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.

A 2D Numerical Model for Simulation of Two-Dimensional Circular Dam-Break

2011 ◽  
Vol 130-134 ◽  
pp. 2993-2996
Author(s):  
Ming Qin Liu ◽  
Y.L. Liu
Keyword(s):  
Solution Procedure ◽  
Dam Break ◽  
Curvilinear Coordinates ◽  
Two Dimensional ◽  
Proposed Model ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Orthogonal Curvilinear Coordinates ◽  
Averaged Model ◽  
The Mathematical Model

The purpose of this paper is to present a 2D depth-averaged model under orthogonal curvilinear coordinates for simulating two-dimensional circular dam-break flows. The proposed model uses an orthogonal curvilinear coordinate system efficiently and accurately to simulate the flow field with irregular boundaries. As for the numerical solution procedure, The SIMPLEC solution procedure has been used for the transformed governing equations in the transformed domain. Practical application of the model is illustrated by an example, which demonstrates that the mathematical model can capture hydraulic discontinuities accurately such as steep fronts, hydraulic jump and drop, etc.

A Calculation Procedure for Three-Dimensional, Viscous, Compressible Duct Flow. Part II—Stagnation Pressure Losses in a Rectangular Elbow

1979 ◽  
Vol 101 (4) ◽  
pp. 423-428 ◽  
Author(s):  
John Moore ◽  
Joan G. Moore
Keyword(s):  
Three Dimensional ◽  
Inviscid Flow ◽  
Stagnation Pressure ◽  
Calculation Procedure ◽  
Duct Flow ◽  
Pressure Losses ◽  
Pressure Distributions ◽  
Starting Point ◽  
Flow Part ◽  
Good Agreement

Three-dimensional, turbulent flow is calculated in an elbow used by Stanitz for an experimental investigation of secondary flow. Calculated wall-static pressure distributions and distributions of stagnation-pressure loss, both spatial and as a function of mass-flow ratio, are in good agreement with Stanitz’ measurements, justifying the use of a relatively simple mixing-length viscosity model. The calculation procedure and the results of two-dimensional “inviscid” flow calculations used as the starting point for the present calculations are described in Part I of this paper. The computed flow field shows clearly the development of the passage vortices.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

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.

The Elliptic Solution of the Secondary Flow Problem

1983 ◽  
Vol 105 (3) ◽  
pp. 530-535 ◽  
Author(s):  
S. Abdallah ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Elliptic Solution ◽  
Dimensional Flow ◽  
Flow Vorticity ◽  
Dependent Variables ◽  
Two Dimensional Flow ◽  
Uniqueness Of The Solution

This paper presents the elliptic solution of the inviscid incompressible secondary flow in curved passages. The three-dimensional flow field is synthesized between 3 sets of orthogonal nonstream surfaces. The two-dimensional flow field on each set of surfaces is considered to be resulting from a source/sink distribution. The distribution and strength of these sources are dependent on the variation in the flow properties normal to the surfaces. The dependent variables in this formulation are the velocity components, the total pressure, and the main flow vorticity component. The governing equations in terms of these dependent variables are solved on each family of surfaces using the streamlike function formulation. A new mechanism is implemented to exchange information between the solutions on the three family surfaces, resulting into a unique solution. In addition, the boundary conditions for the resulting systems of equations are carefully chosen to insure the existence and uniqueness of the solution. The numerical results obtained for the rotational inviscid flow in a curved duct are discussed and compared with the available experimental data.

The aerodynamic theory of sails. I. Two-dimensional sails

1961 ◽  
Vol 261 (1306) ◽  
pp. 402-422 ◽  
Keyword(s):  
Lift Coefficient ◽  
Linear Equations ◽  
Three Dimensional ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Two Dimensional Flow ◽  
Linearized Theory ◽  
High Degree ◽  
Additional Equation

This paper deals with the preliminaries essential for any theoretical investigation of three-dimensional sails—namely, with the two-dimensional flow of inviscid incompressible fluid past an infinitely-long flexible inelastic membrane. If the distance between the luff and the leach of the two-dimensional sail is c , and if the length of the material of the sail between luff and leach is ( c + l ), then the problem is to determine the flow when the angle of incidence α between the chord of the sail and the wind, and the ratio l / c are both prescribed; especially, we need to know the shape of, the loading on, and the tension in, the sail. The aerodynamic theory follows the lines of the conventional linearized theory of rigid aerofoils; but in the case of a sail, there is an additional equation to be satisfied which ex­presses the static equilibrium of each element of the sail. The resulting fundamental integral equation—the sail equation—is consequently quite different from those of aerofoil theory, and it is not susceptible to established methods of solution. The most striking result is the theoretical possibility of more than one shape of sail for given values of α and l / c ; but there appears to be no difficulty in choosing the shape which occurs in reality. The simplest result for these realistic shapes is that the lift coefficient of a sail exceeds that of a rigid flat plate (for which l / c = 0) by an amount approximately equal to 0.636 ( l / c ) ½ . It seems very doubtful whether analytical solutions of the sail equation will be found, but a method is developed in this paper which comes to the next best thing; namely, an explicit expression, as a matrix quotient, which gives numerical values to a high degree of accuracy at so many chord-wise points. The method should have wide application to other types of linear equations.

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.

The Effect of a Wall Boundary Layer on Local Mass Transfer From a Cylinder in Crossflow

1984 ◽  
Vol 106 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. J. Goldstein ◽  
J. Karni
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Tunnel Wall ◽  
Wall Boundary Layer ◽  
Naphthalene Sublimation Technique ◽  
Displacement Thickness ◽  
Two Dimensional Flow

A naphthalene sublimation technique is used to determine the circumferential and longitudinal variations of mass transfer from a smooth circular cylinder in a crossflow of air. The effect of the three-dimensional secondary flows near the wall-attached ends of a cylinder is discussed. For a cylinder Reynolds number of 19000, local enhancement of the mass transfer over values in the center of the tunnel are observed up to a distance of 3.5 cylinder diameters from the tunnel wall. In a narrow span extending from the tunnel wall to about 0.066 cylinder diameters above it (about 0.75 of the mainstream boundary layer displacement thickness), increases of 90 to 700 percent over the two-dimensional flow mass transfer are measured on the front portion of the cylinder. Farther from the wall, local increases of up to 38 percent over the two-dimensional values are measured. In this region, increases of mass transfer in the rear portion of the cylinder, downstream of separation, are, in general, larger and cover a greater span than the increases in the front portion of the cylinder.

Calculations of Three-Dimensional, Viscous Flow and Wake Development in a Centrifugal Impeller

1981 ◽  
Vol 103 (2) ◽  
pp. 367-372 ◽  
Author(s):  
J. Moore ◽  
J. G. Moore
Keyword(s):  
Viscous Flow ◽  
Pressure Field ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Calculation Procedure ◽  
Wake Flow ◽  
Centrifugal Impeller ◽  
Duct Flow ◽  
Reduced Pressure ◽  
Flow Calculation

A partially-parabolic calculation procedure is used to calculate flow in a centrifugal impeller. This general-geometry, cascade-flow method is an extension of a duct-flow calculation procedure. The three-dimensional pressure field within the impeller is obtained by first performing a three-dimensional inviscid flow calculation and then adding a viscosity model and a viscous-wall boundary condition to allow calculation of the three-dimensional viscous flow. Wake flow, resulting from boundary layer accumulation in an adverse reduced-pressure gradient, causes blockage of the impeller passage and results in significant modifications of the pressure field. Calculated wake development and pressure distributions are compared with measurements.

Theoretical Aspects of Thrust Vector Control by Secondary Gas Injection in Rocket Nozzles

1968 ◽  
Vol 72 (686) ◽  
pp. 171-177 ◽  
Author(s):  
John H. Neilson ◽  
Alastair Gilchrist ◽  
Chee K. Lee
Keyword(s):  
Vector Control ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Side Force ◽  
Thrust Vector Control ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Thrust Vector ◽  
Secondary Injection

This work deals with theoretical aspects of thrust vector control in rocket nozzles by the injection of secondary gas into the supersonic region of the nozzle. The work is concerned mainly with two-dimensional flow, though some aspects of three-dimensional flow in axisymmetric nozzles are considered. The subject matter is divided into three parts. In Part I, the side force produced when a physical wedge is placed into the exit of a two-dimensional nozzle is considered. In Parts 2 and 3, the physical wedge is replaced by a wedge-shaped “dead water” region produced by the separation of the boundary layer upstream of a secondary injection port. The modifications which then have to be made to the theoretical relationships, given in Part 1, are enumerated. Theoretical relationships for side force, thrust augmentation and magnification parameter for two- and three-dimensional flow are given for secondary injection normal to the main nozzle axis. In addition, the advantages to be gained by secondary injection in an upstream direction are clearly illustrated. The theoretical results are compared with experimental work and a comparison is made with the theories of other workers.

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