Library Subscription: Guest
ICHMT DL Home Current Year Archives Executive Committee International Centre for Heat and Mass Transfer

On analogy between transition to turbulence in fluids and plasticity in solids

DOI: 10.1615/ICHMT.2006.TurbulHeatMassTransf.370
pages 221-224

S. Ananiev
Institute of Aerospace Engineering, Technische Universitat Dresden, Mommsenstr. 13, 01069 Dresden, Germany

Abstract

The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in solids is explored. It allows an extension of the Navier-Stokes equations making the simple shear flows unstable.
Following von Mises [4], the existence of maximal allowed shear stress or "yield stress" in fluid is assumed. After the actual stresses have reached this value, a new physical mechanism will be activated attempting to reduce them. This mechanism results in a pressure-like force, which has to be added to the Navier-Stokes equations. The yield stress itself is a material constant, which does not depend on the Reynolds number of particular flow. It will be shown how to estimate its value from experimental data.
To demonstrate how the character of flow changes if the additional force is taken into account, an unsteady flow in a 2D nozzle is presented. The momentum source was introduced in the Navier-Stokes equations through the user-defined function's interface offered by Fluent [6]. The initial data and the results of simulation are summarized in appendix.

ICHMT Digital Library

Bow shocks on a jet-like solid body shape. Thermal Sciences 2004, 2004. Pulsed, supersonic fuel jets - their characteristics and potential for improved diesel engine injection. PULSED, SUPERSONIC FUEL JETS - THEIR CHARACTERISTICS AND POTENTIAL FOR IMPROVED DIESEL ENGINE INJECTION
View of engine compartment components (left). Plots of temperature distributions in centreplane, forward of engine (right). CHT-04 - Advances in Computational Heat Transfer III, 2004. Devel... DEVELOPMENT AND CURRENT STATUS OF INDUSTRIAL THERMOFLUIDS CFD ANALYSIS
Pratt & Whitney's F-135 Joint Strike Fighter Engine under test in Florida is a 3600F class jet engine. TURBINE-09, 2009. Turbine airfoil leading edge stagnation aerodynamics and heat transfe... TURBINE AIRFOIL LEADING EDGE STAGNATION AERODYNAMICS AND HEAT TRANSFER - A REVIEW
Refractive index reconstructed field. (a) Second iteration. (b) Fourth iteration. Radiative Transfer - VI, 2010. Theoretical development for refractive index reconstruction from a radiative ... THEORETICAL DEVELOPMENT FOR REFRACTIVE INDEX RECONSTRUCTION FROM A RADIATIVE TRANSFER EQUATION-BASED ALGORITHM
Two inclusion test, four collimated sources. Radiative Transfer - VI, 2010. New developments in frequency domain optical tomography. Part II. Application with a L-BFGS associated to an inexa... NEW DEVELOPMENTS IN FREQUENCY DOMAIN OPTICAL TOMOGRAPHY. PART II. APPLICATION WITH A L-BFGS ASSOCIATED TO AN INEXACT LINE SEARCH