Linear Source Model Research Articles

Flow-field characteristics of the thermal plume above an elliptical high-temperature heat source surface

The thermal plume formed by the high-temperature elliptical heat source surface during the smelting process is often captured and removed by the local exhaust system. Accurately mastering the flow-field characteristics of such high-temperature elliptical heat plumes is helpful for efficient design of local exhaust systems. In this paper, the effects of the ratio of long and short axes (5/4 ≤ ξ ≤ 5/1) and the intensity of heat source (80 ≤ F ≤ 160 W) on the axial and radial velocity distribution of thermal plume in an elliptical heat source are investigated by numerical simulation combined with experimental validation. The results show that in the range of ξ ≤ 5/1, the axial dimensionless velocity distribution of the elliptical plume field and the spreading range of the plume field are mainly affected by ξ instead of F. For 5/4 ≤ ξ ≤ 5/1, the maximum axial velocity Um appears at 1.7 to 2.7 times Z/L (plume height to heat source long axis ratio). For ξ ≤ 5/2, the height at which the cross-sectional velocity field transitions to a circular distribution aligns with the height of Um. It is found that the plume velocity field is characterized by applying the point source model for ξ ≤ 5/3, and vice versa for the linear source model. The plume flow rate formulation obtained by modifying the linear source model for ξ > 5/3 has a better predictive ability in the Z/L ≤ 5 region. This study provides a reference for the design of ventilation systems for elliptical surface heat sources.

Apparatus Development for the Measurement of the Thermal Conductivity of Geothermal Backfill Materials

This paper describes the design, construction, validation, and calibration of a thermal conductivity measuring apparatus for geothermal backfill materials in the range from 0.13–2.80 W/m·K. The developed apparatus is based on the Transient Hot Wire (THW) method whose mathematical basis is the Infinite Linear Source (ILS) model. The apparatus consists of a nichrome hot wire, an adjustable direct current power supply, a temperature sensor (K-type thermocouple), and a datalogger. For the validation and calibration of the developed apparatus, four standard samples have been used with a known thermal conductivity, to 3.0 W/m·K. Furthermore, the thermal conductivity of four geothermal backfill materials of common use (bentonite, neat cement, cement–sand mortar, and cement–bentonite mortar) has been measured using both the developed apparatus and a commercial meter.

Study on Calculation Method of Heat Exchange Capacity and Thermal Properties of Buried Pipes in the Fractured Rock Mass-Taking a Project in Carbonate Rock Area as an Example

Fractures are developed in carbonate rock areas, and the fracture water flow significantly influences the heat exchange between buried pipes and the rock mass by induing heat convection, providing the carbonate rock area a strong heat exchange capacity and preferable conditions for shallow geothermal development and utilization. In this paper, the calculation method of heat exchange capacity of buried pipes based on fracture distribution characteristics is proposed and deduced, featuring such advantages as quick speed and low cost. Taking an actual project in carbonate rock area as an example, the heat exchange capacity of buried pipes was obtained by the following two methods: in-situ thermal response test and calculation based on fracture distribution characteristics. In the thermal response test, the initial ground temperatures of the two test holes were 15.18 °C and 12.72 °C. By fitting the linear equation of time and average temperature with a linear thermal source model, the heat exchange capacities were 57.21 W/m and 58.22 W/m, the thermal conductivities were 3.56 W/(m·K) and 2.32 W/(m·K), the thermal diffusivities were 1.71 × 10−6 m2/s and 1.12 × 10−6 m2/s, and the volume specific heat capacity was 2.08 × 106 J (m3·K). The test results indicated that the thermal property parameters of rock and soil mass were higher than those of other areas, with obvious wide-range distribution characteristics. Through the statistical analysis of outcrop fracture characteristics, combined with the cube law to calculate the fracture water flow and convective heat transfer, an alternative method for the calculation and optimization of buried pipe heat transfer in fractured rock mass area is also proposed in this paper. According to the measured fracture distribution characteristics of the field outcrop, the heat exchange capacities of the two holes were 57.26 W/m and 58.56 W/m, which were basically consistent with the thermal response test values and verified the reliability of the calculation method of heat exchange capacity of buried pipes based on fracture distribution characteristics.

Can deep borehole heat exchangers operate stably in long-term operation? Simulation analysis and design method

Deep borehole heat exchanger (DBHE) extracts heat from medium-depth geothermal energy through heat transfer process, and its annual accumulative heat extraction directly influences the stability and safety in long-term operation. To calculate the maximum annual accumulative heat extraction ( Q a,max ) per DBHE rapidly and accurately at design stage, a method combining numerical simulation, modified finite linear heat source model (FLM), and analytical solutions is proposed in this paper. Based on the superposition feature of ground excess temperature, this method divides heat flow of DBHE to one constant value and one extra periodic value. The effect of constant heat flow on ground temperature is calculated by modified FLM rapidly, and the extra periodic effect in first year is calculated by numerical simulation. Then the actual ground temperature variation at any time can be rapidly calculated with the superposition of these two effects. After obtaining ground temperature, the water temperature distribution in DBHE is directly calculated by analytical solutions. Results show that Q a,max per DBHE with depth of 2500 m and normal conditions could reach about 3000 GJ per heating season. However, the specific value is significantly influenced by geothermal conditions, DBHE parameters and heating season duration. This paper then studies the effects of these key factors quantitatively and further raises a system design method for DBHE based on Q a,max , so as to guarantee the stability, safety, and feasibility in long-term operation. • Long-term operational performance of deep borehole heat exchanger (DBHE) is studied. • Maximum annual accumulative heat extraction ( Q a,max ) is key design parameter. • Q a,max is affected by geothermal conditions, DBHE parameters, heating season duration. • System design method based on Q a,max is raised to design the number of DBHEs.

Study on Heat Transfer Model and Applicability of Energy Piles in Nanning Basin under Subtropical Climate

In order to meet the requirements of peak carbon dioxide emissions, energy pile systems have been widely used in more and more regions because of their low-carbon, energy-saving, and emission-reducing characteristics. To explore the applicability of the energy pile project in Nanning, which has typical subtropical climate characteristics with warm winters and hot summers, some research work has been carried out in this paper. Firstly, through indoor thermophysical property tests, the geotechnical thermophysical parameters of typical composite strata in this area are obtained. Then a transient heat transfer model of the energy pile is established, which can fully reflect the heat transfer characteristics of the pile and the soil. On this basis, the superposition principle and stepped heat flow theory are used to analyze the temperature recovery characteristics of typical strata in Nanning area under different intermittent operation conditions. The results show that: the rock-soil mass of the typical stratum in Nanning area has good heat transfer characteristics, which is conducive to the promotion of energy pile engineering. The heat transfer model proposed in this paper has higher accuracy than the classical linear heat source model, which can reflect the material characteristics of energy pile system and avoid overestimating or underestimating the temperature field of energy pile system. The operation of energy pile system in a subtropical climate will produce an unbalanced heat load, and corresponding measures need to be taken to achieve the balance of heat load. The research results can provide a reference for energy pile engineering design in different climate regions.

The deviation of thermal conductivity under different operating power is analyzed by linear heat source superposition method

Heat conductivity and multiple correlation coefficients of various drill holes under high and low-power levels were acquired through the field heat response test, so as to capture heat exchanging performances of the ground heat pump system. Moreover, by analyzing the changing characteristics of heat conductivity with IGSHPA linear heat source model, significant deviations were found between test results of heat conductivity when the high and low-power tests are conducted at short intervals, which was resulted from the influence of the residual temperature field of the first test on the second test, that is, the temperature is not returned to the initial temperature yet. Deviation caused by short test intervals between high and low-power test results can be eliminated by the line-source superposition method. In addition, by introducing the time function, the exact value of heat conductivity obtained by the second test can be solved with the utilization of linear relationship between the time function and the average temperature of the fluid. The dependence of fitting the linear heat source was verified. By calculating the linear regression of important parameters in the linear heat source superposition method, the linear fitting upon processing is characterized by good degree of fitting, small temperature deviation, and significant linear correlation. The linear heat source superposition method was proven to be reliable and accurate. Also, the analysis result shows that there is no need to process data using the linear heat source superposition method when two tests are conducted at long intervals.

A Novel Approach to the Analysis of Thermal Response Test (TRT) with Interrupted Power Input

The quality of measuring datasets of the thermal response test (TRT) significantly influences the interpretation of borehole thermal parameters (BTP). A thermal response test with an unstable power input may induce an unacceptable error in the estimation of the borehole thermal parameters. This paper proposes a novel approach to treat the dataset with interrupted power input. In this approach, the test records were segmented into several subsections with a constant time interval of 100 min, 60 min, and 30 min, separately. The quality of each data section was assessed and analyzed. Then, two algorithms, including the continuous algorithm and semi-superposition algorithm, were developed. The results estimated by the linear source model (LSM) were compared with one Thermal response test datasets with a stable power input at the same testing site. It shows that the effects of power interruption during the test can be effectively mitigated by deploying both the continuous and semi-superposition methods. The lowest deviation of the calculated thermal conductivity to a thermal response test with stable power input was 2.8% in the continuous method and 0.9% using the semi-superposition method. Thus, the proposed approaches are effective measures to mitigate the effects of interrupted power input on the interpretation of the thermal properties of the ground.

Evaluation of Liquefaction Potential of Soil at a Power Plant Site in Chittagong, Bangladesh

This study presents an evaluation of liquefaction potential for combined cycle power plant site located in the Chittagong district, Bangladesh, using standard penetration test blow counts (SPT-N values). The peak ground acceleration (PGA) values at a bedrock level were estimated deterministically using both linear and point source models as well as different ground motion prediction equations (GMPEs). The surface level hazard was estimated using amplification factors for the soil conditions present and the response spectrum at the center of the plant site was plotted. The liquefaction potential for the site was arrived at by using the SPT-N values of 33 boreholes in the site and at every 3-meter interval from the ground level to a depth of 30 meters. The results from the LPI contours at successive depths indicate that in the majority of the borehole locations, the soil up to 15 meters depth had a significant hazard of liquefaction. These findings from the present study can prove to be crucial from the structural point of view, for any future construction activities in the area.

Analysis of effective thermal conductivity stability of geothermal heat exchanger according to ambient environmental conditions

At present, geothermal energy is a promising research area but still has numerous areas to be explored. The thermal performance verification of U-shaped closed geothermal heat exchange was proposed to improve the effective thermal conductivity value applying initial ignoring time (IIT). To verify the thermal performance of the underground heat exchanger in the rock layer according to the surrounding environment and groundwater conditions, verifications were conducted for the amount of circulating water, amount of heat input, and groundwater conditions. The circulating fluid flow rate of the system, supply of water into the ground, and influence of the change of supplied heat source were analyzed. The effective heat conduction characteristics were analyzed using the linear heat source model and initial exclusion time. Therefore, in the thermal response test, the main error occurs according to the determined initial removal time, and the reliability of the effective thermal conductivity value is increased by applying IIT to reduce this error.

Study of Ground Heat Exchangers in the Form of Parallel Horizontal Pipes Embedded in the Ground

In order to predict long-term changes in the temperature of the ground in which a horizontal ground heat exchanger has been installed, it is beneficial to implement simplified mathematical models of heat transfer. The possibility of using a one-dimensional equation of heat conduction while modelling heat transfer in a ground heat exchanger with horizontal pipes has been demonstrated in the work. A theoretical analysis based on the linear heat source model as well as experimental research works have been carried out. It has been concluded that the temperature profiles of the ground in which parallel pipes of the heat exchanger are placed do not significantly differ from the profiles for the heat exchanger in the form of a plate; in particular, this refers to large distances from the level in which the pipes are positioned, small distances between pipes axes and the long duration of the process. Discrepancies between the calculated temperature increases for pipe and plate exchangers varied significantly in the individual time intervals, and were approx. 20–30%. The conducted experiments have demonstrated that the temperature field around parallel pipes of the heat exchanger may be described by the linear heat source model. The compatibility of temperature maps that were determined theoretically and experimentally was satisfactory with a good degree of accuracy.

Determination of ground thermal properties for energy piles by thermal response tests

Thermal properties of ground heat exchanger (GHE) such as effective thermal conductivity and borehole thermal resistance are commonly measured in the field by thermal response tests (TRTs). TRT has been proved to be a consolidated method to determine thermal properties of traditional borehole heat exchangers (BHEs). However, there is still lack of data for adopting TRT on energy piles with often a large diameter and deficiency in validation of TRT results with geological materials. In this study, ground thermal properties for typical configured GHEs of energy piles are investigated. Three TRTs are conducted and the obtained results are analyzed. Effective thermal conductivity, λeff, of the ground derived by following the traditional linear source model shows large deviation as compared to the thermal conductivity of the geological materials. In order to determine λeff properly, the linear source model is modified and an equivalent radius, req, of energy piles is considered. The λeff estimated by the modified model shows a good agreement with thermal conductivity of the in situ geological materials. In addition, there has been no obvious correlation between borehole thermal resistances and thermal efficiency due to heat transport of energy piles that depends not only by borehole thermal resistance but also by the pile’s diameter and ground conditions. The findings drawn from this study indicate that the modified model is reasonable and useful in determining thermal properties of energy piles.

Probabilistic seismic hazard assessment of Nepal using multiple seismic source models

The potential for devastating earthquakes in the Himalayan orogeny has long been recognized. The 2015 MW7.8 Gorkha, Nepal earthquake has heightened the likelihood that major earthquakes will occur along this orogenic belt in the future. Reliable seismic hazard assessment is a critical element in development of policy for seismic hazard mitigation and risk reduction. In this study, we conduct probabilistic seismic hazard assessment using three different seismogenic source models (smoothed gridded, linear, and areal sources) based on the complicated tectonics of the study area. Two sets of ground motion prediction equations are combined in a standard logic tree by taking into account the epistemic uncertainties in hazard estimation. Long-term slip rates and paleoseismic records are also incorporated in the linear source model. Peak ground acceleration and spectral acceleration at 0.2 s and 1.0 s for 2% and 10% probabilities of exceedance in 50 years are estimated. The resulting maps show significant spatial variation in seismic hazard levels. The region of the Lesser Himalaya is found to have high seismic hazard potential. Along the Main Himalayan Thrust from east to west beneath the Main Central Thrust, large earthquakes have occurred regularly in history; hazard values in this region are found to be higher than those shown on existing hazard maps. In essence, the combination of long span earthquake catalogs and multiple seismogenic source models gives improved seismic hazard constraints in Nepal.

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.

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.

Simulation of thin film thickness distribution for thermal evaporation process using a scanning linear source

Thermal evaporation process is the main process involved in the production of OLED displays and with the trends toward larger substrate size and display resolution, film thickness uniformity must be carefully controlled in order to implement exact pixel data. To secure stable film thickness uniformity on the substrate area, thin films are deposited on large-area glass substrates via thermal evaporation process using a linear source. We designed a linear source and mathematical model was developed to describe the system with a focus on the linear source. Then, system parameters were determined to guarantee uniform thickness using computer-based simulation, replacing wasteful actual experiments, followed by carrying out experiments based on the determined parameters. After the deposition process, data from the mathematical model and experiments was compared and the resulting agreement was good, verifying the validity of the proposed method. Consequently, by applying the proposed method, display manufacturing process related to thermal evaporation can be controlled within a tight tolerance in order to maximize the production yield rate.

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.

An analytic linear accelerator source model for GPU-based Monte Carlo dose calculations

Recently, there has been a lot of research interest in developing fast Monte Carlo (MC) dose calculation methods on graphics processing unit (GPU) platforms. A good linear accelerator (linac) source model is critical for both accuracy and efficiency considerations. In principle, an analytical source model should be more preferred for GPU-based MC dose engines than a phase-space file-based model, in that data loading and CPU-GPU data transfer can be avoided. In this paper, we presented an analytical field-independent source model specifically developed for GPU-based MC dose calculations, associated with a GPU-friendly sampling scheme. A key concept called phase-space-ring (PSR) was proposed. Each PSR contained a group of particles that were of the same type, close in energy and reside in a narrow ring on the phase-space plane located just above the upper jaws. The model parameterized the probability densities of particle location, direction and energy for each primary photon PSR, scattered photon PSR and electron PSR. Models of one 2D Gaussian distribution or multiple Gaussian components were employed to represent the particle direction distributions of these PSRs. A method was developed to analyze a reference phase-space file and derive corresponding model parameters. To efficiently use our model in MC dose calculations on GPU, we proposed a GPU-friendly sampling strategy, which ensured that the particles sampled and transported simultaneously are of the same type and close in energy to alleviate GPU thread divergences. To test the accuracy of our model, dose distributions of a set of open fields in a water phantom were calculated using our source model and compared to those calculated using the reference phase-space files. For the high dose gradient regions, the average distance-to-agreement (DTA) was within 1 mm and the maximum DTA within 2 mm. For relatively low dose gradient regions, the root-mean-square (RMS) dose difference was within 1.1% and the maximum dose difference within 1.7%. The maximum relative difference of output factors was within 0.5%. Over 98.5% passing rate was achieved in 3D gamma-index tests with 2%/2 mm criteria in both an IMRT prostate patient case and a head-and-neck case. These results demonstrated the efficacy of our model in terms of accurately representing a reference phase-space file. We have also tested the efficiency gain of our source model over our previously developed phase-space-let file source model. The overall efficiency of dose calculation was found to be improved by ~1.3–2.2 times in water and patient cases using our analytical model.

TH‐EF‐BRD‐02: An Analytic Linear Accelerator Source Model and Automatic Source Commissioning for GPU‐Based Fast Monte Carlo Dose Calculation

Purpose:GPU‐based Monte Carlo (MC) dose calculations have become available. Linac source modeling for it is still a problem to be addressed. The model should be carefully designed for sufficient accuracy, ease of automatic commissioning, and more importantly suitability for parallelization. This abstract presents an analytical source model for GPU‐based MC dose engines with these factors considered.Methods:Analytical source models are preferred for GPU comparing to phase‐space‐file based models due to the avoidance of loading and transferring large data. In our model, we introduced a phase‐space‐ring (PSR) concept. A PSR contains particles of the same type and close in energy and radial distance on a plane above jaws. We parameterized probability densities of particle location, energy, and direction for three sub‐source types: primary photon PSR, scattered photon PSR and electron PSR. Model parameters were derived by analyzing reference phase‐space files. To incorporate this model into our GPU dose engine, we designed an efficient sampling scheme to reduce GPU thread divergence. Automatic commissioning was achieved by solving an optimization problem to adjust PSR weight.Results:Our model built for Varian Truebeam 6MV photon beam was able to represent the reference phase‐space. Comparing open‐field doses in water computed using our model and the phase‐space file, average distance‐to‐agreement(DTA)≤1mm for high‐gradient regions, root‐mean‐square(RMS) difference≤1.1% for low‐gradient regions and output factor difference≤0.5% were observed. Good agreements were seen in IMRT cases. Our model improved efficiency by 1.70–4.41 times compared to phase‐space‐based source model. It took ∼20sec to perform commissioning. Compared to uncommissioned model, DTA was reduced from 0.04–0.28cm to 0.04–0.12cm for depth dose at build‐up region, and RMS from 0.32%–0.67% to 0.21%–0.48%, 0.31%–2.0% to 0.06%–0.78% and 0.20%–1.25% to 0.10%–0.51% for depth dose after build‐up, lateral profiles of inner beam and outer beam, respectively.Conclusion:The analytic source model achieved high accuracy, efficiency, and suitability for GPU‐based dose calculations.

On the nonlinear and time-varying acoustic modeling of the simplified intake or exhaust silencing system

The intake or exhaust noise of an internal combustion engine is usually predicted by the linear, time-invariant source model in frequency domain with reasonable precision. However, the actual finite amplitude pulsation involves the nonlinear, time-varying characteristics that are prominent in time-domain. To overcome the discrepancy between two source models, an approximate nonlinear and time-varying frequency domain source model can be employed by appending the nonlinear or time-varying terms to the linear, time-invariant source model. Proper selection of the nonlinear describing terms varying with time is important for the realistic and precise prediction of the radiated sound. For the selection of such terms, flow and motional characteristics in the valve and orifice of a simplified fluid machine comprised of very large reservoir, valve, and duct is considered. Effects of each describing term and the combined terms are investigated by comparing the sound spectrum predicted from nonlinear source model to that from linear source model. In the comparison, the sound spectrum calculated by the method of characteristics is used as a reference. It is found that the source model using only the velocityrelated terms yields the best result among all the models using various combinations of the terms with different characteristics. The best model yields a difference from the linear source model within ±5 dB in overall sound level. Change of acoustic loads results in a difference of 20–27 dB in linear source model from the reference data; however, maximum 10–22 dB deviations are observed in using the various nonlinear source models. It is concluded that more than 4 describing terms should be employed in the nonlinear model to obtain a realistic result of the radiated sound from the intake or exhaust system.

Assessment of Seismically Induced Landslide Hazard for the State of Karnataka Using GIS Technique

Landslide hazards are a major natural disaster that affects most of the hilly regions around the world. In India, significant damages due to earthquake induced landslides have been reported in the Himalayan region and also in the Western Ghat region. Thus there is a requirement of a quantitative macro-level landslide hazard assessment within the Indian subcontinent in order to identify the regions with high hazard. In the present study, the seismic landslide hazard for the entire state of Karnataka, India was assessed using topographic slope map, derived from the Digital Elevation Model (DEM) data. The available ASTER DEM data, resampled to 50 m resolution, was used for deriving the slope map of the entire state. Considering linear source model, deterministic seismic hazard analysis was carried out to estimate peak horizontal acceleration (PHA) at bedrock, for each of the grid points having terrain angle 10A degrees and above. The surface level PHA was estimated using nonlinear site amplification technique, considering B-type NEHRP site class. Based on the surface level PHA and slope angle, the seismic landslide hazard for each grid point was estimated in terms of the static factor of safety required to resist landslide, using Newmark's analysis. The analysis was carried out at the district level and the landslide hazard map for all the districts in the Karnataka state was developed first. These were then merged together to obtain a quantitative seismic landslide hazard map of the entire state of Karnataka. Spatial variations in the landslide hazard for all districts as well as for the entire state Karnataka is presented in this paper. The present study shows that the Western Ghat region of the Karnataka state is found to have high landslide hazard where the static factor of safety required to resist landslide is very high.