Thermal Mathematical Model Research Articles

Features of Providing Air Temperature and Humidity Parameters in the Engine Room Working Area at Sewage Pumping Stations

Statement of the problem. There is an important task for engineers to improve the working conditions of workers in industrial facilities. The waste water system includes a large number of structures with different temperature and humidity microclimate characteristics. The possibility has been discussed to improve these characteristics by redistributing air flows in the engine room of a city sewage pumping station with PLI panel. Results. There are the results of the temperature and humidity microclimate parameters research in the working area of the engine room at a high-voltage sewage pumping station which is located in Moscow. The author has proved the possibility of use the cooled air from the machine room lower level in a high-voltage pumping station at the machine room main working area. It has been described the calculation features of the heat transfer coefficients in the proposed model for local ventilation at the main technological working area. It has been described the results of temperature and humidity parameters instrumental study in the main working area and the lower level. Conclusion. Thelocal ventilation systems could be used for the working area, where an employee performs repair work of the main technical equipment in a sewage pumping station. The balanced mathematical thermal model includes PLI panel’s potential location.

Thermal parameter determination in underdetermined spacecraft thermal models using surrogate modeling

This study introduces a data-driven surrogating modeling approach for determining thermal parameters in undetermined thermal mathematical models (TMM) used in spacecraft systems. Maintaining appropriate temperature levels for onboard components is crucial for the success and safety of space missions. However, accurately determining thermal parameters in the undetermined TMM presents a challenge. To address this, we propose an approach that combines TMM correlation with test data and data-driven surrogate modeling.Our approach minimizes an objective function that measures the deviation between predicted temperatures from a surrogate model, incorporating thermal parameters, and steady state temperatures obtained from thermal vacuum balance test results. This optimization is performed using a genetic algorithm while imposing constraints to ensure the physical validity of the thermal parameters and correlation criteria related to temperatures.We demonstrate the effectiveness and validity of our approach by applying the obtained thermal parameters to the TMM. The resulting calculated temperatures exhibit excellent agreement with the test results. This methodology offers a user-friendly and reliable way to determine thermal parameters in undetermined TMM within spacecraft systems, ultimately enhancing temperature control and mission success.

Performance evaluation of semitransparent PV window systems employing periodic thermal model

A conventional window system can be replaced by a semitransparent PV window system, which generates electrical energy, provides natural daylighting, and improves the building's overall energy efficiency. The present study evaluates the performance of three different types of PV window systems, namely, STPV (Semitransparent Photovoltaic), SAG (Semitransparent-photovoltaic-Airgap-Glass), and VSAG (Ventilated Semitransparent-photovoltaic-Airgap-Glass) operating in heating and cooling mode, for the climatic conditions of Calgary, Canada. Periodic mathematical thermal models based on the energy balance equations of the window systems are developed to evaluate the systems' performance under the shading and non-shading effects of a curtain. The results indicate that the VSAG window system can be operated in heating mode to increase the room air temperature and in cooling mode to decrease the room temperature. Additionally, the curtain's transmissivity, PV modules' packing factor, and airflow rates could be used as a controlling measure to keep the room temperature within a comfortable range in different climatic conditions. Reducing the transmissivity of the curtains by 20% lowers the room temperature by 2.5 °C while decreasing the packing factor by 10% increases the room temperature by 4.8 °C.

Data-driven thermal state estimation for in-orbit systems via physics-informed machine learning

Thermal analysis of spacecraft systems is a critical process for mission operations. However, knowing the temperature distribution of entire systems is not easy due to the uncertainty of the thermal mathematical model (TMM) and limited temperature sensors. This paper proposes a temperature estimation method using physics-informed machine learning (PIML). The PIML-based thermal analysis allows us to estimate the actual temperature distribution by seamlessly bridging the limited observations and the TMM. To evaluate the estimation accuracy of the proposed method, we conducted a numerical experiment using a pseudo small satellite model consisting of 100 nodes. The proposed method was applied to three different model error cases and was found to improve temperature estimation accuracy in all cases. In addition, the impact of the number of temperature sensors and their placement on estimation accuracy was investigated.

Passively Maintained Closed Cavity Façade—Experimental Validation of the Mathematical Thermal Model

Although glass façades have been on the market for over a century, new improvements, following sustainable standards, are still being invented. An improvement of the actively maintained CCF has occurred in passive maintenance with natural ventilation of the cavity and insulation glass unit placed on the external side, which has served as a true motivation for further research. To develop the idea, a new type of CCF was invented, followed by the creation of the software, whose purpose is to determine optimal CCF façade components. During this research, an experimental and mathematical model was made regarding the thermal behavior, later validated by the measurements on-site in Rugvica, Croatia. Using simplified but unconventional methods, numerous formulae and variables, a simulation of climatic loads onto the CCF was conducted. Validations of the thermal model were made during winter and summer periods for southern and western façade orientation, explaining how heat transfers from the environment to close cavity façade elements. It was found from the analysis that air temperatures of the façade elements follow the outer air temperature, by constant air exchange with the outer space. The results showed great potential with up to 3 °C (5–10%) of difference in experimental and calculated results, thus creating a basis for further improvement of the software with the addition of structural and hygric behavior of the façade element, regarding climate conditions.

Thermal surrogate model for spacecraft systems using physics-informed machine learning with POD data reduction

Thermal analysis of spacecraft systems is one of the most critical processes in the design and operation of space missions. However, it is computationally costly to predict the temperature under all conditions including attitude, orbit, or all combinations of equipment use cases. This study proposes a novel surrogate model for full-scale thermal models using data reduction via proper orthogonal decomposition and physicsinformed machine learning. The prediction accuracy of the proposed method is evaluated using two types of thermal mathematical models to investigate the dependency of the training dataset and the size of the models. In addition, the prediction accuracy and training cost were compared between data-driven machine learning and physics-informed machine learning. As a result, the proposed method successfully predicted the full model temperature for both models under various heat input conditions. Moreover, the proposed method decreased the total training cost by 26% to 81% compared to data-driven machine learning.

Ascent phase convective heat transfer of a stratospheric-balloon-borne payload

Stratospheric ballooning flights are becoming more relevant due to these platforms can place payloads to an altitude above almost 99% of the atmosphere, where the environmental conditions are very similar to the space ones. From a thermal point of view, during the ascent phase convection is very relevant and, despite what a priori may be thought, depending on the element considered, convection may not be negligible at the float phase. With this in mind, the Thermal Analysis Support and Environment Characterization Laboratory (TASEC-Lab) was born. It is an experiment based on COTS, which consists in a 3U CubeSat-like experiment, which was launched onboard a stratospheric balloon in León (Spain) on 16th, July 2021. The upper unit of the 3U box contains a heated plate, with the aim of quantifying the relevance of convection during the flight. In this paper, the relevance of convection during the ascent phase is described, the correlation of in-flight temperature measurements with those provided by the thermal mathematical model developed in ESATAN-TMS is performed, using the air mass flow inside the cavity as a fitting parameter with a fitting error lower than 5 °C during the ascent phase.

Study of pyrolitic graphite sheet potential as thermal passive element in CubeSats

CubeSats have become in the last decade ideal platforms to demonstrate new technology or to facilitate access to space due to the reduction in development time and costs. However, one of the main problems is the short lifetime of their missions. In many cases, it is due to the lack of correct thermal design and thermal analysis or even no thermal analysis at all. Specifically, the solar panel thermal design affects the global satellite behavior as the electric power supplied by the solar cells depends on their temperature. Typically, the solar panel thermal design is reduced to use its backside as a radiator (if they are deployable). This paper presents a new thermal solar panel assembly using an intermediate layer of PGS (Pyrolitic Graphite Sheet), which at room temperature has a thermal conductivity 3.8 times greater than pure copper, between the solar cells and the solar panel support, in order to homogenize the solar cells temperature. The new design is compared to the standard design developing the GMM (Geometrical Mathematical Model) and TMM (Thermal Mathematical Model) of a CubeSat 6U located in LEO using ESATAN-TMS. The proposed design gets a reduction of up to 5 °C in the temperature variation of the solar cells.

Experiments and simulations on the energy performance of semi-transparent photovoltaic roof-integrated skylight glazing

Photovoltaic (PV) cells integrated with building roof skylights not only generate electricity but also influence the thermal performance of the roof. In this paper, the thermal mathematical model of a semi-transparent photovoltaic insulating glass unit (STPV-IGU) integrated with the roof is established and validated by experiments. Case studies are conducted by using the roof-integrated STPV-IGU in Shanghai, and an equivalent electrical method is used to evaluate the energy performance of roof-integrated skylight STPV-IGU. The equivalent electricity of heat-gain entering the room through STPV-IGU and total equivalent electricity of roof-integrated STPV-IGU is 16.6 kWh/m2 and 12.1 kWh/m2 in summer, respectively. The equivalent electricity of heat-gain entering the room through STPV-IGU and total equivalent electricity of roof-integrated STPV-IGU are −16.3 kWh/m2 and −4.0 kWh/m2 in winter, respectively. Compared with traditional insulating glass unit, the STPV-IGU can significantly reduce the heat-gains through glazing in summer, but increase indoor heat-loss in winter.

Thermal analysis of a high-altitude solar platform

High Altitude Long Endurance (HALE) aircraft operate under adverse thermal conditions, with ambient pressures and temperatures very low and at the same time high amounts of heat introduced by sun radiation. Thus, thermal management of the aircraft systems, such as electronics and batteries is a very challenging task. A first step in solving this is generating accurate models of the thermal dynamics of the HALE. This paper presents the thermal analysis of a solar-electric stratospheric HALE at the ground case. A thermal mathematical model based on first principles was developed for such an analysis. In a further step, an initial test campaign was performed. The test campaign included static and dynamic temperature measurements on an aircraft wing structure segment. The experiments throughout this test campaign showed good compliance of the results with the previously derived mathematical models, with differences of less than 5 ,^{circ }C between the measured and simulated temperature curves.

Influence of the Measurements Uncertainties in the Correlation of Spacecraft Thermal Models against Thermal Results

Ground thermal tests are always mandatory before any space mission is flown into space. The collected results of these tests are mainly temperatures of the different parts of the spacecraft (nodes) for different mission scenarios. The measured temperatures always show differences with the expected values coming from the computer thermal mathematical models. The origin of these differences is partially related to the inherent error coming from physical measurements. The thermal parameters that compose the computer thermal mathematical models must always be correlated with the results coming from tests. This paper studies, through three thermal models, the difficulties that are found in the correlation process when the measured temperatures reach a certain level of error. Thermal parameters become more difficult to be identified when the measurement error level increases. However, the temperature fields obtained with these poor thermal parameters are good enough for the mission thermal analysis. Several error levels, different load cases and correlation for steady-state and transient cases are studied to probe these findings.

Transient thermal parameters correlation of spacecraft thermal models against test results

There are always differences between the computer predicted temperatures of a spacecraft thermal model and the temperatures measured during the mandatory laboratory thermal tests. As a consequence, the model must be correlated before the spacecraft is launched to space, in order to identify the correct parameters that match the experimentally measured temperatures.A new technique is presented to identify the parameters, based on the minimization of the error of the transient equations which governs the heat transfer in the spacecraft. The steady state minimization was presented in a previous work, but the transient techniques presented hereafter enable a better and more extended identification of parameters despite the higher complexity of the computational problem.The use of a set of available subroutines (TOLMIN), which permits the constrained optimization of a general function, makes possible to ensure that the obtained parameters are non-negative, a requirement to have physical sense. The gradient function must be calculated for each problem, but this can be done automatically.Results show that for small and medium size transient Thermal Mathematical Models (TMM), a good correlation of thermal parameters can be achieved even if some of the nodes temperatures are not measured in the thermal tests.

Modified load flow algorithm suitable for modern power systems under variable weather conditions

Conventional load flow algorithms are very commonly used in the system planning. In the conventional load flow methods, system electrical parameters at specific weather conditions will be considered. These methods gives results for given loading condition and have no provision to incorporate weather condition of a specific geographical location. If the load flow has the provision to incorporate the dynamic electrical characteristics of the conductors based on the operating weather condition, the results of the methods are going to be more accurate or in other words the results are close to the real values. In view of the above, in this paper a modified load flow algorithm incorporating the thermal modeling of the conductors with ambient temperature, wind velocity, conductor surface absorptivity, global solar radiation, Wind direction factor etc. is proposed. To verify the effectiveness of the proposed algorithm, the thermal mathematical model of transmission lines available in IEEE Std. 738™ -2006, IEEE Std. 738™ -2012 and CIGRE WG 22.12 are considered. In the proposed algorithm, new variables corresponding to Conductor Temperature are incorporated. The proposed algorithm is tested with the real time weather data of India and demonstrated on IEEE 30 and 118 bus systems.

Irreversibility analysis of time-dependent magnetically driven flow of Sutterby hybrid nanofluid: a thermal mathematical model

As hybrid nanofluids have dispersion and diffusion abilities along with greater stability on the surface compared with the conventional fluids, they are introduced as heat transfer fluids. In the present analysis, investigations are made on flow, volumetric entropy formation and convection heat transmission in Sutterby hybrid nanofluid (SBHNF). Keeping slip velocity on the interface of horizontal uniform permeable stretching surface, hybrid nanofluid takes the space on it. Viscous dissipation along with the impact of linearized thermal radiation is employed in a disentangle model. Assumptions about boundary layer SBHNF flow are interpreted for simplification of governing equations regarding conservation of momentum, mass, entropy, and energy. Similarity variables are employed for the similarity solutions for the change of governing partial differential equations to ordinary differential equations (ODEs). Suitable solutions for the reduced ODEs are found with the implementation of the Keller-box method. Ordinary copper–sodium alginate (Cu–SA) nanofluid and Zirconium dioxide–copper/sodium alginate (ZrO2–Cu/SA) hybrid nanofluid are utilized for numerical and computational results. The influence of governing factors is studied with the help of plots about temperature, velocity, and entropy. The parameter of skin friction along with the local Nusselt number is examined at the boundary.

Верификация тепловой математической модели с сосредоточенными параметрами малого космического аппарата серии «АИСТ» на основе телеметрических данных, полученных в ходе его экспериментальной эксплуатации

The purpose of the study was to model a small spacecraft of the AIST series and verify this thermal mathematical lumped-parameter model using differential equations and relying on telemetry data obtained during the experimental operation of the spacecraft. Thermal lumped-parameter models are widely spread in designing small-sized onboard equipment for small spacecraft. The model calculation was done by Simulink, the MATLAB-based graphical programming environment for modeling multidomain dynamical systems. We developed a system of equations, consisting of equations for each zone from the outer and inner sides, as well as the equations for scientific equipment. The small spacecraft design is based on three-layer honeycomb panels with heat pipes. Photocells are installed on the outer sides of the panels of the spacecraft, thus making a significant contribution to its thermal state.

Thermal mathematical model of a circuit with the coolant capillary pumping containing several evaporator pumps and condensers

Thermal mathematical model of a circuit with the coolant capillary pumping containing several evaporator pumps and condensers

Study of a Thermal Mathematical Model for Pre-Diagnosis of Photo-Mechanic Induced by Laser Based on Light Transport Equation

Study of a Thermal Mathematical Model for Pre-Diagnosis of Photo-Mechanic Induced by Laser Based on Light Transport Equation

Thermal parameters identification in the correlation of spacecraft thermal models against thermal test results

Temperatures predicted by the Thermal Mathematical Models (TMMs) used in the thermal control design of spacecraft, usually present differences with the values measured during the thermal test campaign. Therefore, the TMMs must be correlated with the thermal tests to reduce these differences to admissible values.This task can be addressed in an automatized way considering the correlation as an optimization problem, where the differences between predicted and measured temperatures are minimized. This is achieved modifying the values assigned to some parameters used in the TMMs. The main drawback of this approximation is the risk of loosing the physical sense of some model parameters. The reason is that the thermal inverse problem, that is, calculate the thermal parameters that produce a specific temperature distribution, often has not a unique solution.A methodology of automatized correlation to calculate the correct values of the model parameters, in the sense that they maintain its physical interpretation, is presented in this article. The key point relies in setting up an overdetermined system of equations. The expression to calculate the minimum number of load cases required, is developed, and several case studies are presented to validate the proposed methodology. A gradient based public available set of subroutines (TOLMIN) has been used as optimization algorithm.

Performance of a shallow solar pond coupled with a heat pump cycle for thermal energy in net zero-energy buildings

Refrigerant evaporation, in heat pumping systems, is a particularly complex process. Since the evaporator is subjected to environmental conditions, several factors weigh in on overall system performance, mainly, the additional energy input from the surroundings. This renders the evaporation process especially susceptible to gaps and fluctuations of said energy availability, particularly in solar-assisted setups. Despite the, comparatively, high heat flux associated to this source, these occurrences make them suitable mostly for low-to-medium thermal requirements, especially in regions with more extreme climates. The present work introduces a novel evaporator design, based on solar ponds. The proposed evaporation device incorporates a short-term, passive, thermal storage solution to compensate for gaps in energy availability. A mathematical-thermal model is developed and a performance assessment is conducted based on real seasonal atmospheric and operation conditions. For this study R134a, R152a, R1234yf and R1234ze(E) were used as working fluids. The proposed heat pump configuration is evaluated for hot water production at 55 °C, indoor air heating at 18–22 °C and a combined simultaneous scheme. The results show that this configuration performs well under moderate climate conditions. For hot water production during spring, highest outlet temperature of 68.54 °C for the R1234yf working fluid, were reached and maintained after the first 13 h. Internal thermal capacitor reached an average temperature of 61.88 °C for R1234yf. During winter, these temperatures decrease almost by a third, with 40.6 °C for R1234yf working fluid. However, daily average outlet temperature of 64.8°Care reached within the first 15 h of operation. Despite a lower thermal storage, with average capacitor, the system yielded consistent average outlet temperature of 20.7 °C. For a simultaneous operation scheme, desired outlet water temperature, is reached within the first 16 h of operation, whilst the indoor air temperature reaches comfort levels within the first 12 h. Despite employing part of the energy absorbed to maintain a stable comfort condition within the dwelling, instead of compensating the heat loss of the hot water tank, both goals are achieved. The inclusion of an inner thermal capacitor that collects and stores energy at a much higher rate provides the refrigerant with an additional heat source. This results in a more effective overall energy absorption of the evaporator, which exceeds the rate at which heat is dissipated from the tank/dwelling to the environment. This heat loss buffer lessens, considerably, the thermal demand during periods with lower energy availability, resulting in achievable outlet conditions.

Effect of optical, geometrical and operating parameters on the performances of glazed and unglazed PV/T system

This work aims to investigate the effect of optical, geometrical and operating parameters on the thermal and electrical performances of both glazed and unglazed hybrid PV/T solar collector. To achieve the goal, a three dimensional mathematical thermal model is developed and solved numerically using implicit finite difference method. In addition, an optical analysis is performed to calculate the optical efficiency of the solar system. The model accuracy is tested by comparing the obtained results with experimental and numerical data available in the literature. The results show that the glass cover system is an important element of the photovoltaic-thermal system. It is found that the thermal efficiency of the glazed system is 21.49% at 0.01kg/s mass flow rate higher than unglazed system, but its electrical production is lower than unglazed collector by 11.78%. It is obtained that the thermal and electrical yields are dropped by 18.07% and 15.93% respectively when the refractive index of glass increases from 1.1 to 1.9. The extinction coefficient of glass has also a significant effect on the hybrid system performances. However, the glass thickness has a slight impact on the collector efficiency.