Molecular transfer in turbulent flows

For modeling the molecular transfer of a passive scalar in a known turbulent field, the equations for the average scalar value and the correlation function for the scalar field are written in a form which makes it possible to examine the effect of molecular transfer on turbulent transfer and scalar dissipation. For the closure of the equation for the correlation function, the Prandtl hypothesis is used. The statistical reliability of this closure is demonstrated. The system proposed makes it possible to predict the dynamics of a decaying uniform scalar field and to explain why the effect of the real value of the molecular-transfer coefficient on the decaying scalar field is weak. Specific features of the transport process in a plane layer with prescribed scalar values on the layer boundaries are considered.     

Heat transfer characteristics and Nusselt number correlation of turbulent pulsating pipe air flows

Heat transfer characteristics to turbulent pulsating pipe flows under a wide range of Reynolds number and pulsation frequency were experimentally investigated under uniform heat flux condition. Reynolds number was varied from 8462 to 48540 while the frequency of pulsation ranged from 1 to 29.5 Hz. The results showed that the relative mean Nusselt number is strongly affected by both pulsation frequency and Reynolds number. Enhancements in mean Nusselt number of up to 50% were obtained at medium pulsation frequency between 4.1 and 13.9 Hz for Reynolds number range of 8462 to 14581. An enhancement of up to 50% in mean Nusselt number was obtained at high pulsation frequency range between 13.9 and 29.5 Hz, specially as Reynolds number is close to 15000, while a reduction was observed at higher Reynolds number more than 21200. This reduction, at high Reynolds number, increased as pulsation frequency increased. Also, there was a reduction in mean Nusselt number of up to 20% that obtained at low pulsation frequency range between 1 and 4.1 Hz for Reynolds number range of 8462 to 48543. A significant reduction in mean Nusselt number of up to 40% was obtained at medium pulsation frequency between 4.1 and 13.9 Hz for Reynolds number range of 21208 to 48543. Empirical equations have been developed for the relative mean Nusselt number that related to Reynolds number and dimensionless frequency with about uncertainty of 10% rms.The support of both King Fahd University of Petroleum and Minerals and Cairo University for this research is acknowledged.     

Steady conjugate heat transfer in turbulent channel flows

The characteristics of steady conjugate heat transfer in turbulent channel flow which is uniformly heated over a finite length are numerically studied. The influences of wall thickness, wall-to-fluid conductivity ratio, and Prandtl number on the nondimensional heat flux and the evolution of temperature field are discussed in great detail. Particular attention is paid to study the wall conduction effects on low-Reynolds number turbulent forced convection heat transfer. The results show that the effects of wall conduction on turbulent forced convection channel flow are significant, especially for the cases with larger wall thickness and wall-to-fluid conductivity ratio.In einer numerischen Studie werden die Eigenschaften der stetig konjugierten Wärmeübertragung in einer turbulenten Kanalströmung, die über eine endliche Länge gleichmäßig beheizt wird, untersucht. Der Einfluß der Wandstärke, des Wärmeleitfähigkeitsverhältnisses von Wand zu Fluid und der Prandtl-Zahl auf den dimensionslosen Wärmestrom und auf die Entwicklung des Temperaturfeldes sind detailliert besprochen worden. Besondere Aufmerksamkeit wird der Untersuchung des Einflusses der Wandwärmeleitung bei niedrigen Reynolds-Zahlen auf die Wärmeübertragung bei turbulenter Zwangskonvektion gewidmet. Die Ergebnisse zeigen, daß der Einfluß der Wandwärmeleitung auf die turbulente Zwangskonvektion bei Kanalströmung sehr bedeutend ist. Dies gilt besonders für den Fall, daß größere Wanddicken und ein hohes Wärmeleitfähigkeitsverhältnis von Wand zu Fluid vorliegen.     

Heat transfer measurements in fully turbulent flows: basic investigations with an advanced thin foil triple sensor

In a former article in this journal a double layer hot film with two 10 μm nickel foils, separated by a 25 μm polyimide foil was introduced as a multi-purpose sensor. Each foil can be operated as a (calibrated) temperature sensor in its passive mode by imposing an electric current small enough to avoid heating by dissipation of electrical energy. Alternatively, however, each foil can also serve as a heater in an active mode with electric currents high enough to cause Joule heating. This double foil sensor can be used as a conventional heat flux sensor in its passive mode when mounted on an externally heated surface. In fully turbulent flows it alternatively can be operated in an active mode on a cold, i.e. not externally heated surface. Then, by heating the upper foil, a local heat transfer is initiated from which the local heat transfer coefficient h can be determined, once the lower foil is heated to the same temperature as the upper one, thus acting as a counter-heater. For further investigations with respect to the underlying sensor concept a triple sensor has been built which consists of three double layer film sensors very close to each other. Various aspects of heat transfer measurements in active modes can be addressed by this sensor.     

Heat transfer and friction in turbulent vortex flow

Summary This paper presents experimentally measured heat transfer and friction coefficients for air and water flowing through a pipe with several types of inserts designed to induce a swirl in the flow. It was observed that inside-surface heat transfer coefficients in swirling flow can, under favourable conditions, be at least four times as large as heat transfer coefficients at the same mass flow rate in purely axial flow. At the same time the pumping power per unit rate of heat transfer can be reduced. The increase in heat transfer coefficients was found to depend on the degree of swirl and on the density or temperature gradient. However, at comparable Reynolds numbers and swirling motions the heat transfer coefficients for air were found to be smaller than the coefficients for water. The reason for this difference is not definitely known, but the phenomenon is qualitatively compatible with that causing the cooling effect in Ranque-Hilsch vortex tubes. The observed phenomena are analyzed qualitatively and it is shown that they are primarily the result of a centrifugal force which induces a radial inward motion of warmer fluid and a radial outward motion of cooler fluid. The application of vortex flow to boiling heat transfer and other high heat flux systems is discussed briefly.

Nomenclature

Symbols c _p Specific heat at constant pressure, BTU/(lb)(deg F) - D _H Hydraulic diameter, (ft) - D Tube diameter, (ft) - f ₀ Fanning friction factor for axial flow, - f Fanning friction factor for swirling flow, - g Acceleration due to gravity, ft/(sec)² - G Mass velocity, lb/(sec) (sq ft) - h _i Inside surface coefficient of heat transfer, BTU/(hr)(sq ft)(deg F) - k Thermal conductivity, BTU/(hr)(sq ft)(deg F/ft) - L Characteristic length used in Grashof numbers, ft - p Frictional pressure drop in a duct, lbs/sq ft - r Radius of tube, ft - t Temperature potential in Grashof number, deg F - U _i Over-all coefficient of heat transfer based on inside tube area, BTU/(hr)(sq ft)(deg F) - V Axial velocity, ft/sec - Coefficient of thermal expansion, (deg F)^–1 - Absolute viscosity, (lbs)/(ft)(hr) - Density, lbs/(ft)³ - Angular velocity of fluid, rad/sec Dimensionless Parameters Nu ₀ Nusselt Number in axial flow, h _i D _H /k - Nu Nusselt Number in swirling flow, h _i D _H /k - Re Reynolds Number, VD _Hp / - Pr Prandtl Number, c _p /k - j Colburn j-Factor, (Nu/RePr)Pr ^2/3 Member of Technical Staff, Bell Telephone Laboratories, Murray Hill, N. J. formerly Baldwin Research Fellow, Lehigh University.     

Heat transfer in buoyancy-driven channel flows with the simultaneous presence of laminar,transitional and turbulent flow regimes

The characteristics of transitional natural convection from laminar to turbulent flows in vertical open channel are numerically investigated. Results are especially presented for air under different conditions. Particular attention is paid to the effects of the channel length, channel width and heating conditions on the transitional natural convection heat transfer and flows.Die Eigenschaften von freier Konvektion im Übergangsbereich von laminarer und turbulenter Strömung in einem senkrechten offenen Kanal wird numerisch untersucht. Die Ergebnisse werden insbesondere für Luft unter verschiedenen Bedingungen vorgestellt. Besonders beachtet wurde der Einfluß der Kanallänge, der Kanalbreite und der Heizbedingungen auf den Wärmeübergang und die Strömung im Übergangsbereich bei freier Konvektion.     

Statistical analysis of instantaneous turbulent heat transfer in circular pipe flows

Turbulent heat transfer in circular pipe flow with constant heat flux on the wall is investigated numerically via Large Eddy Simulations for frictional Reynolds number Re _τ  = 180 and for Prandtl numbers in the range 0.1 ≤ Pr ≤ 1.0. In our simulations we employ a second-order finite difference scheme, combined with a projection method for the pressure, on a collocated grid in cylindrical coordinates. The predicted statistical properties of the velocity and temperature fields show good agreement with available data from direct numerical simulations. Further, we study the local thermal flow structures for different Prandtl numbers. As expected, our simulations predict that by reducing the Prandtl number, the range of variations in the local heat transfer and the Nusselt number decrease. Moreover, the thermal flow structures smear in the flow and become larger in size with less sharpness, especially in the vicinity of the wall. In order to characterize the local instantaneous heat transfer, probability density functions (PDFs) for the instantaneous Nusselt number are derived for different Prandtl number. Also, it is shown that these PDFs are actually scaled by the square root of the Prandtl number, so that a single PDF can be employed for all Prandtl numbers. The curve fits of the PDFs are presented in two forms of log-normal and skewed Gaussian distributions.     

Heat transfer characteristics of pulsated turbulent pipe flow

Heat Transfer characteristics of pulsated turbulent pipe flow under different conditions of pulsation frequency, amplitude and Reynolds number were experimentally investigated. The pipe wall was kept at uniform heat flux. Reynolds number was varied from 5000 to 29 000 while frequency of pulsation ranged from 1 to 8 Hz. The results show an enhancement in the local Nusselt number at the entrance region. The rate of enhancement decreased as Re increased. Reduction of heat transfer coefficient was observed at higher frequencies and the effect of pulsation is found to be significant at high Reynolds number. It can be concluded that the effect of pulsation on the mean Nusselt numbers is insignificant at low values of Reynolds number. Received on 29 June 1998     

Conjugate heat transfer study of incompressible turbulent offset jet flows

In the present case, the conjugate heat transfer involving a turbulent plane offset jet is considered. The bottom wall of the solid block is maintained at an isothermal temperature higher than the jet inlet temperature. The parameters considered are the offset ratio (OR), the conductivity ratio (K), the solid slab thickness (S) and the Prandtl number (Pr). The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then it becomes independent of the Reynolds number. The ranges of parameters considered are: OR = 3, 7 and 11, K = 1–1,000, S = 1–10 and Pr = 0.01–100. High Reynolds number two-equation model (k–ε) has been used for turbulence modeling. Results for the solid–fluid interface temperature, local Nusselt number, local heat flux, average Nusselt number and average heat transfer have been presented and discussed.     

Heat mass transfer in a turbulent layer above permeable membranes

The temperature and concentration fields in a boundary layer above perforated membranes are presented, and their relationship with the velocity fields given in [1] is established. Measurements of the thermal state of membranes are made with various geometric and thermophysical properties and various coolant drafts. Empirical formulas are also presented for thermal flux and temperature of the permeable walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 22–31, July–August, 1973.     

Heat transfer in a turbulent boundary layer with stepped injection

The asymptotic theory of a turbulent boundary layer has been applied to derive relationships for the heat and mass transfer when there is injection and consequent nonuniformity in the gas composition. Experimental studies are reported on heat and mass transfer with stepped injection of homogeneous and inhomogeneous gases; the results confirm the equations for the heat and mass transfer at a permeable surface when a foreign gas is blown in.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 124–129, July–August, 1973.     

Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.     

Heat transfer in asymmetric transverse flows over bundles of tubes

Heat transfer was studied on a separate transverse row of tubes with the relative pitch ofs ₁/d=1.5 and a staggered bundle with the relative pitches ofs ₁/d×s ₂/d=1.15×0.98. A test tube in the transverse row was used with a variable displacement from the symmetric position. The tube bundle was placed at different gaps from the shell wall. Experiments were performed in air and water in the range ofRe from 10³ to 6×10⁵. Asymmetric flows over transverse rows are accompanied by augmented heat transfer rates and steady state lift force which becomes higher with the amount of displacement. The presence of the shell wall introduces alterations in the thermal and fluid dynamics over outside tubes in a bundle.     

Heat transfer in turbulent natural convection on a vertical permeable surface

A theoretical and experimental study is presented for heat transfer in turbulent natural convection on vertical surfaces with uniform and homogeneous air injection and withdrawal.