Linear Heat Source Research Articles

Study on the influence of the identification model on the accuracy of the thermal response test

A 3-D numerical heat transfer model of a ground-source heat pump thermal response test is established in this paper and verified by testing. The numerical model is used to simulate the thermal response test. The soil thermo-physical parameters are estimated based on the cylindrical heat source and the linear heat source theory and contrasted with the values setting in the numerical heat transfer model. The effect of the identification model of the in-situ thermal response on the accuracy of the identification results is studied under different soil thermal properties. The results show that there is an optimal time to identify the soil thermo-physical parameters based on the two models. Identifying the physical parameters at the non-optimal time points will produce a large error. Under the same conditions, the optimal identification time of the cylindrical heat source model is earlier than that of the linear heat source model and is also related to the soil physical properties. Therefore, the test time should be selected to ensure the accuracy of the results. Furthermore, there is no evident influence of the initial soil temperature on the identification accuracy of the two models. This paper offers a reference for improving the thermal response test of ground source heat pumps.

Mathematical modelling of thermal and flow processes in vertical ground heat exchangers

Abstract The main task of mathematical modelling of thermal and flow processes in vertical ground heat exchanger (BHE-Borehole Heat Exchanger) is to determine the unit of borehole depth heat flux obtainable or transferred during the operation of the installation. This assignment is indirectly associated with finding the circulating fluid temperature flowing out from the U-tube at a given inlet temperature of fluid in respect to other operational parameters of the installation. The paper presents a model of thermal and flow processes in BHE consisting of two analytical models separately-handling processes occurring inside and outside of borehole. A quasi-three-dimensional model formulated by Zeng was used for modelling processes taking place inside the borehole and allowing to determine the temperature of the fluid in the U-tube along the axis of BHE. For modelling processes occurring outside the borehole a model that uses the theory of linear heat source was selected. The coupling parameters for the models are the temperature of the sealing material on the outer wall of the borehole and the average heat flow rate in BHE. Experimental verification of the proposed model was shown in relation to BHE cooperating with a heat pump in real conditions.

Utilization of the Horner plot for determining the temperature of frozen formations — A novel approach

The most important data on the thermal regime of the Earth’s interior come from temperature measurements in deep boreholes. The drilling process greatly alters the temperature field of formations surrounding the wellbore. In permafrost regions, due to thawing of the formation surrounding the wellbore during drilling, representative data can be obtained only by repeated observations over a long period of time (up to 10 years). Usually a number of temperature logs (3–10) are taken after the well's shut-in. Significant expenses are required to monitor the temperature regime of deep wells. In this paper, we introduce a new approach in predicting the undisturbed formations temperatures from shut-in temperature logs in deep wells. The main features of the suggested method are following: the refreezing of the thawed formations (around the wellbore) is completed, the temperature logs are taken after refreezing, the starting point in the well thermal recovery is moved from the end of well completion to the moment of time when the first shut-in temperature log was conducted. It is shown that after refreezing the further cooling of a well can be approximated by a constant (per unit of length) linear heat source. Hence, the Horner equation can be used for predicting the temperature of frozen formations for estimation of the formation temperature. A simple method to process field temperature data is presented. To demonstrate this approach, temperature shut-in time data for four depths from four wells in Alaska were successfully used.

Transient forced convection from an infinite cylindrical heat source in a saturated Darcian porous medium

This paper deals with the problem of an infinite cylindrical heat source embedded into a saturated porous medium and subject to a cross-axial Darcian flow. Only forced convection is considered. We derived the transient dimensionless solution through a combined analytical – numerical method consisting of four steps: (a) a preliminary dimensional analysis of the constitutive equations of the problem in order to find the dimensionless groups governing the solution; (b) the identification of the validity range of the model as a function of the just-mentioned dimensionless groups; (c) the numerical resolution of the problem; (d) the synthesis of the numerical results in a general dimensionless form. Specifically, we provide several dimensionless maps of the 2D thermal field evolution for six different orders of magnitude of the Péclet number (10-3–102). The evolution of the temperature of the heat source is fully illustrated and discussed through plain dimensionless criteria. Then, we discuss the time, space and fluid velocity scales in which the solution is practically equivalent to the ones given by a linear heat source and a purely conductive model. We conclude that the present model has to be employed to evaluate the temperature in proximity of the heat source when the reference Péclet number is greater than 0.5. On the contrary, the linear model can be successfully used for radial distances 5–10 times greater that the heat source radius, depending on the reference Péclet number.

Finite element code FENIA verification and application for 3D modelling of thermal state of radioactive waste deep geological repository

The verification of the FENIA finite element code on some problems and an example of its application are presented in the paper. The code is being developing for 3D modelling of thermal, mechanical and hydrodynamical (THM) problems related to the functioning of deep geological repositories. Verification of the code for two analytical problems has been performed. The first one is point heat source with exponential heat decrease, the second one - linear heat source with similar behavior. Analytical solutions have been obtained by the authors. The problems have been chosen because they reflect the processes influencing the thermal state of deep geological repository of radioactive waste. Verification was performed for several meshes with different resolution. Good convergence between analytical and numerical solutions was achieved. The application of the FENIA code is illustrated by 3D modelling of thermal state of a prototypic deep geological repository of radioactive waste. The repository is designed for disposal of radioactive waste in a rock at depth of several hundred meters with no intention of later retrieval. Vitrified radioactive waste is placed in the containers, which are placed in vertical boreholes. The residual decay heat of radioactive waste leads to containers, engineered safety barriers and host rock heating. Maximum temperatures and corresponding times of their establishment have been determined.

Optimization of Measurements of the Thermophysical Parameters of Heat-Insulating Materials by Means of a Linear Pulse Heat Source

Optimization of Measurements of the Thermophysical Parameters of Heat-Insulating Materials by Means of a Linear Pulse Heat Source

The Simulation of Temperature Field in Induction Welding of Composite Aluminum Alloy Thin-Walled Tube

Welding temperature is the main factor that influences the welding quality in the high frequency induction welding of composite aluminum alloy thin-walled tubes. The finite element analysis software ANSYS was used to simulate the temperature field. One complete penetration of thin-walled tube and boundary conditions of convection and radiation as well as latent heat phase change were taken into account. Then a linear heat source is used to load and calculate the temperature distribution and to draw thermal cycle curves of welding process. Research results of the temperature filed also provided the corresponding basis for further analysis of welding stress and strain.

A Research on Seepage Detection Technology of Water Storage Dam in Secondary Disaster Prevention of Water Resources

Dam leakage is an important aspect of secondary disaster of water resources. The heat transfer theory is used for the quantitative analysis of the abstract linear heat source model, which determines the flow rate of water leakage. Based on the abstract model of dam seepage, we use the thermal fluid knowledge to analyze and solve the key parameters. Based on the measured data, the model quantitatively calculates the water velocity and radius of seepage channel. Compared with the measured flow velocity of drill channel, the two conclusions basically proves the accuracy and validity of the method.

Dimensionless Maps for the Validity of Analytical Ground Heat Transfer Models for GSHP Applications

This article provides plain and handy expressions to decide the most suitable analytical model for the thermal analysis of the ground source in vertical ground-coupled heat pump applications. We perform a comprehensive dimensionless analysis of the reciprocal deviation among the classical infinite, finite, linear and cylindrical heat source models in purely conductive media. Besides, we complete the framework of possible boreholes model with the “hollow” finite cylindrical heat source solution, still lacking in the literature. Analytical expressions are effective tools for both design and performance assessment: they are able to provide practical and general indications on the thermal behavior of the ground with an advantageous tradeoff between calculation efforts and solution accuracy. This notwithstanding, their applicability to any specific case is always subjected to the coherence of the model assumptions, also in terms of length and time scales, with the specific case of interest. We propose several dimensionless criteria to evaluate when one model is practically equivalent to another one and handy maps that can be used for both design and performance analysis. Finally, we found that the finite line source represents the most suitable model for borehole heat exchangers (BHEs), as it is applicable to a wide range of space and time scales, practically providing the same results of more complex models.

Thermophysical method for quantitative estimation of hydrate content in samples imitating bottom sediments

Gas hydrates in sediments can dissociate on heating, which causes a characteristic change in temperature over time. This can be used to detect hydrates and estimate their content. The geothermal method for gas hydrate prospecting consists in obtaining thermograms and defining regularities related to the presence of gas hydrates in the medium. The aim of this study was a quantitative estimation of hydrate content in sediments, based on data from repeated measurements of the temperature of a linear heat source (needle probe). The power of the source is chosen so that hydrate does not decompose in the first measurement but decomposes in the second. Afterward, we solve the optimization inverse problem of determination of the model parameters, one of which is a hydrate content. Experimental data on heating of the laboratory samples are processed, and hydrate contents are obtained with an accuracy of 30%. These values agree with independent estimates. The analytical solution of the axially symmetric problem of gas hydrate dissociation, based on the solution of the Stefan problem, is applied as a mathematical model for hydrate heating and decomposition in the sample.

Numerical prediction of thermo-aeraulic behavior for a cavity with internal linear heat source

Computational Fluid Dynamics (CFD) is a promising way, nowadays, to predict the air Flow in enclosures. As a result, the objective of this study is to assess the potential of CFD technique to predict the air Flows driven by buoyancy in heated real-scale rooms. The numerical model is validated using experimental data for fullscale test rooms; therefore, the experimental set-up is rst presented. This is followed by the numerical model description, focusing on its principal elements: computational domain geometry, discretization, turbulence model, radiation model, and thermal boundary conditions. In addition, a simpli ed approach is proposed to integrate a heat source in CFD models: Term source homogeneously spread all over the volume of the heat source. Comprehensive experimental-numerical comparisons are presented in terms of heat transfer to the walls of the test room, heat source behavior, and plume development. The results show that the model developed in this study leads to realistic predictions. Finally, the simpli ed CFD description of heat sources developed here can be extrapolated for other con gurations - di erent power, heat emission (convection/radiation), dimensions, and shape. Consequently, this method can be applied in detailed studies dealing with thermal comfort, indoor air quality, and energy consumption for heated rooms.

Analysis of temperature fields of aircraft components

The problem of analyzing of temperature fields of aircraft components is central for ensuring the operational reliability of the latter. The results of developing methods of calculating temperature fields of the existing products and those being designed based on analytical solution of thermal conductivity equations for the principal types of structures are outlined in the paper. The thermal conductivity equation for a parallelepiped and cylinder with heat sources of a similar form is solved using the variable separation method. A common expression of the solution of thermal conductivity equation for bodies of the simplest form ( parallelepiped, cylinder or its segment, sphere or its segment) with spatial, flat, linear or point heat sources is obtained. A mathematical model for the analysis of thermal fields of aircraft components is proposed. Mathematical and thermal models are developed for the analysis of temperature fields of onboard REA.

Experimental Analysis of Thermal Fields Surrounding Horizontal Cylindrical Geothermal Exchangers

In the engineering field there are many applications where it is important to evaluate the heat exchange between cylindrical surfaces and the surrounding ground (horizontal geothermal exchangers for heat pumps, underground pipelines, underground electric cables, etc...). For these reasons, there is an increased interest in the correct analysis of the soil thermal resistance. In this study different types of soils with linear heat sources were considered and, through a physical model reproduced in laboratory, the thermal field was evaluated. The model reproduced an “undisturbed” portion of soil and the influence of different thermal conditions of the linear heat sources and of the environmental parameters were evaluated. This paper will be extended through the implementation of the experimental device into a numerical model by applying a calculation software to the finite volumes; the result is a predictive model of the soil resistance able to furnish accurate information of the real mean radial thermal resistivity surrounding the geothermal exchanger.

A methodology for the calculation of response functions for geothermal fields with arbitrarily oriented boreholes – Part 2

In the modeling of shallow geothermal systems, the accurate representation of the borehole field configuration is important for a proper estimation of the long term thermal behavior of borehole field systems. Modeling tools based on the so-called g-functions method, utilized for the design of borehole fields, assume that boreholes are vertical. This is a limitation since this condition might not apply in a real installation.This paper is focused on the calculation of g-functions of borehole fields featuring non-vertical boreholes. The strategy utilized consists in representing the boreholes as stacked finite line sources. The temperature along these finite lines, can be calculated by superposition of the effects of each linear heat source in the field. This modeling technique allows to approximate uneven heat distribution among the boreholes and along the axis of each individual borehole. This is a required feature for the calculation of g-functions according to Eskilson's boundary conditions.The test cases presented show that the method yields results that are compatible with the expected physical behavior of the system, and similar to previous results by Eskilson. The computational performance achieved indicates that the method proposed could be potentially utilized during the design phase of these systems.

English

English

Field demonstration of a first thermal response test with a low power source

Thermal response tests conducted to assess the subsurface thermal conductivity for the design of ground-coupled heat pump systems require a power source of about 7–12 kW to heat water circulating in a ground heat exchanger. This high power is commonly supplied with a fuel-fired generator, which is an important source of cost. An alternative method relying on a power source of less than 1 kW was consequently developed and used for a first field demonstration. Heat was injected along ten short sections of heating cable standing in the water column filling the pipe of the exchanger. Recovery temperatures measured at the middle height of each heating section were analyzed with a linear heat source solution of finite length. The ten local measurements distributed over a depth of 139 m and averaged according to the site stratigraphy revealed a subsurface thermal conductivity that is within an acceptable range of the bulk value determined with a conventional test. The new method has the potential to reduce the use of generators for thermal response tests since a low power source is common to construction sites.

Influences on the thermal efficiency of energy piles

Energy piles have recently emerged as a viable alternative to borehole heat exchangers, but their energy efficiency has so far seen little research. In this work, a finite element numerical model is developed for the accurate 3D analysis of transient diffusive and convective heat exchange phenomena taking place in geothermal structures. The model is validated by reproducing both the outcome of a thermal response test carried out on a test pile, and the average response of the linear heat source analytical solution. Then, the model is employed to carry out a parametric analysis to identify the key factors in maximising the pile energy efficiency. It is shown that the most influential design parameter is the number of pipes, which can be more conveniently increased, within a reasonable range, compared to increasing the pile dimensions. The influence of changing pile length, concrete conductivity, pile diameter and concrete cover are also discussed in light of their energetic implications. Counter to engineering intuition, the fluid flowrate does not emerge as important in energy efficiency, provided it is sufficient to ensure turbulent flow. The model presented in this paper can be easily adapted to the detailed study of other types of geothermal structures.

Underground electric cables a correct evaluation of the soil thermal resistance

Nowadays companies supplying medium/high voltage electric energy, near residential areas, tend to use underground cables laying. Hence the design engineer is required to estimate the thermal resistance around the underground cable to perform a right dimensioning of the cables; as a matter of fact what it should be avoided is the overheating determined by a bad heat dissipation due to the Joule effect.IEC rules provides a formula for the evaluation of the soil thermal resistance which is easy to apply. But from an experimental point of view, as the bibliography shows, it was discovered it tends to underestimate the problem when dealing with very dry soils in particular.Thanks to an experimental system, some useful data were collected for the validation of a 2D FEM model of an excavated area with a linear heat source reproducing the underground conduit. The numerical model presents a variation of both the geometrical parameters of the excavated area and the distance characterizing other cables (hence heat sources) located in the same site of installation examined. In this way two dimensionless coefficients, useful to correct the values of the thermal resistance furnished by the current regulations, were determined.

A model for the evaluation of heat loss from underground cables in non-uniform soil to optimize the system design

With the proliferation of technologies and underground systems, analysis of thermal fields in soil has become a topic of great interest in the developing technology of buried structures. In this work, we have investigated the steady-state temperature field (from linear heat sources – buried cable) in a different type of soil and excavation geometry. In a laboratory, a physical model was built on scale, which reproduces an “undisturbed” area containing a linear thermal source. This scale model was produced for experimental activity. A measuring chain was made to analyze the thermal field in various types of soils, by varying the electrical current through the line source. The physical model was recreated using a finite volume calculation software. Analysis of the different field system configurations were completed and we have studied a model for the improvement of the design method.

Algorithm to optimize transient hot-wire thermal property measurement.

The transient hot-wire method has been widely used to measure the thermal conductivity of fluids. The ideal working equation is based on the solution of the transient heat conduction equation for an infinite linear heat source assuming no natural convection or thermal end effects. In practice, the assumptions inherent in the model are only valid for a portion of the measurement time. In this study, an algorithm was developed to automatically select the proper data range from a transient hot-wire experiment. Numerical simulations of the experiment were used in order to validate the algorithm. The experimental results show that the developed algorithm can be used to improve the accuracy of thermal conductivity measurements.