A study has been conducted, using an unsteady three-dimensional Reynolds-averaged Navier-Stokes simulation, to define the effect of impeller-diffuser interaction on the performance of a centrifugal compressor stage. The principal finding from the study was that the most influential aspect of this unsteady interaction was the effect on impeller tip leakage flow. In particular, the unsteadiness due to the upstream potential effect of the diffuser vanes led to larger viscous losses associated with the impeller tip leakage flow. The consequent changes at the impeller exit with increasing interaction were identified as reduced slip, reduced blockage, and increased loss. The first two were beneficial to pressure rise, while the third was detrimental. The magnitudes of the effects were examined using different impeller-diffuser spacings and it was shown that there was an optimal radial gap size for maximum impeller pressure rise. The physical mechanism was also determined: When the diffuser was placed closer to the impeller than the optimum, increased loss overcame the benefits of reduced slip and blockage. The findings provide a rigorous explanation for experimental observations made on centrifugal compressors. The success of a simple flow model in capturing the pressure rise trend indicated that although the changes in loss, blockage, and slip were due largely to unsteadiness, the consequent impacts on performance were mainly one-dimensional. The influence of flow unsteadiness on diffuser performance was found to be less important than the upstream effect, by a factor of seven in terms of stage pressure rise in the present geometry. It is thus concluded that the beneficial effects of impeller-diffuser interaction on overall stage performance come mainly from the reduced blockage and reduced slip associated with the unsteady tip leakage flow in the impeller.Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/ on 05/29/2015 Terms of Use: http://asme.org/terms Table 4 Change of stage total-to-total pressure ratio and other performance parameters due to a reduction of radial gap size r 2 ЈÕr 2 from 1.092 to 1.054 Journal of Turbomachinery OCTOBER 2000, Vol. 122 Õ 785 Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/ on 05/29/2015 Terms of Use: http://asme.org/terms
A study has been conducted, using an unsteady three-dimensional Reynolds-averaged Navier-Stokes simulation, to define the effect of impeller-diffuser interaction on the performance of a centrifugal compressor stage. The principal finding from the study was that the most influential aspect of this unsteady interaction was the effect on impeller tip leakage flow. In particular, the unsteadiness due to the upstream potential effect of the diffuser vanes led to larger viscous losses associated with the impeller tip leakage flow. The consequent changes at the impeller exit with increasing interaction were identified as reduced slip, reduced blockage, and increased loss. The first two were beneficial to pressure rise while the third one was detrimental. The magnitudes of the effects were examined using different impeller-diffuser spacings and it was shown that there was an optimal radial gap size for maximum impeller pressure rise. The physical mechanism was also determined: when the diffuser was placed closer to the impeller than the optimum, increased loss overcame the benefits of reduced slip and blockage. The findings provide a rigorous explanation for experimental observations made on centrifugal compressors. The success of a simple flow model in capturing the pressure rise trend indicated that although the changes in loss, blockage and slip were due largely to unsteadiness, the consequent impacts on performance were mainly one-dimensional. The influence of flow unsteadiness on diffuser performance was found to be less important than the upstream effect, by a factor of seven in terms of stage pressure rise in the present geometry. It is thus concluded that the beneficial effects of impeller-diffuser interaction on overall stage performance come mainly from the reduced blockage and reduced slip associated with the unsteady tip leakage flow in the impeller.
Midchord laminar separation bubbles, which act as a transition mechanism on low Reynolds number airfoils, make a contribution to wing section profile drag that becomes increasingly important at low Reynolds number. A model for the analysis of the boundary layer through the bubble is needed. The model developed here, which is based on Horton's method, provides a simple computationally efficient analysis that matches the integral boundary-layer analysis methods used on most existing boundary-layer codes. The bubble calculation is initiated by the detection of laminar separation. Transition location and boundary-layer growth in the laminar region are determined using Van Ingen's shortcut e" method and Schmidt's correlations, respectively. Following Horton, the turbulent region is calculated using an iterative scheme that also functions as a bursting criterion, but the original linear velocity distribution has been replaced by Wortmann's concave velocity distribution. Both computation efficiency and prediction accuracy were improved after this change. Testing against experimental data showed that the bubble model greatly improved the drag prediction accuracy of the analysis in the Reynolds number range from 0.2 to 1.5 x 10 6 , especially in cases when the midchord bubble was dominant. The validity of the bubble model was further confirmed by accurate prediction of bubble size and reattachment velocity gradient. B-Nomenclature laminar separation angle parameter drag coefficient dissipation integral, 2 /« r(du/drj) skin friction coefficient, [2r/(pw^)] TJ=0 lift coefficient chord shape factor, 81/82 shape factor, 8 3 /8 2 maximum amplification integral total bubble length, l v + / 2 length of bubble laminar region, S T -s s length of bubble turbulent region, S R --S T velocity distribution exponent defined in Eq. (9) exponential growth of Tollmien-Schlichting waves in the e" method chord Reynolds number, u^clv distance Reynolds number, u^slv momentum thickness Reynolds number, u e 8 2 /v distance along surface from stagnation point freestream turbulence level velocity component, tangential to surface external velocity position along the chord line angle of attack velocity distribution parameter used in Eq. (8) displacement thickness, /o (1 -u/u e ) drj momentum thickness, Jo (u/u e )[l -(u/u e )] dr; energy thickness, /" (ulu e ][l -(ulu e ) 2 ] dr/ distance normal to airfoil surface velocity gradient parameter, (8 2 /u e )(du e /ds) Pohlhausen velocity gradient parameter, P T = density = shear stress v = kinematic viscosity Subscripts m = mean value R = reattachment S = separation T = transition Superscripts = lengths and velocities normalized by 8 2S and u es , respectively A = lengths and velocities normalized by 8 2T and u eT , respectively
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