating unsteady flows with surfaces in relative motion was developed, based upon a multi-block structured U-RANS flow solver1. Meshes produced in zones of the flow field with different rotation speed are connected by sliding boundaries. The procedure developed guarantees that the flux conservation properties of the original scheme are maintained across the sliding boundaries during the rotation at every time step.

The solver turns out to be very efficient, allowing computation in scalar mode with single core processors as well as in parallel. It was tested by simulating the unsteady flow on a propfan configuration with two counter-rotating rotors. The comparison of results and performances with respect to an existing commercial flow solver (unstructured) is reported.

This paper fulfils an identified need to allow for efficient unsteady flow computations (structured solver) with different bodies in relative motion.

The purpose of this paper is to elucidate the detailed flow field and cavitation effect in the centrifugal pump volute at partial load condition.

Unsteady flows in a centrifugal pump volute at non-cavitation and cavitation conditions are investigated by using a computation fluid dynamics framework combining the re-normalization group k-e turbulence model and the mass transport cavitation model.

The flow field in pump volute is very complicated at part load condition with large pressure gradient and intensive vortex movement. Under cavitation conditions, the dominant frequency for most of the monitoring points in volute transit from the blade passing frequency to a lower frequency. Generally, the maximum amplitudes of pressure fluctuations in volute at serious cavitation condition is twice than that at non-cavitation condition because of the violent disturbances caused by cavitation shedding and explosion.

The detailed flow field and cavitation effect in the centrifugal pump volute at partial load condition are revealed and analysed.

A numerical method is developed for steady and unsteady turbulent flows with significant regions of separation. A finite element formulation of the Navier‐Stokes equations with a modified Baldwin‐Lomax eddy viscosity closure is used. The method of averaging is employed to obtain a periodic solution of unsteady flow. The formulation is tested on a problem of flow over a backward‐facing step and the results are compared with experimental and other numerical results. The gross features of both steady and unsteady flows are reasonably well predicted by the numerical analysis, at least for the limited range of parameters tested so far.

The purpose of this paper is to investigate, experimentally and numerically, the pressure pulse characteristics and unsteady flow behavior in a Francis turbine runner for moderate flow heads. The pressure pulses in the runner blade passage were predicted numerically for both moderate and high heads. The calculations were used to partition the turbine operating regions and to clarify the various for the unsteady flow behavior, especially the blade channel vortex in the runner.

Experimental and numerical analyses of pressure pulse characteristics at moderate flow heads in a Francis turbine runner were then extended to high heads through numerical modeling with 3D unsteady numerical simulations performed for a number of operating conditions. The unsteady Reynolds‐averaged Navier‐Stokes equations with the k‐ω‐based shear stress transport turbulence model were used to model the unsteady flow within the entire flow passage of a Francis turbine.

The dominate frequency of the predicted pressure pulses at runner inlet agree with the experimental results in the head cover at moderate flow heads. The influence of the blade passing frequency causes the simulated peak‐to‐peak amplitudes in the runner inlet to be larger than in the head cover. The measured and predicted pressure pulses at different positions along the runner are comparable. At the most unstable operating condition of 0.5a₀ guide vane opening, the pressure pulses in the runner blade passage are due to the blade channel vortex and the rotor‐stator interference. The predictions show that the frequency of the blade channel vortex is relatively low and it changes with the operating conditions.

The paper describes a study which experimentally and numerically investigated the pressure pulses characteristics in a Francis turbine runner at moderate flow heads. The pulse characteristics and unsteady flow behavior due to the blade channel vortex in the runner at high heads were investigated numerically, with the turbine operating regions then partitioned to identify safe operating regions.

This paper aims to improve the computational efficiency and to achieve high-order accuracy for the computation of helicopter rotor unsteady flows in forward flight during the industrial preliminary design stage.

The integral arbitrary Lagrangian–Eulerian form of unsteady compressible Navier–Stokes equations with low Mach number preconditioned pseudo time terms based on non-inertial frame of reference undergoing rotating and translating was derived and discretized in the framework of multi-block structured finite volume grid using three types of spatial reconstruction schemes, i.e. the third-order accurate monotonic upwind scheme for conservation laws, the fifth-order accurate weighted essentially non-oscillatory and the fifth-order accurate weighted compact nonlinear schemes.

The results show that the present non-inertial computational method can obtain comparable results with other methods, such as the dynamic overset method, and make sure that the higher-order spatial schemes can significantly improve the tip vortex resolution.

The computational grid used by the present method remained static during the whole unsteady computation process, with only local deformations induced by blade cyclic pitch and other operating motions, which greatly reduced the complexity of grid motion and enhanced the efficiency and robustness.

This paper describes two accurate and efficient numerical methods for computing unsteady viscous flows. The first one solves the incompressible Navier‐Stokes equations in their vorticity‐velocity formulation, using a staggered‐grid finite‐volume spatial discretization to provide second‐order accuracy on arbitrary grids, and combines effectively an alternating direction implicit scheme for the vorticity transport equation and a multigrid line‐Gauss‐Seidel relaxation for the velocity equations. The second method solves the compressible Reynolds‐averaged Navier‐Stokes equations in strong conservation form, with a k−ω turbulence closure model. The equations are discretized in time using an implicit three‐time‐level scheme, combined with a dual time stepping approach, so that the residual at every physical time step is annihilated using an efficient multigrid Runge‐Kutta iteration with variable time stepping and implicit residual smoothing. The space discretization uses a Roe’s flux difference splitting for the convective terms and standard central differences for the diffusive ones. A turbulent unsteady cascade flow is used to demonstrate the accuracy and efficiency of the method. The authors are currently working towards extending the two approaches described in this paper to three space dimensions.

The purpose of this paper is to examine the ability of the harmonic balance method for predicting the aerodynamic characteristics of rigid finned spinning vehicle.

The aerodynamic characteristics of a rigid four-finned spinning vehicle at Mach number 2.5 and angle of attack of 20 degrees are simulated using the harmonic balance method and the unsteady time-accurate approach based on the dual-time method. The numerical results are analyzed, and the computed aerodynamic coefficients of the harmonic balance method are compared with those of the dual-time method. The influence of the number of harmonics is presented. The computed Magnus force and moment coefficients are compared with the experimental data. The flow fields at different roll angles are presented. The computational efficiency of harmonic balance method is analyzed.

The results show that the aerodynamic coefficients of spinning vehicle could be predicted by the harmonic balance method with reasonable accuracy compared with the dual-time method. For the harmonic balance method, the accuracy of the computed leeward side flow is relatively poor compared with that of the computed windward side flow. Meanwhile, the computational efficiency is influenced by initial guess and the intensity of unsteady effect.

The harmonic balance method could be used for the aerodynamic prediction of spinning vehicle, which may improve the efficiency of vehicle design.

This paper presents the results of the harmonic balance method for simulating the aerodynamic characteristics of finned spinning vehicle. The accuracy and efficiency of the method are analyzed.