A new skin friction balance and selected measurements

A new skin friction balance with moving belt has been developed for measurement of the surface shear stress component in the direction of belt motion. The device is described in this paper with typical measurement results. This instrument is symmetric in design with small moving mass and negligible internal friction. It is 3.8 cm high, 3.8 cm long and 2.1 cm wide, with the sensing surface 0.7 cm wide and 1.5 cm long, and it can be made in various sizes. The unique design of this instrument has reduced some of the errors associated with conventional floating-element balances. The instrument can use various sensing systems and the ouput signal is a linear function of the wall shear stress. Measurements show good agreement with data obtained by the floating element balances and flat plate prediction techniques. Dynamic measurements have been made in a limited range. The overall uncertainty of measurement is estimated to be ±2%.     

Turbulent flow of non-Newtonian substances

Summary A unique shear stress-shear rate relationship exists for laminar flow of any time independent substance in a tube, whereas this is not the case for turbulent flow. In order to obtain a unique relationship for turbulent flow, a new approach based on the elementary theoretical interpretation of experimental data is adopted in the present paper. In particular, wall shear stress is found to be a unique function of a new turbulent pseudo shear rate term. In this relationship therè are two parameters which characterize a given substance — the limiting viscosity at high shear rateµ _m and a factor _m which takes into account modification of turbulent structure by the non-Newtonian properties. Both of these parameters must be determined experimentally. Methods of predicting pressure gradients and of scaling up are outlined. In applying the approach to suspensions in which the solid phase has a density greater than that of the liquid medium, it may be important to determine the increment in shear stress equivalent to the energy required to maintain the solid particles in suspension.The validity of this approach is confirmed by data for the flow of a variety of substances including kaolin suspensions and Carbopol solutions in tubes ranging in diameter from 1.5 to 20 mm. Nomenclature C volume fraction solid in suspension - D tube diameter - f Darcy-Weisbach friction factor - g gravitational acceleration - K _s proportionality constant defined by eq. [10] - L length of tube - P pressure - Re Reynolds number - t exponent defined by eq. [1] - V mean velocity - V ^* volume of particles in pipe lengthL - W settling velocity of particles - _m factor defined by eq. [1] - shear rate - turbulent pseudo shear rate defined by eqs. [8] and [9] - _w wall shear stress - ( _w) _s increment in wall shear stress due to presence of settling particles - µ _m limiting viscosity at high rate of shear - ₁ density of carrier liquid - _m density of mixture - _s density of solid Professor of Chemical Engineering, University of Toronto and scientific advisor to Worthington (Canada) Ltd.With 8 figures     

The theory of dispersion of chemically active solutes in a rectilinear flow field

We report a procedure for the construction of the dispersion coefficients which define the dispersion approximation to the transverse average of the solution of the scalar convective diffusion equation; the procedure enjoys a generalization to the vector convective diffusion equation. We exhibit the full time dependence of the dispersion coefficients in any transverse average and identify a mathematically preferred transverse average for the dispersion of chemically active solute.     

Pulsatile flow in a tube with wall injection and suction

This paper studies similarity solutions for pulsatile flow in a tube with wall injection and suction. The Navier-Stokes equations are reduced to a system of three ordinary differential equations. Two of the equations represent the effects of suction and injection on the steady flow while the third represents the effects of suction and injection on pulsatile flow. Since the equations for steady flow have been studied previously, the analysis centers on the third equation. This equation is solved numerically and by the method of matched asymptotic expansions. The exact numerical solutions compare well with the asymptotic solutions.The effects of suction and injection on pulsatile flow are the following: a) Small values of suction can cause a resonance-like effect for low frequency pulsatile flow. b) The annular effect still occurs but for large injection or suction the frequency at which this effect becomes dominant depends on the cross-flow Reynolds number. c) The maximum shear stress at the wall is decreased by injection, but may be increased or decreased by suction.Nomenclature a radius of the tube - a ₀ ² i ² - A₀, B₀, C₀, D₀, E₀ constant coefficients appearing in the expression for pressure - b a non-dimensionalized length - b ₀ ² i ^{2 2} - b _k complex coefficients of a power series - B - C ₁, C ₂, D complex constants - d - D _1,2 - f() F(a ^1/2)/aV - f ₀,f ₁,... functions of order one used in asymptotic expansions of f() - F(r) rv _r - g() - G(r) a steady component of velocity in axial direction - h() 4/C₀ a ² H(a ^1/2) - h ₀,h ₁,h ₂,...;l ₀,l ₁,l ₂,... functions of order one used in asymptotic expansions for h() in outer regions - H(r) complex valued function giving unsteady component of velocity - H ₀, H ₁, H ₂, ... K ₀, K ₁, K ₂, ...; L ₀, L ₁, L ₂, ... functions of order one used in asymptotic expansions for h() in inner regions - i - J ₀, J ₁, Y ₀, Y ₁ Bessel functions of first and second kind - k - K Rk/2b ² - O order symbol - p pressure - p ₁(z, t) arbitrary function related to pressure - r radial coordinate - r ₀ (1+16 ^{4 4})^1/4 - R Va/, the crossflow Reynolds number - t time - u() G(r)/V - v _r radial velocity - v _z axial velocity - V constant velocity at which fluid is injected or extracted - z axial coordinate - ² a ²/4 - 4.196 - small parameter; =–2/R (Sect. 4); =–R/2 (Sect. 5); =2/R(Sect. 6) - r ²/a ² - * 0.262 - Arctan (4 ^{2 2}) - , inner variables - kinematic viscosity - b - * zero of g() - density - (r, t) arbitrary function related to axial velocity - frequency     

Recoil in macromolecular solutions according to rigid dumbbell kinetic theory

A macromolecular solution is represented by the simple model of rigid dumbbells suspended in a Newtonian fluid with Brownian motion included. Hydrodynamic interaction is not taken into account. It is found that for this model there will be recoil after the cessation of steady shearing flow. The ultimate shear recovery S _∞ is developed as a power series in κ^?, the shear rate prior to the cessation of the steady shear flow: $$S_\infty = (\theta _0 /2\eta _0 ) \kappa ^\user1{ - } + O(\kappa ^\user1{ - } )^3$$ where η₀ and θ₀ values of the viscosity and primary normal stress functions respectively at zero-shear rate. The coefficient of the term in (κ^?)³ is calculated. In addition, the behavior of the normal stresses during the recoil process is found; during recoil τ₂₂?τ₃₃ has the opposite sign from τ₁₁?τ₂₂.     

Effect of two drille holes on the elastic and elastic-plastic strain distribution around a Charpy V-notch

Two small holes (0.0292 in.), appropriately drilled near the root of a Charpy V-notch, have been shown to reduce markedly the Charpy V-notch transition temperature of various steels. In the present study, three experimental techniques were used to define the effect of two holes on the mechanics of deformation and fracture of notched bars loaded in three- and four-point bending: (1) two-dimensional photoelastic stress analyses were performed on models of both the standard Charpy and drilled geometries; (2) a sensitive dislocation etch-pitting technique was used to observe directly the plastic-strain fields developed in V-notch samples of Fe?3% Si alloy loaded in slow bending; and (3) the Charpy striker was instrumented to record load-time curves during impact-bending and thereby determine the dynamic fracture strength of notched and drilled mildsteel samples. It was determined that two holes donot significantly reduce the elastic stress-concentration factor although they cause considerable redistribution of the local shear stresses around the notch. Consequently, the elastic-plastic state develops quite differently in the presence of two holes, and hole drilling can increase the load-carrying capacity of notched mild-steel bars by more than 100 percent even when bars fail by brittle cleavage prior to general yielding. The implications of these results with respect to other forms of “stress-relieving notches” are discussed.     

结构设计中的混沌优化方法及其改进

在变尺度混沌优化方法研究中．结合结构优化问题的特点，提出了一种改进的混沌优化求解算法，用来解决带有多种约束条件的结构优化设计问题。在有限元分析和优化设计软件JEFIX中实现了上述算法．并通过数值算例讨论了变尺度混沌优化方法在结构优化中的可行性及存在的问题，得到了一些重要结论。     

DNA molecular configurations in flows near adsorbing and nonadsorbing surfaces

We investigate experimentally -phage and T2-coliphage DNA molecules near both non-adsorbing glass and adsorbing 3-aminopropyltriethoxysilane (APTES)-coated glass surfaces in a simple steady shearing flow generated by a torsional flow cell. The DNA molecular deformations near the surface are found to be considerably weaker than in bulk flow at the same shear rate. This affects the DNA molecules deposition and stretching on the adsorbing surface. Surprisingly, for a simple shearing flow in the torsional shearing device, the observed stretch, for molecules both near (<10 µm) the surface and adsorbed to it, is much less than predicted by simulations.     

Slow viscoelastic radial flow between parallel disks

A perturbation analysis is presented for the steady-state radial flow of a third-order fluid between two parallel disks. The results include previous perturbation analyses in which various other rheological models were used. The pressure drop needed to maintain the radial flow is less than that for the Newtonian creeping-flow solution because of fluid inertia and shear-thinning viscosity, whereas the normal stresses have the opposite effect. Possible use of the “radial flow viscometer” for experimental evaluation of second-order constants is also discussed. Finally, molecular stretching in the flow system is examined using the elastic dumbbell model for a polymer molecule.     

Unsteady state diffusion of vapour in a closed tube

Results of one-dimensional calculations for unsteady state diffusion of a vapour in a closed tube are compared to calculations (a) for unsteady state diffusion of a vapour in an open tube, and (b) for heat conduction in a finite slab and an infinite slab. In the cases of (b) the effect of the convective term in the transport equation is absent.The total pressure is calculated and differences in the two cases are explained.An experiment is described in which the pressure increase in a closed tube due to the diffusion of water vapour in dry air is measured as a function of time. The experimental results agree quite well with the theoretical predictions. The results of this investigation may be used for the experimental determination of the diffusion coefficient of a vapour in a gas and in pressure measurements in systems with an evaporating liquid.Nomenclature a thermal diffusivity - D diffusion coefficient - w mean particle velocity - g particle flux in the laboratory system - g* particle flux in a system moving with the mean particle velocity w - L length of the tube - n number density of molecules - n _vs saturation number density of vapour molecules - p pressure - p _vs saturation pressure of the vapour - t time - z distance from the liquid surface - N total quantity of evaporated liquid