Free convection heat transfer from an isothermal plate with arbitrary inclination

This paper presents a new formulation for the laminar free convection from an arbitrarily inclined isothermal plate to fluids of any Prandtl number between 0.001 and infinity. A novel inclination parameter is proposed such that all cases of the horizontal, inclined and vertical plates can be described by a single set of transformed equations. Moreover, the self-similar equations for the limiting cases of the horizontal and vertical plates are recovered from the transformed equations by setting=0 and=1, respectively. Heated upward-facing plates with positive and negative inclination angles are investigated. A very accurate correlation equation of the local Nusselt number is developed for arbitrary inclination angle and for 0.001 Pr .

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Wärmeübertragung bei freier Konvektion an einer isothermen Platte mit beliebiger Neigung

Zusammenfasssung Diese Untersuchung stellt eine neue Formulierung der laminaren freien Konvektion von Flüssigkeiten mit einer Prandtl-Zahl zwischen 0,001 und unendlich an einer beliebig schräggestellten isothermen Platte dar. Ein neuer Neigungsparameter wird eingeführt, so daß alle Fälle der horizontalen, geneigten oder vertikalen Platte von einem einzigen Satz transformierter Gleichungen beschrieben werden können. Die unabhängigen Gleichungen für die beiden Fälle der horizontalen and vertikalen Platte wurden für=0 und=1 aus den transformierten Gleichungen wieder abgeleitet. Es wurden erwärmte aufwärtsgerichtete Platten mit positiven und negativen Neigungswinkeln untersucht. Eine sehr genaue Gleichung wurde für die lokale Nusselt-Zahl bei beliebigen Neigungswinkeln und für 0,001 Pr entwickelt.

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Nomenclature C _p specific heat - f reduced stream function - g gravitational acceleration - Gr local Grashof number,g(T _w –T _w ) x³/v² - h local heat transfer coefficient - k thermal conductivity - n constant exponent - Nu local Nusselt number,hx/k - p pressure - Pr Prandtl number, v/ - Ra local Rayleigh number,g(T _w –T )J x³/v - T fluid temperature - T _w wall temperature - T temperature of ambient fluid - u velocity component in x-direction - v velocity component in y-direction - x coordinate parallel to the plate - y coordinate normal to the plate Greek symbols thermal diffusivity - thermal expansion coefficient - (Ra¦sin¦)^1/4/( Ra cos()^1/5 - pseudo-similarity variable, (y/) - dimensionless temperature, (T–T )/(T _w–T ) - ( Ra cos)^1/5+(Rasin)^1/4 - v kinematic viscosity - 1/[1 +(Ra cos)^1/5/( Ra¦sin)^1/4] - density of fluid - Pr/(1+Pr) - _w wall shear stress - angle of plate inclination measured from the horizontal - stream function - dimensionless dynamic pressure     

The effect of background particulates on the delayed transition of a heated 9:1 ellipsoid

An experimental study was done to quantify the effects of a variety of background particulates on the delayed laminar-turbulent transition of a thermally stabilized boundary layer in water. A Laser-Doppler Velocimeter system was used to measure the location of boundary layer transition on a 50 mm diameter, 9:1 fineness ratio ellipsoid. The ellipsoid had a 0.15 m RMS surface finish. Boundary layer transition locations were determined for length Reynolds numbers ranging from 3.0 × 10⁶ to 7.5 × 106. The ellipsoid was tested in three different heating conditions in water seeded with particles of four distinct size ranges. For each level of boundary layer heating, measurements of transition were made for clean water and subsequently, water seeded with 12.5 m, 38.9 m, 85.5 m and 123.2 m particles, alternately. The three surface heating conditions tested were no heating, T = 10°C and T = 15°C where T is the difference between the inlet model heating water temperature, T _i, and free stream water temperature, T . The effects of particle concentration were studied for 85.5 m and 123.2 m particulates.The results of the study can be summarized as follows. The 12.5 m and 38.9 m particles has no measurable effect on transition for any of the test conditions. However, transition was significantly affected by the 85.5 m and 123.2 m particles. Above a length Reynolds number of 4 × 10⁶ the boundary layer transition location moved forward on the body due to the effect of the 85.5 m particles for all heating conditions. The largest percentage changes in transition location from clean water, were observed for 85.5 m particles seeded water.Transition measurements made with varied concentrations of background particulates indicated that the effect of the 85.5 m particles on the transition of the model reached a plateau between 2.65 particulates/ml concentration and 4.2 particles/ml. Measurements made with 123.3 m particles at concentrations up to 0.3 part/ml indicated no similar plateau.     

Untersuchungsergebnisse über die kapillare Leitfähigkeit von Baustoffen

Zusammenfassung Krischer hat die kapillare Flüssigkeitsbewegung als Potentialströmung beschrieben, deren Ursache ein Feuchtegefälle ist und führte als Stoffeigenschaft die Flüssigkeitsleitzahl als Funktion des Feuchtegehaltes ein. Trennt man durch einen modifizierten Ansatz Kapillar- und Reibungskräfte, so erhält man Kapillarfunktionen, die für den Fall der stationären Strömung bei horizontaler Flüssigkeitsbewegung oder bei lotrechter Flüssigkeitsbewegung unter Vernachlässigung der Schwerkraft in der Krischerschen Flüssigkeitsleitzahl (Kapillarleitkoeffizient) zusammengefaßt werden können.Diese Kapillarfunktionen für Wasser wurden von Quarzsand, Ziegel, Kalksandstein, Gasbeton und Bimsbeton ermittelt und der Kapillarleitkoeffizient als Funktion des Feuchtegehaltes für den Befeuchtungsvorgang angegeben. Zur experimentellen Bestimmung des Feuchtegehaltes war das Durchstrahlungsverfahren mit Gammastrahlen gewählt worden, um den volumenbezogenen Feuchtegehalt während eines quasistationären Vorganges der kapillaren Flüssigkeitsbewegung in Abhängigkeit von Zeit und Ort ohne Störung des Vorganges ermitteln zu können.

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Results of investigations on the capillary motion of moisture in building materials

Krischer described the capillary motion of moisture as a water transfer proportional to the gradient of water content by volume, and defined a coefficient of capillary conductivity as a function of moisture content. Equations of general validity, however, can be developed by separation in terms for capillary and gravity forces and capillary resistance. These capillary functions can be transferred in the coefficient for processes with horizontal motion and for those cases where gravity does not have any impact on the motion in small capillary pore spaces.The capillary functions and the coefficients of capillary conductivity for quasi-steady processes of humidification were determined of quartz sand, brick, sandlime brick, cellular concrete and pumice concrete. The temporally and locally changing moisture content during capillary rising tests was measured non-destructively by means of the attenuation effect of penetrating gamma rays.

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Formelzeichen F Stoffquerschnitt - H() feuchtigkeitsabhängige maximale kapillare Steighöhe - H_max maximale kapillare Steighöhe beim maximalen Feuchtegehalt - I₀ Intensität der auffallenden Gammastrahlung - I Intensität der durchfallenden Gammastrahlung - R() feuchtigkeitsabhängiger kapillarer Reibungskoeffizient - R_max kapillarer Reibungskoeffizient beim maximalen Feuchtegehalt - V Volumstrom - h kapillare Steighöhe - q_S Volumanteil des Feststoffes - q_W Volumanteil des Wassers - q_L Volumanteil der Luft - s Weglänge - t Zeit - x Schichtdicke - y Impulszahl - Neigungswinkel gegen die Lotrechte - statistischer Fehler bei der Impulsmessung - Kapillarleitkoeffizient bzw. Flüssigkeitsleitzahl na ch Krischer - Schwächungskoeffizient für Gammastrahlen - Dichte - / Massenschwächungskoeffizient - volumenbezogener Feuchtegehalt - _max maximaler volumenbezogener Feuchtgehalt - _S Schwächungskoeffizient des Feststoffes - _W Schwächungskoeffizient des Wassers - _L Schwächungskoeffizient der Luft Herrn Professor Dr.-Ing. H. Glaser, Stuttgart, zum 70. Geburtstag gewidmet.Die Untersuchungen erfolgten mit Mitteln der AIF (Arbeitsgemeinschaft industrieller Forschungsvereinigungen e.V., Köln). Der Aufbau der Versuchs-anordnung und die Gammastrahlungsmessungen mit Auswertung wurden von H. Perk durchgeföhrt, der zugleich der för den Strahlenschutz Verantwortliche des Instituts im Sinne des § 20 der I. Strahlenschutzverordnung ist.     

Nonlinear rheological behavior of a concentrated spherical silica suspension

Linear and nonlinear viscoelastic properties were examined for a 50 wt% suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G^* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain (0.2) while the nonlinear relaxation modulus G(t, ) characterizing strong stress damping behavior was obtained for large (>0.2). G(t, ) obeyed the time-strain separability at long time scales, and the damping function h() (–G(t, )/G(t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity () for small shear rates (< ^–1; = linear viscoelastic relaxation time) and shear-thickening for larger (>^–1). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, + (t, ) and _– (t, ). In the shear-thinning regime, the and dependence of ₊(t,) and _–(t,) as well as the dependence of () were well described by a BKZ-type constitutive equation using the G(t) and h() data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shearthinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.Dedicated to the memory of Prof. Dale S. Parson     

Asymptotic theory for calculating heat fluxes near the corner of a body

A method is presented for calculating the distribution of the thermal fluxes, friction stresses, and pressure near the corner point of a body contour in whose vicinity the outer supersonic flow passes through an expansion wave. The method is based on a study of the asymptotic solutions of the Navier-Stokes equations as the Reynolds number R approaches infinity for the flow region in which the longitudinal gradients of the flow functions are large, invalidating conventional boundary layer theory. This problem was examined in part in [1], in which the distribution of the friction and pressure in a region with length on the order of a few thicknesses of the approaching boundary layer was obtained in the first approximation. The leading term of the expansion for the thermal flux to the surface of the body vanishes for a value of the Prandtl number equal to unity and for other values of the Prandtl number does not match directly with its value in the undisturbed boundary layer.The thermal-flux distribution is obtained for values of the Prandtl number approaching unity. For this purpose it was necessary to consider a more general double passage to the limit as 1 and 0 for a finite value of the parameter B=[(–1)/] [–ln ^1/4/]^1/4 characterizing the ratio of the effects of thermal conduction, viscous dissipation, and convection. The solution obtained previously [1] corresponds to the particular case B and therefore for actual values of R=10⁴–10⁶, ~ 0.7 overestimates considerably the effect of the dissipative term on heat transfer, although even in first approximation it describes the pressure distribution well and the friction distribution satisfactorily. For smooth matching of the solutions with the corresponding flow functions in the undisturbed boundary layer it was necessary to introduce a flow region with free interaction for the expansion flow. Equations and boundary conditions which describe the flow as a whole are presented. Examples are given of numerical calculations and comparison with experiment.     

Turbulent dispersion of droplets for air flow in a pipe

An optical technique was used to study the dispersion of 50 m, 90 m and 150 m droplets downstream of a source located in the center of a vertical pipe through which turbulent air is flowing. A turbulent dispersion coefficient, _P, and a mean-square of the fluctuations in the turbulent velocity, v _p ² , are determined from the change of the measured mean-square displacement of the droplets over the pipe cross section with time. The interesting aspect of the experiments is that they explored conditions where the inertia of the particles is believed to be a much more important effect than that of the crossing of trajectories associated with the inequality of the average velocities of the particles and the fluid.     

Effect of Streamwise Streaky Structures on Turbulization of a Circular Jet

Experimental investigations of the influence of streamwise streaky structures on turbulization of a circular laminar jet are described. The qualitative characteristics of jet evolution are studied by smoke visualization of the flow pattern in the jet and by filming the transverse and longitudinal sections of the jet illuminated by the laser sheet with image stroboscopy. It is shown that the streaky structures can be generated directly at the nozzle exit, and their interaction with the Kelvin–Helmholtz ring vortices leads to emergence of azimuthal beams ( structures) by a mechanism similar to threedimensional distortion of the twodimensional Tollmien–Schlichting wave at the nonlinear stage of the classical transition in nearwall flows. The effect of the jetexhaustion velocity and acoustic action on jet turbulization is considered.     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some large-scale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u/U).List of symbols a speed of sound - b total mixing layer thickness between U ₁ – 0.1 U and U ₂ + 0.1 U - f normalized third moment of u-velocity, f u³/(U)³ - g normalized triple product of u² , g u²/(U)³ - h normalized triple product of u ², h u ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁ = ₂), M _c (U ₁ – U ₂)/(a ₁ + a ₂) - P static pressure - r freestream velocity ratio, r U ₂/U ₁ - Re unit Reynolds number, Re U/ - s freestream density ratio, s ₂/₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation of u-velocity, uu – U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - average of freestream velocities, (U ₁ + U ₂)/2 - U freestream velocity difference, U U ₁ – U ₂ - instantaneous transverse velocity - v deviation of -velocity, – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y – y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U – U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

Über die Übertragungseinheiten und ein „Vierfelderdiagramm” zur Berechnung von Wärmeübertragern

Zusammenfassung Es wird dargelegt, wie man nach Einführung des bekannten Begriffes Übertragungseinheit und mit Hilfe eines Vierfelderdiagramms zu einer relativ einfachen und durchsichtigen Berechnung von Gleich- und Gegenstrom-Wärmeübertragern gelangt.

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On transfer units and a four-quadrant-diagram for the calculation of heat exchangers

It is shown that the introduction of the known concept of a transfer unit and the use of a four-quadrant diagram leads to a relatively simple and clear computation method for co-current and counter-current heat exchangers.

     

Peristaltic pumping of a second-order fluid in a planar channel

The peristaltic motion of a non-Newtonian fluid represented by the constitutive equation for a second-order fluid was studied for the case of a planar channel with harmonically undulating extensible walls. A perturbation series for the parameter ( half-width of channel/wave length) obtained explicit terms of 0(²), 0(²Re²) and 0(₁Re²) respectively representing curvature, inertia and the non-Newtonian character of the fluid. Numerical computations were performed and compared to the perturbation analysis in order to determine the range of validity of the terms.Presented at the second conference Recent Developments in Structured Continua, May 23–25, 1990, in Sherbrooke, Québec, Canada     

An application of nonsymmetric Lax-Milgram lemma to nonassociated plasticity

Based on a general assumption for plastic potential and yield surface, some properties of the nonassociated plasticity are studied, and the existence and uniqueness of the distribution of incremental stress and displacement for work-hardening materials are proved by using nonsymmetric Lax-Milgram lemma, when the work-hardening parameter A>F/Q/–F/, Q/.     

Die Torsionsspannungen in Wellen mit tiefen Längsnuten

Übersicht MitF(x, y) als Spannungsfunktion einer Welle ohne Nut und(, y) als Potentialfunktion des Quelle-Senke-Systems erhält man Spannungsfunktionen(, y) =F(x, y) –(, y) für Wellen mit tiefen Längsnuten. Es wird gezeigt, daß sich damit die Schubspannungen in den Läufern von Schraubenverdichtern ermitteln lassen.

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Shearing stresses in shafts with deep longitudinal grooves

Summary The stress functions(, y) of shafts with deep longitudinal grooves may be represented by(, y) =F(x, y) –(, y) whereF(x, y) is the stress function of a cylindrical shaft without grooves and(, y) denotes the potential function of the source-sink system. It is shown that the shearing stresses in rotors of screw-compressors may be obtained in this way.

     

Flow in vicinity of blunt body stagnation point in diverging hypersonic stream

In the hypersonic thin shock layer approximation for a small ratio k of the densities before and after the normal shock wave the solution of [1] for the vicinity of the stagnation point of a smooth blunt body is extended to the case of nonuniform outer flow. It is shown that the effect of this nonuniformity can be taken into account with the aid of the effective shock wave radius of curvature R_*, whose introduction makes it possible to reduce to universal relations the data for different nonuniform outer flows with practically the same similarity criterion k. The results of the study are compared with numerical calculations of highly underexpanded jet flow past a sphere.Notations x, y a curvilinear coordinate system with axes directed respectively along and normal to the body surface with origin at the forward stagnation point - R radius of curvature of the meridional plane of the body surface - uV, vV., , p V ² respectively the velocity projections on the x, y axes, density, and pressure - and V freestream density and velocity The indices =0 and=1 apply to plane and axisymmetric flows Izv. AN SSSR, Mekhanika Zhidkosti i Gaza, Vol. 5, No. 3, pp. 102–105, 1970.     

Mathematics and Rheology

Summary The great advances made in Rheology during the last forty years owe much to the application of mathematics. But in some cases, there have been misunderstandings. As a result, rheologists have sometimes been unnecessarily restricted. Mathematics is limited only by self-consistency: Rheology deals with the physical world.In particular, three terms are discussed: infinity, zero and negative, all of which have at least two meanings which have been confused. Rheological phenomena cannot be explained merely by mathematical formulation. Unnecessary mathematics should be avoided but professional rheologists must not shirk mathematics.This paper was read in an abbreviated form, at aConference of the British Society of Rheology in April 1971 The Proceedings were not published.     

Transport in ordered and disordered porous media V: Geometrical results for two-dimensional systems

In this paper we continue the geometrical studies of computer generated two-phase systems that were presented in Part IV. In order to reduce the computational time associated with the previous three-dimensional studies, the calculations presented in this work are restricted to two dimensions. This allows us to explore more thoroughly the influence of the size of the averaging volume and to learn something about the use of anon-representative region in the determination of averaged quantities.

Nomenclature

Roman Letters A interfacial area of the– interface associated with the local closure problem, m² - a _i i=1, 2, gaussian probability distribution used to locate the position of particles - l unit tensor - characteristic length for the-phase particles, m - ⁰ reference characteristic length for the-phase particles, m - characteristic length for the-phase, m - _i i=1,2,3 lattice vectors, m - m convolution product weighting function - m _V special convolution product weighting function associated with a unit cell - n _i i=1, 2 integers used to locate the position of particles - n unit normal vector pointing from the-phase toward the-phase - r _p position vector locating the centroid of a particle, m - r gaussian probability distribution used to determine the size of a particle, m - r ₀ characteristic length of an averaging region, m - V averaging volume, m³ - V volume of the-phase contained in the averaging volume,V, m³ - x position of the centroid of an averaging area, m - x ₀ reference position of the centroid of an averaging area, m - y position vector locating points in the-phase relative to the centroid, m Greek Letters V /V, volume average porosity - _{a i} standard deviation ofa _i - _r standard deviation ofr - intrinsic phase average of      

Direct derivation of the two-shaft system balance conditions for the second order reciprocal inertia forces on the V-type eight cylinders internal combustion engines with a plane crankshaft

By employing the four shafts balance concept paper [1] has reported a balance regime for the second order reciprocal inertia forces on the V-type eight cylinder internal combustion engines with a plane crankshaft. Thereafter, paper [2] has acquired a two-shafts balance regime, but through a rather tedious roudabout degenerating manipulation. The present article has, but starting out directly from the two-shafts balance concept, successfully acquired the same results as those in paper [2]. In addition, we propose, herein, a third balance system which might be, in general, called the slipper balance regime.     

Transport in ordered and disordered porous media II: Generalized volume averaging

In this paper we develop the averaged form of the Stokes equations in terms of weighting functions. The analysis clearly indicates at what point one must choose a media-specific weighting function in order to achieve spatially smoothed transport equations. The form of the weighting function that produces the cellular average is derived, and some important geometrical theorems are presented.Roman Letters A interfacial area of the- interface associated with the local closure problem, m² - A _e area of entrances and exits for the-phase contained within the averaging system, m² - A _p surface area of a particle, m² - d _p 6V _p/A_p, effective particle diameter, m - g gravity vector, m/s² - I unit tensor - K _m permeability tensor for the weighted average form of Darcy's law, m² - L general characteristic length for volume averaged quantities, m - L _p general characteristic length for volume averaged pressure, m - L characteristic length for the porosity, m - L _v characteristic length for the volume averaged velocity, m - l characteristic length (pore scale) for the-phase - l _i i=1, 2, 3 lattice vectors, m - (y) weighting function - m(–y) (y), convolution product weighting function - _v special weighting function associated with the traditional averaging volume - m _v special convolution product weighting function associated with the traditional averaging volume - m _g general convolution product weighting function - m _V unit cell convolution product weighting function - m _C special convolution product weighting function for ordered media which produces the cellular average - m _D special convolution product weighting function for disordered media - m _M master convolution product weighting function for ordered and disordered media - n unit normal vector pointing from the-phase toward the-phase - p pressure in the-phase, N/m² - p_m superficial weighted average pressure, N/m² - p _m intrinsic weighted average pressure, N/m² - p traditional intrinsic volume averaged pressure, N/m² - p p p _m , spatial deviation pressure, N/m² - r ₀ radius of a spherical averaging volume, m - r _m support of the convolution product weighting function, m - r position vector, m - r position vector locating points in the-phase, m - V averaging volume, m³ - V volume of the-phase contained in the averaging volume, m³ - V _cell volume of a unit cell, m³ - V velocity vector in the-phase, m/s - vm superficial weighted average velocity, m/s - v _m intrinsic weighted average velocity, m/s - V volume of the-phase contained in the averaging volume, m³ - V _p volume of a particle, m³ - v traditional superficial volume averaged velocity, m/s - v v p _m spatial deviation velocity, m/s - x position vector locating the centroid of the averaging volume or the convolution product weighting function, m - y position vector relative to the centroid, m - y position vector locating points in the-phase relative to the centroid, m Greek Letters indicator function for the-phase - Dirac distribution associated with the- interface - V /V, volume average porosity - _m m * . weighted average porosity - mass density of the-phase, kg/m³ - viscosity of the-phase, Ns/m² - V /V, volume fraction of the-phase     

Development of a full-field planar Mie scattering technique for evaluating swirling mixers

A full-field planar optical diagnostic technique for studying mixing in swirling flows is described. Results were obtained using this technique to provide planar mixing information by seeding a simulated fuel stream with aluminum oxide particles, then inferring concentration from Mie scattering intensity distributions. This facility and measurement technique are unique for several reasons. First, they allow spatial variations in laser sheet energy to be corrected for on a shot-to-shot basis. Second, they allow experiments to be performed for swirlers with practical fuel and oxidizer flow rates, i.e. on the order of 150 g/s (0.33 lbm/s). Finally, they allow full size swirler models to be evaluated, with the entire exit plane imaged simultaneously. Representative results are presented as false color images of the planar mixing fields. These images allow rapid assessment of the mixing process and its changes with variations in operating conditions or swirler geometry.List of Symbols C seed particle concentration, m^–3 - mean component of seed particle concentration, m^–3 - C fluctuating component of seed particle concentration, m^–3 - C ^* time averaged ratio of rms particle concentration fluctuations to average particle concentration, dimensionless - d _p particle diameter, m - I laser energy after passing through the flow, J/m² - mean laser energy, J/m² - I ₀ laser energy before passing through the flow, J/m² - L _v eddy length scale, m - l laser beam path length, m - U _v eddy velocity scale, m/s - V diode voltage reading after passing through the flow, V - mean diode voltage, V - V ₀ diode voltage reading before passing through the flow, V - absorptivity, m² - _rel relative equivalence ratio, dimensionless - fluid viscosity, Ns - _p particle density, kg/m³ - Stokes number= _p / _f , dimensionless - _f flow time scale, s - _p particle response time, s     

Some general rheological properties of dilute polymer solutions predicted from intrinsic viscosity measurements

Expressions for the rheological properties of dilute polymer solutions at low and moderate deformation rates are established through the computation and analysis of exact Zimm's eigenvalues. It is shown that they can be expressed in terms of measurable parameters from intrinsic viscosity data. Under moderate deformation rates one needs to introduce a slippage between the solvent and the smoothed polymer to be able to describe shear-thinning behaviour.     

Time studies of ionization processes

Summary Measurements of the temporal growth of ionization between parallel plane electrodes in hydrogen have been made. The results show that for low values ( 40 V/cm mm Hg) of the ratio of electric fieldE to gas pressurep the growth times can be short ( 1s for over-voltages V 1 %) while at values ofE/p 300 V/cm mm Hg the times are of the order of milli seconds withV 5%. Comparison of the experimental data with Davidson's mathematical analysis of current growth based upon the action of primary and secondary ionization processes shows that the relative significance of the possible secondary processes changes asE/p is altered. For the low values ofE/p, the predominant secondary process contributing to the growth was found to be photoelectric emission from the cathode, but with increasing values ofE/p the role of positive ion interaction with the cathode becomes increasingly important. No single secondary process was exclusively operating in any of the conditions examined.