In this paper, the effect of water, air, and their combined injection from two different injection points is studied in order to reduce vorticity effects in a draft tube of prototype turbine working at three operating points. The flow from spiral case to the end of draft tube is simulated using the shear stress transport k–ω turbulence and two-phase models. Using an appropriate validation method, acceptable results were obtained under the noninjection condition. To determine suitable number of points and inlet flow rate for air injection as well as the appropriate nozzle diameter for air and water injection, a new method which considers the ratio of total loss to the pressure recovery factor is used, in addition to using the traditional method which calculates the total loss in the draft tube. Comparing results of the three types of injections shows air injection in the operating range greater than 70% of turbine design flow rate, is much more effective than water injection or the combination of air and water injection. However, in the operating range below 70%, either water or air injections are not suitable, but combination of these two fluids can improve system performance.
A new reduced-order modeling approach is presented. This approach is based on fluid eigenmodes and without using the static correction. The vortex lattice method is used to analyze unsteady flows over two-dimensional airfoils and three-dimensional wings. Eigenanalysis and reduced-order modeling are performed using a conventional method with and without the static correction technique. In addition to the conventional method, eigenanalysis and reduced-order modeling are also performed using the new proposed method, that is, without static correction requirement. Numerical examples are presented to demonstrate the accuracy and computational efficiency of the proposed method. Based on the obtained results, it is shown that the accurate reduced-order models of unsteady flows can be constructed without using the static correction technique.
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