A simple method for obtaining the fully developed heat transfer coefficient in turbulent pipe flow

This paper addresses a distinct and direct computational technique for calculating the characteristics of a thermally developed turbulent pipe flow in a circular pipe. The technique seeks to replace a partial differential energy equation into an equivalent ordinary differential energy equation. The latter is valid in the thermally developed region of the pipe. Numerical results show good agreement with experimental observations for gas and water flows over a wide range of Reynolds numbers.     

Experimental study of developing turbulent flow and heat transfer in ribbed convergent/divergent square ducts

The local heat transfer and pressure drop characteristics of developing turbulent flows of air in three stationary ribbed square ducts have been investigated experimentally. These are: ribbed square duct with constant cross-section (straight duct), ribbed divergent square duct and ribbed convergent square duct. The convergent/divergent duct has an inclination angle of 1°. The measurement was conducted within the range of Reynolds numbers from 10 000 to 77 000. The heat transfer performance of the divergent/convergent ducts is compared with the ribbed straight duct under three constraints: identical mass flow rate, identical pumping power and identical pressure drop. Because of the streamwise flow acceleration or deceleration, the local heat transfer characteristics of the divergent and convergent ducts are quite different from those of the straight duct. In the straight duct, the fluid flow and heat transfer become fully developed after 2–3 ribs, while in the divergent and convergent ducts there is no such trend. The comparison shows that among the three ducts, the divergent duct has the highest heat transfer performance, the convergent duct has the lowest, while the straight duct locates somewhere in between.     

Experimental and numerical study of developing turbulent flow and heat transfer in convergent/divergent square ducts

 The work reported in this paper is a systematic experimental and numerical study of friction and heat transfer characteristics of divergent/convergent square ducts with an inclination angle of 1^∘ in the two direction at cross section. The ratio of duct length to average hydraulic diameter is 10. For the comparison purpose, measurement and simulation are also conducted for a square duct with constant cross section area, which equals to the average cross section area of the convergent/divergent duct. In the numerical simulation the flow is modeled as being three-dimensional and fully elliptic by using the body-fitted finite volume method and the kɛ turbulence model. The uniform heat flux boundary condition is specified to simulate the electrical heating used in the experiments. The heat transfer performance of the divergent/convergent ducts is compared with the duct with uniform cross section under three constraints (identical mass flow rate, pumping power and pressure drop). The agreement of the experimental and numerical results is quite good except at the duct inlet. Results show that for the three ducts studied there is a weak secondary flow at the cross section, and the circumference distribution of the local heat transfer coefficient is not uniform, with an appreciable reduction in the four corner regions. In addition, the acceleration/deceleration caused by the cross section variation has a profound effect on the turbulent heat transfer: compared with the duct of constant cross section area, the divergent duct generally shows enhanced heat transfer behavior, while the convergent duct has an appreciable reduction in heat transfer performance. Received on 18 September 2000 / Published online: 29 November 2001     

Numerical investigations on the heat transfer in turbulent oscillating pipe flow

 The examinations on the heat transfer in developing laminar oscillating pipe flow presented before [1] have been extended to include turbulence as well. A suitable low-Reynolds-number k-ɛ-turbulence model was incorporated in an existing 2D-simulation code for oscillating flow conditions and subsequent examinations focused on the heat transfer associated with turbulent oscillating flow. The calculations cover a wide range of the characteristic parameters and the results are summarised in form of new heat transfer correlations to suit with the operating conditions of regenerative thermal machines. Received on 5 July 1999     

Experimental and numerical study of turbulent flow and heat transfer inside hexagonal duct

Flow and heat transfer characteristics in transition and turbulent regions are studied experimentally and numerically in a horizontal smooth regular hexagonal duct under constant wall temperature boundary condition covering a range of Reynolds number from 2.3 × 10³ to 52 × 10³. Two types of k-omega (standard and shear stress transport (SST)) and three types of k-ε (standard, renormalization (RNG), and realizable) turbulence model are employed for transition and turbulent regions, respectively. Both average and fully developed Darcy friction factor and Nusselt number are presented as a function of Reynolds number. It is seen that k-omega SST and k-ε realizable turbulence models gave the best agreement with the experimental data in transition and turbulent regions, respectively. All the experimental results are correlated within an accuracy of ±13 % and ±7 % for Nusselt number and Darcy friction factor, respectively. Results obtained in this study are compared with circular duct results using hydraulic diameter.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

Large-scale computer simulation of fully developed turbulent channel flow with heat transfer

Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.     

Numerical simulation of fully developed turbulent flow and heat transfer in annular-sector ducts

 The mixing length theory is employed to simulate the fully developed turbulent heat transfer in annular-sector ducts with five apex angles (θ₀=18,20,24,30,40^∘) and four radius ratios (R _o/R _i=2,3,4,5). The Reynolds number range is 10⁴10⁵. The numerical results agree well with an available correlation which was obtained in following parameter range: θ₀=18,20,24,30,40^∘, R _o/R _i=4 and Re=10⁴5×10⁴. The present work demonstrates that the application range of the correlation can be much extended. Apart from the mixing length theory, the kɛ model with wall function and the Reynolds stress model are also employed. None of the friction factor results predicted by the three models agrees well with the test data. For the heat transfer prediction the mixing length theory seems the best for the cases studied. Received on 17 July 2000 / Published online: 29 November 2001     

Quantitative measurement of spatio-temporal heat transfer to a turbulent water pipe flow

A technique using high-speed infrared thermography was applied to measure the spatio-temporal heat transfer to a turbulent water flow in a horizontal circular pipe. The instantaneous distribution of the heat transfer coefficient and its temporal fluctuation was evaluated by solving inverse heat conduction equation of the heated thin-test-surface. As a result, it was demonstrated that the quantitative measurement, not only the time-averaged heat transfer, but also the statistics of the spatio-temporal fluctuation, was possible using this technique. In addition, a unique feature of the spatio-temporal heat transfer was clearly visualized for the turbulent pipe flow, which was dominated by the streaky structure similar to that for the turbulent boundary layer and the turbulent channel flow.     

Conjugate heat transfer in thermally developing laminar flow with viscous dissipation effects

In this study, thermally developing laminar forced convection in a pipe including viscous dissipation and wall conductance is investigated numerically. The constant heat flux is assumed to be imposed at the outer surface of the pipe wall. The finite volume method is used. The distributions for the developing temperature and local Nusselt number in the entrance region are obtained. The dependence of the results on the Brinkman number and the dimensionless thermal conductivity are shown. The viscous heating effect on the wall is shown. Significant viscous dissipation effects have been observed for large Br.     

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     

Numerical investigation of fully developed turbulent fluid flow and heat transfer in a square duct

Three-dimensional fully developed turbulent fluid flow and heat transfer in a square duct are numerically investigated with the author's anisotropic low-Reynolds-number k-ε turbulence model. Special attenton has been given to the regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, instead of the common wall function approach, the no-slip boundary condition at the wall is directly used. Velocity and temperature profiles are predicted for fully developed turbulent flows with constant wall temperature. The predicted variations of both local wall shear stress and local wall heat flux are shown to be in close agreement with available experimental data. The present paper also presents the budget of turbulent kinetic energy equation and the systematic evaluation for existing wall function forms. The commonly adopted wall function forms that are valid for two-dimensional flows are found to be inadequate for three-dimensional turbulent flows in a square duct.     

Drag reduction effectiveness of dilute and entangled xanthan in turbulent pipe flow

The ability to reduce the frictional drag in turbulent flow in pipes and channels by addition of a small amount of a high molecular weight polymer has application in myriad industries and processes. Here, the drag reduction properties of the polyelectrolyte xanthan are explored in differing solvent environments (salt free versus salt solution) and delivery configurations (homogeneous versus stock solution dilution). Drag reduction effectiveness increases when an entangled xanthan solution is diluted compared to solutions prepared in the dilute regime. Based on dynamic rheological measurements of the elastic modulus, residual entanglements and network structure are hypothesized to account for the observed change in drag reduction effectiveness. Drag reduction effectiveness is unchanged by the presence of salt when the stock solution concentration is sufficiently above the critical concentration c_D. Finally, the drag reduction effectiveness decreases with time when diluted from an entangled stock solution but remains greater than the homogeneous case after more than 24 h.     

Experimental study of heat transfer and flow characteristics of liquid falling film on a horizontal fluted tube

The aim of the present study is to investigate experimentally the effect of the fluted surface tube on the heat transfer and flow characteristics of liquid falling film. Experiments have indicated that, when a liquid falling film falls on a horizontal fluted surface tube, the transition starts at low Reynolds number than that of the plain tube. The value of the film thickness has been slightly decreased by decreasing the fluted pitch. A reduction of the film thickness was observed at about 9% for tube number 4, which has lower pitch, at Reynolds number of 485. A clear reduction of the dimensionless wavelength, λ*, has occurred at low fluted pitch tube. The use of enhanced surfaces can provide heat transfer coefficients higher values than those obtained from plain tube. Heat transfer enhancement was noticed due to the use of fluted tube surface. An improvement of the Nusselt number reached about 45% for tube 4. However, the low values of the fluted pitch increased the heat transfer enhancement than that of the high values.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Effects of dynamic load on flow and heat transfer of two-phase boiling water in a horizontal pipe

An experimental investigation was performed to obtain the flow and heat transfer characteristics of single-phase water flow and two-phase pipe boiling water flow under high gravity (Hi-G) in present work. The experiments were conducted on a rotating platform, and boiling two-phase flow state was obtained by means of electric heating. The data were collected specifically in the test section, which was a lucite pipe with inner diameter of 20 mm and length of 400 mm. By changing the parameters, such as rotation speed, inlet temperature, flow rate, and etc., and analyzing the fluid resistance, effective heat and heat transfer coefficient of the experimental data, the effects of dynamic load on the flow and heat transfer characteristics of single phase water and two-phase boiling water flow were investigated and obtained. The two-phase flow patterns under Hi-G condition were obtained with a video camera. The results show that the dynamic load significantly influences the flow characteristic and boiling heat transfer of the two-phase pipe flow. As the direction of the dynamic load and the flow direction are opposite, the greater the dynamic load, the higher the outlet pressure and the flow resistance, and the lower the flow rate, the void fraction, the wall inner surface temperature and the heat transfer capability. Therefore, the dynamic load will block the fluid flow, enhance heat dissipation toward the ambient environment and reduce the heat transfer to the two-phase boiling flow.     

Combined convection and radiation heat transfer to thermally developing laminar droplet flow in concentric annuli

This paper presents numerical results for combined convection and radiation heat transfer to a laminar mist flow in the thermal entrance region of a concentric annulus with a heated core at constant wall temperature and an insulated outer wall. The saturated droplets in the mist flow are considered as equivalent heat sinks distributed in the superheated vapor stream. Numerical calculations are performed for the variations of droplet size, mean vapor velocity, and the local Nusselt number in the streamwise direction until the single-phase fully-developed condition is reached. The important role of the saturated droplets on combined convection and radiation heat transfer to mist flow is clearly demonstrated.

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Kombinierte Wärmeübertragung durch Konvektion und Strahlung im thermischen Einlauf einer laminaren Tröpfchenströmung in einem konzentrischen Ringspalt

Zusammenfassung Dieser Artikel stellt numerische Ergebnisse für kombinierte Wärmeübertragung durch Konvektion und Strahlung im thermischen Einlauf einer laminaren Tröpfchenströmung in einem konzentrischen Ringraum mit beheiztem Kern bei konstanter Wandtemperatur und isolierter Außenwand dar. Die gesättigten Tröpfchen wirken als verteilte Wärmesenken im überhitzten Dampfstrom. Numerische Berechnungen werden unter Variation des Tröpfchendurchmessers, der durchschnittlichen Dampfgeschwindigkeit und der Nusselt-Zahl durchgeführt, bis eine einphasige vollausgebildete Strömung erreicht ist. Der wichtige Einfluß der gesättigten Tröpfchen auf die kombinierte Wärmeübertragung durch Konvektion und Strahlung wird klar gezeigt.

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Nomenclature A liquid loading parameter, defined in Eq. (3) - A _d heat transfer area of droplets per unit volume of vapor - A _w heat transfer area of heated wall per unit volume of vapor - C wall superheat parameter, defined in Eq. (5) - C _p specific heat of vapor - D dimensionless droplet diameter,d/d ₀ - D _h hydraulic diameter, 2(r ₀–r _i) - d droplet diameter - d ₀ droplet diameter at thermal entrance (x=0) - E dimensionless parameter, defined in Eq. (6) - H dimensionless parameter, defined in Eq. (7) - F _w–d geometric view factor - h _d heat transfer coefficient for evaporating droplets - h _p0 heat transfer coefficient of non-evaporating droplet or solid sphere with diameter ofd ₀ - k thermal conductivity of vapor - n droplet number density (number of droplets per unit volume of vapor) - n ₀ droplet number density at thermal entrance (x=0) - Nu _x local Nusselt number, defined by Eq. (17) - Pr Prandtl number of vapor,C _p/k - Q _r radiative heat transfer to droplets (per unit volume of vapor) - q _w heat flux at the inner wall - R dimensionless radial position,r/r _i - Re Reynolds number of vapor, 2 _v V₀ r _i/ - r radial position - r _i radius of inner tube - r _o radius of outer tube - S heat sink parameter, defined in Eq. (4) - T temperature of vapor - T _m bulk mean temperature of vapor - T _s saturated temperature - T _w inner wall temperature - V mean vapor velocity - V fully-developed vapor velocity, given in Eq. (12) - V ₀ mean vapor velocity atx=0 - x axial position in thermal entrance region - X dimensionless axial position, (x/r _i)/(Re·Pr) - z ₀ flow quality atx=0 Greek symbols ₀ vapor void fraction atx=0 - ratio of radius,r _i/r₀ - _d emissivity of droplets - _w emissivity of inner heated wall - dimensionless vapor temperature, defined in Eq. (9) - _m dimensionless vapor mean temperature, given by Eq. (14) - _wi dimensionless inner wall temperature - _wo dimensionless outer wall temperature - dynamic viscosity of vapor - _l liquid density - _v vapor density - Stefan-Boltzmann constant     

Predicting the deposit velocity for horizontal turbulent pipe flow of slurries

The sliding bed theory of deposition recently developed by Wilson and others has been compared with a range of experimental results most of them not previously published. This comparison has confirmed the suitability of this theory for the claimed range of particle sizes for solids suspended in water. However, the results for higher viscosity fluids do not show such good agreement. This disparity is later explained following the development of a theory of deposition, based on the sliding bed concept, for very fine particles smaller than the thickness of the viscous sub-layer. Furthermore, by adding the contributions of both Wilson's theory and the viscous sub-layer theory an equation is obtained which describes deposition for particles in the transition region between the two types of deposition. The two theories combined now cover the complete particle size range for unflocculated particles. In the case of flocculated particles the new viscous sub-layer theory is shown to be consistent with experimental data providing the particle properties are used instead of the floc properties.