does not predict a streamwise stress level that is signi® cantly higher than the simulation of Beaudan and Moin. 5 However, this can be explainedby noting that, for this¯ow, most of the contributionto the Reynolds stress comes from¯uctuationsin a narrow frequencyband extending from about 0.5x s t to 3.0x st , and in this frequency band, the energy in both simulations is comparable. Thus, even though the simulations of Beaudan and Moin 5 exhibit signi® cant damping of the higher frequencies,this does not have a signi® cant impact on the low-order turbulence statistics.By comparing the vertical stress pro® les at these locations, we observe that prediction from the two simulations at x/ D = 7.0 is quite similar. At x/ D = 10.0, the two simulations predict roughly the same peak stress level; however, the shape of the experimental pro® le matches the pro® le of Beaudan and Moin 5 better than it does for the current simulation. Furthermore, we have found that vertical velocity and shear stress pro® les (not shown here) from both the simulations are also in reasonable agreement with experiments. 11 ConclusionsIt is found that in the downstream portion of the wake, where the grid is relatively coarse, the numerical dissipation inherent in the higher-order upwind-biased schemes removes substantial energy from roughly three-quarters of the resolved wave number range. In the central difference simulation, because there is no numerical dissipation, the smaller scales are more energetic. Because of this reduction in the damping of smaller scales, we ® nd that the computed power spectra agree well with the experiment up to about half of the resolved wave number range. However, the enhanced energy in the small scales has no signi® cant effect on the low-order statistics, and the mean velocity and Reynolds stress pro® les in this region obtained from the two simulations are comparable. This is because most of the contribution to the normal stress comes from uctuations whose frequency is centered in a narrow band around the shedding frequency and change in the energy of the small scales does not have a signi® cant effect on the magnitudes of the Reynolds stresses. However, in applications such as¯ow generated noise and reactive¯ows, small-scale¯uctuations play a crucial role, and it is, therefore, critical to retain the energy in the small scales. In such applications,energy conservativeschemes would be preferableover upwind schemes. We also ® nd that with about 20±30% smaller grid spacing, the second-order central difference scheme gives results that are comparable to those obtained by the high-order upwind biased schemes. The higher-order upwind based solver is more expensive on a per-pointbasis than the second-ordercentral difference solver, and this partially offsets the additional cost of the increased resolution required by the second-order method. A drawback of the second-order central scheme is that the simulations are sensitive to numerical factors such as grid discontinuities and out¯ow boundary conditions and, thus, g...

This paper presents an analysis methodology for the calculation of the flow through internal flow components with a rotating wall such as annular seals, impeller cavities, and enclosed rotating disks. These flow systems are standard components in gas turbines and cryogenic engines and are characterized by subsonic viscous flow and elliptic pressure effects. The Reynolds-averaged Navier-Stokes equations for turbulent flow are used to model swirling axisymmetric flow. Bulk-flow or velocity profile assumptions aren’t required. Turbulence transport is assumed to be governed by the standard two-equation high Reynolds number turbulence model. A low Reynolds number turbulence model is also used for comparison purposes. The high Reynolds number turbulence model is found to be more practical. A novel treatment of the radial/swirl equation source terms is developed and used to provide enhanced convergence. Homogeneous wall roughness effects are accounted for. To verify the analysis methodology, the flow through Yamada seals, an enclosed rotating disk, and a rotating disk in a housing with throughflow are calculated. The calculation results are compared to experimental data. The calculated results show good agreement with the experimental results.

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This paper describes the development of the source-doublet-based potential paneling method for oscillating cascade unsteady aerodynamic load predictions. By using the integral influence coefficient method and by using the interblade phase angles, the unsteady loads on an oscillating cascade can be accurately predicted at a minimum cost. As the grids are placed only on the blade surfaces, the blades are allowed to vibrate without grid deformation problems. Four notable subsonic oscillating cascade test cases that cover most important parameters, e.g., blade geometry, interblade phase angle, flow coefficient, flow speed, frequency, etc., are studied in this paper. The agreement between the present solutions and other numerical/experimental results demonstrates the robustness of the present model. Applicability of the method for realistic compressible flow cascades is also discussed.

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