Multi-fidelity modelling of mixed convection based on experimental correlations and numerical simulations

2016 ◽  
Vol 809 ◽  
pp. 895-917 ◽  
Author(s):  
H. Babaee ◽  
P. Perdikaris ◽  
C. Chryssostomidis ◽  
G. E. Karniadakis
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Natural Convection ◽  
Mixed Convection ◽  
Numerical Simulations ◽  
Response Surface ◽  
Forced Convection ◽  
High Fidelity ◽  
Variable Fidelity ◽  
Fidelity Model

For thermal mixed-convection flows, the Nusselt number is a function of Reynolds number, Grashof number and the angle between the forced- and natural-convection directions. We consider flow over a heated cylinder for which there is no universal correlation that accurately predicts Nusselt number as a function of these parameters, especially in opposing-convection flows, where the natural convection is against the forced convection. Here, we revisit this classical problem by employing modern tools from machine learning to develop a general multi-fidelity framework for constructing a stochastic response surface for the Nusselt number. In particular, we combine previously developed experimental correlations (low-fidelity model) with direct numerical simulations (high-fidelity model) using Gaussian process regression and autoregressive stochastic schemes. In this framework the high-fidelity model is sampled only a few times, while the inexpensive empirical correlation is sampled at a very high rate. We obtain the mean Nusselt number directly from the stochastic multi-fidelity response surface, and we also propose an improved correlation. This new correlation seems to be consistent with the physics of this problem as we correct the vectorial addition of forced and natural convection with a pre-factor that weighs differently the forced convection. This, in turn, results in a new definition of the effective Reynolds number, hence accounting for the ‘incomplete similarity’ between mixed convection and forced convection. In addition, due to the probabilistic construction, we can quantify the uncertainty associated with the predictions. This information-fusion framework is useful for elucidating the physics of the flow, especially in cases where anomalous transport or interesting dynamics may be revealed by contrasting the variable fidelity across the models. While in this paper we focus on the thermal mixed convection, the multi-fidelity framework provides a new paradigm that could be used in many different contexts in fluid mechanics including heat and mass transport, but also in combining various levels of fidelity of models of turbulent flows.

Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between 10−1 and 104 and Rayleigh numbers between 105 and 109

2010 ◽  
Vol 662 ◽  
pp. 409-446 ◽  
Author(s):  
G. SILANO ◽  
K. R. SREENIVASAN ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Numerical Simulations ◽  
Multiple Solutions ◽  
Large Scale ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We summarize the results of an extensive campaign of direct numerical simulations of Rayleigh–Bénard convection at moderate and high Prandtl numbers (10−1 ≤ Pr ≤ 104) and moderate Rayleigh numbers (105 ≤ Ra ≤ 109). The computational domain is a cylindrical cell of aspect ratio Γ = 1/2, with the no-slip condition imposed on all boundaries. By scaling the numerical results, we find that the free-fall velocity should be multiplied by $1/\sqrt{{\it Pr}}$ in order to obtain a more appropriate representation of the large-scale velocity at high Pr. We investigate the Nusselt and the Reynolds number dependences on Ra and Pr, comparing the outcome with previous numerical and experimental results. Depending on Pr, we obtain different power laws of the Nusselt number with respect to Ra, ranging from Ra2/7 for Pr = 1 up to Ra0.31 for Pr = 103. The Nusselt number is independent of Pr. The Reynolds number scales as ${\it Re}\,{\sim}\,\sqrt{{\it Ra}}/{\it Pr}$, neglecting logarithmic corrections. We analyse the global and local features of viscous and thermal boundary layers and their scaling behaviours with respect to Ra and Pr, and with respect to the Reynolds and Péclet numbers. We find that the flow approaches a saturation state when Reynolds number decreases below the critical value, Res ≃ 40. The thermal-boundary-layer thickness increases slightly (instead of decreasing) when the Péclet number increases, because of the moderating influence of the viscous boundary layer. The simulated ranges of Ra and Pr contain steady, periodic and turbulent solutions. A rough estimate of the transition from the steady to the unsteady state is obtained by monitoring the time evolution of the system until it reaches stationary solutions. We find multiple solutions as long-term phenomena at Ra = 108 and Pr = 103, which, however, do not result in significantly different Nusselt numbers. One of these multiple solutions, even if stable over a long time interval, shows a break in the mid-plane symmetry of the temperature profile. We analyse the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. A wide variety of large-scale circulation and plume structures has been found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other regimes at lower Pr, the mean flow generally consists of two opposite toroidal structures; at higher Pr, the flow is organized in the form of multi-jet structures, extending mostly in the vertical direction. At high Pr, plumes mainly detach from sheet-like structures. The signatures of different large-scale structures are generally well reflected in the data trends with respect to Ra, less in those with respect to Pr.

Effect of Driven Sidewalls on Mixed Convection in an Open Trapezoidal Cavity With a Channel

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Muneer A. Ismael ◽  
Ahmed Kadhim Hussein ◽  
Fateh Mebarek-Oudina ◽  
Lioua Kolsi
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Airflow Velocity ◽  
Driven Cavity ◽  
Thermal Fields ◽  
Number Ratio ◽  
The Right

Abstract The mixed convection in an open trapezoidal lid-driven cavity connected with a channel is investigated in the present paper. Four different cases were considered depending on the movement of the cavity sidewalls. For case I, the left sidewall moves downward; for case II, the left sidewall moves downward and the right one moves upward; while for case III, only the right sidewall moves upward. A comparative case (case 0) is accounted when both sidewalls are assumed stationary. The base of the cavity is subjected to a localized heat source of constant temperature Th. The effects of Richardson number Ri and Reynolds number ratio Rer on the flow and thermal fields have been investigated. The results indicated that for cases I and II, the average Nusselt number increases with the increase of the Richardson number and Reynolds number ratio. Moreover, it was found that the maximum average Nusselt number occurs with case I. When the lid-driven speed is three times that of the inlet airflow velocity, the augmentations of the average Nusselt number compared with stationary walls are 163%, 158%, and 96% for cases I, II, and III, respectively.

Variable Fidelity Modeling in Closed Loop Dynamical Systems

2014 ◽  
Author(s):  
Matthew A. Williams ◽  
Andrew G. Alleyne
Keyword(s):  
Dynamical Systems ◽  
Closed Loop ◽  
System Development ◽  
Computational Cost ◽  
Computational Effort ◽  
High Fidelity ◽  
Vapor Compression System ◽  
Variable Fidelity ◽  
Time Required ◽  
Fidelity Model

In the early stages of control system development, designers often require multiple iterations for purposes of validating control designs in simulation. This has the potential to make high fidelity models undesirable due to increased computational complexity and time required for simulation. As a solution, lower fidelity or simplified models are used for initial designs before controllers are tested on higher fidelity models. In the event that unmodeled dynamics cause the controller to fail when applied on a higher fidelity model, an iterative approach involving designing and validating a controller’s performance may be required. In this paper, a switched-fidelity modeling formulation for closed loop dynamical systems is proposed to reduce computational effort while maintaining elevated accuracy levels of system outputs and control inputs. The effects on computational effort and accuracy are investigated by applying the formulation to a traditional vapor compression system with high and low fidelity models of the evaporator and condenser. This sample case showed the ability of the switched fidelity framework to closely match the outputs and inputs of the high fidelity model while decreasing computational cost by 32% from the high fidelity model. For contrast, the low fidelity model decreases computational cost by 48% relative to the high fidelity model.

Heat Transfer by Mixed Convection Opposing Laminar Flow From the Inside Surface of Uniformly Heated Inclined Circular Tube

2006 ◽  
Author(s):  
H. Mohammed ◽  
T. Yusaf
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Flow Direction ◽  
Convection Heat Transfer ◽  
Heat Transfer Process ◽  
Secondary Flows ◽  
Opposed Flow ◽  
Wide Range

This paper aims to investigate the effect of the flow pattern on the mixed convection heat transfer. A 28 thermocouples wire were installed along a 900mm copper tube to measure the temperature distribution. Three insulation layers of fiber glass, asbestos and gypsum were used to minimize to heat lost to the surrounding. A forced convection at the entrance region of a fully developed opposing laminar air flow was investigated to evaluate the flow direction effect on the Nusselt number. The investigation covered a wide range of Reynolds number from 410 to 1600 and heat flux varied from 63W/m2 to 1260W/m2, with different angles of tube inclination of 30°, 45°, 60°, and 90°. It was found that the surface temperature variation along the tube for opposed flow higher than the assisted flow but lower than the horizontal orientation. The Reynolds number has a significant effect on Nusselt number in opposed flow while the effect of Reynolds number was found to be small in the case of assisted flow. The Nusselt number values were lower for opposed flow than the assisted flow. The temperature profiles results have revealed that the secondary flows created by natural convection have a significant effect on the heat transfer process. The obtained average Nusselt number values were correlated by dimensionless groups as Log Nu against Log Ra/Re.

A Variable Fidelity Model Management Framework for Multiscale Computational Design of Continuous Fiber SiC-Si3N4 Ceramic Composites

2007 ◽  
Author(s):  
Gilberto Meji´a Rodri´guez ◽  
John E. Renaud ◽  
Vikas Tomar
Keyword(s):  
Material Design ◽  
Ceramic Composites ◽  
Design Tool ◽  
Material Behavior ◽  
Model Management ◽  
High Fidelity ◽  
Management Framework ◽  
Design Cycle ◽  
Variable Fidelity ◽  
Fidelity Model

Research applications involving design tool development for multiple phase material design are at an early stage of development. The computational requirements of advanced numerical tools for simulating material behavior such as the finite element method (FEM) and the molecular dynamics method (MD) can prohibit direct integration of these tools in a design optimization procedure where multiple iterations are required. The complexity of multiphase material behavior at multiple scales restricts the development of a comprehensive meta-model that can be used to replace the multiscale analysis. One, therefore, requires a design approach that can incorporate multiple simulations (multi-physics) of varying fidelity such as FEM and MD in an iterative model management framework that can significantly reduce design cycle times. In this research a material design tool based on a variable fidelity model management framework is presented. In the variable fidelity material design tool, complex “high fidelity” FEM analyses are performed only to guide the analytic “low-fidelity” model toward the optimal material design. The tool is applied to obtain the optimal distribution of a second phase, consisting of silicon carbide (SiC) fibers, in a silicon-nitride (Si3N4) matrix to obtain continuous fiber SiC-Si3N4 ceramic composites (CFCCs) with optimal fracture toughness. Using the variable fidelity material design tool in application to one test problem, a reduction in design cycle time around 80 percent is achieved as compared to using a conventional design optimization approach that exclusively calls the high fidelity FEM.

Three-Dimensional Forced Convection Flow in Plane Symmetric Sudden Expansion

2003 ◽  
Author(s):  
J. H. Nie ◽  
B. F. Armaly
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Forced Convection ◽  
Three Dimensional ◽  
Sudden Expansion ◽  
Recirculation Region ◽  
Number Range ◽  
Plane Symmetric ◽  
Reynolds Number Range

Simulations of three-dimensional flow and heat transfer in laminar incompressible forced convection in plane symmetric sudden expansion (backward-facing step in rectangular duct) are presented for different Reynolds numbers. The duct’s downstream (H) and upstream (h) heights are 0.04m and 0.02m, respectively, thus providing a step height (S) of 0.01m and an expansion ratio of 2. The duct’s width (W) is 0.08m, thus resulting in an aspect ratio of 4 before and 2 after the expansion, respectively. The incoming flow is considered to be isothermal, hydro-dynamically steady and fully developed. Uniform and constant heat flux is specified on the stepped walls, while the other walls are treated as adiabatic surfaces. The flow appears to be symmetric for the low Reynolds number range that is considered in this study (Re=150). A “jet-like” flow develops near the sidewall and its impingement on the stepped wall creates a swirling flow inside the primary recirculation region adjacent to the stepped wall, and that is responsible for creating a maximum in the Nusselt number distribution. The results reveal that the location where the streamwise component of wall shear stress is zero on the stepped wall does not coincide with the location of the outer edge of the primary recirculation region, especially in the region near the sidewall. Neither one of these boundary lines represents the reattachment region of the separated flow in the region adjacent to the sidewall. The maximum Nusselt number on the stepped wall is located inside the primary recirculation region and is not identical to the “jet-like” flow impingement point. The maximum friction coefficient on the stepped wall is located inside the primary recirculation region, and it is at the center of the duct for the Reynolds number range considered in this study. The minimum friction coefficient on the stepped wall is located at the impingement of the “jet-like” flow.

scholarly journals Effect of Reynolds and Prandtl Numbers on Mixed Convection in an Obstructed Vented Cavity

2011 ◽  
Vol 3 (2) ◽  
pp. 271-281
Author(s):  
M. M. Rahman ◽  
M. M. Billah ◽  
M. A. Alim
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Reynolds Number ◽  
Finite Element ◽  
Free Convection ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Forced Convection ◽  
Thermal Field ◽  
Heat Transfer Characteristics

A numerical investigation is conducted to analyze the steady flow and thermal fields as well as heat transfer characteristics in a vented square cavity with a built-in heat conducting horizontal solid circular obstruction. Hydrodynamic behavior, thermal characteristics and heat transfer results are obtained by solving the couple of Navier-Stokes and energy equations by using a weighted residuals Finite element method. The computation was made for different Reynolds number, Prandtl number ranging from 50 to 200 and from 0.71 to 7.1 at the three different convective regimes. Three different regimes are observed with increasing Ri: forced convection (with negligible free convection), mixed convection (comparable free and forced convection) and free convection dominated region (with higher free convection). The results are presented to show the effects of the Reynolds number, Prandtl number on flow pattern, thermal field and heat transfer characteristics at the three convective regimes. It is found that the flow and thermal field strongly depend on the Reynolds number, Prandtl number as well as Richardson number. As the Reynolds number and Prandtl number increase, the heat transfer rate increases but average fluid temperature in the cavity and temperature at the cylinder center decrease at the three convective regimes.Keywords: Mixed convection; Finite element method; Obstructed vented cavity; Prandtl number.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.4344                J. Sci. Res. 3 (2), 271-281 (2011)

Bouyancy Effect on Forced Convection in Vertical Tubes at High Reynolds Numbers

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
LiDong Huang ◽  
Kevin J. Farrell
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Natural Convection ◽  
Mixed Convection ◽  
Transfer Coefficient ◽  
Flow Regime ◽  
Forced Convection ◽  
Reynolds Numbers ◽  
Buoyancy Effect ◽  
Vertical Tubes

The complex interaction of forced and natural convections depends on flow regime and flow direction. Aiding flow occurs when both driving forces act in the same direction (heating upflow fluid and cooling downflow fluid), opposing flow occurs when they act in different directions (cooling upflow fluid and heating downflow fluid). To evaluate mixed convection methods, Heat Transfer Research, Inc. (HTRI) recently collected water and propylene glycol data in two vertical tubes of different tube diameters. The data cover wide ranges of Reynolds, Grashof, and Prandtl numbers and differing ratios of heated tube length to diameter in laminar, transition, and turbulent forced flow regimes. In this paper, we focus the buoyancy effect on forced convection of single-phase flows in vertical tubes with Reynolds numbers higher than 2000. Using HTRI data and experimental data in literature, we demonstrate that natural convection can greatly increase or decrease the convective heat transfer coefficient. In addition, we establish that natural convection should not be neglected if the Richardson number is higher than 0.01 or the mixed turbulent parameter Ra1/3/(Re0.8 Pr0.4) is higher than 0.05 even in forced turbulent flow with Reynolds numbers greater than 10,000. High resolution Reynolds-averaged Navier–Stokes simulations of several experimental conditions confirm the importance of the buoyancy effect on the production of turbulence kinetic energy. We also determine that flow regime maps are required to predict the mixed convection heat transfer coefficient accurately.

A Variable Fidelity Model Management Framework for Designing Multiphase Materials

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
Gilberto Mejía-Rodríguez ◽  
John E. Renaud ◽  
Vikas Tomar
Keyword(s):  
Material Design ◽  
Design Tool ◽  
Model Management ◽  
High Fidelity ◽  
Management Framework ◽  
Cycle Times ◽  
Design Cycle ◽  
Numerical Tools ◽  
Variable Fidelity ◽  
Fidelity Model

Research applications involving design tool development for multi phase material design are at an early stage of development. The computational requirements of advanced numerical tools for simulating material behavior such as the finite element method (FEM) and the molecular dynamics (MD) method can prohibit direct integration of these tools in a design optimization procedure where multiple iterations are required. One, therefore, requires a design approach that can incorporate multiple simulations (multiphysics) of varying fidelity such as FEM and MD in an iterative model management framework that can significantly reduce design cycle times. In this research a material design tool based on a variable fidelity model management framework is presented. In the variable fidelity material design tool, complex “high-fidelity” FEM analyses are performed only to guide the analytic “low-fidelity” model toward the optimal material design. The tool is applied to obtain the optimal distribution of a second phase, consisting of silicon carbide (SiC) fibers, in a silicon-nitride (Si3N4) matrix to obtain continuous fiber SiC–Si3N4 ceramic composites with optimal fracture toughness. Using the variable fidelity material design tool in application to two test problems, a reduction in design cycle times of between 40% and 80% is achieved as compared to using a conventional design optimization approach that exclusively calls the high-fidelity FEM. The optimal design obtained using the variable fidelity approach is the same as that obtained using the conventional procedure. The variable fidelity material design tool is extensible to multiscale multiphase material design by using MD based material performance analyses as the high-fidelity analyses in order to guide low-fidelity continuum level numerical tools such as the FEM or finite-difference method with significant savings in the computational time.

Combined forced and natural convection with low-speed air flow over horizontal cylinders

1970 ◽  
Vol 42 (1) ◽  
pp. 17-31 ◽  
Author(s):  
A. P. Hatton ◽  
D. D. James ◽  
H. W. Swire
Keyword(s):  
Natural Convection ◽  
Mixed Convection ◽  
Forced Convection ◽  
Experimental Work ◽  
Air Flow ◽  
Limited Range ◽  
Convection Regime ◽  
Flow Parameters ◽  
Horizontal Cylinders ◽  
Good Agreement

This article describes experimental work on the mixed convection régime with flow normal to electrically heated cylinders. The forcing velocities used were in the range 0·0085–3 ft./sec (i.e. 10−2 < Ref < 45) and temperature differences in the range 30°C to 200°C (i.e. 10−3 < Ra < 10) were covered.Correlations are proposed for the forced convection and natural convection conditions. A correlation is also developed for the combined forced and natural convection region by a vectorial addition of the flow parameters, which gives good agreement with the experiments except over a limited range in the contraflow régime.

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