Reynolds number

Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.

Abstract: Preface Conventions and notation 1. The physical properties of fluids 2. Kinematics of the flow field 3. Equations governing the motion of a fluid 4. Flow of a uniform incompressible viscous fluid 5. Flow at large Reynolds number: effects of viscosity 6. Irrotational flow theory and its applications 7. Flow of effectively inviscid liquid with vorticity Appendices.

Abstract: Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, flow through porous media, colloid science, aerosol and hydrosal technology, lubrication theory, blood flow, Brownian motion, geophysics, meteorology, and a host of other disciplines. This text provides a comprehensive and detailed account of the physical and mathematical principles underlying such phenomena, heretofore available only in the original literature.

Abstract: A new k -ϵ eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed in this paper. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints; the positivity of normal Reynolds stresses and the Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (i) rotating homogeneous shear flows; (ii) boundary-free shear flows including a mixing layer, planar and round jets; (iii) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (iv) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k -ϵ eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k -ϵ eddy viscosity model.

Abstract: The paper presents a new model of turbulence in which the local turbulent viscosity is determined from the solution of transport equations for the turbulence kinetic energy and the energy dissipation rate. The major component of this work has been the provision of a suitable form of the model for regions where the turbulence Reynolds number is low. The model has been applied to the prediction of wall boundary-layer flows in which streamwise accelerations are so severe that the boundary layer reverts partially towards laminar. In all cases, the predicted hydrodynamic and heat-transfer development of the boundary layers is in close agreement with the measured behaviour.