High Grashof number turbulent natural convection on an infinite vertical wall

2021 ◽  
Vol 929 ◽  
Author(s):  
Junhao Ke ◽  
N. Williamson ◽  
S.W. Armfield ◽  
A. Komiya ◽  
S.E. Norris
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Vertical Wall ◽  
Integral Model ◽  
Turbulent Regime ◽  
Grashof Number ◽  
Turbulent Natural Convection ◽  
Self Similar ◽  
Near Wall

The present study concerns a temporally evolving turbulent natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall, with Prandtl number 0.71. Three-dimensional direct numerical simulations (DNS) are carried out to investigate the turbulent flow up to $\textit {Gr}_\delta =1.21\times 10^8$ , where $\textit {Gr}_\delta$ is the Grashof number based on the boundary layer thickness $\delta$ . In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.g. George & Capp, Intl J. Heat Mass Transfer, vol. 22, 1979, pp. 813–826). Beyond a wall-normal distance $\delta _i$ , the NCBL can be characterised as a plume-like region. We find that this region is well described by a self-similar integral model with profile coefficients (cf. van Reeuwijk & Craske, J. Fluid Mech., vol. 782, 2015, pp. 333–355) which are $\textit {Gr}_\delta$ -independent after $\textit {Gr}_\delta =10^7$ . In this Grashof number range both the outer plume-like region and the near-wall boundary layer are turbulent, indicating the beginning of the so-called ultimate turbulent regime (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Grossmann & Lohse, Phys. Fluids, vol. 23, 2011, 045108). Solutions to the self-similar integral model are analytically obtained by solving ordinary differential equations with profile coefficients empirically obtained from the DNS results. In the present study, we have found the wall heat transfer of the NCBL is directly related to the top-hat scales which characterise the plume-like region. The Nusselt number is found to follow $\textit {Nu}_\delta \propto \textit {Gr}_\delta ^{0.381}$ , slightly higher than the empirical $1/3$ -power-law correlation reported for spatially developing NCBLs at lower $\textit {Gr}_\delta$ , but is shown to be consistent with the ultimate heat transfer regime with a logarithmic correction suggested by Grossmann & Lohse (Phys. Fluids, vol. 23, 2011, 045108). By modelling the near-wall buoyancy force, we show that the wall shear stress would scale with the bulk velocity only at asymptotically large Grashof numbers.

Entropy Generation in Laminar and Turbulent Natural Convection Heat Transfer From Vertical Cylinder With Annular Fins

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Jnana Ranjan Senapati ◽  
Sukanta Kumar Dash ◽  
Subhransu Roy
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Entropy Generation ◽  
Vertical Cylinder ◽  
Turbulent Regime ◽  
Maximum Heat ◽  
Turbulent Natural Convection ◽  
Maximum Heat Transfer ◽  
Wide Range ◽  
Annular Fins

Entropy generation due to natural convection has been calculated for a wide range of Rayleigh number (Ra) in both laminar (104 ≤ Ra ≤ 108) and turbulent (1010 ≤ Ra ≤ 1012) flow regimes, for diameter ratio of 2 ≤ D/d ≤ 5, for an isothermal vertical cylinder fitted with annular fins. In the laminar regime, the entropy generation was predominantly caused by heat transfer (conduction and convection) and the viscous contribution was negligible with respect to heat transfer. But in the turbulent regime, entropy generation due to fluid friction is significant enough although heat transfer entropy generation is still dominant. The results demonstrate that the degree of irreversibility is higher in case of finned configuration when compared with unfinned one. With the deployment of a merit function combining the first and second laws of thermodynamics, we have tried to delineate the thermodynamic performance of finned cylinder with natural convection. So, we have defined the ratio (I/Q)finned/(I/Q)unfinned. The ratio (I/Q)finned/(I/Q)unfinned gets its minimum value at optimum fin spacing where maximum heat transfer occurs in turbulent flow, whereas in laminar flow the ratio (I/Q)finned/(I/Q)unfinned decreases continuously with the increase in number of fins.

A Numerical Study Concerning the Influence of the Grashof Number in the Indirect Ice Storage Tanks Performance

2006 ◽  
Author(s):  
Cleyton S. Stampa ◽  
Angela O. Nieckele
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Phase Change ◽  
Flow Pattern ◽  
Storage Tank ◽  
Vertical Wall ◽  
Heat Transfer Analysis ◽  
Ice Storage ◽  
Storage Tanks ◽  
Grashof Number

The present paper deals with typical chiller-based ice storage tanks. Natural convection of water (Phase Change Material-PCM) near its density maximum leads to a peculiar nature of the flow pattern in the liquid phase of the PCM, giving rise to a multi-cellular regime that affects drastically the heat transfers within the tank. So, this work intends to examine numerically how the flow pattern affects qualitatively the performance of such thermal storage devices. This is done by investigating the influence of the non-dimensional parameter Grashof number during the charging operation step of such devices that corresponds to the ice making process occurring within the storage tank. Besides, the tank is assumed to be vertically positioned, as well as their internal tubes through which the secondary fluid flows. In order to analyze the heat transfer between the PCM and one internal tube during the growth of an ice layer around it, one selected a vertical annulus as the physical model. The inner vertical wall represents one of the tubes packed into a typical storage tank, while the outer vertical wall represents the thickness of formed ice around the tube. Regarding the annulus, the top and bottom walls, as well as the outer vertical wall were considered thermally insulated. The thermal analysis is focused in the heat transfer at the inner wall for different values of Grashof, keeping unchanged all other parameters that govern the natural convection problem with phase change. An overview of the cooling process is analyzed through streamlines and isotherms, for specific instants of the physical process. Further, a heat transfer analysis for the total charging stage is presented.

scholarly journals Turbulent Natural Convection from a Vertical Plane Surface

1968 ◽  
Vol 90 (1) ◽  
pp. 1-6 ◽  
Author(s):  
R. Cheesewright
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Vertical Plane ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Convection Boundary Layer ◽  
Transfer Coefficients ◽  
Turbulent Natural Convection ◽  
Heat Transfer Coefficients

The paper reports the results of an experimental investigation which was intended to clarify the present uncertain position with regard to the distributions of mean temperature and mean velocity in a turbulent natural-convection boundary layer. Data reported for the turbulent boundary layer for Grashof numbers between 1010 and 1011 include local heat transfer coefficients as well as temperatures and velocities. Local heat transfer coefficients and temperature distributions are also reported for the laminar and transitional boundary-layer regions. Results are compared with other experimental data and with theoretical predictions.

Experimental, Variable Properties Natural Convection From a Large, Vertical, Flat Surface

1985 ◽  
Vol 107 (1) ◽  
pp. 124-132 ◽  
Author(s):  
D. L. Siebers ◽  
R. F. Moffatt ◽  
R. G. Schwind
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Ambient Temperature ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Variable Properties ◽  
Transfer Coefficients ◽  
Turbulent Natural Convection

Natural convection heat transfer from a vertical, 3.02 m high by 2.95 m long, electrically heat surface in air was studied. The air was at the ambient temperature and the atmospheric pressure, and the surface temperature was varied from 60 C to 520 C. These conditions resulted in Grashof numbers up to 2 × 1012 and surface-to-ambient temperature ratios up to 2.7. Convective heat transfer coefficients were measured at 105 locations on the surface by an energy balance. Boundary layer mean temperature profiles were measured with a thermocouple. Results show that: (1) the turbulent natural convection heat transfer data are correlated by the expression Nuy=0.098Gry1/3TwT∞−0.14 when all properties are evaluated at T∞; (2) variable properties do not have a significant effect on laminar natural convection heat transfer; (3) the transition Grashof number decreases with increasing temperature; and (4) the boundary layer mean temperaturue profiles for turbulent natural convection can be represented by a “universal” temperature profile.

Lattice Boltzmann Modeling of Natural Convection in a Large-Scale Cavity Heated From Below by a Centered Source

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Noureddine Abouricha ◽  
Mustapha El Alami ◽  
Ayoub Gounni
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Heat Source ◽  
Flow Structure ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Vertical Wall ◽  
Convection Heat Transfer ◽  
Turbulent Natural Convection

Turbulent natural convection in a large-scale cavity has taken a great attention thanks to its importance in many engineering applications such as building. In this work, the lattice Boltzmann method (LBM) is used to simulate turbulent natural convection heat transfer in a small room of housing heated from below by means of a heated floor. The ceiling and the four vertical walls of the room are adiabatic except for a portion of one vertical wall. This portion simulates a glass door with a cold temperature θc = 0. The cavity is filled by air (Pr = 0.71) and heated from below with uniformly imposed temperature θh = 1. The effects of the heat source length (Lr) and Rayleigh number (Ra) on the flow structure and heat transfer are studied for ranges of 0.2 ≤ Lr ≤ 0.8 and 5 × 106 ≤Ra ≤ 108. The heat transfer is examined in terms of local and mean Nusselt numbers. The results show that an increase in Rayleigh number or in heat source length increases the temperature in the core of the cavity. The flow structure shows that turbulent natural convection regime is fully developed for Ra = 108. Correlations for mean Nusselt number as a function with Ra for different values of Lr are expressly derived.

An Experimental Study of Turbulent Natural Convection Boundary Layers

1969 ◽  
Vol 91 (4) ◽  
pp. 517-531 ◽  
Author(s):  
G. C. Vliet ◽  
C. K. Liu
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Layers ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Physical Structure ◽  
Longitudinal Vortex ◽  
Turbulent Regime ◽  
Turbulent Natural Convection ◽  
Convection Boundary

An experimental investigation on turbulent natural convection boundary layers has been conducted with water on a vertical plate of constant heat flux. Local heat transfer data are presented for laminar, transition, and turbulent natural convection, with the emphasis on the turbulent regime. The data extend to a modified Rayleigh number of 1016 for a threefold range in Prandtl number. The results indicate that natural transition occurs in the range 1012 < Ra* < 1014; i.e., fully developed turbulent flow occurs by Ra* = 104. This latter value can be as low as 2 × 1013 with the use of a trip rod. The physical structure of the turbulent boundary-layer flow was studied using the combined time-streak marker hydrogen bubble method. Temperature data and temperature corrected velocity data obtained by hot-film sensors are presented for Ra* values between 8.7 × 1013 and 7.1 × 1014. For the range of variables investigated, the major conclusions are (a) the local heat transfer coefficient exhibits a slight decrease with length, (b) confirmation that the vortex street layer in the transition region decays into a longitudinal-vortex-type structure, and (c) the outer portion of the thermal and velocity fields can be approximated by power profiles that fit almost all the data available to date.

Sign in / Sign up

Export Citation Format

Share Document