Evaluation of the Theory for the Flow Pattern of a Hydrofoil of Finite Span

1960 ◽  
Vol 4 (01) ◽  
pp. 13-29
Author(s):  
Paul Kaplan ◽  
John P. Breslin ◽  
Winnifred R. Jacobs
Keyword(s):  
Surface Wave ◽  
Flow Field ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Limited Data ◽  
Flow Properties ◽  
Dimensional Theory ◽  
Finite Span ◽  
Wave Elevation ◽  
Experimental Values

Expressions for various properties of the flow field aft of a finite-span hydrofoil in smooth water are presented and discussed in this paper. Potential functions for the motion that have been derived previously on the basis of linearized free-surface theory serve as the basic terms from which the flow field is derived. Both two-dimensional and three-dimensional theories are used, and the expressions derived for the surface-wave elevation and downwash from the various theories are compared with experimental values. As a result of this study, it is shown that three-dimensional effects are of great importance and hence terms derived from the two-dimensional theory do not accurately represent the true flow properties. Recommended formulas, whose validity is demonstrated by the comparison with the limited data presented herein, are given for the evaluation of both the surface-wave amplitude and downwash.

scholarly journals Improved Particle Trajectory Calculations Through Turbomachinery Affected by Coal Ash Particles

1981 ◽  
Author(s):  
B. Beecher ◽  
W. Tabakoff ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Coal Ash ◽  
Two Dimensional ◽  
Flow Properties ◽  
Trajectory Calculations ◽  
Blade Thickness ◽  
Spline Fitting ◽  
Numerical Grid

Trajectories of small coal ash particles encountered in coal-fired gas turbines are calculated with an improved computer analysis currently under development. The analysis uses an improved numerical grid and mathematical spline-fitting techniques to account for three-dimensional gradients in the flow field and blade geometry. The greater accuracy thus achieved in flow field definition improves the trajectory calculations over previous two-dimensional models by allowing the small particles to react to radial variations in the flow properties. A greater accuracy thus achieved in the geometry definition permits particle rebounding in a direction perpendicular to the blade and flow path surfaces rather than in a two-dimensional plane. The improved method also accounts for radial variations in airfoil chord, stagger, and blade thickness when computing particle impact at a blade location.

Improved Particle Trajectory Calculations Through Turbomachinery Affected by Coal Ash Particles

1982 ◽  
Vol 104 (1) ◽  
pp. 64-68 ◽  
Author(s):  
B. Beacher ◽  
W. Tabakoff ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Coal Ash ◽  
Two Dimensional ◽  
Flow Properties ◽  
Trajectory Calculations ◽  
Blade Thickness ◽  
Spline Fitting ◽  
Numerical Grid

Trajectories of small coal ash particles encountered in coal-fired gas turbines are calculated with an improved computer analysis currently under development. The analysis uses an improved numerical grid and mathematical spline-fitting techniques to account for three-dimensional gradients in the flow field and blade geometry. The greater accuracy thus achieved in flow field definition improves the trajectory calculations over previous two-dimensional models by allowing the small particles to react to radial variations in the flow properties. A greater accuracy thus achieved in the geometry definition permits particle rebounding in a plane perpendicular to the blade and flow path surfaces rather than in a two-dimensional plane. The improved method also accounts for radial variations in airfoil chord, stagger, and blade thickness when computing particle impact at a blade location.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

Effects of Stator Wakes and Spanwise Nonuniform Inlet Conditions on the Rotor Flow of an Axial Turbine Stage

1993 ◽  
Vol 115 (1) ◽  
pp. 128-136 ◽  
Author(s):  
J. Zeschky ◽  
H. E. Gallus
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Axial Flow ◽  
Tip Clearance ◽  
Hot Wire ◽  
Turbine Stage ◽  
Static Pressure Distribution ◽  
Inlet Conditions ◽  
Experimental Values ◽  
Rotor Flow

Detailed measurements have been performed in a subsonic, axial-flow turbine stage to investigate the structure of the secondary flow field and the loss generation. The data include the static pressure distribution on the rotor blade passage surfaces and radial-circumferential measurements of the rotor exit flow field using three-dimensional hot-wire and pneumatic probes. The flow field at the rotor outlet is derived from unsteady hot-wire measurements with high temporal and spatial resolution. The paper presents the formation of the tip clearance vortex and the passage vortices, which are strongly influenced by the spanwise nonuniform stator outlet flow. Taking the experimental values for the unsteady flow velocities and turbulence properties, the effect of the periodic stator wakes on the rotor flow is discussed.

Numerical and Experimental Investigation of Return Channel Vane Aerodynamics With Two-Dimensional and Three-Dimensional Vanes

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
A. Hildebrandt ◽  
F. Schilling
Keyword(s):  
Experimental Investigation ◽  
Flow Field ◽  
Static Pressure ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Field Performance ◽  
Two Dimensional ◽  
Flow Angle ◽  
Overall Performance ◽  
Return Channel

The present paper deals with the numerical and experimental investigation of the effect of return channel (RCH) dimensions of a centrifugal compressor stage on the aerodynamic performance. Three different return channel stages were investigated, two stages comprising three-dimensional (3D) return channel blades and one stage comprising two-dimensional (2D) RCH vanes. The analysis was performed regarding both the investigation of overall performance (stage efficiency, RCH total pressure loss coefficient) and detailed flow-field performance. For detailed experimental flow-field investigation at the stage exit, six circumferentially traversed three-hole probes were positioned downstream the return channel exit in order to get two-dimensional flow-field information. Additionally, static pressure wall measurements were taken at the hub and shroud pressure and suction side (SS) of the 2D and 3D return channel blades. The return channel system overall performance was calculated by measurements of the circumferentially averaged 1D flow field downstream the diffuser exit and downstream the stage exit. Dependent on the type of return channel blade, the numerical and experimental results show a significant effect on the flow field overall and detail performance. In general, satisfactory agreement between computational fluid dynamics (CFD)-prediction and test-rig measurements was achieved regarding overall and flow-field performance. In comparison with the measurements, the CFD-calculated stage performance (efficiency and pressure rise coefficient) of all the 3D-RCH stages was slightly overpredicted. Very good agreement between CFD and measurement results was found for the static pressure distribution on the RCH wall surfaces while small CFD-deviations occur in the measured flow angle at the stage exit, dependent on the turbulence model selected.

scholarly journals Numerical simulation of the dimensional transformation of atomization in a supersonic aerodynamic atomization dust-removing nozzle based on transonic speed compressible flow

2020 ◽  
Vol 7 (3) ◽  
pp. 597-610 ◽  
Author(s):  
Tian Zhang ◽  
Deji Jing ◽  
Shaocheng Ge ◽  
Jiren Wang ◽  
Xiangxi Meng ◽  
...  
Keyword(s):  
Flow Field ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Three Dimensional Model ◽  
Speed Flow ◽  
Complex Process ◽  
Study Results ◽  
Laval Nozzles

Abstract To simulate the transonic atomization jet process in Laval nozzles, to test the law of droplet atomization and distribution, to find a method of supersonic atomization for dust-removing nozzles, and to improve nozzle efficiency, the finite element method has been used in this study based on the COMSOL computational fluid dynamics module. The study results showed that the process cannot be realized alone under the two-dimensional axisymmetric, three-dimensional and three-dimensional symmetric models, but it can be calculated with the transformation dimension method, which uses the parameter equations generated from the two-dimensional axisymmetric flow field data of the three-dimensional model. The visualization of this complex process, which is difficult to measure and analyze experimentally, was realized in this study. The physical process, macro phenomena and particle distribution of supersonic atomization are analyzed in combination with this simulation. The rationality of the simulation was verified by experiments. A new method for the study of the atomization process and the exploration of its mechanism in a compressible transonic speed flow field based on the Laval nozzle has been provided, and a numerical platform for the study of supersonic atomization dust removal has been established.

Axial Transport Effects on Natural Convection Inside of an Open-Ended Annulus

1991 ◽  
Vol 113 (3) ◽  
pp. 627-634 ◽  
Author(s):  
K. Vafai ◽  
J. Ettefagh
Keyword(s):  
Temperature Distribution ◽  
Flow Field ◽  
Three Dimensional ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Subsequent Effect ◽  
Transport Effects ◽  
Temperature And Velocity Fields

The present work centers around a numerical three-dimensional transient investigation of the effects of axial convection on flow and temperature fields inside an open-ended annulus. The transient behavior of the flow field through the formation of a three-dimensional flow field and its subsequent effect on the temperature distribution at different axial locations within the annulus were analyzed by both finite difference and finite element methods. The results show that the axial convection has a distinctly different influence on the temperature and velocity fields. It is found that in the midportion of the annulus a two-dimensional assumption with respect to the temperature distribution can lead to satisfactory results for Ra<10,000. However, such an assumption is improper with respect to the flow field. Furthermore, it is shown that generally the errors for a two-dimensional assumption in the midportion of the annulus are less at earlier times (t<50Δt) during the transient development of the flow and temperature fields.

Comparison of Two Base-Potentials for a Slender-Body Method

2012 ◽  
Author(s):  
Mahmoud Alidadi ◽  
Sander Calisal
Keyword(s):  
Three Dimensional ◽  
Slender Body ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Wave Elevation ◽  
Surface Boundary Conditions ◽  
Perturbation Potential ◽  
Order Of Magnitude ◽  
Body Method

The effects of two base-potentials on the accuracy of a slender-body method are studied in this paper. In the formulation for this method which is developed for the slender ships, the velocity potential is decomposed into a base-potential and a perturbation potential. Then using an order of magnitude analysis, the three-dimensional flow problem is simplified into a series of two-dimensional problems for the perturbation potential. These two-dimensional problems are solved with the linearized free surface boundary conditions, using a mixed Eulerian-Lagrangian method. Finally for the two base-potentials, the numerical wave elevation along a Wigleyull are compared with the experimental results.

Towed Underwater SPIV Measurement of Flow Fields Around a Surface-Piercing Cylinder With Free Surface Effects

2015 ◽  
Author(s):  
Jeonghwa Seo ◽  
Bumwoo Han ◽  
Shin Hyung Rhee
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Surface Wave ◽  
Flow Field ◽  
Cross Section ◽  
Surface Effects ◽  
Flow Fields ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Wave Induced

Effects of free surface on development of turbulent boundary layer and wake fields were investigated. By measuring flow field around a surface piercing cylinder in various advance speed conditions in a towing tank, free surface effects were identified. A towed underwater Stereoscopic Particle Image Velocimetry (SPIV) system was used to measure the flow field under free surface. The cross section of the test model was water plane shape of the Wigley hull, of which longitudinal length and width were 1.0 m and 100 mm, respectively. With sharp bow shape and slender cross section, flow separation was not expected in two-dimensional flow. Flow fields near the free-surface and in deep location that two-dimensional flow field was expected were measured and compared to identify free-surface effects. Some planes perpendicular to longitudinal direction near the model surface and behind the model were selected to track development of turbulent boundary layer. Froude numbers of the test conditions were from 0.126 to 0.40 and corresponding Reynolds numbers were from 395,000 to 1,250,000. In the lowest Froude number condition, free-surface wave was hardly observed and only free surface effects without surface wave could be identified while violent free-surface behavior due to wave-induced separation dominated the flow fields in the highest Froude number condition. From the instantaneous velocity fields, Time-mean velocity, turbulence kinetic energy, and flow structure derived by proper orthogonal decomposition (POD) were analyzed. As the free-surface effect, development of retarded wake, free-surface waves, and wave-induced separation were mainly observed.

Contact Temperature in Dry Bearings. Three Dimensional Theory and Verification

1981 ◽  
Vol 103 (2) ◽  
pp. 243-251 ◽  
Author(s):  
A. Floquet ◽  
D. Play
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Experimental Verification ◽  
Three Dimensional ◽  
Contact Temperature ◽  
3D Analysis ◽  
New Work ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Infra Red

Boundary conditions were arbitrarily specified in an earlier two dimensional (2D) analysis of contact temperature. In this new work a general three dimensional (3D) Fourier transform solution is obtained from which for specific cases, the boundary conditions can be estimated. Further, experimental verification of 3D analysis was performed using infra-red technique.

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