StationÄrer und instationÄrer Vorgang der Filmkondensation auf der ebenen Platte,dem senkrechten Kegel,dem horizontalen Rohr und der Kugel

Zusammenfassung Die vorliegende Arbeit untersucht die Filmkondensation auf verschiedenen KörperoberflÄchen. Dabei wird sowohl der instationÄre Anlaufvorgang als auch der stationÄre Proze\ betrachtet. Die Ergebnisse für die Schichtdicke des abflie\enden Kondensates werden eingehend diskutiert. Ist die Schichtdicke als Funktion des Ortes und der Zeit bekannt, ist die Berechnung des kondensierenden bzw. abflie\enden Volumenstromes, sowie die Berechnung des lokalen bzw. für die Praxis bedeutungsvolleren globalen WÄrmeübergangs möglich.

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Steady and unsteady process of film condensation on a flat plate, a vertical coin, a horizontal pipe and a sphere

This paper investigates film condensation on different surfaces of geometric bodies. In this connection the unsteady starting process and the steady process are considered. The results for the thickness of layer of the flowing-off condensate are discussed detailed. If the thickness of layer is given as a function of time and location the computation of the condensing, respective flowing-off volume stream and the computation of the local, respective global heat transfer is possible.

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Bezeichnungen C Konstante - R Rohr- bzw. Kugelradius [m] - T Temperatur [K] - kondensierender Volumenstrom pro LÄngeneinheit [m² s^–1] - abflie\ender Volumenstrom pro LÄngeneinheit [m² s^–1] - kondensierender Volumenstrom [m³ s^–1] - abflie\ender Volumenstrom [m³ s^–1] - a Kegelachse - c spez. WÄrme der kondensierenden Flüssigkeit [J kg^–1 K^–1] - e ErzeugendenlÄnge des Kegels, an der die Randbedingung vorgeschrieben ist [m] - g Erdbeschleunigung [m s^–2] - l Platten- bzw. KegellÄnge [m] - p Druck [Nm^–2] - q WÄrmestromdichte [J m^–2 s^–1] - r VerdampfungswÄrme der Flüssigkeit [J kg^–1] - t Zeit [s] - u örtliche Geschwindigkeit des Fluids [m s^–1] - x, y kartesische Ortskoordinaten - r, Zylinder bzw. Kugelkoordinaten - WÄrmeübergangszahl [J m^–2 s^–1] - Neigungswinkel der Platte - öffnungswinkel des Kegels - Schichtdicke der kondensierten Flüssigkeit [m] - WÄrmeleitzahl der kondensierten Flüssigkeit [J m^–1 s^–1] - Dichte der kondensierten Flüssigkeit [kg m^–3] - OberflÄchenspannung der kondensierten Flüssigkeit [Nm^–1] - Schubspannung in der kondensierten Flüssigkeit [Nm^–2] - v kinematische ZÄhigkeit [m² s^–1] - dynamische ZÄhigkeit [kg m^–1 s^–1] - Winkelkoordinate (Rohr, Kugel), bei der eine Randbe-dingung vorgeschieben ist Indizes g gasförmige Phase - m mittlere - s SÄttigungszustand des gasförmigen Mediums - w auf die OberflÄche der Wand (Platte, Kegel, Rohr,Kugel) bezogen - 0 Ursprung der jeweiligen Störungsausbreitung Dimensionslose Kennzahlen Nu Nu\elt-Zahl - Pr Prandtl-Zahl - Re Reynolds-Zahl Kurzfassung der bei Prof. Dr. W. Schneider, Institut für Strömungslehre und WÄrmeübertragung TU Wien, angefertigten Diplomarbeit     

Messung der Wärmeleitfähigkeit von Stickstoff und Kohlenmonoxid bei hohen Temperaturen im Stoßwellenrohr

Zusammenfassung Die Meßergebnisse für die Wärmeleitfähigkeit von Stickstoff bei Temperaturen zwischen 1230 und 6000 K und Drückenzwischen 1 und 10 bar und von Kohlenmonoxid zwischen 1150 und 5000 K bei 1 bar werden mitgeteilt. Diese mit dem Stoßwellenrohr gemessenen Werte werden mit jenen verglichen, die sich aus der strengen kinetischen Gastheorie ergeben. Auch verfügbare Daten anderer Autoren werden zum Vergleich herangezogen.

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Measurement of thermal conductivity of nitrogen and carbon monoxide at high temperatures in a shock tube

The paper presents results of shock-tube measurements of thermal conductivity of nitrogen at temperatures between 1230 and 6000 K and at pressures between 1 and 10 bar and of carbon monoxide at temperatures between 1150 and 5000 K at 1 bar. Experimental results are compared with several variants of theoretical values, computed from rigorous kinetic theory, and with available data of other authors.

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Bezeichnungen (Einheiten in Klammern) a [m² s^–1] Temperaturleitzahl - C _p[J mol^–1 K^–1] molare Wärmekapazität - k [J K^–1] Boltzmann-Konstante - M [kg mol^–1] molare Masse - p bar Gesamtdruck - R [J mol^–1 K^–1] Gaskonstante - T [K] thermodynamische Temperatur - t [s] Zeit - U [J mol^–1] innere Energie - w [m s^–1] Geschwindigkeit - x [m] Ortskoordinate - x _i [1] Molanteil der Komponentei im Gasgemisch - [Wm^–1 K^–1] Wärmeleitfähigkeit - [mol m^–3] molare Konzentration Indizes i die Komponentei im Gasgemisch - g bezieht sich auf das (kalte) Gas bei der Wandtemperatur - w bezieht sich auf die feste Wand - p bei konstantem Druck Dieser Beitrag wurde auf dem Thermodynamik-Kolloquium des VDI im Oktober 1969 in Zürich vorgetragen.     

Injection moulding of plastics

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.

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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.

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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 _i –T _l)/(T _g –T _m)) - _i dimensionless temperature (= (T _i –T _l)/(T _i –T _m)) - _l dimensionless temperature (= (T _i –T _l)/(T _l –T _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     

Numerical analysis of simulation accuracy for hypersonic heat transfer in subsonic jets of dissociated nitrogen

One-dimensional problems of the flow in a boundary layer of finite thickness on the end face of a model and in a thin viscous shock layer on a sphere are solved numerically for three regimes of subsonic flow past a model with a flat blunt face exposed to subsonic jets of pure dissociated nitrogen in an induction plasmatron [1] (for stagnation pressures of (10⁴–3·10⁴) N/m² and an enthalpy of 2.1·10⁷ m²/sec²) and three regimes of hypersonic flow past spheres with parameters related by the local heat transfer simulation conditions [2, 3]. It is established that given equality of the stagnation pressures, enthalpies and velocity gradients on the outer edges of the boundary layers at the stagnation points on the sphere and the model, for a model of radius R_m=1.5·10^–2 m in a subsonic jet the accuracy of reproduction of the heat transfer to the highly catalytic surface of a sphere in a uniform hypersonic flow is about 3%. For surfaces with a low level of catalytic activity the accuracy of simulation of the nonequilibrium heat transfer is determined by the deviations of the temperatures at the outer edges of the boundary layers on the body and the model. For this case the simulation conditions have the form: dU_e/dx=idem, p₀=idem, T_e=idem. At stagnation pressuresP ₀2·10⁴ N/m² irrespective of the catalycity of the surface the heat flux at the stagnation point and the structure of the boundary layer near the axis of symmetry of models with a flat blunt face of radius R_m1.5·10^–2 m exposed to subsonic nitrogen jets in a plasmatron with a discharge channel radius R_c=3·10^–2 m correspond closely to the case of spheres in hypersonic flows with parameters determined by the simulation conditions [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 135–143, March–April, 1990.     

Understanding the Piche evaporimeter as a simple integrating mass transfer meter

Results are presented of a comparison of measured and calculated evaporation rates of the Piche evaporimeter under indoor and outdoor (within a meteorological screen) conditions. In both cases, application of mass transfer formulae in use for horizontal (turbulent) flow to the evaporating blotting paper of the instrument yield very good results under pure forced convection conditions. For mixed convection regimes, comparisons using either pure free (combined heat and mass transfer) or pure forced convection equations give as expected too low calculated values. Reasons for such differences with measured values are reviewed. Our forced convection results confirm that main stream turbulence is only of influence on mass transfer to a zero incidence flow in combination with pressure gradient (bluff body) effects, which under our conditions appear to be absent around the Piche surfaces. The same results prove absence of any influence of the particular temperature distribution over the blotting paper on the mass transfer. The understanding and importance of these conclusions in relation to the use of the Piche evaporimeter as a simple integrating mass transfer meter under actual farming conditions are discussed. The importance to obtain such mass transfer data is explained in the introduction.Nomenclature A Numerical constant in free convection Sherwood number - Coefficient of thermal expansion (K^–1) - C _{(s, b)} Water vapour concentration average at the evaporating surface (s) and in the bulk air (b) (g m^–3) - D Coefficient of molecular diffusion of water vapour in air (m² s^–1) - d Characteristic dimension of the paper disc in the direction of flow (m) - E _{(c, m)} Evaporation rates of the Piche evaporimeter, calculated (c) and measured (m) (units in text) - e _{(s, b)} Partial water vapour pressure average at the evaporating surface (s) and in the bulk air (b) (mbar) - Gr Grashof number - g Acceleration of gravity (m s^–2) - m Number of measuring periods - n Numerical constant in free convection Sherwood number - Coefficient of kinematic viscosity of air (m² s^–1) - P Atmospheric pressure (mbar) - Re Reynolds number - _{(s, b)} Air density average at the evaporating surface (s) and of the bulk air (b) (g m^–3) - Sh Sherwood number - T _{(s, b)} Temperature average of the evaporating surface (s) and in the bulk air (b) (K) - T _{(vs, vb)} Virtual temperature average at the evaporating surface (s) and in the bulk air (b) (K) - U Wind speed (air movement) average of the bulk air (m s^–1)     

On the part played by the local pressure gradient in forming the flow in a corner

Special experiments were made in the subsonic low-turbulence wind tunnel T-324 of the Institute of Theoretical and Applied Mechanics of the Siberian Branch, USSR Academy of Sciences with the aim of making a more detailed study of the conditions of occurrence of transverse flows in the case of laminar flow along a corner. The velocity U of the undisturbed flow was varied from 2.3 to 5.5 m/sec [Re₁ = (1.5–3.5) · 10⁵ m^–1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 95–100, March–April, 1982.     

Atmospheric boundary layer simulation in a wind tunnel, using air injection

The inner part of a neutral atmospheric boundary layer has been simulated in a wind tunnel, using air injection through the wind tunnel floor to thicken the boundary layer. The flow over both a rural area and an urban area has been simulated by adapting the roughness of the wind tunnel floor. Due to the thickening of the boundary layer the scaling factor of atmospheric boundary layer simulation with air injection is considerably smaller than that without air injection. This reduction of the scaling factor is very important for the simulation of atmospheric dispersion problems in a wind tunnel.The time-mean velocity distribution, turbulence intensity, Reynolds stress and turbulence spectra have been measured in the inner part of the wind tunnel boundary layer. The results are in rather good agreement with atmospheric measurements.Nomenclature d Zero plane displacement, m - h Height of roughness elements, m - k Von Kármán's constant - n Frequency of turbulence velocity component, s^–1 - S _u(n) Energy spectrum for longitudinal turbulence velocity component, m² s^–1 - S _v(n) Energy spectrum for lateral turbulence velocity component, m² s^–1 - S _w(n) Energy spectrum for vertical turbulence velocity component, m² s^–1 - U _o Free stream velocity outside the boundary layer, m s^–1 - Time-mean velocity inside the boundary layer, m s^–1 - u* Wall-friction velocity, m s^–1 - u Longitudinal turbulence intensity, m s^–1 - v Lateral turbulence intensity, m s^–1 - w Vertical turbulence intensity, m s^–1 - Reynolds stress, m² s^–2 - z Height above earth's surface or wind tunnel floor, m - z _o Roughness length, m - Thickness of inner part of boundary layer, m - Thickness of boundary layer, m - Kinematic viscosity, m² s^–1     

On the laminar forced convection with axial conduction in a circular tube with exponential wall heat flux

The values of the fully developed Nusselt number for laminar forced convection in a circular tube with axial conduction in the fluid and exponential wall heat flux are determined analytically. Moreover, the distinction between the concepts of bulk temperature and mixing-cup temperature, at low values of the Peclet number, is pointed out. Finally it is shown that, if the Nusselt number is defined with respect to the mixing-cup temperature, then the boundary condition of exponentially varying wall heat flux includes as particular cases the boundary conditions of uniform wall temperature and of convection with an external fluid.

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Über laminare Zwangskonvektion mit Längswärmeleitung in einem Kreisrohr mit exponentiell veränderlichem Wandwärmefluß

Zusammenfassung Es werden die Endwerte der Nusselt-Zahlen für vollausgebildete laminare Zwangskonvektion in einem Kreisrohr mit Längswärmeleitung und exponentiell veränderlichem Wandwärmefluß analytisch ermittelt. Besondere Betonung liegt auf dem Unterschied zwischen den Konzepten für die Mittel- und die Mischtemperatur bei niedrigen Peclet-Zahlen. Schließlich wird gezeigt, daß bei Definition der Nusselt-Zahl bezüglich der Mischtemperatur die Randbedingung exponentiell veränderlichen Randwärmeflusses die Spezialfälle konstanter Wandtemperatur und konvektiven Wärmeaustausches mit einem umgebenden Fluid einschließt.

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Nomenclature A _n dimensionless coefficients employed in the Appendix - Bi Biot numberBi=h _e r ₀/ - c _n dimensionless coefficients defined in Eq. (17) - c _p specific heat at constant pressure of the fluid within the tube, [J kg^–1 K^–1] - f solution of Eq. (15) - h ₁,h ₂ specific enthalpies employed in Eqs. (2) and (4), [J kg^–1] - h _e convection coefficient with a fluid outside the tube, [W m^–2 K^–1] - rate of mass flow, [kg s^–1] - Nu bulk Nusselt number,2r ₀ q _w /[(T _w –T _b )] - Nu _H fully developed value of the bulk Nusselt number for the boundary condition of uniform wall heat flux - Nu _T fully developed value of the bulk Nusselt number for the boundary condition of uniform wall temperature - Nu ^* mixing Nusselt number,2r ₀ q _w /[(T _w –T _m )] - Nu _C ^* fully developed value of the mixing Nusselt number for the boundary condition of convection with an external fluid - Nu _H ^* fully developed value of the mixing Nusselt number for the boundary condition of uniform wall heat flux - Nu _T ^* fully developed value of the mixing Nusselt number for the boundary condition of uniform wall temperature - Pe Peclet number, 2r ₀/ - q ₀ wall heat flux atx=0, [W m^–2] - q _w wall heat flux, [W m^–2] - r radial coordinate, [m] - r ₀ radius of the tube, [m] - s dimensionless radius,s=r/r ₀ - T temperature, [K] - T ₀ temperature constant employed in Eq. (14), [K] - T reference temperature of the fluid external to the tube, [K] - T _b bulk temperature, [K] - T _m mixing or mixing-cup temperature, [K] - T _w wall temperature, [K] - u velocity component in the axial direction, [m s^–1] - mean value ofu, [m s^–1] - x axial coordinate, [m] Greek symbols thermal diffusivity of the fluid within the tube, [m² s^–1] - exponent in wall heat flux variation, [m^–1] - dimensionless parameter - dimensionless temperature =(T _w –T)/(T _w –T _b ) - ^* dimensionless temperature ^*=(T _w –T)/(T _w –T _m ) - thermal conductivity of the fluid within the tube, [W m^–1 K^–1] - density of the fluid within the tube, [kg m^–3]     

Rheologische Messungen an Kunststoff-Schmelzen mit einem neuen Rotationsrheometer

Zusammenfassung In der vorliegenden Arbeit wird ein neues Rotationsrheometer vorgestellt und über Messungen an zwei Polymethylmethacrylat-Formmassen berichtet. Bei dem Rheometer handelt es sich um ein Couette-Rheometer mit feststehendem Innenzylinder als Meßkörper. Der Meßkörper ist beidseitig eingespannt. In dem geschlossenen Meßraum können die Schmelzen bis zu einem Druck von 500 bar belastet werden.Der zeitliche Verlauf der Schubspannung in den Schmelzen wird in Abhängigkeit von Temperatur und Druck aufgezeichnet.

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Summary A new type of rotational rheometer is described, and results for two samples of polymethylmethacrylate are reported. The rheometer consists of a Couette system with fixed inner cylinder, supported at both ends for torque measurements. Pressure may be varied up to 500 bar. Shear stresses have been recorded as a function of time, temperature and pressure.

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Nomenklatur C [kp cm^–2 s^–1] Steigung der Anlaufkurve im Nullpunkt - D [kp cm rad^–1] Direktionsmoment - E ₀ [kcal mol^–1] Aktivierungsenergie der Newtonschen Viskosität - G [kp cm^–2] Schubmodul - G [—] Griffith-Zahl - l [mm] Länge des Meßkörpers - p [kp cm^–2] Druck - R _i [mm] Radius des Innenzylinders - R _a [mm] Radius des Außenzylinders - t _max [s] Zeit, bei der das Maximum in der Anlaufkurve auftritt - T [°C] Temperatur - ₀ [cm² kp^–1] Druckkoeffizient der Newtonschen Viskosität - [s^–1] Schergeschwindigkeit - ₀ [kp s cm^–2] Newtonsche Viskosität - (g cm²] Trägheitsmoment des Meßkörpers - v ₀ [s^–1] Eigenfrequenz des Meßsystems - _max [kp cm^–2] maximale Schubspannung - _st [kp cm^–2] stationäre Schubspannung Mit 7 Abbildungen und 1 Tabelle     

Two-phase geothermal flows with conduction and the connection with Buckley-Leverett theory

Two-phase flows of boiling water and steam in geothermal reservoirs satisfy a pair of conservation equations for mass and energy which can be combined to yield a hyperbolic wave equation for liquid saturation changes. Recent work has established that in the absence of conduction, the geothermal saturation equation is, under certain conditions, asymptotically identical with the Buckley-Leverett equation of oil recovery theory. Here we summarise this work and show that it may be extended to include conduction. In addition we show that the geothermal saturation wave speed is under all conditions formally identical with the Buckley-Leverett wave speed when the latter is written as the saturation derivative of a volumetric flow.Roman Letters C(P, S,q) geothermal saturation wave speed [ms^–1] (14) - c _t (P, S) two-phase compressibility [Pa^–1] (10) - D(P, S) diffusivity [m s^–2] (8) - E(P, S) energy density accumulation [J m^–3] (3) - g gravitational acceleration (positive downwards) [ms^–2] - h _w (P),h _w (P) specific enthalpies [J kg^–1] - J _M (P, S,P) mass flow [kg m^–2 s^–1] (5) - J _E (P, S,P) energy flow [J m^–2s^–1] (5) - k absolute permeability (constant) [m²] - k _w (S),k _s (S) relative permeabilities of liquid and vapour phases - K formation thermal conductivity (constant) [Wm^–1 K^–1] - L lower sheetC<0 in flow plane - m, c gradient and intercept - M(P, S) mass density accumulation [kg m^–3] (3) - O flow plane origin - P(x,t) pressure (primary dependent variable) [Pa] - q volume flow [ms^–1] (6) - S(x, t) liquid saturation (primary dependent variable) - S ^*(x,t) normalised saturation (Appendix) - t time (primary independent variable) [s] - T temperature (degrees Kelvin) [K] - T _sat(P) saturation line temperature [K] - TdT _sat/dP saturation line temperature derivative [K Pa^–1] (4) - T _c ,T _D convective and diffusive time constants [s] - u _w (P),u _s (P),u _r (P) specific internal energies [J kg^–1] - U upper sheetC > 0 in flow plane - U(x,t) shock velocity [m s^–1] - x spatial position (primary independent variable) [m] - X representative length - x, y flow plane coordinates - z depth variable (+z vertically downwards) [m] Greek Letters _P , _S remainder terms [Pa s^–1], [s^–1] - double-valued saturation region in the flow plane - h =h _s –h _w latent heat [J kg^–1] - = _w – _s density difference [kg m^–3] - line envelope - =D _K /D ₀ diffusivity ratio - porosity (constant) - _w (P), _s (P), _t (P, S) dynamic viscosities [Pa s] - v _w (P),v _s (P) kinematic viscosities [m²s^–1] - v ₀ =kh/KT kinematic viscosity constant [m² s^–1] - ₀ =v ₀ dynamic viscosity constant [m² s^–1] - _w (P), _s (P) density [kg m^–3] Suffixes r rock matrix - s steam (vapour) - w water (liquid) - t total - av average - 0 without conduction - K with conduction     

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     

MOTIONS, FORCES AND MODE TRANSITIONS IN VORTEX-INDUCED VIBRATIONS AT LOW MASS-DAMPING

These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low mass and damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined mass-damping parameter (low m^*ζ), or a high mass-damping (highm^*ζ ). For our low m^*ζ, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at highm^*ζ , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the mass-damping (m^*ζ), whereas the regime of synchronization (measured by the range of velocity U^*) is dependent primarily on the mass ratio, m^*ζ. At low (m^*ζ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper–lower branches. A 180° jump in phase angle φ is found only when the flow jumps between the upper–lower branches of response. The good collapse of peak-amplitude data, over a wide range of mass ratios (m^*=1–20), when plotted against (m^*+C_A) ζ in the “Griffin” plot, demonstrates that the use of a combined parameter is valid down to at least (m^*+C_A)ζ 0·006. This is two orders of magnitude below the “limit” that had previously been stipulated in the literature, (m^*+C_A) ζ>0·4. Using the actual oscillating frequency (f) rather than the still-water natural frequency (f_N), to form a normalized velocity (U^*/f^*), also called “true” reduced velocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of mass ratiosm^* . Such a collapse of response plots cannot be predicted a priori, and appears to be the first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson–Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m^*.     

Estimation of zero-shear viscosity of polymer solutions from falling sphere data

Summary Extrapolation methods for the determination of zero-shear viscosity from falling sphere tests are compared with each other and in particular with dicrect viscometric measurements of this parameter. It is found that all methods of extrapolation overestimate the true zero-shear viscosity and that the discrepancy depends on the degree of shear thinning encountered by the falling spheres. Falling sphere tests only yield the true zero-shear viscosity when the spheres fall in the lower Newtonian region of fluid behaviour. In most instances a suitable combination of sphere properties to achieve this can only be found in the case of very viscous fluids which can in any case also be characterized by direct viscometric measurements in this region.If sphere fall data must be extrapolated, methods based on shear rate rather than shear stress appear preferable since they generally yield lower values of zero-shear viscosity, which are therefore nearer to the true value.

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Zusammenfassung Verschiedene Extrapolationsmethoden zur Bestimmung der Null-Viskosität mit Hilfe von Kugelfallversuchen werden miteinander und insbesondere mit der direkten viskosimetrischen Messung dieses Parameters verglichen. Es wird gefunden, daß alle Extrapolationsmethoden den wahren Wert der Null-Viskosität überschätzen und daß der Unterschied vom Grad der Scherentzähung abhängt, der beim Kugelfall vorliegt. Kugelfallversuche liefern nur dann die wahre Nullviskosität, wenn diese im unteren newtonschen Bereich durchgeführt werden. In den meisten Fällen kann eine geeignete Kombination von Kugeleigenschaften zur Realisierung dieser Bedingungen aber nur bei sehr viskosen Flüssigkeiten gefunden werden, die dann genausogut durch direkte viskosimetrische Messungen in diesem Bereich gekennzeichnet werden können.Wenn Kugelfalldaten extrapoliert werden müssen, scheinen Methoden der Auftragung gegen die Schergeschwindigkeit besser geeignet zu sein als solche gegen die Schubspannung. Im ersten Fall werden nämlich durchweg niedrigere Werte der Null-Viskosität erhalten, die somit näher bei den wahren Werten liegen.

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Nomenclature c a constant [—] - d sphere diameter [m] - D container diameter [m] - v sphere fall velocity in an infinite medium [ms^–1] - shear rate [s^–1] - shear rate for = 0.95 ₀ [s^–1] - apparent viscosity [kg m^–1 s^–1] - ₀ zero shear viscosity [kg m^–1 s^–1] - f fluid density [kg m^–3] - _p particle density [kg m^–3] With 8 figures and 2 tables     

Optimum rib size to enhance forced convection in a horizontal triangular duct with ribbed internal surfaces

The optimum rib size to enhance heat transfer had been proposed through an experimental investigation on the forced convection of a fully developed turbulent flow in an air-cooled horizontal equilateral triangular duct fabricated on its internal surfaces with uniformly spaced square ribs. Five different rib sizes (B) of 5 mm, 6 mm, 7 mm, 7.9 mm and 9 mm, respectively, were used in the present investigation, while the separation (S) between the center lines of two adjacent ribs was kept at a constant of 57 mm. The experimental triangular ducts were of the same axial length (L) of 1050 mm and the same hydraulic diameter (D) of 44 mm. Both the ducts and the ribs were fabricated with duralumin. For every experimental set-up, the entire inner wall of the duct was heated uniformly while the outer wall was thermally insulated. From the experimental results, a maximum average Nusselt number of the triangular duct was observed at the rib size of 7.9 mm (i.e. relative rib size ). Considering the pressure drop along the triangular duct, it was found to increase almost linearly with the rib size. Non-dimensional expressions had been developed for the determination of the average Nusselt number and the average friction factor of the equilateral triangular ducts with ribbed internal surfaces. The developed equations were valid for a wide range of Reynolds numbers of 4,000 < Re _D < 23,000 and relative rib sizes of under steady-state condition. A Inner surface area of the triangular duct [m²] - A _C Cross-sectional area of the triangular duct [m²] - B Side length of the square rib [mm] - C _P Specific heat at constant pressure [kJ·kg^–1·K^–1] - C ₁, C ₂, C ₃ Constant coefficients in Equations (10), (12) and (13), respectively - D Hydraulic diameter of the triangular duct [mm] - Electric power supplied to heat the triangular duct [W] - f Average friction factor - F View factor for thermal radiation from the duct ends to its surroundings - h Average convection heat transfer coefficient at the air/duct interface [W·m^–2 ·K^–1] - k Thermal conductivity of the air [W·m^–1 ·K^–1] - L Axial length of the triangular duct [mm] - Mass flow rate [kg·s^–1] - n ₁, n ₂, n ₃ Power indices in Equations (10), (12) and (13), respectively - Nu _D Average Nusselt number based on hydraulic diameter - P Fluid pressure [Pa] - Pr Prandtl number of the airflow - _c Steady-state forced convection from the triangular duct to the airflow [W] - _l Heat loss from external surfaces of the triangular duct assembly to the surroundings [W] - _r Radiation heat loss from both ends of the triangular duct to the surroundings [W] - Re _D Reynolds number of the airflow based on hydraulic diameter - S Uniform separation between the centre lines of two consecutive ribs [mm] - T Fluid temperature [K] - T _a Mean temperature of the airflow [K] - T _ai Inlet mean temperature of the airflow [K] - T _ao Outlet mean temperature of the airflow [K] - T _s Mean surface temperature of the triangular duct [K] - T Ambient temperature [K] - U Mean air velocity in the triangular duct [m·s^–1] - _r Mean surface-emissivity with respect to thermal radiation - Dynamic viscosity of the fluid [kg·m^–1·s^–1] - Kinematic viscosity of the airflow [m²·s^–1] - Density of the airflow [kg·m^–3] - Stefan-Boltzmann constant [W·m^–2·K^–4]     

Transients in flow and local heat transfer due to a pressure wave in pipe flow

The effect of a pressure wave on the turbulent flow and heat transfer in a rectangular air flow channel has been experimentally studied for fast transients, occurring due to a sudden increase of the main flow by an injection of air through the wall. A fast response measuring technique using a hot film sensor for the heat flux, a hot wire for the velocities and a pressure transducer have been developed. It was found that in the initial part of the transient the heat transfer change is independent of the Reynolds number. For the second part the change in heat transfer depends on thermal boundary layer thickness and thus on the Reynolds number. Results have been compared with a simple numerical turbulent flow and heat transfer model. The main effect on the flow could be well predicted. For the heat transfer a deviation in the initial part of the transient heat transfer has been found. From the turbulence measurements it has been found that a pressure wave does not influence the absolute value of the local turbulent velocity fluctuations. They could be considered to be frozen.Nomenclature A surface area (m²) - D diameter (m) - h heat transfer coefficient (Wm^–2 K^–1) - p pressure drop (Pa) - P pressure (Pa) - Q heat flow (W) - R tube radius (m) - T bulk temperature (K) - T _s surface temperature (K) - t time (s) - u velocity (m/s) - V voltage (V) - y distance from wall (m) - viscosity (N s m^–2) - kinematic viscosity (m^–2 s^–1) - density (kg m^–3) - _w wall shear stress (N m^–2) - Nu Nusselt number - Re Reynolds number     

Application of Hildebrand's fluidity model to non-Newtonian solutions

Summary The fluidity model ofHildebrand has been applied to dilute aqueous polymer solutions exhibiting non-Newtonian behaviour. As for Newtonian fluids, it is found that the temperature dependence of apparent viscosity of non-Newtonian fluids is determined entirely by the temperature dependence of fluid density. However, whereas the parameters ofHildebrand's equation are constants, independent of the conditions of shear for Newtonian fluids, these parameters become shear-rate dependent for non-Newtonian fluids. The magnitude of the parameters and their variation with shear rate can be explained qualitatively in terms of interactions of polymer molecules and their behaviour in a shear field.

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Zusammenfassung Das Fließmodell vonHildebrand wird auf verdünnte wäßrige Polymerlösungen mit nicht-newtonschem Verhalten angewandt. Wie bei newtonschen Flüssigkeiten findet man hierfür, daß die Temperaturabhängigkeit der schergeschwindigkeitsabhängigen Viskosität ausschließlich durch die Temperaturabhängigkeit der Flüssigkeitsdichte bestimmt ist. Während jedoch die Parameter derHildebrandschen Gleichung für newtonsche Flüssigkeiten von den Scherbedingungen unabhängige Konstanten darstellen, werden diese bei nichtnewtonschen Flüssigkeiten schergeschwindigkeitsabhängig. Die Größe dieser Parameter und ihrer Variation mit der Schergeschwindigkeit kann qualitativ als eine Folge der Wechselwirkung der Polymermoleküle und ihres Verhaltens im Scherfeld gedeutet werden.

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Notation B Parameter inHildebrand's fluidity equation, eq. [1] (N^–1 m² s^–1) - K Consistency parameter in the power-law (Nm^–2 s ⁿ ) - n Flow behaviour index in the power-law (–) - T Temperature (K) - V Molar volume (m³ mol^–1) - V ₀ Intrinsic molar volume; parameter inHildebrand's fluidity equation, eq. [1] (m³ mol^–1) - Shear rate (s^–1) - Viscosity or apparent viscosity (Nm^–2 s) - Density (kg m^–3) - ₀ Intrinsic density; modified parameter inHildebrand's fluidity equation; eq. [5] (kg m^–3) - Shear stress (Nm^–2) With 4 figures and 1 table     

Simultaneous PIV and pulsed shadow technique in slug flow: a solution for optical problems

A recent technique of simultaneous particle image velocimetry (PIV) and pulsed shadow technique (PST) measurements, using only one black and white CCD camera, is successfully applied to the study of slug flow. The experimental facility and the operating principle are described. The technique is applied to study the liquid flow pattern around individual Taylor bubbles rising in an aqueous solution of glycerol with a dynamic viscosity of 113×10^–3 Pa s. With this technique the optical perturbations found in PIV measurements at the bubble interface are completely solved in the nose and in annular liquid film regions as well as in the rear of the bubble for cases in which the bottom is flat. However, for Taylor bubbles with concave oblate bottoms, some optical distortions appear and are discussed. The measurements achieved a spatial resolution of 0.0022 tube diameters. The results reported show high precision and are in agreement with theoretical and experimental published data.Symbols D internal column diameter (m) - g acceleration due to gravity (m s^–2) - l _w wake length (m) - Q _v liquid volumetric flow rate (m³ s^–1) - r radial position (m) - r * radial position of the wake boundary (m) - R internal column radius (m) - U _s Taylor bubble velocity (m s^–1) - u _z axial component of the velocity (m s^–1) - u _r radial component of the velocity (m s^–1) - z distance from the Taylor bubble nose (m) - Z * distance from the Taylor bubble nose for which the annular liquid film stabilizes (m) Dimensionless groups Re Reynolds number ( ) - N _f inverse viscosity number ( ) Greek letters liquid film thickness (m) - liquid kinematic viscosity (m² s^–1) - liquid dynamic viscosity (Pa s) - liquid density (kg m^–3)     

Investigation of chemically reacting and radiating supersonic flow in channels

The two-dimensional time dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multi-stage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for general configuration, and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species.The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack to determine a convenient numerical procedure for the present study. The specific problem considered is of the flow in a channel with a 10° compression-expansion ramp. The calculated results are compared with the results of an upwind scheme and no significant differences are noted. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flowfield.Nomenclature A band absorptance (m^–1) - A _o band width parameter (m^–1) - C _j concentration of thejth species (kg mol/m³) - C _o correlation parameter ((N/m²)^–1m^–1) - C _p constant pressure specific heat (J/kgK) - e Planck's function (J/m²S) - E total internal energy (J/kg) - f _j mass fraction of thejth species - h static enthalpy of mixture (J/kg) - H total enthalpy (J/kg) - I identity matrix - I _v spectral intensity (J/m s) - I _bv spectral Planck function - k thermal conductivity (J/m sK) - K _b backward rate constant - K _f forward rate constant - I unit vector in the direction of - M _j molecular weight of thejth species (kg/kg mol) - P pressure (N/m²) - P _j partial pressure of thejth species (N/m²) - P _e equivalent broadening pressure ratio - Pr Prandtl number - P _w a point on the wall - q _R total radiative heat flux (J/m² s) - spectral radiative heat flux (J/m³ s) - R gas constant (J/KgK) - r _w distance between the pointsP andP _w(m) - S integrated band intensity ((N/m²)^–1/m^–2) - S integrated band intensity ((N/m²)^–1 m^–2) - T temperature (K) - u, v velocity inx andy direction (m/s) - production rate of thejth species (kg/m³ s) - x, y physical coordinate - z dummy variable in they direction Greek symbols ratio of specific heats - t _ch chemistry time step (s) - t _f fluid-dynamic time step (s) - absorption coefficient (m^–1) - ,_v spectral absorption coefficient (m^–1) - _p Planck mean absorption coefficient - second coefficient of viscosity, wavelength (m) - dynamic viscosity (laminar flow) (kg/m s) - , computational coordinates - density (kg/m³) - Stefan-Boltzmann constant (erg/s cm² K³) - shear stress (W/m²) - equivalence ratio - wave number (m^–1) - _c frequency at the band center     

A new transient method for analysis of solidification in the continuous casting of metals

Solidification processes involve complex heat and mass transfer phenomena, the modelling of which requires state-of-the art numerical techniques. An efficient and accurate transient numerical method is proposed for the analysis of phase change problems. This method combines both the enthalpy and the enhanced specific heat approaches in incorporating the effects of latent heat released due to phase change. The sensitivity and accuracy of the proposed method to both temporal and spatial discretization is shown together with closed-form solutions and the results from the enhanced specific heat approach. In order to explore the proposed method fully, a non-linear heat release, as is the case for binary alloys, is also examined. The number of operations required for the new transient approach is less than or equal to the enhanced heat capacity method depending on the averaging method adopted. To demonstrate the potential of this new finite-element technique, measurements obtained on operating machines for the casting of zinc, aluminum and steel are compared with the model predictions. The death/birth technique, together with the proper heat-transfer coefficients, were employed in order to model the casting process with minimal error due to the modelling itself.Nomenclature [A] conductance matrix - [B] matrix containing the derivative of the element shape functions - c, C _p specific heat (J kg^–1°C^–1) - effective specific heat (J kg^–1°C^–1) - f(T) local liquid fraction - f thermal load vector - H enthalpy (J kg^–1) - [H] capacitance matrix - h, h _r,h _c heat transfer coefficient (W m^–2°C^–1) - K thermal conductivity (W m^–1°C^–1) - L latent heat of solidification (J kg^–1) - l overall length (m) - N _i shape functions - Q rate of heat generation per unit volume (J m^–3) - q heat flux (W m^–2) - R residual temperature (°C) - T temperature (°C) - T _s solidus temperature (°C) - T _l liquidus temperature (°C) - T _pouring pouring temperature (°C) - T _top temperature at the top of the mould (°C) - T _w temperature of the water spray (°C) - approximated temperature (°C) - T surrounding temperature (°C) - cooling rate (°C/s) - t time (seconds) - x _i,x, y, z spatial variables (m) - t time step (s) - x element size (m) - diffusivity (m²s^–1) - density (kg m^–3) - time marching parameter - _n direction cosines of the unit outward normal to the boundary     

A specific slit die rheometer for extruded starchy products. Design,validation and application to maize starch

A novel in-line rheometer, called Rheopac, has been designed and built in order to study the rheological behaviour of starchy products or, more generally, of products sensitive to a thermomechanical treatment. It is based on the principle of a twin channel, using a balance of feed rate between each of them, in order to make local shear rate vary in the measuring section without changing the flow conditions into the extruder. A wide range of shear rate could be reached and measurements were performed more swiftly than with a classical slit die. The viscous behaviour of maize starch was studied by taking into account the influence of the thermomechanical history, which modified the starch degradation and thus led to important variations in the viscosity. Experimental results were satisfactorily compared to previously published models.Nomenclature E activation energy (J · mol^–1) - h channel depth (m) - h ₁ depth under the piston valve in channel 1 (m) - h ₂ depth under the piston valve in channel 2 (m) - K consistency (Pa·s ⁿ ) - K ₀ reference consistency (Pa·s ⁿ ) - L total channel length (m) - L _p length of the piston valve (m) - MC moisture content (wet basis) - n power law index - N screw rotation speed (rpm) - P ₀ entrance pressure (Pa) - P _e pressure at the entry of the piston valve (Pa) - Q ₁ flow rate in channel 1 (m3 · s^–1) - Q ₂ flow rate in channel 2 m³·s^–1) - Q _T total flow rate (m3 · s^–1) - R constant of perfect gas (8.314 J·mol^–1·K^–1) - SME specific mechanical energy (kWh · t^–1) - T temperature (°C) - T _a absolute temperature (K) - T _b barrel temperature (°C) - T _d die temperature (°C) - T _p product temperature (°C) - w channel width (m) - W energetical term (J·m^–3) - viscosity (Pa · s) - [gh ₀] intrinsic viscosity of native starch (ml·g^–1) - [] intrinsic viscosity (ml·g^–1) - shear rate (s^–1) - shear rate in measuring section (s^–1) - maximum shear rate (s^–1)