Application of the series truncation method to two-dimensional internal flows

2005 ◽  
pp. 138-143 ◽  
Author(s):  
S. C. R. Dennis
Keyword(s):  
Two Dimensional ◽  
Internal Flows ◽  
Truncation Method ◽  
Series Truncation Method

scholarly journals The Two-Dimensional Heat Transfer Analysis in Arrayed Fins with the Thermal Dissipation Substrate

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Hai-Ping Hu
Keyword(s):  
Heat Transfer ◽  
Thermal Dissipation ◽  
Heat Transfer Analysis ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Governing Equations ◽  
Point Matching ◽  
Truncation Method ◽  
Laplace Equations ◽  
Series Truncation Method

The aim of the present study is to investigate the two-dimensional heat transfer analysis in arrayed fins with thermal dissipation substrate. The governing equations for the fins and the substrate are expressed with Laplace equations, and the boundary conditions around the fins and substrate are Robin conditions. The present investigation first aims to provide a solution with regard to the geometry models by a series truncation method. Then the research will compare the results of the series truncation method with the point-matching method. Furthermore, the present study will also discuss the effects of dimension and Biot number of the fins on local dimensionless temperature, mean temperature, and heat transfer rate.

Two-Dimensional Miter-Bend Flow

1971 ◽  
Vol 93 (3) ◽  
pp. 433-443 ◽  
Author(s):  
G. Heskestad
Keyword(s):  
Reynolds Number ◽  
Constant Width ◽  
Outer Wall ◽  
Two Dimensional ◽  
Mean Flow ◽  
Internal Flows ◽  
Concave Corner ◽  
Reynolds Number Effects ◽  
Bend Flow ◽  
The Mean

Measurements have been made of the mean flow in a two-dimensional, constant-width, ninety-degree miter bend and compared with predictions of available free-streamline theories. Agreement is quite favorable, especially with a model incorporating separation ahead of the concave corner. Reynolds number effects observed in real flows are argued to be associated with changes in the location of the outer-wall separation point. Requirements for relevancy of free-streamline models of internal flows separating at a salient edge are suggested and confirmed for cases examined.

Time-Split Inflow Boundary Treatment

1985 ◽  
Author(s):  
Siu Shing Tong
Keyword(s):  
Three Dimensional ◽  
Internal Flow ◽  
Leading Edge ◽  
Two Dimensional ◽  
Governing Equations ◽  
Internal Flows ◽  
One Dimensional ◽  
Boundary Treatment

This paper describes a new non-reflective inflow treatment for viscous and inviscid internal flow calculations. The method approximates the multi-dimensional governing equations at the inflow boundary in a series of one-dimensional split equations. This treatment allows the artificial inflow boundary to be brought in just in front of the leading edge, while allowing upstream running waves to penetrate without significant reflection. Calculation examples of two dimensional inviscid internal flows are presented. Extension of the method to three-dimensional problems is also discussed.

Numerical Investigation of Transonic Compressor Rotor Flow Using an Implicit 3D Flow Solver With One-Equation Spalart-Allmaras Turbulence Model

2001 ◽  
Author(s):  
Fangfei Ning ◽  
L. Xu
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Model Equation ◽  
Stokes Equations ◽  
Turbulence Closure ◽  
Two Dimensional ◽  
Mean Flow ◽  
Internal Flows ◽  
Flow Equations ◽  
Transonic Compressor

A CFD code for three-dimensional viscous flows, in particular for those in turbomachinery, has been developed based on Favre-averaged compressible Navier-Stokes equations and one-equation Spalart-Allmaras turbulence closure. The model equation of Spalart-Allmaras turbulence closure is converted into conservative form and discretized in the same manner as that for mean flow equations. A two-dimensional transonic diffuser flow and a two-dimensional transonic nozzle flow which feature pressure-gradient induced separation and shock wave/boundary layer interaction respectively are used to validate the code and application of the Spalart-Allmaras model (hereafter the S-A model) in internal flows. It is shown that the S-A model can give fairly good results compared to the experimental data. Some modifications of model equation are introduced for improving the grid insensitivity of the turbulence model. To validate the applicability of the code to the complex flows in transonic turbomachines, flows through two transonic compressor rotors, NASA Rotors 67 and 37 are calculated, and numerical results are compared with the well documented experimental data. The calculated results agree reasonably well with the experiments, and as expected, the S-A model, which is primarily developed for external flows, can also be effectively applied to internal flows. Discrepancies between the experimental data and calculations and the possible causes are also discussed.

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