Stably stratified canopy flow in complex terrain

Abstract. Stably stratified canopy flow in complex terrain has been considered a difficult condition for measuring net ecosystem–atmosphere exchanges of carbon, water vapor, and energy. A long-standing advection error in eddy-flux measurements is caused by stably stratified canopy flow. Such a condition with strong thermal gradient and less turbulent air is also difficult for modeling. To understand the challenging atmospheric condition for eddy-flux measurements, we use the renormalized group (RNG) k–&varepsilon; turbulence model to investigate the main characteristics of stably stratified canopy flows in complex terrain. In this two-dimensional simulation, we imposed persistent constant heat flux at ground surface and linearly increasing cooling rate in the upper-canopy layer, vertically varying dissipative force from canopy drag elements, buoyancy forcing induced from thermal stratification and the hill terrain. These strong boundary effects keep nonlinearity in the two-dimensional Navier–Stokes equations high enough to generate turbulent behavior. The fundamental characteristics of nighttime canopy flow over complex terrain measured by the small number of available multi-tower advection experiments can be reproduced by this numerical simulation, such as (1) unstable layer in the canopy and super-stable layers associated with flow decoupling in deep canopy and near the top of canopy; (2) sub-canopy drainage flow and drainage flow near the top of canopy in calm night; (3) upward momentum transfer in canopy, downward heat transfer in upper canopy and upward heat transfer in deep canopy; and (4) large buoyancy suppression and weak shear production in strong stability.

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Stably stratified canopy flow in complex terrain

Atmospheric Chemistry and Physics Discussions ◽

10.5194/acpd-14-28483-2014 ◽

2014 ◽

Vol 14 (21) ◽

pp. 28483-28522

Author(s):

X. Xu ◽

C. Yi ◽

E. Kutter

Keyword(s):

Complex Terrain ◽

Stokes Equations ◽

Ground Surface ◽

Strong Stability ◽

Constant Heat Flux ◽

Navier Stokes ◽

Two Dimensional ◽

Canopy Layer ◽

Canopy Flow ◽

Navier Stokes Equations

Abstract. The characteristics of stably stratified canopy flows in complex terrain are investigated by employing the Renormalized Group (RNG) k-ε turbulence model. In this two-dimensional simulation, we imposed persistent constant heat flux at ground surface and linearly increasing cooling rate in the upper canopy layer, vertically varying dissipative force from canopy drag elements, buoyancy forcing induced from thermal stratification and the hill terrain. These strong boundary effects keep nonlinearity in the two-dimensional Navier–Stokes equations high enough to generate turbulent behavior. The fundamental characteristics of nighttime canopy flow over complex terrain measured by a few multi-tower advection experiments can be produced by this numerical simulation, such as: (1) unstable layer in the canopy, (2) super-stable layer associated with flow decoupling in deep canopy and near the top of canopy, (3) upward momentum transfer in canopy, and (4) large buoyancy suppression and weak shear production in strong stability.

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Natural convection melting of nano-enhanced phase change material in a cavity with finned copper profile

MATEC Web of Conferences ◽

10.1051/matecconf/201824001006 ◽

2018 ◽

Vol 240 ◽

pp. 01006 ◽

Cited By ~ 1

Author(s):

Nadezhda Bondareva ◽

Mikhail Sheremet

Keyword(s):

Heat Transfer ◽

Natural Convection ◽

Stokes Equations ◽

Volume Fraction ◽

Melting Process ◽

Navier Stokes ◽

Two Dimensional ◽

Navier Stokes Equations ◽

Dimensional Approximation ◽

Change Material

Present study is devoted to numerical simulation of heat and mass transfer inside a cooper profile filled with paraffin enhanced with Al2O3 nanoparticles. This profile is heated by the heat-generating element of constant volumetric heat flux. Two-dimensional approximation of melting process is described by the Navier-Stokes equations in non-dimensional variables such as stream function, vorticity and temperature. The enthalpy formulation has been used for description of the heat transfer. The influence of volume fraction of nanoparticles and intensity of heat generation on melting process and natural convection in liquid phase has been studied.

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Numerical analysis of non-isothermal viscous jet with peripheral heat transfer

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962316500124 ◽

2016 ◽

Vol 07 (03) ◽

pp. 1650012

Author(s):

Sulagna Chatterjee ◽

Trisha Sen ◽

Anindya Mitra

Keyword(s):

Heat Transfer ◽

Energy Balance ◽

Balance Equation ◽

Stokes Equations ◽

Numerical Study ◽

Energy Balance Equation ◽

Navier Stokes ◽

Two Dimensional ◽

Isothermal Model ◽

Jet Velocity

A fluid jet ejected from micron size nozzle is a commonly occurring phenomenon in biomedical engineering, printing technology and micro-fluidic applications. Disintegration of a jet into drops occurs due to disturbances induced by external sources. This work explores the various sources of perturbation and their effect on jet disintegration through numerical simulation of a two-dimensional non-isothermal model. The mathematical approach uses a novel technique to combine analytical solutions for the energy balance equation in the radial direction to solve the complete two dimensional problem. The two dimensional energy balance equation is simultaneously solved together with the axi-symmetric Navier–Stokes equations using the slender-jet approximation to predict jet velocity. The energy balance takes into account of peripheral heat transfer to the environment through analytical expressions derived from radial approximations. The model helps in understanding the factors in dynamic temperature variations that eventually render the jet unstable. The distinguishing aspect of this work is the analysis of the effect of a periodic thermal perturbation applied at any point in the domain of a progressive jet, a situation typically encountered in thermal inkjet printers and not considered previously. Results presented for non-isothermal jets which are both stationary and moving illustrate the effect of jet velocity in propagation of perturbation and subsequent drop formation. The major contribution of this numerical study is that it provides an insight on novel ways of controlling droplet formation in bubble jet printers. This study demonstrates that thermal disturbance propagating from periodic heating can be manipulated to shape the droplets and control their breakage point along the jet.

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Experimental and Numerical Investigation of Forced Convective Characteristics of Arrays of Channel Mounted Obstacles

Journal of Heat Transfer ◽

10.1115/1.2825962 ◽

1999 ◽

Vol 121 (1) ◽

pp. 34-42 ◽

Cited By ~ 42

Author(s):

T. J. Young ◽

K. Vafai

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Stokes Equations ◽

Heat Fluxes ◽

Large Temperature ◽

Air Cooling ◽

Airflow Rate ◽

Two Dimensional ◽

Nusselt Numbers ◽

Critical Measure

An experimental investigation of the forced convective heat transfer of individual and arrays of multiple two-dimensional obstacles is reported. The airflow rate was varied from 800 ≤ ReDh ≤ 13000. The effects upon the Nusselt numbers and obstacle temperature differences of parametric changes in the Reynolds number, channel height, array configuration, and input heat flux are established. The input heat fluxes to the obstacles ranged from 950 ≤ q″ ≤ 20200 W/m2, which significantly extends beyond that seen in the open literature for forced convective air cooling of simulated electronic components. Comparisons of the obstacle mean Nusselt numbers are made with a two-dimensional laminar numerical model employing the Navier-Stokes equations. A set of correlations characterizing the heat transfer from the protruding heat sources within the channel is obtained. It was found that the obstacle temperature, the critical measure for electronic device failure, must be shown along with the corresponding Nusselt number to fully characterize the thermal state of the heated obstacle as the ratio definition of the Nusselt number can obscure large temperature increases. The results find that the proper placement of geometrically dissimilar obstacles, such as a taller obstacle, can be used to passively enhance the heat transfer in its vicinity. This effect would be dependent upon the flow rate and geometries in order to control the reattachment zones and their subsequent convective augmentation. The experimental results are found to be in good agreement with the results from the numerical simulation. Finally, a set of pertinent correlations for the arrays of channel mounted obstacles is given.

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CFD Analysis of the Vortex Dynamics Generated by a Synthetic Jet Impinging on a Heated Surface

Volume 10: Heat and Mass Transport Processes, Parts A and B ◽

10.1115/imece2011-64185 ◽

2011 ◽

Cited By ~ 1

Author(s):

Luis Silva ◽

Alfonso Ortega

Keyword(s):

Heat Transfer ◽

Stokes Equations ◽

Heated Surface ◽

Target Surface ◽

Synthetic Jet ◽

Navier Stokes ◽

Secondary Vortex ◽

Two Dimensional ◽

Vortex Identification ◽

Dependent Flow

A canonical geometry has been used to investigate the flow and heat transfer of a purely oscillatory jet that is not influenced by the manner in which it is produced. Such a jet has been popularly termed a synthetic jet in the literature, and recently has been investigated for thermal management of electronics by causing the jet to impinge onto the heated surface. Because of its oscillatory nature, the impinging jet thus formed is dominated by vortices that are advected towards the surface. This surface-vortex interaction is key to understanding the fundamental mechanisms of convective heat transfer by the impinging synthetic jet and hence is the subject of the current investigation. The unsteady two-dimensional Navier-Stokes equations and the convection-diffusion equation were solved using a fully unsteady, two-dimensional finite volume approach in order to capture the complex time dependent flow field. Various vortex identification methods were investigated for proper identification of the train of vortices emanating from the jet and their evolution and eventual dissipation. Intuitive definitions of vortices such as spiraling streamlines, pressure minima and isovorticity surfaces suffer from inaccuracies. In the present work, the vortex-identification criteria employed was the Q-criterion (Hunt et al. 1988), which defines vortices as connected fluid regions with positive second invariant of the velocity gradient tensor. By tracking vortices, it was found that a primary vortex advecting parallel to the target surface gives rise to a secondary vortex with opposite net vorticity. It was found that the secondary vortex is largely responsible for enhancement of the heat transfer within the wall jet region. In addition it was found that in some situations vortex coalescence or pairing occurs, leading to degradation in the heat transfer enhancement due to the reduction in the frequency of vortices interacting with the surface.

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Performance of Pre-Swirl Rotating-Disc Systems

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.1285838 ◽

2000 ◽

Vol 122 (3) ◽

pp. 442-450 ◽

Cited By ~ 11

Author(s):

Hasan Karabay ◽

Robert Pilbrow ◽

Michael Wilson ◽

J. Michael Owen

Keyword(s):

Heat Transfer ◽

Stokes Equations ◽

Three Dimensional ◽

Tangential Velocity ◽

Cover Plate ◽

Two Dimensional ◽

Swirl Ratio ◽

Rotating Disc ◽

Blade Cooling ◽

Cooling Air

This paper summarizes and extends recent theoretical, computational, and experimental research into the fluid mechanics, thermodynamics, and heat transfer characteristics of the so-called cover-plate pre-swirl system. Experiments were carried out in a purpose-built rotating-disc rig, and the Reynolds-averaged Navier-Stokes equations were solved using two-dimensional (axisymmetric) and three-dimensional computational codes, both of which incorporated low-Reynolds-number k-ε turbulence models. The free-vortex flow, which occurs inside the rotating cavity between the disc and cover-plate, is controlled principally by the pre-swirl ratio, βp: this is the ratio of the tangential velocity of the air leaving the nozzles to that of the rotating disc. Computed values of the tangential velocity are in good agreement with measurements, and computed distributions of pressure are in close agreement with those predicted by a one-dimensional theoretical model. It is shown theoretically and computationally that there is a critical pre-swirl ratio, βp,crit, for which the frictional moment on the rotating discs is zero, and there is an optimal pre-swirl ratio, βp,opt, where the average Nusselt number is a minimum. Computations show that, for βp<βp,opt, the temperature of the blade-cooling air decreases as βp increases; for βp>βp,opt, whether the temperature of the cooling air increases or decreases as βp increases depends on the flow conditions and on the temperature difference between the disc and the air. Owing to the three-dimensional flow and heat transfer near the blade-cooling holes, and to unquantifiable uncertainties in the experimental measurements, there were significant differences between the computed and measured temperatures of the blade-cooling air. In the main, the three-dimensional computations produced smaller differences than the two-dimensional computations. [S0742-4795(00)01902-5]

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