J. M. Owen

Aerodynamic aspects of the sealing of gas-turbine rotor-stator systems: Part 1: The behavior of simple shrouded rotating-disk systems in a quiescent environment

The sealing characteristics of a shrouded rotor-stator system have been studied using flow visualization, pressure, and concentration measurements. Seven shroud geometries, incorporating axial clearance, radial clearance, or mitered seals, have been tested for a range of clearance ratios and rotational Reynolds numbers up to Reθ = 1.2 × 106. For all axial clearance seals, the superimposed airflow rate necessary to prevent the ingress of external fluid into the rotor-stator wheel space increased with rotational speed and with seal clearance. Owing to a “pressure inversion effect,” where the pressure in the wheel space increased rather than decreased with rotational speed, the increase of sealing flow rate with rotational speed for two of the radial clearance seals was less than that for the other seals. As expected, the mitered seal had a performance intermediate between the purely axial clearance seals and the radial clearance seals exhibiting the pressure inversion effect. The tests referred to above were conducted in a quiescent environment. In parts 2 and 3, the effect of an external axial flow of air at the periphery of the system is studied.

Source–sink flow inside a rotating cylindrical cavity

The axisymmetric flow inside a rotating cavity with radial outflow or inflow of fluid is discussed. The basic theoretical model of Hide (1968) is extended, using the integralmomentum techniques of von Karman (1921), to include laminar and turbulent flows; both linear and nonlinear equations are considered. The size of the source region is estimated using a ‘free disk’ model for the outflow case and a free vortex for the inflow case. In both cases, the estimates are in good agreement with available experimental data. Theoretical values of the tangential component of the velocity outside the Ekman layers on the disks, obtained from solutions of the laminar and turbulent integral equations, are compared with experimental values. The experiments were conducted in a number of rotating-cavity rigs, with a radial outflow or inflow of air, and laser-Doppler anemometry was used to measure the velocity in the ‘interior core’ between the Ekman layers. The measurements provide good support for the theoretical models over a wide range of flow rates, rotational speeds and radial locations. Although only isothermal flow is considered in this paper, the methods can be readily extended to non-isothermal flow and heat transfer.

Velocity measurements inside a rotating cylindrical cavity with a radial outflow of fluid

Flow visualization and laser-doppler anemometry have been used to determine the flow structure and measure the velocity distribution inside a rotating cylindrical cavity with an outer to inner radius ratio of 10, and an axial spacing to inner radius ratio of 2·67. A flow structure comprising an inner layer, Ekman layers, an outer layer and an interior potential core has been confirmed for the cases where the inlet air enters the cavity either axially, through a central hole, or radially, through a central gauze tube, and leaves radially through a series of holes in the peripheral shroud. Velocity measurements in the laminar Ekman layers agree well with the ‘modified linear theory’, and long-and short-wavelength disturbances (which have been reported by other experimenters) have been observed on the Ekman layers when the radial Reynolds number exceeds a critical value. The phenomenon of reverse flow in the Ekman layers and the possibility of ingress of external fluid through the holes in the shroud have also been observed.

Aerodynamic aspects of the sealing of gas-turbine rotor-stator systems: Part 3: The effect of nonaxisymmetric external flow on seal performance

Abstract The effect of a nonaxisymmetric external flow on the sealing performance of a shrouded rotor-stator system has been studied using flow visualization and pressure measurements. When ingress occurred, ingested fluid moved transversely across the wheel space from regions of high to low pressure in the external-flow annulus. One of the four seal geometries tested contained a double-shrouded seal, and the inner shroud attenuated the external pressure asymmetries so that most of the ingested fluid was confined to the space between the shrouds. Six different circumferential variations of pressure were used to separate the effects of flow rate and pressure asymmetry, and it was found that, for all four seals, the minimum sealing-flow rate necessary to prevent ingress could be correlated with the maximum circumferential pressure difference measured in the external-flow annulus.

Flow and Heat Transfer in a Preswirl Rotor–Stator System

Conditions in the internal-air system of a high-pressure turbine stage are modeled using a rig comprising an outer preswirl chamber separated by a seal from an inner rotor-stator system. Preswirl nozzles in the stator supply the blade-cooling air, which leaves the system via holes in the rotor, and disk-cooling air enters at the center of the system and leaves through clearances in the peripheral seals. The experimental rig is instrumented with thermocouples, fluxmeters, pitot tubes, and pressure taps, enabling temperatures, heat fluxes, velocities, and pressures to be measured at a number of radial locations. For rotational Reynolds numbers of Re Φ ≃ 1.2 x 10 6 , the swirl ratio and the ratios of disk-cooling and blade-cooling flow rates are chosen to be representative of those found inside gas turbines. Measured radial distributions of velocity, temperature, and Nusselt number are compared with computations obtained from an axisymmetric elliptic solver, featuring a low-Reynolds-number κ-∈ turbulence model. For the inner rotor-stator system, the computed core temperatures and velocities are in good agreement with measured values, but the Nusselt numbers are underpredicted. For the outer preswirl chamber, it was possible to make comparisons between the measured and computed values for cooling-air temperatures but not for the Nusselt numbers. As expected, the temperature of the blade-cooling air decreases as the inlet swirl ratio increases, but the computed air temperatures are significantly lower than the measured ones. Overall, the results give valuable insight into some of the heat transfer characteristics of this complex system.

Aerodynamic aspects of the sealing of gas-turbine rotor-stator systems: Part 2: The performance of simple seals in a quasi-axisymmetric external flow

The sealing characteristics of a shrouded rotor-stator system with an external flow of air have been studied using flow visualization, pressure, and concentration measurements. Three shroud geometries, incorporating axial clearance or radial clearance seals, have been tested for a range of clearance ratios for both rotational and axial Reynolds numbers Reθ and Rew respectively, up to 1.2 × 106. It was found that there were two regimes: a rotation-dominated regime at low values of Rew/Reθ, and an external-flow-dominated regime at high values. For Rew = 0, Cw, min (the dimensionless flow rate of sealing air necessary to prevent the ingress of external fluid into the rotor-stator wheel space) increased with increasing Reθ. For small values of Rew/Reθ, Cw, min decreased with increasing Rew; for large values of Rew/Reθ, Cw, min was proportional to Rew and was independent of Reθ. The latter effect is attributed to the nonaxisymmetric pressure distribution in the external flow: fluid moved transversely across the wheel space from high-pressure to low-pressure regions of the external flow.

Heat transfer measurements in rotating-disc systems part 1: The free disc

Abstract Heat transfer measurements have been made with an internally heated disc of 950 mm diameter rotating at speeds up to 3000 2/min in air. Tests were conducted for four different radial temperature profiles: in three, the temperature increased with radius; in the fourth, it decreased. Local and average Nusselt numbers were determined from the numerical solutions of Laplaces equation (using the measured heat input and surface temperatures as boundary conditions) and from fluxmeters embedded in the surface of the disc. Over most of the disc surface, and for most of the tests, these experimentally measured Nusselt numbers were in reasonable agreement with values obtained from existing solutions of the energy integral equation for turbulent flow over a free disc. Having validated the experimental technique on the free disc, we use it in Part 2 to study the heat transfer inside a rotating cavity.

HEAT TRANSFER IN AN AIR-COOLED ROTOR-STATOR SYSTEM

This paper describes a combined experimental and computational study of the heat transfer from an electrically heated disk rotating close to an unheated stator. A radial outflow of cooling air was used to remove heat from the disk, and local Nusselt numbers were measured, using fluxmeters at seven radial locations, for nondimensional flow rates up to C w . = 9680 and rotational Reynolds numbers up to Re Φ = 1.2 X 10 6 . Computations were carried out using an elliptic solver with a low-Reynolds-number k- e turbulence model, and the agreement between the measured and computed velocities and Nusselt numbers was mainly good.

Transitional flow between contra-rotating disks

This paper describes a combined computational and experimental study of the flow between contra-rotating disks for – 1 ≤ Γ ≤ 0 and Re ϕ = 10 5 , where Γ is the ratio of the speed of the slower disk to that of the faster one and Re ϕ is the rotational Reynolds number of the faster disk. For Γ = 0, the rotor-stator case, laminar and turbulent computations and experimental measurements show that laminar Batchelor-type flow occurs: there is radial outflow in a boundary layer on the rotating disk, inflow on the stationary disk and a rotating core of fluid between. For Γ = – 1, the laminar computations produce Batchelor-type flow: there is radial outflow on both disks and inflow in a free shear layer in the mid-plane, on either side of which is a rotating core of fluid. The turbulent computations and the velocity measurements for Γ = – 1 show Stewartson-type flow: radial outflow occurs in laminar boundary layers on the disks and inflow occurs in a non-rotating turbulent core between the boundary layers. For intermediate values of Γ, transition from Batchelor-type flow to Stewartson-type flow is associated with a two-cell structure, the two-cells being separated by a streamline that stagnates on the slower disk; Batchelor-type flow occurs radially outward of the stagnation point and Stewartson-type flow radially inward. The turbulent computations are mainly in good agreement with the measured velocities for Γ = 0 and Γ = – 1, where either Batchelor-type flow or Stewartson-type flow occurs; there is less good agreement at intermediate values of Γ, particularly for Γ = – 0.4 where the double transition of Batchelor-type flow to Stewartson-type flow and laminar to turbulent flow occurs in the two-cell structure.

Computation of the flow and heat transfer due to a rotating disc

The boundary-layer momentum and energy equations have been solved numerically using a Keller-☐ scheme and, for turbulent flow, an eddy-viscosity model. The numerical method has been successfully validated on a number of standard test cases for unheated discs, including data for velocity profiles and moment coefficients in both laminar and turbulent flow, and some old and new test cases for heated discs, including average and local Nusselt numbers for a range of disc-temperature distributions and for Reynolds numbers up to 3.2×106. The method is shown to be sufficiently simple, efficient, and accurate for all practical purposes.