Airfoil Design in Subcritical and Supercritical Flows

1979 ◽  
Vol 46 (4) ◽  
pp. 761-766 ◽  
Author(s):  
W. C. Chin ◽  
D. P. Rizzetta
Keyword(s):  
Reasonable Agreement ◽  
Relaxation Method ◽  
Supercritical Pressure ◽  
Small Disturbance ◽  
Trailing Edge ◽  
Difference Analysis ◽  
Pressure Distributions ◽  
Basic Ideas ◽  
New Formulation ◽  
Supercritical Flows

The “inverse” or “design” problem in aerodynamics, which solves for the airfoil shape that induces a prescribed chordwise surface pressure subject to additional requirements on trailing edge closure, is considered in the transonic small-disturbance limit. A new formulation for the stream function ψ is suggested which uses well-set Neumann conditions on the chordwise slit, with the degree of closure dictated by a specified jump in ψ across the downstream slit emanating from the trailing edge. The boundary-value problem is solved by a type-dependent relaxation method that automatically generates closed airfoils on convergence. Computed airfoil shapes using subcritical and supercritical pressure distributions obtained from existing finite-difference analysis codes, in the latter case, with and without shockwaves, give results in reasonable agreement with the original specified shapes, and validate the basic ideas.

Early Thoughts on the Jet Flap

1956 ◽  
Vol 7 (1) ◽  
pp. 45-59 ◽  
Author(s):  
B. S. Stratford
Keyword(s):  
Present State ◽  
Deflection Angle ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Quantitative Theory ◽  
The Deflection Angle ◽  
Basic Ideas ◽  
Historical Sketch

SummaryAn historical sketch shows how the basic ideas of the jet flap were evolved. The exploratory work included the prediction that lift would be induced on an aerofoil by a two-dimensional jet deflected from the trailing edge, and that the magnitude of the total lift would be of the order of four times the direct jet lift. The prediction was confirmed experimentally and a first quantitative theory evolved. Meanwhile the hypothesis was put forward that, ideally, the forward thrust on the aerofoil would be independent of the deflection angle of the jet.This paper is the first of a series of papers that will describe the development and present state of knowledge of the jet flap.

Improvement of Cooled Turbine Airfoils by Special Cutback

2010 ◽  
Author(s):  
Boris I. Mamaev ◽  
Mikhail M. Petukhovskiy ◽  
Alexander V. Pozdnyakov ◽  
Marat R. Valeev
Keyword(s):  
Substantial Reduction ◽  
Reynolds Numbers ◽  
Pressure Side ◽  
Trailing Edge ◽  
Turbine Efficiency ◽  
Flow Parameters ◽  
Pressure Distributions ◽  
Turbine Airfoils ◽  
Bend Angles ◽  
Cooling Air

A substantial reduction in high temperature turbine efficiency due to a thickening trailing edge on the blades can be compensated by ejection of cooling air on the airfoil pressure side near the edge, which is made thinner at the expense of a pressure-side contour bend. A blade-row midspan section of the aircraft high-pressure turbine was chosen for investigations. Flow parameters of the section: inlet and outlet angles were 36° and 65°, respectively (axial reference), outlet isentropic Mach number was 0.94. Four linear cascades were examined. They differed mainly in the airfoil trailing edge geometry. Three airfoils had the same thin trailing edges and contour bend angles ε = 10, 15 and 20°; one airfoil with a thick round edge had no bend. Widths of the slot for cooling air ejection were the same for all airfoils tested. Measurements were made for exit Mach numbers from 0.6 to 0.95 and relative cooling mass flows from 0 to 1.5%. The respective Reynolds numbers varied from 7.5·106 to 9·106. The incidence value was 2°. Pressure distributions along profiles, outlet total and static pressures, back pressures for cooling air with gas-outlet angles were measured. The experiments showed streamlining of all cascades were favorable. For the airfoils with ε = 10 and 15° the profile losses were low and normal for uncooled cascades with thin trailing edge. Hence, for such bends losses due to a step on the airfoil pressure side were negligible. As expected, the losses in the cascade with the thick rounding edge were significantly higher. The losses in the cascade with ε = 20° were the greatest. The coolant exit had no distinct influence on streamlining airfoils. The back-pressure for cooling air was approximately equal to the outlet static pressure. For cascades with ε = 10 and 15° the ejection of coolant led to a small increase of losses due to additional mixing losses. Thus, the airfoil contour bend is a powerful tool for the aerodynamic improvement of cooled turbines. It may lead to gains in stage efficiency of 1…1.5%. It should be noted that this tool has already been used successfully for several aircraft and industrial turbines of recent design.

Separated inviscid sheet flows

2011 ◽  
Vol 678 ◽  
pp. 511-534 ◽  
Author(s):  
BUM-SANG YOON ◽  
YURIY A. SEMENOV
Keyword(s):  
Free Surface ◽  
Free Surface Flows ◽  
Bottom Surface ◽  
Free Boundaries ◽  
Trailing Edge ◽  
Hodograph Method ◽  
Inviscid Incompressible Fluid ◽  
Wide Range ◽  
Finite Distance ◽  
Supercritical Flows

A steady sheet flow of an inviscid incompressible fluid along a curvilinear surface ending with a rounded trailing edge is considered in the presence of gravity. The effect of surface tension is ignored. The formulation of the problem is applicable to the study of free-surface flows over obstacles in channels, weirs and spillways, and pouring flows. An advanced hodograph method is employed for solving the problem, which is reduced to a system of two integro-differential equations in the velocity modulus on the free surface and in the slope of the bottom surface. These equations are derived from the dynamic and kinematic boundary conditions. The Brillouin–Villat criterion is applied to determine the location of the point of flow separation from the rounded trailing edge. Results showing the effect of gravity on the flow detachment and the geometry of the free boundaries are presented over a wide range of Froude numbers including both subcritical and supercritical flows. For supercritical flows two families of solutions for an arbitrary bottom shape are reproduced. It is shown that the additional condition requiring the free surface to be flat at a finite distance from the end of the channel selects a unique solution for a given bottom height and geometry for supercritical flows. This solution is continuous in going from the subcritical to the supercritical flow regime.

A wake singularity potential flow model for airfoils experiencing trailing-edge stall

1993 ◽  
Vol 251 ◽  
pp. 203-218 ◽  
Author(s):  
W. W. H. Yeung ◽  
G. V. Parkinson
Keyword(s):  
Potential Flow ◽  
Inviscid Flow ◽  
Near Wake ◽  
Trailing Edge ◽  
Pressure Distributions ◽  
Free Streamlines ◽  
Potential Flow Model ◽  
Theoretical Pressure ◽  
Simple Sequence ◽  
Good Agreement

An incompressible inviscid flow theory for single and two-element airfoils experiencing trailing-edge stall is presented. For the single airfoil the model requires a simple sequence of conformal transformations to map a Joukowsky airfoil, partially truncated on the upper surface, onto a circle over which the flow problem is solved. Source and doublet singularities are used to create free streamlines simulating shear layers bounding the near wake. The model's simplicity permits extension of the method to airfoil-flap configurations in which trailing-edge stall is assumed on the flap. Williams’ analytical method to calculate the potential flow about two lifting bodies is incorporated in the Joukowsky-arc wake-singularity model to allow for flow separation. The theoretical pressure distributions from these models show good agreement with wind-tunnel measurements.

Computations of Three-Dimensional Viscous Flow Through Turbine Blade Passage

1999 ◽  
Author(s):  
Yumin Xiao ◽  
R. S. Amano
Keyword(s):  
Experimental Data ◽  
Viscous Flow ◽  
Flow Pattern ◽  
Three Dimensional ◽  
Trailing Edge ◽  
Blade Passage ◽  
Good Convergence ◽  
Pressure Distributions ◽  
Flow Through ◽  
Transonic Cascade

Abstract An implicit 3-D solver for computations of viscous flow has been developed and the computations of the flow through a blade passage are presented. The validation cases include subsonic and transonic viscous flows in C3X cascade. Results for these turbine cascade flows are presented and compared with the experimental data. Computed pressure distributions on blade surfaces show good agreement with the published experimental data. From these computations it was found that the proposed method possesses good convergence characteristics and can be extended to unsteady flow calculations. Three-dimensional calculations show that the flow pattern in the trailing edge is quite complicated. There appear a couple of sinks near the trailing edge caused by the endwall vortices. The change of the flow pattern was clearly observed at several vertical planes away from the endwall. It was also demonstrated that the secondary flow mechanism in a transonic cascade exhibit different patterns from those in a subsonic case.

Surface Static Pressures in an Inlet Vortex Flow Field

1985 ◽  
Vol 107 (2) ◽  
pp. 387-393 ◽  
Author(s):  
W. Liu ◽  
E. M. Greitzer ◽  
C. S. Tan
Keyword(s):  
Flow Field ◽  
Static Pressure ◽  
Velocity Ratio ◽  
Ground Plane ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Static Pressure Distribution ◽  
Pressure Distributions ◽  
Parametric Data ◽  
Basic Ideas

An experimental investigation of the three-dimensional flow field associated with an inlet vortex is reported. The specific configuration investigated is an inlet, in proximity to a ground plane, in crosswind. Parametric data are presented to define the regimes of vortex formation in this configuration, as a function of inlet height to diameter ratio and inlet velocity ratio. The detailed static pressure distribution on the inlet is given for two quite different flow regimes, one with a strong inlet vortex and one with no inlet vortex. These new quantitative data are supplemented by flow visualization studies that allow an estimate to be made of the circulation around the inlet vortex. It is argued that the static pressure distributions in both cases can be clearly interpreted using the basic ideas of inlet vortex formation that were previously developed from (qualitative) water tunnel studies.

A Combined Experimental and Theoretical Study of Flow and Pressure Distributions in a Brush Seal

1993 ◽  
Vol 115 (2) ◽  
pp. 404-410 ◽  
Author(s):  
F. J. Bayley ◽  
C. A. Long
Keyword(s):  
Experimental Data ◽  
Reasonable Agreement ◽  
Theoretical Study ◽  
Isothermal Flow ◽  
Empirical Constant ◽  
Pressure Distributions ◽  
Brush Seal ◽  
Mass Flows ◽  
Porosity Measurements ◽  
Experimental Rig

A relatively simple theory is presented that can be used to model the flow and pressure distribution in a brush seal matrix. The model assumes laminar, compressible, isothermal flow and requires knowledge of an empirical constant: the seal porosity value. Measurements of the mass flow rate together with radial and axial distributions of pressure were taken on a nonrotating experimental rig. These were obtained using a 122 mm bore brush seal with 0.25 mm radial interference. The experimental data are used to estimate the seal porosity. Measurements of the pressure distributions along the backing ring and under the bristle tips and discussed. Predicted mass flows are compared with those actually measured and there is reasonable agreement considering the limitations of the model.

A Method for Estimating the Influence of Time-Dependent Vane and Blade Pressure Fields on Turbine Rim Seal Ingestion

2006 ◽  
Author(s):  
Bruce V. Johnson ◽  
Ralf Jakoby ◽  
Dieter E. Bohn ◽  
Didier Cunat
Keyword(s):  
Pressure Distribution ◽  
Reasonable Agreement ◽  
Present Model ◽  
Turbine Disk ◽  
Time Dependent ◽  
Cavity Pressure ◽  
Cooling Effectiveness ◽  
Pressure Distributions ◽  
Pressure Fields ◽  
Bow Wave

A method of estimating the turbine rim seal ingestion rates was developed using the time-dependent pressure distributions on the hub of turbines and a simple orifice model. Previous methods use the time-averaged pressure distribution downstream of the vanes to estimate seal ingestion. The present model uses the pressure distribution near the turbine hub, obtained from 2-D time-dependent stage calculations, and a simple-orifice model to estimate the pressure-driven ingress of gas path fluid into the turbine disk cavity and the egress of cavity fluid to the gas path. The time-dependent pressure distribution provides the influence of both the vane wakes and the bow wave from the blade on the pressure difference between hub pressure at an azimuthal location and the cavity pressure. Results from the simple-orifice model are used to determine the effective Cd that matches the cooling effectiveness at radii near the rim seal with the amount of gas-path-ingested flow required to mix with the coolant flow. Cavity ingestion data from rim-seal-ingestion experiments in a 1.5-stage turbine and numerical simulations for a 1-vane-2-blade sector of the 16 vane, 32 blade turbine were used to evaluate the method. The experiments and simulations were performed for close-spaced and wide-spaced half stages between both the vane and blade and between the blade and a trailing teardrop-shaped strut. The comparison of the model with a single Cd for axial gap seals and the experiments showed reasonable agreement for both close- and wide-spaced stages.

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