A Small Eddy Correction Method for a 3D Navier–Stokes-Type System of Equations Related to the Primitive Equations of the Ocean

2007 ◽  
Vol 45 (5) ◽  
pp. 1843-1870 ◽  
Author(s):  
T. Tachim Medjo
Keyword(s):  
Type System ◽  
Correction Method ◽  
Primitive Equations ◽  
Navier Stokes ◽  
System Of Equations ◽  
Small Eddy

Measurement and Calculation of Nozzle Guide Vane End Wall Heat Transfer

1998 ◽  
Author(s):  
Neil W. Harvey ◽  
Martin G. Rose ◽  
John Coupland ◽  
Terry Jones
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Guide Vane ◽  
Correction Method ◽  
Navier Stokes ◽  
Design Data ◽  
Navier Stokes Equations ◽  
Wall Functions ◽  
Transfer Rates ◽  
Nozzle Guide

A 3-D steady viscous finite volume pressure correction method for the solution of the Reynolds averaged Navier-Stokes equations has been used to calculate the heat transfer rates on the end walls of a modern High Pressure Turbine first stage stator. Surface heat transfer rates have been calculated at three conditions and compared with measurements made on a model of the vane tested in annular cascade in the Isentropic Light Piston Facility at DERA, Pyestock. The NGV Mach numbers, Reynolds numbers and geometry are fully representative of engine conditions. Design condition data has previously been presented by Harvey and Jones (1990). Off-design data is presented here for the first time. In the areas of highest heat transfer the calculated heat transfer rates are shown to be within 20% of the measured values at all three conditions. Particular emphasis is placed on the use of wall functions in the calculations with which relatively coarse grids (of around 140,000 nodes) can be used to keep computational run times sufficiently low for engine design purposes.

scholarly journals On a mixed problem for the parabolic Lamé type operator

2015 ◽  
Vol 23 (6) ◽  
Author(s):  
Roman Puzyrev ◽  
Alexander Shlapunov
Keyword(s):  
Stokes Equations ◽  
Type System ◽  
Type Operator ◽  
Navier Stokes ◽  
Cylindrical Domain ◽  
Smooth Functions ◽  
Navier Stokes Equations ◽  
Solvability Conditions ◽  
Ill Posed ◽  
Well Posed

AbstractWe consider a boundary value problem for a Lamé type operator, which corresponds to a linearisation of the Navier–Stokes' equations for compressible flow of Newtonian fluids in the case where pressure is known. It consists of recovering a vector function, satisfying the parabolic Lamé type system in a cylindrical domain, via its values and the values of the boundary stress tensor on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding Hölder spaces; besides, additional initial data do not turn the problem to a well-posed one. Using the integral representation's method we obtain a uniqueness theorem and solvability conditions for the problem. We also describe conditions, providing dense solvability of the problem.

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