Spatial and Temporal Stabilities of Flow in a Natural Circulation Loop: Influences of Thermal Boundary Condition

2003 ◽  
Vol 125 (4) ◽  
pp. 612-623 ◽  
Author(s):  
Y. Y. Jiang ◽  
M. Shoji
Keyword(s):  
Boundary Condition ◽  
Multiple Scales ◽  
Natural Circulation ◽  
Three Dimensional ◽  
Thermal Boundary Condition ◽  
Circular Loop ◽  
Thermal Boundary Conditions ◽  
Natural Circulation Loop ◽  
Control Of Flow ◽  
Multiple Scales Analysis

In a natural circular loop, the thermal convection demonstrates various spatial patterns and temporal instabilities. Problem consists in determining them with respects to thermal boundary conditions. To this end a multiple scales analysis is applied which resembles the inherent characteristic of the pattern formation in the Rayleigh-Be´nard convection. A three-dimensional nonlinear model is proposed by incorporating the flow modes derived along the analysis. The differences of thermal boundary condition are reflected by a coefficient δ. For small δ, numerical solution to the model shows that only temporal instability exists and Lorenz chaos is possible, otherwise, for large values both spatial and temporal instabilities occur leading to cellular flow and intermittency chaos. The model predicted some additional phenomena opening for experimental observation. It seems significant that this study proposes an algorithm for the control of flow stability and distribution by varying the thermal boundary condition.

Three Dimensional Numerical Analysis of Laminar Slip-Flow Heat Transfer in Rectangular Microchannels

2008 ◽  
Author(s):  
H. D. Madhawa Hettiarachchi ◽  
Mihajlo Golubovic ◽  
William M. Worek
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Temperature Jump ◽  
Slip Flow ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Thermal Boundary Condition ◽  
Navier Stokes ◽  
Constant Wall Temperature ◽  
Rectangular Microchannels

Slip-flow and heat transfer in rectangular microchannels are studied numerically for constant wall temperature (T) and constant wall heat flux (H2) boundary conditions under thermally developing flow. Navier-Stokes and energy equations with velocity slip and temperature jump at the boundary are solved using finite volume method in a three dimensional cartesian coordinate system. A modified convection-diffusion coefficient at the wall-fluid interface is defined to incorporate the temperature-jump boundary condition. Validity of the numerical simulation procedure is stabilized. The effect of rarefaction on heat transfer in the entrance region is analyzed in detail. The velocity slip has an increasing effect on the Nusselt (Nu) number whereas temperature jump has a decreasing effect, and the combined effect could result increase or decrease in the Nu number. For the range of parameters considered, there could be high as 15% increase or low as 50% decrease in fully developed Nu is plausible for T thermal boundary condition while it could be high as 20% or low as 35% for H2 thermal boundary condition.

A numerical and three-dimensional analysis of steady state rectangular natural circulation loop

2012 ◽  
Vol 244 ◽  
pp. 61-72 ◽  
Author(s):  
G. Angelo ◽  
D.A. Andrade ◽  
E. Angelo ◽  
W.M. Torres ◽  
G. Sabundjian ◽  
...  
Keyword(s):  
Steady State ◽  
Dimensional Analysis ◽  
Natural Circulation ◽  
Three Dimensional ◽  
Circulation Loop ◽  
Natural Circulation Loop

Radially Polarized and Magnetized Rotating Cylinders Under Thermal Loading

2012 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
Z. T. Chen
Keyword(s):  
Boundary Condition ◽  
Thermal Loading ◽  
Thermal Boundary Condition ◽  
Inertial Effects ◽  
Exact Form ◽  
Decoupling Method ◽  
Thermal Boundary Conditions ◽  
Mechanical Boundary Condition ◽  
Steady State Heat ◽  
Radially Polarized

Analytical solutions are acquired for radially polarized and magnetized rotating magnetoelectroelastic hollow and solid cylinders. The cylinders are orthotropic and infinitely long and are subjected to a combination of thermal, magnetic, electric, and mechanical loadings. The symmetric and steady state heat conduction equation is solved based on a general form of thermal boundary conditions to give the temperature distribution along the radial direction of cylinders. The governing ordinary differential equations in terms of displacement, electric potential, and magnetic potential with considering the thermal and inertial effects are obtained and solved in an exact form using the straightforward successive decoupling method. Numerical results are illustrated to reveal influences of thermal boundary condition, angular velocity, aspect ratio, and magneto-electro-mechanical boundary condition on the multiphysical responses of the rotating hollow and solid cylinders. The results are validated with those available in the literature.

Heat Transfer Prediction With Unknown Thermal Boundary Conditions Using Physics-Informed Neural Networks

2020 ◽  
Author(s):  
Shengze Cai ◽  
Zhicheng Wang ◽  
Chryssostomos Chryssostomidis ◽  
George Em Karniadakis
Keyword(s):  
Heat Transfer ◽  
Neural Networks ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Thermal Boundary Condition ◽  
Temperature Measurements ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Thermal Boundary Conditions ◽  
Energy Equations

Abstract Simulating convective heat transfer using traditional numerical methods requires explicit definition of thermal boundary conditions on all boundaries of the domain, which is almost impossible to fulfill in real applications. Here, we address this ill-posed problem using machine learning techniques by assuming that we have some extra measurements of the temperature at a few locations in the domain, not necessarily located on the boundaries with the unknown thermal boundary condition. In particular, we employ physics-informed neural networks (PINNs) to represent the velocity and temperature fields while simultaneously enforce the Navier-Stokes and energy equations at random points in the domain. In PINNs, all differential operators are computed using automatic differentiation, hence avoiding discretization in either space or time. The loss function is composed of multiple terms, including the mismatch in the velocity and temperature data, the boundary and initial conditions, as well as the residuals of the Navier-Stokes and energy equations. Here, we develop a data-driven strategy based on PINNs to infer the temperature field in the prototypical problem of convective heat transfer in flow past a cylinder. We assume that we have just a couple of temperature measurements on the cylinder surface and a couple more temperature measurements in the wake region, but the thermal boundary condition on the cylinder surface is totally unknown. Upon training the PINN, we can discover the unknown boundary condition while simultaneously infer the temperature field everywhere in the domain with less than 5% error in the Nusselt number prediction. In order to assess the performance of PINN, we carried out a high fidelity simulation of the same heat transfer problem (with known thermal boundary conditions) by using the high-order spectral/hp-element method (SEM), and quantitatively evaluated the accuracy of PINN’s prediction with respect to SEM. We also propose a method to adaptively select the location of sensors in order to minimize the number of required temperature measurements while increasing the accuracy of the inference in heat transfer.

Effect of Tilt Angle on Subcritical/Supercritical Carbon Dioxide-Based Natural Circulation Loop With Isothermal Source and Sink

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Ajay Kumar Yadav ◽  
M. Ram Gopal ◽  
Souvik Bhattacharyya
Keyword(s):  
Carbon Dioxide ◽  
Tilt Angle ◽  
Flow Instability ◽  
Natural Circulation ◽  
Three Dimensional ◽  
Extensive Literature ◽  
Cfd Models ◽  
Natural Circulation Loop ◽  
Carbon Dioxide Co2 ◽  
Source And Sink

In recent years, a growing popularity of carbon dioxide (CO2) as a secondary fluid has been witnessed in both forced as well as in natural circulation loops (NCLs). This may be attributed to the favorable thermophysical properties of CO2 in addition to the environmental benignity of the fluid. However, an extensive literature review shows that studies on CO2-based NCLs are very limited. Also, most of the studies on NCLs do not consider the three-dimensional variation of the field variables. In the present work, three-dimensional computational fluid dynamics (CFD) models of a NCL with isothermal source and sink have been developed to study the effect of tilt angle in different planes. Studies have been carried out employing subcritical (liquid and vapor) as well as supercritical phase of CO2 as loop fluid at different operating pressures and temperatures. Results are obtained for a range of tilt angles of the loop, and a significant effect is observed on heat transfer, mass flow rate, and stability of the loop. It was also found that changing the orientation of the loop could be an elegant and effective solution to the flow instability problem of NCLs.

Effects of thermal boundary conditions on rotating Rayleigh-Bénard convection with implications on geophysical and astrophysical systems

2021 ◽  
Author(s):  
Janet Peifer ◽  
Onno Bokhove ◽  
Steve Tobias
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Biot Number ◽  
Thermal Flux ◽  
Thermal Boundary Condition ◽  
Actual Condition ◽  
Fixed Temperature ◽  
Thermal Boundary Conditions ◽  
Core Dynamics

<p>Rayleigh-Bénard convection (RBC) is a fluid phenomenon that has been studied for over a century because of its utility in simplifying very complex physical systems. Many geophysical and astrophysical systems, including planetary core dynamics and components of weather prediction, are modeled by including rotational forcing in classic RBC. Our understanding of these systems is confined by experimental and numerical limits, as well as theoretical assumptions. </p><p>The role of thermal boundary condition choice on experimental studies of geophysical and astrophysical systems has been often been overlooked, which could account for some lack of agreement between experimental and numerical models as well as the actual flows. The typical thermal boundary conditions prescribed at the top and the bottom of a convection system are fixed temperature conditions, despite few real geophysical systems being bounded with a fixed temperature. A constant heat flux is generally more applicable for real large-scale geophysical systems. However, when this condition is applied in numerical systems, the lack of fixed temperature can cause a temperature drift. In this study, we seek to minimize temperature drifting by applying a fixed temperature condition on one boundary and a fixed thermal flux on the other.</p><p>Experimental boundary conditions are also often assumed to be a fixed temperature. However, the actual condition is determined by the ratio of the height and thermal conductivity of the boundary material to that of the contained fluid, known as the Biot number. The relationship between the Biot number and thermal boundary condition behavior is defined by the Robin, or 'thin-lid', boundary condition such that low Biot number boundaries are essentially fixed thermal flux and high Biot number boundaries are essentially fixed temperature. </p><p>This study seeks to strengthen the link between numerical and experimental models and geophysical flows by investigating the effects of thermal boundary conditions and their relationship to real-world processes. Both fixed temperature and fixed flux boundary conditions are considered. In addition, the Robin boundary condition is studied at a range of Biot numbers spanning from fixed temperature to fixed flux, allowing intermediate conditions to be investigated. Each system is studied at increasingly rapid rotation rates, corresponding to decreasing Ekman numbers as low as Ek=10<sup>-5</sup> Heat transport is analyzed using the Nusselt number, Nu, and the form of the solution is described by the number of convection rolls and time-dependency. Further investigations will analyze Nu and fluid movement within a system with heterogeneous heat flux condition on the  sidewall boundary conditions, which is useful in the study of planetary core dynamics. The results of this study have implications for improvements in modeling geophysical systems both experimentally and numerically. </p>

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