Modeling Of Natural Convection Research Articles

Natural convection in vertical enclosures with conjugate boundary conditions

A numerical investigation and reduced-order modelling of natural convection in a cavity with differentially heated sidewalls is discussed. The effect of conjugate boundary conditions on the cavity's heat transfer and natural flow circulation with varying aspect ratios and Rayleigh numbers is examined. Validation of the canonical differentially heated cavity reveals that a modification to the definition of the Rayleigh number (Ra) is required to reconcile the $Nu\sim Ra^{1/4}$ scaling (where Nu is the Nusselt number) and validity of previously proposed correlations for the heat transfer in vertical enclosures. Dynamic mode decomposition is used to uncover the underlying time-dependent flow structures and the results are compared with stability bifurcation studies in the literature. A flow mode previously associated with smaller aspect ratio cavities is identified as the unstable mode for a larger aspect ratio of 4. The effect of conjugate boundary conditions is scaled based on the ratio of the internal and external boundary layers, wherein higher external Reynolds numbers aid in the heat transfer as the Nusselt number approaches the isothermal limit. A reduced-order theoretical model is proposed to predict the Nusselt number for the conjugate boundary conditions. The performance of conjugate boundary conditions is connected to the flow stability, with the parallel-flow configuration acting in a destabilizing manner while the counterflow configuration has a stabilizing effect and results in the highest heat transfer. We also found that relatively large heat transfer can be achieved with substantially lower external actuation with intermediate aspect ratios, translating to less power in practice.

The performance analysis of a novel photocatalytic-thermal-catalytic-photovoltaic-Trombe wall system integrated with compound parabolic concentrator

This paper proposes a novel photocatalytic-thermal-catalytic-photovoltaic-Trombe wall system integrated with compound parabolic concentrator (CPC/PTCPV-TW), which can make full use of outdoor solar radiation and make the system have multiple functions of heating, purification and photovoltaic power generation. The experimental detection platform of CPC/PTCPV-TW system was built and then turbulent natural convection model and indoor formaldehyde diffusion and transfer model were established to study the performance of CPC/PTCPV-TW system. The results were: (1) In the photocatalytic flow channel, the average daily thermal efficiency and the single pass rate of formaldehyde were 0.36 and 0.25–0.56, respectively. In the thermal catalytic flow channel, the average daily thermal efficiency and the single pass rate of formaldehyde were 0.26 and 0.18–0.38, respectively. The average daily photoelectric conversion efficiency of CPCPTCPV-TW system was 6.68%; (2) The greater the solar irradiation intensity and the lower the air inlet temperature, the higher the instantaneous thermal efficiencies of the photocatalytic channel and thermal catalytic channel and the photoelectric conversion efficiency of the system. The lower the formaldehyde inlet concentration, the greater the amount of clean air delivery rate (CADR) and the smaller ventilation times, the better the degradation effect of formaldehyde in the room equipped with CPC/PTCPV-TW system, and the lower the indoor formaldehyde concentration in a stable state.

Numerical and experimental studies on the cooling performance of backfill containing phase change materials

A novel method for deep mine cooling based on using backfill containing phase change materials (PCMs) was verified by numerical simulations and experiments. A laboratory-scale experimental system was designed to test the cooling process of backfill with ice particles as the PCM. Two boxes connected by a median clapboard were used to simulate the backfill and adjacent stope regions. A 3D numerical heat transfer model was developed in which the backfill region was modelled using an enthalpy method model and a porous medium model and the stope region was modelled using DTRM and a natural convection model. The numerical model was validated against experimental results and used to conduct a simulation study. The simulation results showed that the backfill containing the PCM produced a clear cooling effect on stope. A sensitivity analysis was performed to investigate the influence of the initial PCM liquid fraction, backfill slurry concentration, and filling strategy on the cooling performance. The analysis results showed that by decreasing the PCM initial liquid fraction enhanced the cooling performance, whereas the backfill slurry concentration had little effect on cooling performance over the recommended concentration range. Furthermore, the filling strategy was optimized.

Performance evaluation of a wrapped around condenser for heat pump water heater applications

• A model has been developed to predict the performance of a HPWH condenser in two wrap patterns. • The impact of condenser design on the heat transfer to the storage tank has been established. • Optimization of the spacing for two wrap patterns shows little difference in performance. • Charge amount, as well as subcooled, saturated and super-heated lengths have been determined for the condenser. Accurate performance evaluation of a wrapped-around condenser for heat pump water heaters (WHPWH) is critical since the COP of the system depends heavily on thermal stratification and condenser design. An analytical, quasi-steady state heat balance method has been developed to determine the optimal spacing between adjacent channels, tube diameter, tube shape, and total refrigerant charge amount for the condenser. The heat transfer rate is compared among three approaches: the refrigerant thermodynamic model, the condenser-wrap fin model, and the analytical natural convection model on the inside of the tank for the three regions based on the refrigerant phase (e.g., super-heated, saturated, or subcooled). The heat transfer rate was predicted by a combination of slug-plug and annular flow for a D-shaped helical tube. Experimental data were used as boundary conditions for validating the model. The rate of heat transfer based on tube shape and tank wall temperatures was compared by CFD analysis. Parametric analysis indicates a tradeoff between refrigerant mass, pressure drop, tube diameter, and tube length to maximize the heat transfer rate. The model suggests the saturated region length can be extended by 400%, and the condenser pressure drop can be reduced by 23% with an optimal spacing pattern.

A Uzawa-Type Iterative Algorithm for the Stationary Natural Convection Model.

In this study, a Uzawa-type iterative algorithm is introduced and analyzed for solving the stationary natural convection model, where physical variables are discretized by utilizing a mixed finite element method. Compared with the common Uzawa iterative algorithm, the main finding is that the proposed algorithm produces weakly divergence-free velocity approximation. In addition, the convergence results of the proposed algorithm are provided, and numerical tests supporting the theory are presented.

Numerical simulation of magnetic fluid thermal coupling of cylindrical heat source based on LBM lattice algorithm

In order to improve the accuracy of numerical simulation of magnetic fluid thermal coupling of cylindrical heat source, a numerical simulation method of magnetic fluid thermal coupling of cylindrical heat source based on LBM grid algorithm was studied. Based on the theoretical model of natural convection and radiative heat dissipation of cylindrical heat source, the boundary conditions were set, and the thermal coupling performance of flow field and temperature field in the process of natural convection and radiative heat dissipation of cylindrical heat source was simulated by LBM grid algorithm. Simulation results show that the relative error between simulation results and experimental results is less than 1.5%. The results show that this method can accurately simulate the magnetofluid-thermal coupling of cylindrical heat source. With the increase of Rayleigh number, different numerical solutions appear: steady state solution when Rayleigh number is 105, periodic oscillation solution when Rayleigh number is 106, chaotic solution when Rayleigh number is 107.

Finite Element Iterative Methods for the Stationary Double-Diffusive Natural Convection Model.

In this paper, we consider the stationary double-diffusive natural convection model, which can model heat and mass transfer phenomena. Based on the fixed point theorem, the existence and uniqueness of the considered model are proved. Moreover, we design three finite element iterative methods for the considered problem. Under the uniqueness condition of a weak solution, iterative method I is stable. Compared with iterative method I, iterative method II is stable with a stronger condition. Moreover, iterative method III is stable with the strongest condition. From the perspective of viscosity, iterative method I displays well in the case of a low viscosity number, iterative method II runs well with slightly low viscosity, and iterative method III can deal with high viscosity. Finally, some numerical experiments are presented for testing the correctness of the theoretic analysis.

Simple computational strategies for more effective physics-informed neural networks modeling of turbulent natural convection

The high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of discretization of the underlying operators very much connected to the flow scales resolution, is capable of sustaining high levels of turbulence. Another concern is whether it can be used as numerical substitutes to full DNS data retrieval and storage; DNS remaining so far the standard tool for validation and inter-comparison with experimental results.We explore the use of PINNs surrogate modeling for turbulent natural convection flows, mainly relying on DNS temperature data from the fluid bulk and velocity data at some fluid boundaries. This technique depends on the minimization of a composite loss-function relying on labels and PDE residuals. We demonstrate the large computational requirements under which PINNs are capable of accurately recovering the flow hidden quantities. We then propose new techniques to mitigate the need for large training datasets. First, we propose a padding technique to better distribute some of the scattered coordinates at which PDE residuals are minimized, in particular in zones where no labels are available. We show how it comes to play as a regularization close to the training boundaries and results in a noticeable global accuracy improvement at iso-budget. We then propose a relaxation of the incompressibility condition involved in the loss function contribution related to the PDE residuals. This development drastically benefits the optimization search and results in a much improved convergence. The results obtained for Rayleigh-Bénard flow at Ra=2⋅109 are particularly impressive. With training data amounting for only 0.32% of the stored DNS dataset, the predictive accuracy of the surrogate over the entire half a billion DNS coordinates yields errors for all flow variables ranging between [0.3%−4%] in the relative L2 norm.

Towards robust and accurate Reynolds-averaged closures for natural convection via multi-objective CFD-driven machine learning

Robust and accurate Reynolds-averaged stresses and scalar fluxes closure models for natural convection developed by machine learning are presented in this work. In comparison to passive scalar flows, the complexity of turbulence modelling for natural convection problems is increased as the velocity and scalar fields are strongly coupled by the buoyancy force. Therefore, the appropriate Reynolds-averaged closure models for natural convection ought to capture this interaction within the second-moment terms. Previous data-driven turbulence modelling approaches have treated the unclosed terms of the velocity and thermal fields separately, which has lead to inaccurate predictions when handling natural convection problems. In this study, we therefore develop fully coupled buoyancy-extended models by using a novel multi-objective and multi-expression machine-learning framework that is based on CFD-driven training (Zhao et al., J. Comput. Phys., 411, 109413, (2020)). The model candidates obtained from a Gene-Expression Programming approach, and thus available in symbolic form, are evaluated by running RANS solvers for different Rayleigh number cases during the model training process. This novel framework is applied to vertical natural convection, with the emphasis of this paper on the importance of coupling the explicit closure model formulations, the choice of cost functions, and the appropriate input flow features (i.e. a generalised flux Richardson number) for developing accurate models. It is shown that the resulting machine-learnt models improve the predictions of quantities of interests, e.g. mean velocity and temperature profiles, across a wide range of Rayleigh numbers.

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO2 sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. We present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7×106 because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

A time filter method for solving the double-diffusive natural convection model

This paper proposes a time filter method to solve the double-diffusive natural convection model. The main idea of this method is to add a simple time filter to the backward Euler scheme which can improve the temporal accuracy of the backward Euler scheme from the first order to the second order. Furthermore, the stability analysis and error estimate of the presented method are proved. Finally, several numerical examples are given to support the theoretical analysis.

Analysis of temperature rapid rise phenomenon during damper-off cycle in side-by-side frost-free refrigerator

The temperature rapid rise phenomenon often happens in the side-by-side frost-free refrigerators during the damper-off cycle, which leads to a decrease in damper-off duration and an increase in energy consumption. A three-dimensional transient model of natural convection during the damper-off cycle is established and experimentally validated to analyze the refrigerating compartment (RC) temperature rapid rise phenomenon. The results show that the violent natural convection airflow driven by the non-uniform temperature distribution will lead to the significant variation of RC temperature. The hot air rises from bottom into top layer along the three passages, which include the front gap (FG) between shelves and door boxes, the side gap (SG) between the right-side wall and door boxes and the rear gap (RG) between shelves and the rear wall. The air enthalpy along FG into the first layer is the dominant factor of the temperature rapid rise, accounting for almost 64.4% of the total inflow air enthalpy. The net air enthalpy flow along FG is larger than other passages in the first 15 s and decreases rapidly as the temperature distribution becomes uniform.

Modeling of natural convection of a concentrated solar power receiver absorber tube in interaction with neighbouring absorbers

Concentrated Solar Power (CSP) technology stands out among other renewable energy sources not only because of its ability to address current energy security and environmental challenges but because its energy can be stored for future use. To ensure optimum performance in this system, the heat losses need to be evaluated for better design.
 This work studies the natural convection in the receiver absorber tube of a CSP plant taking into consideration the influence of neighboring absorbers. A 2-Dimensional model was adopted in this study. Initially, a single absorber tube was considered, it was subjected to heat flux at the top wall, the bottom wall was insulated and a temperature differential was set up at the lateral walls. The dimensionless forms of Navier-Stokes and energy equations were solved using the finite element formulation of COMSOL Multiphysics software. The result obtained for a single absorber tube showed good agreement with existing research works. This validated model was then extended to multiple absorber tubes (two to six absorber tubes). On the basis of the study, there is an observed increase in the intensity and dominance of convective heat transfer with an increase in the number of absorber tubes. This is occasioned by an increase in the average surface temperature as well as average Nusselt number. For the Rayleigh number of 104, 105 and 106, the average Nusselt number increases with the number of absorber tubes by 13.87 %, 6.26 %, and 1.55 %, respectively. This increment suggests effect of thermal interactions among the neighboring absorber tubes

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$ , is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. (J. Fluid Mech, vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$ ) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a ‘two-length-scale diffusion’ model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$ . In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations.

Numerical modeling of free convection in a partially heated triangular enclosure with chamfer

Two-dimensional numerical modelling of water natural convection inside a chamfered triangular cavity, that is being partially heated from below has been investigated in this paper. The walls of the cavity are considered isothermally isolated except a source part of heat which is inserted at the bottom wall while the inclined wall is considered as cold wall. A COMSOL Multiphysics 5.5 has been used to solve the numerical solutions. This paper considered some variables such as Rayleigh number (Ra = 103 to 106), heating length ratio (HL= 0.2, 0.4, and 0.5) and the ratio of the chamfer’s radius (R= 0.1, 0.2, and 0.25) while all other physical parameters are considered constant such as the length of the cold wall and the adiabatic wall. The results have been validated with previous published work in order to ensure the accuracy of the current coding. The main results observed an increase in streamlines and isotherms with the rise of Rayleigh (Ra) number and the rise of heating length ratio; additionally, the average Nusselt number (Nuavg) value increases with the rise of the Ra number and the length of the heating source. For example, average Nusselt number increased from 2.0443 at Ra=103 to 7.2793 at Ra= 106 for (R=0.25 and HL = 0.5).

Thermo-bioconvection in horizontal wavy-walled porous annulus

The present investigation centers around a numerical study of the impact of the presence of phototactic microorganisms on the thermo-bioconvection inside a wavy-walled horizontal porous annulus that is saturated with a Newtonian fluid. Consequently, an equation describing the movement of the microorganism cells is added to the mathematical model of natural convection. The thermal equilibrium, Oberbeck–Boussinesq approximations and Darcy law are taken into consideration. The transformed dimensionless partial differential equations with the temperature-concentration-stream function formulation are discretized applying the alternate direction implicit finite difference scheme. Results confirm that in the absence of microorganisms the Nusselt number decreases with the increase of the amplitude of wall waviness. It was also observed that the wall waviness influence the thermo-bioconvective instabilities and the flow regime structure.

An Uzawa iterative method for the natural convection problem based on mixed finite element method

In this paper, an Uzawa iterative method combined with a mixed finite element method is presented for solving the natural convection model, where a decoupling discrete system is solved and no saddle point system is required to solve at each iterative step. Moreover, the authors establish convergence result of the method and find an interval of relaxation parameter that is crucial for the convergence of the presented method.

Resolving nonuniform temperature distributions with single-beam absorption spectroscopy. Part II: Implementation from broadband spectra

Several past studies have described how absorption spectroscopy can be used to determine spatial temperature variations along the optical path by measuring the unique, nonlinear response to temperature of many molecular absorption transitions and performing an inversion. New laser absorption spectroscopy techniques are well-suited to this nonuniformity measurement, yet present analysis approaches use only isolated features rather than a full broadband spectral measurement. In this work, we develop a constrained spectral fitting technique called E″-binning to fit an absorption spectrum arising from a nonuniform environment. The information extracted from E″-binning is then input to the inversion approach from the previous paper in this series (Malarich and Rieker, JQSRT 107455 [1]) to determine the temperature distribution. We demonstrate this approach by using dual frequency comb laser measurements to resolve convection cells in a tube furnace. The recovered temperature distributions at each measurement height agree with an existing natural convection model. Finally, we show that for real-world measurements with noise and absorption model error, increasing the bandwidth and the number of measured absorption transitions may improve the temperature distribution precision. We make the fitting code publicly available for use with any broadband absorption measurement.

Artificial intelligence prediction of natural convection of heat in an oscillating cavity filled by CuO nanofluid

BackgroundIn the last five years, a new generation of advanced numerical methods was developed to reduce computational costs and improve the prediction process. The combination of Artificial Intelligence and traditional computational methods is the best sample of this generation. Employing this method can expand the horizon of numerical modeling. This method is also suitable for complex processes such as natural convection and oscillating heat transfer. This case study tries to peruse the effects of variable boundary conditions such as magnetic field, angle, and nanofluids volume fraction on the heat transfer. Also, the impact of oscillation has been studied. MethodsTo accomplish these aims, numerical modeling of natural convection based on Boussinesq approximation was used. Techniques from machine learning were employed to develop a predictive tool that utilizes the data generated by computational analysis of the problem. The Ra and Ha were considered in the ranges of 103<Ra<106 and 0<Ha<40, respectively. Oscillation frequencies between 20 and 50 Hz and amplitudes of 0.5, 1, and 2 mm were studied. FindingsThe result showed that Nu increased in initial steps and then decreased at a constant Ha by increasing the rotation angle. It appeared that the amplitude of oscillation has a pronounced effect on the heat transfer rate. The results show that the Ha could affect streamlines of fluid. By increasing Ha=0 to Ha=52, the maximum velocity point in the close enclosure moved 14% closer to the hot side.

Improved water freezing with baffles attached to a freezing tunnel: Mathematical modeling and numerical simulation by a conjugate finite volume model

• Addition of baffles to tunnel walls originated major improvements in water freezing. • A CFD conjugate model describes convective processes in a refrigeration tunnel. • Control of vortex shedding behind foods is a key issue in enhanced cooling process. • Water freezing front and Nusselt number validated with experimental results. Unsteady conjugate mathematical model for natural heat convection with change phase of pure water inside of a square container caused by external mixed heat convection of cool air and the effect of baffles attached to a freezing tunnel has been studied numerically. The coupled equations were solved by Finite Volume method with the SIMPLE algorithm. Effect of the baffles on freezing time, evolution of local dimensionless heat flux and surface temperature distribution at the container with water were studied. The results showed that the hydrodynamic and thermal boundary layer were reduced due to the baffles, this effect reduced the freezing time and homogenized the superficial temperature of the container. Additionally, the effect of the length of baffles on the heat flux and vortex shedding frequency behind the water container were assessed.