Thermal Non-equilibrium Effects Research Articles

Multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media under local thermal non-equilibrium condition

In this work, a thermal multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for simulating convection heat transfer in porous media under local thermal non-equilibrium (LTNE) condition. In the present model, the thermal non-equilibrium effects are incorporated into the model by adding source terms into the temperature-based MRT-LB equations. The discrete effects of the source terms are eliminated, and the temperatures of the fluid and solid phases are obtained through algebraic operations. Moreover, the error term which exists in the macroscopic temperature equation of the fluid phase is eliminated via a way that is consistent with the philosophy of the LB method. Numerical simulations show that thermal non-equilibrium natural convection problems can be well simulated.

Nanofluid convection under Hall currents and LTNE effects

The nanofluid instability is studied under Hall currents and local thermal non-equilibrium (LTNE) effects. A mathematical approach is used to examine the problem in which nanoparticles, pressure and temperature are taken to be variable in vertical direction at the primary state. Very small amount of nanoparticles (volume fraction < 0.05) of size 1–100 nm are suspended in the fluid using either surfactant or surface charge technology which prevents the agglomeration of the particles and it is assumed that no chemical reaction takes place. The additional factors due to Hall currents and LTNE are introduced in the process of non-dimensionalization of conservation equations which influence the onset of convection significantly. The influence of different parameters is studied using normal modes and analyzed graphically using the software Mathematica for permissible range of values of various nanofluid parameters. The thermal lagging within the fluid and particle results in quickening the convection in the layer. Unlike LTE model, critical wave number gets influenced appreciably with the presence of nanoparticles through LTNE parameters.

Thermal transport in microchannels partially filled with micro-porous media involving flow inertia, flow/thermal slips, thermal non-equilibrium and thermal asymmetry

The theoretical investigation of the fully-developed forced convection heat transfer in a microchannel partially filled with a porous medium core is performed by considering the local thermal non-equilibrium (LTNE) effect between the solid and fluid phases. The two walls sandwiching the channel are exposed to the boundary conditions of the thermal asymmetry. The flexible porous medium core is not connected to the boundary walls. Influences of the flow inertia in the porous medium region, the velocity jumps at the porous/fluid interfaces, and the flow and thermal slips at the solid-fluid interfaces are involved. A set of exact solutions is derived for the flow and heat transfer in the porous medium region and the fluid region. The flow heterogeneity coefficient for the nonuniform distribution of the fluid flow is especially considered, and the relationship between the flow heterogeneity and the thermal performance is discussed. The effects of some basic factors on the temperature distribution and the Nusselt numbers of the two walls are analyzed. The present benchmark solution is useful for improving the numerical scheme accuracy and validating similar researches.

LTNE effects on a nanofluid layer heated and soluted from below embedded by Darcy medium

Thermosolutal convection of a nanofluid layer which is heated underneath with local thermal non-equilibrium (LTNE) effects is investigated by applying one term Galerkin approach and Darcy model. A three-temperature model is applied for considering the impact of LTNE along with Brownian motion and thermophoretic effects to account for nanoparticles. With the addition of LTNE model embedded by porous medium four non-dimensional parameters have come into existence whereas due to the presence of solute two more parameters came into picture. Numerical computations are carried out with software Mathematica and it is observed that the destabilizing influence of nanoparticles is balanced with the stabilizing effect of solute to a large extent. Further effect of solute is to enhance the stability where as there is no significant variation in thermal Rayleigh number due to LTNE effects.

Experimental investigation of thermal retardation and local thermal non-equilibrium effects on heat transport in highly permeable, porous aquifers

Actively stimulated temperature changes are common in many groundwater applications. A widely used concept to determine water fluxes, mean transit times, and other parameters from heat tracer tests is the use of the thermal retardation factor. Different methods are available to determine the thermal velocity from thermal breakthrough curves (BTCs) depending on the input signal. This study systematically compares these methods and investigates possible local thermal non-equilibrium effects (LTNE) in coupled solute and heat tracer experiments for highly permeable, porous aquifers. One-dimensional column experiments with saturated gravel of grain size 7–15 mm are conducted to compare the measured, effective thermal retardation with the computed thermal retardation predicted by the apparent thermal retardation factor. The results demonstrate that for scenarios with a step input of the heat tracer, the effective thermal retardation for thermal velocities derived by an analytical model, and the mean between injection temperature and initial temperature, can be predicted by the apparent thermal retardation factor. This indicates that possible LTNE effects do not significantly influence the derived velocities within the investigated range of seepage velocity between 5 and 50 md−1. Other methods showed constant deviation from the apparent retardation factor at higher seepage velocities. In scenarios with a finite duration pulse input of the heat tracer, the effective retardation derived by the peak velocity showed deviations from the apparent retardation up to 35% at seepage velocities lower than 10 m d−1. At higher seepage velocities, the peak velocity could be predicted by the apparent retardation factor.

Thermal Performance of a PCM-Based Thermal Energy Storage with Metal Foam Enhancement

The energy transport inside a phase change material (PCM) based thermal energy storage system using metal foam as an enhancement technique is investigated numerically. The paraffin is used as the PCM and water as the heat transfer fluid (HTF). The transient heat transfer during the charging and discharging processes is solved, based on the volume averaged conservation equations. The flow in PCM/foam and HTF/foam composites is modelled by the Forchheimer-extended Darcy equation, while the two-temperature model is employed to account for the local thermal non-equilibrium effect between the foam matrix and fluid phase. The results show that the overall performance is greatly improved by inserting metal foam in both HTF and PCM sides. A nearly 84.9% decrease in the time needed for the total process is found compared with the case of pure PCM, and 40% compared with the case of metal foam insert only in the PCM side. Foam porosity and HTF inlet temperature greatly affect the dynamic heat storage/release process.

Numerical modelling of flashing flow phase change in convergent-divergent nozzle: A sensitivity analysis

A sensitivity analysis of a computational fluid dynamics (CFD) model of flashing flow phenomenon including the thermal non-equilibrium effect is proposed in the present paper. The model uses a two-phase mixture approach and the phase-change process is based on the difference between the vaporization pressure and the vapour partial pressure. Thermal non-equilibrium effect is included in the model by a sub-routine for the boiling delay. A two-dimensional axisymmetric convergent-divergent nozzle is used as benchmark for the proposed study. Such geometry is representative of well-known applications in nuclear, refrigeration and energy engineering (e.g., primary flow in the motive nozzle of ejectors). The results are compared to experimental data and previous numerical results available in literature. Present results show good agreement with global and local experimental fluid dynamic quantities used to validate the model. The paper includes in the first part a brief description of physical phenomenon of flashing flow, the experimental benchmark geometry and operating conditions. In the second part, the physical model and the numerical modeling approach are reported, showing the validation and the results related to the sensitivity analyses of the artificial coefficients characterizing the modelling approach.

Conjugate local thermal non-equilibrium heat transfer in a cavity filled with a porous medium: Analysis of the element location

The problem of conjugate natural convection heat transfer in a cavity filled with a porous medium is addressed by considering the local thermal non-equilibrium effects. The thickness of the solid walls of the cavity is taken into account, and the vertical walls are assumed to be partially active. The effect of the heat transfer bifurcation in the interface of the solid walls and the porous medium is also taken into account. The governing equations for the heat and momentum of the fluid in the porous space, heat transfer in the porous matrix, and heat transfer in the solid walls are represented in the form of partial differential equations. The governing equations along with the corresponding boundary conditions are transformed into a generalized form of the non-dimensional equations and solved by the finite element method. Considering various values of the non-dimensional parameters, the effect of the location of the active walls on the flow patterns and the local and overall heat transfer are addressed. The results demonstrate that the location of the active walls can significantly affect the streamlines and the fluid isotherm contours in the porous space and the isotherms in the solid walls. Moreover, it is found that in most of the cases the highest total rate of heat transfer corresponds to the case in which the elements are in the center of the active wells. In contrast, the lowest total rate of the heat transfer corresponds to a case, in which the active hot element is at the top of the wall, and the cold element is at the bottom.

Thermal Non-Equilibrium Heat Transfer Modeling of Hybrid Nanofluids in a Structure Composed of the Layers of Solid and Porous Media and Free Nanofluids

The free convection heat transfer of hybrid nanofluids in a cavity space composed of a clear flow, porous medium and a solid part is addressed. The cavity is heated from the bottom and cooled from the top. The side walls are well insulated. The upper part of the cavity is a clear space with no porous or solid materials and is filled with hybrid nanofluid. The bottom part is divided into two parts of a porous space saturated with the hybrid nanofluid and a solid thermal conductive block. There are conjugate heat transfer mechanisms between the solid block and the porous medium filled with the hybrid nanofluid as well as the hybrid nanofluid in the clear space. For the porous medium model, the local thermal non-equilibrium effects are considered. The hybrid nanofluids contain copper (20 nm) and alumina nanoparticles (40 nm) hybrid nanoparticles. The governing equations for the flow and heat transfer of the hybrid nanofluid in the clear space and the porous medium are introduced. Considering the conjugate heat transfer between the solid block and the hybrid nanofluid fluid in the pores and the porous matrix, appropriate boundary conditions for heat channeling are utilized. The governing equations are transformed into non-dimensional form to generalize the model. The finite element method is employed to solve the equations. The grid check and validation procedure are performed. Subsequently streamlines, isotherms, and Nusselt number are studied as important aspects of flow and heat transfer in the cavity. The increase in the portion of the clear flow part in the cavity enhances heat transfer due to better hybrid nanofluid circulation.

Infrared radiation characteristics of a hypersonic vehicle under time-varying angles of attack

Hypersonic vehicles emit strong infrared (IR) radiation signatures that can be treated as a detecting source for object identification and routine diagnosis. This paper is aimed at examining the intrinsic radiation characteristics of a Boost-Glide Vehicle (BGV) under the condition of various Angles of Attack (AOAs). A two-temperature model considering the thermal and chemical non-equilibrium effects is coupled with Navier-Stokes equations solved by the finite volume technique. A gas–solid conjunction heat transfer model is also added into the fluid solver to simulate the surface temperature of the vehicle. The radiative transfer equation is solved with Line of Sight (LOS) algorithm. The computational results for a Hypersonic Technology Vehicle-2 (HTV-2) type vehicle show that radiances of the vehicle are strongly dependent on the surface temperature. The presence of AOA results in the significant difference of the surface temperature. Infrared radiation characteristics are also changed in intensity and spectral band due to the AOA. Simulations are performed with two time-varying AOAs. Transient results indicate that the variation of AOA does have a great effect on the infrared radiance and is closely related to observation angle, spectral band, angle size, angular velocity and time history.

High temperature and thermal non-equilibrium effects on the determination of free-stream flow properties in hypersonic wind tunnels

Various methodologies used to derive free-stream conditions in hypersonic wind tunnels using different sets of experimental inputs are reviewed. The accuracy of a relevant but seldom used approach, involving free-stream static pressure measurements, is improved in the present work by solving numerically shock conservation equations and by accounting for the high-temperature effects typically expected in hypersonic flows (vibrational excitation, dissociation, and ionization). The numerical method implemented is also extended to handle free-stream thermal non-equilibrium provided that free-stream vibrational temperature measurements are available. The performances of the present approach are evaluated against conventional methods by determining free-stream flow properties in the von Karman Institute Longshot hypersonic wind tunnel. Uncertainties are quantified for each of the derived free-stream flow conditions. It is demonstrated that methodologies limited to Pitot pressure diagnostics in the test section fail to detect departures from ideal nozzle flow expansions, due to their inherent isentropic flow assumptions. Involving free-stream static pressure diagnostics does, however, improve the results, as validated by independent investigations. It is shown that the non-ideal nozzle flow expansion is not induced by free-stream thermal non-equilibrium since this phenomenon leads to opposite trends on free-stream flow properties with respect to those observed. Overall, free-stream static pressure probes represent a useful complement and their benefits for free-stream rebuilding methodologies are emphasized. The present free-stream rebuilding methodology is recommended to enhance the relevance of every hypersonic ground experiment.

Charged Species Concentration in Combusting Mixtures Using Equilibrium Chemistry

Ionization in flames is of interest in the design and development of modern combustion devices. The identity and concentration of various charged species in reacting mixtures can play an important role in the diagnostics and control of such devices. Simplified chemistry computations that provide good estimates of ionic species in complex flow-fields can be used to model turbulent reacting flows in various combustion devices, greatly reducing the required computational resources for design and development studies. A critical assessment of the use of the equilibrium chemistry method to compute charged species concentration in combusting mixtures under various temperatures, pressures, and thermal disequilibrium conditions is presented. The use of equilibrium chemistry to compute charged species concentrations in propane-air mixtures performed by Calcote and King has been extended. A more accurate computational methodology that includes the effect of negative ions, chemi-ions (H3O+ and CHO+), and thermal nonequilibrium was investigated to evaluate the suitability of equilibrium computations for estimating charged species concentrations in reacting mixtures. The results show that equilibrium computations which include the effects of H3O+ and elevated electron temperatures can indeed explain the levels of ion concentrations observed in laboratory flame experiments under lean and near-stoichiometric conditions. Furthermore, under engine-like conditions at higher temperatures and pressures, equilibrium computations can be used to obtain useful estimates of charged species concentrations in modern combustion devices.

Continuum Simulations of Hypersonic Flows in Chemical and Thermal Nonequilibrium

The ability of the Navier–Stokes equations to capture the effects of strong chemical and thermal nonequilibrium on gas composition in a manner similar to the direct simulation Monte Carlo (DSMC) method is tested with the introduction of a nonequilibrium chemistry model. Although this chemistry model has the ability to reasonably reproduce measured Arrhenius rates in conditions of thermal equilibrium, it results in reaction rates that vary significantly for the most commonly used Arrhenius rates in conditions of thermal nonequilibrium. The nonequilibrium chemistry model is implemented in the three-temperature Navier–Stokes computational fluid dynamics (CFD) solver, Data-Parallel Line Relaxation (DPLR), and tested on high-altitude, hypersonic flow conditions. The results of the simulations show that the model predicts a greater amount of NO compared with previous Navier–Stokes using nonequilibrium quasi-classical trajectory derived rates and remains consistent with DSMC computations over altitudes ranging from 53.5 to 87.5 km. The most commonly used chemistry model for Navier–Stokes solvers was found unable to match this performance, indicating the importance of including nonequilibrium effects when modeling chemically reacting hypersonic flowfields.

Nano-encapsulated phase change material slurry (Nano-PCMS) saturated in metal foam: A new stable and efficient strategy for passive thermal management

Nano-encapsulated phase change material slurry (nano-PCMS) has the merits of high latent heat and high surface area, and overcomes the defects of supercooling and volume expansion that exist in most organic/inorganic PCMs. Subjected to the low thermal conductivity, the thermal management systems using nano-PCMS are highly dependent on slurry's convection coefficient, which cannot be guaranteed in the condition where the natural convection is constrained. Here, this article proposed a novel thermally stable and efficient hybrid PCM that infiltrating nano-PCMS into metal foam for passive thermal management. The experimental results indicated that the addition of metal foam could reduce the heated surface temperature by maximum 38% in regardless of heated angle, while this contribution was 24% achieved by natural convection of pristine nano-PCMS. The flow convection of nano-PCMS was completely suppressed in the foam cells due to the high viscosity of slurry and flow resistance of foam matrix. Higher porosity composite obtained lower heat transfer efficiency and more pronounced thermal non-equilibrium effect attributed to its lower effective thermal conductivity and less interfacial area. This newly-proposed foam/nano-PCMS composite not only provides high heat transfer efficiency, but reduces the dependency on the convection coefficient of nano-PCMS.

Pore-scale visualization and measurement of paraffin solidification in high porosity open-cell copper foam

In this work, a pore-scale experimental investigation on solidification of paraffin in high porosity open-cell copper foam is performed based on the visualization and measurement technique. With the use of high definition camera and infrared camera, the phase and temperature fields of the copper foam/paraffin sample are obtained to directly visualize the solidification process. Simultaneously, T-type thermocouples are employed to measure the local thermal response characteristic and thermal non-equilibrium effect of the copper foam/paraffin sample. For comparison, the corresponding solidification experiment with pure paraffin sample is also conducted. Local details of solidification phase change including the evolution of phase change interface within foam pore region, the liquid phase flow and air gap formation due to the volume shrinkage effect of paraffin are revealed. It is found that the highly conductive copper foam remarkably extends the phase change interface, avoids the formation of overlarge-size air gap that forms in the pure paraffin sample and enables a higher thermal response rate of the copper foam/paraffin sample. As a result, an attractive solidification enhancement (about 2.8 times) of paraffin in copper foam is achieved. Moreover, strong effect of local thermal non-equilibrium between copper foam and paraffin is detected during the solidification process. Finally, through generalizing the present experimental results, a correlation for dimensionless solidification time of the copper foam/paraffin sample is developed at pore scale.

Numerical investigation of local thermal non-equilibrium effects in coal porous media with cryogenic nitrogen injection

The technology of fire prevention and extinguishing using liquid nitrogen or cryogenic nitrogen has been widely applied in underground coal fire. In this paper, a multi-scale model has been proposed to investigate the complex heat transfer characteristics in coal porous media (CPM) with cryogenic nitrogen injection. In the model, the fluid energy equation at representative elementary volume (REV) scale is coupled with the heat conduction equation of a solid particle at pore scale considering the temperature variation in the coal particle, and the equivalent diameter is employed to simplify the heat conduction process in the solid particle. The experiment has been carried out and the result is consistent with the simulation obtained by the multi-scale model. The influences of equivalent diameter, mass flow rate, inlet fluid temperature and initial temperature on the local thermal non-equilibrium (LTNE) effects have been investigated numerically by using the multi-scale model. The results show that the time to reach local thermal equilibrium (LTE) between fluid and solid center is longer due to the small thermal conductivity of coal matrix, and it is affected dramatically by equivalent diameter and mass flow rate. The results also indicate that the inlet fluid temperature and initial temperature of CPM have important influence on the temperature difference between solid center and fluid.

Modeling and Simulation of Local Thermal Non-equilibrium Effects in Porous Media with Small Thermal Conductivity

The two-equation model in porous media can describe the local thermal non-equilibrium (LTNE) effects between fluid and solid at REV scale, with the temperature differences in a solid particle neglected. A multi-scale model has been proposed in this study. In the model, the temperature differences in a solid particle are considered by the coupling of the fluid energy equation at REV scale with the heat conduction equation of a solid particle at pore scale. The experiments were conducted to verify the model and numerical strategy. The multi-scale model is more suitable than the two-equation model to predict the LTNE effects in porous media with small thermal conductivity. The effects of particle diameter, mass flow rate, and solid material on the LTNE effects have been investigated numerically when cryogenic nitrogen flows through the porous bed with small thermal conductivity. The results indicate that the temperature difference between solid center and fluid has the same trend at different particle diameters and mass flow rates, while the time to reach the local thermal equilibrium is affected by solid diameter dramatically. The results also show that the temperature difference between solid center and surface is much greater than that between solid surface and fluid. The values of $$ \rho {\text{c}} $$ for different materials have important influence on the time to reach the local thermal equilibrium between solid and fluid.

Non-equilibrium 3-D simulator applied to air injection EOR in light oil reservoirs

In this paper, a 3-D simulator based on the assumption of both chemical and thermal non-equilibrium is presented for a more realistic view of non-equilibrium process for simulating air injection EOR (enhanced oil recovery). The mathematical model is based on a non-equilibrium stage with dynamic mass transfer process between different fluid phases and energy transfer process between fluid and matrix (solid). The light crude oil oxidation and air injection process are both simulated by this simulator, through which the pore blocking, gas breakthrough and gas override process are presented through the visualization of oil, gas saturation distributions. The crude oil oxidation is refined as in-phase and interphase reactions to investigate the effect of reactant dispersion caused by the gas-liquid mass transfer. The oxygen dissolution and the evaporation of light components in crude oil are considered in the non-equilibrium process. The results without mass transfer, with dynamic mass transfer and with instantaneous mass transfer between gas and liquid phases are compared through multiplying the gas-liquid interface area 0, 1 and 100 times respectively, and the influence of these different mass transfer conditions on the migration of temperature peak front and oil recovery is revealed. In addition, the effect of local chemical and thermal non-equilibrium in different matrix permeability as well as porosity scenarios is also investigated to obtain non-equilibrium behavior in different reservoir conditions when implementing air injection EOR. In the last section, we investigated the result with different simulation timescale to see if the non-equilibrium behavior can be captured in the simulator used in this paper. This study suggests that the non-equilibrium behavior would show obvious influence on oil recovery for air injection in the lower permeability reservoir. The non-equilibrium behavior is desirable to be considered for simulating air injection EOR in light oil reservoirs. The developed 3-D simulator is robust that can better reflect the mechanism of air injection EOR in light oil reservoirs. We hope this work encouraging more investigations for the simulation side of non-equilibrium phase behavior and energy transfer in the air injection process.

Thermal non-equilibrium effect of small-scale structures in compressible turbulence

The thermal non-equilibrium effect of the small-scale structures in the canonical two-dimensional turbulence is studied. Comparative studies of Unified Gas Kinetic Scheme (UGKS) and GKS-Navier–Stokes (NS) for Taylor–Green flow with initial Ma = 1, Kn = 0.01 and decaying isotropic turbulence with initial [Formula: see text], [Formula: see text] show that the discrepancy exists both in small and large scales, even beyond the dissipation range to 10[Formula: see text] with accuracy to 8% in the SGS energy transfer of the decaying isotropic turbulence, illustrating the necessity for resolving the kinetic scales even at moderated [Formula: see text].

Computational Fluid Dynamics Modeling of Flashing Flow in Convergent-Divergent Nozzle

In this paper, a computational fluid dynamics model of flashing flow, which considers the thermal nonequilibrium effect, has been proposed. In the proposed model, based on the two-phase mixture approach, the phase-change process depends on the difference between the vaporization pressure and the vapor partial pressure. The thermal nonequilibrium effect has been included by using ad hoc modeling of the boiling delay. The proposed model has been applied to the case of two-dimensional axisymmetric convergent-divergent nozzle, which is representative of well-known applications in nuclear and energy engineering applications (e.g., the primary flow in the motive nozzle of ejectors). The numerical results have been validated based on a benchmark case from the literature and have been compared with the numerical results previously obtained by different research groups. The proposed approach has shown a good level of agreement as regards the global and the local experimental fluid dynamic quantities. In addition, sensitivity analyses have been carried out concerning (a) grid independency, (b) turbulence modeling approaches, (c) near-wall treatment approaches, (d) turbulence inlet parameters, and (e) semi-empirical coefficients. In conclusion, the present paper aims to provide guidelines for the simulation of flash boiling flow in industrial applications.