scholarly journals Boundary layers in turbulent vertical convection at high Prandtl number

2021 ◽  
Vol 930 ◽  
Author(s):  
Christopher J. Howland ◽  
Chong Shen Ng ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Environmental Flows ◽  
Three Dimensional ◽  
Vertical Channel ◽  
Vertical Surface ◽  
Wide Range ◽  
High Prandtl Number ◽  
Prandtl Numbers

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$ . This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$ . For the considered parameter range $1\leq {Pr} \leq 100$ , $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$ , we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$ , the heat flux is found to scale linearly with the friction velocity $V_\ast$ . Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

scholarly journals Bifurcations from steady to quasi-periodic flows in a laterally heated cavity filled with low Prandtl number fluids

2018 ◽  
Vol 861 ◽  
pp. 223-252 ◽  
Author(s):  
A. Medelfef ◽  
D. Henry ◽  
A. Bouabdallah ◽  
S. Kaddeche
Keyword(s):  
Prandtl Number ◽  
Liquid Metals ◽  
Three Dimensional ◽  
Numerical Continuation ◽  
Arnoldi Method ◽  
Periodic Flows ◽  
Bifurcation Points ◽  
Prandtl Numbers ◽  
Stable Flow ◽  
Flow States

This study deals with the transition toward quasi-periodicity of buoyant convection generated by a horizontal temperature gradient in a three-dimensional parallelepipedic cavity with dimensions $4\times 2\times 1$ (length $\times$ width $\times$ height). Numerical continuation techniques, coupled with an Arnoldi method, are used to locate the steady and Hopf bifurcation points as well as the different steady and periodic flow branches emerging from them for Prandtl numbers ranging from 0 to 0.025 (liquid metals). Our results highlight the existence of two steady states along with many periodic cycles, all with different symmetries. The bifurcation scenarios consist of complex paths between these different solutions, giving a succession of stable flow states as the Grashof number is increased, from steady to periodic and quasi-periodic. The change of these scenarios with the Prandtl number, in connection with the crossing of bifurcation points, was carefully analysed.

Scale Analysis of Thermocapillary Weld Pool Shape With High Prandtl Number

2011 ◽  
Author(s):  
P. S. Wei ◽  
C. L. Lin ◽  
H. J. Liu
Keyword(s):  
Prandtl Number ◽  
Boundary Layers ◽  
Molten Pool ◽  
Surface Flow ◽  
Transport Processes ◽  
Surface Boundary ◽  
Scale Analysis ◽  
Melting Front ◽  
Pool Shape ◽  
High Prandtl Number

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from parametric scale analysis for the first time. Determination of the molten pool shape is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative values, indicating an outward surface flow, whereas high Prandtl number represents the thermal boundary layer thickness to be less than that of momentum. Since Marangoni number is usually very high, the scaling of transport processes is divided into the hot, intermediate and cold corner regions on the flat free surface, boundary layers on the solid-liquid interface and ahead of the melting front. Coupling among distinct regions and thermal and momentum boundary layers, the results find that the width and depth of the pool can be determined as functions of Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The predictions agree with numerical computations and available experimental data.

Numerical Study of Three-Dimensional Oscillatory Natural Convection at Low Prandtl Number in Rectangular Enclosures

2000 ◽  
Vol 123 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Shunichi Wakitani
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Width Ratio ◽  
Three Dimensional Flow ◽  
Longitudinal Vortices ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Prandtl Numbers

Numerical investigations are presented for three-dimensional natural convection at low Prandtl numbers (Pr) from 0 to 0.027 in rectangular enclosures with differentially heated vertical walls. Computations are carried out for the enclosures with aspect ratios (length/height) 2 and 4, and width ratios (width/height) ranging from 0.5 to 4.2. Dependence of the onset of oscillation on the Prandtl number, the aspect ratio, and the width ratio is investigated. Furthermore, oscillatory, three-dimensional flow structure is clarified. The structure is characterized by some longitudinal vortices (rolls) as well as cellular pattern.

scholarly journals Assessment of Machine-Learned Turbulence Models Trained for Improved Wake-Mixing in Low-Pressure Turbine Flows

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8327
Author(s):  
Roberto Pacciani ◽  
Michele Marconcini ◽  
Francesco Bertini ◽  
Simone Rosa Taddei ◽  
Ennio Spano ◽  
...  
Keyword(s):  
Boundary Layers ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Computational Domain ◽  
Trailing Edge ◽  
Low Pressure Turbine ◽  
Wide Range ◽  
Turbulence Closures ◽  
The Impact

This paper presents an assessment of machine-learned turbulence closures, trained for improving wake-mixing prediction, in the context of LPT flows. To this end, a three-dimensional cascade of industrial relevance, representative of modern LPT bladings, was analyzed, using a state-of-the-art RANS approach, over a wide range of Reynolds numbers. To ensure that the wake originates from correctly reproduced blade boundary-layers, preliminary analyses were carried out to check for the impact of transition closures, and the best-performing numerical setup was identified. Two different machine-learned closures were considered. They were applied in a prescribed region downstream of the blade trailing edge, excluding the endwall boundary layers. A sensitivity analysis to the distance from the trailing edge at which they are activated is presented in order to assess their applicability to the whole wake affected portion of the computational domain and outside the training region. It is shown how the best-performing closure can provide results in very good agreement with the experimental data in terms of wake loss profiles, with substantial improvements relative to traditional turbulence models. The discussed analysis also provides guidelines for defining an automated zonal application of turbulence closures trained for wake-mixing predictions.

A study of Bénard convection with and without rotation

1969 ◽  
Vol 36 (2) ◽  
pp. 309-335 ◽  
Author(s):  
H. T. Rossby
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Linear Theory ◽  
Silicone Oil ◽  
Taylor Number ◽  
Subcritical Instability ◽  
Two Fluids ◽  
Wide Range

An experimental study of the response of a thin uniformly heated rotating layer of fluid is presented. It is shown that the stability of the fluid depends strongly upon the three parameters that described its state, namely the Rayleigh number, the Taylor number and the Prandtl number. For the two Prandtl numbers considered, 6·8 and 0·025 corresponding to water and mercury, linear theory is insufficient to fully describe their stability properties. For water, subcritical instability will occur for all Taylor numbers greater than 5 × 104, whereas mercury exhibits a subcritical instability only for finite Taylor numbers less than 105. At all other Taylor numbers there is good agreement between linear theory and experiment.The heat flux in these two fluids has been measured over a wide range of Rayleigh and Taylor numbers. Generally, much higher Nusselt numbers are found with water than with mercury. In water, at any Rayleigh number greater than 104, it is found that the Nusselt number will increase by about 10% as the Taylor number is increased from zero to a certain value, which depends on the Rayleigh number. It is suggested that this increase in the heat flux results from a perturbation of the velocity boundary layer with an ‘Ekman-layer-like’ profile in such a way that the scale of boundary layer is reduced. In mercury, on the other hand, the heat flux decreases monotonically with increasing Taylor number. Over a range of Rayleigh numbers (at large Taylor numbers) oscillatory convection is preferred although it is inefficient at transporting heat. Above a certain Rayleigh number, less than the critical value for steady convection according to linear theory, the heat flux increases more rapidly and the convection becomes increasingly irregular as is shown by the temperature fluctuations at a point in the fluid.Photographs of the convective flow in a silicone oil (Prandtl number = 100) at various rotation rates are shown. From these a rough estimate is obtained of the dominant horizontal convective scale as a function of the Rayleigh and Taylor numbers.

Closed-Form Analytical Solutions for Laminar Natural Convection on Horizontal Plates

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Abhijit Guha ◽  
Subho Samanta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Temperature Profiles ◽  
Integral Analysis ◽  
Laminar Natural Convection

A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T¯w(x¯)-T¯∞=ax¯n whereas the heat flux is assumed to vary according to qw(x¯)=bx¯m. Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr ≤ 1 or Pr ≈ 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.

Stability of Mixed Convection in a Differentially Heated Vertical Channel

1998 ◽  
Vol 120 (1) ◽  
pp. 127-132 ◽  
Author(s):  
Y.-C. Chen ◽  
J. N. Chung
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Local Minimum ◽  
Wave Speed ◽  
Vertical Channel ◽  
Shear Instability ◽  
Wave Number ◽  
Wave Numbers ◽  
Prandtl Numbers

In this study, the linear stability of mixed convection in a differentially heated vertical channel is investigated for various Prandtl numbers. The results indicate that this fully developed heated flow can become unstable under appropriate conditions. It is found that both the Prandtl number and Reynolds number hold very important effects on the critical Grashof number, wave number, wave speed, and instability mechanism for higher Prandtl numbers. For low Prandtl numbers, the effects from the Prandtl number and Reynolds number are relatively small. The most significant finding is that the local minimum wave numbers can be as high as eight for Pr = 1000, which is substantially higher than those found before for other heated flows. The existence of multiple local minimum wave numbers is responsible for the sudden jumps of the critical wave number and wave speed and the sudden shift of instability type for higher Prandtl numbers. The energy budget analysis shows that the thermal-shear and shear instabilities dominate at both low and high Reynolds numbers for Pr = 0.7 and 7. It is the thermal-buoyant instability for Re < 1365 and shear instability for Re ≥ 1365 for Pr = 100. The thermal-buoyant and mixed instabilities are the possible instability types for Pr = 1000. In general, for mixed convection channel flows, the instability characteristics of differentially heated flows are found to be substantially different from those of uniformly heated flows.

Natural Convection Within an Elongated Vertical Cylinder: Heat Loss From Bore of Oil Well Christmas Tree

2012 ◽  
Author(s):  
Mauricio A. Sanchez ◽  
Egidio (Ed) Marotta ◽  
Sumit Arora
Keyword(s):  
Oil And Gas ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Vertical Surface ◽  
Density Variation ◽  
Primary Objective ◽  
Christmas Tree ◽  
Oil Well ◽  
Fluid Properties ◽  
Prandtl Numbers

Internal natural convective heat transfer from a thin walled, vertical cylinder with an exposed vertical surface is investigated numerically. The top and bottom end faces are assumed isothermal. This setup approximates the vertical wellbore of a christmas tree for simulating cool-down of subsea oil and gas equipment during shutdown operations. The primary objective of this study is to determine the cooling rate of the interior fluid and the onset of fluid rotation caused by the two non-adiabatic surfaces as a function of Biot (Bi) at the vertical cylindrical wall. The flow is assumed to be three-dimensional, non-steady, and transitional with constant fluid properties except for the density variation with temperature. This latter effect gives rise to the buoyancy forces; being treated by using the Boussinesq approach. The solution is obtained by numerically solving the governing equations; these equations were written in terms of dimensionless variables. The solution is obtained using a commercial finite element method based-code, COMSOL Multiphysics. The specific application that motivated this investigation involved a range of Prandtl numbers (Pr) from 0.7, to 168. The results for these cases are presented herein. In addition, a range of other governing parameters has been considered. From the numerical results for small and moderate values of Rayleigh number, it is observed that steady state solutions (i.e. temperature and velocity) are stratified at the source temperature region regardless of the Biot number.

Progress in the Modeling and Simulation of Flow Boiling Heat Transfer of Binary Fluids Using Advanced Multi-Fluid Modeling Techniques

2012 ◽  
Author(s):  
Vedanth Srinivasan ◽  
Rok Kopun
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Heat Flux ◽  
Phase Change ◽  
Bubble Dynamics ◽  
Flow Boiling ◽  
Three Dimensional ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Wide Range

In this paper, we discuss the implementation and testing of a novel boiling mass transfer model to simulate the thermal and phase transformation behavior, generated due to boiling of binary mixtures, using the commercial CFD code AVL FIRE® v2011. The phase change model, based on detailed bubble dynamics effects, is solved in conjunction with incompressible phasic momentum, turbulence and energy equations in a segregated fashion, to study the flow boiling process inside a rectangular duct. Full three dimensional validation studies including the effect of flow velocity and exit pressure conditions, acting on a wide range of operating wall (superheat) temperatures, clearly shows the suppression of heat and mass transfer coefficients with enhancement in flow convection. Competing mechanisms such as phase change process and turbulent convection are identified to influence the heat transfer characteristics. In particular, the varying influence of the mass transfer effects on the heat flux characteristics with alteration in wall temperature is well demonstrated. Comparisons of the predicted total heat flux, computed as the sum of the convection and phase change components, indicate a very good agreement with experimental data, wherever available. Description of the flow field inclusive of phasic fraction, temperature and velocity field provides extensive details of the multiphase behavior of the boiling flow. Some preliminary results on the phase change work flow to model heat transfer in cooling jackets, for automotive applications, is also discussed.

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