PIV measurements of velocities and concentrations of wood fibres in pneumatic transport

A method for simultaneous measurement of the concentration and velocity of wood fibres suspended in air was developed. The velocity of the wood fibres was measured by the use of particle image velocimetry (PIV). The concentration of wood fibres was measured using the raw images from the PIV equipment as input data. An image processing procedure was used to determine the volume fraction of the fibre particles in the images. The method gave good qualitative and quantitative results for low volume fractions of fibres; for higher volume fractions the quantitative results were unsatisfactory.Latin letters C Concentration of fibres [g/m³] - d Diameter of fibre [m] - M_w Water mass [kg] - M_f Fibre mass [kg] - m Calibration mass flow [kg/s] - m₂₅ Calibration mass flow at C=25 g/m³ [kg/s] - n Fan rpm [-] - t Thickness of light sheet [m] - t Time between laser pulses [s] - U_i Velocity component in i-direction [m/s] - v Streamwise velocity [m/s] - v_average Average streamwise velocity [m/s] - x_i Particle displacement in i-direction [m] Greek letters _f Volume fraction of fibres [-] - _average Average volume fraction of fibres [-] - Area fraction of fibres in image [-] - Density of fibre particle [kg/m³]     

An integrated multiphase flow sensor for microchannels

The flow regimes of microscale multiphase flows affect the yield and selectivity of microchemical systems, and the heat transfer properties of micro heat exchangers. We describe an integrated optical sensor that uses total internal reflection to detect the structure of multiphase flows in microchannels. The non-intrusive sensor enables detection of individual slugs, bubbles, or drops, and can be used to continuously determine their number and velocity. The sensor performance is modeled using ray-tracing techniques, and tested for several channel geometries. Both gas-liquid and liquid-liquid flows are investigated in microchannels with rectangular and triangular cross-sections. Statistical properties of the flow, derived from the sensor signal, compare favorably to commonly-used dynamic pressure measurements. We demonstrate the integration of the sensor into a planar multichannel microreactor. An existing glass layer used as a waveguide allows us to monitor flows in optically inaccessible channels. This sensor configuration can be integrated into layers of vertically-stacked multichannel microreactors.

List of symbols

Roman symbols a Radius of largest sphere inscribed in channel [m] - A_ch Channel cross-sectional area [m²] - Ca Capillary number [-] - Critical capillary number [-] - d_h Hydraulic diameter [m] - d_sensor Distance prism surface-sensor origin [m] - E₀ Incident light energy [J] - E_r Emerging light energy [J] - f(t_pass) Probability density function (PDF) of slug dwell times [1/s] - f Focal length [m] - f_slug Slug frequency [Hz] - F(t_pass) Probability distribution of slug dwell times [-] - g(t) Arbitrary function of time [-] - h Liquid film thickness [m] - j_G Superficial gas velocity [m/s] - j_L Superficial liquid velocity [m/s] - l Slug length [m] - N Number of samples [-] - n Refractive index [-] - N_c Number of channel corners [-] - n_i Refractive index of incident medium [-] - n_r Number of reflections [-] - n_t Refractive index of transmitting medium [-] - n_slug Number of slugs [-] - p Gas inlet pressure [Pa] - r Reflectance [-] - R_XX(x,) Autocorrelation function [-] - R_Xp(x,) Cross correlation function [-] - r Slug radius at infinite distance from leading slug tip [m] - s Standard deviation of measured slug dwell times [s] - t Time [s] - t Measurement time interval [s] - t_pass Slug dwell time [s] - U_b Slug (bubble) velocity [m/s] - W Bin size of slug dwell time histogram [-] - x Streamwise coordinate [m] - X(x,t) Phase density function [-] - Y Surface tension of the gas-liquid interface [N/m] - Volumetric gas flow rate [m³/s] - Volumetric liquid flow rate [m³/s] - Volumetric oil flow rate [m³/s] - Volumetric water flow rate [m³/s] - z Normal coordinate [m]Greek symbols Void fraction [-] - _c Critical angle for total internal reflection [^°] - _i Incident angle [^°] - Laser wavelength [m] - µ Liquid viscosity [Pa s] - Normalization factor [-] - _h Dimensionless liquid film thickness [-] - _r Dimensionless radius [-] - _x Dimensionless streamwise position [-] - _r Dimensionless slug radius at infinite distance from leading slug end [-] - Standard deviation of the slug dwell time distribution [s] - Time shift [s] - Contact angle [^°]     

A new method for measuring time constants of a thermocouple wire in varying flow states

A new measuring method is suggested for determining the time constant of a thermocouple wire to be applied for the measurement of the true fluid temperatures in varying flow states. Based on the techniques of internal heating which are commonly used to measure mean time constants, we extend the existing method to measure instantaneous time constants continuously. A method of measurement and analysis is presented and verified experimentally.List of Symbols A _s surface area [m²] - c specific heat [J/kg K] - D diameter [m] - h heat transfer coefficient [W/m² K] - I current [A] - k thermal conductivity [W/m K] - L length [m] - r resistance per unit length [/m] - T temperature [°C] - t time [s] - t _c characteristic time to reach uniform state [s] - u velocity of stream [m/s] - V volume [m³] - x axial coordinate [m] - thermal diffusivity [m²/s] - normalized temperature (TT )/(T _RT )) - density [kg/m³] - time constant [s] - angular velocity [rad/s] - a amplitude - i initial condition - j junction of thermocouple - R reference point - surrounding The work was supported by Turbo and Power Machinery Research Center at Seoul National University and the authors are grateful to Mr. M. H. Yang for his assistance in the experiment.     

Three-segment electrodiffusion probe for velocity measurements

A cylindrical electrodiffusion probe for the measurement of liquid velocity vectors in the plane perpendicular to its axis was developed as an analogue to the triple-split film thermoanemometer. The geometry of the probe enables high directional resolution in the whole range of 360°. The total mass transfer of the probe was well correlated by the relation Sh = 0.76 Sc ^0.33 Re ^0.47.List of symbols A _kj , B _kj Fourier coefficient - c [mol/m³] depolarizer concentration - te]D [m²/s] diffusion coefficient of species - d [m] diameter of probe - f [1/s] frequency of vortex formation - h [mol/m²s] coefficient of mass transfer - I _k normalized current of K-th segment - i [A] total current - i _k [A] current of K-th segment - Re Reynolds number, u d/v - Sc Schmidt number, v/D - Sh Sherwood number, h d/c D - Sr Strouhal number, f d/v - v [m/s] free stream velocity - [°] flow angle, i.e. angle between approaching stream and reference direction of probe - v [m²/s] kinematic viscosity     

The effects of span position of winglet vortex generator on local heat/mass transfer over a three-row flat tube bank fin

The naphthalene sublimation method was used to study the effects of span position of vortex generators (VGs) on local heat transfer on three-row flat tube bank fin. A dimensionless factor of the larger the better characteristics, JF, is used to screen the optimum span position of VGs. In order to get JF, the local heat transfer coefficient obtained in experiments and numerical method are used to obtain the heat transferred from the fin. A new parameter, named as staggered ratio, is introduced to consider the interactions of vortices generated by partial or full periodically staggered arrangement of VGs. The present results reveal that: VGs should be mounted as near as possible to the tube wall; the vortices generated by the upstream VGs converge at wake region of flat tube; the interactions of vortices with counter rotating direction do not effect Nusselt number (Nu) greatly on fin surface mounted with VGs, but reduce Nu greatly on the other fin surface; the real staggered ratio should include the effect of flow convergence; with increasing real staggered ratio, these interactions are intensified, and heat transfer performance decreases; for average Nu and friction factor (f), the effects of interactions of vortices are not significant, f has slightly smaller value when real staggered ratio is about 0.6 than that when VGs are in no staggered arrangement. A cross section area of flow passage [m²] - A _mim minimum cross section area of flow passage [m²] - a width of flat tube [m] - b length of flat tube [m] - B _pT lateral pitch of flat tube: B _pT = S ₁/T _p - d _h hydraulic diameter of flow channel [m] - D _naph diffusion of naphthalene [m²/s] - f friction factor: f = pd _h/(Lu ² _max/2) - h mass transfer coefficient [m/s] - H height of winglet type vortex generators [m] - j Colburn factor [–] - JF a dimensionless ratio, defined in Eq. (23) [–] - L streamwise length of fin [m] - L _PVG longitudinal pitch of vortex generators divided by fin spacing: L _pVG = l _VG/T _p - l _VG pitch of in-line vortex generators [m] - m mass [kg] - m mass sublimation rate of naphthalene [kg/m²·s] - Nu Nusselt number: Nu = d _h/ - P pressure of naphthalene vapor [Pa] - p non-dimensional pitch of in-line vortex generators: p = l _VG/S ₂ - Pr Prandtl number [–] - Q heat transfer rate [W] - R universal gas constant [m²/s²·K] - Re Reynolds number: Re = ·u _max·d _h/ - S ₁ transversal pitch between flat tubes [m] - S ₂ longitudinal pitch between flat tubes [m] - Sc Schmidt number [–] - Sh Sherwood number [–]: Sh = hd _h/D _naph - Sr staggered ratio [–]: Sr = (2Hsin – C)/(2Hsin) - T _p fin spacing [m] - T temperature [K] - u _max maximum velocity [m/s] - u average velocity of air [m/s] - V volume flow rate of air [m³/s] - x,y,z coordinates [m] - z sublimation depth[m] - heat transfer coefficient [W/m²·K] - heat conductivity [W/m·K] - viscosity [kg/m²·s] - density [kg/m³] - attack angle of vortex generator [°] - time interval for naphthalene sublimation [s] - fin thickness, distance between two VGs around the tube [m] - small interval - C distance between the stream direction centerlines of VGs - p pressure drop [Pa] - 0 without VG enhancement - 1, 2, I, II fin surface I, fin surface II, respectively - atm atmosphere - f fluid - fin fin - local local value - m average - naph naphthalene - n,b naphthalene at bulk flow - n,w naphthalene at wall - VG with VG enhancement - w wall or fin surface     

Strömungsmodell der Gas-Flüssigreaktoren nach der Filmtheorie

Zusammenfassung Es wird ein mathematisches Strömungsmodell für Gas-Flüssigreaktoren aufgestellt, das auf der Filmtheorie basiert. Für den Fall einer chemischen Reaktion erster Ordnung läßt sich eine geschlossene analytische Lösung finden, mit deren Hilfe man den Stoffaustauschgrad, den Reaktionsumsatz und die Reaktorkapazität leicht ermitteln kann. Das Modell eignet sich also unmittelbar als Auslegungsbasis für Gas-Flüssigreaktoren.

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A flowingmodel for gas-liquid reactors based on the film theory

A design model for gas-liquid reactors is developed based on the film theory and under condition that the gas and liquid phase are in plug flow. An analytical solution of this system has been achieved. The mass transfer degree, the reaction conversion and the reactor capacity can be easily calculated by means of the analytical solutions. Therefore, this model can be used directly to design the gas-liquid reactors.

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Formelzeichen a _i [m ²/m ³] spezifische Phasengrenzfläche - C [kmol/m³] Konzentration - D [m²/s] Diffusionskoeffizient - F [kmol/s] Masseneinströmung der Gasphase - H [J/kmol] Henry'sche Konstante - Ha [J/kmol] Hatta-Zahl definiert in Gl. (3) - L [m] charakteristische Länge des Reaktors - Q _L [m ³/s] Volumenströmung der Flüssigphase - N [kmol/m²·s] Stoffübergangsgeschwindigkeit - p [N/m²] Partialdruck einer Komponente - p [N/m²] Gesamtdruck des Systems - r [N/m²] Strömungsstatus - x [m] Ortskoordinate längs der Diffusionsrichtung - x _A [m] Reaktionsumsatz des EduktesA - V [m³] Reaktorvolumen Griechische Buchstaben [m] Diffusionsgrenzschichtdicke - _L Flüssig-Holdup - [m] Austauschgrad - [m] Abkürzung definiert in Gl. (13) - 0 bezogen auf Anfangsstelle des Reaktors - A bezogen auf KomponenteA - b bezogen auf Bulkphase - L bezogen auf Flüssigphase - bezogen auf Einströmung - bezogen auf Ausströmung     

The mathematical modelling of thermal radiation in high temperature fluidized bed

The aim of this study is composed of two parts. One of them is to calculate the radiation heat flux and the other is to determine the overall heat transfer coefficient for the gas-fluidized bed. The radiative heat transfer model is developed for predicting the total heat transfer coefficients between submerged surfaces and fluidized beds for several working temperatures. The role of radiation heat transfer in the overall heat transfer process at an immersed surface in a gas-fluidized bed at high temperatures is investigated. Analytical results are compared with the previously done experiments and a good agreement between the two, is obtained.

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Bestimmung der Wärmeübertragungs-Koeffizienten in Gas-Wirbelschichten

Zusammenfassung Diese Untersuchung besteht aus folgenden zwei Teilen: 1. Kalkulation des Radiationswärmeübergangs in Gas-Wirbelschichten. 2. Bestimmung des Wärmeübergangs-Koeffizienten in Gas-Wirbelschichten. Dieses Radiationswärmeübergangsmodell wurde entwickelt, um die Wärmeübertragungs-Koeffizienten zwischen der eingetauchten Oberfläche und der Wirbelschicht bei verschiedener Wärme schätzungsweise zu bestimmen. Es wurde das Verhältnis der Radiationswärmeübertragung in Gas-Wirbelschichten zum totalen Wärmeübergang untersucht. Die Meßwerte wurden mit theoretischen Resultaten verglichen.

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Nomenclature c (x) specific heat capacity of packet [J/kg K] - c _p specific heat capacity of particle [J/kg K] - c _pg specific heat capacity of gas [J/kg K] - d _p average diameter of the bed particles [m] - f ₀ the fraction of time that a unit surface exposed to the bubble phase - 1–f ₀ the fraction of time that a unit surface exposed to the packet phase - g acceleration due to gravity [m/s²] - h _b heat transfer coefficient for the surface in contact with bubble [W/m² K] - h _bc conduction heat transfer coefficient for the surface/bubble [W/m²K] - h _br radiation heat transfer coefficient for the surface/bubble [W/m²K] - h _p heat transfer coefficient for the surface in contact with packet [W/m²K] - h _pc conduction heat transfer coefficient for the surface/packet [W/m² K] - h _pr radiation heat transfer coefficient for the surface/packet [W/m² K] - h _T total heat transfer coefficient between bed and surface [W/m² K] - k ⁰ thermal conductivity of the emulsion phase for fixed bed [W/m K] - k(x) thermal conductivity of packet [W/m K] - k _e the logarithmic mean of conductivity for first layer in packet [W/m K] - k _g the logarithmic mean of conductivity for the first layer in packet [W/m K] - K extinction coefficient [1/m] - m mass [kg] - n number of layers - p air pressure [pa] - q _pc mean local conduction heat transfer for packet [kW/m²] - q _pr mean local radiation heat transfer for packet [kW/m²] - Q _p average heat flux during packet contact with surface [kW/m²] - Q _b average heat flux during bubble contact with surface [kW/m²] - R gas constant [287.04 J/kg K] - t time [s] - t _g residence time for gas bubble [s] - t _k residence time for packet [s] - T temperature [K] - T _b bed temperature [K] - T _W surface temperature [K] - V _mf minimum fluidization velocity [m/s] - v _t terminal velocity [m/s] - x distance [m] Greek symbols t time increment - x thickness of the layer - emissivity - thermal diffusivity [m²/s] - (x) voidage of fluidized bed - _mf void ratio of the bed at minimum fluidization - ₀ voidage of fixed bed - _g dynamic viscosity of gas [kg/m s] - _g kinematic viscosity of gas [m²/s] - (x) density of packet [kg/m³] - _p density of particles [kg/m³] - _g density of gas [kg/m³] - Stefan-Boltzmann constant [5.66·10^–8 W/m²K⁴] - geometric shape factor for particles Dimensionless numbers Ar Archimedes numberAr=g d _p ³ ( _p – _g ) _g / _g ² - Nu Nusselt numberNu=h·d/k - Re Reynolds numberRe=d _p ·V _mf / _g - Pr Prandtl numberPr=C _{pg g} /k _g      

Modelling Turbulent Premixed Combustion Using the Level Set Approach for Reynolds Averaged Models

A model for premixed turbulent combustion is investigated using a RANS-approach. The evolution of the flame front is described in terms of the G-equation. The numerical instabilities of the G-field are resolved using a reinitialisation procedure. For the G-points near the flame surface an algorithm proposed by Russo and Smereka [1] and modificated by Düsing [2] is presented. For all other points the standard Sussman algorithm is employed. Fluid properties are conditioned on the flame front position using a burnt-unburnt probability function across the flame front. Computations are performed using the code FASTEST-3D [3] which is a flow solver for a non-orthogonal, block-structured grid. The computational examples include two test cases, the first containing the propagation of two circular merging flames and the second one containing the simulation of the ORACLES-burner [4].     

On the use of crack-tip-opening displacement to predict the fracture strength of notched graphite/epoxy laminates

The fracture strength and crack-opening displacement of notched graphite/epoxy laminates were measured experimentally using the center-cracked tension-specimen geometry. Four replicate tests were conducted for a variety of laminate stacking sequences, thicknesses, and notch lengths. Most laminates exhibited extensive notch-tip damage prior to fracture. Values of crack-tip-opening displacement (CTOD) at fracture were estimated from values of crack-opening displacement measured at the crack center line. CTOD was independent of specimen crack length for the [0/±45/90] _s , [0/±45/90]_15s , [0/±45] _s , [0/±45/]_15s , and [0/90]_24s laminates. In addition, notched laminate strength was accurately predicted using a Dugdale-type model along with the estimated CTOD.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Onset of viscous fingering for miscible liquid-liquid displacements in porous media

The displacement of one fluid by another miscible fluid in porous media is an important phenomenon that occurs in petroleum engineering, in groundwater movement, and in the chemical industry. This paper presents a recently developed stability criterion which applies to the most general miscible displacement. Under special conditions, different expressions for the onset of fingering given in the literature can be obtained from the universally applicable criterion. In particular, it is shown that the commonly used equation to predict the stable velocity ignores the effects of dispersion on viscous fingering.Nomenclature C Solvent concentration - Unperturbed solvent concentration - D _L Longitudinal dispersion coefficient [m²/s] - D _T Transverse dispersion coefficient [m²/s] - g Gravitational acceleration [m/s²] - I _sr Instability number - k Permeability [m²] - K Ratio of transverse to longitudinal dispersion coefficient - L Length of the porous medium [m] - L _x Width of the porous medium [m] - L _y Height of the porous medium [m] - M Mobility ratio - V Superficial velocity [m/s] - V _c Critical velocity [m/s] - V _s Velocity at the onset of instability [m/s] - µ Viscosity [Pa/s] - Unperturbed viscosity [Pa/s] - µ ₀,µ _s Viscosities of oil and solvent, respectively [Pa/s] - Density [kg/m³] - ₀, _s Densities of oil and solvent, respectively [kg/m³] - Porosity - Dimensionless length     

Displacement of trapped oil from water-wet reservoir rock

Displacement of oil trapped in water-wet reservoirs was analyzed using percolation theory. The critical capillary number of the CDC (Capillary Desaturation Curve) was be predicted based on the pore structure of the medium. The mobilization and stability theories proposed by Stegemeier were used to correlate oil cluster length to the capillary number needed to mobilize the trapped oil. Under the assumption that all pore chambers have the same size, a procedure was developed using the drainage capillary pressure curve and effective accessibility function to predict the CDC curve for a given medium. The prediction of critical capillary numbers was compared with the experimental data from 32 sandstone samples by Chatzis and Morrow. Also, the CDC curve of one sandstone sample was calculated using the procedure developed in this work and compared with the measured data. Very good agreements were obtained.Nomenclature a average radius of a liquid filament [m] - c constant - D pore throat diameter [m] - D _a advancing diameter of an oil cluster [m] - D _af average flowing diameter of the medium [m] - D _da controlling diameter of the medium [m] - D _r receding diameter of an oil cluster [m] - D _X difficulty index - f ratio of length to average radius of an oil cluster - F _i interfacial forces [N] - F _p force from pressure gradient [N] - g wettability function - k absolute permeability [m²] - l length of an oil cluster [m] - l _m mobile oil cluster length [m] - l _s stable oil cluster length [m] - l _w wavelength [m] - n* relative length of an oil cluster - N _c 1 capillary number defined by Equation (1) - N _c 2 capillary number defined by Equation (2) - P _b probability of oil filling a pore - P _c percolation threshold value - p _c capillary pressure [N/m²] - r radius of a pore [m] - r _e average pore radius [m] - S _n the nonwetting phase saturation - S _or residual oil saturation - S _orn normalized oil saturation - v Darcy flow rate [m/s] - X _t total fraction of pores - X _t ^a accessibility - X _e ^a effective accessibility - (D) pore throat size distribution function - _a advancing contact angle - _r receding contact angle - porosity - density of the liquid [kg/m³] - constant in Equation (4) - dynamic length of an oil cluster [m] - interfacial tension [N/m] - viscosity [N/(m s)] - p pressure gradient [N/m³]     

A new look at the laminar flow of power law fluids through granular beds

Summary The paper deals with laminar flow of power law fluids through granular beds. A critical review of the assumptions concerning the capillary model of the bed, applied by various authors, led us to the conclusion that the derivation of the correlation eq. [13] given byChristopher andMiddleman was based on a too simplified model of the granular bed. Taking advantage of the approach presented in the classical works ofKozeny andCarman (which seems to be partly overlooked by some authors, including our own previous works) a modified correlation equation for power law fluids [21], a corrected formula for shear rate in the bed [29] and for Deborah number [32], as well as corrected correlation equation for fluids exhibiting memory effects [34] were presented.

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Zusammenfassung Diese Arbeit betrifft laminare Strömungen von Potenzgesetzflüssigkeiten durch Kornschüttungen. Eine kritische Prüfung der Annahmen, die von verschiedenen Autoren für das Kapillar-Modell der Schüttung gemacht worden sind, führt uns zu der Folgerung, daß die Herleitung der Korrelationsgleichung [13] nachChristopher undMiddleman auf einem übervereinfachten Modell der Kornschüttung basiert. Unter Nutzbarmachung der Annahmen, die in den klassischen Arbeiten vonKozeny undCarman dargestellt worden sind (sie wurden sowohl von manchen anderen Autoren als auch in unseren früheren Arbeiten nicht beachtet), werden nun eine modifizierte Korrelationsgleichung für die Potenzgesetzflüssigkeiten [21], eine korrigierte Formel für die Schergeschwindigkeit in der Schüttung [29], eine korrigierte Formel für die Deborah-Zahl [32] und eine korrigierte Korrelationsgleichung für Flüssigkeiten, die Gedächtnis-Effekte zeigen [34], angegeben.

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Notation A constant in eq. [9] - d _p effective particle diameterd _p = 6/a (wherea is the specific surface of the bed), m - f _BK modified friction factor, defined by eq. [1] - k power law parameter, N s ⁿ /m² - K Kozeny constant, defined by eq. [8] - K ₀ constant depending on the shape of the channel cross-section - K ₁ constant, defined by eq. [5] - l bed height, m - l _e channel length, m - n power law parameter - p pressure drop due to friction, N/m² - r _h hydraulic radius, defined by eq. [6], m - s bed permeability, defined by eq. [16], m² - v ₀ mean linear velocity related to an empty crosssection of the column, m/s - v _e mean linear velocity in the channel, m/s - shear rate at the wall of the channel, s^–1 - shear rate at the wall of the channel calculated according to the formula [29], s^–1 - bed porosity - characteristic time of the fluid, s - friction factor, defined by eq. [25] - µ dynamic viscosity of the fluid, N s/m² - parameter, defined by eq. [15], N s ⁿ /m¹⁺ⁿ - De Deborah number, defined by eq. [33] - De ^* Deborah number, defined by eq. [32] - Re _BK modified Reynolds number, defined by eq. [2] - Re _BK modified Reynolds number, defined by eq. [26] - Re _BK ^* modified Reynolds number, defined by eq. [23] - Re _CM modified Reynolds number byChristopher andMiddleman, defined by eq. [14] - Re _CM modified Reynolds number, defined by eq. [17] With 3 figures and 1 table     

Second-order cnoidal waves at the free surface and interface of a two-fluid system

In this paper, using the PLK method and reductive perturbation method, we obtained the second approximation to cnoidal waves at the free surface and interface for the two-fluid system considered in [1]. The corresponding results in [3] and [4] may be obtained as special cases in this paper.Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

A class of variational difference schemes for a singular perturbation problem

In this paper, a singularly perturbed boundary value problem for second order self-adjoint ordinary differential equation is discussed. A class of variational difference schemes is constructed by the finite element method. Uniform convergence about small parameter is proved under a weaker smooth condition with respect to the coefficients of the equation. The schemes studied in refs. [1], [3], [4] and [5] belong to the class.     

Heat transfer enhancement in a channel with a built-in rectangular cylinder

A two dimensional numerical investigation of the unsteady laminar flow pattern and forced convective heat transfer in a channel with a built-in rectangular cylinder is presented. The channel in the entrance region has a length to plate spacing of ten. The computations were made for several Reynolds number and two rectangular cylinder aspect ratios. Hydrodynamic behavior and heat transfer results are obtained by solution of the complete Navier-Stokes and energy equation. The results show that these flow exhibits laminar self-sustained oscillations for Reynolds numbers above the critical one. This study show that oscillatory separated flows result in a significant heat transfer enhancement but also in a significant pressure drop increase.

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Erhöhung des Wärmeübergangs in einem Spaltkanal mit quer eingebautem Rechteckprisma

Zusammenfassung Es wird eine zweidimensionale numerische Untersuchung des instationären Wärmeübergangs und Druckverlustes im laminar durchströmten Spaltkanal mit quer eingebautem Rechteckprisma dargelegt und zwar für verschiedene Reynoldszahlen und zwei Prismenabmessungen. Als Lösung der Navier-Stokes- und der Energiegleichung resultieren selbsterregt oszillieren de Strömungs- und Temperaturfelder, verbunden mit starker Erhöhung des Wärmeübergangs und des Druckverlustes.

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List of symbols C _f skin friction coefficient, Eq. (11) - C _D drag coefficient, Eq. (11) - D drag [N/m] - f _app apparent friction factor, Eq. (10) - h cylinder height [m] - H channel height [m] - k thermal conductivity of cylinder [W/mK] - k ₀ thermal conductivity of air [W/mK] - l cylinder length [m] - L channel length [m] - Nu Nusselt number, Eq. (7) - P dimensionless pressure - Pr Prandtl number of air - Re Reynolds number, Eq. (6) - t time [s] - T temperature [K] - T _b bulk temperature [K], Eq. (8) - U, V dimensionless velocity components - X, Y dimensionless coordinates Greek symbols thermal diffusivity [m²/s] - velocity factor, Eq. (11) - dimensionless temperature, Eq. (5) - fluid density [kg/m³] - kinematic viscosity [m²/s] - dimensionless time, Eq. (5) - difference     

Study of thermal flows from two-dimensional,upward-facing isothermal surfaces using a laser speckle photography technique

A laser specklegram or speckle photography technique allows a direct measurement of surface temperature gradients and provides a full field interrogation with an extremely high resolution from a single data taking. The specklegram technique has been successfully applied to investigate the natural convection heat transfer from an upward-facing isothermal plate. For a plate with a large aspect ratio of 15, both local and global Nusselt numbers have been determined from the direct measurement of local temperature gradients. The Rayleigh number, based on the length scale equivalent to the ratio of the surface area to the perimeter, has been varied from 9.0 × 10³ to 4.0 × 10⁴. The present result for the global heat transfer has shown that a 1/5-power law, i.e., Nu = C₁ Ra ^1/5, correlates the data more properly whilst previously published results showed a large scatter in the exponent, ranging from 1/8-power to 1/4-power. The proportional constant, C₁ has been determined to be 0.56 which shows a fairly good agreement with previously published theoretical results. The laser specklegram technique has shown a strong potential as a powerful and convenient method for an experimental assessment of natural convection heat transfer problems. The specklegram technique at the same time has eliminated the deficiencies of both the mass transfer analogy technique and the classical heat transfer measurement technique.List of symbols a characteristic length scale defined as a = A/P where A is the surface area and P is the perimeter of the plate edge [mm] - AR aspect ratio [L/H] - c defocusing distance [mm] - d image distance of Young's fringes from speckle negative - h thermal convection coefficient [W/m² · K] - average thermal convection coefficient [W/m² · °C] - H width of the test section measured perpendicular to the optic axis [mm] - k thermal conductivity [W/m · K] - L length of the test section measured parallel to the optical axis [mm] - n index of refraction - Nu local Nusselt number [ha/k] - global Nusselt number - Pr Prandtl number [v/] - q heat flux per unit area [W/m² · s] - Ra Rayleigh number - s fringe spacing [mm] - Sc Schmidt number [v/D] - T temperature [K] Greek symbols thermal diffusivity [m²/s] - volumetric coefficient of expansion (1/T) - v kinematic viscosity of air [m²/s] - wavelength of helium-neon laser [632.8 nm] - amount of speckle dislocation     

Der Einfluß der Diffusion auf die Selektivität der Desorption in einer Rieselfilmsäule

Zusammenfassung Bei der Verdunstung eines Zweistoffgemisches in ein inertes Trägergas in einer Rieselfilmsäule hängt der Trenneffekt nicht allein von der relativen Flüchtigkeit, sondern auch vom Verhältnis der Diffusionsgeschwindigkeiten beider Stoffe im Trägergas ab. Bei der Verdunstung von Isopropanol-Wasser-Gemischen in trockene Luft zeigte sich, daß das Verhältnis der gasseitigen Stoffübergangskoeffizienten bei großen Gasgeschwindigkeiten etwa gleich der Wurzel aus dem Verhältnis der Diffusionskoeffizienten war. Da der Alkolhol im Trägergas langsamer diffundiert als das Wasser, konnten flüssige Mischungen durch absatzweise Verdunstung mit Alkohol angereichert werden, obwohl der Alkohol leichterflüchtig war.Bei kleinen Gasgeschwindigkeiten lieferte der Gleichstrom immer höhere Stoffübergangskoeffizienten als der Gegenstrom. Beim Gleichstrom wurde der Einfluß des Diffusionskoeffizienten auf den Stoffübergangskoeffizienten mit abnehmender Geschwindigkeit größer, beim Gegenstrom wurde er schwächer.

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The influence of diffusion on selectivity of desorption in a wetted wall column

The desorption of a binary mixture into a stripping gas flowing through a wetted-wall column is not only governed by the vapour-liquid-equilibrium. Gas-phase diffusivities of the evaporating components have also to be taken into account. Batch wise stripping experiments of Propanol(2)-water-mixtures using dry air as the stripping gas showed, that at high gas rates the mass transfer coefficients were proportional to the square root of the diffusivities. Therefore it was possible to enrich the residual mixture with Propanol(2) because of its lower diffusivity, although Propanol(2) is more volatile.At low gas rates the mass-transfer coefficients were higher for cocurrent flow than for countercurrent flow. Besides at low gas rates the diffusivities had more influence on mass-transfer for cocurrent flow than for countercurrent flow.

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Abbreviations

Formelzeichen A [m²] Oberfläche des Rieselfilms2 r_ph·L - F [m²] freie Strömungsquerschnittfläche für das Gas in der Rieselfilmsäule: r _ph ² - K _g [–] kinetischer Trennfaktor - k _l [–] Kennzahl für den flüssigseitigen Widerstand - L [m] Länge der Rieselfilmsäule - n [mol/m³] molare Dichte - n _l [mol] Behältermolmenge - N _l,0 [mol] Behältermolmenge zu Beginn des Versuchs - n _i [mol/m² s] Molenstromdichte der Komponentei - N _i [mol/s] Molenstrom der Komponentei - N _g [mol/s] Molenstrom des Trägergases - p [Pa] Druck - p _i ⁰ [Pa] Dampfdruck der reinen Komponente - r [m] Radius - r _i [m] Innenradius des Rieselrohres - r ₁ [–] molarer bezogener Verdunstungsstrom, definiert in Gl. (3) - r ₁ [–] molarer bezogener Verdunstungsstrom, definiert in Gl. (9) - S ₁ [–] Selektivität der Desorption - s _l [m] Filmdicke - u [m/s] Geschwindigkeit - t [s] Zeit - V [m³/s] Volumenstrom - x [–] Molenbruch in der Flüssigkeit - y [–] Molenbruch in der Gasphase - z [m] Längenkoordinate Griechische Buchstaben _T [–] thermodynamischer Trennfaktor - [m/s] Stoffübergangskoeffizient - [–] Aktivitätskoeffizient - [m²/s] Diffusionszahl - [°C] Temperatur - v [m²/s] kinematische Viskosität - [–] Absättigung Indices a Austritt - e Eintritt - g gasseitig - i Komponente - l flüssigseitig - Ph Phasengrenze, Gleichgewicht - RFS Rieselfilmsäule - 1 Isopropanol - 2 Wasser dimensionslose Kennzahlen St _g = _g/¯u _g - Gz _g =4/ V _g/ _g·L - Sh _g = _g·2r _ph - Re _g =¯u _g·2r _ph/v_g - Sc _g =v _g/ _g - NTU _g =·A{itdn_g/N _g - Re _l =V _l/2r _i·v _l     

Experimentelle Prüfung der Analogie zwischen konvektiver Wärme- und Stoffübertragung bei nichtabgelöster Strömung

Zusammenfassung Stoffübertragung für das System Naphthalin/Luft und Wärmeübertragung an Luft werden an der Platte mit laminarer und turbulenter Grenzschicht, in einem Rechteckkanal im Bereich des thermischen Analufs bei hydraulisch ausgebildeter turbulenter Strömung und am Kreisrohr bzw. Ringspalt bei vollausgebildeter Strömung gemessen. Die bekannten Gesetze bei Wärmeübertragung für Platte, Kreisrohr und Ringspalt in der Schreibweise für Stoffübertragung werden bestätigt. Die Gleichung vonElser für den thermischen Analufvorgang wird den Versuchsergebnissen angepaßt. Der Exponent der Prandtl- bzw. Schmidt-Zahl nimmt im Bereich 0,7<(Pr;Sc)<2,5 je nach Strömungsform Werte zwischen 0,33 und 0,67 an.

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Mass transfer for the system naphthalin/air and heat transfer with air were measured for the following geometries: a plate with laminar and turbulent boundary-layer, a rectangular channel with fully developed turbulent velocity distribution in the thermal entrance region, a pipe of circular cross-section, an annular both in fully developed turbulent flow. For the plate, pipe and annular, the results of the two measuring methods agree very well and confirm the well known laws of heat transfer.Elser equation for the thermal entrance region is adapted to the results. The exponent of the Prandtl and Schmidt numbers varies in the range of 0,7<(Pr;Sc)<2,5 between the values 0,33 and 0,67 depending on the state of flow.

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Bezeichnungen A empirische Zahlenkonstante - B empirische Zahlenkonstante - A Austauschgröße für Impuls [kg/ms] - A _q Austauschgröße für Wärme [kg/ms] - A _S Austauschgröße für Stoff [kg/ms] - B Plattenbreite [m] - C _f Widerstandsbeiwert - D Diffusionskoeffizient [m²/s] - F freier Strömungsquerschnitt [m²] - K empirische Zahlenkonstante - K _h Korrekturfaktor für Stefanstrom - L Plattenlänge [m] - M relative Molekülmasse [g/mol] - P Gesamtdruck [N/m²] - R Gaskonstante [Nm/kg grd] - S Oberfläche [m²] - T absolute Temperatur [°K] - U benetzter Umfang [m] - W Strömungswiderstand [N] - a Temperaturleitfähigkeit [m²/s] Exponent - b Exponent - c _p spezifische Wärme [J/kg grd] - d Rohrdurchmesser [m] - hydraulischer Durchmesser [m] - l charakteristische Bezugslänge [m] - Massenstromdichte [kg/m²s] - m Exponent - n Exponent - p Partial- bzw. Dampfdruck [N/m²] - q Wärmestromdichte [W/m²] - t Zeit [s] - u Exponent - mittlere Strömungsgeschwindigkeit [m/s] - y laufende Koordinate [m] - y* mittlere Lauflänge der Grenzschicht [m] - mittlere Wärmeübergangszahl [W/m²grd] - örtliche Wärmeübergangszahl [W/m²grd] - mittlere Stoffübergangszahl [m/s] - örtliche Stoffübergangszahl [m/s] - Temperatur [°C] - Wärmeleitfähigkeit [W/m grd] - kinematische Zähigkeit [m²/s] - Dichte [kg/m³] - Druckverlustbeiwert - P Druckverlust [N/m²] - G Gewichtsverlust [kg] Dimensionslose Kenngrößen Pr=/a Prandtl-Zahl - Sc=/D Schmidt-Zahl - Le=a/D Lewis-Zahl - Pr _t=A /A _q turbulente Prandtl-Zahl - Sc _t=A /A _S turbulente Schmidt-Zahl - Re=ie225-8 ·l/ Reynolds-Zahl - Nu= ·l/ Nusselt-Zahl - Sh _l= · l/D Sherwood-Zahl - St=Nu/Re Pr Stanton-Zahl - St=Sh/ReSc Stanton-Zahl für Stoffübertragung - j _W=St Pr ^1–n Wärmeübertragungskoeffizient - j _S=St Sc ^1–n Stoffübertragungskoeffizient - Tu % Turbulenzgrad Indizes A Stoff eines Zweistoffsystems - L Luft, Plattenlänge - M Mischung, bezogen auf den Massenstrom - N Naphthalin - S Stoffübertragung - W Wand; Wärmeübertragung - a, i außen, innen - 0 Bezugszustand     

Helical flow of molten polymers in a cylindrical annulus

Summary The paper is concerned with an analytical investigation of helical flow of a non-Newtonian fluid through an annulus with a rotating inner cylinder. The shear dependence of viscosity is described by a power law and the temperature dependence by an exponential function.Velocity and temperature profiles, energy input and shear along the stream lines, pressure drop, and torque are presented for the range of input parameters encountered in polymer extrusion.The results of the study can be applied to a mixing element in a screw extruder and for a device to control extrudate temperature and output.Nomenclature a thermal diffusivity [m²/s] - b temperature coefficient [K^–1], see eq. [4] - c heat capacity [J/kg K] - h slot width [m] - I ₁,I ₂,I ₃ invariants of the rate of deformation tensor, see eq. [5] - k thermal conductivity [J/m s K] - l, L = 1/h length of the slot - l _T ,l _K thermal and kinematic entrance length - m power law exponent, see eq. [3] - M torque [m N] - p pressure [N/m²] - P dimensionless pressure gradient, see eq. [24] - P _R,P _RZ dimensionless components of the shear stress tensor, see eq. [25] and eq. [26] - r, R = r/r _wa radial coordinate - r _wa, r_wi outer and inner radius of annulus [m] - t time [s]; dwell time in the annulus - T temperature [K] - v , v_r, V_z velocity components [m/s] - v ₀ angular velocity at inner wall [m/s] - average velocity inz-direction [m/s] - V , V_R, V_Z dimensionless velocity components,v /v₀, v_r/v₀, v_z/v₀ - V _z velocity ratio, helical parameter - Y coordinate inr-direction, see eq. [20] - z, Z = z/h Pe axial coordinate - deformation - rate of deformation tensor [s^–1] - apparent viscosity [N s/m²], see eq. [3] - dimensionless temperature,b (T – T ₀) - azimuth coordinate - ratio of radii,r _wi/r_wa - density [kg/m³] - , kl shear stress tensor [N/m²] - fluidity [m²w/Nw s], see eq. [4] - Gf Griffith number, see eq. [12] - Pe Péclet number, see eq. [13] - Re Reynolds number, - 0 initial state, reference state - equilibrium state - e entrance - wi, wa at surface of inner or outer wall - r, R, z, Z, coordinates - i, j radial and axial position of nodal point in the grid - k, l tensor components Presented at Euromech 37, Napoli 6. 20–23. 1972.With 15 figuresDedicated to Prof. Dr.-Ing. G. Schenkel on his 60th birthday     

An analytical solution for the temperature profiles during injection molding,including dissipation effects

An analytical solution is obtained for the stationary temperature profile in a polymeric melt flowing into a cold cavity, which also takes into account viscous heating effects. The solution is valid for the injection stage of the molding process. Although the analytical solution is only possible after making several (at first sight) rather stringent assumptions, the calculated temperature field turns out to give a fair agreement with a numerical, more realistic approach. Approximate functions were derived for both the dissipation-independent and the dissipation-dependent parts which greatly facilitate the temperature calculations. In particular, a closed-form expression is derived for the position where the maximum temperature occurs and for the thickness of the solidified layer.The expression for the temperature field is a special case of the solution of the diffusion equation with variable coefficients and a source term.Nomenclature a thermal diffusivity [m²/s] - c specific heat [J/kg K] - D channel half-height [m] - L channel length [m] - m 1/ - P pressure [Pa] - T temperature [°C] - T _W wall temperature [°C] - T _i injection temperature [°C] - T _A Br independent part of T - T _B Br dependent part of T - T ^core asymptotic temperature - v _z() axial velocity [m/s] - W channel width [m] - x cross-channel direction [m] - z axial coordinate [m] - (x) gamma function - (a, x) incomplete gamma function - M(a, b, x) Kummer function - small parameter - () temperature function - thermal conductivity [W/mK] - viscosity [Pa · s] - ₀ consistency index - power-law exponent - density [kg/m] - similarity variable Dimensionless variables Br Brinkman number - Gz Graetz number -