scholarly journals General Curved Surface Fitting and Calculation of Flow Along Arbitrarily Twisted Stream Surface

1985 ◽  
Author(s):  
Wu Wenquan ◽  
Yu Haoyu
Keyword(s):  
Stream Function ◽  
Engineering Application ◽  
Small Deformation ◽  
Surface Fitting ◽  
Curved Surface ◽  
Coordinate Surface ◽  
Stream Surface ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Stream Lines

This paper consists of two parts. (1) General curved surface fitting and grid refining. A method of fitting a set of given discrete points on several stream lines to give a smooth and arbitraily twisted stream surface was developed. Based upon the small deformation theory for thin plate, the Kirchhoff’s Equation was solved and twofold transformations were incorporated. The first step is the transformation from physical surface into computational surface and the second is affine transformation. The accuracy of the result is about 0.004% and the CPU time needed is reasonable for engineering application. Then the refined computational grid and the calculation for the geometrical quantities of the grid are carried out on the fitted surface. (2) Calculation of the flow along the fitted stream surface. Employing non-orthogonal curvilinear coordinate system, the fitted stream surface is selected as a coordinate surface, so that there are only two velocity components even when the stream surface is arbitrarily twisted, and it is very convenient to define the stream function. The general equation for the quasi-linear stream function governing the flow along the fitted stream surface was employed. This was solved with the method of direct decomposition of matrix. The numerical examples are also included in this paper. The present method can be used for S1 and S2 stream surfaces and other engineering calculations.

A Method for Calculating Axial Turbomachine End Wall Turbulent Boundary Layers

1989 ◽  
Author(s):  
Kang Shun ◽  
Liu Fengjun ◽  
Wang Zhongqi
Keyword(s):  
Boundary Layer ◽  
Iterative Solution ◽  
Stream Surface ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Layer Flow ◽  
End Wall ◽  
Differential And Integral Equations

Based on two families of relative stream-surface theory, the differential and integral equations of the endwall boundary layer in the S2 stream surface (hub to tip stream surface) have been established in the orthogonal curvilinear coordinate system in the present paper. By directly associating the blade force defects with the warping of S2 stream surface near the endwall, we have proposed a new method for predicting the endwall boundary layer. This method can be used to conduct the interactions of the end wall boundary layer with the S2 stream surface potentisl flow, in order to get the iterative solution of the end wall boundary layer flow with the potential flow in S2 stream surface. The predicted results have shown that the present method is acceptable.

A Discussion of the Mean S2 Stream Surfaces Applied to Quasi-Three-Dimensional Calculation Programs for Turbomachinery Design

1987 ◽  
Author(s):  
Zhu Xujin ◽  
Wang Zhongqi
Keyword(s):  
Three Dimensional ◽  
Inviscid Flow ◽  
Curvilinear Coordinate System ◽  
Governing Equations ◽  
Flow Properties ◽  
Stream Surface ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
The Mean ◽  
Turbomachinery Design

This paper attempts to clarify the various definitions of the “S2m” surfaces applied to quasi-3-d inviscid flow computation in turbomachinery by adopting an extended concept of true S2 stream surface (PAG S2) in the discussion. It is indicated that PAG S2 gives a more universal and applicable model to solve the pitch -averaged flow properties through turbine blade passages, especially when a non-orthogonal curvilinear coordinate system is introduced into its governing equations in the present paper.

scholarly journals Implementation of an Approximate Conformal UPML in 2-D DGTD

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Linqian Li ◽  
Bing Wei ◽  
Qian Yang ◽  
Debiao Ge
Keyword(s):  
Good Accuracy ◽  
Computation Time ◽  
Elliptic Cylinder ◽  
Auxiliary Equation ◽  
Coordinate Systems ◽  
Absorbing Boundary ◽  
Computational Region ◽  
Curvilinear Coordinate ◽  
Orthogonal Curvilinear Coordinate System ◽  
Absorbing Layer

Using the numerical discrete technique with unstructured grids, conformal perfectly matched layer (PML) absorbing boundary in the discontinuous Galerkin time-domain (DGTD) can be set flexibly so as to save lots of computing resources. Based on the DGTD equations in an orthogonal curvilinear coordinate system, the processes of parameter transformation for 2-D UPML between the coordinate systems of elliptical and Cartesian are given; and the expressions of transition matrix are derived. The calculation scheme of conductivity distribution in elliptic cylinder absorbing layer is given, and the calculation coefficient of DGTD in elliptic UPML is calculated. Furthermore, the 2-D iterative formulas of DGTD and that of auxiliary equation in the elliptical cylinder UPML are derived; the conformal UPML calculation in DGTD is realized. Numerical results show that very good accuracy and computational efficiency are achieved by using the method in this paper. Compared to the rectangular computational region, both the memory and computation time of conformal UPML absorbing boundary are reduced by more than 20%.

Mass transport in water waves over an elastic bed

1995 ◽  
Vol 450 (1939) ◽  
pp. 371-390 ◽  
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Mass Transport ◽  
Water Waves ◽  
Viscous Boundary Layer ◽  
Curvilinear Coordinate ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Orthogonal Curvilinear Coordinate System ◽  
Viscous Boundary

The mass transport velocity in water waves propagating over an elastic bed is investigated. Water is assumed to be incompressible and slightly viscous. The elastic bed is also incompressible and satisfies the Hooke’s law. For a small amplitude progressive wave perturbation solutions via a boundary-layer approach are obtained. Because the wave amplitude is usually larger than the viscous boundary layer thickness and because the free surface and the interface between water and the elastic bed are moving, an orthogonal curvilinear coordinate system (Longuet-Higgins 1953) is used in the analysis of free surface and interfacial boundary layers so that boundary conditions can be applied on the actual moving surfaces. Analytical solutions for the mass transport velocity inside the boundary layer adjacent to the elastic seabed and in the core region of the water column are obtained. The mass transport velocity above a soft elastic bed could be twice of that over a rigid bed in the shallow water.

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.

scholarly journals Study on Curved Surface Fitting of Countersink Based on Point Cloud

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 106464-106470
Author(s):  
Jiming Sa ◽  
Hanwen Gu ◽  
Yilun An ◽  
Yijie Luo ◽  
Zhushanying Zhang
Keyword(s):  
Point Cloud ◽  
Surface Fitting ◽  
Curved Surface

scholarly journals A Stream Function Relaxation Method for Solving Transonic S1 Stream Surface With Pre-Determination of the Density

1985 ◽  
Author(s):  
Ge Manchu
Keyword(s):  
Difference Scheme ◽  
Stream Function ◽  
Flow Theory ◽  
Relaxation Method ◽  
Curvilinear Coordinates ◽  
Transonic Flows ◽  
Stream Surface ◽  
Numerical Examples ◽  
Orthogonal Curvilinear Coordinates

On the basis of Prof. Wu’s 3-D flow theory (ref.1, 2, 3, 4, 5), a general streamfunction equation in non-orthogonal curvilinear coordinates is developed. The equation can be used to calculate subsonic or transonic flows on S1 or S2 stream surfaces of turbomachinery. In this paper streamlines coordinates and a mixed difference scheme are adopted in solving the stream function equation. A procedure for pre-determination of the density is developed and used to determine the unique-value of density from the known value of the stream function. Numerical examples are given.

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