Integral Method of Calculation of a Turbulent Centrifugal Underswirl Flow in a Gap between Parallel Rotating

Abstract

I. V. Shevchuk Institute of Engineering Thermophysics National Academy of Sciences of Ukraine Kiev, Ukraine ]A turbulent centrifugal flow in a gap between parallel rotating disks was studied in a special case that the flow tangential velocity at the inlet is less than or equal to the tangential velocity of the disks (flow underswirl at the inlet). The equations of a boundary layer were numerically solved by an integral method based on a power approximation of the tangential velocity and a quadratic approximation of the tangent of the flow swirl angle. The unknown variables in the source region were the tangent of the flow swirl angle at the wall and the thickness of a boundary layer, and those in the region of the Ekman-type layers were the tangent of the flow swirl angle at the wall and the tangential flow velocity in the core. The developed method allowed us to achieve significantly better agreement between the results of calculation and the available experimental data than did various methods proposed earlier. Introduction Radial ambient air flowing of the end surfaces of rotors in gas turbines is a widely used method of their cooling [1-5]. A cooling air from a compressor is supplied to a gap between two rotating disks of a turbine (or between a disk and a covering baffle) at the axis of rotation, then moves in the radial direction to the periphery, and is removed from the gap. This type of flowing is also called the centrifugal flow in a rotating interdisk hollow [4,5]. The hydrodynamics under the centrifugal radial flow in interdisk rotating hollows was experimentally studied in many works [1-8]. The reviews of investigations carried out in the former USSR and abroad are given in [1-5]. If the velocity profiles and the boundary conditions at the wall are adequately approximated, integral methods of calculation of the flows in the most general form are still quite competitive with rapidly developing simulation methods (three-dimensional flows) in terms of the accuracy of calculation of the averaged flow parameters. Under these conditions, the time required to calculate one variant is shorter than 15-20 s [4, 5, 9].