Potential flow in a semi-infinite channel with multiple sub-channels using the Schwarz–Christoffel transformation

Trevelyan, P. M. J.; Elliott, L.; Ingham, D.B.

doi:10.1016/s0045-7825(99)00299-6

Cited by 3 publications

(5 citation statements)

References 14 publications

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“…All the previous works determined these parameters using various integration methods along the real axis of the λ plane, together with some form of iterative procedure. Some examples of such methods are presented in [3,4,7,10,15,[16][17][18]. Milne-Thomson [15] gave analytic solution by using a hodograph method, Modi et al [10], Ali [3] and Ali and Gommah [4] have used conventional Schwarz-Christoffel transformation to map walls on a straight line.…”

Section: Determination Of Subsidiary Parametersmentioning

confidence: 99%

“…The most used iterative procedure is the Newton-Raphson method, with the Jacobian matrix approximated by a finite difference quotient matrix, as applied to branched channels by Hassenpfug [7]. Trevelyan et al [18] had used an alternative integration approach from that employed by Hassenpflug [7] in the iterative mathematical technique for determining the parameters involved in the Schwarz-Christoffel transformation Numerical solutions are also available by using standard programs SCPACK by Trefethen [20], or Algorithm 756 of MATLAB by Driscoll [21] who compute points in the physical plane by numerical integration of the Schwarz-Christoffel integral. In this research, the Algorithm 756 of MATLAB by Driscoll [21] is used to find the unknown parameters.…”

Section: Determination Of Subsidiary Parametersmentioning

confidence: 99%

“…Thereafter, the values of K 2 , K 3 are obtained from Eqns. (14) and (18) respectively. Then the relative depths X 1 , X 2 and X 3 are found from Eqns.…”

Section: Discharge and Flow Depthmentioning

confidence: 99%

See 2 more Smart Citations

Numerical and Experimental Analysis of Dividing Flow in Short Open Channel Tributaries

Ali

Abozeid

A.M

et al. 2008

JES. Journal of Engineering Sciences

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Dividing flow in open channel junction is of interest in environmental and hydraulic engineering. It occurs in many hydraulic structures ranging from wastewater treatment facilities to fish passage conveyance structures, irrigation and drainage canals and natural river system. In this research, Schwarz-Christoffel transformation and principle of energy are used to predict the flow rates, the flow depths and values of Froude number in the tributary channels of rectangular open channel junction with three tributary channels. Also, an experimental program is performed to verify the numerical results of the theoretical solutions. The difficulty of a theoretical study of the dividing flow in an open channel due to the flow separation, recirculation regions and possibility of formation of hydraulic jump makes the complete numerical analysis of the problem impossible. However, in this study, with some particular assumptions to the problem, by adopting the conformal mapping technique (Schwarz-Christoffel transformation theory) and by applying the principle of conservation of energy, the flow pattern at a rectangular junction with three tributary channels is simulated; the numerical model is programmed on the computer with MATLAB Version 6.0.0.88 and the flow characteristics are evaluated. The verification of the results of the numerical model shows a will agreement between these results and those from the experimental model. The results revealed that: 1) Froude number in the main channel has negligible influence on the flow rates in the branches. 2) Flow characteristics in the main channel extension or in the branches depend largely on the geometrical dimensions of the junction. 3) The relative depths in the tributary channels independent of the junction geometry.

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Section: Determination Of Subsidiary Parametersmentioning

confidence: 99%

Section: Determination Of Subsidiary Parametersmentioning

confidence: 99%

See 1 more Smart Citation

Numerical and Experimental Analysis of Dividing Flow in Short Open Channel Tributaries

Ali

Abozeid

A.M

et al. 2008

JES. Journal of Engineering Sciences

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“…Two-dimensional flows can be modelled by assuming the flow to be inviscid and irrotational [3,[6][7][8]. Given these assumptions, the velocity field can be calculated using conformal maps.…”

Section: Introductionmentioning

confidence: 99%

Understanding heat transfer in 2D channel flows including recirculation

Dirkse

Loon

Stigter

et al. 2007

International Journal of Thermal Sciences

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“…Conformal mapping is one of the most powerful tools of complex analysis, and has been applied in many mathematical and physical fields, including those dealing with transmission lines12345, integrated circuit components67891011, electrostatic actuators1213141516, transformation optics1718192021, channel flows2223, and rough surfaces242526. Conformal mapping transforms a structure with a complex shape into a geometry that makes the problem more easily solvable.…”

mentioning

confidence: 99%

Conformal mapping for multiple terminals

Wang

et al. 2016

Sci Rep

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Conformal mapping is an important mathematical tool that can be used to solve various physical and engineering problems in many fields, including electrostatics, fluid mechanics, classical mechanics, and transformation optics. It is an accurate and convenient way to solve problems involving two terminals. However, when faced with problems involving three or more terminals, which are more common in practical applications, existing conformal mapping methods apply assumptions or approximations. A general exact method does not exist for a structure with an arbitrary number of terminals. This study presents a conformal mapping method for multiple terminals. Through an accurate analysis of boundary conditions, additional terminals or boundaries are folded into the inner part of a mapped region. The method is applied to several typical situations, and the calculation process is described for two examples of an electrostatic actuator with three electrodes and of a light beam splitter with three ports. Compared with previously reported results, the solutions for the two examples based on our method are more precise and general. The proposed method is helpful in promoting the application of conformal mapping in analysis of practical problems.

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Potential flow in a semi-infinite channel with multiple sub-channels using the Schwarz–Christoffel transformation

Cited by 3 publications

References 14 publications

Numerical and Experimental Analysis of Dividing Flow in Short Open Channel Tributaries

Numerical and Experimental Analysis of Dividing Flow in Short Open Channel Tributaries

Understanding heat transfer in 2D channel flows including recirculation

Conformal mapping for multiple terminals

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