Two-Dimensional Laminar Flow in Elbows

1979 ◽  
Vol 101 (2) ◽  
pp. 276-283 ◽  
Author(s):  
P. Orlandi ◽  
D. Cunsolo
Keyword(s):  
Laminar Flow ◽  
Finite Difference ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Internal Wall ◽  
Primary Flow ◽  
Parabolic Profile ◽  
Pressure Distributions ◽  
Internal Radius ◽  
Two Dimensional Flow

A finite difference procedure is employed to evaluate the primary flow field in two typical elbows. The first has an internal wall radius equal to the width; the internal radius of the second sharper elbow is equal to one half of the width. Two dimensional flow is assumed and a 20 by 20 grid network is employed in both cases. The field is transformed into a rectangular one by generalized curvilinear coordinates. Velocity profiles and streamline patterns are presented and discussed. In both cases the outflow attains the parabolic profile assumed for the inflow. The pressure distributions on the internal and external walls have been calculated.

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.

scholarly journals Unsteady stagnation point flow of a non-Newtonian second-grade fluid

2003 ◽  
Vol 2003 (60) ◽  
pp. 3797-3807 ◽  
Author(s):  
F. Labropulu ◽  
X. Xu ◽  
M. Chinichian
Keyword(s):  
Finite Difference ◽  
Stagnation Point ◽  
Infinite Plate ◽  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Harmonic Oscillations ◽  
Finite Difference Technique ◽  
Two Dimensional Flow ◽  
Grade Fluid

The unsteady two-dimensional flow of a viscoelastic second-grade fluid impinging on an infinite plate is considered. The plate is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations are obtained.

Further contributions on the two-dimensional flow in a sudden expansion

1997 ◽  
Vol 330 ◽  
pp. 169-188 ◽  
Author(s):  
N. ALLEBORN ◽  
K. NANDAKUMAR ◽  
H. RASZILLIER ◽  
F. DURST
Keyword(s):  
Laminar Flow ◽  
Continuation Method ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Governing Equations ◽  
Bifurcation Structure ◽  
Bifurcation Points ◽  
Flow Parameters ◽  
Two Dimensional Flow ◽  
The Stability

Two-dimensional laminar flow of an incompressible viscous fluid through a channel with a sudden expansion is investigated. A continuation method is applied to study the bifurcation structure of the discretized governing equations. The stability of the different solution branches is determined by an Arnoldi-based iterative method for calculating the most unstable eigenmodes of the linearized equations for the perturbation quantities. The bifurcation picture is extended by computing additional solution branches and bifurcation points. The behaviour of the critical eigenvalues in the neighbourhood of these bifurcation points is studied. Limiting cases for the geometrical and flow parameters are considered and numerical results are compared with analytical solutions for these cases.

Pressure Distributions and Forces on Rectangular and D-shaped Cylinders

1972 ◽  
Vol 23 (1) ◽  
pp. 1-6 ◽  
Author(s):  
B R Bostock ◽  
W A Mair
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Drag Coefficient ◽  
Pressure Distribution ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Two Dimensional Flow ◽  
Rectangular Cylinders ◽  
Shaped Section

SummaryMeasurements in two-dimensional flow on rectangular cylinders confirm earlier work of Nakaguchi et al in showing a maximum drag coefficient when the height h of the section (normal to the stream) is about 1.5 times the width d. Reattachment on the sides of the cylinder occurs only for h/d < 0.35.For cylinders of D-shaped section (Fig 1) the pressure distribution on the curved surface and the drag are considerably affected by the state of the boundary layer at separation, as for a circular cylinder. The lift is positive when the separation is turbulent and negative when it is laminar. It is found that simple empirical expressions for base pressure or drag, based on known values for the constituent half-bodies, are in general not satisfactory.

Rock/Bit-Tooth Interaction for Conical Bit Teeth

1971 ◽  
Vol 11 (02) ◽  
pp. 162-170 ◽  
Author(s):  
T.W. Miller ◽  
J.B. Cheatham
Keyword(s):  
Finite Difference ◽  
Approximate Method ◽  
Plane Strain ◽  
Numerical Results ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Flat Punch ◽  
Pressure Distributions ◽  
Finite Difference Equations ◽  
Punch Problem

Abstract Insert-type bit teeth are axially symmetric and therefore cannot be properly described by a two-dimensional, plane-strain analysis of a wedge-shaped tooth. Since few exact plasticity solutions exist for axially symmetric problems, an approximate method is developed and applied to the interaction of a conical bit tooth with rock. Numerical results of the approximate method compare favorably with the known exact solutions. Alter making allowance for the experimental result of little or no lip formation around an indentation, numerical results using the approximate method correlate well with experimental measurements for the indentation of conical teeth into marble and sandstone. Introduction Previous studies of the interaction of bit teeth with rock have been concerned primarily with two-dimensional wedge-shaped teeth. This provides a good approximation to the shape of most bit teeth, and the two-dimensional analysis simplifies the problem. However, some bits have inserts or so-called "buttons", which cannot be adequately represented by a wedge. Also, "end effects" exist for the finite-length wedges, whereas cones, flat-circular cylinders and hemispheres, while axially symmetric, are truly three-dimensional. These axially symmetric punches pose a more difficult problem analytically; hence one of the objectives of this paper is to provide an approximate method for analysis of this class of problems. problems. The analysis of problems concerned with the indentation of a rigid/plastic half space by an axially symmetric indenter is more difficult than the analogous problem in plane strain due to the radial expansion that occurs with increased distance from the axis of symmetry. The axially symmetric solutions are also of interest because they give insight into other practical problems, such as analysis of Rockwell-type hardness tests and end effect corrections for plane-strain solutions. DISCUSSION OF EXACT SOLUTIONS Ishlinski has solved the problem of the indentation of a plastic half space by a perfectly smooth, flat punch by tedious hand calculations, whereas Shield and Cox et al. have rigorously solved the perfectly smooth, flat-punch problem for metals and soils, respectively, using finite-difference techniques requiring a digital computer. Mroz has developed a graphics technique for the above problem for metals, but it, too, is a long, tedious procedure. Lockett has solved problems for the indentation of metals by perfectly smooth, conical indenters with half-cone angles between 52.5 degrees and 90 degrees, also using finite-difference equations. Berezancev has presented values of average pressure on cones with hall-cone angles of 15 degrees and 30 degrees for indentation of both metals and soils. Eason and Shield have given the solution for the indentation of metals by a perfectly rough, flat indenter, again using finite-difference equations. Problems for perfectly rough, flat indenters Problems for perfectly rough, flat indenters penetrating soils and perfectly rough, conical penetrating soils and perfectly rough, conical indenters penetrating soils and metals have not yet been solved to the authors' knowledge. Spencer has presented an approximate solution for an annular, flat punch using perturbation methods. This method does not seem applicable to conical indenters, however, since it requires a fixed punch radius that is large with respect to other dimensional quantities of the problem. If the approximate method presented here were applied to the annular punch problem, it would give results corresponding to Spencer's first-order solution. It is the purpose of the present paper to compare the results of the approximate method of finding pressure distributions on a conical indenter with pressure distributions on a conical indenter with some of the exact results discussed above; and then to use other results of the approximate method to analyze experimental data. The numerical results used to analyze experimental data are calculated using a modified slip-line field for a formation. SPEJ P. 162

Two-dimensional flow of a compressible fluid past given curved obstacles with infinite wakes

1955 ◽  
Vol 227 (1170) ◽  
pp. 367-386 ◽  
Keyword(s):  
Flow Separation ◽  
Subsonic Flow ◽  
Constant Pressure ◽  
Boundary Layer Separation ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Infinite Extent ◽  
Two Dimensional Flow ◽  
Experimental Pressure ◽  
Good Agreement

This paper extends in a number of ways the classical Helmholtz theory of incompressible flow about obstacles behind which are constant-pressure cavities or ‘bubbles’ of infinite extent. The theory given in the paper applies to compressible subsonic flow about given curved obstacles with bubble pressures varying down the wake. As an example the flow is calculated past a circular cylinder for a number of points of flow separation and Mach numbers. When the points of flow separation are the same as those found experimentally, the theoretical and experimental pressure distributions over the cylinder are in good agreement. It is shown that the point of flow separation for ‘proper’ cavitation is almost coincident with the point found experimentally for laminar boundary-layer separation.

A Calculation Procedure for Three-Dimensional, Viscous, Compressible Duct Flow. Part I—Inviscid Flow Considerations

1979 ◽  
Vol 101 (4) ◽  
pp. 415-422 ◽  
Author(s):  
John Moore ◽  
Joan G. Moore
Keyword(s):  
Three Dimensional ◽  
Inviscid Flow ◽  
Solution Procedure ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Duct Flow ◽  
Conservation Equations ◽  
Two Dimensional Flow ◽  
Flow Part ◽  
Orthogonal Curvilinear Coordinates

A method for computing three-dimensional duct flows is described. The procedure involves iteration between a marching integration of the conservation equations through the flow field and the solution of an elliptic pressure-correction equation. The conservation equations are written in orthogonal curvilinear coordinates. The solution procedure is illustrated by calculations of two-dimensional flow in an accelerating rectangular elbow with 90 deg of turning. An approach to calculating three-dimensional viscous flow, starting with the solution for two-dimensional inviscid flow is suggested. This approach is used in Part II which starts with the results of the present two-dimensional “inviscid” flow calculations.

Aerodynamic Throttling of a Two-Dimensional Flow by a Thick Jet

1976 ◽  
Vol 27 (3) ◽  
pp. 229-242 ◽  
Author(s):  
J B Stek ◽  
H Brandt
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Maximum Height ◽  
Pressure Measurements ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Air Jet ◽  
Two Dimensional Flow ◽  
Made In

SummaryThe velocity and pressure distributions in a flow generated by a thick air jet that throttles a confined airstream have been studied analytically and experimentally. Velocity and pressure measurements were made in a duct with a rectangular cross section of 102 mm height and 19 mm depth, through which air flowed at velocities ranging from 65 to 80 m/s. The airstream was throttled by a thick air jet having velocities ranging from 130 to 150 m/s that entered the mainstream at angles ranging from 60° to 135°. The jet-mainstream contour was found to be elliptical and agreement within six per cent was obtained between the theoretically and experimentally determined maximum height of the contour. Jet spreading was found to be linear. The theory permits determination of the velocity profile in the jet and gives velocities that deviate less than ten per cent from values obtained experimentally.

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