The Third Two-Dimensional Problem of Three-Dimensional Blade Systems of Hydraulic Machines—Part 1: Theoretical Analysis

1981 ◽  
Vol 103 (1) ◽  
pp. 33-41
Author(s):  
P. K. Agarwal ◽  
G. V. Viktorov
Keyword(s):  
Three Dimensional ◽  
Tangential Velocity ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Analysis Method ◽  
Flow Conditions ◽  
Three Dimensional Flow ◽  
Hydraulic Machines ◽  
The Mean ◽  
Axisymmetric Stream

This is the first part of a study of “third” two-dimensional problem of three-dimensional blade systems of hydraulic machines. Proposed herein is a method of obtaining and evaluating the three-dimensional effect on a system of hydraulic machine blades with arbitrary geometry. An analysis method indicating the velocity distributions on surfaces perpendicular to the mean axisymmetric stream surfaces has been formulated to help create a general understanding and awareness of the flow conditions in the runner passage. An application of generalized analytic functions for inviscid, incompressible flow has been made to find out the general solution on an auxiliary plane, transformed conformally from the physical plane. Integral equation systems for the tangential velocity and the velocity potential function have been deduced. Thus, the solution of the three-dimensional flow problem is supplied by two-dimensional computation methods.

The Third Two-Dimensional Problem of Three-Dimensional Blade Systems of Hydraulic Machines—Part 2: Analytical Results

1981 ◽  
Vol 103 (1) ◽  
pp. 42-51
Author(s):  
P. K. Agarwal ◽  
G. V. Viktorov
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Blade Profile ◽  
Flow Conditions ◽  
Numerical Examples ◽  
The Third ◽  
Hydraulic Machines ◽  
Method Of Solution ◽  
Axisymmetric Stream

This is the second part of a study of the “third” two-dimensional problem of three-dimensional blade systems of hydraulic machines. Part I described the formulation of the problem and the proposed method of solution to determine the velocity field on surfaces orthogonal to mean axisymmetric stream surfaces. Part II presents the numerical method of solving the integral equations; a few numerical examples for actual impellers/runners are also given. The results are presented in a series of figures and tables showing the distribution of the velocity component c2 along the blade profile on the surface q1 = const. The purpose of these numerical examples is to demonstrate the method and to help create a general understanding and awareness of the flow conditions existing in the runner passage.

scholarly journals Networked configurations as an emergent property of transverse aeolian ridges on Mars

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
T. P. Nagle-McNaughton ◽  
L. A. Scuderi
Keyword(s):  
Three Dimensional ◽  
Spatial Density ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Martian Surface ◽  
Three Dimensional Flow ◽  
Linear Forms ◽  
Dimensional Flow ◽  
Roughness Elements ◽  
Two Dimensional Flow

AbstractTransverse aeolian ridges – enigmatic Martian features without a proven terrestrial analog – are increasingly important to our understanding of Martian surface processes. However, it is not well understood how the relationships between different ridges evolve. Here we present a hypothesis for the development of complex hexagonal networks from simple linear forms by analyzing HiRISE images from the Mars Reconnaissance Orbiter. We identify variable morphologies which show the presence of secondary ridges, feathered transverse aeolian ridges and both rectangular and hexagonal networks. We propose that the formation of secondary ridges and the reactivation of primary ridge crests produces sinuous networks which then progress from rectangular cells towards eventual hexagonal cells. This morphological progression may be explained by the ridges acting as roughness elements due to their increased spatial density which would drive a transition from two-dimensional bedforms under three-dimensional flow conditions, to three-dimensional bedforms under two-dimensional flow conditions.

The Influence of Blade Wakes on the Performance of Interturbine Diffusers

1996 ◽  
Vol 118 (2) ◽  
pp. 347-352 ◽  
Author(s):  
R. G. Dominy ◽  
D. A. Kirkham
Keyword(s):  
Performance Modeling ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Correct Performance ◽  
Analysis Methods ◽  
Flow Factor ◽  
The Mean ◽  
Lp Turbine

Interturbine diffusers provide continuity between HP and LP turbines while diffusing the flow upstream of the LP turbine. Increasing the mean turbine diameter offers the potential advantage of reducing the flow factor in the following stages, leading to increased efficiency. The flows associated with these interturbine diffusers differ from those in simple annular diffusers both as a consequence of their high-curvature S-shaped geometry and of the presence of wakes created by the upstream turbine. It is shown that even the simplest two-dimensional wakes result in significantly modified flows through such ducts. These introduce strong secondary flows demonstrating that fully three-dimensional, viscous analysis methods are essential for correct performance modeling.

Three-dimensional flow in cavities

1963 ◽  
Vol 16 (4) ◽  
pp. 620-632 ◽  
Author(s):  
D. J. Maull ◽  
L. F. East
Keyword(s):  
Static Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Large Span ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Oil Flow ◽  
Two Dimensional Flow

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

Compressor Performance 2D Modelling at Reverse Flow Conditions

2010 ◽  
Author(s):  
L. Gallar ◽  
I. Tzagarakis ◽  
V. Pachidis ◽  
R. Singh
Keyword(s):  
Experimental Data ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Engine Performance ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Compressor Surge ◽  
Compressor Performance ◽  
Shaft Failure

After a shaft failure the compression system of a gas turbine is likely to surge due to the heavy vibrations induced on the engine after the breakage. Unlike at any other conditions of operation, compressor surge during a shaft over-speed event is regarded as desirable as it limits the air flow across the engine and hence the power available to accelerate the free turbine. It is for this reason that the proper prediction of the engine performance during a shaft over-speed event claims for an accurate modelling of the compressor operation at reverse flow conditions. The present study investigates the ability of the existent two dimensional algorithms to simulate the compressor performance in backflow conditions. Results for a three stage axial compressor at reverse flow were produced and compared against stage by stage experimental data published by Gamache. The research shows that due to the strong radial fluxes present over the blades, two dimensional approaches are inadequate to provide satisfactory results. Three dimensional effects and inaccuracies are accounted for by the introduction of a correction parameter that is a measure of the pressure loss across the blades. Such parameter is tailored for rotors and stators and enables the satisfactory agreement between calculations and experiments in a stage by stage basis. The paper concludes with the comparison of the numerical results with the experimental data supplied by Day on a four stage axial compressor.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

A Three-Dimensional Inverse Method for Turbomachinery: Part I—Theory

1990 ◽  
Vol 112 (3) ◽  
pp. 346-354 ◽  
Author(s):  
J. E. Borges
Keyword(s):  
Velocity Field ◽  
Inverse Method ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Inverse Methods ◽  
Meridional Section ◽  
Low Speed ◽  
Present Procedure ◽  
Blade Row ◽  
The Mean

There are surprisingly few inverse methods described in the literature that are truly three dimensional. Here, one such method is presented. This technique uses as input a prescribed distribution of the mean swirl, i.e., radius times mean tangential velocity, given throughout the meridional section of the machine. In the present implementation the flow is considered inviscid and incompressible and is assumed irrotational at the inlet to the blade row. In order to evaluate the velocity field inside the turbomachine, the blades (supposed infinitely thin) are replaced by sheets of vorticity, whose strength is related to the specified mean swirl. Some advice on the choice of a suitable mean swirl distribution is given. In order to assess the usefulness of the present procedure, it was decided to apply it to the design of an impeller for a low-speed radial-inflow turbine. The results of the tests are described in the second part of this paper.

Reconstruction of three-dimensional flow fields from two-dimensional data

2020 ◽  
Vol 407 ◽  
pp. 109239
Author(s):  
José Miguel Pérez ◽  
Soledad Le Clainche ◽  
José Manuel Vega
Keyword(s):  
Three Dimensional ◽  
Flow Fields ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow

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.

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