Hysteresis Characteristic in the Hump Region of a Pump-Turbine Model
The hump feature is one of the major instabilities in pump-turbines. When pump-turbines operate in the hump region, strong noise and serious fluctuations can be observed, which are harmful to their safe and stable operation and can even destroy the whole unit as well as water conveyance system. In this paper, a low specific speed ( n q = 36.1 min −1 ) pump-turbine model was experimentally investigated. Firstly, the hump characteristic was obtained under 19 mm guide vane opening conditions. More interestingly, when the hump characteristic was measured in two directions (increasing and decreasing the discharge), characteristic hysteresis was found in the hump region. The analysis of performance characteristics reveals that the hump instability is the result of Euler momentum and hydraulic losses, and different Euler momentum and hydraulic losses in the two development processes lead to the hysteresis phenomenon. Then, 12 pressure sensors were mounted in the different parts of the pump-turbine model to obtain the time and frequency characteristics. The analysis of the corresponding fast Fourier transform confirms that the hump characteristic is related to low-frequency (0.04–0.15 times rotational frequency) vortices. The occurrence and cessation of vortices depend on the operating condition and measurement direction, which contribute to the hysteresis feature. Finally, the type of the low-frequency vortices was analyzed through the cross power spectrum.
Unsteady simulation and analysis for hump characteristics of a pump turbine model
Presently, hydropower is the world's largest source of renewable energy. Pump Storage Power Plant develops the rapidly because of its effective electricity storage and becomes the most part of hydropower. A pump turbine is the vital component of a Pump Storage Power Plant. To obtain efficient generation, safe and stable operation of a pump turbine is pretty important. However, the existence of the hump characteristics of a pump-turbine in pump mode usually leads to operating instability. Thus it is necessary to analyze regions of the hump characteristics. In this research experimental investigation and numerical simulation are employed in order to study the hump characteristics. Unsteady incompressible turbulent flow simulations for the full pump turbine model water domain are performed using the SST k–ω turbulence model. A refinement grid is generated, which allows the corresponding y-plus values of the runner blades, stay vanes and guide vanes less than 2 in average. Calculation results of torque in different discharges as well as head and efficiency in the small discharge regions are in solid agreement with the experimental data. The results show that there are three vortex groups which distribute in the tandem cascade passages when entering the hump region. They are equally located in the circumferential direction in the tandem cascade, and one vortex group is located in two passages of the special stay vane. The strength and range of the vortex group change with different discharges. It also shows certain instability during one runner revolution. This work can provide a basic understanding for the improvement of the stable operation of a pump turbine.
Laminar heat or mass transfer in rectangular channels and in cylindrical tubes for fully developed flow: comparison of solutions obtained for various boundary conditions
Abstract A comparison is made of results obtained with various boundary conditions at the wall of the channels. By comparing blood Sherwood numbers for finite wall resistance with those for constant concentration boundary condition only a small variation is found for various points along the blood channel.