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.     

An experimental investigation of heat transfer to pulsating pipe air flow with different amplitudes

Heat transfer characteristics to both laminar and turbulent pulsating pipe flows under different conditions of Reynolds number, pulsation frequency, pulsator location and tube diameter were experimentally investigated. The tube wall of uniform heat flux condition was considered for both cases. Reynolds number varied from 750 to 12,320 while the frequency of pulsation ranged from 1 to 10 Hz. With locating the pulsator upstream of the inlet of the test section tube, results showed an increase in heat transfer rate due to pulsation by as much as 30% with flow Reynolds number of 1,643 and pulsation frequency of 1 Hz, depending on the upstream location of the pulsator valve. Closer the valve to the tested section inlet, the better improvement in the heat transfer coefficient is achieved. Upon comparing the heat transfer results of the upstream and the downstream pulsation, at Reynolds number of 1,366 and 1,643, low values of the relative mean Nusselt number were obtained with the upstream pulsation. Comparing the heat transfer results of the two studied test sections tubes for Reynolds number range from 8,000 to 12,000 and pulsation frequency range from 1.0 to 10 Hz showed that more improvement in heat transfer rate was observed with a larger tube diameter. For Reynolds number ranging from 8,000 to 12,000 and pulsation frequency of 10 Hz, an improvement in the relative mean Nusselt number of about 50% was obtained at Reynolds number of 8,000 for the large test section diameter of 50 mm. While, for the small test section diameter of 15 mm, at same conditions of Reynolds number and frequency, a reduction in the relative mean Nusselt number of up to 10% was obtained.     

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     

Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel

An experimental study was conducted of incompressible, moderate Reynolds number flow of air over heated rectangular blocks in a two-dimensional, horizontal channel. Holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in self- sustained oscillatory flow. Experiments were conducted in the laminar, transitional and turbulent flow regimes for Reynolds numbers in the range from Re = 520 to Re = 6600. Interferometric measurements were obtained in the thermally and fluiddynamically periodically fully developed flow region on the ninth heated block. Flow oscillations were first observed between Re = 1054 and Re = 1318. The period of oscillations, wavelength and propagation speed of the Tollmien–Schlichting waves in the main channel were measured at two characteristic flow velocities, Re = 1580 and Re = 2370. For these Reynolds numbers it was observed that two to three waves span one geometric periodicity length. At Re = 1580 the dominant oscillation frequency was found to be around 26 Hz and at Re = 2370 the frequency distribution formed a band around 125 Hz. Results regarding heat transfer and pressure drop are presented as a function of the Reynolds number, in terms of the block-average Nusselt number and the local Nusselt number as well as the friction factor. Measurements of the local Nusselt number together with visual observations indicate that the lateral mixing caused by flow instabilities is most pronounced along the upstream vertical wall of the heated block in the groove region, and it is accompanied by high heat transfer coefficients. At Reynolds numbers beyond the onset of oscillations the heat transfer in the grooved channel exceeds the performance of the reference geometry, the asymmetrically heated parallel plate channel. Received on 26 April 2000     

Average Nusselt number correlation in the thermal entrance region of steady and pulsating turbulent pipe flows

Empirical correlation has been developed for local and average Nusselt numbers in the thermal entrance region of steady and pulsating turbulent air-flows in a pipe. The correlation was based on experimental data obtained from experiment carried out on a pipe heated under uniform heat flux conditions. The rate of flow was periodically varied at frequencies ranging from 1 Hz to 13 Hz while the average Reynolds number varied from 6400 to 42000. Received on 20 October 1998     

A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

Flow structure and heat transfer characteristics of an unconfined impinging air jet at high jet Reynolds numbers

The flow and heat transfer characteristics of an unconfined air jet that is impinged normally onto a heated flat plate have been experimentally investigated for high Reynolds numbers ranging from 30,000 to 70,000 and a nozzle-to-plate spacing range of 1–10. The mean and turbulence velocities by using hot-wire anemometry and impingement surface pressures with pressure transducer are measured. Surface temperature measurements are made by means of an infrared thermal imaging technique. The effects of Reynolds number and nozzle-to-plate spacing on the flow structure and heat transfer characteristics are described and compared with similar experiments. It was seen that the locations of the second peaks in Nusselt number distributions slightly vary with Reynolds number and nozzle-to-plate spacing. The peaks in distributions of Nusselt numbers and radial turbulence intensity are compatible for spacings up to 3. The stagnation Nusselt number was correlated for the jet Reynolds number and the nozzle-to-plate spacing as Nu _st∝Re ^0.69(H/D)^0.019.     

Computation of Vortex Shedding and Radiated Sound for a Circular Cylinder: Subcritical to Transcritical Reynolds Numbers

The Lighthill acoustic analogy combined with Reynolds-averaged Navier–Stokes flow computations are used to investigate the ability of existing technology to predict the tonal noise generated by vortex shedding from a circular cylinder for a range of Reynolds numbers (100 < Re < 5 million). Computed mean drag, mean coefficient of pressure, Strouhal number, and fluctuating lift are compared with experiment. Two-dimensional calculations produce a Reynolds number trend similar to experiment but incorrectly predict many of the flow quantities. Different turbulence models give inconsistent results in the critical Reynolds number range (Re≈ 100000). The computed flow field is used as input for noise prediction. Two-dimensional inputs overpredict both noise amplitude and frequency; however, if an appropriate correlation length is used, predicted noise amplitudes agree with experiment. Noise levels and frequency content agree much better with experiment when three-dimensional flow computations are used as input data. Received 5 May 1998 and accepted 28 September 1998     

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 × 10³ to 6.5 × 10⁵ to study the effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics. In the subcritical range of Re (<2 × 10⁵), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 × 10⁵), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag. Received: 8 September 1998 / Accepted: 1 January 2000     

Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries

This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - c_m mass concentration of microcapsules - c_p specific heat, kJ kg^–1 K^–1 - h_fs phase change material heat of fusion, kJ kg^–1 - h_m* modified convective heat transfer coefficient, W m^–2 K^–1 - k thermal conductivity, W m^–1 K^–1 - k_e effective thermal conductivity of slurry, W m^–1 K^–1 - k_b slurry bulk thermal conductivity, W m^–1 K^–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - q_wⁿ wall heat flux, Wm^–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r₀ duct radius, m - r₁ dimensionless radial coordinate - Ste Stefan number - T temperature, K - T₁ lower phase change temperature limit, K - T₂ upper phase change temperature limit, K - T_i slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x₁ dimensionless axial coordinate - thermal diffusivity, m²/s - dimensionless temperature - dynamic viscosity, N·s/m² - kinematic viscosity, m²/s - _t width of thermal boundary, m - degree of heat transfer enhancement, = h_m*/(h_m*)_single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid     

Slot/slots air jet impinging cooling of a cylinder for different jets–cylinder configurations

Heat transfer characteristics of a slot/slots jet air impinging on a cylinder have been experimentally investigated for two different orientations of slot/slots jet plan with respect to cylinder axis. The experiments were carried out to study the effects of orientation of slot/slots jet plan with respect to cylinder axis on the rate of heat transfer from the cylinder. Two different jet–cylinder configurations were studied: (1) single slot jet aligned with cylinder axis (slot length = cylinder length), and (2) multiple slot jets equally spaces distributed orthogonal to cylinder axis (each slot length = cylinder diameter and sum of slots lengths = cylinder length). For each configuration, parametric effects of Reynolds numbers (Re) ranging from 1,000 to 10,000, dimensionless slot widths (W/d) ranging from 0.125 to 0.5, and dimensionless slot orifice-to-cylinder spacing (Z/W) ranging from 1 to 12 on local and average Nusselt numbers around cylinder surface have been investigated. The results showed that: (1) cooling the cylinder by multiple slots jets situated orthogonal to cylinder axis gave more uniform surface temperature distributions and higher heat transfer rate than the case of cooling the cylinder by single slot jet aligned with cylinder axis, (2) for both configurations the Nusselt number around the cylinder increased with increasing Re and W/d, and (3) for both configurations there was a certain Z/W in the range 4<Z/W<6 at which the stagnation and mean Nusselt number were maximum. Correlations for the mean Nusselt numbers around cylinder surface have been presented for both configurations. Comparisons between the correlations predictions and the present and other previous experimental data have been conducted.     

Numerical investigation of turbulent flow,heat transfer and entropy generation in a helical coiled tube with larger curvature ratio

Three-dimensional turbulent forced convective heat transfer and flow characteristics, and the non-dimensional entropy generation number in a helical coiled tube subjected to uniform wall temperature are simulated using the k–ε standard turbulence model. A finite volume method is employed to solve the governing equations. The effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor and Nusselt number are discussed. The results presented in this paper cover a Reynolds number range of 2 × 10⁴ to 6 × 10⁴, a pitch range of 0.1–0.2 and a curvature ratio range of 0.1–0.3. The results show that the coil pitch, curvature ratio and Reynolds number have different effects on the average friction factor and Nusselt number at different cross-sections. In addition, the flow and heat transfer characteristics in a helical coiled tube with a larger curvature ratio for turbulent flow are different from that of smaller curvature ratio for laminar and turbulent flow in certain ways. Some new features that are not obtained in previous researches are revealed. Moreover, the effects of Reynolds number, curvature ratio, and coil pitch on the non-dimensional entropy generation number of turbulent forced convection in a helical coiled tube are also discussed.     

Heat transfer and friction factor of turbulent flow through a horizontal semi-circular duct

Forced convection heat transfer and pressure drop characteristics of air flow inside a horizontal semi-circular duct are investigated experimentally. The experiments are carried out on a semi-circular duct of 23 mm inner radius, 2 mm thickness, and 2,000 mm length within a range of Reynolds number (8,242 ≤ Re ≤ 57,794)., under uniform wall heat flux conditions. The friction factor is determined by measuring the axial static pressure at different selected axial stations along the semi-circular duct. The variations of surface and mean air temperatures, local heat transfer coefficient, local Nusselt number, and the friction factor with the axial dimensionless distance are presented. It is observed that, for a given value of Reynolds number, each of the local heat transfer coefficient and the friction factor has a relatively high value near the entrance of the semi-circular duct then it decreases with increasing the dimensionless axial distance until it approaches a nearly constant value at the fully developed region. Also, it is found that, with increasing the Reynolds number the average heat transfer coefficient is increased and the friction factor is decreased. Moreover, empirical correlations for the heat transfer coefficient and friction factor as a function of the Reynolds number are obtained.     

Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section

The flow and heat transfer in an inclined and horizontal rectangular duct with a heated plate longitudinally mounted in the middle of cross section was experimentally investigated. The heated plate and rectangular duct were both made of highly conductive materials, and the heated plate was subjected to a uniform heat flux. The heat transfer processes through the test section were under various operating conditions: Pr ≈ 0.7, inclination angle ϕ = −60° to +60°, Reynolds number Re = 334–1,911, Grashof number Gr = 5.26 × 10²–5.78 × 10⁶. The experimental results showed that the average Nusselt number in the entrance region was 1.6–2 times as large as that in the fully developed region. The average Nusselt numbers and pressure drops increased with the Reynolds number. The average Nusselt numbers and pressure drops decreased with an increase in the inclination angle from −60° to +60° when the Reynolds number was less than 1,500. But when the Reynolds number increased to over about 1,800, the heat transfer coefficients and pressure drops were independent of inclination angles.     

Anomalous predictions of pressure drop and heat transfer in ducts of arbitrary cross-section with modified power law fluids

 The apparent viscosities of purely viscous non-Newtonian fluids are shear rate dependent. At low shear rates, many of such fluids exhibit Newtonian behaviour while at higher shear rates non-Newtonian, power law characteristics exist. Between these two ranges, the fluid's viscous properties are neither Newtonian or power law. Utilizing an apparent viscosity constitutive equation called the “Modified Power Law” which accounts for the above behavior, solutions have been obtained for forced convection flows. A shear rate similarity parameter is identified which specifies both the shear rate range for a given fluid and set of operating conditions and the appropriate solution for that range. The results of numerical solutions for the friction factor–Reynolds number product and for the Nusselt number as a function of a dimensionless shear rate parameter have been presented for forced fully developed laminer duct flows of different cross-sections with modified power law fluids. Experimental data is also presented showing the suitability of the “Modified Power Law” constitutive equation to represent the apparent viscosity of various polymer solutions. Received on 21 August 2000     

Comparative evaluation of three heat transfer enhancement strategies in a grooved channel

 Results of a comparative evaluation of three heat transfer enhancement strategies for forced convection cooling of a parallel plate channel populated with heated blocks, representing electronic components mounted on printed circuit boards, are reported. Heat transfer in the reference geometry, the asymmetrically heated parallel plate channel, is compared with that for the basic grooved channel, and the same geometry enhanced by cylinders and vanes placed above the downstream edge of each heated block. In addition to conventional heat transfer and pressure drop measurements, holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in the self-sustained oscillatory flow. The locations of increased heat transfer within one channel periodicity depend on the enhancement technique applied, and were identified by analyzing the unsteady temperature distributions visualized by holographic interferometry. This approach allowed gaining insight into the mechanisms responsible for heat transfer enhancement. Experiments were conducted at moderate flow velocities in the laminar, transitional and turbulent flow regimes. Reynolds numbers were varied in the range Re = 200–6500, corresponding to flow velocities from 0.076 to 2.36 m/s. Flow oscillations were first observed between Re = 1050 and 1320 for the basic grooved channel, and around Re = 350 and 450 for the grooved channels equipped with cylinders and vanes, respectively. At Reynolds numbers above the onset of oscillations and in the transitional flow regime, heat transfer rates in the investigated grooved channels exceeded the performance of the reference geometry, the asymmetrically heated parallel plate channel. Heat transfer in the grooved channels enhanced with cylinders and vanes showed an increase by a factor of 1.2–1.8 and 1.5–3.5, respectively, when compared to data obtained for the basic grooved channel; however, the accompanying pressure drop penalties also increased significantly. Received on 5 April 2001     

Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers

 The lift force experienced by a spinning sphere moving in a viscous fluid, with constant linear and angular velocities, is measured by means of a trajectographic technique. Measurements are performed in the range of dimensionless angular velocities γ=aω/V lying between 1 and 6, and in the range of Reynolds numbers Re=2aV/ν lying between 10 and 140 (a sphere radius, ω angular velocity, V relative velocity of the sphere centre, ν fluid kinematic viscosity). A notable departure from the theoretical relationship at low Reynolds number, C _L =2γ, is obtained, the ratio C _L /γ being found to significantly decrease with increasing γ and increasing Re. The following correlation is finally proposed to estimate the lift coefficient in the range 10<Re<140: C _L ≅0.45+(2γ−0.45) exp (−0.075γ^0.4 Re ^0.7) Received: 20 May 1996/Accepted: 9 November 1997     

Development of localized arc filament RF plasma actuators for high-speed and high Reynolds number flow control

Recently developed localized arc filament plasma actuators (LAFPAs) have shown tremendous control authority in high-speed and high Reynolds number flow for mixing enhancement and noise mitigation. Previously, these actuators were powered by a high-voltage pulsed DC plasma generator with low energy coupling efficiency of 5–10%. In the present work, a new custom-designed 8-channel pulsed radio frequency (RF) plasma generator has been developed to power up to 8 plasma actuators operated over a wide range of forcing frequencies (up to 50 kHz) and duty cycles (1–50%), and at high energy coupling efficiency (up to 80–85%). This reduces input electrical power requirements by approximately an order of magnitude, down to 12 W per actuator operating at 10% duty cycle. The new pulsed RF plasma generator is scalable to a system with a large number of channels. Performance of pulsed RF plasma actuators used for flow control was studied in a Mach 0.9 circular jet with a Reynolds number of about 623,000 and compared with that of pulsed DC actuators. Eight actuators were distributed uniformly on the perimeter of a 2.54-cm diameter circular nozzle extension. Both types of actuators coupled approximately the same amount of power to the flow, but with drastically different electrical inputs to the power supplies. Particle image velocimetry measurements showed that jet centerline Mach number decay produced by DC and RF actuators operating at the same forcing frequencies and duty cycles is very similar. At a forcing Strouhal number near 0.3, close to the jet column instability frequency, well-organized periodic structures, with similar patterns and dimensions, were generated in the jets forced by both DC and RF actuators. Far-field acoustic measurements demonstrated similar trends in the overall sound pressure level (OASPL) change produced by both types of actuators, resulting in OASPL reduction up to 1.2–1.5 dB in both cases. We conclude that pulsed RF actuators demonstrate flow control authority similar to pulsed DC actuators, with a significantly reduced power budget.     

Experimental investigation of mixed convection heat transfer in a horizontal and inclined rectangular channel

 Mixed convection heat transfer in rectangular channels has been investigated experimentally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Experiments were conducted for Pr=0.7, aspect ratios AR=5 and 10, inclination angles 0° ≤ θ ≤ 30°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr*=7.0 × 10⁵ to 4.0 × 10⁷. From the parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results related to the buoyancy affected secondary flow and the onset of instability have been discussed. Some of the results obtained from the experimental measurements are also compared with the literature, and a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number and increasing aspect ratio. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle. Received on 19 March 2001 / Published online: 29 November 2001     

Shallow wakes generated on smooth and rough surfaces

This study deals with the behavior of shallow turbulent wakes generated on smooth and rough surfaces. The wake generator used is a flat plate placed normal to the flow. Experiments were conducted at flow depths of 40 and 80 mm. The boundary layer thickness in the approaching flow occupies 60–75% of the flow depth. The Reynolds number based on the plate width and approaching freestream velocity varies from 13.0 × 10³ to 14.5 × 10³. Velocity measurements were carried out in the near-wake region (1–10 plate widths) using a laser-Doppler anemometer. The mean velocity distributions at various axial stations collapse onto a single curve by a proper choice of the length and velocity scales. It is important to note that a sense of self-similarity is attained even in the near-wake region. Attempts were made to clarify the relative effects of the transverse shear and bed friction in shallow open channel wakes. Received: 11 February 1999/Accepted: 30 August 2000