Effects of boundary conditions and unsteadiness on draft tube flow

Abstract: The present research focuses on flow properties of the elbow draft tube. This element has a major function in low head turbines, since up to half of the losses may arise there at part load. The use of computational fluid dynamic (CFD) to redisign a draft tube necessitates detailed knowledged of the boundary conditions. They are generally not available and qualified guesses must be made. This applies in particular to the radial velocity at the inlet. A method to estimate this component in swirling flow from experimental values of the axial and tangential velocities is derived. The method uses a two dimensional non- viscous description of the flow, the Squire-Long formulation. It is tested against swirling flow in a diffuser and applied to the Turbine-99 draft tube flow. As several other boundary conditions are difficult to estimate and many input parameters are available to perform a simulation, the use of factorial design is proposed as an alternative to design simulations in a systematic, objective and quantitative way. The method allows the deternmination of the main and joint effects of input parameters on the numerical simulation. The input parameters may be experimental uncertainty on boundary conditions, unknown boundary conditions, grid and turbulence models. The method is applied to the Turbine-99 test case, where the radial velocity, the surface roughness, the turbulence length scale and the grid were the factors investigated. The inlet radial velocity is found to have a major effect on the pressure recovery. The flow in water turbines is highly unsteady due to the runner blade rotation, guide vanes and stay vanes. Unsteady pressure measurements on a Kaplan prototype point out unsteadiness in the high and low pressure regions of the turbine. Since model and prototype are not running in dynamically similar conditions, the influence of unsteadiness on the losses is of interest. The derivation of the variation of the mechanical energy for the mean, oscillating and turbulent fields point out the contribution of unsteadiness to the losses and the turbulent production. Application to turbulent channel flow reveals that the contribution is a function of the amplitude of the oscillation, the frequency and the friction velocity. Turbulent pulsating flow in a generic model of the rectangular diffuser found at the end of elbow draft tube is studied in detail with laser Doppler anemometry (LDA). Three frequencies, corresponding to the quasi-steady, relaxation and quasi-laminar regimes with an amplitude of about 10% are investigated. The results indicate no alteration of the mean flow by the excitation of a single frequency. Furthermore. the existence of the different regimes, as found in turbulent pulsating turbulent pipe and channel flows, is confirmed.