On flow past a supercavitating cascade of cambered blades
Two dimensional flow past supercavitating cascade of cambered blades
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Two dimensional flow past supercavitating cascade of cambered blades
A finite difference code has been developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model 'real' airfoils that have thickness and camber. Sample predictions are presented for a cascade of loaded airfoils and show appreciable differences in the unsteady surface pressure distributions when compared with the flat plate results.
A finite difference code was developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model real airfoils that have thickness and camber. Sample predictions are presented for a section of the rotor on a supersonic throughflow compressor designed at NASA Lewis Research Center. Preliminary results indicate that two-dimensional, flat plate analysis predicts conservative flutter boundaries.
A finite difference code was developed for modeling inviscid, unsteady supersonic flow by solution of the compressible Euler equations. The code uses a deforming grid technique to capture the motion of the airfoils and can model oscillating cascades with any arbitrary interblade phase angle. A flat plate cascade is analyzed, and results are compared with results from a small-perturbation theory. The results show very good agreement for both the unsteady pressure distributions and the integrated force predictions. The reason for using the numerical Euler code over a small-perturbation theory is the ability to model real airfoils that have thickness and camber. Sample predictions are presented for a section of the rotor on a supersonic throughflow compressor designed at NASA Lewis Research Center. Preliminary results indicate that two-dimensional, flat plate analysis predicts conservative flutter boundaries.
Flow-visualization studies, using smoke, were made of the secondary flows in rectangular bends, tandem cascades, and high-turning configurations. The roll-up of the wall boundary layer of a rectangular bend forms a passage vortex near the suction surface similar to that previously observed for cascades. The vortex so formed then shifts out into the main stream. Because of leading-edge effects, the boundary-layer flows in bends were found to be sufficiently different from the flows in blade rows to make direct application of bend results to blade rows inadvisable. Passage vortices are shown, in the tandem-cascade study, to resist turning with the main stream through which they pass and to disturb the flow in subsequent blade rows. This disturbance may explain in part the appreciable size of the losses sometimes attributed to secondary flows in turbomachines despite the fact that the energy involvement in vortex formation is slight. Tip-flow studies of high-turning blades with relative motion between blades and end wall indicated that if the relative sizes of the passage vortex forces, the tip clearance forces, and the blade-scraping effects are properly controlled, it may be possible to improve the blade-tip loading characteristics in turbomachine.
A reliable method is presented for calculating the flowfield about a cascade of arbitrary 2-D airfoils. The method approximates the three-dimensional flow in a turbomachinery blade row by correcting for streamtube convergence and radius change in the throughflow direction. The method is a fully conservative solution of the full potential equation incorporating the finite volume technique on a body-fitted periodic mesh, with an artificial density imposed in the transonic region to ensure stability and the capture of shock waves. Comparison of results for several supercritical blades shows good agreement with their hodograph solutions. Other calculations for these profiles as well as standard NACA blade sections indicate that this is a useful scheme for analyzing both the design and off-design performance of turbomachinery blading.
The effect of small differences between the individual blades (mistuning) on the aeroelastic stability and response of a cascade were studied. The aerodynamic, inertial, and structural coupling between the bending and torsional motions of each blade and the aerodynamic coupling between the blades was considered. A digital computer program was developed to conduct parametric studies. Results indicate that the mistuning has a beneficial effect on the coupled bending torsion and uncoupled torsion flutter. On forced response, however, the effect may be either beneficial or adverse, depending on the engine order of the forcing function. The results also illustrate that it may be feasible to utilize mistuning as a passive control to increase flutter speed while maintaining forced response at an acceptable level.
Replacing the mechanical check-valve in a Stirling engine with a micromachined, non-moving-part flow diode eliminates moving parts and reduces the risk of microparticle clogging. At very small scales, helium gas has sufficient mass momentum that it can act as a flow controller in a similar way as a transistor can redirect electrical signals with a smaller bias signal. The innovation here forces helium gas to flow in predominantly one direction by offering a clear, straight-path microchannel in one direction of flow, but then through a sophisticated geometry, the reversed flow is forced through a tortuous path. This redirection is achieved by using microfluid channel flow to force the much larger main flow into this tortuous path. While microdiodes have been developed in the past, this innovation cascades Tesla diodes to create a much higher pressure in the gas bearing supply plenum. In addition, the special shape of the leaves captures loose particles that would otherwise clog the microchannel of the gas bearing pads.
The steady flow of a compressible fluid past two-dimensional infinite cascades is obtained by using the Chaplygin's simplified pressure-density relation.
A mathematical model is developed and utilized to demonstrate the enhanced torsion mode stability associated with alternate blade circumferential aerodynamic detuning of a rotor operating in an incompressible flow field. The oscillating cascade aerodynamics, including steady loading effects, are determined by developing a complete first order unsteady aerodynamic analysis. An unsteady aerodynamic influence coefficient technique is then utilized, thereby enabling the stability of both conventional uniformly spaced rotors and detuned nonuniform circumferentially spaced rotors to be determined. To demonstrate the enhanced flutter aeroelastic stability associated with this aerodynamic detuning mechanism, this model is applied to a baseline unstable rotor with a Gostelow flow geometry.
A nonlinear boundary value problem governing the subsonic flow in a single, extended, blade passage region of a high-deflection, two dimensional, oscillating cascade is derived. The blades are assumed to be undergoing identical harmonic motions of small amplitude with constant phase angle between the motion of adjacent blades. An asymptotic perturbation approach is used to determine the velocity potential. This formulation can be used in the numerical determination of unsteady potential and thus the unsteady aerodynamic force and moment under various combinations of cascade and flow parameters.
Viscous effects on two-dimensional incompressible flow about compressor blade profiles in cascade
Linearized theory is used to predict the unsteady flow in a supersonic cascade with subsonic axial flow velocity. A closed-form analytical solution is obtained by using a double application of the Wiener-Hopf technique. Although numerical and semianalytical solutions of this problem have already appeared in the literature, this paper contains the first completely analytical solution. It has been stated in the literature that the blade source should vanish at the infinite duct resonance condition. The present analysis shows that this does not occur. This apparent discrepancy is explained in the paper.
The present conference covers computational method applications, viscous-inviscid interaction techniques, viscous flow computational methods, and design-related methods. Attention is given to viscous flows in turbomachinery cascades, forbidden signals and apparent Mach numbers in supersonic cascades, the flow field in an engine particle separator, two-dimensional separated channel flows, turbulent separating flows over a rearward-facing step, the semielliptic analysis of two-dimensional internal and compressible viscous flows, spline solutions of the incompressible Navier-Stokes equations in a mildly nonorthogonal coordinate system, the design of highly loaded blades with blockage in cascade, and a finite analytic method for unsteady, three-dimensional Navier-Stokes equations.
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Annular blade-element data obtained primarily from single-stage compressor installations are correlated over a range of inlet Mach numbers and cascade geometry. The correlation curves are presented in such a manner that they are related directly to the low-speed two-dimensional-cascade data of part VI of this series. Thus, the data serve as both an extension and a verification of the two-dimensional-cascade data. In addition, the correlation results are applied to compressor design.