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1.
Two molten low-density polyethylene melts, shaped as plates, have been inflated into a circular cylinder during isothermal conditions. Lowering the inflation rates allow the plates to be inflated into a larger volume of the cylinder before bursting. Numerical simulations of the inflations have been performed, using a time-strain separable constitutive K-BKZ equation based on the potential function from the Doi–Edwards theory. The material parameters in the constitutive model are based on liner viscoelastic and time dependent uniaxial elongational viscosities. The numerical calculations show quantitative agreement with the experiments, including the appearance of the burst, for a wide range of experimental conditions. This strongly suggests that the initiation of the burst in the polymer melts is a hydrodynamic phenomenon.  相似文献   

2.
The linear viscoelastic material functions of linear flexible polymers of uniform length are calculated from the BSW spectrum (Baumgaertel et al., 1990, 1992), and explicit analytic expressions are presented for several of the most common material functions for transient and dynamic experiments. However, numerical calculations are presented whenever needed. The BSW spectrum was determined from experimental G, G data of two sets of molten polymers of narrow molecular weight distribution, polystyrene and polybutadiene. The purpose of the mapping is to show a wide range of viscoelastic behavior which otherwise is not available in such comprehensive form. Experimental check of these predictions is still needed in most cases. Also, some insight into the predictions for the non-linear (including the non-equilibrium) viscoelastic behavior is achieved by studying two particular experiments: the start-up of uniaxial extension at constant rate and the start-up of shear flow at constant rate.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.  相似文献   

3.
We study the simultaneous one-dimensional flow of water and oil in a heterogeneous medium modelled by the Buckley-Leverett equation. It is shown both by analytical solutions and by numerical experiments that this hyperbolic model is unstable in the following sense: Perturbations in physical parameters in a tiny region of the reservoir may lead to a totally different picture of the flow. This means that simulation results obtained by solving the hyperbolic Buckley-Leverett equation may be unreliable.Symbols and Notation f fractional flow function varying withs andx - value off outsideI - value off insideI - local approximation off around¯x - f ,f + values of - f j n value off atS j n andx j - g acceleration due to gravity [ms–2] - I interval containing a low permeable rock - k dimensionless absolute permeability - k * absolute permeability [m2] - k c * characteristic absolute permeability [m2] - k ro relative oil permeability - k rw relative water permeability - L * characteristic length [m] - L 1 the space of absolutely integrable functions - L the space of bounded functions - P c dimensionless capillary pressure function - P c * capillary pressure function [Pa] - P c * characteristic pressure [Pa] - S similarity solution - S j n numerical approximation tos(xj, tn) - S 1, S2,S 3 constant values ofs - s water saturation - value ofs at - s L left state ofs (wrt. ) - s R right state ofs (wrt. ) - s s for a fixed value of in Section 3 - T value oft - t dimensionless time coordinate - t * time coordinate [s] - t c * characteristic time [s] - t n temporal grid point,t n=n t - v * total filtration (Darcy) velocity [ms–1] - W, , v dimensionless numbers defined by Equations (4), (5) and (6) - x dimensionless spatial coordinate [m] - x * spatial coordinate [m] - x j spatial grid piont,x j=j x - discontinuity curve in (x, t) space - right limiting value of¯x - left limiting value of¯x - angle between flow direction and horizontal direction - t temporal grid spacing - x spatial grid spacing - length ofI - parameter measuring the capillary effects - argument ofS - o dimensionless dynamic oil viscosity - w dimensionless dynamic water viscosity - c * characteristic viscosity [kg m–1s–1] - o * dynamic oil viscosity [kg m–1s–1] - w * dynamic water viscosity [k gm–1s–1] - o dimensionless density of oil - w dimensionless density of water - c * characteristic density [kgm–3] - o * density of oil [kgm–3] - w * density of water [kgm–3] - porosity - dimensionless diffusion function varying withs andx - * dimensionless function varying with s andx * [kg–1m3s] - j n value of atS j n andx j This research has been supported by VISTA, a research cooperation between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap a.s. (Statoil).  相似文献   

4.
Summary A family of sensors which measure the complex coefficient of dynamic viscosity ( *) is discussed. Using a first order approximation to a general viscoelastic fluid, it is shown how these instruments determine * for a general linear viscoelastic fluid. The measurement technique employed relates the linear viscous damping and resonant frequency of these instruments in the presence and absence of fluid to *. This analysis also provides the inherent limitations of the sensors.
Resonante Torsionsschwingungen: Eine Anwendung zur Dynamischen Viscometrie
Übersicht Eine Familie von Sensoren wird diskutiert, welche den komplexen Koeffizienten ( *) der Viskosität misst. Mit Hilfe einer Approximation erster Ordnung eines allgemeines viskoelastisches Fluid wird gezeigt, wie diese Instrumente verwendet werden können, um * für ein allgemeines linear viskoelastisches Fluid zu bestimmen. Die Messtechnik verwendet die Tatsache, daß Resonanzfrequenz und linearviskose Dämpfung der Sensoren abhängig sind vom Fluid, welches sich in der direkten Umgebung des Sensors befindet. Die Analyse, die hier verwendet wird, zeigt Möglichkeiten und Grenzen der Sensoren auf.
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5.
The linear viscoelastic modulus G(t) predicted by the analytical formulations of Schieber (1993), Wedgewood (1993), Dasbach et al. (1992), and Booij and van Wiechen (1970) for the free-draining Hookean dumbbell with internal viscosity (IV) are compared with exact analytical results and exact numerical results obtained from Brownian dynamics simulations. All of these analytical formulations employ the Booij and van Wiechen expression for the IV force, thereby eliminating errors associated with linearization of the deformational velocity, however the theories differ in the approximations employed to solve configuration moment equations. Comparison with the exact G(t) results provides a means of testing these approximations. The approximate theories all correctly predict the singular part of G(t) at t = 0, providing correct predictions of , however deviations from the exact G(t) are seen in all cases for t > 0.  相似文献   

6.
A. Kaye 《Rheologica Acta》1969,8(2):244-244
An apparatus designed to measure the dynamic viscoelastic response of polymer melts is described. Dynamic elasticity (G) and viscosity () can be measured over a frequency range 10–2-10–3 Hz and at temperatures up to 350 °C. The sample under test is held in a cone and plate assembly. A small strain is introduced by driving the plate with a variable speed synchronous motor and off-centre cam at low frequencies and by an electromagnetic vibrator at high frequencies. The amplitudes of the cone and plate are detected using the optical lever principle and photocell strips. The phase difference between the cone and plate is measured from a recorder trace at low frequencies and by direct reading on a meter at high frequencies.Results are described of measurements on silicone fluids, and on commercial grades of polyethylene with different molecular weight distributions and degrees of branching.A discussion is given of the correlation between the dynamic viscosity measurements and those taken under steady-flow conditions.Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968. — Original paper published in J. Sci. Instruments Series 2,1, 1102–1112 (1968).  相似文献   

7.
A small fixed cylinder attached to a load cell almost touches a larger, rotating cylinder (axes parallel). Newtonian liquids in the gap give reasonable loads, but viscoelastic liquids give markedly enhanced load bearing in relation to their apparent viscosities. F normal load on small cylinder - h minimum film thickness between cylinders - L length of smaller cylinder - R reduced radius, defined by equation 1/R = 1/R 1 + 1/R 2 - R 1 radius of small cylinder - R 2 radius of large cylinder - U surface velocity of large cylinder - load factor defined by equation = Fh/URLµ - µ viscosity of liquid  相似文献   

8.
The growth of two-dimensional disturbances generated in a supersonic (M = 6) boundary layer on a flat plate by a periodic perturbation of the injection/suction type is investigated on the basis of a numerical solution of the Navier-Stokes equations. For small initial perturbation amplitudes, the second-mode growth rate obtained from the numerical modeling coincides with the growth rate calculated using linear theory with account for the non-parallelism of the main flow. Calculations performed for large initial perturbation amplitudes reveal the nonlinear dynamics of the perturbation growth downstream, with rapid growth of the higher multiple harmonics.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 33–44. Original Russian Text Copyright © 2004 by Egorov, Sudakov, Fedorov.  相似文献   

9.
Planar oscillations of thin piezoplates are important within the context of using this type of piezoelements as resonator frequency filters, frequency stabilizers, elements of piezotransformers, and other technological devices. In the publications currently known one usually considers piezoplates with elastic material behavior and linear governing equations. By their mechanical nature, however, a number of piezoelements, particularly piezoceramics, are viscoelastic, which, depending on the loading conditions, can lead to substantial dissipative heating of the piezoelement and confine its operation [3]. The use of piezopolymers and their composites raises particularly important issues of dissipative heating. At the present time the behavior of a piezoelement including heating can be described by the theory of thermoelectroviscoelasticity (TEVE) [2, 3], including the interaction between electromechanical and thermal fields. The complexity of TEVE problems leads to the necessity of using numerical methods to solve them, with the finite element method (FEM) being widely used in recent years. The present study is devoted to stating and solving TEVE problems concerning thin piezoceramic plates by the FEM. We treat a thin piezoceramic plate, confined by an arbitrary contour L and polarized across its thickness. A harmonic potential difference eit is supplied to electrodes located on the smooth boundaries of the plate. Convective heat exchange with the surrounding media of temperatures T k s and Ts is implemented at the contour surfaces and boundaries free of electrodes. The heat transfer coefficients equal, respectively, k T and T. The initial plate temperature is T0. The smooth boundary are free of mechanical loading. The mechanical forces at the contour surfaces are distributed symmetrically with respect to the mean plane of the plate.S. P. Timoshenko Institute of Mechanics, Ukrainian Academy of Sciences, Kiev (Ukraine). Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 69–76, February 1994.  相似文献   

10.
A homogeneous, isotropic plate occupies the region 0x 1, |x 2|a, |x 3|h, where the ratio h/a is sufficiently small so that the classical theory of thin plate bending applies. The short end of the plate at x 1=0 is clamped while the long sides are free. This cantilever plate is now loaded at x 1=+ by an applied twisting moment, by a bending moment or by flexure. Despite the fundamental nature of these problems, and the long history of thin plate theory, no solutions are to be found in the existing literature that will determine (for instance) the important unknown resultants V 1, M 11 at the clamped end x 1=0. The main reason for this is that this combination of boundary conditions leads to severe oscillating singularities of the field in the corners (0, ±a). The fact that such singularities must exist is widely known, but we present here for the first time a method of solution that takes these singularities fully into account.Our numerical results show that the values of M 11, V 1 on x 1=0 bear little resemblance to those of the corresponding Saint-Venant solutions, which do not fully satisfy the boundary conditions at the clamped end. Indeed, significantly large values of these resultants were found at points far enough from the corners so as to be relevant in actual engineering applications. Also of interest are certain weighted integrals of M 11, V 1 which we calculate. These constants determine the effect of the clamping at large distances (greater than 4a, say) from the cla,ped end. At such distances, the effect of the clamping is merely to impose an additional rigid body deflection on the plate.Finally, we consider the plate of finite length. Provided that the aspect ratio is 2 or more, we give accurate approximate solutions for the torsion, bending or flexure of a finite plate clamped at both ends.  相似文献   

11.
In this paper a simplified three-dimensional constitutive equation for viscoelastic rubber-like solids is derived by employing a generalized strain measure and an asymptotic expansion similar to that used by Coleman and Noll (1961) in their derivation of finite linear viscoelasticity (FLV) theory. The first term of the expansion represents exactly the time and strain separability relaxation behavior exhibited by certain soft polymers in the rubbery state and in the transition zone between the glassy and rubbery states. The relaxation spectra of such polymers are said to be deformation independent. Retention of higher order terms of the asymptotic expansion is recommended for treating deformation dependent spectra.Certain assumptions for the solid theory are relaxed in order to obtain a constitutive equation for uncross-linked liquid materials which exhibit large elastic recovery properties.Apart from the strain energyW(I1,I 2), which alternatively characterizes the long-time elastic response of solids or the instantaneous elastic response of elastic liquids, only the linear viscoelastic relaxation modulus is required for the first-order theory. Both types of material functions can be obtained, in theory, from simple laboratory testing procedures. The constitutive equations for solids proposed by Chang, Bloch and Tschoegl (1976) and a special form of K-BKZ theory for elastic liquids are shown to be particular cases of the first-order theory.Previously published experimental data on a cross-linked styrene-butadiene rubber (SBR) and an uncross-linked polyisobutylene (PIB) rubber is used to corroborate the theory.  相似文献   

12.
In this paper we show that problems concerning the development of a boundary layer on a semi-infinite plate when the outer flow speed is of the form U = (1 + ct)b a, and on a cylinder when the outer flow speed has the forms U = ctxm and U = (1 + ct)b axm, are self-similar. We present the results of numerical calculations for various values of , b, and m. We consider the problem of a stepwise nonstationary heating of a plate, impulsively set into motion in an incompressible fluid; we show that this problem is self-similar and obtain its solution numerically.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 122–125, July–August, 1975.  相似文献   

13.
Strouhal numbers in the wake of two inline cylinders   总被引:2,自引:0,他引:2  
The dominant vortex frequencies f s in the wake of two tandem circular cylinders of identical diameter d have been measured simultaneously using two hot wires placed behind each cylinder. Measurements were conducted over the Reynolds number Re (U d/, where U and are the free-stream velocity and the kinematic viscosity of fluid, respectively) =800–4.2×104 and the cylinder centre-to-centre spacing L/d=1–15. The Strouhal number St (f s d/U ) exhibits a strong dependence on L/d and Re. For L/d<(L/d)c, which is a critical value and ranges between 3.5 and 5, there is no vortex street formed in the gap between the cylinders, and St measured behind the downstream cylinder drops rapidly for increasing L/d. For L/d>(L/d)c, co-shedding occurs, that is, vortices are shed from the upstream as well as the downstream cylinder, and their frequencies are found to be identical. St climbs with increasing L/d, approaching a constant between 0.18 and 0.22 for L/d>10. The StRe relationship is classified into four categories, based on their behaviours, which are associated with distinct flow physics—category 1: for 1L/d<2, the shear layers separated from the upstream cylinder roll up behind the downstream cylinder; category 2: for 2L/d3, there is a transition from the shear layer rollup behind to reattachment on the downstream cylinder; category 3: for 3<L/d5, transition from the reattachment to co-shedding regime occurs at a critical Reynolds number; and category 4: the flow for L/d>5 is characterized by co-shedding only. The present measurements reconfirm the previous observation of a bi-stable flow at the transition from the reattachment to co-shedding regime. It is found for the first time that another bi-stable flow occurs at the transition from category 1 to 2, that is, the stable reattachment co-exists with the stable rollup (behind the downstream cylinder) of shear layers separating from the upstream cylinder, resulting in two distinct vortex-shedding frequencies even at the same Re and L/d. The St behaviour is further discussed along with flow visualization using the laser-induced fluorescence technique.  相似文献   

14.
We focus on the linear viscoelastic response of heterogeneous nematic polymers to small amplitude oscillatory shear, paying special attention to the macroscopic influence of strong plate anchoring conditions. The model consists of the Stokes hydrodynamic equations with viscous and nematic stresses, coupled to orientational dynamics and structure driven by the flow gradient, an excluded-volume potential, and a two-constant distortional elasticity potential. We show that the dynamical response simplifies when plate anchoring is either tangential or homeotropic, recovering explicitly solvable Leslie–Ericksen–Frank behavior together with weakly varying order parameters across the plate gap. With these plate conditions, we establish “model consistency” so that all experimental driving conditions (plate-controlled velocity [strain] or shear stress, imposed oscillatory pressure) yield identical dynamic moduli for the same material parameters and anchoring conditions, eliminating the culpability of device influence in scaling behavior. Two physical predictions emerge that imply significant macroscopic elastic and viscous effects controlled by plate anchoring relative to flow geometry: (1) The storage modulus is enhanced by two to three orders of magnitude for homeotropic relative to parallel anchoring, across all frequencies. (2) The loss modulus exhibits enhancement of a factor of two to three for homeotropic over tangential anchoring, restricted to low frequencies. We further deduce a scaling law for the dynamic moduli versus anisotropy of the distortional elasticity potential.
Eric P. ChoateEmail:
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15.
In the introduction some postulates on which the linear theory of viscoelasticity is based are recalled, and the postulate of passivity is substituted by a stronger postulate called detailed passivity.Next, a symmetric formulation of this theory is presented which is founded in a well-balanced way on the limiting properties of elasticity and viscosity. This leads to the introduction of the basic functions of creep compliance J +(t) and stressing viscosity +(t) associated to one another, whereas the basic functions retardation fluidity +(t) and relaxation modulus G +(t) emerge as their time derivatives. Correspondingly, four complex basic functions are defined as their Carson transforms.In addition to the proper retardation and relaxation terms, these basic functions contain the non-disappearing constants of either instantaneous compliance J 0 or instantaneous viscosity 0 and also of either ultimate fluidity or ultimate modulus G . Therefrom ensues a classification of linear viscoelastic materials into four types: instantaneous elasticity or viscosity is allowed to combine with ultimate viscosity or elasticity. The latter alternative, signifying fluidlike or solidlike materials, leads, of course, to a quite different behavior in many situations; however, remarkable distinctive features are associated to the first one as well.A few respective examples are outlined: 1) propagation of shear waves in a half-space with periodic and step-shaped excitation, 2) dissipation of work in a torsional vibration damper, and 3) shear flow between two parallel porous plates with injection and suction.Finally, materials with viscous initial behavior are defended against the notion that they be of no or almost no real significance.Delivered as a Plenary Lecture at the Fourth European Rheology Conference, Seville (Spain), 4–9 September 1994. The herein only outlined topics are taken from a recently pulished monograph (Geisekus, 1994) in which complete derivations of the results and more detailed discussions are given.Dedicated to Professor K. Walters on the occasion of his 60th birthday.  相似文献   

16.
The droplet dynamics passing through a cylinder obstruction was investigated with direct numerical simulations with FE-FTM (Finite Element-Front Tracking Method). The effect of droplet size and capillary number (Ca) was studied for both Newtonian and viscoelastic fluids. In the case of Newtonian droplet immersed in Newtonian medium, the droplet breakup induced by the geometric hindrance depends on the droplet size. As Ca increases, the short droplets (1.3 times longer than the channel width) break up while passing through the obstruction. However, the breakup does not occur for longer droplets (1.8 times longer than the channel width). When the viscoelastic fluid characterized by the Oldroyd-B model is considered, the Newtonian droplet immersed in viscoelastic medium breaks up into two smaller droplets while passing through the cylinder obstruction with increasing Dem (Deborah number of the medium). We also show that the normal stress difference plays a key role on the droplet breakup and the droplet extension. The normal stress difference is enhanced in the negative wake region due to the droplet flow, which also promotes droplet extension in that region. This numerical study provides information not only on underlying physics of the droplet flows passing through a cylinder obstruction but also on the useful guidelines for microfluidic applications.  相似文献   

17.
The equations governing the free convection boundary-layer flow on a horizontal circular cylinder on which there is a prescribed surface heat flux are solved using a finite-difference scheme. This numerical solution is then used to compare the accuracy of two proposed series expansions, a Blasius expansion and a Görtler-type expansion. It is shown that the former method is better at estimating temperature profiles while the latter is better at estimating velocity profiles.
Bemerkung über die freie Konvektionsgrenzschicht an einem horizontalen Kreiszylinder mit gleichförmigem Wärmestrom
Zusammenfassung Die Grenzschichtgleichungen für die freie Konvektion an einem horizontalen Kreiszylinder mit gleichförmigem Wärmestrom durch die Oberfläche wird mit Hilfe eines finiten Differenzverfahrens gelöst. Die numerisch ermittelten Ergebnisse werden nachher für den Vergleich der Genauigkeit von zwei Reihendarstellungen der Lösung der Grenzschichtsgleichungen benützt. Diese Reihen sind vom Blasiusbzw. Görtier-Typ. Es wird bemerkt, daß die Reihendarstellung von Blasius die Temperaturprofile besser beschreibt, während die Reihenentwicklung der Görtlerschen Art für die Geschwindigkeitsprofile eine gute Übereinstimmung mit der exakten Lösung zeigt.

Nomenclature a radius of the cylinder - g acceleration of gravity - P r Prandtl number - Q prescribed (constant) heat flux - T temperature of the fluid - t 0 temperature of the ambient fluid - u velocity in thex-direction - v velocity in they-direction - x co-ordinate measuring distance round the cylinder - y co-ordinate measuring distance normal to the cylinder - G r Grashof number=g Q a 4/v2 - coefficient of thermal expansion - x thermal conductivity - v kinematic viscosity - w skin friction  相似文献   

18.
Übersicht Mit Substitutionen für die Spalthöhe und den hydrodynamischen Druck wird eine neue Differentialgleichung abgeleitet, welche an die Stelle der Reynoldsschen Gleichung tritt. Gegenüber dieser hat sie den Vorteil, nicht nur spezielle Lösungen — die mit dem physikalischen Geschehen meist nicht übereinstimmen-zu geben, sondern für alle praktisch wichtigen Fälle geschlossene Lösungen zu ermöglichen, sofern geeignete Ansätze für die Spaltkontur gewählt werden. Solche Ansätze lassen sich entsprechend dem Aufbau der neuen Differentialgleichung unschwer in einem Konturen-Katalog zusammenfassen, der für alle Bedürfnisse der Praxis ausreicht. Zwei Beispiele, deren Lösungen bekannt sind (die unendlich breite Platte und der unendlich breite Kreiszylinder), sollen der Einführung in die neue Methode dienen und die Genauigkeit aufzeigen. Im Hauptteil wird das bisher ungelöste Problem Kugel auf Ebene behandelt und der Verlauf des hydrodynamischen Druckes im Kugelspalt angegeben.
Summary By substitutions for the distance across the gap and for the hydrodynamic pressure a new differential equation is derived which replaces the Reynolds equation. Compared to the latter the new equation has the advantage that it has analytical solutions not only in special cases which usually do not correspond to practical problems, but also in all essential practical cases if suitable expressions are chosen for the gap profile. Corresponding to the structure of the new differential equation such profile expressions can easily be listed up in a profile-catalogue which meets all practical requirements. Two examples with known results (the infinitely wide plate and the infinitely long cylinder) are presented for the purpose of introduction into the new method and for proof of accuracy. In the main part the problem of a sphere on a plate is treated which is still unsolved, and the hydrodynamic pressure profile between the two bodies is calculated.
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19.
A procedure was developed to enable the direct numerical integration of the Fourier integral transform equation relating G(t) to G() by considering integration limits that vary as a function of time and which define a range of discrete sub-intervals within the complete frequency domain data set. The method provides results that are in very close agreement to results determined from a relaxation spectrum. However, at low values of time the solution to the variable limit integral transform is sensitive to the absence of a contribution beyond the upper experimental limit of the frequency domain data. G(t) results determined from the conversion of shifted master G() experimental data using the variable limit integral transformation and the relaxation spectrum compared favourably with actual shifted master G(t) experimental data. The former curves were characterised by the same form and trend as the experimental results, confirming that the underlying viscoelastic behaviour is well represented. While the variable limit Fourier integral transform procedure provides a good approximation to relaxation spectrum results, the latter is clearly the more robust method of converting data from the frequency to the time domain.It was observed that the time-temperature superposition procedure used in the construction of shifted master curves can magnify potential differences between the shifted G(t) values determined from the conversion of G() data and the actual experimental G(t) results, when compared to data that has not been shifted to a master curve.  相似文献   

20.
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.
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.

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  相似文献   

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