The stability of flow of a viscous incompressible fluid contained between a stationary outer sphere and rotating inner sphere is studied theoretically and experimentally. Previous theoretical results concerning the basic laminar flow (part 1) are compared with experimental results. Small and large Reynolds number results are compared with Stokes-flow and boundary-layer solutions. The effect of the radius ratio of the two spheres is demonstrated. A linearized theory of stability for the laminar flow is formulated in terms of toroidal and poloidal potentials; the differential equations governing these potentials are integrated numerically. It is found that the flow is subcritically unstable and that the observed instability occurs at a Reynolds number close to the critical value of the energy stability theory. Observations of other flow transitions, at higher values of the Reynolds number, are also described. The character of the stability of the spherical annulus flow is found to be strongly dependent on the radius ratio.
Erosion damage was estimated for the first stage of a large electric utility gas turbine based on projected particle distributions in the gas leaving the hot gas cleaning system of a pressurized fluidized-bed gasifier system. Based on the assumptions used in making the estimates, cleaning of the turbine expansion gas to a particulate concentration of 0.005 gram per standard cubic metre (0.002 grain per standard cubic foot) with particles larger than 6-μm diameter effectively removed should give satisfactory blade life from an erosion standpoint. Two stages of high-performance cyclone cleanup to 0.1 gram per standard cubic metre (0.5 grain per standard cubic foot) with 0.05 weight percent of 12-μm diameter particles remaining in the gas would wear stator vane trailing edges by 0.25 cm (0.1 in.) thickness (roughly equivalent to full wall thickness in upstream stage vanes) in 10000 h of operation. The numerical results presented in this paper are based on the estimate that coal ash and sulfur sorbent particles will have, when impacting superalloy turbine materials under turbine conditions, 1/25th of the erosivity of silicon carbide particles impacting a nickel alloy at room temperature. The estimates do not account for the appreciable slowing of the 1- to 3-μm particles in the blade boundary layers before they reach the blading, even though these small particles account for most of the damage. The numerical results are in this way conservative. Actual data on the damage which coal gas particulates do to blade materials under turbine conditions are needed to establish the erosion tolerance of the turbine more accurately.
A theory is presented to predict deposition rates of fine particles in two-dimensional compressible boundary layer flows. The mathematical model developed accounts for diffusion due to both molecular and turbulent fluctuations in the boundary layer flow. Particle inertia is taken into account in establishing the condition on particle flux near the surface. Gravitational settling and thermophoresis are not considered. The model assumes that the fraction of particles sticking upon arrival at the surface is known, and thus, treats it as a given parameter. The theory is compared with a number of pipe and cascade experiments, and a reasonable agreement is obtained. A detailed application of the model to a turbine is also presented. Various regimes of particle transport are identified, and the range of validity of the model is discussed. An order of magnitude estimate is obtained for the time the turbine stage can be operated without requiring cleaning.
Experiments using cascades and small turbines have been conducted or are being considered to simulate large utility turbine operation with future coal-fired power plants. The purpose of these experiments is to evaluate utility turbine tolerances to particulates and to determine gas cleanup requirements for successful turbine performance. Since these tests do not fully reproduce the flow and erosion conditions in large utility turbines, this paper explores the interpretation of data from simulation experiments to assess erosion in large utility turbines. Effects of physical scale, rotation speed, and pressure differences between test cascades and small test turbines and large utility turbines are considered.
As an extension to the inviscid gas flow particle trajectory model presented in earlier papers, a complementary model has been developed to establish the effect of the blade boundary layer on the trajectories of particles and thus on the resulting erosion and/or deposition. The method consists essentially in tracing particles inside the boundary layer with initial conditions taken from the inviscid flow model. The flow data required for the particle trajectory calculations are obtained by using a compressible boundary layer flow computer program. This model has been applied to the first stage stator of a large electric utility gas turbine operating with coal gas. Results are compared with the predictions of the inviscid flow model. It is shown that the effect of the boundary layer on the trajectories of particles smaller than 6 μm is important. Since the hot gas cleaning system of a pressurized fluidized-bed gasifier system is projected to remove particles larger than 6 μm diameter effectively, it is concluded that an accurate assessment of turbine erosion and deposition requires inclusion of the boundary layer effect. Although these results emphasize the relative importance of the blade boundary layer, the absolute accuracy of the method remains to be demonstrated and is thought to be largely dependent on the basic data concerning the erosivity and sticking probability of particles.
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