On the Application of a Linearized Unsteady Potential-Flow Analysis to Fan-Tip Cascades

1986 ◽  
Vol 108 (1) ◽  
pp. 59-67
Author(s):  
W. J. Usab ◽  
J. M. Verdon
Keyword(s):  
Potential Flow ◽  
Vibrational Frequency ◽  
Numerical Solutions ◽  
Flow Analysis ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Good Qualitative Agreement ◽  
Blade Loading ◽  
Unsteady Aerodynamic ◽  
Flow Phenomena

A linearized potential flow analysis, which accounts for the effects of nonuniform steady flow phenomena on the unsteady response to prescribed blade motions, has been applied to five two-dimensional cascade configurations. These include a flat-plate cascade and three cascades which are representative of the tip sections of current fan designs. Here the blades are closely spaced, highly staggered, and operate at low mean incidence. The fifth configuration is a NASA Lewis cascade of symmetric biconvex airfoils for which experimental measurements are available. Numerical solutions are presented that clearly illustrate the effects and importance of blade geometry and mean blade loading on the linearized unsteady response at high subsonic inlet Mach number and high blade-vibrational frequency. In addition, a good qualitative agreement is shown between the analytical predictions and experimental measurements for the cascade of symmetric biconvex airfoils. Finally, recommendations on the research needed to extend the range of application of linearized unsteady aerodynamic analyses are provided.

scholarly journals Design and Testing of Swept and Leaned Outlet Guide Vanes to Reduce Stator-Strut-Splitter Aerodynamic Flow Interactions

1998 ◽  
Author(s):  
A. R. Wadia ◽  
P. N. Szucs ◽  
K. L. Gundy-Burlet
Keyword(s):  
Dimensional Analysis ◽  
Test Performance ◽  
Potential Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Angle Distribution ◽  
Two Dimensional ◽  
Guide Vanes ◽  
Flow Interactions ◽  
Design And Testing

Large circumferential varying pressure levels produced by aerodynamic flow interactions between downstream stators and struts present a potential noise and stability margin liability in a compression component. These interactions are presently controlled by tailoring the camber and/or stagger angles of vanes neighboring the fan frame struts. This paper reports on the design and testing of a unique set of swept and leaned fan outlet guide vanes (OGVs) that do not require this local tailoring even though the OGVs are closely coupled with the fan frame struts and splitter to reduce engine length. The swept and leaned OGVs not only reduce core-duct diffusion, but they also reduce the potential flow interaction between the stator and the strut relative to that produced by conventional radial OGVs. First, the design of the outlet guide vanes using a single bladerow three-dimensional viscous flow analysis is outlined. Next, a two-dimensional potential flow analysis was used for the coupled OGV-frame system to obtain a circumferentially non-uniform stator stagger angle distribution to further reduce the upstream static pressure disturbance. Recognizing the limitations of the two-dimensional potential flow analysis for this highly three-dimensional set of leaned OGVs, as a final evaluation of the OGV-strut system design, a full three-dimensional viscous analysis of a periodic circumferential sector of the OGVs, including the fan frame struts and splitter, was performed. The computer model was derived from a NASA-developed code used in simulating the flow field for external aerodynamic applications with complex geometries. The three-dimensional coupled OGV-frame analysis included the uniformly-staggered OGVs configuration and the variably-staggered OGVs configuration determined by the two-dimensional potential flow analysis. Contrary to the two-dimensional calculations, the three-dimensional analysis revealed significant flow problems with the variably-staggered OGVs configuration and showed less upstream flow non-uniformity with the uniformly-staggered OGVs configuration. The flow redistribution in both the radial and tangential directions, captured fully only in the three-dimensional analysis, was identified as the prime contributor to the lower flow non-uniformity with the uniformly-staggered OGVs configuration. The coupled three-dimensional analysis was also used to validate the design at off-design conditions. Engine test performance and stability measurements with both uniformly- and variably-staggered OGVs configurations with and without the presence of inlet distortion confirmed the conclusions from the three-dimensional analysis.

A rapidly convergent procedure for solving the equations of subsonic potential flow. I. Numerical solutions

1960 ◽  
Vol 255 (1280) ◽  
pp. 101-113 ◽  
Keyword(s):  
Potential Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Local Density ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Approximation Solution ◽  
Flow Equations ◽  
Bernoulli’S Equation ◽  
First Approximation

The subsonic potential flow equations for a perfect gas are transformed by means of dependent variables s = ( ρ / ρ 0 ) n q/ a 0 and σ = 1/2 In ( ρ 0 / ρ ), where q is the local velocity, ρ and a the local density and speed of sound, and the suffix 0 indicates stagnation conditions, n is a parameter which is to be chosen to optimize the approximations. Bernoulli’s equation then becomes a relation between s 2 and σ which is independent of initial conditions. A family of first-approximation solutions in terms of the incompressible solution is obtained on linearizing. It is shown that for two-dimensional flow, the choice n = 0∙5 gives results as accurate as those obtained with the Karman—Tsien solution. The exact equations are then transformed into the plane of the incompressible velocity potential and stream function and the first-approximation results substituted in the non ­linear terms. The resulting second-approximation equations can then be solved by a relaxation method and the error in this approximation estimated by carrying out the third-approximation solution. Results are given for a circular cylinder at a free-stream Mach number, M ∞ = 0∙4, and a sphere at M ∞ = 0∙5. The error in the velocity distribution is shown to be less than ±1 % in the two-dimensional case. A rough and ready compressibility rule is formulated for axisymmetric bodies, dependent on their thickness ratios.

Design and Testing of Swept and Leaned Outlet Guide Vanes to Reduce Stator–Strut–Splitter Aerodynamic Flow Interactions

1999 ◽  
Vol 121 (3) ◽  
pp. 416-427 ◽  
Author(s):  
A. R. Wadia ◽  
P. N. Szucs ◽  
K. L. Gundy-Burlet
Keyword(s):  
Dimensional Analysis ◽  
Potential Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Angle Distribution ◽  
Two Dimensional ◽  
Guide Vanes ◽  
Flow Interactions ◽  
Design And Testing ◽  
Flow Nonuniformity

Large circumferentially varying pressure levels produced by aerodynamic flow interactions between downstream stators and struts present a potential noise and stability margin liability in a compression component. These interactions are presently controlled by tailoring the camber and/or stagger angles of vanes neighboring the fan frame struts. This paper reports on the design and testing of a unique set of swept and leaned fan outlet guide vanes (OGVs) that do not require this local tailoring even though the OGVs are closely coupled with the fan frame struts and splitter to reduce engine length. The swept and leaned OGVs not only reduce core-duct diffusion, but they also reduce the potential flow interaction between the stator and the strut relative to that produced by conventional radial OGVs. First, the design of the outlet guide vanes using a single blade row three-dimensional viscous flow analysis is outlined. Next, a two-dimensional potential flow analysis was used for the coupled OGV–frame system to obtain a circumferentially nonuniform stator stagger angle distribution to reduce the upstream static pressure disturbance further. Recognizing the limitations of the two-dimensional potential flow analysis for this highly three-dimensional set of leaned OGVs, as a final evaluation of the OGV–strut system design, a full three-dimensional viscous analysis of a periodic circumferential sector of the OGVs, including the fan frame struts and splitter, was performed. The computer model was derived from a NASA-developed code used in simulating the flow field for external aerodynamic applications with complex geometries. The three-dimensional coupled OGV–frame analysis included the uniformly staggered OGV configuration and the variably staggered OGV configuration determined by the two-dimensional potential flow analysis. Contrary to the two-dimensional calculations, the three-dimensional analysis revealed significant flow problems with the variably staggered OGV configuration and showed less upstream flow nonuniformity with the uniformly staggered OGV configuration. The flow redistribution in both the radial and tangential directions, captured fully only in the three-dimensional analysis, was identified as the prime contributor to the lower flow nonuniformity with the uniformly staggered OGV configuration. The coupled three-dimensional analysis was also used to validate the design at off-design conditions. Engine test performance and stability measurements with both uniformly and variably staggered OGV configurations with and without the presence of inlet distortion confirmed the conclusions from the three-dimensional analysis.

Instability of erodible beds

1970 ◽  
Vol 42 (2) ◽  
pp. 225-244 ◽  
Author(s):  
Frank Engelund
Keyword(s):  
Mathematical Model ◽  
Internal Friction ◽  
Potential Flow ◽  
Transport Mechanism ◽  
Flow Analysis ◽  
Two Dimensional ◽  
Alluvial Channel ◽  
The Stability ◽  
Vorticity Transport ◽  
Erodible Beds

The stability of a sand bed in an alluvial channel is investigated by a two-dimensional mathematical model, based on the vorticity transport equation. The model takes account of the internal friction and describes the non-uniform distribution of the suspended sediment. It turns out that the inclusion of the friction and of a definite model of the sediment transport mechanism leads to results rather different from those obtained previously by potential-flow analysis.

Influence of Viscous Effects on the Hydrodynamics of Ship-Like Sections Undergoing Symmetric and Anti-Symmetric Motions, Using RANS

2008 ◽  
Author(s):  
A. Que´rard ◽  
P. Temarel ◽  
S. R. Turnock
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Systematic Approach ◽  
Added Mass ◽  
Experimental Measurements ◽  
Hydrodynamic Coefficients ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Numerical Predictions ◽  
Fluid Damping

The aim of this investigation is to assess the influence of viscous effects on the predicted hydrodynamic coefficients for a range of ship-like sections, such as rectangular, triangular, chine and bulbous. Hydrodynamic coefficients, of added mass or inertia and fluid damping, for two-dimensional sections harmonically heaving, swaying and rolling at the undisturbed free surface are obtained using the ANSYS-CFX11.0 RANS solver, for a range of frequencies of oscillation. All predictions are compared with available experimental measurements and other numerical predictions (potential flow and RANS). It is concluded from these comparisons that the proposed RANS approach can offer a better prediction for the hydrodynamic coefficients when viscous effects become significant, in particular for sway and roll motions. It is important that a reliable and systematic approach is adopted for the application of the unsteady free surface RANS methodology.

The Effect of Radius Change on Two-Dimensional Cascade Solutions

1985 ◽  
Author(s):  
Joseph R. Caspar ◽  
David E. Hobbs
Keyword(s):  
Potential Flow ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Rotating Frame ◽  
Steady Flows ◽  
Two Dimensional ◽  
Potential Solution ◽  
Radius Variation ◽  
Stators And Rotors ◽  
Euler Solution

The effects of varying radius along a streamsurface are included in a two dimensional blade-to-blade potential flow analysis of turbomachinery rotors and stators in order to model better three dimensional effects. On a cylindrical streamsurface, flows in rotors can be treated as steady flows in the rotating frame; the rotation can be ignored. On a streamsurface with varying radius, however, the flow, even in the rotating frame, is not potential. Thus the physical flow is related to a non-physical, potential flow for calculation purposes. Computed results for compressor stators and rotors show that the potential solution agrees well with an Euler solution, that effects of radius variation are very important for both stators and rotors, and that effects of radius contouring and of rotation can also be important.

Closed-form solution of the potential flow in a contracted flume

2008 ◽  
Vol 599 ◽  
pp. 299-307 ◽  
Author(s):  
G. BELAUD ◽  
X. LITRICO
Keyword(s):  
Closed Form ◽  
Potential Function ◽  
Complex Plane ◽  
Potential Flow ◽  
Complex Potential ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Experimental Measurements

The potential flow upstream from a contraction in a rectangular flume is analysed. In order to calculate the potential function, the flow is considered as the superposition of sinks uniformly distributed in the contraction. The effect of boundaries is taken into account by introducing virtual sinks. The calculation is performed in the complex plane and provides a closed-form solution of the complex potential function. As an illustration, the effect of contraction size and position is analysed, and the solution is compared to experimental measurements and other numerical solutions for vertical sluice gates.

Approximate Numerical Solutions for Two-Dimensional Potential Flow Problems

1978 ◽  
Vol 100 (1) ◽  
pp. 122-124 ◽  
Author(s):  
A. Kieda ◽  
H. Yano
Keyword(s):  
Numerical Method ◽  
Surface Pressure ◽  
Potential Flow ◽  
General Class ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Weighted Residuals ◽  
Flow Problems ◽  
Pressure Distributions ◽  
Method Of Weighted Residuals

An approximate numerical method is proposed for solving two-dimensional potential flow problems. The method is included in the general class of “Method of Weighted Residuals.” Typical computed results are presented for the surface pressure distributions on an airfoil and single noncircular cylinders immersed in a uniform infinite stream.

VISCOUS POTENTIAL FLOW ANALYSIS OF STRESS-INDUCED CAVITATION IN AN APERTURE FLOW

2006 ◽  
Vol 16 (7) ◽  
pp. 763-776 ◽  
Author(s):  
T. Funada ◽  
J. Wang ◽  
Daniel D. Joseph
Keyword(s):  
Potential Flow ◽  
Flow Analysis ◽  
Viscous Potential Flow
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