Engineering data on flow of fluids in pipes and heat transmission.

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NOISE GENERATED BY CAVITATION IN ORIFICE-PLATES WITH SOME GASEOUS EFFECTS.

An experimental investigation of the noise generated by cavitation in turbulent shear flows produced by confined sharp-edge orifice-plates is reported. The acoustic source strength of cavitation was determined by means of reciprocity type measurements. Experimentally determined scaling parameters are applied to a model to prototype scaling formula derived from dimensional analysis. The proposed formula is checked experimentally. Comparative photographic observations of the cavitation patterns for two different values of gas content are presented. The observed sound reduction, that occurs when supersaturated conditions exist downstream the orifice-plates, is explained by the effects of gas diffusion into the cavitation bubbles, and by simple acoustic attenuation.

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

The Inertio-Elastic Planar Entry Flow of Low-Viscosity Elastic Fluids in Micro-fabricated Geometries

The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through microfabricated planar abrupt contraction-expansions is investigated. The contraction geometries are fabricated from a high-resolution chrome mask and cross-linked PDMS gels using the tools of soft-lithography. The small length scales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. The dimensionless extra pressure drop across the contraction increases by more than 200% and is accompanied by significant upstream vortex growth. Streak photography and videomicroscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.03 ≤ Re ≤ 44) associated with these high Deborah number (0 ≤ De ≤ 600) microfluidic flows results in the exploration of new regions of the Re-De parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in microfluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = De/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

Laminar forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumption used in this work is a laminar flow of a power flow inside elliptical tube, under a boundary condition of first kind with constant physical properties and negligible axial heat diffusion (high Peclet number). To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number and the average Nusselt number for various cross-section aspect ratios. (C) 2006 Elsevier. SAS. All rights reserved.

Irrotational flow of frictionless fluids : mostly of invariable density /

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Bibliography on flow of compressible fluids,

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Flow of Complex Fluids in Geological Fractures

In this study, the lubrication theory is used to model flow in geological fractures and analyse the compound effect of medium heterogeneity and complex fluid rheology. Such studies are warranted as the Newtonian rheology is adopted in most numerical models because of its ease of use, despite non-Newtonian fluids being ubiquitous in subsurface applications. Past studies on Newtonian and non-Newtonian flow in single rock fractures are summarized in Chapter 1. Chapter 2 presents analytical and semi-analytical conceptual models for flow of a shear-thinning fluid in rock fractures having a simplified geometry, providing a first insight on their permeability. in Chapter 3, a lubrication-based 2-D numerical model is first implemented to solve flow of an Ellis fluid in rough fractures; the finite-volumes model developed is more computationally effective than conducting full 3-D simulations, and introduces an acceptable approximation as long as the flow is laminar and the fracture walls relatively smooth. The compound effect of shear-thinning fluid nature and fracture heterogeneity promotes flow localization, which in turn affects the performance of industrial activities and remediation techniques. In Chapter 4, a Monte Carlo framework is adopted to produce multiple realizations of synthetic fractures, and analyze their ensemble statistics pertaining flow for a variety of real non-Newtonian fluids; the Newtonian case is used as a benchmark. In Chapter 5 and Chapter 6, a conceptual model of the hydro-mechanical aspects of backflow occurring in the last phase of hydraulic fracturing is proposed and experimentally validated, quantifying the effects of the relaxation induced by the flow.

Forced convection to laminar flow of liquid egg yolk in circular and annular ducts

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.

An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the finger mobility, which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.

FORCED CONVECTION TO LAMINAR FLOW OF LIQUID EGG YOLK IN CIRCULAR AND ANNULAR DUCTS

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.