The vortex instability characteristics of laminar free convection flow over horizontal and inclined isothermal surfaces are studied analytically by linear theory. As a prelude to the analysis, the effects of the angle of inclination on the main flow and thermal fields are re-examined by a new approach. Numerical results are presented for wall shear stress, surface heat transfer, neutral stability curve, and critical Grashof number for Prandtl numbers of 0.7 and 7 over a wide range of angles of inclination, φ, from the horizontal. It is found that as the angle of inclination increases the rate of surface heat transfer increases, whereas the susceptibility of the flow to the vortex mode of instability decreases. The present study provides new vortex instability results for small angles of inclination (φ≤30 deg) and more accurate results for large angles of inclination (φ ≥ 30 deg) than previous studies. The present results are also compared with available wave instability results.

Wave instability of nautral convection boundary layer flow adjacent to inclined surfaces is analyzed by a linear theory. The effects of the nonparallelism of the main flow and thermal fields are taken into account in the analysis. Neutral stability results for Prandtl numbers of 0.7 and 7.0 are presented for upward-facing heated surfaces, for angles of inclination ranging from 0 to 90 deg. These results are compared with available analytical wave instability results for small angles of inclination. They are also compared with analytical vortex instability results and with available experimental data.

Recent trend toward lightweight, compact compression systems for advanced aircraft gas turbine engines has created a need for very high pressure ratio fan and compressor stages. One way of achieving pressure ratio in excess of 3:1 in an axial blade row is to introduce splitters (partial vanes) between the principal blades, a concept pioneered by Wennerstrom during early 70s for application in a 3:1 pressure ratio single axial stage. This paper presents an advanced methodology for high pressure ratio splittered rotor design. The methodology centers around combining a meridional flow calculation, an arbitrary meanline blade generation procedure, and 3-D inviscid and viscous analyses. Methods for specifying work distribution, solidity, loss, and deviation distributions, as well as the airfoil generation and splitter vane placement are discussed in detail. Importance of 3-D viscous effects along with results from a 3-D viscous calculation for Wennerstrom’s splittered rotor are also presented.

ResultsThe typical case considered is for a freestream Mach number of 2.0, a Reynolds number of 0.296X 10 6 based on the distance X SHK from the leading edge to the shock impingement point, and an incident shock angle of 32.585 deg. 4 For this set of data, the shock is strong enough (pressure ratio =1.4) to trigger separation. The computation was done for five cases: 1) no suction along the wall, 2) normal suction, 0 = 90 deg at the location from X/X SHK = 0.7817 to 1.1569,3) vectored suction, 0 = 45 deg at the locations as in case 2, 4) normal suction from X/X SHK = Q.1\92 to 0.8442, and 5) vectored suction at the same locations as in case 4.The computed surface pressure distribution in the interaction region is presented in Fig. 2. For the vectored upstream suction case 5, the pressure jump is closes to the inviscid flow conditions case and reaches its postshock value quite smoothly. It is interesting to note that the pressure rise is steeper than that corresponding to normal suction. Though the pressure plateau indicating separation has vanished for all the examples in which suction is considered, the upstream vectored suction has a minimum effect in the downstream direction (Fig. 3).This study indicates that the upstream vectored suction not only eliminates separation but that its influence in the neighborhood is limited. If the prior knowledge of separation bubble location is not available or some minor changes in the input data are required, a judicious choice of upstream vectored suction can control the flow effectively. However, a detailed assessment regarding the locations, rates, and angles, for such suction should be carried out to optimize its fruitful usage.

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