scholarly journals Lagrangian Statistics of Heat Transfer in Homogeneous Turbulence Driven by Boussinesq Convection

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 127
Author(s):  
Jane Pratt ◽  
Angela Busse ◽  
Wolf-Christian Müller
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Flows ◽  
Statistical Approach ◽  
Homogeneous Turbulence ◽  
Turbulent Convection ◽  
Clear Trend ◽  
Tracer Particles ◽  
Non Gaussian ◽  
Natural Settings

The movement of heat in a convecting system is typically described by the nondimensional Nusselt number, which involves an average over both space and time. In direct numerical simulations of turbulent flows, there is considerable variation in the contributions to the Nusselt number, both because of local spatial variations due to plumes and because of intermittency in time. We develop a statistical approach to more completely describe the structure of heat transfer, using an exit-distance extracted from Lagrangian tracer particles, which we call the Lagrangian heat structure. In a comparison between simulations of homogeneous turbulence driven by Boussinesq convection, the Lagrangian heat structure reveals significant non-Gaussian character, as well as a clear trend with Prandtl number and Rayleigh number. This has encouraging implications for simulations performed with the goal of understanding turbulent convection in natural settings such as Earth’s atmosphere and oceans, as well as planetary and stellar dynamos.

Fluid Flow and Heat Transfer Behavior for Turbulent Flows in a Tube With Vortex Generator Pairs for an Efficient Heat Exchanger

2018 ◽  
Author(s):  
Md. Islam ◽  
Z. Chong ◽  
S. Bojanampati
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Flow Behavior ◽  
Vortex Generator ◽  
Tube Diameter ◽  
Vortex Generators ◽  
Blockage Ratio ◽  
Delta Winglet

Various technologies have been developed to enhance flow mixing and heat transfer in order to develop an efficient compact heat exchanging devices. Vortex generators/turbulent promoters generate the vortices which reduce the boundary layer thickness and introduce the better mixing of the fluid to enhance the heat transfer. In this research experimental investigations have been carried out to study the effect of delta winglet vortex generator pairs on heat transfer and flow behavior. To generate longitudinal vortex flow, two pairs of the delta winglet vortex generators (DWVG) with the length of 10mm and winglet-pitch to tube-diameter ratio (PR = 4.8) are mounted on the inner wall of a circular tube. The DWVG pairs with two different winglet-height to tube-diameter ratios (Blockage ratio, BR = 0.1 and 0.2), three attack angles (α = 10°, 20°, 30°) and three spacings between leading edges (S = 10, 15 and 20mm) are studied. The experiments were conducted with DWVGs pairs for the air flow range of Reynolds numbers 5000–25000. The influence of the DWVGs on heat transfer and pressure drop was investigated in terms of the Nusselt number and friction factor. The experimental results indicate that DWVG pair in a tube results in a considerable enhancement in Nusselt number (Nu) with some pressure penalty. It is found that DWVG increases Nu up to 85% over the smooth tube. It is also observed that Nusselt number increases with Re, blockage ratio and attack angle. Friction factor decreases with Re but increases with blockage ratio, spacing and attack angle. And 30° DWVG pair with S = 20mm, BR = 0.2 gets the highest friction factor. The Highest thermal performance enhancement (TPE) was noticed for α = 10°, S = 20mm, BR = 0.2 for turbulent flows. To obtain qualitative information on the flow behavior and vortex structures, flow was visualized by laser sheet using smoke as a tracer supplied at the entrance of the test section. The generation and development of longitudinal vortices influenced by DWVG pairs were clearly observed.

Convection in a long box driven by heating and cooling on the horizontal boundaries

1996 ◽  
Vol 310 ◽  
pp. 61-87 ◽  
Author(s):  
J. J. Sturman ◽  
G. N. Ivey ◽  
J. R. Taylor
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Flow ◽  
Flow Visualization ◽  
Turbulent Flows ◽  
Heat Fluxes ◽  
Temperature Fields ◽  
Glycerol Water ◽  
Heating And Cooling ◽  
Scaling Arguments

Convection driven by spatially variable heat transfer across the water surface is an important transport mechanism in many geophysical applications. This flow is modelled in a rectangular tank with an aspect ratio, H/L, of 0.1 (where H and L are the tank height and length, respectively). Heat fluxes are applied through horizontal copper plates of length 0.1 L located at the top of one end of the tank and at the bottom of the other end. Experimental flows have been forced with heating at the bottom of the tank and cooling at the top, which gives rise to unstable convection in the end regions. Using water and a glycerol/water mix as the experimental fluids, flow visualization studies and measurements of temperature, velocity and heat flux have been made. Flow visualization studies revealed that complex unsteady turbulent flows occupied the end regions, while cubic velocity profiles characterized the horizontal laminar flow in the interior of the tank. Simple scaling arguments were developed for steady-state velocity and temperature fields, which are in good agreement with the experimental data. In the current experiments the portion of the plates closest to the tank interior (and to the tank endwall in the case of the glycerol/water experiments) were occupied by laminar boundary layers, while the remainder of the plates were occupied by turbulent flow. An effective Rayleigh number Ra* was defined, based upon the portion of the plate occupied by turbulent flow, as was a corresponding modified Nusselt number Nu*. The heat transfer was well predicted by classical Rayleigh-Bénard scaling with the Nusselt number Nu* ∼ Ra*1/3. The range of Ra* was 4.3 × 105 ≤ Ra* ≤ 1.7 × 108. Scaling arguments predicted the triple occupancy of the plates by differing boundary layer regimes within the range of 105 ≤ Ra* ≤ 1014.

scholarly journals Determination of the Reference Temperature for a Convective Heat Transfer Coefficient in a Heated Tube Bank

2021 ◽  
Vol 11 (22) ◽  
pp. 10564
Author(s):  
Stanislav Kotšmíd ◽  
Zuzana Brodnianská
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Turbulent Flows ◽  
Convective Heat Transfer Coefficient ◽  
Reference Temperature ◽  
Tube Bank ◽  
Heated Tube ◽  
Tube Banks

The paper presents a theoretical analysis of heat transfer in a heated tube bank, based on the Nusselt number computation as one of the basic dimensionless criteria. To compute the Nusselt number based on the heat transfer coefficient, the reference temperature must be determined. Despite the value significance, the quantity has several different formulations, which leads to discrepancies in results. This paper investigates the heat transfer of the inline and staggered tube banks, made up of 20 rows, at a constant tube diameter and longitudinal and transverse pitch. Both laminar and turbulent flows up to Re = 10,000 are considered, and the effect of gravity is included as well. Several locations for the reference temperature are taken into consideration on the basis of the heretofore published research, and the results in terms of the overall Nusselt number are compared with those obtained by the experimental correlations. This paper provides the most suitable variant for a unique reference temperature, in terms of a constant value for all tube angles, and the Reynolds number ranges of 100–1000 and 1000–10,000 which are in good agreement with the most frequently used correlating equations.

Numerical Study of Heat Transfer in Turbulent Cross-Flow Over Porous-Coated Cylinder

2017 ◽  
Author(s):  
N. Rahmati ◽  
Z. Mansoori ◽  
M. Saffar-Avval ◽  
G. Ahmadi
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Nusselt Number ◽  
Turbulent Flows ◽  
Metal Foam ◽  
Numerical Study ◽  
Flow Analysis ◽  
Cross Flow ◽  
Local Thermal Equilibrium ◽  
Turbulent Regime

In the present paper, a numerical study has been conducted to investigate the heat transfer from a constant temperature cylinder covered with metal foam. The cylinder is placed horizontally and is subjected to a constant mean cross-flow in turbulent regime. The Reynolds Averaged Navier-Stokes (RANS) and Darcy-Brinkman-Forchheimer equations are combined and used for flow analysis. The energy equation used assumes local thermal equilibrium between fluid and solid phases in porous media. The k-ω SST turbulence model is used to evaluate the eddy viscosity that is implemented in the momentum and energy equations. The flow in the metal foam (porous media) is in laminar regime. Governing equations are solved using the finite volume SIMPLEC algorithm. The effect of thermophysical properties of metal foam such as porosity and permeability on the Nusselt number is investigated. The results showed that using a metal porous layer with low porosity and high Darcy number in high Reynolds number turbulent flows markedly increases heat transfer rates. The corresponding increase in the Nusselt number is as high as 10 times that of a bare tube without the metal foam.

Direct numerical simulation of heat transfer from a cylinder immersed in the production and decay regions of grid-element turbulence

2018 ◽  
Vol 847 ◽  
pp. 452-488 ◽  
Author(s):  
I. Paul ◽  
G. Papadakis ◽  
J. C. Vassilicos
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Direct Numerical Simulation ◽  
Stagnation Point ◽  
Turbulent Wake ◽  
Production Region ◽  
Grid Element ◽  
Non Gaussian

The present direct numerical simulation (DNS) study, the first of its kind, explores the effect that the location of a cylinder, immersed in the turbulent wake of a grid-element, has on heat transfer. An insulated single square grid-element is used to generate the turbulent wake upstream of the heated circular cylinder. Due to fine-scale resolution requirements, the simulations are carried out for a low Reynolds number. Three locations downstream of the grid-element, inside the production, peak and decay regions, respectively, are considered. The turbulent flow in the production and peak regions is highly intermittent, non-Gaussian and inhomogeneous, while it is Gaussian, homogeneous and fully turbulent in the decay region. The turbulence intensities at the location of the cylinder in the production and decay regions are almost equal at 11 %, while the peak location has the highest turbulence intensity of 15 %. A baseline simulation of heat transfer from the cylinder without oncoming turbulence was also performed. Although the oncoming turbulent intensities are similar, the production region increases the stagnation point heat transfer by 63 %, while in the decay region it is enhanced by only 28 %. This difference cannot be explained only by the increased approaching velocity in the production region. The existing correlations for the stagnation point heat transfer coefficient are found invalid for the production and peak locations, while they are satisfied in the decay region. It is established that the flow in the production and peak regions is dominated by shedding events, in which the predominant vorticity component is in the azimuthal direction. This leads to increased heat transfer from the cylinder, even before vorticity is stretched by the accelerating boundary layer. The frequency of oncoming turbulence in production and peak cases also lies close to the range of frequencies that can penetrate the boundary layer developing on the cylinder, and therefore the latter is very responsive to the impinging disturbances. The highest Nusselt number along the circumference of the cylinder is shifted 45 degrees from the front stagnation point. This shift is due to the turbulence-generating grid-element bars that result in the prevalence of intense events at the point of maximum Nusselt number compared to the stagnation point.

Developing Heat Transfer and Friction in a Ribbed Rectangular Duct With Flow Separation at Inlet

1992 ◽  
Vol 114 (3) ◽  
pp. 565-573 ◽  
Author(s):  
Tong-Miin Liou ◽  
Jenn-Jiang Hwang
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Flows ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Equal Mass ◽  
Rectangular Duct ◽  
Entry Length ◽  
A Value ◽  
Semi Empirical

The local heat transfer and pressure drop characteristics of developing turbulent flows in a rectangular duct with an abrupt-contraction entrance and repeated square-rib pairs on the two opposite walls have been investigated experimentally. Both entrance-region and periodic-fully-developed-region results were obtained. Laser holographic interferometry was employed in the local and average heat transfer measurements. The Reynolds number was varied from 5.0 × 103 to 5.0 × 104; the rib pitch-to-height ratios were 10, 15, and 20; and the rib height-to-duct height ratio was kept at a value of 0.13. The results allowed the entry length to be determined and the regions susceptible to hot spots to be located. Semi-empirical heat transfer and friction correlations for the periodic fully developed region were developed. Moreover, performance comparisons between the ribbed and smooth ducts were made under two types of constraint, namely equal mass flow rate and equal pumping power. Finally, the effect of thermal entry length on the length mean Nusselt number was also investigated. The results showed that the length mean Nusselt number ratio was a function of only the duct length and independent of PR and Re, and could be further correlated by an equation of the form Num/Nup = 1 + 1.844/(X/De).

Heat Transfer Regimes and Hysteresis in Porous Media Convection

2000 ◽  
Vol 123 (1) ◽  
pp. 145-156 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Media ◽  
Nusselt Number ◽  
Transition Point ◽  
Initial Conditions ◽  
Turbulent Convection ◽  
Practical Significance ◽  
Lorenz Equations ◽  
Adomian’S Decomposition Method

Results of an investigation of different heat transfer regimes in porous media convection are presented by using a truncated Galerkin representation of the governing equations that yields the familiar Lorenz equations for the variation of the amplitude in the time domain. The solution to this system is obtained analytically by using a weak non-linear analysis and computationally by using Adomian’s decomposition method. Expressions for the averaged Nusselt number are derived for steady, periodic, as well as weak-turbulent (temporal-chaotic) convection. The phenomenon of Hysteresis in the transition from steady to weak-turbulent convection, and backwards, is particularly investigated, identifying analytically its mechanism, which is confirmed by the computational results. While the post-transient chaotic solution in terms of the dependent variables is very sensitive to the initial conditions, the affinity of the averaged values of these variables to initial conditions is very weak. Therefore, long-term predictability of these averaged variables, and in particular the Nusselt number, becomes possible, a result of substantial practical significance. Actually, the only impact that the transition to chaos causes on the predicted results in terms of the averaged heat flux is a minor loss of accuracy. Therefore, the predictability of the results in the sense of the averaged heat flux is not significantly affected by the transition from steady to weak-turbulent convection. The transition point is shown to be very sensitive to a particular scaling of the equations, which leads the solution to an invariant value of steady-state for sub-transitional conditions, a result that affects the transition point in some cases.

An Experimental Study of Mixed Convection in Vertical, Open-Ended, Concentric and Eccentric Annular Channels

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
L. Maudou ◽  
G. H. Choueiri ◽  
S. Tavoularis
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Turbulent Flows ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Annular Channel ◽  
High Eccentricity ◽  
Convection Regime ◽  
Annular Channels

The effect of eccentricity on heat transfer in upward flow in a vertical, open-ended, annular channel with a diameter ratio of 0.61, an aspect ratio of 18:1, and both internal surfaces heated uniformly has been investigated experimentally. Results have been reported for eccentricities ranging from the concentric case to the near-contact case and three inlet bulk Reynolds numbers, equal approximately to 1500, 2800, and 5700. This work complements our recently reported experimental results on natural convection in the same facility. The present results are deemed to be largely in the mixed convection regime with some overlap with the forced convection regime and likely to include cases with laminar, transitional, and turbulent flows in at least a part of the test section. Small eccentricity had an essentially negligible effect on the overall heat transfer rate, but high eccentricity reduced the average heat transfer rate by up to 60%. High eccentricity also resulted in wall temperatures in the narrow gap region that were much higher than those in the open channel. The concentric-case Nusselt number was higher than the Dittus–Boelter prediction, whereas the highly eccentric-case Nusselt number was significantly lower than that.

scholarly journals Enhanced heat transfer under the influence of coherent structure induced by arc vortex generator in square pipe flows

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1379-1386
Author(s):  
Wei Wang ◽  
Xiao-Jiao Sun ◽  
Yang Gao ◽  
Xin-Lei Guan ◽  
Chu-Wen Guo ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Flows ◽  
Transfer Process ◽  
Coherent Structures ◽  
Vortex Generator ◽  
Heat Transfer Process ◽  
Turbulent Fluctuation ◽  
Hairpin Vortices ◽  
Eddy Simulation

Experiments and numerical simulations were both performed to investigate coherent structures and heat transfer process in a square pipe turbulent flows induced by arc vortex generator. The velocity fields of induced turbulent flow was obtained by planar particle image velocimetry. The analysis of velocity profiles revealed the co-existence of various coherent structures. Turbulent fluctuation quantities, such as turbulent intensities, Reynolds stress, etc. exhibited the different behaviors of fluid motions introduced by arc vortex generator. Probability density function of swirling strength showed the complication of the vortex-rotating. Heat transfer process was simulated using large eddy simulation. The results of Nusselt number achieved the maximal improvement 57% with the use of arc vortex generator. The distribution of Nusselt number was in good agreement with the distribution of coherent structures, especially hairpin vortices and subsequent secondary coherent structures, which highlighted the influence of coherent structures by arc vortex generator on heat transfer enhancement.

Numerical Investigation of Natural Convection Heat Transfer From a Stack of Horizontal Cylinders

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Subhasisa Rath ◽  
Sukanta Kumar Dash
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Investigation ◽  
Turbulent Flows ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Horizontal Cylinders

Natural convection heat transfer from horizontal solid cylinders has been studied numerically by varying the Rayleigh number in the range of (104≤Ra≤108) and (1010≤Ra≤1013) for both laminar and turbulent flows, respectively. The computations were carried out for three different geometries of three, six, and ten cylinders in a stack arranged in a triangular manner having same characteristic length scale. The present numerical investigation on natural convention is able to capture a very interesting flow pattern and temperature field over the stack of horizontal cylinders which has never been reported in the literature so far. Visualization of plume structure over the horizontal cylinders has also been obtained pictorially in the present work. From the numerical results, it has been observed that the total heat transfer is marginally higher for three-cylinder stack in the laminar range. In contrast, for turbulent flow, starting from Ra = 1010, heat transfer for six-cylinder case is higher but when Ra exceeds 5 × 1011, heat transfer for ten cylinders stack is marginally higher. The average surface Nusselt number is higher for the stack of three cylinders compared to six- and ten-cylinder cases for all range of Ra in both laminar and turbulent regimes. A correlation for the average Nusselt number has also been developed as a function of Rayleigh number which may be useful for researchers and industrial purposes.

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