The turbulent wall plume from a vertically distributed source of buoyancy

2015 ◽  
Vol 787 ◽  
pp. 237-253 ◽  
Author(s):  
Craig D. McConnochie ◽  
Ross C. Kerr
Keyword(s):  
Theoretical Model ◽  
Reynolds Numbers ◽  
Vertical Surface ◽  
Distributed Source ◽  
Plume Model ◽  
Plume Velocity ◽  
Entrainment Coefficient ◽  
Turbulent Plume ◽  
Turbulent Wall ◽  
Wall Plume

We experimentally investigate the turbulent wall plume that forms next to a uniformly distributed source of buoyancy. Our experimental results are compared with the theoretical model and experiments of Cooper & Hunt (J. Fluid Mech., vol. 646, 2010, pp. 39–58). Our experiments give a top-hat entrainment coefficient of $0.048\pm 0.006$. We measure a maximum vertical plume velocity that follows the scaling predicted by Cooper & Hunt but is significantly smaller. Our measurements allow us to construct a turbulent plume model that predicts all plume properties at any height. We use this plume model to calculate plume widths, velocities and Reynolds numbers for typical dissolving icebergs and ice fronts and for a typical room with a heated or cooled vertical surface.

Small Scale Modeling of Vertical Surface Jets in Cross-Flow: Reynolds Number and Downwash Effects

2006 ◽  
Vol 129 (3) ◽  
pp. 311-318 ◽  
Author(s):  
K. Shahzad ◽  
B. A. Fleck ◽  
D. J. Wilson
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Water Channel ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Vertical Surface ◽  
Small Scale ◽  
Mean Velocity ◽  
Entrainment Coefficient ◽  
Surface Jets

Jet-crossflow experiments were performed in a water channel to determine the Reynolds number effects on the plume trajectory and entrainment coefficient. The purpose was to establish a lower limit down to which small scale laboratory experiments are accurate models of large scale atmospheric scenarios. Two models of a turbulent vertical surface jet (diameters 3.175mm and 12.7mm) were designed and tested over a range of jet exit Reynolds numbers up to 104. The results show that from Reynolds number 200–4000 there is about a 40% increase in the entrainment coefficient, whereas from Reynolds number 4000–10,000, the increase in entrainment coefficient is only 2%. The conclusion is that Reynolds numbers significantly affect plume trajectories when the model Reynolds numbers are below 4000. Changing the initial turbulence in the exit flow from 12% to 2% without changing its mean velocity profile caused a less than one source diameter increase in the final plume rise.

scholarly journals Dynamics of Three-Dimensional Turbulent Wall Plumes and Implications for Estimates of Submarine Glacier Melting

2018 ◽  
Vol 48 (9) ◽  
pp. 1941-1950 ◽  
Author(s):  
Ekaterina Ezhova ◽  
Claudia Cenedese ◽  
Luca Brandt
Keyword(s):  
Three Dimensional ◽  
Characteristic Parameters ◽  
Buoyant Plumes ◽  
Tidewater Glaciers ◽  
Glacier Melting ◽  
Order Of Magnitude ◽  
Layer Flow ◽  
Using Data ◽  
Turbulent Wall ◽  
Wall Plume

AbstractSubglacial discharges have been observed to generate buoyant plumes along the ice face of Greenland tidewater glaciers. These plumes have been traditionally modeled using classical plume theory, and their characteristic parameters (e.g., velocity) are employed in the widely used three-equation melt parameterization. However, the applicability of plume theory for three-dimensional turbulent wall plumes is questionable because of the complex near-wall plume dynamics. In this study, corrections to the classical plume theory are introduced to account for the presence of a wall. In particular, the drag and entrainment coefficients are quantified for a three-dimensional turbulent wall plume using data from direct numerical simulations. The drag coefficient is found to be an order of magnitude larger than that for a boundary layer flow over a flat plate at a similar Reynolds number. This result suggests a significant increase in the melting estimates by the current parameterization. However, the volume flux in a wall plume is found to be one-half that of a conical plume that has 2 times the buoyancy flux. This finding suggests that the total entrainment (per unit area) of ambient water is the same and that the plume scalar characteristics (i.e., temperature and salinity) can be predicted reasonably well using classical plume theory.

scholarly journals Convection at an isothermal wall in an enclosure and establishment of stratification

2016 ◽  
Vol 799 ◽  
pp. 448-475 ◽  
Author(s):  
T. Caudwell ◽  
J.-B. Flór ◽  
M. E. Negretti
Keyword(s):  
Experimental Studies ◽  
Vertical Plane ◽  
Flow Characteristics ◽  
Similarity Solutions ◽  
Closed Cavity ◽  
Turbulent Transition ◽  
Image Velocimetry ◽  
Entrainment Coefficient ◽  
Isothermal Wall ◽  
Wall Plume

In this experimental–theoretical investigation, we consider a turbulent plume generated by an isothermal wall in a closed cavity and the formation of heat stratification in the interior. The buoyancy of the plume near the wall and the temperature stratification are measured across a vertical plane with the temperature laser induced fluorescence method, which is shown to be accurate and efficient (precision of $0.2\,^{\circ }$C) for experimental studies on convection. The simultaneous measurement of the velocity field with particle image velocimetry allows for the calculation of the flow characteristics such as the Richardson number and Reynolds stress. This enables us to give a refined description of the wall plume, as well as the circulation and evolution of the stratification in the interior. The wall plume is found to have an inner layer close to the heated boundary with a laminar transport of hardly mixed fluid which causes a relatively warm top layer and an outer layer with a transition from laminar to turbulent at a considerable height. The measured entrainment coefficient is found to be dramatically influenced by the increase in stratification of the ambient fluid. To model the flow, the entrainment model of Morton, Taylor & Turner (Proc. R. Soc. Lond. A, vol. 234 (1196), 1956, pp. 1–23) has first been adapted to the case of an isothermal wall. Differences due to their boundary condition of a constant buoyancy flux, modelled with salt by Cooper & Hunt (J. Fluid Mech., vol. 646, 2010, pp. 39–58), turn out to be small. Next, to include the laminar–turbulent transition of the boundary layer, a hybrid model is constructed which is based on the similarity solutions reported by Worster & Leitch (J. Fluid Mech., vol. 156, 1985, pp. 301–319) for the laminar part and the entrainment model for the turbulent part. Finally, the observed variation of the global entrainment coefficient, which is due to the increased presence of an upper stratified layer with a relatively low entrainment coefficient, is incorporated into both models. All models show reasonable agreement with experimental measurements for the volume, momentum and buoyancy fluxes as well as for the evolution of the stratification in the interior. In particular, the introduction of the variable entrainment coefficient improves all models significantly.

Theoretical Model of Wall Heat Transfer in Turbulent Flow

2011 ◽  
Vol 201-203 ◽  
pp. 171-175
Author(s):  
Wei Zheng Zhang ◽  
Xiao Liu ◽  
Chang Hu Xiang
Keyword(s):  
Heat Transfer ◽  
Theoretical Model ◽  
Turbulent Flow ◽  
Local Heat ◽  
Turbulent Heat Transfer ◽  
Wall Region ◽  
Turbulent Heat ◽  
Wall Heat Transfer ◽  
Local Heat Flux ◽  
Turbulent Wall

The turbulent flow in the near-wall region affects the wall heat transfer dominantly. The farther it is from the wall, the less effect it has. So a two-step mechanism of the turbulent wall heat transfer is released: first, the energy is transferred to the outside of the viscous sub-layer by the rolling of the micro-eddy; secondly, the energy gets to the wall by conduction. Then, a theoretical model of wall heat transfer is developed with this concept. The constant in the model is confirmed by experiment and simulation of the transient turbulent heat transfer in pipe flow. Finally, the model is used to predict the local heat flux under different conditions, and the results agree well with the experimental results as well as the simulation results.

A note on non-Boussinesq plumes in an incompressible stratified environment

1997 ◽  
Vol 345 ◽  
pp. 347-356 ◽  
Author(s):  
ANDREW W. WOODS
Keyword(s):  
Point Source ◽  
Similarity Solution ◽  
Similarity Solutions ◽  
Fundamental Difference ◽  
Integral Model ◽  
Neutral Buoyancy ◽  
Entrainment Velocity ◽  
Plume Velocity ◽  
Vertical Scale ◽  
Entrainment Coefficient

The recent work of Rooney & Linden (1996) is generalized to describe the motion of non-Boussinesq plumes in both uniform and stratified environments. Using an integral model in which the horizontal entrainment velocity is assumed to take the form uε=α(ρ¯/ρe) 1/2w where α is the entrainment coefficient, ρ¯ is the plume density, w the plume velocity and ρe the ambient density, it is shown that the vertical scale over which non-Boussinesq effects are significant is given by zB=5/3 (B2o/ (20α4g3))1/5 where Bo is the buoyancy flux at the source. In a uniform environment, the system admits similarity solutions such that the location of the source of a real plume lies a distance zB[mid ]ρo/Δρ[mid ] −5/3 beyond the point source of the similarity solution. The above entrainment law implies a fundamental difference between the motion of upward and downward propagating non-Boussinesq plumes, with the radius of upward propagating plumes being greater than that of the equivalent Boussinesq plume, while the radius of downward propagating plumes is smaller. In a stratified but incompressible environment the model predicts that non-Boussinesq effects are confined close to the source and that at each height, the plume velocity and the fluxes of mass, momentum and buoyancy coincide exactly with those of the equivalent Boussinesq plume. Furthermore, at the neutral buoyancy height, the plume radius equals that of the equivalent Boussinesq plume.

One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to δ+≈ 2000

2013 ◽  
Vol 25 (10) ◽  
pp. 105102 ◽  
Author(s):  
Juan A. Sillero ◽  
Javier Jiménez ◽  
Robert D. Moser
Keyword(s):  
Reynolds Numbers ◽  
Wall Bounded Flows ◽  
Turbulent Wall

Enhanced ablation of a vertical ice wall due to an external freshwater plume

2016 ◽  
Vol 810 ◽  
pp. 429-447 ◽  
Author(s):  
Craig D. McConnochie ◽  
Ross C. Kerr
Keyword(s):  
Laboratory Experiments ◽  
Buoyancy Flux ◽  
Interface Temperature ◽  
Volume Flux ◽  
Salty Water ◽  
Plume Velocity ◽  
Freshwater Plume ◽  
Wall Plume

We investigate the effect of an external freshwater plume on the dissolution of a vertical ice wall in salty water using laboratory experiments. We measure the plume velocity, the ablation velocity of the ice and the temperature at the ice wall. The freshwater volume flux, $Q_{s}$, is varied between experiments to determine where the resultant wall plume transitions from being dominated by the distributed buoyancy flux due to dissolution of the ice, to being dominated by the initial buoyancy flux, $B_{s}$. We find that when $B_{s}$ is significantly larger than the distributed buoyancy flux from dissolution, the plume velocity is uniform with height and is proportional to $B_{s}^{1/3}$, the interface temperature is independent of $B_{s}$, and the ablation velocity increases with $B_{s}$.

scholarly journals Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160092 ◽  
Author(s):  
J. C. Klewicki ◽  
G. P. Chini ◽  
J. F. Gibson
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
High Fidelity ◽  
Dynamical Structure ◽  
Mathematical Methods ◽  
High Reynolds ◽  
Turbulent Wall

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier–Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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