Radial Heat Conduction Research Articles

Analytical solution for transient radial interaction between energy piles and soils: Thermo-elastic cavity expansion analysis

Bearing capacity of energy piles may be affected by the Radial Interaction between Energy Piles and Soils (RIEPS) such as energy pile expansion and transient radial heat conduction. This paper proposes a cavity-expansion-based solution to investigate the thermo-elastic RIEPS. Transient temperature distributions are shown by assuming heat conduction in the radial direction and constant temperature at the pile-soil interface. With the temperature distributions, a thermo-elastic solution is obtained to capture the changes in stresses and displacements around energy piles. It is found that the solution under the combined thermal-mechanical loading pattern is the linear superposition of those under the thermal loading and mechanical loading patterns. Hence, the stresses, strains and displacements in soils are determined by the competitive relationships between thermal and mechanical loading patterns. The expression for radial stress change at the pile-soil interface is discussed by the cavity expansion analysis and comparison with field data. For typical soil and pile parameters, the expression could be quite general considering transient temperature distributions and soil/pile moduli. This paper can benefit to the capacity design of energy piles by taking the RIEPS into account.

Numerical modeling and experimental verification for anisotropic heat conduction process in velocity probe of the thermal mass flowmeter

Traditional models ignore the temperature gradients caused by anisotropic heat conduction process in the axial and radial directions of the velocity probe of a thermal mass flowmeter (TMF), essentially assuming constant wall temperature. Recently, a novel TMF with a large length–diameter ratio of the velocity probe and more evident temperature gradient was proposed; although this novel TMF is insensitive to the radial velocity profile, it leads to significant calculation errors. To reduce the error of this TMF, this study proposes a numerical model of pipeline flow heat transfer that considers the axial and radial heat conduction of the velocity probe. The velocity probe axial heat conduction numerical model is proposed, and the results of apparent thermal conductivity are verified using empirical formulas. A feedback adjustment convergence program is performed to maintain the average temperature of the velocity probe at 10 K above the temperature of the observed fluid. The simulation results showed that a temperature gradient forms in both the axial and radial directions of the velocity probe of the improved model. Moreover, the higher the flow velocity and the farther it is from its central axis, the lower the temperature. Experimental results revealed that, at a velocity rang of 1.0–7.0 m/s, the average relative error between the improved simulated results and current experimental data is 2.92 % and the maximum relative error is 10.91 %, whereas the average relative error between the traditional simulated results and original experimental data is 7.44 % and the maximum relative error is 19.45 %. Thus, the improved model better simulates the real process.

Is monolithic configuration superior to random packing in a fixed bed reactor for CLC like processes?

In light of the geometric deficiencies and diffusion constraints of conventional packed-bed reactors, the potential application of monolithic configurations in fixed-bed reactors was explored using the structure-resolved CFD approach. This work delves into how geometric features of fixed beds influence flow patterns and related transport phenomena. To assess the performance of mass transfer and heterogeneous reactions in different configurations, we conducted simulations of fixed-bed chemical looping combustion (CLC) processes, in which a simplified model of non-catalytic gas-solid reactions is implemented to reduce the computational costs. Our findings highlight the importance of face contact between reaction tube and the monolithic structure, which effectively eliminates the inherent wall effects of random packing and enhances the radial heat conduction. More uniform geometry in the monolithic configuration naturally suppresses violent interstitial channeling flow in the random packing. Notably, the honeycomb configuration demonstrates an exceptionally low pressure drop, about two orders of magnitude smaller than that of the Raschig ring packing, and the designable monolithic configurations offers the potential to further reduce the pressure drop with enlarged voidage. Open-cell foams exhibit excellent convective and radial heat transport properties, promote homogeneous flow fields, and demonstrate superior performance in conjugate transport and heterogeneous reactions.

In-situ investigation on the effects of groundwater flows around bore-hole heat exchangers

Although vertical Borehole Heat Exchangers (BHE) is a booming technology for both cooling and heating buildings, several improvements could still be proposed in the dimensioning of such systems. Nowadays, most of the dimensioning methods consider only radial conductive heat flux around BHE using a homogeneous ground thermal conductivity determined from thermal response tests (TRT) or tables. Impacts of groundwater flows on the heat refurbishment around BHE are generally not explicitely considered. 
 Many numerical or analytical studies have investigated and quantified the positive impact of groundwater flows on the performance of BHE [4]. However, those results are rarely compared and validated with in-situ temperature measurements around BHE. Such measurements require the installation of temperature sensors in the ground around BHE.
 In this work, an experimental platform composed of 4 vertical BHE drilled at depths of 85 m has been exploited. The 4 vertical BHE cross a succession of horizontal geological layers (Fig. 1). The study focuses on the heat transfers in a 30-m thick sand unconfined aquifer layer, whose 17 m are saturated. Each BHE is equipped with PT100 (installed at the extremities of the unconfined aquifer and just below the groundwater table level). Based on the expected direction of groundwater fluxes, the upstream BHE is thermally activated with a pre-determined heat injection and duration. The temperature evolution is recorded by means of PT100 sensors in the activated BHE and in the three non-activated BHEs. Groudwater velocity in the upper part of the aquifer is characterized through a non-convential tracer test [1] performed in a piezometer drilled at the center of the 4 BHE (v= 7 10-7 m/s).
 A clear impact on the groundwater flows on the temperature field in the aquifer around the activated BHE is observed. To quantify the heat transfers in the ground around the activated BHE, a methodology was developed to infer the hydro-geothermal parameters of the ground, namely the intrinsic thermal conductivity, the volumetric heat capacity and groundwater velocity and direction. From an analytical solution considering conductive, advective and dispersive heat transfers [2], the hydro-geothermal parameters of the ground are obtained by fitting the measured to the predicted temperatures evolution (Fig. 2 – Table 1). The obtained hydro-geothermal parameters demonstrate (i) a groundwater velocity in the upper part consistent with the value measured in-situ, (ii) the important role of the saturated aquifer that significantly enhances the apparent thermal conductivity of the ground and, in case of groundwater flows, induces an anisotropic propagation of the temperature plume [3](Fig.3), as well as (iii) the non-uniform groundwater flows along the saturated part of the aquifer (Table 1).

Experimental study on coupled quenching behavior in a dual-cooled annular rod channel

In this paper, a bottom reflooding experiment was performed in a single annular rod channel to investigate the coupled quench characteristics of the dual-cooled annular fuel. An indirect-heated annular rod with the axial uniform power shape was used. The asymmetric quench front propagation between the external and internal sides of the annular rod was observed. The internal cladding was quenched earlier than the external cladding, owing to heat accumulation in cylindrical shell and the blockage of the vapor flow by the grid spacers in external channel. A unique “secondary quenching” phenomenon was observed at the internal side of annular rod due to the radial heat conduction. The effects of reflooding velocity, inlet subcooling, initial cladding temperature and heating power on quenching behavior were also studied. The present study can contribute to the understanding of the coupled quenching characteristics of dual-cooled annular fuel and obtains valid data for the development of reflooding models and the validation of thermal hydraulics codes of annular fuel.

Neutronics and thermal-hydraulics coupling analysis for a small lead-based fast reactor based on the discrete ordinate nodal and parallel channel method

The full-core neutronics/thermal-hydraulics (NE/TH) coupling analysis for a small lead-based fast reactor (SLFR) was presented. The NE-to-TH coupling occurs via power distribution, whereas the TH-to-NE coupling occurs via the material cross section, which is related to the temperature distribution. In the NE module, a discrete ordinate (SN) nodal solver is implemented based on the hexagonal prism mesh. In the TH module, a parallel channel model is implemented with each hexagonal fuel assembly as a channel. The mass flow of each channel is searched according to the same pressure drop, the temperature and density of the coolant within each channel is calculated with a one-dimensional axial heat convection model, and the temperature distribution along the fuel pin is calculated with a one-dimensional radial heat conduction model. In order to update the cross section, a temperature-dependent homogenized microscopic cross-section library is prepared in advance, and based on the temperature distribution obtained from the TH calculation, the cross-section data required by the NE calculation are obtained by interpolation. The results of the NE/TH coupling analysis for SLFR indicate that the TH parameters (the maximum temperature of the fuel, cladding, and coolant and the maximum velocity of the coolant) are all within the design limits, and the TH feedback provides negative reactivity feedback (about −200 pcm) and has a fairly small effect on the power distribution (<1.0%).

Modeling smoldering ignition by an irradiation spot

Irradiation spots, such as lasers, lightning strikes, and concentrated sunlight, are common ignition sources in building and wildland fires, where smoldering is generally first ignited and then transitions to flaming. In this work, a physics-based 2-D computational model that integrates heat-and-mass transfer and heterogeneous chemistry is built to investigate the smoldering ignition of typical solid fuels using irradiation spots. Simulation results predict that, given the size of the irradiation spot, the ignition time decreases as the radiant heat flux increases. However, as the diameter of the irradiation spot decreases, the modeled minimum heat flux of smoldering ignition increases significantly, agreeing well with experiments and theoretical analysis. When the irradiation spot is smaller than 20-50 mm, assumptions of constant ignition temperature and fuel-burning flux become invalid. The commonly-used physical dimensions of thermally thin/thick fuels are not applicable for smoldering spotting ignition due to the significant radial conductive heat loss in the lateral direction. Further analyses show that the minimum irradiation of smoldering ignition increases as the fuel thickness increases, but it is insensitive to the fuel moisture content. This is the first time that a sophisticated 2-D model has been used to predict the smoldering ignition using irradiation spots, which deepens the understanding of the ignition by a remote heating source and large irradiation.

Investigation of radial heat conduction with 1D self-consistent model in helicon plasmas

A 1D radially self-consistent model in helicon plasmas has been established to investigate the influence of radial heat conduction on plasma transport and wave propagation. Two kinds of 1D radial fluid models, with and without considering heat conduction, have been developed to couple the 1D plasma–wave interaction model, and self-consistent solutions have been obtained. It is concluded that in the low magnetic field range the radial heat conduction plays a moderate role in the transport of helicon plasmas and the importance depends on the application of the helicon source. It influences the local energy balance leading to enhancement of the electron temperature in the bulk region and a decrease in plasma density. The power deposition in the plasma is mainly balanced by collisional processes and axial diffusion, whereas it is compensated by heat conduction in the bulk region and consumed near the boundary. The role of radial heat conduction in the large magnetic field regime becomes negligible and the two fluid models show consistency. The local power balance, especially near the wall, is improved when conductive heat is taken into account.

An asymptotic expansion method vs a self-similar solution for convective heat transfer in rotating cone-disk systems

This paper compares an asymptotic expansion method and a self-similar solution for modeling Couette flow and convective heat transfer in a conical gap at small conicity angles up to 4°. The cases of rotation of a cone with a stationary disk and rotation of a disk with a stationary cone are considered. The self-similar system of equations provides the best agreement with experiments compared to the asymptotic expansion method. In any case, both methods are applicable only to conicity taper angles up to 4°, while at large conicity angles, the calculation results become significantly inaccurate. Calculations also showed that, at small conicity angles, convective heat transfer can be modeled using the self-similar energy equation in the boundary-layer approximation without considering radial heat conduction. In this study, analytical solutions were also obtained for limiting cases of a stationary fluid in a gap at small conicity angles without and with allowance for radial heat conduction.

A semi-analytical solution technique for predicting circulating mud temperatures

Accurate prediction of circulating fluid temperature in wellbore is required for proper drilling operations and design of the closed-loop systems. This study involves the improvement of the traditional analytical solution based on the assumption of constant input values. The presented solutions are derived from the analytical solution of the transient radial heat conduction. Application of the superposition theorem and combination of the analytical solutions established for each segment constituting the wellbore to account for temporal and positional variations are the main features of the semi-analytical solution presented in this study. In this respect, it can be asserted that the solution is also valid for variable mud/water circulation in deviated and horizontal wells.The presented solution is validated using the pertinent results of the traditional analytical solution. The results of the semi-analytical solution for realistic wellbore design reveal the possible deviations from temperature profile corresponding to analytical solution. The temperature profile as a result of the circulation with variable rate in a designed horizontal well is examined to test the presented semi-analytical solution. The trials indicate that the semi-analytical solution which is able to be implemented with plausible computational effort can be an alternative improvement for the traditional analytical solution.

Investigation on a new scheme for the transient simulation of the research pulsed reactor

In some Research Pulsed Reactor, the homogenization region is small and its spectrum is greatly affected by the leakage, which may lead to errors by traditional computational scheme. Thus, in this paper, based upon the pointwise cross sections, we use an equivalent 1D cylinder geometry in the lattice calculation to obtain spatial homogenized micro-cross sections. The few-group cross sections are then condensed by the spectrum obtained by the whole core calculation with the equivalent R-Θ -Z model. In addition, the three-dimensional transport kinetic solver is coupled with the single channel flow model and the 1D radial heat conduction model for the fuel rod. The simulation of the two pulse transient cases of Xi’an Pulsed Reactor indicates that the results obtained by the code agree well with the experimental values and the computational cost is acceptable, which corroborates the accuracy and efficiency of the calculation scheme designed by this work.

Concerning the effect of radial thermal conductivity in a self-similar solution for rotating cone-disk systems

PurposeThus, the purposes of this study are to study the limits of applicability of the self-similar solution to the problem of fluid flow, heat and mass transfer in conical gaps with small conicity angles, to substantiate the impossibility of using a self-similar formulation of the problem in the case of large conicity angles and to substantiate the absence of the need to take into account the radial thermal conductivity in the energy equation in its self-similar formulation for the conicity angles up to 4°.Design/methodology/approachIn the present work, an in-depth and extended analysis of the features of fluid flow and heat transfer in a conical gap at small angles of conicity up to 4° is performed. The Couette-type flow arising, in this case, was modeled using a self-similar formulation of the problem. A detailed analysis of fluid flow calculations using a self-similar system of equations showed that they provide the best agreement with experiments than other known approaches. It is confirmed that the self-similar system of flow and heat transfer equations is applicable only to small angles of conicity up to 4°, whereas, at large angles of conicity, this approach becomes unreasonable and leads to significantly inaccurate results. The heat transfer process in a conical gap with small angles of conicity can be modeled using the self-similar energy equation in the boundary layer approximation. It was shown that taking into account the radial thermal conductivity in the self-similar energy equation at small conicity angles up to 4° leads to maximum deviations of the Nusselt number up to 1.5% compared with the energy equation in the boundary layer approximation without taking into account the radial thermal conductivity.FindingsIt is confirmed that the self-similar system of fluid flow equations is applicable only for small conicity angles up to 4°. The inclusion of radial thermal conductivity in the model unnecessarily complicates the mathematical formulation of the problem and at small conicity angles up to 4° leads to insignificant deviations of the Nusselt number (maximum 1.5%). Heat transfer in a conical gap with small conicity angles up to 4° can be modeled using the self-similar energy equation in the boundary layer approximation.Originality/valueThis paper investigates the question of the validity of taking into account the radial heat conduction in the energy equation.

Improvement and Validation of the System Analysis Model and Code for Heat-Pipe-Cooled Microreactor

Heat-pipe-cooled microreactors (HPMR) use a passive high-temperature alkali metal heat pipe to directly transfer the heat of solid core to the hot end of the intermediate heat exchanger or thermoelectric conversion device, thus avoiding a single point failure. To analyze and evaluate the transient safety characteristics of an HPMR system under accident conditions, such as heat pipe failure in the core or a loss of system heat sink and other accidents, a previously developed model for transient analysis of a heat-pipe-cooled space nuclear reactor power system (HPSR) was improved and validated in this study. The models improved mainly comprise: (1) An entire 2-D solid-core heat transfer model is established to analyze the accident conditions of core heat pipe failure and system heat sink loss. In this model, radial and axial Fourier heat conduction equations are used to divide the core into r-θ direction control volumes. The physical parameters of the material in the control volume are calculated according to the volume-weighted average. (2) By coupling the heat transfer limit model and the two-dimensional thermal resistance network model, the transient model of a heat pipe for HPMR system analysis is improved. (3) Conversion system models are established to simulate the system characteristics of the advanced HPMR concept, such as thermoelectric conversion, Stirling conversion, and the open Brayton conversion analysis model. Based on the improved models, the HPMR system analysis program TAPIRSD was developed, which was verified by experimental data of the separated conversion components and the ground nuclear test device KRUSTY. The maximum deviation of the power output predicted by the energy conversion model is less than 8%. The accident conditions of the KRUSTY tests, such as load change, core heat pipe failure, and heat sink loss accident, were studied by using TAPIRSD. The results show that the simulation results of the TAPIRSD code agree well with the experimental data of the KRUSTY prototype reactor. The maximum error between the TAPIRSD code prediction and the measured value of the core temperature under accident conditions is less than 10 K, and the maximum deviation is less than 2%. The results show that the developed code can predict the transient response process of the HPMR system well. At the same time, the accuracy and reliability of the improved model are proved. The TAPIRSD is suitable for system transient analysis of different types of HPMRs and provides an optional tool for the system safety characteristics analysis of HPMR.

Enhancement of thermal performance of latent thermal energy storage systems using periodically reciprocating flows

• Periodic reciprocating flow enhances radial heat conduction in PCM. • Lower sensible heat transfer and higher latent heat transfer rates are observed. • Increasing flow rate or fluid temperature increases effects of reciprocating flow. • An optimal reciprocation period maximizes effects of reciprocating flow. • Higher thermal conductivity of PCM increases effects of reciprocating flow. From the perspective of increasing heat transfer rates in latent thermal energy storage systems (LTESS), less attention has been paid to the thermodynamic characteristics at the physical boundary between phase change material (PCM) and heat transfer fluid (HTF). The current numerical study analyzes a simple method of enhancing the thermal performance of a shell and tube LTESS, wherein the flow direction of HTF is periodically reversed. The periodically reciprocating flow creates higher temperature gradients across the HTF-PCM boundary which leads to higher and more uniform heat transfer rates and thereby lower average temperatures, lower maximum temperatures, and lower temperature differences across the PCM than unidirectional flow. Detailed parametric studies are performed to understand the effects of flow and heat transfer parameters of HTF, thermophysical properties of PCM, and design of PCM container on the relative thermal efficiency of the LTESS with reciprocating flow to unidirectional flow. For certain conditions, the time required for melting could be reduced by over 11.5% by using periodically reciprocating HTF flow instead of unidirectional HTF flow. Increasing the heat transfer rate by increasing the temperature or velocity of the HTF, or enhancing thermal conductivity of PCM, increases the relative effects of reciprocating flow compared to unidirectional flow.

Measurements of the thermal conductivity of reference liquids using a modified transient hot-wire needle probe

Many power generation processes feature some type of working fluid that plays a critical role in the transfer of heat throughout the system. To optimize thermal efficiencies, an accurate characterization of the temperature-dependent thermal conductivity of the fluid is needed. This study develops a time-domain Modified Transient Hot-wire Needle Probe to overcome phenomena that have impaired traditional measurement techniques when the fluid is both corrosive and at an elevated temperature. First, the physical design of the instrument is presented to demonstrate features that limit interference from corrosion, electrical conduction, and convective and radiative heat transfer. Next, a governing equation for 1D (radial) heat conduction is fully developed using the thermal quadrupoles technique. A finite-element study is performed for validation. A sensitivity analysis is done to assess the time-dependent influence of critical parameters in the governing equation for several samples. Finally, thermal conductivity measurements are presented for seven different liquid substances by fitting the thermal model to experimental data across a range of temperatures. Reference correlations are included for comparison. The sample thermal conductivity and ambient temperature of the experimental conditions range from 0.125–16.5WmK and 10–400∘C, respectively. The total uncertainty, comprised of both the experimental design and fitting process, of all measurements is quantified.

Numerical Investigation on Turbulent Flow and Heat Transfer of Helium-Xenon Gas Mixture in a Circular Tube

Gas-cooled space nuclear reactor system usually utilizes the helium-xenon gas mixture as the working fluid. Since the typical helium-xenon mixture has the Prandtl number of about 0.2, which is lower than that of water and air, the turbulent flow and heat transfer features need to be further investigated among the helium-xenon mixture and other fluids. In the current paper, numerical investigations by ANSYS Fluent are performed on helium-xenon mixture flow (HeXe40, M = 40.0 g/mol, Pr = 0.21), airflow (Pr = 0.71), and water flow (Pr = 6.99) in the circular tube. Direct numerical simulation results of liquid metal flow (Pr = 0.01) are also adopted for comparison. Results show that the dimensionless velocity profile and shear stress in the boundary layer of HeXe40 are close to those of other fluids. The empirical correlations from other fluids can also predict well the friction factor of helium-xenon mixtures. Due to the discrepancy in turbulent heat diffusivity ratio, the dimensionless radial temperature profile and turbulent heat conduction of HeXe40 significantly differ from those of other fluids. The molecular conduction region of HeXe40 develops up to y+ ≈ 30 and extends to the logarithmic region of the flow boundary layer. Moreover, the available experimental Nusselt numbers of helium-xenon mixtures are compared with several convective heat transfer correlations, in which Kays correlation is better.

A MULTIPHYSICS SIMULATION SUITE FOR SODIUM COOLED FAST REACTORS

A simulation suite has been developed to model reactor power distribution and multiphysics feedback effects in Sodium-cooled Fast Reactors (SFRs). This suite is based on the Finite Element Method (FEM) and employs a general, unstructured mesh to solve the Simplified P3 (SP3) neutron transport equations. In the FEM implementation, two-dimensional triangular elements and three-dimensional wedge elements are selected. Wedge elements are selected for their natural description of hexagonal geometry common to fast reactors. Thermal feedback effects within fast reactors are modeled within the simulation suite. A thermal hydraulic model is developed, modeling both axial heat convection and radial heat conduction within fuel assemblies. A thermal expansion model is included and is demonstrated to significantly affect reactivity. This simulation suite has been employed to model the Advanced Burner Reactor (ABR) benchmark, specifically the MET-1000. It has been demonstrated that these models sufficiently describe the multiphysics feedback phenomena and can be used to estimate multiphysics reactivity feedback coefficients.

Numerical reconstruction of a non-smooth heat flux in the inverse radial heat conduction problem

When gun barrels are multiple fired, monitoring the non-smooth heat flux of the gun with the additional input data makes it possible to identify the corrosion of the gun. Based on this background, we study the identification of the non-smooth heat flux in a 1-dimensional heat transfer system. Aiming to overcome the non-smoothness of the unknown heat flux and to simplify the choice of regularization parameter, we transform the inverse problem to a constraint optimization problem and prove the existence and convergence properties of the regularization solution. Then an algorithm based on minimizing the data-match term and penalty term alternatively is proposed. Finally, a numerical experiment supports our regularization scheme quantitatively, especially for input data with high noise level.

Effect of Operating and Geometrical Parameters on Ammonia Decomposition in a Tubular Reactor Driven by Concentrating Solar Power

Following the massive consumption of traditional fossil fuels, the technology of concentrating solar power embedded with energy storage is becoming more and more attractive. Within this new trend, ammonia-based thermochemical energy storage is prospectively promising. The aim of this study is to simulate the ammonia decomposition reaction in a tubular reactor fully packed with homogeneously isotropic catalyst particles. Ignoring the radial heat conduction and pressure drop, a one-dimensional thermodynamic mathematical model is established to simulate ammonia conversion accounting for operating pressure and temperature, solar flux distribution, and geometric structure. It is concluded from the simulation results that the effect of the operating temperature on ammonia conversion is more predominant than the effect of the operating pressure. Furthermore, for the four styles of solar flux distribution, the distribution with the lowest effective deviation is the most suitable style for ammonia decomposition, and the efficiency is improved about 15% compared with σ=0.5. Regarding the geometric structure, the conversion rate progressively increases with diameter and length of the tubular reactor, and an optimization formula is subsequently proposed for geometric design. Ultimately, the design and optimization criterion for the tubular reactor are presented.

Thermal energy storage in embankments: Investigation of the thermal properties of an unsaturated compacted soil

Thermal energy storage in compacted soils can be considered as a new economically efficient and environmentally friendly technology in geotechnical engineering. Compacted soils are usually unsaturated; therefore, reliable estimates and measurements of their thermal properties are important in the efficiency analysis of these structures. In this study, a method is used to estimate the thermal properties of an unsaturated compacted soil. Several temperature sensors were placed in a thermo-regulated metric scale container to monitor the imposed temperature variation in the range of the 20 to 50 °C. This imposed temperature variation reproduced the temperature variation in the thermal energy storages. An inverse analytical model based on a one-dimensional radial heat conduction equation is used to estimate the thermal diffusivity using the temperature variation between two temperature sensors. The volumetric heat capacity was measured using a calorimeter in the laboratory, enabling the estimation of the thermal conductivity of the compacted soil. Then, this estimated thermal conductivity was compared with the thermal conductivity values measured with two other methods (steady-state and transient-state method). The difference between them are discussed in terms of the sample heterogeneity, sample size, and measurement method.