Heat Pump Subsystem Research Articles

Multi-objective optimization and influence degree analysis of the thermally integrated HP-ORC carnot battery based on the orthogonal design method and grey relational analysis

Thermally integrated heat pump (HP)-organic Rankine cycle (ORC) Carnot battery is a promising solution for efficient energy storage and waste heat utilization. Firstly, in order to research the influence degree of the operating parameters on the system performance, single-objective optimization is conducted by the orthogonal design method. Then, multi-objective optimization is conducted by combining the grey relational analysis (GRA) and orthogonal design method to assess the comprehensive performance of the system. The importance order and contribution rates of the operating parameters and the optimal operating combinations are determined. Finally, in order to explore the influence mechanism of the parameters on the system performance, the influence of the parameters on the subsystems and the subsystems on the whole system is quantitatively analyzed. The results show that thermal storage temperature difference, waste heat temperature difference and cold source temperature are the most important parameters affecting the comprehensive performance of the whole system. Under the optimal operating conditions, round-trip efficiency, exergy efficiency, energy storage capacity (ESC), energy storage density (ESD) and levelized cost of storage (LCOS) are 47.05 %, 22.66 %, 1943 kW, 2.90 kWh/m3 and 0.38$/kWh, respectively. Compared to the ORC subsystem, the HP subsystem is more important to round-trip efficiency and exergy efficiency.

Analysis of Energy Consumption and Economy of Regional Gas Tri-Supply Composite System

With the development of Chinese society, there is an increasing demand for emissions reduction and the stable operation of the power grid. Regional comprehensive energy supply systems have entered the public’s view owing to their advantages of reducing capacity, unified dispatch, improving efficiency, and reducing energy consumption. This paper focuses on a system under construction in Chongqing, which adopts a combined gas tri-supply (combined cooling, heat, and power, CCHP) and dynamic ice storage cooling system as the research object. By establishing a mathematical model for the simulation research, this study examines the start–stop priority sequence of the gas tri-supply subsystem and the heat pump subsystem under the ice storage priority strategy in winter and summer and proposes corresponding optimization solutions. By comparing the annual operating energy consumption of the system, we conclude that the gas tri-supply composite system has good economic efficiency and peak-shaving capability, indicating that regional gas tri-supply composite systems have great application potential in the future. The proposed optimized operation strategy and simulated energy consumption calculation provide theoretical guidance for the construction and operation of both this project and similar projects.

Experimental investigation of a solar-assisted absorption-compression system for heating and cooling

Decarbonizing the energy sector becomes a key topic to solving man-made climate change. For achieving indoor thermal comfort conditions, conventional heating, ventilating, and air-conditioning systems consume so much energy in both residential and public buildings. In this paper, a novel solar-assisted absorption-compression system for both heating and cooling is proposed to utilize solar thermal energy throughout the year for the heating/cooling supply. The experimental prototype was built and operational modes including solar-assisted heating/cooling mode and vapor compression individual heating/cooling mode. The performance enhanced by assisted heat input of the proposed system is evaluated by comparing it with air-source heat pumps operated under the same ambient conditions. Performance indices consisting of COPele increment, power-saving ratio (PSR) and energy-saving ratio (ESR) are presented. The results indicate that the combination of the absorption heat pump subsystem and the vapor compression subsystem lowers the heat-driven temperature to 60 °C and thus makes higher solar collection efficiency possible. The maximum of the COPele increment and the PSR under solar-assisted heating mode are achieved at conditions with 80 °C hot water temperature, of 45.8% and 31.4%, respectively, and the corresponding value for solar-assisted cooling mode are 18.9% and 16.0%. The speed of compressor as well as fan frequency of terminal has a greater influence on heating performance that on cooling performance due to the different coupling mechanisms.

Koopman Model Predictive Control of an Integrated Thermal Management System for Electric Vehicles

AbstractThis paper is concerned with energy efficient operation of an integral thermal management system (ITMS) for electric vehicles using a nonlinear model predictive control (MPC). Driven by a heat pump (HP), this ITMS can handle battery thermal management (BTM) while serving the need for cabin cooling or heating need. The objectives of the ITMS MPC control strategy include minimization of power consumption and achieving temperature setpoint regulation for the battery and cabin space based on predictive information of traction power and cabin thermal load. The control design is facilitated by a gray-box modeling framework, in which the nonlinear dynamics of HP subsystem are characterized with a data-driven Koopman subspace model, while the BTM subsystem dynamic is a bilinear physics-based model. The computational efficiency of the proposed MPC framework is improved with two aspects of convexification for the underlying receding-horizon constrained optimization problem: the Koopman-operator lifting and the McCormick envelopes implemented for handling the bilinear dynamics. The proposed control method is evaluated with simulation study, by developing a Modelica-Python cosimulation platform via the functional mockup interface (FMI), where the electric vehicle (EV)-ITMS plant is modeled in Modelica with Dymola and the MPC design is implemented in Python. By benchmarking against a recurrent-neural-networks (RNN) model based nonlinear MPC, the simulation results validate the effectiveness and improved computational efficiency of the proposed method.

Evaluation of a heat pump coupled two-stage humidification-dehumidification desalination system with waste heat recovery

Humidification and dehumidification (HDH) desalination technology has attracted wide attention in the field of small-scale dispersed fresh water demand, because of its advantages such as simple configuration, low investment, and utilization of low-grade renewable energy and waste heat. In this paper, a heat pump coupled two-stage humidification-dehumidification desalination system with waste heat recovery is proposed, where the waste heat is used to heat the feed seawater of the first-stage humidifier, and the brine leaving the bottom is further heated by the condenser of heat pump and then taken as the feed of the second-stage humidifier, while the evaporator of heat pump is used to recover the heat of humid air from the first-stage dehumidifier. Performance evaluation of the proposed system with various working fluids are conducted regarding the fresh water production mpw, gained output ratio (GOR), recovery ratio (RR), specific entropy generation stot, and unit cost of fresh water production Zpw, and parametric studies are performed to identify the key operating parameters. Results show that the largest entropy generation occurs in evaporator, followed by the first-stage humidifier and condenser. Taking R22 as the working fluids is corresponding to the largest mpw, while the lowest Zpw and stot, and the highest GOR are obtained by R600. Higher spraying temperature of the first humidifier T4 is conducive to improving the mpw and Zpw, but leading to a larger stot. The GOR increases first and then decreases with the rise of T4, and the peak value is 4.57 at T4 = 340.65 K. The mass flow rate ratio of the first stage MR1 has significant effects on the system performance. When MR1 is about 3.5, the mpw, GOR and RR reach the peak. However, the bottom value of Zpw is 8.74 $/m3 corresponding to the MR1 of 2.2–2.5. With the increase of compression ratio (CR) of heat pump subsystem, the mpw, GOR and RR climb up first and then decrease, while Zpw and stot get raised.

Conventional and advanced exergy analysis of a novel wind-to-heat system

Exergy analysis are carried out on a novel 100 kW wind-to-heat system to investigate the thermodynamic performances by employing the experimental data. Nine different combinations of the wind speed and water flow rate are selected as the typical operating conditions. Through the conventional exergy analysis, the wind turbine accounts for the most of the system's total exergy destruction at high wind speeds. In terms of the heat pump subsystem, the compressor is the most critical component, followed by the condenser. For further obtaining the optimal design directions of the key components, the advanced exergy analysis is applied to this system. By establishing the mathematical model, the exergy analysis of the ideal conditions, experimental conditions and unavoidable conditions are compared. Averagely 87.32% exergy destruction of the compressor is endogenous and avoidable, which can be decreased by optimizing the internal structure parameters. The average proportions of the avoidable exergy and endogenous exergy destruction of the condenser are 57.48% and 68.41%, respectively. Both the internal parameters of the condenser and interactions with other components must be taken into consideration. The optimizing potential of the wind-to-heat system through exergy analysis methods can be used for further research and improvement of the system.

Development of a novel flexible multigeneration energy system for meeting the energy needs of remote areas

This paper introduces a flexibility concept in development of a novel multigeneration energy system driven by a renewable energy heat source. Nevertheless, the energy system can be upgraded to a highly productive system by incorporating other subsystems for achieving more production such as domestic hot water and freshwater. A novel design is proposed for a system comprising organic Rankine cycle, absorption compression heat pump, liquid natural gas to natural gas converting system, domestic water heater, and humidifier-dehumidifier desalination to exploit the Sabalan geothermal source for multigeneration purposes. Due to its high-efficient and environmentally friendly characteristics, n-pentane is utilized in the organic Rankine cycle. Also, the Ammonia-water is employed in the absorption compression heat pump subsystem. Energy, exergy, and thermoeconomic analysis is conducted on the plant along with multi-objective optimization based on the parametric study of key variants. According to the results, the novel step-by-step flexibility analysis can give a wide viewpoint to the designers to make the best multiple plant. The results of multi-objective optimization indicate that the freshwater production increases from 0.803 kg/s to 0.834 kg/s, the capacity of the domestic water heater rises from 1254 kW to 1265 kW, and the net output power surges up by 137.96 kW. However, the heating production falls from 1276 to 1088 kW. Furthermore, the total energy and exergy efficiencies increase by 6.43% and 4.47% with a 2.08 $/GJ reduction in the unit cost of the product.

Economic, energy and exergy assessments of a Carnot battery storage system: Comparison between with and without the use of the regenerators

Energy storage plays a critical role in balancing the power distribution grid and can provide more flexible and reliable grids. In addition, renewable energy based-systems integrated with energy storage systems can be a desirable solution to energy challenges nowadays. Carnot battery is one of the candidate systems for energy storage that allow storing electricity at low cost with no geographical constraints. The aim of this paper is to provide an economic, energy and exergy analyses of a Carnot battery based on the organic Rankine cycle (ORC) and the vapor compression heat pump (HP) with the use of regenerators in both subsystems. Providing thermodynamic analysis and calculating the exergy destruction and Levelized cost of storage (LCS) of the proposed energy process are the main objectives of the present study. In addition, LCS (as the objective function) is minimized using the genetic algorithm. The results showed that at a thermal storage temperature of 125 °C, the value of LCS for the proposed process is approximately $ 0.3 per kWh. In addition, the total cost of investing in such a system is nearly k$ 5700. It was also found that if the regenerators are not used, the value of power to power efficiency can be lower. However, the use of regenerator in the HP subsystem has a significant impact compared to the ORC. The performance of the proposed system is also discussed according to the optimization results.

Experiment investigation on a LiBr-H2O concentration difference cold storage system driven by vapor compression heat pump

Solar-powered LiBr absorption cooling system is of potential in the application of air-conditioning. A LiBr-H2O concentration difference cold storage system driven by vapor compression heat pump was proposed. This cold storage process is not affected by the environmental conditions, since the main energy input is low price electricity at night. The experimental results show that the energy storage density (ESD) can reach 77.8 kWh/m3 and the energy storage coefficient of performance (ESCOP) is 2.81 with low heat loss. The ESCOP means the energy stored in the cold storage process divided by the total electricity consumption in the absorption and heat pump subsystem. The heat transfer in the condenser of the absorption subsystem approximately equals that in the evaporator of the heat pump, and the electricity consumption of the circulating pump in the absorption subsystem is low. Therefore, the value of ESCOP should be slightly lower than the COP of the heat pump system but for higher than 1. These results indicate the feasibility of improving the system efficiency, the operation cost, and long term operation of the solar air conditioning system by coupling the absorption and vapor compression cooling cycles. Finally, the influence of working parameters on the system performance is discussed based on the experimental and simulation analyses. The energy balance between the absorption cycle and the heat pump cycle in the cold storage system is analyzed. It is found that the coefficient of performance of the heat pump (COPele,HP) and ESCOP increase with a low initial LiBr-H2O solution concentration. The ESCOP decreases by 34.4% when the initial concentration increases from 52% to 57%. The average ESD increases to 140.2 kWh/m3 with a concentration difference of 8%. Based on the experiment results, the payback period of the proposed system is estimated as 2.4 years comparing with the traditional LiBr-H2O absorption system.

Experimental study on a fresh air heat pump desiccant dehumidification system using rejected heat

Desiccant coated heat exchanger (DCHE) was proposed for highly efficient dehumidification process due to the adsorption heat could be eased by inner cooling during the sorption process. Meanwhile, heat pump is probably used with DCHE together in humidity control processes because cooling and heating generated by vapor compression heat pump system match with the energy demand of DCHE well. A fresh air heat pump desiccant dehumidification system using rejected heat with desiccant coated heat exchanger (DCHE) was set up and experimentally tested in this paper. Near isothermal dehumidification process could be realized due to the utilization of DCHE which could convert the sensible cooling provided by vapor compression heat pump subsystem to latent cooling to increase the moisture removal of the system. The optimal average moisture removal and COP are 7.02 g/kgDA and 4.10, respectively, under the near ARI humid condition. Most of the total cooling generated by vapor compression heat pump subsystem is used for dehumidification. The moisture removal per kilowatt hour electric power consumption of the system is 1.60–2.88 times that of conventional condensation dehumidification method.

Development and techno-economic assessment of a new biomass-assisted integrated plant for multigeneration

In this paper, a novel renewable power-assisted multigeneration system is introduced for useful commodities such as cooling, hydrogen, heating, drying, hot water, and power generations. The biomass energy is preferred as a renewable power source. The proposed plant is including the biomass gasifier unit, gas turbine cycle, Kalina cycle, reverse osmosis unit, proton exchange membrane electrolyzer, absorption cooling cycle, dryer and heat pump subsystem. The primary purpose of this paper is to analyze a biomass assisted combined plant in terms of thermodynamic and economic viewpoints. In this regard, the thermodynamic performance, exergy destruction rate and economic examination are performed according to the various parameters. Results demonstrated that the whole energy and exergy efficiencies of the examined plant are 63.84% and 59.26%, respectively. Furthermore, the total irreversibility and hydrogen production rates are found as 53,406 kW and 0.072 kg/s. The overall purchase cost rate of the suggested cycle is about 2000 $/s.

Complementary Configuration Research of New Combined Cooling, Heating, and Power System Driven by Renewable Energy under Energy Management Modes

To optimize the use of distributed energy, this work builds a combined cooling heating and power system (CCHP) driven by distributed energy, including three subsystems: the electricity subsystem, CCHP subsystem, and ground source heat pump (GSHP) subsystem. Then, energy, economic and environmental performance indicators are constructed using a natural gas‐driven CCHP system (NG CCHP) as the frame of reference. Thirdly, three system operation modes are put forward, including following the thermal load (FTL) mode, following the electric load (FEL) mode, and electric load combine thermal load (ECT) mode. In the meantime, three kinds of system operation modes are proposed, including optimization of energy rate (ER), total operation cost (TOC), and carbon dioxide emission reduction (CER). Finally, Shanghai World Expo is analyzed as a simulation object. The results show that the optimal target operation strategy can balance the results of different optimization by increasing the partial load rate of the gas‐steam combined cycle system and reducing the pumping ratio of the steam turbine. Compared with the NG CCHP system, the new CCHP system performs better. The sensitivity analysis shows, as the coefficient of performance of the chiller increases and the price of NG decreases, the performance of the new CCHP system will become better.

A Study of Hybrid-Power Gas Engine-Driven Heat Pump Control Strategy Based on Instantaneous Optimization

The control strategy for a coaxial parallel hybrid-power gas engine-driven heat pump system is studied based on instantaneous optimization, aiming at minimizing the equivalent energy consumption. The system includes two main subsystems, drive subsystem and heat pump subsystem. Continuously variable transmission (CVT) is applied to combine the two subsystems for a continuous transmission ratio adjustment. The steady-state models of components of the two subsystems are established, and based on which equivalent energy consumption function is proposed. Meanwhile, a penalty factor is introduced into study of battery to maintain SOC in range of 0.2 to 0.8, where the internal resistance is relatively small. Then computational simulation work is performed on Simulink platform. Result shows that battery SOC runs stable between 0.49∼0.66 and equivalent energy consumption is 10.4% lower than that of system with multi-stage gear ratios.

Performance of a Hybrid Solar Photovoltaic - Air Source Heat Pump System with Energy Storage

Abstract The paper introduced a smart renewable energy based microgrid system which is composed of three subsystems: solar photovoltaic subsystem, air source heat pump subsystem and energy storage subsystem. This microgrid system was applied to the demonstration project located in Xining City, Qinghai Province, China. The energy performance of the smart renewable energy based microgrid system was evaluated and compared with that of traditional energy supply system which totally depends on the electricity grid and natural gas. The comparison study demonstrates that the proposed hybrid energy supply system is superior to traditional system, significantly decreasing additional energy consumption for buildings and reducing pollutant emissions.

Thermodynamic and economic assessment of a novel CCHP integrated system taking biomass, natural gas and geothermal energy as co-feeds

The combined cooling, heating and power (CCHP) system based on biomass, geothermal energy and fossil energy contributes to less fossil fuel-dependent, alleviate the climate change and improve the flexibility of integrated system. Therefore, this paper presents a novel combined cooling, heating and power (CCHP) system based on biomass, natural gas and geothermal energy. The CCHP system consists of an air-biomass gasification subsystem, steam turbine electricity generation subsystem, gas turbine electricity generation subsystem, waste heat utilization subsystem and ground source heat pump subsystem. The thermodynamic and economic analysis of proposed system are investigated, and the influences of some key operating parameters (gas mass ratio and flue gas split ratio) and economic factors (such as biomass and natural gas price, interest rate, operating time coefficient and service life) on integrated system performances are also carried out. The results indicate that the introduction of natural gas contributes to improve the overall energy efficiency of proposed CCHP system and reduce the levelized cost of energy significantly. In the case study (gas mass ratio: 0.5, flue gas split ratio: 0.5), the overall energy efficiency and electricity generation efficiency of CCHP system can be reached at about 97.05% and 30.89%, respectively; the levelized cost of energy is 0.0315 $/kWh. The proposed system provides a new way for utilization of renewable energy and fossil fuels based poly-generation system, which is a promising approach for the utilization of biomass, natural gas and geothermal energy in the rural of China.

Exergetic and exergoeconomic assessment of a novel CHP system integrating biomass partial gasification with ground source heat pump

The renewable energy has drawn increasingly attention for the utilization of energy in the worldwide, especially biomass and geothermal energy. The total biomass gasification usually leads to the higher exergy destruction and lower exergy efficiency of gasification process subsequently, and the flue gas at middle temperature (400 °C) is always used to generate domestic hot water from environment temperature to required temperature e.g. 55 °C, the relative large temperature difference leads to high exergy loss. For adopting ground source heat pump system to generate domestic hot water, relative high target temperature (e.g. 55 °C) always leads to the high compression ratio, which decreases the coefficient of performance (COP) of the ground source heat pump host. Therefore, so as to make a better use of biomass and increase the COP of ground source heat pump systems, a novel CHP system coupling biomass partial gasification and ground source heat pump is presented. It mainly consists of four parts: biomass partial gasification subsystem; gas turbine power generation subsystem; steam turbine power generation subsystem; and ground source heat pump subsystem. The main products of proposed system are electricity and domestic hot water (55 °C). The exergetic and exergoeconomic performance analysis of proposed system are investigated, and in a further way, the effects of several key system integrating parameters on system performance are also studied. The results show that the system exergy efficiency can be reached at about 13.65%. The main exergy destruction exists in gasifier and followed by char boiler, which accounts for 38% and 21.71% of total exergy destruction, respectively. Moreover, the unit cost of hot water, power generated by gas turbine and steam turbine are 92.5 $/GJ, 12.4 $/GJ and 23.9 $/GJ, respectively. The proposed CHP integration system is valuable to other advanced biomass and geothermal based multi-generation systems.

Proposal and research on a combined heating and power system integrating biomass partial gasification with ground source heat pump

Biomass and geothermal energy are becoming promising traditional energy alternatives. For biomass utilization with thermal-chemical gasification technologies, adopting total gasification scheme always leads to large exergy destruction and low thermal efficiency. Besides that, in typical biomass based combined heating and power systems, the flue gas at middle temperature is usually utilized to produce domestic hot water directly, which also leads to large exergy loss for relative large energy grade difference. In the light of geothermal energy utilization, i.e. ground source heat pump systems, for the relative high temperature required of output stream, a relative high compression ratio is required accordingly, which leads to a low coefficient of performance of ground source heat pump. In order to solve the above referred problems, a novel heating and power co-generation system coupling biomass partial gasification and ground source heat pump is proposed and analyzed in this study. The proposed system consists of four subsystems: biomass partial gasification subsystem; gas turbine power generation subsystem; steam turbine power generation subsystems; and ground source heat pump subsystem. The features of this novel system focus on: only part of the biomass is gasified not all (partial gasification), the syngas and un-reacted char are used as fuels for gas turbine (Brayton cycle) and steam turbine (Rankine cycle) power generation respectively; in the ground source heat pump subsystem, the temperature of required water is reduced to 39°C instead of 55°C, and will be further reheated to 55°C by flue gas at middle temperature from biomass based combined heating and power subsystem. The thermodynamic performance of the proposed system is numerically investigated. The results indicate that the proposed system can make a better use of biomass and geothermal energy, which can achieve an overall energy efficiency of 72.12% with a heat to power ratio 3.93, and the coefficient of performance of ground source heat pump subsystem can be improved to 5.6 with the compression ratio 3.2. What's more, the system integrating mechanism in this study is very helpful for other advanced biomass based and multi-energy coupling systems.

A novel fouling measurement system: Part I. design evaluation and description

The enhanced tube is being used more often in water-chiller condensers because of their superior performance in heat transfer. Both the predicted and real-world performance of these heat exchangers is affected by the fouling build-up on the heat transfer surfaces. Thus, accurate quantification of fouling thermal resistance is required to address the correlation between the fouling resistance of heat transfer tubes and operation conditions. A newly developed Fouling Measurement System (FMS) supports research on the relationships between fouling development and operation condition by measuring fouling thermal resistance on the heat transfer surface. Part I of this two-part series describes the design and evaluation of FMS. An uncertainty analysis of fouling thermal resistance was conducted to identify measurement component contributions to the uncertainty of final results and guide component selection. In Part II, FMS commissioning was performed, and a primary fouling test and analysis on cooling water quality were conducted. The FMS consists of three subsystems: heat pump subsystem, cooling/chilled water subsystem and control and data acquisition (DAQ) subsystem. The FMS has three heat pumps individually installed with a shell-and-tube condenser and separately equipped with a cooling/chilled water supply loop. In the cooling/chilled water subsystem, these three heat pumps share the same cooling water pool and chilled water pool, which ensures that the cooling/chilled water supplied to each heat pump is uniform. A cooling water tower was installed outside the Air Quality Lab in University of Illinois at Urbana-Champaign to cool down the cooling water of the FMS, and to evaporate water and keep the cooling water at the required range. In the control and DAQ subsystem, the control of water temperature, water quality, water velocity, and refrigerant saturation temperature are described.

Theoretical analyses of a new two-stage absorption-transcritical hybrid refrigeration system

In this context, a two-stage absorption-transcritical hybrid refrigeration system is proposed. R744 is chosen as a refrigerant for the transcritical heat pump subsystem and LiBr-H2O working pair for the two-stage absorption refrigeration subsystem. Based on the mathematical and physical models, theoretical investigation is carried out on its performance. The main effects are discussed on COPnet (the ratio of cooling capacity powered by low-grade heat to the low-grade heat consumption for the hybrid system) and COPmt (the ratio of cooling capacity powered by mechanical work to the mechanical work consumption for the hybrid system). Comparing with the normal two-stage absorption refrigeration system, theoretical results show that COPnet could be improved up to about 55% when the refrigeration temperature is 7 °C. In addition, COPmt are more than 50% higher than that of the conventional transcritical refrigeration system. It is also found that both 45–55 °C low-grade heat and condensing heat could be used as actuating heat of the two-stage absorption refrigeration subsystem.

A feasible system integrating combined heating and power system with ground-source heat pump

A system integrating CHP (combined heating and power) subsystem based on natural gas and GSHP (ground-source heat pump subsystem) in series is proposed. By help of simulation software-Aspen Plus, the energy performance of a typical CHP&GSHP-S (S refers to ‘in series’) system was analyzed. The results show that the system can make a better use of waste heat in flue gas from CHP (combined heating and power subsystem). The total system energy efficiency is 123% and the COP (coefficient of performance) of GSHP (ground-source heat pump) subsystem is 5.3. A referenced CHP&GSHP-P (P refers to ‘in parallel’) system is used for comparison; its total system energy efficiency and COP of GSHP subsystem are 118.6% and 3.5 respectively. Compared with CHP&GSHP-P system with different operating parameters, the CHP&GSHP-S system can increase total system energy efficiency by 0.8–34.7%, with related output ratio of heat to power (R) from 1.9 to 18.3. Furthermore, the COP of GSHP subsystem can be increased between the range 3.6 and 6, which is much higher than that in conventional CHP&GSHP-P system. This study will be helpful for other efficient GSHP systems integrating if there is waste heat or other heat resources with low temperature.