Use of temperature derivative to analyze thermal response tests on borehole heat exchangers (2024)

Parameter estimation from thermal response tests (TRTs) becomes unreliable when testing time reduces or the number of estimated parameters increases because of low identifiability and ill-posed mathematical feature. To overcome this challenge, this paper reports an inversion algorithm integrating a short-time temperature response model and the zero-order Tikhonov regularization strategy. We applied the algorithm to a reference sandbox dataset and examined four scenarios: simultaneous estimation of four, five, six, or seven parameters of U-shaped geothermal heat exchangers. The preliminary results indicate that the Tikhonov regularization can improve the accuracy and precision of the nonlinear multi-parameter estimation of ground heat exchangers for both long (>48h) and short (<48h) tests. The improved performance is contributed to the short-time model, which enables the short-time high-sensitivity data to be useable, and the regularization, which stabilizes the iterative optimization-solving procedure.

The ground thermal properties are the basic parameters for the design of borehole heat exchanger (BHE) in ground–coupled heat pump system (GCHPs), and their accuracy directly affects the economy and reliability of the heat pump system. In traditional design, ground is usually regarded as an isotropic hom*ogeneous medium, and its thermal properties are obtained by solving the inverse heat transfer problem in BHE through in-situ thermal response test (TRT). In fact, different geological layers can be observed along the depth of BHE, and thermal physical properties of each layer are different based on the ground geological conditions. In order to investigate the effect of geological stratification on estimated accuracy of ground thermal parameters in TRT, a validated numerical layered BHE model (NLBM) is presented to simulated TRT, and the fluid temperature response is used to estimate effective ground thermal conductivity and borehole thermal resistance based on line source model (LSM). Secondly, the distributions of fluid temperature in U-pipe and heat flux of BHE along the depth are compared and analyzed based on the NLBM and the numerical hom*ogeneous BHE model (NHBM). At last, borehole thermal resistance from the NLBM and estimated borehole thermal resistance from LSM are compared. The results show the maximum heat flux in the 3rd layer of the NLBM is 21.1% higher than that of NHBM, and the minimum heat flux in the 1st layer is reduced by 46.9% in the 100h duration. The estimated ${\lambda }_{\text{LSM}}$ using the fluid temperature responses in the NLBM is 1.3% higher than the thickness-weighted thermal conductivity in the NLBM. The minimum relative error between $R_{\text{LSM}}$ and $R_{\text{b}}$ is still up to 10.45% in the duration of 100h even though extending the duration is helpful to improve the estimated accuracy of $R_{\text{LSM}}$.

The thermal parameters of the ground and the borehole, combined with a thermal model such as the infinite line source, enable fitting a short-term g-function by using a unit heating profile. This classical method is sensitive to model errors. The approach developed in this work extracts the short-term g-function and its derivative directly by deconvolution of thermal response test data, without having to specify a thermal model. The method minimizes a least squares-based multi-objective function on a set of nodes. The approach is robust to random power fluctuations affecting the thermal response test and allows using different heating and cooling scenarios. Results show that the deconvolved short-term g-functions display expected characteristics, and the temperature reconstructions have an error of less than 0.1°C across various numerical and field test cases, an accuracy hardly attainable by classical analytic approaches.

Obtaining soil thermophysical parameters is the premise for design ground heat exchanger in ground source heat pump system, but it may not be accurately determined due to the limitations of the analytical models. In this paper, artificial neural network (ANN) is used to directly establish the mapping relationship between temperature response and soil thermophysical parameters, and the identification accuracy of traditional method and ANN under different measurement errors is compared. In addition, Kalman filter and fitting regression are used to remove the interference noise. The results show that the identification accuracy and stability of the traditional method are relatively weak affected by temperature measurement error, but the identification accuracy is limited. The maximum deviation errors of thermal conductivity and volumetric heat capacity are 10.68% and 18.42%, respectively, and no matter which kind of noise reduction method cannot improve the identification accuracy. The identification stability of ANN is relatively greatly affected by temperature measurement error, but the identification accuracy is high. The maximum deviation errors of the two parameters are 10.05% and 5.4%, respectively. Through the logarithmic function fitting of noise date can further improve the identification accuracy and stability, the maximum deviation errors are only 2.12% and 3.65%.

It is critical to determine the thermal parameters of the soil and pile before designing energy piles. A new parameter estimation method is proposed to interpret the thermal response test (TRT) data of energy piles. A cylindrical heat source model that considers the difference in the thermal properties between the soil and pile is adopted. This analytical model accurately describes the heat transfer process inside and outside the pile at the initial stage. First, a three-dimensional numerical model is established and verified by a large sandbox experiment in the literature. The numerical model is used to simulate a series of virtual TRTs. Second, the sensitivities and correlations of different thermal parameters are investigated. Based on the above analyses, a stepwise parameter estimation method combined with the pattern search algorithm is proposed to estimate the thermal resistance in the pile R_b, effective thermal conductivity k_s and diffusivity a_s of the soil successively. The results show that the proposed method is feasible and effective for using the early-time data to estimate multiple parameters accurately. The relative errors of R_b, k_s, and a_s are equal to 5.2%, 1.2%, and 13.3%, respectively. Finally, the influences of pile diameters and configurations on the accuracy of the estimation results are discussed in detail. Compared with the traditional slope method and parameter estimation methods based on other analytical models, this proposed method can save the time cost of TRTs and obtain more accurate thermal parameters.

Applied Thermal Engineering, Volume 134, 2018, pp. 369-378

This paper evaluates the potential advantages of introducing a new injector concept with a dual set of orifices in a 2-stroke engine operating with gasoline partially premixed combustion (PPC gasoline), specially in terms of combustion noise reduction. The injector is based on a configuration with two concentric needle valves and dual actuators, which allows to switch among two independent crowns of holes. The first set of orifices is controlled by the primary needle valve while an additional needle valve manages the secondary holes crown. Moreover, both valves are coupled with the two actuators separately, providing enhanced selective control over injection with an extra degree of freedom. In this investigation, a combination of Computational Fluid Dynamics (CFD) simulations and the Design of Experiments (DoE) technique is proposed with the specific purpose of optimizing this new injector configuration. In addition to determining the most convenient design, this method is extremely useful to establish cause/effect relationships between the injection design parameters and their impact on the engine performance and emissions. Results show how this solution could increase the operating range of the PPC gasoline concept by improving the combustion stability while acoustic emissions are reduced.

Applied Thermal Engineering, Volume 134, 2018, pp. 341-352

In this work, the induction heating of heavy cylinder is numerically and experimentally studied. The electromagnetic-temperature-stress multi-field coupling simulation are performed, using the ANSYS software in order to investigated the induction heating process of heavy cylinder, simulation results show that the end of heavy cylinder would be overheating and burning because of the acute angle effect and the high magnetic flux density when the rectangular coil is used. And then, the acute angle effect problem of heavy cylinder in the induction heating process is investigated, a solution of welding heat treatment ring at the end of the heavy cylinder and adding the magnetizer at the end of coil is proposed, and the acute angle effect can be eliminated. Furthermore, the heating effects of heavy cylinder by traditional heating method and induction heating method proposed are compared, simulation results show that the heating efficiency and the energy saving of induction heating are improved greatly. Finally, the heat treatment experiment of heavy cylinder material based on induction heating is investigated, experiment results show that the mechanical properties of the heavy cylinder can meet the application requirements.

Applied Thermal Engineering, Volume 134, 2018, pp. 360-368

Aiming at the complexity of the process calculation of the spiral-wound heat exchangers (SWHEs) with bilateral phase change, a method of segmented calculation is presented. According to the general working conditions of oil refinery, the engineering calculation model is established. The optimal design of the spiral-wound heat exchanger is carried out, based on the genetic algorithm. When the total heat transfer capacity is constant, the total heat exchange area is used as the objective function, and the winding angle $\alpha$ (10–30°), the thickness of the spacer a (0–10 mm) and the axial tube spacing of the same layer c (0–10 mm) are taken as the design variables. When the heredity is given to a certain algebra, the heredity terminates, the a value is 0.00237 m, the c value is 0.00814 m, the $\alpha$ value is 11.7°, and the objective function is the total heat exchange area, which is 4900.6 m². The optimization results show that the optimized heat transfer area is reduced by about 23.4%, The tube side and shell side pressure drop are within the allowable range, although increased.

Applied Thermal Engineering, Volume 134, 2018, pp. 353-359

Applied Thermal Engineering, Volume 134, 2018, pp. 333-340

This paper describes a 3D numerical simulation to model the two-phase separation of refrigerants in a horizontal run-type T-junction. The computations are based on the Eulerian method with the k-ε turbulence model. Compared with data from existing experiments and phenomenological models, the average deviation of the established model is less than 5% when the liquid mass flow rate ratio is in the range 0.2–0.6. The effect of multiple parameters on phase separation is investigated using the validated model. The results show that the inlet qualities (0.3–0.7), saturation temperatures (279.15–284.15 K), and working fluids of R22 and R134a have little influence on the phase separation at the T-junction, whereas the gas mass flow rate ratio increases with the increase in inlet mass flux (100–500 kg m⁻² s⁻¹). Furthermore, it is found that two symmetric recirculation regions occur directly after the junction at the entrance to the branch.

Applied Thermal Engineering, Volume 134, 2018, pp. 322-332

A numerical investigation was carried out to study the condensation flow and heat transfer coefficient of methane/propane and ethane/propane mixtures in a helically coiled tube. Two-phase heat transfer simulations had been performed at saturation pressures of 0.3–3.7 MPa with mass flux of 200, 300, 400 kg/(m² s) and heat flux of 5 kW/m². The effects of mass flux, saturation pressure, vapor quality and component ratios on the heat transfer coefficient were examined. In addition, annular/non-annular flow patterns were obtained by numerical simulations and experiments, and a new flow pattern transitional line for annular/non-annular flows was proposed. Meanwhile, the results were compared with the existing condensation heat transfer correlations, and the improved heat transfer correlation was proposed and well coincided with the data with a mean absolute relative deviation (MARD) of 9.2%.