Maximum Absolute Percentage Error Research Articles

Short-term wind speed prediction of wind farm based on TSO-VMD-BiLSTM

Aiming at the random and intermittent characteristics of wind speed, a short-term wind speed prediction (SWSP) method based on TSO-VMD-BiLSTM is proposed in this article. Firstly, open-source historical data from a certain region in 2022, including wind speed, direction, pressure, and temperature is analyzed. The data is processed through variational mode decomposition (VMD) to fully extract feature data from historical wind speed records. Secondly, taking historical wind speed, direction, pressure, and temperature as inputs and wind speed as output, a SWSP model based on long short-term memory (LSTM) network is constructed. Thirdly, the tuna swarm optimization (TSO) algorithm is utilized for parameters optimization, and a bi-directional long short-term memory (BiLSTM) network is incorporated to enhance prediction accuracy for micrometeorological parameters. The proposed TSO-VMD-BiLSTM model is validated through comparison with other models, demonstrating its higher accuracy with the maximum absolute error of only 2.52 m/s, the maximum root mean square error of 0.81, the maximum mean absolute error of only 0.54, and the maximum mean absolute percentage error of 6.89%.

Comprehensive thermal performance analysis of an air-cooled staggered configured Li-ion battery pack- A numerical and experimental approach

The discharge rate, ambient temperature, and airflow cooling velocity of a Li-ion battery pack BTMS have a direct impact on the battery's temperature, performance, and safety. Monitoring these is essential for avoiding overheating, ensuring optimal performance, and extending the battery's lifespan. This study comprehensively assesses the thermal performance of staggered structured cells of a 24.00V, 10.00Ah Li-ion battery pack cooled by ambient air. Both experimental and numerical methods are employed to achieve this evaluation. The primary objective is to investigate how varying discharge rates (0.50, 1.00, 1.50, 2.00, and 2.50; C), the seasonal temperatures in Prayagraj, India (282.00, 296.00, 305.00, and 315.00; K), and airflow velocities (0.50, 1.00, 1.50, and 2.00; m/s) influence the battery pack's thermal behaviour. A comparative analysis is also conducted between the present study and the author's prior research, focusing on the aligned configuration. The study observed a temperature increase in the airflow direction, from the inlet to the outlet, with the highest temperature recorded in the second-to-last column of the battery pack. Both numerical analysis and experimental testing confirmed that decreasing the airflow velocity from 2.00 m/s to 0.50 m/s reduced thermal performance by enhancing temperature in the airflow path, as well as transverse and circumferential temperature variations. Conversely, as the load on the battery (discharge rate) decreased from 2.50 C to 0.50 C, the thermal performance estimating parameters; Tmax, Tavg., ΔTmax, and σT, exhibited a declined trend. This is due to the greater heat generation at higher discharge rates. Furthermore, it was observed that as the ambient temperature increased from 282.00 K to 315.00 K, the temperature of the battery cells also increased. Nonetheless, the cooling patterns remained similar across these different temperature range conditions. Moreover, experimental results compete with the numerical outcomes with a maximum absolute percentage error of 1.21%. The staggered configuration gives lower and uniform temperature distributions within the battery packs than the aligned arrangements.

An ensemble of artificial neural network models to forecast hourly energy demand

AbstractWe propose an ensemble artificial neural network (EANN) methodology for predicting the day ahead energy demand of a district heating operator (DHO). Specifically, at the end of one day, we forecast the energy demand for each of the 24 h of the next day. Our methodology combines three artificial neural network (ANN) models, each capturing a different aspect of the predicted time series. In particular, the outcomes of the three ANN models are combined into a single forecast. This is done using a sequential ordered optimization procedure that establishes the weights of three models in the final output. We validate our EANN methodology using data obtained from a A2A, which is one of the major DHOs in Italy. The data pertains to a major metropolitan area in Northern Italy. We compared the performance of our EANN with the method currently used by the DHO, which is based on multiple linear regression requiring expert intervention. Furthermore, we compared our EANN with the state-of-the-art seasonal autoregressive integrated moving average and Echo State Network models. The results show that our EANN achieves better performance than the other three methods, both in terms of mean absolute percentage error (MAPE) and maximum absolute percentage error. Moreover, we demonstrate that the EANN produces good quality results for longer forecasting horizons. Finally, we note that the EANN is characterised by simplicity, as it requires little tuning of a handful of parameters. This simplicity facilitates its replicability in other cases.

Forecasting electricity demand of municipalities through artificial neural networks and metered supply point classification

This study develops a methodology to characterise and forecast large consumers’ electricity demand, particularly municipalities, with hundreds of different metered supply points based on the previous characterisation of facilities’ consumption. Demand forecasting allows consumers to improve their participation in electricity markets and manage their electricity consumption. The method considers a classification by different types of metered supply points combined with artificial neural networks to obtain hourly forecasts using well-known parameters such as day types, hourly temperature, the last hour of electricity consumption, and sunrise and sunset time. We apply the methodology to the municipality of Valencia using over five hundred hourly load profiles for a year during 2017 and 2018. Our results present aggregated forecasts with a maximum Mean Absolute Percentage Error of 3.8% per day, outperforming the same forecast without classifying Metered Supply Points. We conclude that a correct electricity demand forecast for a consumer with different types of consumption does not need submetering, but characterising Metered Supply Points is an option with lower costs that allows for better predictions.

Novel battery power capability assessment for improved eVTOL aircraft landing

A key aspect in the deployment of electric vertical take-off and landing (eVTOL) aircraft is the safety and performance capabilities of the batteries used. A component of the safety requirements is the need for reserve energy, which would only be utilised in case of emergencies. In the literature, it has been observed that the lower bound of the reserve region of battery energy should be limited to avoid the area where a precipitous drop in voltage would occur. Here, a method for defining the lower bound is proposed. This seeks to extend the amount of time the aircraft can cruise before landing can no longer be completed. A novel power capability testing procedure is used to measure the lowest state-of-charge (SoC) at which a constant power pulse can be completed. This differs from existing power capability tests that perform pulses at predetermined SoC points. The goal of the proposed method is to replicate the conditions of landing to understand the power capability performance at low SoC. The test is performed for a variety of environmental conditions and use cases, which includes temperature and power pulses, as well as two sets of differently aged cells. For the defined test conditions, the lowest SoC values for the calendar aged cells ranges from 6% to 14% SoC, whereas the range for cycle aged cells is 8% to 27% SoC. The outcome of this test is a characteristic map which correlates temperature, pulse power and pulse duration to the lowest SoC the pulse can be completed. The characteristic map indicates the lowest SoC value allowed for the battery before landing needs to be performed. The accuracy of the characteristic map is compared to a battery equivalent circuit model, parametrised from the test data. The defined approaches are experimentally validated based on a set of previously unmeasured experimental conditions. Overall, the characteristic map provides good accuracy compared to measured values, with both map and model methods having an average maximum absolute percentage error of at most 7.5%. Additionally, the test results show that if the worst case landing scenario is used as the lower bound of the reserve region, the useable SoC range for nominal flight would be greatly affected if cell degradation is not considered.

Prediction of Tropospheric Ducting for UHF Signals In Plateau State Using Adaptive Neuro-Fuzzy Inference Systems (ANFIS)

A study on the occurrence of tropospheric ducting for UHF signal in Plateau State using ANFIS had been investigated using the variation of the meteorological data; temperature, pressure, and relative humidity collected from NIMET for Jos, Plateau State Nigeria. The refractivity gradient was calculated using MATLAB as computational software. The conditions of occurrence of path clearance and tropospheric ducting were utilized to checkmate the occurrence of ducting over the period. The data gotten is used to train an ANFIS model, taking 70% of the data for model training, 20% for testing and 10% for validation. The integrity of the ANFIS model was tested using root mean square error (RMSE) and maximum absolute percentage error (MAPE) which confirmed that the model is accurate to 99% considered fit for forecasting. The developed model was able to mimic the tropospheric ducting trend up to a period of 7 years (2019- 2025) after successful simulation with an assertion that the rainy months are more prevailed to chances of tropospheric ducting occurrence as higher humidity prevails during this time which has more significance on refractivity gradient. An investigation was carried out on the effect of variation of tropospheric parameters; temperature, pressure and humidity on refractivity gradient using linear regression and Spearman correlation to ascertained the degree of dependence of each parameter and the result showed that refractivity gradient is strongly influenced by relative humidity with a correlation coefficient of -0.9772 as against temperature and pressure having correlation coefficients of -0.2587 and 0.2866 respectively.

Experimental Investigation and Soft Computing-based Assessment using ANN-MOGWO-A Hybrid Approach for Inconel(825)

In this paper, a strategy has been set for minimizing the corner error in the modification of pulse and non-pulse parameters. Taguchi’s philosophy has been used to design the experiment by varying process parameters (i.e. Spark-on Time (STon), Wire Tension (WT), Servo-Voltage (Sv), Discharge Current (DC) and Wire-speed (Sw)), to explore the machining outcomes. The response characteristics have been measured in terms of cutting speed (Cs), Corner Error (CD) and surface Roughness (RA) using Topas plus X wire of [Formula: see text] 0.25[Formula: see text]mm diameter. The machining performance characteristics were analyzed using main effect plots and analysis of variance (ANOVA). Furthermore, a soft computing-based hybrid optimization technique (Artifical Neural Network (ANN)-based Multi-Objective Grey Wolf Optimizer (MOGWO)) has been utilized to search the multi-optimum parameter setting for superior machining results. The most significant parameter observed is DC for Cs, which is determined to be 34.81%. Moreover, WT found 26.29% and 34.10% for CD and RA, respectively. The confirmation test shows that the maximum absolute percentage errors are observed as 3.89%, 6.3% and 9.7% for Cs, CD and RA, respectively. The proposed hybrid technique can generate superior solutions compared to the existing algorithms. Notably, the outcomes obtained on new instances exhibit potential, purposeful, and efficacy.

Optimal discretization of geothermal boreholes for the calculation of g-functions

The effect of the discretization of geothermal boreholes on the accuracy of g-function evaluations is studied. A data set of 557,056 bore field configurations covering a large range of geometrical parameters is generated using pygfunction. A nonuniform discretization of borehole segments geometrically expanding in length toward the middle of the borehole is proposed. A nonuniform discretization is shown to achieve better accuracy than a uniform discretization. The nonuniform discretization is optimized to minimize the maximum absolute percentage error over the entire data set. The discretization is optimized for each bore field configuration, and an artificial neural network (ANN) is trained to predict the optimal discretization given only geometrical and thermal parameters of the boreholes, excluding the borehole positions. Thermal parameters that quantify the bore field temperature distribution are introduced as inputs to the ANN. The maximum absolute percentage error using a uniform discretization is 99.0% in the worst studied case of a dense rectangular field of Nb = 1116 boreholes with lengths of 418.8 m and spacings of 3.14 m and 3.18 m along rows and columns, while only 1% of the cases feature an error above 26.7%. The error is reduced to 3.6% using the global optimal discretization and 3.3% using the ANN.

Construction and Estimation of Battery State of Health Using a De-LSTM Model Based on Real Driving Data

Electric vehicles (EVs) have considerable potential in promoting energy efficiency and carbon neutrality. State of health (SOH) estimations for battery systems can be effective for avoiding accidents involving EVs. However, existing methods have rarely been developed using real driving data. The complex working environments of EVs and their limited data acquisition capability increase the challenges for estimating SOH. In this study, a novel battery SOH definition for EVs was established by analyzing and extracting six potential SOH indicators from driving data. The definition proposed using the entropy weight method (EWM) described the degradation trend for different EV batteries. Combined with a denoising autoencoder, a novel long short-term memory neural network model was established for SOH prediction. It can learn robust features using noisy input data without being affected by different environments or driver behaviors. The network achieved a maximum mean absolute percentage error (MAPE) of 0.8827% and root mean square error (RMSE) of 0.9802%. The results have shown that the proposed method has a higher level of accuracy and is more robust than existing methods in the field.

Dynamic performance of industrial robots in the secondary carbon fiber-reinforced plastics machining

Carbon fiber-reinforced plastics (CFRPs) find many applications given their superior properties. These materials are usually formed using a near-net-shape method that requires secondary machining, such as drilling and trimming, after molding. Industrial robots are becoming increasingly popular machining tools in industries exhibiting high demand for CFRPs. However, it remains challenging to achieve high dimensional accuracy when using such robots and dynamic performance is poor. We experimentally investigated the dynamic properties of the tool tip according to the dominant robot posture during CFRP secondary machining. Based on the results, multi-layer perceptron models were developed to predict the dominant natural frequency and dynamic stiffness of the tool tip. The minimum and maximum mean absolute percentage errors were 1.99 and 7.94, respectively; the error changed markedly with robot posture. Our models improved CFRP robotic machinability. Experimentally, the delamination rates of drilled holes decreased by 15 % and 75 % in terms of length and area, respectively, and the trimmed surface roughness improved by 27 %.

Time series analysis of groundwater quality at selected sites of Purba and Paschim Burdwan, West Bengal, India.

The Water Quality Index (WQI) is used to monitor the health and usability of a water body. In this study, we aimed to construct time series prediction models using groundwater WQI (GW-WQI) at four sites: IISCO-Asansol, Durgapur Town, Burdwan University, and Burdwan Station. While statistical spatio-temporal analysis has been reported earlier, no time series analysis of the data or predictive modelling has been done. Pre-monsoon and post-monsoon physico-chemical data from 2010 to 2022 were obtained from the West Bengal Pollution Control Board website to calculate the GW-WQI. Prediction modelling was performed using R 4.1.3 software. Best fit forecast models were selected to predict future trends of GW-WQI with 80% of the data. Subsequently, the models were validated using R-squared, root mean square error (RMSE), mean absolute error (MAE), maximum absolute percentage error (MAPE), and Thiel's U for the model using 20% of the data. Our results show that GW-WQI was good in pre-monsoon but unfit for drinking in post-monsoon in IISCO-Asansol, Durgapur Town, Burdwan University, and Burdwan Station. Arsenic, fluoride, and mercury were the major contaminants resulting in poor GW-WQI. Seasonal ARIMA was the best model for Burdwan University and IISCO-Asansol, ETSfor Durgapur Station, and BaggedARIMA for Burdwan Station. The forecast model for Durgapur and Burdwan Station predicted a sharp increase until 2027 but was fluctuating for IISCO-Asansol and Burdwan University. Thus, GW-WQI is a major problem in the industrial belt of West Bengal that is likely to remain high or worsen in the future.

Development of Nusselt number and friction factor correlations for double-pass solar air heater duct

A solar air heater exhibits a low heat transfer rate due to the formation of a laminar thermal boundary layer across the absorber plate. Furthermore, the artificial roughness contributes to the intensification of turbulence along the absorber plate, which interrupts and breaks the thermal boundary layer. Keeping in this view, a three-dimensional simulation is performed to investigate the heat transfer and frictional characteristics of a double-pass solar air heater with semicircular tubes and perforated baffles as artificial roughness. This numerical investigation is performed for the parameters considered in the study: tube amplitude ratios (a/H) from 0.2 to 0.5, baffle height ratios (e/H) from 0.4 to 0.8, open area ratios (β) from 13 % to 30 % and Reynolds number (Re) from 3000 to 19000. The experimental testing rig is designed to validate numerical results corresponding to e/H of 0.4, an open area ratio of 30 %, a/H of 0.3, and Reynolds number varying from 3000 to 15000. Numerical results are found to be in good agreement with the experimental results, with a maximum absolute percentage error of 1.82 % and 5.28 % for the Nusselt number (Nur) and friction factor (fr), respectively. The maximum Nusselt number is observed as 274.29 at Reynolds number of 19,000 and e/H of 0.8; however, the maximum friction factor is observed as 0.6290 at Reynolds number of 3000 and e/H of 0.8 at a constant value of open area ratio of 30 % and a/H of 0.3. Within the range parameters studied, the maximum THPP value is reported to be 2.51 at Reynolds number of 3000, β of 30 %, e/H of 0.4, and a/H of 0.3. Further, correlations for the Nusselt number and friction factor in the function of a/H, e/H, open area ratio, and Reynolds number have been derived based on simulation results.

Compositional numerical analysis of multiphase flow of crude oil in porous media under non-isothermal conditions

Abstract The present work details the development of a compositional model to replicate the heavy hydrocarbon flow in porous reservoir systems under non-isothermal conditions. The mathematical model considers mass and energy conservation equations describing the reactive of natural variables distributed in a multiphase hydrocarbon system. Such natural variable based compositional models better suit fully implicit numerical schemes with inexpensive Jacobian matrix computations. Further, the model accommodates a switch of primary variables for the disappearance and reappearance of a phase. The resulting nonlinear conservation equations are numerically discretized using a block-centered finite-difference scheme and solved with a quasi-Newton based implicit iterative solver. The present model is validated with the thermal profiles presented in the literature for the multiphase flow during the combustion of heavy crude oil in petroleum reservoir system with performance coefficient (R 2), mean absolute error (MBE), and maximum absolute percentage error (MAPE) of about 0.954, 0.37, and 0.01 respectively. The developed compositional model projected 26 and 72 % of light and heavy oil recoveries respectively in about 160 days with a maximum or peak temperature of about 798 K. Further, the thermal and production profiles projected by the sensitivity analysis on various operating parameters are presented. It is noteworthy that the present works aid in providing an economical numerical based tool in evaluating the flow and transport during underground or in-situ combustion process for efficient energy exploration.

Data-Driven State of Health Estimation for Lithium-Ion Batteries Based on Universal Feature Selection

A simple yet effective health indicator (HI)-based data-driven model forecasting the state of health (SOH) of lithium-ion batteries (LIBs) and thus enabling their efficient management is developed. Five HIs with high physical significance and predictive power extracted from voltage, current, and temperature profiles are used as model inputs. The generalizability and robustness of the proposed ridge regression–based linear regularization model are assessed using three NASA datasets containing information on the behavior of batteries over a wide range of temperatures and discharge rates. The maximum mean absolute error, maximum root-mean-square error, and maximum mean absolute percentage error of the SOH for the three groups of batteries are determined as 0.7%, 0.86%, and 2.1%, respectively. Thus, the developed model exhibits high accuracy in estimating the SOH of LIBs under multiworking conditions and is sufficiently robust to be applicable to low-quality datasets obtained under other conditions.

Transfer Learning With Deep Neural Network for Capacity Prediction of Li-Ion Batteries Using EIS Measurement

In this study, transfer learning (TL) technique is used in conjunction with deep neural network (DNN) to predict the capacity of lithium-ion batteries. First, the base DNN model is trained and validated based on the source dataset containing electrochemical impedance spectroscopy (EIS) measurement at temperatures of 25 °C and 35 °C. Then, the base DNN model is retrained and validated using different proportions, i.e., the first 50% and 20% of the target dataset, which contains EIS measurement at the temperature of 45 °C. This will create a new model called DNN-TL carrying the knowledge from the base model. The DNN-TL model is used to predict the second proportions, i.e., the second 50% and 80% of the target dataset considered as missing data. The maximum mean absolute percentage error (MAPE), when the first 50% and 20% of the target dataset are used for retraining DNN-TL with no fixed-layer, is found to be 0.605% and 0.999%, respectively, which indicates the accuracy of the model to estimate the capacity of batteries. The average <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> -squared of 0.9683 is achieved by DNN-TL with no fixed-layer indicating the goodness of its fit and its capability to follow the actual missing datasets.

Parameter estimation in unbalanced three-phase distribution lines using general regression neural networks with inconsistent data handling capacity

The feeder parameters of a power system play an important role in its operation and analysis. However, in many situations, the values used in the calculations differ from the actual parameters, resulting in large errors. Therefore, in this study, a highly accurate feeder parameter estimation method for a three-phase distribution line was proposed. The proposed method uses the measured node voltages and power quantities from the two ends of the distribution line. A precise electrical model of the three-phase distribution line was used. An improved type of neural network, namely general regression neural networks (GRNN), is used to solve the complex non-linear equation and then estimate the actual parameters. However, the proposed estimation process does not require synchronised phasors or phasor-measurement units installed at the point of measurement. Nonetheless, the estimation process is also capable of handling incorrect data information, noisy datasets, and measurement errors while maintaining accuracy at the desired level. The estimator process is examined and analysed using four different IEEE unbalanced three-phase systems. In addition, the proposed methodology is compared with standard algorithms of radial basis function networks, quasi-Newton, and multi-run optimisation methods on the basis of maximum absolute percentage error and other standard error functions. The hyperparameter-tuned GRNN model was also tested using several statistical significance tests. In all scenarios, the performance and accuracy of the proposed methodology and model exceeded those of the other methods.

An ANN-entropy-FA model for prediction and optimization of biodiesel-based engine performance

The present work incorporated full factorial experimentation for performance analysis of Nahar oil-based biodiesel in a four-stroke diesel engine. The controllable input parameters are engine revolution per minute (N), engine load (EL), and blend mixture (BM) respectively. The measured engine performance characteristics are brake thermal efficiency (BTE), brake-specific fuel consumption (BSFC), and exhaust gas temperature (ET). Prediction and optimization of engine output characteristics have been computed through the ANN-entropy-FA hybrid model. In this model, a trained Artificial Neural Network (ANN) is used to compute the objective function value during optimization using the Firefly algorithm (FA). The maximum absolute percentage error of trained ANN during the prediction of output parameters is found as less than 3%. The entropy method is employed to determine the weight of output parameters in the combined objective function. ANN-FA optimization determined minimum BSFC = 0.386 kg/kW-hr, maximum BTE = 24.60%, and minimum ET = 163.24 °C with corresponding operational input parameter setting of low engine rpm (1250 rpm), medium engine load (15.20 kg), and a high percentage of blend mixture (≈25%) respectively. A significantly low absolute % error of around 1.75% during experimental validation of ANN-FA optimized output indicates the efficacy of the proposed model.

Online Model Parameter and State of Charge Estimation of Li-Ion Battery Using Unscented Kalman Filter Considering Effects of Temperatures and C-Rates

This paper proposed a technique for online modeling and state of charge (SoC) estimation of Li-ion batteries considering the effects of operating temperatures and C-rates. The proposed battery model, which is updated in real-time, is incorporated with the unscented Kalman filter (UKF) for accurate and online SoC estimation. In the proposed technique, Thevenin-based equivalent circuit model of Li-ion battery is used. Each of the RC networks of the Thevenin model is represented as a first-order linear time-invariant (LTI) system. The offline RC parameters are extracted as the parameters of the first-order LTI system using the final value theorem. Then the offline RC parameters are converted to the online model parameters compensating the effects of operating temperatures and C-rates. Finally, the UKF technique is augmented with the proposed online battery model for higher accurate and online SoC estimation. An experimental setup has been developed in the LabVIEW platform to validate the proposed battery model and apply it for online SoC estimation. The proposed online battery model and UKF are developed in Matlab and then integrated with the LabVIEW program using the Matlab-LabVIEW interface called Math Script. The proposed technique has been rigorously validated in the laboratory under hybrid pulse power characterization (HPPC) and federal urban driving schedule (FUDS) tests under wide range of varying operating temperatures and C-rates. In the HPPC test, the SoC estimated using the proposed technique has a maximum absolute relative percentage error (ARPE) of less than 2%, whereas the battery model that does not account for temperature and C-rate effects has a maximum ARPE of 8.79 percent, which is 4.30 times higher than the proposed technique. The proposed approach yielded mean ARPE of 0.30%, 1.02%, and 0.81% in the FUDS test at 25 °C, 0 °C, and 40 °C, respectively, which is performed in dynamic identical C-rates. Furthermore, higher accuracy and effectiveness of the proposed technique have been validated under the presence of white and coloured measurement noises.

A machine learning framework for evaluating the biodiesel properties for accurate modeling of spray and combustion processes

The environment-friendly nature of biodiesel coupled with its inherent compression ignition fuel characteristics like better ignition quality, and fuel bound oxygen may reduce sooting combustion, and attract wide attention. The variation of thermophysical properties with temperature is essential for accurately modeling the combustion and emission characteristics of biodiesel fuelled diesel engines. Hence, the current paper attempts to predict the thermo-physical properties such as density, viscosity, specific heat, thermal conductivity, latent heat of vaporization, vapor pressure, mass diffusivity etc., and their variation with respect to the temperature following a machine learning approach for biodiesel fuels. Twenty feedstock samples are chosen for predicting the biodiesel thermo-physical properties and are validated with the available experimental data within a maximum error of 14 %. To evaluate the thermo-physical properties of a variety of feedstock, the predicted data are used for training an artificial neural network (ANN) and the developed ANN function is used for generating the various thermophysical properties of biodiesel fuels based on their composition and temperature. A good agreement is observed between the predicted and ANN results with a maximum mean absolute percentage error of 10 %. Hence in the current work, a collective mathematical modeling approach is proposed to accurately determine the spray and combustion-related fuel properties. The proposed model provides the various liquid and vapor properties and their variation with temperature which could be effectively employed for detailed spray and biodiesel-combustion modeling. An exhaustive data generation of eleven major liquid and vapour properties of twenty biodiesel fuels within the actual temperature range from 300 K to their respective critical temperature is presented.

Heat transfer analysis of a borehole heat exchanger array in a layered subsurface

In the engineering design of borehole heat exchanger arrays, the subsurface is generally regarded as homogeneous, which leads to a large deviation in the prediction of actual performance. An analytical model with good flexibility describing the heat transfer behavior of BHE array in a layered subsurface is introduced using the Green’s function. The Green’s function which is the exact solutions to the temperature response of a ring coil heat source imbedded in a layered ground domain is obtained directly from the governing equations of the problem by the separation of variables techniques. Meanwhile, the nonuniformity of the heat flow rate along the borehole wall depth is addressed in the analytical layered model. Then, a numerical model of BHE array heat transfer in a layered subsurface is proposed based on the modified pipeline flow model. The numerical model is systematically verified with three experiment tests from the literatures and one test performed by the authors. The maximum RSM error and mean absolute percentage error for four test cases are 0.66 °C and 3.25%, showing a good agreement between the proposed numerical model and the measurements. Then, the accuracy of the analytical solution is validated with the existing simple homogeneous model and the proposed numerical model for multiple BHEs and multiple layers scenarios. The effects of the BHEs array and ground stratification on the temperature response are examined in details employing the analytical and numerical models, with the analytical model focusing on the thermal responses of the layered ground and the numerical model on the circulating fluid in the U-tubes. Results show that the presence of the BHE array increases the magnitude of the discrepancy in the temperature prediction between the layered and homogeneous model, particularly in the layers with low thermal diffusivities at large timescales. For the simulated case, the dimensionless temperature difference between the layered and homogeneous scenarios at the borehole wall in the BHE array is 0.35, while it is only 0.11 in a single BHE, resulting in an increase by 218%. Moreover, the ground stratification could affect the prediction of fluid temperature profile along the BHE depth, thus influencing the thermal circuiting between the two pipes of the U-tube. Compared with the homogeneous model, the coefficient of the thermal circuiting increases by up to 11.6% when the ground stratification is considered. Using the homogeneous model with equivalent thermal properties to design the ground source heat pump system in a layered subsurface would underestimate the short circuiting of the U-pipes and undersize the BHE system. The results of this study provide analytical formalism and numerical method to understand better how the design and operation of actual ground source heat pump is engineered.