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1.
Summary Transient stresses including normal stresses, which are developed in a polymer melt by a suddenly imposed constant rate of shear, are investigated by mechanical measurement and, indirectly, with the aid of the flow birefringence technique. For the latter purpose use is made of the so-called stress-optical law, which is carefully checked.It appears that the essentially linear model of the rubberlike liquid, as proposed byLodge, is capable of describing the behaviour of polymer melts rather well, if the applied total shear does not exceed unity. In order to describe also steady state values of the stresses successfully, one should extend measurements to extremely low shear rates.These statements are verified with the aid of a method which was originally designed bySchwarzl andStruik for the practical calculation of interrelations between linear viscoelastic functions. In the present paper dynamic shear moduli are used as reference functions.
Zusammenfassung Mit der Zeit anwachsende Spannungen, darunter auch Normalspannungen, wie sie sich nach dem plötzlichen Anlegen einer konstanten Schergeschwindigkeit in einer Polymerschmelze entwickeln, werden mit Hilfe mechanischer Messungen und indirekt mit Hilfe der Strömungsdoppelbrechung untersucht. Für den letzteren Zweck wird das sogenannte spannungsoptische Gesetz herangezogen, dessen Gültigkeit sorgfältig überprüft wird.Es ergibt sich, daß das im Wesen lineare Modell der gummiartigen Flüssigkeit, wie es vonLodge vorgeschlagen wurde, sich recht gut zur Beschreibung des Verhaltens von Polymerschmelzen eignet, solange der im ganzen angelegte Schub den Wert Eins nicht überschreitet. Um auch stationäre Werte der Spannungen in die Beschreibung erfolgreich einzubeziehen, sollte man die Messungen bis zu extrem niedrigen Schergeschwindigkeiten ausdehnen.Die gemachten Feststellungen werden mit Hilfe einer Methode verifiziert, die vonSchwarzl undStruik ursprünglich für die praktische Berechnung von Beziehungen zwischen Zustandsfunktionen entwickelt wurde, die dem linear viskoelastischen Verhalten entsprechen. In der vorliegenden Veröffentlichung dienen die dynamischen Schubmoduln als Bezugsfunktionen.

a T shift factor - B ij Finger deformation tensor - C stress-optical coefficient, (m2/N) - f (p jl ) undetermined scalar function - G shear modulus, (N/m2) - G(t) time dependent shear modulus, (N/m2) - G() shear storage modulus, (N/m2) - G() shear loss modulus, (N/m2) - G r reduced shear storage modulus, (N/m2) - G r reduced shear loss modulus, (N/m2) - H() shear relaxation time spectrum, (N/m2) - k Boltzmann constant, (Nm/°K) - n ik refractive index tensor - p undetermined hydrostatic pressure, (N/m2) - p ij ,p ik stress tensor, (N/m2) - p 21 shear stress, (N/m2) - p 11p 22 first normal stress difference, (N/m2) - p 22p 33 second normal stress difference, (N/m2) - q shear rate, (s–1) - t, t time, (s) - T absolute temperature, (°K) - T 0 reference temperature, (°K) - x the ratiot/ - x position vector of a material point after deformation, (m) - x position vector of a material point before deformation, (m) - 0, 1 constants in eq. [37] - 0, 1 constants in eq. [37] - shear deformation - (t, t) time dependent shear deformation - ij unity tensor - n flow birefringence in the 1–2 plane - (q) non-Newtonian shear viscosity, (N s/m2) - * () complex dynamic viscosity, (N s/m2) - | * ()| absolute value of complex dynamic viscosity, (N s/m2) - () real part of complex dynamic viscosity, (N s/m2) - () imaginary part of complex dynamic viscosity, (N s/m2) - (t — t) memory function, (N/m2 · s) - v number of effective chains per unit of volume, (m–3) - temperature dependent density, (kg/m3) - 0 density at reference temperatureT 0, (kg/m3) - relaxation time, (s) - integration variable, (s) - (x) approximate intensity function - 1 (x) error function - extinction angle - m orientation angle of the stress ellipsoid - circular frequency, (s–1) - 1 direction of flow - 2 direction of the velocity gradient - 3 indifferent direction - t time dependence The present investigation has been carried out under the auspices of the Netherlands Organization for the Advancement of Pure Research (Z. W. O.).North Atlantic Treaty Organization Science Post Doctoral Fellow.Research Fellow, Delft University of Technology.With 11 figures and 2 tables  相似文献   

2.
We report on measurements of the velocity field and turbulence fluctuations in a hexagonal array of circular jets, impinging normally on a plane wall, using particle image velocimetry (PIV). Results for mean velocity and turbulent stresses are presented in various horizontal and vertical planes. From the measurements, we have identified some major features of impinging jet arrays and we discuss their mutual interaction, collision on the plate, and consequent backwash, which generate recirculating motion between the jets. The length of the jet core, the production of turbulence kinetic energy, and the model of the exhaust mechanisms for spent fluid are also discussed. The measurements indicated that the interaction between the self-induced cross flow and the wall jets resulted in the formation of a system of horseshoe-type vortices that circumscribe the outer jets of the array. The instantaneous snapshots of the velocity field reveal some interesting features of the flow dynamics, indicating a breakdown of some of the jets before reaching the plate, which may have consequences on the distribution of the instantaneous heat transfer.List of symbols Dm Nozzle diameter in multiple jet array nozzle plate (m) - Ds Pipe diameter in single jet rig (m) - H Distance between nozzle and impingement plate (m) - k Turbulent kinetic energy (m2/s2) - L Pipe length (m) - Pk Production of turbulent kinetic energy (m2/s3) - Puu , Pvv Normal components of Pk (m2/s3) - Puv Shear component of Pk (m2/s3) - s Pitch (m) - Ubulk Surface-averaged exit velocity (single jet) (m/s) - UCL Center line jet exit velocity (jet array), m/s - u, v Mean velocity components in x and y directions (m/s) - u, v, w Instantaneous velocity in x, y, and z directions (m/s) - u, v, w Velocity fluctuation in x, y, and z directions (m/s) - u2, v2, w2 Reynolds normal stress components (m2/s2) - uv Reynolds shear stress component (m2/s2) - x, z Coordinates parallel to impingement plate (m) - y Coordinate perpendicular to impingement plate (m)  相似文献   

3.
This paper deals with theoretical aspects of momentum, heat and mass transfer in turbulent channel flow and in particular with phenomena occurring close to the wall. The analysis presented involves the use of a boundary-layer growth-breakdown model. Theoretical expressions have been derived predicting heat and mass transfer at smooth surfaces in the fully developed and entrance region and at surfaces provided with ideal two-dimensional roughness elements. The analysis is restricted to fluids having Prandtl and Schmidt numbers larger than one. Good agreement appears to exist between theoretical predictions and experimental observations.
Zusammenfassung Diese Arbeit behandelt die Theorie der Übertragungsvorgänge von Impuls, Wärme und Stoff in turbulenter Kanalströmung unter besonderer Berücksichtigung der Vorgänge in Wandnähe. Das verwendete Modell beruht auf dem Zusammenbruch der anwachsenden Grenzschicht. Für die ausgebildete Strömung und für den Einlaufbereich bei glatter Wand und bei Oberflächen mit idealen zweidimensionalen Rauhigkeitselementen werden theoretische Ausdrücke abgeleitet bei Beschränkung auf Prandtl- und Schmidt-Zahlen über Eins. Zwischen den theoretischen Voraussagen und den Versuchsergebnissen scheint gute Übereinstimmung zu herrschen.

Nomenclature a thermal diffusivity [m2/s] - c concentration [kg/m3] - c p specific heat [J/kg °C] - D molecular diffusivity [m2/s] - G relative increase in friction factor due to surface roughening - d pipe diameter [m] - e height (depth) of roughness element [m] - e p+ dimensionless roughness height (depth) - F parameter denoting the ratio - f friction factor for smooth surface and isothermal conditions - f h friction factor for heating conditions - f r friction factor for artificially roughened surface - n av average frequency of fluctuations at the wall [s–1] - q heat flux [W/m2] - q w heat flux at the wall [W/m2] - q wr heat flux at roughened wall [W/m2] - q wx wall heat flux to growing laminar boundary layer at positionx [W/m2] - R ma longitudinal correlation coefficient for mass transfer - R mo longitudinal correlation coefficient for momentum transfer - T temperature [°C] - T b bulk temperature of fluid [°C] - T 0 fluid temperature at edge of viscous boundary layer (edge of viscous region) [°C] - T w wall temperature [°C] - T wx wall temperature at positionx for growing laminar boundary layer [°C] - t time [s] - t 0 characteristic time period associated with boundary layer growth [s] - u local axial fluid velocity, at wall distancey, for turbulent flow also denoting the mean velocity at that distance [m/s] - u b bulk fluid velocity [m/s] - u 0 fluid velocity at edge of viscous boundary layer (edge of viscous region) [m/s] - u 0r fluid velocity at edge of viscous region for the case of an artificially roughened wall [m/s] - u axial fluid velocity fluctuation [m/s] - u + dimengionless fluid velocity,u/(w/)1/2 - u i + instantaneous value ofu + - u min + minimum value ofu i + - u r + root mean square value of dimensionless axial velocity - u 0 + value ofu + at edge of viscous region - v fluid velocity normal to flow direction and normal to wall [m/s] - v fluctuation of the velocityv [m/s] - x coordinate in flow direction [m] - x axial distance interval [m] - x + dimensionless distance interval - x 0 viscous boundary layer growth length [m] - x 0 + dimensionless boundary growth length - x r axial dixtance between roughness elements [m] - x r + dimensionless distance between roughness elements - x h value of viscous boundary growth length for heating conditions [m] - y distance from wall [m] - y + dimensionless wall distance - y v thickness of viscous region [m] - y v + dimensionless form ofy v - z u unheated (zero mass transfer) part of elementary viscous boundary layer in entrance region [m] - z h heated (mass transfer) part of elementary viscous boundary layer [m] - z v lateral extent of elementary viscous boundary layer [m] Greek symbols heat transfer coefficient defined with respect to bulk fluid temperature [W/m2 °C] - 0 viscous region heat transfer coefficient [W/m2 °C] - 0h viscous boundary layer heat transfer coefficient averaged over lengthx 0 for conditions of heating [W/m2 °C] - 0hh viscous region heat transfer coefficient averaged over lengthx h for conditions of heating [W/m2 °C] - entrance region heat transfer coefficient at position [W/m2 °C - ,t viscous boundary layer heat transfer coefficient at position and timet [W/m2 °C] - mass transfer coefficient [m/s] - av average value of mass transfer coefficient [m/s] - x mass transfer coefficient for viscous boundary layer at positionx [m/s] - entrance region mass transfer coefficient at position [m/s] - thickness of laminar (viscous) boundary layer evaluated atu=1/2u 0 [m] - max maximum value of boundary layer thickness [m] - i turbulent diffusivity for momentum transfer [m2/s] - h turbulent diffusivity for heat transfer [m2/s] - m turbulent diffusivity for mass transfer [m2/s] - turbulent intensity - thermal conductivity [W/m °C] - kinematic viscosity [m2/s] - 0 value ofv at edge of viscous region [m2/s] - w value ofv at the wall [m2/s] - density [kg/m3] - shear stress [N/m2] - tx local value of wall shear stress associated with viscous boundary layer growth [N/m2] - 0 value of wall shear stress averaged over lengthx 0 [N/m2] - 0r value of 0 for the case of an artificially roughened wall [N/m2] - 0h value of 0 for heating conditions [N/m2] - h value of wall shear stress for heating conditions, averaged over lengthx h [N/m2] - w wall shear stress for conditions of turbulent flow [N/m2] - wh value of w for heating conditions [N/m2] - dimensionless axial distancex/x 0 in extrance region Dimensionless numbers Nu Nusselt number (d/) - Nu x Entrance region Nusselt number at axial positionx - Nu h Nusselt number for heating conditions - Nu r Nusselt number for the case of artificially roughened surface - Pr Prandtl number (v/a) - Re Reynolds number (d u b/v) - Re b Boundary layer Reynolds number (1/2 u 0/v) - Re ber Critical value ofRe b - Sh Sherwood number (d/D) - Sh x entrance region Sherwood number at axial positionx - Sc Schmidt number (v/D)  相似文献   

4.
Zusammenfassung Die Dephlegmation ist eine nicht-adiabate Rektifikation ohne Rücklauf am Apparatekopf, die durch die Ackermann/Colburn-Drew-Gleichungen beschrieben werden. In diesem Beitrag wird eine vergleichende Analyse von stationären makroskopischen Modellen mit unterschiedlicher Reduktion gegeben.
On simple calculation procedures of binary mixed vapour dephlegmation
The dephlegmation is a non-adiabatic rectification without reflux at the top of the column, which for calculation can be described by the Ackermann/Colburn-Drew-equations. In this paper a comparing analysis of steady macroscopic models with different degree of model reduction is given.

Nomenklatur A Austauschfläche pro Apparate- m2/m länge - C Korrekturfunktion - D Diffusionskoeffizient m2/h - Enthalpiestrom J/h - Impulsstrom kmol m/h - N Zahl der theoretischen Trennstufen - N Molstrom kmol/h - T Temperatur °C - Molmasse kg/kmol - L Apparatelänge m - cp molare Wärmekapazität J/kmol grd - d Durchmesser m - Enthalpiestromdichte J/h m2 - g Erdbeschleunigung m/h2 - h molare Enthalpie J/kmol - j Impulsstromdichte kmol/h m - n Molstromdichte kmol/h m2 - 1 Länge m - u axiale Geschwindigkeit m/h - x Molkonzentration im Fluid kmol/kmol - y Molkonzentration im Dampf kmol/kmol - z Molkonzentration (S. G1.2) kmol/kmol - Differenz - t Kontaktzeit h - Austauschkoeffizient für die J/h m2 grd Enthalpie - ß Austauschkoeffizient für die kmol/h m2 Komponente - Austauschkoeffizient für den kmol/h m Impuls - Massendichte kg/m2 - Zähigkeit kg/m h - f Rieselfilmdicke m - f Wärmedurchgangskoeffizient J/h m2 grd Kennzahlen Re u·d·/ - Sc /·D - Sh ··d/·D Indizes a außen - d dampfseitig - f flüssigkeitsseitig - g Phasengrenze - h hydraulisch - i innen - k Kühlmedium - m mittel - o oberes Apparateende - t total - u unteres Apparateende - w Wand - x Komponente an LS im Fluid - y Komponente an LS im Dampf - gültig für große übergehende Molströme  相似文献   

5.
Zusammenfassung Es wird gezeigt, daß bei Kenntnis der Fließkurve viskoelastischer Flüssigkeiten allein aus der Drehmomentkennlinie des stationär betriebenen Kugel-Kugel-Rheometers eine Relaxationszeit der räumlichen Beanspruchung bestimmt werden kann. Ausgehend von derColeman-Nollschen Entwicklungsschreibweise der rheologischen Zustandsfunktion wird das Geschwindigkeitsfeld als Potenzreihe der Kreisfrequenz bis zur 3. Ordnung bestimmt und zur Drehmomentbeziehung integriert.Messungen an einigen Versuchssubstanzen bestätigen die Tauglichkeit der entwickelten Methode.Häufig verwendete Formelzeichen –a N/m2 isotroper Druckanteil - m/s Geschwindigkeitsvektor - e 14 Integrationskonstanten - f i() Geometriefunktionen - m vektorielle Feldfunktion - ms vektorielle Feldfunktion - ms2 vektorielle Feldfunktion - k i() Geometriefunktionen - t 0 s Relaxationszeit der räumlichen Beanspruchung - m/s Geschwindigkeitsvektor erster Ordnung - m/s Geschwindigkeitsvektor zweiter Ordnung - m/s Geschwindigkeitsvektor dritter Ordnung - D 1/s Deformationsgeschwindigkeitstensor - 1/s2, 1/s3 korotationale, zeitliche Ableitung vonD - 1 Einheitstensor - M Nm Antriebsmoment der rotierenden Kugel - M i Nm Teilmomente - R m Kugelradius - R G m Hohlkugelradius - S N/m2 Spannungstensor - W 1/s Rotationsgeschwindigkeitstensor - 1 N s/m2 Stoffparameter 1. Ordnung - 2, 3 N s2/m2 Stoffparameter 2. Ordnung - 4, 5, 6 N s3/m2 Stoffparameter 3. Ordnung - RadienverhältnisR/R G - 0 N s/m2 Anfangsviskosität - kg/m3 Dichte der Flüssigkeit - 1/s Kreisfrequenz der rotierenden Kugel Vorgetragen auf dem 6. Internationalen Rheologie-Kongreß in Lyon-Frankreich vom 4.–8. September 1972.Jetzt: BASF-AG, LudwigshafenMit 4 Abbildungen  相似文献   

6.
The effect of a uniform external magnetic field on the laminar, incompressible rarefied gas flow along an infinite porous flat plate is studied under the following conditions: 1) there is uniform suction, 2) the external flow velocity varies periodically with time in magnitude but not in direction, 3) the magnetic Reynolds number is small and 4) the current occurs under slip flow boundary conditions. Expressions for the velocity and temperature fields in the boundary layer are obtained. The response of skin friction, and heat transfer to the fluctuating stream is studied for variations in the rarefaction parameter h 1, the magnetic field parameter M, and the frequency of the fluctuating stream.Nomenclature c p specific heat of the gas - f 1 Maxwells reflection coefficient - f 2 thermal accommodation coefficient - G as defined in (36) - h 1 rarefaction parameter (L 1 v 0/) - h 2 nondimensional temperature jump coefficient (L 2 v 0/) - H amplitude of the skin friction - k thermal conductivity - K n Knudsen number - L mean free path - L 1 (2–f 1/f 1) L - L 2 - M magnetic field parameter ( 0 B 0 2 /v 0 2 ) - m 1/2[1+(1+4M+4i)1/2], m r+im i - n 1 1/2[1+(1+4M)1/2] - q heat flux - R suction Reynolds number - T temperature - x, y coordinates along and perpendicular to the plates - u, v velocity components along x, y-directions - density - kinematic viscosity - 0 electrical conductivity - Prandtl number - frequency of the fluctuating stream - nondimensional frequency parameter (/v 0 2 ) - nondimensional distance from wall (v 0 y/) - phase lead - U 0 0 mean velocity in the boundary layer - U 0 1, U 0 2 amplitude of the velocity fluctuation in the boundary layer - specific heat ratio  相似文献   

7.
Zusammenfassung Die beiden Differentialgleichungssysteme vonKrischer undLykow werden miteinander verglichen. Dabei ergibt sich, daß die in der deutschen und russischen Literatur angewandten mathematischen Modelle der Trocknung von kapillarporösen Körpern praktisch übereinstimmen. Es werden die Transformationsgleichungen der dimensionslosen Kenngrößen angegeben, die die Beziehungen zwischen den beiden Systemen herstellen.
The differential equations ofKrischer andLuikow for unsteady internal heat and mass transfer in the porous medium are compared. It is shown, that the mathematical models for drying in the German and Russian literature are equivalent. The transform relations of the non-dimensional parameters between the two models are given.

Formelzeichen nach Krischer z laufende Koordinate in Strömungsrichtung in m - R kennzeichnende Abmessung des Körpers in m - t Zeit in h - Raumgewicht bei mittlerer Feuchtigkeit in kg/m3 - w Teilgewicht des Wassers in 1 m3 Trockengut in kg/m3 - wa Anfangsfeuchtigkeit in kg/m3 - D Dampfdichte in kg/m3 - L Luftvolumen je m3 Trocknungsgut in m3/m3 - Temperatur in °C - u Umgebungstemperatur in °C - a Anfangstemperatur in °C - r Verdampfungswärme in kcal/kg - q E Wärmeentwicklung in kcal/m3 h - c spezifische Wärmekapazität des Trockengutes in kcal/kg grd - Wärmeleitfähigkeit in kcal/m h grd - Feuchtigkeitsleitzahl des Trockengutes in m2/h - wirksame Diffusionszahl von Wasserdampf in Luft in m2/h - Diffusionswiderstandszahl des Trockengutes — - Konstante — - Konstante in kg/m3 grd Formelzeichen nach Lykow X=r/R dimensionslose Koordinate des Körpers;r laufende Koordinate in m;R kennzeichnende Abmessung in m; - Fo=a/R 2 Fourier-Zahl;a Temperaturleitzahl in m2/h; Zeit in h - T(X, Fo)=t(r, )– 0/t dimensionslose Temperatur des Körpers im Punkt mit KoordinateX für den ZeitpunktFo;t(r, ) Temperatur in °C; 0 mittlere Anfangstemperatur in °C; t ein vorher angenommener Temperaturunterschied in grd - (X, Fo)= 0u(r, )/u dimensionsloses Potential des Stoffübergangs im Punkt mit KoordinateX für den ZeitpunktFo;u(r, ) Feuchtigkeitsgehalt des Trockengutes in kg/kg; 0 mittlerer Anfangsfeuchtigkeitsgehalt in kg/kg; u ein vorher angenommener Unterschied des Feuchtigkeitsgehalts in kg/kg - Ko= u/c t Kosowitsch-Zahl; Verdampfungswärme in kcal/kg;c spezifische Wärmekapazität des Trockengutes in kcal/kg - Ko*=Ko modifizierte Kosowitsch Zhal; Kenngröße der Zustandsänderung - Pn= t/u Posnowsche Zahl;=a T m /a m Thermogradientkoeffizient in 1/grd;a T m thermische Stoffübergangszahl (charakterisiert den Stoffstrom unter der Einwirkung von Temperaturgradienten) in m2/h grd;a m Stoffübergangszahl (charakterisiert den Stoffstrom unter der Einwirkung von Feuchtigkeitsgradienten) in m2/h - Lu=a m/a Lykowsche Zahl - Ki q=q q ()·R/ q t dimensionsloser Wärmestrom (Kirpitschew-Zahl);q q() Wärmestrom durch die Körperoberfläche in kcal/m2; q Wärmeleitfähigkeit in kcal/m2 h grd - Ki m=q m ()·R/a m 0 u dimensionsloser Stoffstrom;q m() Stoffstrom durch die Körperoberfläche in kg/m2 h; 0 Wichte des Trockengutes in kg/m3  相似文献   

8.
In this paper a numerical analysis of the heat transfer between a bubbling fluidized bed of mono-dispersed glass beads of Geldart type B and an immersed heated tube bundle is investigated. The numerical procedure is based on a solution of the mass, momentum and energy equations of both phases with an Eulerian approach. Different physical models for the thermal transport coefficient of the solid phase were used. The results are compared with new experimental data. The numerical and the experimental results show a strong correlation between fluid dynamics and heat transfer similar to the packet theory of Mickley and Fairbanks (1955). B Defined in equation (15) – - c p Specific heat J/kg/K - d s Particle diameter m - d Tube Diameter of the heat transfer tube m - g, Gravitational constant m/s2 - g 0 Radial distribution function – - h Specific enthalpy J/kg - k Solids fluctuating energy diffusion coefficient Pa s - Nu Nusselt number – - p Pressure N/m2 - p s Solid pressure N/m2 - Heat flux W - Heat flux W - Re Reynolds number – - T Temperature K - T(t) Measured foil temperature K - t Time s - tr Trace of a tensor (sum of main-diagonal elements) m/s - v Velocity, v-direction m/s - Velocity vector m/s - x x-coordinate m - y y-coordinate m - Volumetric interphase heat transfer coefficient W/m3/K - Bed-to-wall heat transfer coefficient W/m2/K - gs Fluid-particle heat transfer coefficient W/m2/K - T Heat transfer coefficient at tube surface W/m2/K - Interphase drag coefficient kg/m3/s - Thickness of CuNi foil m - Dissipation of fluctuating energy Pa/s - Volume fraction – - Angle ° - Thermal conductivity W/m/K - cyl Defined in equation (13) – - Fluctuating energy exchange Pa/s - Volumetric heat generation rate W/m3 - Density kg/m3 - Granular temperature m2/s2 - Viscous stress tensor N/m2 - Defined in equation (14) – - Bulk Bulk properties - g Gas phase - gas Gas - i i = g, s (gas or solid) - m Mixture - pen Penetration theory - pm Particle material - s Solid phase - T Tube - Tube Tube - t total - W Wall - * Parameter multiplied by the volume fraction of its phase  相似文献   

9.
Summary In continuation of a previous investigation a simple analytical expression is derived in closed form for the thickness distribution of the freeze-off layer which is vitrified at the (flat) wall of an oblong rectangular cavity. As has been pointed out previously, this layer is marked for amorphous polymers by the molecular orientation (birefringence pattern) in the moulded sample. One can show that a more detailed study with the aid of the coupled equations of energy and of motion will not furnish essential improvements. Problems of polymer physics like glass transition or crystallization kinetics at extreme rates of cooling and shearing must be solved first.
Zusammenfassung In Fortsetzung einer früheren Untersuchung wurde ein einfacher analytischer Ausdruck in geschlossener Form für die Dickenverteilung der eingefrorenen Schicht abgeleitet, die an der (flachen) Wand eines langgestreckten rechteckigen Formnestes während des Einspritzvorgangs glasig erstarrt. Wie früher auseinandergesetzt wurde, wird diese Schicht bei amorphen Polymeren durch die Molekülorientierung (Doppelbrechungsmuster) im gespritzten Formteil markiert. Man kann zeigen, daß eine eingehendere Studie mit Hilfe der gekoppelten Energie- und Impulsgleichungen keine essentiellen Verbesserungen bringt. Probleme der Polymerphysik, wie Glasübergang oder Kristallisationskinetik bei extremen Abkühlungs- und Schergeschwindigkeiten, müssen erst gelöst werden.

List of Symbols a heat diffusivity of polymer melt (averaged overT) [m2s–1] - B breadth of mould cavity [m] - Br Brinkman number ( ) - c heat capacity of polymer melt (averaged overT) [J kg–1 K–1] - F 0 Fourier number (at i/4H 2) - h heat transfer coefficient by melt flow [J K–1 s–1 m–2] - h heat transfer coefficient by layer growth [J K–1 s–1 m–2] - H half height of mould cavity [m] - L length of mould cavity [m] - n exponent in eq. [18] (= 0.417) - Nu Nußelt number (2Hh/) - P pressure gradientdP/dz in mould [N m–3] - t time [s] - t i injection time [s] - T g glass transition temperature of polymer [K] - T i injection temperature of polymer melt [K] - T l stagnation temperature [K] - T m mould wall temperature [K] - speed of flow front during mould filling [m s–1] - x coordinate perpendicular to mould wall [m] - z coordinate in the injection direction [m] - thickness of stagnant layer (atT l) [m] - 0 optically detectable freeze-off thickness [m] - + apparent layer thickness (atT i) [m] - dimensionless freeze-off thickness (= 0/2H) - dimensionless distance from entrance (=z/L) - m dimensionless coordinate of layer maximum - g dimensionless temperature (= (T iT l)/(T gT m)) - i dimensionless temperature (= (T iT l)/(T iT m)) - l dimensionless temperature (= (T iT l)/(T lT m)) - i viscosity of polymer atT i [N s m–3] - l viscosity of polymer atT l [N s m–3] - heat conductivity of polymer melt (averaged) [J K–1 s–1 m–1] - density of polymer melt (averaged) [kg m–3] - dimensionless time (eq. [11]) - + dimensionless parameter (eqs. [19a] and [19b]) - dimensionless layer thickness (eq. [12]) - + dimensionless parameter (eq. [20a]) - dimensionless parameter (eqs. [11a] and [11b]) Formerly at Delft University of Technology, Delft (The Netherlands).Paper presented at the Conference on Chemical Engineering Rheology, Annual Meeting of the Deutsche Rheologische Gesellschaft in Aachen, March 5–7, 1979.With 3 figures and 1 table  相似文献   

10.
Numerous optical probe designs to measure particle volume fraction have been proposed in the literature. Unfortunately, almost all of them suffer from an ill-defined measurement volume, poor sensitivity or require frequent and tedious calibration. We propose an improvement in the design of a dual optical fibre probe. It has a well-defined measuring volume and a near-linear sensitivity. A general calibration theory for optical fibre probes is also proposed. The design and the theory have been tested in a simple experimental set-up with encouraging results.

List of symbols

Latin letters a probe glass thickness (m) - b glare diameter (m) - d p particle diameter (m) - dS surface element (m2) - D optical fibre diameter (m) - f maximum packing signal, function of distance to the probe (V) - g radial distribution, function of particle volume fraction - h probe sensitivity, function of distance to the probe (V) - I intensity of light reflected off a particle (V) - l light ray length (m) - N number of elements - n p number of particles - p penetration depth of light distribution, function of distance and particle volume fraction (m–1) - q glare correction, function of probe geometry and particle size - r distance to the probe surface (m) - r distance from the probe surface to the first particle in a given direction ( , ) in a given suspension (m) - R probe receptivity to light, function of angle of incidence and distance to particle - S probe response signal (V) - S 0 probe response at zero volume fraction of particles (V) - S dense probe response at maximum packing of particles (V) - V cyl cylinder volume (m3) - V p particle volume (m3) - z independent length variable (m) Greek letters p volume fraction of particles - p,max volume fraction of particles at maximum packing - angle between incident and receiving optical fibre (rad) - exponent - exponent - altitude angle in spherical coordinates (rad) - azimuthal angle in spherical coordinates (rad) - mean free path of light (m) - dimensionless probe response signal - dimensionless reciprocal mean free path of light - dimensionless distance to probe surface - independent dimensionless length Other symbols ~ instantaneous value - <> expectancy value  相似文献   

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