Upstream Separation Point for an Internal Corner in a Two-Dimensional Channel Flow

1963 ◽  
Vol 30 (4) ◽  
pp. 505-508 ◽  
Author(s):  
J. F. Barrows
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Turbulent Boundary Layer ◽  
Channel Flow ◽  
Series Solution ◽  
Separation Point ◽  
Two Dimensional ◽  
The Mathematical Model

A solution is presented for predicting the upstream separation point in a two-dimensional channel flow in which an obstacle is present. The paper considers only the separation of a laminar boundary layer but could also be applied to the turbulent boundary-layer case. The mathematical model considers free-streamline theory to get the pressure distribution ahead of separation. Go¨rtler’s series solution and Witting’s finite-difference method are then used to predict separation. The theory is checked experimentally.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

Simulation of Hydraulic Pipeline Pressure Transients Accompanying Cavitation and Gas Bubbles Using Matlab/Simulink

2006 ◽  
Author(s):  
Jiang Dan ◽  
Songjing Li
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Gas Bubbles ◽  
Simulation Method ◽  
Low Pressure ◽  
Matlab Simulink ◽  
Pressure Transients ◽  
The Mathematical Model

In order to predict pressure transients accompanying cavitation and gas bubbles in hydraulic pipeline operating at low pressure, a mathematical model and a simulation method are studied. The mathematical model is based on the two basic equations of motion and continuity. The growing and collapsing of cavitation and gas bubbles accompanying pressure pulsations are modelled to calculate the volumes of cavitation and gas bubbles. The pipeline dynamic friction model is introduced. Meanwhile, a simulation method, using finite difference method and Matlab/Simulink platform, is developed to handle the prediction of pressure transients. Finally an example of fluid transients inside hydraulic pipeline is simulated after a downstream valve is closed rapidly. Simulation results show that, for a certain example pipeline, the mathematical model can handle the prediction of pressure transients accompanying cavitation and gas bubbles in low pressure pipeline. The use of combining finite difference method with Matlab/Simulink platform provides a relatively simple and effective tool to understand the nature of pressure transients accompanying cavitation and gas bubbles.

A Finite-Difference Method for Calculating Compressible Laminar and Turbulent Boundary Layers

1970 ◽  
Vol 92 (3) ◽  
pp. 523-535 ◽  
Author(s):  
T. Cebeci ◽  
A. M. O. Smith
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Turbulent Boundary Layer ◽  
Turbulent Flows ◽  
Difference Method ◽  
Eddy Viscosity ◽  
Energy Equation ◽  
Composite Layer ◽  
Computation Time

This paper presents a finite-difference method for solving laminar and turbulent-boundary-layer equations for incompressible and compressible flows about two-dimensional and axisymmetric bodies and contains a thorough evaluation of its accuracy and computation-time characteristics. The Reynolds shear-stress term is eliminated by an eddy-viscosity concept, and the time mean of the product of fluctuating velocity and temperature appearing in the energy equation is eliminated by an eddy-conductivity concept. The turbulent boundary layer is regarded as a composite layer consisting of inner and outer regions, for which separate expressions for eddy viscosity are used. The eddy-conductivity term is lumped into a “turbulent” Prandtl number that is currently assumed to be constant. The method has been programed on the IBM 360/65, and its accuracy has been investigated for a large number of flows by comparing the computed solutions with the solutions obtained by analytical methods, as well as with solutions obtained by other numerical methods. On the basis of these comparisons, it can be said that the present method is quite accurate and satisfactory for most laminar and turbulent flows. The computation time is also quite small. In general, a typical flow, either laminar or turbulent, consists of about twenty x-stations. The computation time per station is about one second for an incompressible laminar flow and about two to three seconds for an incompressible turbulent flow on the IBM 360/65. Solution of energy equation in either laminar or turbulent flows increases the computation time about one second per station.

The Calculation of Ship Wave in Shallow Water by Finite Difference Method

2013 ◽  
Vol 409-410 ◽  
pp. 1461-1464
Author(s):  
Deng Hui ◽  
Zhi Hong Zhang ◽  
Jian Nong Gu
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Shallow Water ◽  
Difference Method ◽  
Integral Transform ◽  
Fourier Integral ◽  
Transform Method ◽  
The Mathematical Model ◽  
Supercritical Speed

Based on the shallow water wave potential flow theory and slender ship assumption, the mathematical model is established for calculating wave caused by ship moving at supercritical speed. The wave pattern caused by ship moving at supercritical speed in shallow water was calculated by using the finite difference method. The effects of channel wall were analyzed. The computed results were compared with the ones calculated by Fourier integral transform method and experiment. A good agreement exists between the calculated with experimental results. The mathematical model and the calculation method were validated.

scholarly journals NON-UNIFORM SUSPENDED SEDIMENTS UNDER WAVES

1988 ◽  
Vol 1 (21) ◽  
pp. 84
Author(s):  
Aronne Armanini ◽  
Piero Ruol
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mathematical Model ◽  
Mathematical Formulation ◽  
Suspended Sediments ◽  
Two Dimensional ◽  
Different Diameters ◽  
Wave Boundary ◽  
The Mathematical Model ◽  
Dimensional Wave

An original mathematical formulation for suspended sediments in a two-dimensional wave boundary layer is presented. The model accounts for non-immediate adaptation of sediments to the hydrodinamic conditions, and allows to include the effect of sorting of the different diameters considered. The mathematical model is numerically solved through a finite difference scheme. It is suitable that results compare favourably with experimental data by Staub et alii.

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