Local Thermal Equilibrium Model Research Articles

Local thermal non-equilibrium effects on phase transition of fiber reinforced thermoplastic composites with temperature-dependent heat generation

Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications.

Exergy and entropy analysis of metal foams based on 2nd law of thermodynamics

The available (exergy) and effective use (entropy generation) of energy at the end of thermodynamic processes are significantly important parameters in the design of optimum thermal system. Entropy analysis based on 2nd law of thermodynamics through various pore density metal foams placed in an asymmetrical heated horizontal channel is presented in the current work. Water flows through the channel at different flow rates (inlet velocity varies from 0.02 to 0.3 m/s). Highly porous and different pore density aluminum metal foams such as 10 (0.95), 20 (0.90), 30 (0.92) and 45 (0.90) are inserted into the channel to boost the heat transfer. Darcy Extended Forchheimer (DEF) and local thermal equilibrium (LTE) models are used for the calculation of flow and thermal variables respectively. The numerical outcomes of the examination are first confirmed by comparing with existing experimental literature results. The mean exergy Nusselt number results presented shows that the 10PPI metal foam stretches 35.41 % and 12.20 % higher thermal presentation with respect to 20PPI and 30PPI metal foam. The entropy examination showed that the 20PPI metal foam produces minimum entropy generation at a Reynolds number of 3464.32 and 10PPI metal foam shows highest presentation based on Bejan and entropy generation number.

Effects of local thermal non-equilibrium on hydraulic stimulation efficiency of enhanced geothermal systems

Motivated by hydraulic stimulation of enhanced geothermal systems, the present paper investigates the coupled thermo-hydro-mechanical response of a geothermal well imbedded in a thermoporoelastic medium, subjected to a non-isothermal fluid flux and convective cooling on the borehole surface. Our focus centers on the effect of local thermal non-equilibrium (LTNE) on the temporal-spatial evolution of temperatures, pore pressure, and stresses, where the solid and fluid phases have two distinct temperatures and local heat transfer between the two phases is addressed. We employ integral transform and load decomposition techniques to derive analytical solutions in the Laplace domain. This methodology allows us to disentangle and separate the individual contributions to changes in pore pressure and stresses from fluid injection and convective heat transfer. The results reveal that compared to the classical local thermal equilibrium model, the thermally induced pore pressure is slightly lower under LTNE conditions. The LTNE has a significant influence on the temporal evolution of thermally induced stresses, especially in the vicinity of the wellbore.

A Unified Approach to Two-Dimensional Brinkman-Bénard Convection of Newtonian Liquids in Cylindrical and Rectangular Enclosures.

A unified model for the analysis of two-dimensional Brinkman-Bénard/Rayleigh-Bénard/ Darcy-Bénard convection in cylindrical and rectangular enclosures (CE/RE) saturated by a Newtonian liquid is presented by adopting the local thermal non-equilibrium (LTNE) model for the heat transfer between fluid and solid phases. The actual thermophysical properties of water and porous media are used. The range of permissible values for all the parameters is calculated and used in the analysis. The result of the local thermal equilibrium (LTE) model is obtained as a particular case of the LTNE model through the use of asymptotic analyses. The critical value of the Rayleigh number at which the entropy generates in the system is reported in the study. The analytical expression for the number of Bénard cells formed in the system at the onset of convection as a function of the aspect ratio, So, and parameters appearing in the problem is obtained. For a given value of So it was found that in comparison with the case of LTE, more number of cells manifest in the case of LTNE. Likewise, smaller cells form in the DBC problem when compared with the corresponding problem of BBC. In the case of RBC, fewer cells form when compared to that in the case of BBC and DBC. The above findings are true in both CE and RE. In other words, the presence of a porous medium results in the production of less entropy in the system, or a more significant number of cells represents the case of less entropy production in the system. For small and finite So, the appearance of the first cell differs in the CE and RE problems.

Effects of Neumann and Robin boundaries on the thermal instability

AbstractThe thermo convective instability of the Darcy-Benard problem (DB) using Robin (third-kind) thermal conditions is investigated here. We consider a viscous Newtonian fluid saturating a porous layer in which the layer is sandwiched between two impermeable boundaries. The upper and the lower walls are modelled in the form of the Neumann (second-kind) and the Robin (third-kind) thermal conditions, respectively. The difference in the temperature distribution between both phases allows the lack of a local thermal equilibrium model to be present. As a consequence, the third kind of thermal condition brings about one extra dimensionless parameter of the Biot number to the usual one of the inter-heat transfer coefficient and the thermal conductivity ratio. The normal modes method adopted in a linear stability analysis gives rise to perturbed governing equations. The eigenvalue problem is handled numerically as a result of the perturbed governing equations leading to the marginal stability condition.

Investigating the impact of modeling assumptions and closure models on the steady-state prediction of solar-driven methane steam reforming in a porous reactor

In this work, the effect of different modeling assumptions and closure models — frequently considered in the literature of solar thermochemical reactors and closely-related areas — is investigated. The application of different modeling assumptions and closure models may strongly affect the results accuracy and compromise a meaningful comparison across literature works. The following is herein investigated: (i) the role of upstream and downstream fluid regions to the two-phase reactor region; (ii) relevance of species and gas-phase thermal diffusion mechanisms; (iii) reaction heat accounted for in gas- or solid-phase energy balance equations; (iv) local thermal equilibrium (LTE) vs. local thermal non-equilibrium (LTNE) models; (v) model dimension (one-dimensional vs. two-dimensional axisymmetric models); (vi) local volumetric convection heat transfer correlations; and (vii) effective solid thermal conductivity correlations. The relevance of this work extends well beyond the current application (methane steam reforming in a volumetric solar reactor), since similar models and assumptions have also been widely applied for predicting the performance of volumetric solar absorbers and dry reforming solar reactors. The results show that an upstream fluid region should be considered while applying inlet first-type boundary conditions and diffusion transport in the corresponding governing equations to ensure full-conservation and simultaneously to account for developing profiles upstream the reactor inlet section. For the operating conditions considered, species diffusion and gas-phase heat conduction are particularly relevant at the reactor centerline but with a negligible integral effect. A significant difference in the reactor performance is observed while accounting for the reaction heat from surface reactions in the solid- or gas-phase energy balances — for the lowest inlet gas velocity herein considered, the thermochemical efficiency (methane conversion) is approximately equal to 70.8% (76.3%) and 77.3% (84.7%) assigning the reaction heat to the gas- and solid-phase energy balances, respectively. LTE model results are strikingly different from the results obtained with the LTNE model considering the reaction heat accounted for in the gas-phase energy balance but not significantly different from the results computed with the LTNE model with the reaction heat assigned to the solid-phase energy balance. One-dimensional reactor modeling provided with an average concentrated solar heat flux value results in a similar average performance as that given by a two-dimensional model but fails to predict the high temperatures observed at reactor centerline — for the lowest inlet gas velocity, the difference between the maximum solid temperatures predicted by one- and two-dimensional models is about 340K.

ALMA 0.5 kpc Resolution Spatially Resolved Investigations of Nuclear Dense Molecular Gas Properties in Nearby Ultraluminous Infrared Galaxies Based on HCN and HCO+ Three Transition Line Data

We present the results of our ALMA ≲0.5 kpc resolution dense molecular line (HCN and HCO+ J = 2–1, J = 3–2, and J = 4–3) observations of 12 nearby (ultra)luminous infrared galaxies ([U]LIRGs). After matching beam sizes of all molecular line data to the same values in all (U)LIRGs, we derive molecular line flux ratios by extracting spectra in the central 0.5, 1, and 2 kpc circular regions and in 0.5–1 and 1–2 kpc annular regions. Based on non–local thermal equilibrium model calculations, we quantitatively confirm that the innermost (≲0.5 kpc) molecular gas is very dense (≳105 cm−3) and warm (≳300 K) in ULIRGs, and that in one LIRG, it is also modestly dense (104–5 cm−3) and warm (∼100 K). We then investigate the spatial variation of the HCN-to-HCO+ flux ratios and high-J to low-J flux ratios of HCN and HCO+. A subtle sign of a decreasing trend in these ratios from the innermost (≲0.5 kpc) to the outer nuclear (0.5–2 kpc) region is discernible in a significant fraction of the observed ULIRGs. For two ULIRGS hosting an active galactic nucleus (AGN), which display the trend most clearly, we find based on a Bayesian approach that the HCN-to-HCO+ abundance ratio and gas kinetic temperature systematically increase from the outer nuclear to the innermost region. We suggest that this trend comes from potential AGN effects because no such spatial variation is found in a starburst-dominated LIRG.

Optimal characteristics of natural convection in a square porous-nanofluid-filled enclosure containing three tubes

A numerical model was used to simulate natural convection heat transfer in a two-dimensional square enclosure filled with nanofluid and saturated with porous media. The enclosure contained three heated tubes with Rayleigh numbers (Ra) ranging from 102 to 3 × 104. The governing equations with Boussinesq approximation for natural convection were solved iteratively using the finite volume technique through ANSYS FLUENT-CFD commercial package. The Darcy–Forchheimer–Brinkman and Local Thermal Equilibrium models were applied for water and nanofluid flow across the porous zone. The numerical analysis was executed systematically for significant parameters that have a substantial impact on natural convection heat transfer, namely, aspect ratio (AR = 1.25 − 3.75), nanoparticle volume fraction (Φ = 0.25%, 0.5%, 0.7% and 1%), and the porosity of metal foam (ε = 0.3, 0.4, 0.5, 0.6 and 0.7). The aspect ratio was found to have a considerable impact on the averaged Nusselt number (Nuave ). For AR = 3.75, the value of Nuave for all Rayleigh numbers increased by approximately 5.22 times compared to AR = 1.25. Moreover, Nuave remained approximately constant as the concentration of alumina-water nanofluid increased from 0.25% to 1%. The novelty of this study lies in the multi-objective optimal design approach adopted by adopting DX-12 with the outcomes of ANSYS FLUENT-CFD. The averaged Nusselt number and convection heat transfer rate reached their optimal values by nearly 13 and 9 times, respectively, at the lowest possible porosity (ε = 0.3), the lowest possible nanofluid concentration (Φ = 0), and the highest possible aspect ratio value (AR = 3.75).

Application of the porous media approach to a Standing Wave Thermoacoustic Engine for CFD simulations

In this article, an application of the macroscopic porous media approach, suitable for CFD simulations in oscillating flows, is proposed for a simplified Standing Wave Thermo-Acoustic Engine (SWTAE), composed of a hot buffer tube, a stack - where the energy conversion takes place - and the rest of the resonator. While for a Travelling Wave Thermo-Acoustic Engine (TWTAE) a macroscopic model for porous media has been successfully applied to both regenerators (similar to the stack in a SWTA) and heat exchangers, for SWTAE this is not true. The results illustrate that a Local-Thermal Non-Equilibrium model is required to start up the SWTAE, otherwise (with the Local Thermal Equilibrium model) the thermoacoustic instability cannot arise. Furthermore, the comparison between the simulation conducted at the microscopic scale and that one at the macroscopic level, depicts that a purely Darcy-linear model employed for the macroscopic model, characterized for oscillating flows, overpredicts the pressure amplitude at periodic steady-state. For this reason, a Forchheimer-like coefficient needs to be implemented to fit the macroscopic solution with the microscopic one.

Secondary ion mass spectrometry quantification: Do you remember when a factor of 2 was good enough?

Well, do you remember when a factor of 2 was good enough? Probably, not unless you have been around secondary ion mass spectrometry (SIMS) since the early 1960s, like one of us has been. This paper will give many references back to the early days of quantification when a local thermal equilibrium model was used to obtain the first results that were accurate to within a factor of 2, but only 60% of the time. It only worked for bulk silicate matrixes. People were not even using SIMS on semiconductors in those days. Several early references showing profiles of ion implants in Si will be referenced, but it was not until 1980 that the first paper was published that explicitly showed how to use ion implants as SIMS standards. People were using ion implants as standards before 1980, but only in limited cases, and with no formal published equations specifying how to use them. But, the samples for which ion implants were used as standards were for dilute concentrations in a single matrix, which had a uniform matrix composition with depth. The rest of the paper will show how we at Eurofins EAG Laboratories tackled the problem of quantification of both major and minor elements in nonuniform, multi-element matrices with continuously graded composition changes using point-by-point CORrected-SIMS. These include SiGe heterostructure bipolar transistors, AlGaAs vertical cavity surface emitting lasers, and B plasma-implanted poly-silicon gates.

Numerical studies on storage process of phase change material with metal foam for prefabricated cabin energy system

Latent heat thermal energy storage (LHTES) is a promising technology in prefabricated cabin energy system. This paper proposed a new thermal energy storage (TES) system with phase-change material (PCM) embedded in metal foam and heating source is steam or hot water. The mathematical formulas and numerical models of representative units are studied. The effect of natural convection is considered in the simulation of melting process. Finite volume method is used to discretize the governing equation The Forchheimer-Darcy law is used to model the porous resistance and a local thermal equilibrium model is developed. The model is firstly validated against low temperature experiments from the literature and then used to simulate the charging behaviour of LHTES system proposed by this paper. Foamed metal and fin are effective means to improve the heat transfer performance and shorten the melting time of heat storage system. In this paper, the effects of pore density, porosity, wall temperature and fin spacing on temperature change and melting rate are discussed.

ALMA ACA study of the H2S/OCS ratio in low-mass protostars

Context. The identification of the main sulfur reservoir on its way from the diffuse interstellar medium to the cold dense star-forming cores and, ultimately, to protostars is a long-standing problem. Despite sulfur’s astrochemical relevance, the abundance of S-bearing molecules in dense cores and regions around protostars is still insufficiently constrained. Aims. The goal of this investigation is to derive the gas-phase H2S/OCS ratio for several low-mass protostars, which could provide crucial information about the physical and chemical conditions in the birth cloud of Sun-like stars. This may also shed new light onto the main sulfur reservoir in low-mass star-forming systems. Methods. Using Atacama Large Millimeter/submillimeter Array (ALMA) Atacama Compact Array (ACA) Band 6 observations, we searched for H2S, OCS, and their isotopologs in ten Class 0/I protostars with different source properties such as age, mass, and environmental conditions. The sample contains IRAS 16293-2422 A, IRAS 16293-2422 B, NGC 1333-IRAS 4A, RCrA IRS7B, Per-B1-c, BHR71-IRS1, Per-emb-25, NGC 1333-IRAS4B, Ser-SMM3, and TMC1. A local thermal equilibrium (LTE) model is used to fit synthetic spectra to the detected lines and to derive the column densities based solely on optically thin lines. Results. The H2S and OCS column densities span four orders of magnitude across the sample. The H2S/OCS ratio is found to be in the range from 0.2 to above 9.7. IRAS 16293-2422 A and Ser-SMM3 have the lowest ratio, while BHR71-IRS1 has the highest. Only the H2S/OCS ratio of BHR71-IRS1 is in agreement with the ratio in comet 67P/Churyumov–Gerasimenko within the uncertainties. Conclusions. The determined gas-phase H2S/OCS ratios can be below the upper limits on the solid-state ratios by as much as one order of magnitude. The H2S/OCS ratio depends in great measure on the environment of the birth cloud, such as UV-irradiation and heating received prior to the formation of a protostar. The highly isolated birth environment (a Bok globule) of BHR71-IRS1 is hypothesized as the reason for its high gaseous H2S/OCS ratio that is due to lower rates of photoreactions and more efficient hydrogenation reactions under such dark, cold conditions. The gaseous inventory of S-bearing molecules in BHR71-IRS1 appears to be the most similar to that of interstellar ices.

Analysis of the laminar flow and enhanced heat transfer rate through a triangular array of cylinders embedded in a fluid-saturated porous media with mixed convection

An investigation of the laminar flow and enhanced heat transfer rate through a triangular array of cylinders embedded in a fluid-saturated porous media is considered. Mixed convection covering forced convection cases has been studied using a finite-volume approach considering the local thermal equilibrium model. Darcy–Brinkman–Forchheimer momentum equations are used to characterize the porous media in question. The study is constrained to the low and intermediate Peclet number (Re = 5 to 40, Pr = 50) and high range of Darcy number (Da = 10−3 to 10−1) for different cylinder spacings (0.7 ≤ φ ≤ 0.99). It is anticipated that porous media would enhance heat transfer, but it derives a multiple order in pressure drop indubitably not desirable in many heat applications. Investigation reveals that both mean drag coefficient (CD ) and Nusselt number (Nu) are strong functions of Da and φ; however, the influence of the buoyancy parameter is mainly witnessed in higher permeability levels and high Peclet numbers. The study also details the effect of governing parameters on mean gap velocities and pressure coefficients. Surprisingly, recirculation wakes exist for the lowest cylinder spacing (φ = 0.7) in high fluid momentum. Low φ and high permeability are desirable in a forced convection regime, whereas both φ and Da should be high in the case of mixed convection. This article also quantifies the combined effect of the Darcy number and buoyancy parameter on the heat-transfer enhancement ratio. A maximum of 112% increase in Nu for φ = 0.7 and 452% for φ = 0.99 are reported at Da = 10−1, but at the cost of higher pressure drop in the latter case.

Transpiration cooling of high pressure turbine vane with optimized porosity distribution

The additive manufacturing allows to fabricate porous structures with elevated mechanical strength, which enable designers to apply transpiration cooling to gas turbine blades. However, most transpiration cooling investigations are carried out using the flat plate geometry. To understand transpiration cooling of a turbine blade better, it is necessary to conduct the investigations using real turbine blade geometry. The current study focuses on the numerical investigation and optimization of a transpiration cooled C3X vane. The C3X vane is designed with multiple porous zones whose porosities are in a range from 0.2 to 0.7. The Darcy-Brinkman-Forchheimer equation and the local thermal equilibrium model are used to simulate the flow and heat transfer in the porous zones. A surrogate-based optimization framework incorporating the Kriging method and the genetic algorithm is built to optimize the transpiration cooling performance. The numerical approach is carefully validated with the available experimental data, and then the optimization method is validated with the numerical results. The optimal designs under injection ratios of 1.2% and 2.0% are obtained, and the underlying flow structure and heat transfer physics are revealed. The results show that for an optimal transpiration cooled turbine vane design, large porosity should be applied first to the leading edge and the pressure side just downstream of the leading edge. The coolant issuing from the leading edge and the upstream pressure side convects downstream, forming an effective transpiration cooling film. The transpiration cooling film adheres well to the pressure surface, while it decays quickly on the suction surface. The temperature non-uniformity of the coolant in the plenum and the suction side endwall vortices can lead to the non-uniform surface temperature distribution along the vane height.

Numerical study of shell and tube latent thermal energy storage partially filled with metal foam and corrugated internal tube with external heat losses

In the present work, a vertical shell and tube Latent Heat Thermal Energy Storage System is analyzed. The cylinder is filled with phase change material and parts of metal foam. The inner face of the cylinder is corrugated, and it is assumed a constant temperature over the melting temperature of the paraffin wax to simulate the heat transfer. The external surface loses heat to the outside and the top and bottom surfaces are adiabatic. Paraffin wax is used as phase change material that melts over a range of temperatures and has a high latent heat of fusion. The thermal conductivity of the phase change material is low and due to this, it is enhanced with metal foam. In this numerical simulation, it is used the aluminum foam. Enthalpy-porosity theory is used to simulate the phase transition process, and the Local Thermal Equilibrium and Darcy-Forchheimer models are used to examine heat transport between the paraffin and the metal foam. Using the commercial code Ansys-Fluent, the governing equations’ solutions are calculated. In the paper, it is considered different conductivity variations on the external wall and the distinct filling ratio of metal foam. The melting time, enthalpy stored, and energy loss from the numerical simulations of the LHTESS charging phase are provided as a function of time and evaluated.

Validation of the local thermal equilibrium assumption for free convection boundary layer flow over a horizontal cylinder embedded in an infinite saturated porous medium

This study numerically investigated the validity of the local thermal equilibrium model for free convection over a horizontal cylinder embedded in an infinitely packed bed of spherical particles saturated with Newtonian fluid. The local thermal non-equilibrium and Forchhemimer-Brinkman extended Darcy model were used by considering the boundary-layer theory assumptions and were solved with the implicit Keller box finite difference scheme. The governing parameters considered are the porosity, thermal conductivity ratio, Rayleigh number, Prandtl number, the ratio of cylinder diameter to spherical particle diameter and Biot number. The results showed the two parameters of conductivity ratio and Biot number can significantly affect the other parameters. For low Biot number and conduction coefficient ratio, the local thermal non-equilibrium assumption was inapplicable in almost all cases. Significantly, for high values of the conductivity ratio and Biot number, the assumption that the fluid and solid matrix are isothermal, could be used in almost all cases studied. Furthermore, increasing the amount of Rayleigh number, Porosity and Prandtl increased the temperature difference between the solid and fluid phases. In addition, increasing the ratio of cylinder diameter to particle diameter reduced the temperature difference between the two phases. The average temperature difference between fluid and solid can have the most changes as follows: It can experience 200% growth when the Prandtl number changes from 2 to 7. Also, it can reduce by 33% by increasing the Bio number from 0.01 to 10. In addition, the temperature difference of two phases can be increased by 7 and 0.5 times by increasing the porosity from 0.25 to 0.85 and increasing the ratio of cylinder diameter to particle diameter from 20 to 100, respectively.

Numerical study on comprehensive performance of flow and heat transfer coupled with ortho-para hydrogen conversion

The energy consumption of hydrogen liquefaction can be effectively reduced by filling the plate-fin heat exchanger with the catalyst to achieve continuous conversion of ortho-para hydrogen while cooling. In this study, a three-dimensional numerical model of heat transfer and flow coupled with ortho-para hydrogen conversion is established, and the simulation results are verified by the experimental data. Both the temperature field and the outlet parahydrogen fraction demonstrate better accuracy of the local thermal non-equilibrium model results compared to the local thermal equilibrium model results, and the thermal non-equilibrium effect is most significant at the inlet of the porous medium, where the temperature difference between the fluid and the solid exceeds 2 K. Furthermore, it is indicated that two typical stages exist in the hot channel: the heat transfer dominates in the inlet section and the ortho-para hydrogen conversion efficiency decreases significantly, even once falling below 30%. In the thermal fully developed section, the catalytic performance is effectively improved along with the decay of velocity, with a 10% improvement compared to the lowest point of performance. Finally, an integrated comprehensive performance evaluation criterion is summarized regarding the overall performance of heat transfer, flow and catalysis, with excellent comprehensive performance being achieved at Reynolds numbers of 170 to 300. This research can provide a reference for the comprehensive performance study of catalyst-filled plate-fin heat exchanger for hydrogen.

Numerical investigation of natural convection in a square enclosure partially filled with horizontal layers of a porous medium

AbstractTwo‐dimensional buoyancy‐induced flow and heat transfer inside a square enclosure partially occupied by copper metallic foam subjected to a symmetric side cooling and constant heat flux bottom heating was tested numerically. Finite Element Method was employed to solve the governing partial differential equations of the flow field and the Local Thermal Equilibrium model was used for the energy equation. The system boundaries were defined as lower heated wall by constant heat flux, cooled lateral walls, and insulated top wall. The three parameters elected to conduct the study are heater length (7 ≤ ζ ≤ 20 cm), constant heat flux (150 ≤ q″ ≤ 600 W m−2), and porous material thickness (5 ≤ H ≤ 20 cm). The porous material used was the copper metal foam of porosity = 0.9 and pore density PPI = 10, and saturated with a fluid of Prandtl number = 0.7. On the basis of the results obtained, it was concluded that at the porous layer thickness = 5 cm, the rate of heat transferred was (74.6%) higher than when the layer height was 20 cm (the cavity is fully filled) and at the same thickness it was found that the heat rate is (51.4%) higher than when using the half filling (H = 10 cm). Further, the local and mean Nusselt number is maximum when using the largest heater size and smallest porous layer thickness. Finally, better circulation and convective modes were observed at high values of heat flux.

The applicability of volume-averaging method to simulate melting in a multi-scaled periodic structure

The additively manufactured multi-scaled periodic structure is considered as a thermal enhancer to accelerate melting rate of a PCM in a storage tank. Simulating this multi-phase problem can be carried out through different techniques each of which offering a unique interplay between accuracy and computational time. Full transient 3D simulations are offered as the most accurate and computationally involved benchmark case. In parallel, porous media models of the periodic structure is offered to save the computational time albeit at the expense of accuracy. Two cases of local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE) are investigated over a range of porosity for different solid matrix materials being copper, aluminium, nickel and stainless steel. To enable the use of LTE, a theoretical model for the effective thermal conductivity is developed and validated against detailed 3D results. The LTNE model, on the other hand, has to rely on an interfacial heat transfer coefficient which is developed in this study to minimize the error between simplified porous media models and the benchmark case. The LTNE model demonstrated excellent accuracy for higher thermal conductivity ratio and/or lower porosity, on the contrary, the LTE model for lower thermal conductivity ratio (stainless-steel cases) outperforms the LTNE model.

Modeling and characterizing the thermal and kinetic behavior of methane hydrate dissociation in sandy porous media

Methane hydrates (MHs) are deemed to be a potential energy source to meet the overwhelmingly growing demand for natural gas. The production of MHs involves many controlling processes such as heat transfer, fluid dynamics and hydrate reaction kinetics. Local thermal equilibrium (LTE) between solid and fluid phases was typically assumed when modeling the hydrate production, however, in many cases the local thermal non-equilibrium (LTNE) caused by the complex heat transfer processes at the pore scale cannot be neglected. In this work, a LTNE model was adopted to reflect the multiple heat transfer forms associated with hydrate dissociation and gas-liquid flow, particularly the solid-fluid interfacial convective heat transfer and the Joule-Thomson effect. The LTNE phenomenon and Joule-Thomson effect were hinted by a hydrate dissociation experiment carried out for model verification. The results show that the average estimation errors of temperature, cumulative gas and water production profiles between experiment and LTNE model were 7.70%, 6.63% and 4.02%, respectively, which are considerably better than those of the traditional LTE model (16.44%, 11.74% and 10.89%, respectively). A tenfold increase of interfacial convective heat transfer coefficient could reduce the local solid-fluid temperature difference by about 78.5%. A special focus was given to the Joule-Thomson effect which seemed to have less impact at the experimental condition in this work but become more significant when the gas saturation exceeds 40%. This work could add further insights into the thermal performance during hydrate dissociation in porous media, help to reveal the thermo-kinetic relationship at the pore scale and provide a more accurate estimation of the hydrate dissociation dynamics. It could be potentially employed to optimize the methane hydrate production strategies, minimize the risk of hydrate re-formation and maximize the overall energy recovery efficiency.