High Temperature Heat Exchanger Research Articles

A Multi-Sized Unit Cell Method for the Design of LPBF Lattice Support Structures Concerning Complex Geometries

Abstract Composed of individual unit cells strategically arranged to achieve a desired function, lattices are a promising solution for laser powder bed fusion (LPBF) support structure design in additive manufacturing. Despite their many advantages (e.g., multifunctionality and reduced material cost), prior work in lattice support structure design primarily focuses on horizontal support domains that are not translatable to support domains for complex geometries, thereby limiting their application. This work introduces a multi-sized unit cell design optimization (MSO) method to create lattice support structures (LSS) for parts with complex geometries. The proposed method utilizes voxelization to generate LSS using box-like unit cells of different sizes. It also allows for efficient, high-dimensional design optimization for the types and locations of user-specified unit cells through a modified simulated annealing-based optimization algorithm. The effectiveness and efficiency of the MSO method are demonstrated through the case study of an adapter pipe for a high-temperature heat exchanger. For this demonstration, LSS using multi-sized unit cells are designed to increase heat transfer rate while satisfying structural integrity and material cost constraints. The case study results indicate that the design of the LSS derived from the MSO method fulfills all constraints, including the design constraint of 50% material cost reduction, compared to the solid support structure. In contrast, the lattice support structure designs derived from equal-sized unit cell methods either cannot satisfy all design constraints or have a lower heat transfer rate than the design of the MSO method.

500 kW closed cycle gas turbine unit with different working fluids

This article considers a 500 kW closed cycle gas turbine unit. In contrast to open or semi-closed cycles, a closed cycle implies a working fluid circulating continuously within a closed loop. In other words, a working fluid (any working fluid) with the required initial parameters depending on the properties of the selected working fluid is injected into a closed circuit consisting of a compressor, heat exchangers of various purposes and a turbine. A unit with recirculation of combustion products at high pressure can be created based on existing units with minor modifications. Instead of emission into the atmosphere, the exhaust gases enter the high-temperature heat exchanger, where it gives heat to the closed-cycle gas turbine unit. First of all, the application of such units is relevant at compressor stations in conjunction with the gas turbine drive of the blower. The study involved thermal calculation of a closed-cycle gas turbine unit with different working fluids: carbon dioxide, helium and argon. The main objective is to study the advantages and disadvantages of alternative working fluids with their subsequent comparison. Since the main chemical and physical properties of alternative working fluids differ from the classical ones, there is a possibility of obtaining higher parameters of the unit. According to the results of calculations it is established that the most promising working fluid is carbon dioxide, because this can be used at a wide range of temperatures and pressures. It should also be noted that the consumption of carbon dioxide is the lowest compared to other working fluids. The efficiency of such an installation is 28%, but there is a possibility of improvement if regeneration is added.

Design and Performance Analysis of a Small-Scale Prototype Water Condensing System for Biomass Combustion Flue Gas Abatement

This article outlines the design and performance of a flue gas condensation system integrated with a biomass combustion plant. The system comprises a biomass plant fuelled by wood chips, generating flue gases. These gases are condensed via a double heat exchanger set-up, extracting water and heat to reduce concentrations of CO, CO2, and NOx while releasing gases at a temperature close to ambient temperature. The 100 kW biomass plant operates steadily, consuming 50 kg of wood chips per hour with fuel energy of 18.98 MJ/kg. Post combustion, the gases exit at 430 °C and undergo two-stage cooling. In the first stage, gases are cooled in a high-temperature tube heat exchanger, transferring heat to air. They then enter the second stage, a flue gas/water heat exchanger, recovering sensible and latent thermal energy, which leads to water condensation. Flue gas is discharged at approximately 33 °C. Throughout, parameters like the flue gas temperatures, mass flow, fuel consumption, heat carrier temperatures, and water condensation rates were monitored. The test results show that the system can condense water from flue gas at 75 g/min at 22 °C while reducing pollutant emissions by approximately 20% for CO2, 19% for CO, 30% for NO, and 26% for NOx.

Macroporous polymer-derived ceramics produced by standard and additive manufacturing methods: How the shaping technique can affect their high temperature thermal behavior

This work proposes the processing of porous ceramic lattices via three polymer-derived ceramic routes, namely powder bed fusion and infiltration, fused filament fabrication and replica, and a direct replica of a foamed polymer. A common feature in the processing of these lattices is the use of the same polysilazane as the preceramic source for the Si-C-N-O network that builds up during ceramization.We adopted rotated cube, honeycomb and randomized cellular geometries as a matter of comparison for thermal exchange when an air flow is forced through the structures up to 1050 °C. The three procedural pathways are discussed in their limitations regarding geometry, polymer-to-ceramic conversion, high-temperature heat exchange performance and durability. In this regard, while rotated cube geometry results in the best thermal exchange and highest pressure drop, we show a correlation between chemical composition and high temperature oxidation of the Si-C-N-O network, possibly attributed to the selection of the processing routes.

Analysis of the causes of waste heat boiler leakage in large-scale chemical plants

A waste heat boiler is a kind of high-temperature and high-pressure heat exchanger in a large chemical plant, and its safe operation is directly related to the production efficiency and safety risk of a chemical plant. In this paper, the leakage failure analysis of a waste heat boiler in an ethylene plant is carried out, and the analysis methods such as field observation, macro observation of fracture, metallographic analysis, micro observation of fracture, phase analysis, and energy spectrum analysis are adopted respectively. The results show that the direct cause of the leakage of the waste heat boiler is the thinning of the wall thickness of the heat exchange tube caused by alkali corrosion, which leads to the overload and fracture of the heat exchange tube. The pits on the outer surface of some heat exchange tubes are caused by mechanical reasons, which are related to this leakage and closure. The corrosion failure of heat exchange tubes is widespread, which has a great influence on safety production and serious consequences. Through this comprehensive analysis, the failure mechanism is clarified, which can provide a reference for the maintenance of similar equipment. At the same time, preventive measures are put forward from the aspects of technology, structure, and detection to reduce the occurrence of similar accidents.

Demonstration of a multi-channel fluidized bed particle–supercritical carbon dioxide heat exchanger for concentrating solar applications

High-temperature thermal energy storage in oxide particles at temperatures above 600°C can couple concentrated solar energy with high-efficiency thermal power cycles to provide dispatchable solar-driven electricity. Challenges remain in developing cost-effective primary heat exchangers, which require expensive alloys, to extract the high-temperature thermal energy from the particles to power cycle fluids, such as supercritical CO2 (sCO2) in recuperated Brayton cycles. To explore one pathway for cost-effective, high-temperature particle heat exchangers, the current study demonstrates a shell-and-plate, particle–sCO2 heat exchanger with narrow-channel fluidized beds coupled with micro-channel sCO2 flows in the heat exchanger walls. This study evaluates the feasibility of multiple parallel, narrow-channel fluidized beds in shell-and-plate particle–sCO2 HXs, to achieve high bed-wall heat fluxes at elevated temperatures. A reduced-order model simulates the narrow-channel, fluidized-bed particle–sCO2 heat exchanger to design the fluidized bed geometry, in terms of depth, height, and number of channels,for a nominal 40-kWth heat exchanger at particle and sCO2 inlet temperatures up to 600°C and 400°C respectively. The resulting shell-and-plate heat exchanger design operates with bubbling fluidization of the downward-flowing oxide particles to enhance bed-wall heat transfer. The heat exchanger core is fabricated with etched sCO2 micro-channels in thin wall plates that are diffusion bonded to spacer frames to form the shell-and-plate structure with 12 parallel, fluidized bed channels, 10.4 mm deep. The heat exchanger is tested at the National Solar Thermal Test Facility at Sandia National Laboratories with CARBOBEAD HSP particles at design particle flow rates of 0.20 kg s−1 and inlet temperatures up to 525°C. Results show that fluidization across multiple parallel channel beds can maintain uniform particle inventory with a common freeboard zone above the heat exchanger core. Bubbling fluidization improves particle–wall heat transfer coefficients but also increases axial dispersion of particle thermal energy, which lowers the log-mean temperature difference such that total heat transfer remains relatively constant to within ±10% over a broad range of fluidization gas velocities. The axial dispersion required particle and sCO2 flow rates to be increased by 25% over model-designed conditions to achieve the targeted 40 kWth, which indicates the importance of incorporating axial dispersion into heat exchanger design models and of deploying bed structures to suppress it. This study demonstrates the feasibility and preferred fluidizing gas conditions for particle heat exchangers for releasing high-temperature thermal energy storage systems.

Enhanced Heat Transfer in Thermoelectric Generator Heat Exchanger for Sustainable Cold Chain Logistics: Entropy and Exergy Analysis

This study investigates the application of thermoelectric power generation devices in conjunction with cold chain logistics transport vehicles, focusing on their efficiency and performance. Our experimental results highlight the impact of thermoelectric module characteristics, such as thermal conductivity and the filling thickness of copper foam, on the energy utilization efficiency of the system. The specific experimental setup involved a simulated logistics cold chain transport vehicle exhaust waste heat recovery thermoelectric power generation system, consisting of a high-temperature exhaust heat exchanger channel and two side cooling water tanks. Thermoelectric modules (TEMs) were installed between the heat exchanger and the water tanks to use the temperature difference and convert heat energy into electrical energy. The analysis demonstrates that using high-performance thermoelectric modules with a lower thermal conductivity results in better utilization of the temperature difference for power generation. Additionally, the insertion of porous metal copper foam within the heat exchanger channel enhances convective heat transfer, leading to an improved performance. Furthermore, the study examines the concepts of exergy and entropy generation, providing insights into the system energy conversion processes and efficiency. Overall, this research offers valuable insights for optimizing the design and operation of thermoelectric generators in cold chain logistics transport vehicles to enhance energy utilization and sustainability.

Experimental and numerical investigation of porous heat exchangers with Kelvin cell structured foam at high temperatures: Coupled conduction-convection and radiation heat transfer

Heat recovery is crucial in the energy sector, especially for industries operating at high temperatures. One way to achieve high-efficiency heat recovery is to use porous materials in heat exchangers. In this work, the performance of a high temperature heat exchanger was investigated. For this purpose, a tube containing a porous cast iron structure was externally heated by radiation inside a tubular furnace and air at ambient temperature was blown into the tube. Experiments were conducted at different temperatures of up to ▪ and different airflow velocities in a specialized bench, considering the combined effects of conduction, convection, and radiation. Temperature profiles in three sections of the porous structure were measured by using sheathed thermocouples brazed to the porous structure. Power and exergy flow rate extracted from the porous structure to the air flow were calculated and analyzed to quantify recovered heat. In addition, a numerical modeling performed at the pore level using Fluent showed an average relative error of 15% compared to experimental results, indicating acceptable agreement with observed trends. This numerical model will serve as a valuable reference tool for future parametric analyses of porous structures in heat exchanger configurations.

General numerical method for hydraulic and thermal modelling of the steam superheaters

Two methods for modelling high-temperature tubular cross-current heat exchangers are presented. Superheated steam flows inside the tubes, and flue gas flows outside perpendicular to the axis of the tubes. The methods proposed are based on the conservation equations of momentum and energy. In both methods, the heat exchanger is divided into finite volumes. The fluid temperatures at the outlet of the finite volume are calculated using closed-form explicit formulas. This makes the computer calculation time for the entire superheater very short. The pressure distribution in the superheater is determined from the numerical solution of the momentum conservation equation. A power correlation was determined to calculate the limiting Reynolds number above which the friction factordepends only on the relative roughness of the tube surface. Convective and radiative heat transfer were taken into account in the calculation of the heat flow rate on the gas side. The results of the calculation of a two-pass co-current heat exchanger were compared to assess the accuracy of the two methods, finding that the two methods give very similar results. The strength of method I is that the steam and flue gas temperatures inside a given finite volume can be determined. A model of a two-pass live steam superheater in a supercritical pressure boiler is presented. The calculated average steam and flue gas temperatures downstream of the superheater show good agreement with the corresponding temperatures determined using the heat exchanger's effectiveness and the measured results.

Numerical method for determining pressure distribution in tube cross-flow heat exchangers

This paper presents a numerical method for determining the pressure distribution along the fluid flow path in a cross-current hightemperature heat exchanger. The pressure drop across the superheater was determined using the momentum conservation equation, which was solved by the finite difference method. Local pressure losses at tube elbows were also taken into account. A new formula for calculating friction factor on rough tubes' inner surface is proposed. A straightforward model for the friction factor in tubes with a rough inner surface for Reynolds numbers in the interval 3000 - 108 has been proposed. The pressure distribution in the last stage of the live steam superheater in a 900 MWe supercritical boiler was calculated.

Effects of variable-temperature heat reservoirs on performance of irreversible Carnot refrigerator with heat recovery

The outlet temperature of the heat recovery reservoir is an important parameter in the design of refrigeration with heat recovery systems. In this paper the second law of thermodynamics has been applied to an irreversible Carnot refrigerator with heat recovery (CRHR) coupled to variable-temperature heat reservoirs. The refrigerating rate, input power, refrigeration coefficient, heat recovery coefficient, comprehensive coefficient of performance and exergy efficiency are chosen as the objective functions. The design rule chosen for this study is that the heat transfer area should be constrained. The mathematical expressions for assessing performance parameters with respect to area ratio, were derived for this study. These expressions are transcendental equations. The numerical solution method was employed to calculate the approximate solutions of the optimum performance parameters in a numerical example. The results indicate that the increase in the outlet temperature of heat recovery reservoir could lead to a rise in the maximum value of refrigerating rate and minimum value of input power; also it will lead to the decline in the maximum value of refrigeration coefficient, heat recovery coefficient, comprehensive coefficient and the exergy efficiency. When the ratio of heat recovery heat exchanger area to the summation of high temperature heat exchanger area and the heat recovery heat exchanger area is 1.0, the performance coefficients would attain their limit values and all of the condensing heat could be recycled. Our findings are helpful to the design and optimization to inform preparation of standard relating to the development of refrigerator with heat recovery.

Design and Multiobjective Dynamic Optimization of Superheaters for Load-Following Operation in Pulverized Coal Power Plants.

Pulverized coal power plants are increasingly participating in aggressive load-following markets, therefore necessitating the design and optimization of primary superheaters for flexible operations. These superheaters play a critical role in maintaining the final steam temperature of the steam turbine, but their high operating temperatures and pressures make them prone to failure. This study focuses on the optimal design of future-generation primary superheaters for a fast load-following operation. To achieve this, a detailed first-principles model of a primary superheater is developed along with submodels for stress and fatigue damage. Two single-objective optimization problems are solved: one for minimizing metal mass as a measure of capital cost and another for minimizing pressure drop on the steam side as a measure of operating cost. Since these objective functions conflict, a multiobjective optimization problem is executed using a weighted metric methodology. Results from these optimization studies show that the base case design can violate stress constraints during the aggressive load-following operation. However, by optimizing the design variables, it is possible to not only satisfy tight stress constraints but also achieve the desired number of allowable cycles and adhere to the steam outlet temperature constraint. In addition, the optimized design reduces either the metal mass or the steam-side pressure drop compared to that of the base case design. Importantly, this approach is not limited to primary superheaters alone but can also be applied to similar high-temperature heat exchangers in other applications.

Numerical and experimental investigation of a combustor-coupled free-piston Stirling electric generator

In this paper, a novel gas combustor with multiple nozzles is proposed to couple with a free-piston Stirling electric generator (FPSG) for distributed power application. Due to the simple layout of the combustor and intrinsic external combustion of the FPSG, the system is highly adaptive to gas fuels, such as butane, natural gas and liquefied petroleum (LPG). In order to unravel the heat transfer characteristics of external combustion with internal oscillating flow, a rigorous numerical simulation was conducted, and a series of experiments were carried out to verify the calculations. Initially, an in-depth analysis was performed in terms of the flow field, temperature distribution and heat flux density within the combustor. The effects of the combustor inlet flow rate, nozzle structure, and preheating temperature on the flow heat transfer characteristics were explored. Numerical calculations reveal that, at a fuel flow rate of 0.55 Nm3/h and an air-fuel ratio of 24, the high-temperature heat exchanger (HHX) absorbs 6.41 kW heating power, with convective heat occupying approximately 73.5 %. Moreover, the simulations unveil the significant influence of optimizing the air–fuel ratio, nozzle structure, and preheating temperature on enhancing the overall heat transfer performance and achieving fuel and air consumption reductions. Subsequently, we meticulously conducted experimental investigations to comprehensively evaluate the performance of the novel combustor-coupled FPSG. The experimental results demonstrate that, under a fuel flow rate of 0.55 Nm3/h, the system achieves an output electric power of 1531 W, corresponding to a net thermal-to-electric efficiency and fuel-to-electric efficiency of 30.9 % and 9.6 %, respectively.

Experimental investigation of additively manufactured high-temperature heat exchangers

This article examines various additively manufactured heat exchangers for high-temperature applications. The heat exchangers differ in terms of their internal fin structure as well as optimizations in terms of manufacturing quality. Starting from a reference fin type, optimizations with focus on low pressure drop and high heat transfer are performed. The heat exchangers are investigated experimentally, focusing on the laminar flow regime between 60<Re<600. By means of a presented evaluation algorithm, the Nusselt numbers for the different fin types and designs are determined. The investigations show that even the smallest manufacturing deviations result in up to 70–120% higher f-factors and up to 30% higher Nu numbers. Taking these manufacturing deviations into account in the design process leads to very good agreement with the numerically determined values and the influence of surface roughness is comparatively small. Furthermore, the influence of internal heat radiation is of minor importance for the heat exchangers considered here.

Experimental and numerical investigation of thermally induced convection along a high-temperature borehole heat exchanger

Thermally induced convection in the vicinity of borehole heat exchangers (BHE) in porous media affects the heat transfer behaviour between the BHE and the surrounding ground and thereby their performance for building climatization, heat extraction and heat storage. This study presents a combined experimental–numerical analysis of the qualitative and quantitative impacts of convection on heat transfer for a laboratory-scale BHE analogue over a wide temperature range. For this purpose, a grouted coaxial high-temperature BHE was installed within a fully saturated porous sand medium in a cylindrical container of 1.4 m3 volume under spatially extensive temperature monitoring. Four transient heat charging/discharging experiments were performed at different charging temperatures of 30, 50, 70, and 90 °C and analysed for the onset and magnitude of convection. After minimal calibration, a numerical model accurately reproduced the experimental data of all experiments and helped quantify the contribution of convection to the total heat transfer at each temperature level. For heat charging at 30 °C, the heat transfer was dominated by conduction. At higher temperatures, convection increased the total heat-transfer rate by up to 35% in the experimental setup. In contrast, for heat discharge, due to thermal stratification in the sand medium, convection reduced the heat transfer rate and heat recovery by up to −30% and −35%, respectively. Rayleigh numbers, buoyant flow velocities, and the centre of heat were derived from the monitoring and simulation data and consistently indicated the onset of convection for the experimental setup at a BHE operating temperature of 50 °C. The Rayleigh number was found to be closely correlated with the magnitude of the convective flow. Overall, the results suggest that the performance of BHEs in cooling applications may benefit from thermal convection, while the performance of BHEs for thermal energy storage may deteriorate markedly at high operating temperatures.

Thermal performance enhancement of a red-hot air furnace for a micro-scale externally fired gas turbine system

Externally-fired gas turbine (EFGT) has been considered an option in variable combined heat and power energy systems. The key elements in such systems are the high-temperature heat exchangers (HTHE), in which the working fluid (typically air) is heated by flue gas. Since both flows are separated, the solution is considered advantageous for utilization of biomass featuring high levels of particulate matter emissions. An increased interest in these devices has therefore been observed along with the development of small-scale CHP units utilizing locally available biomass. The effectiveness of HTHE, along with the inlet turbine temperature, appears to be one of the main factors influencing the efficiency of EFGT-based systems. Numerous studies on the HTHE designs have been carried out, basically focusing on the use of high-temperature resistant materials to provide safe conditions for long-term operation under elevated temperatures. There is a lack of research considering other methods to improve the effectiveness of the HTHE. The paper presents the analysis of thermal performance of the laboratory-scale 20 kW red-hot air furnace to demonstrate the HTHE effectiveness enhancement by adding water to airflow. The experimental results showed a significant increase (by almost 45%) in the heat exchanger effectiveness for the case of ∼10%wt. water addition. This is due to the enhanced heat capacity of a cooling medium and its absorption properties that results from the steam content. The proposed method for effectiveness increment appears to be beneficial to compensate for the low effectiveness of air-to-fumes tube HTHE.

Description and Analytical Modeling for a Solid Block Cross-flow High Temperature Heat Exchanger

In this report, the design specifics, and performance modeling results, for a simple, solid metal block, liquid–liquid cross-flow heat exchanger, intended for high temperature applications, are given. The design consists of a solid block of metal, with cylindrical channels providing the cross-flow passageways for two non-mixing liquids. In this design, all flow channels are separated by a certain minimum thickness of the host solid block material. This particular design is limited by the length of pores that can be machined from a solid block. In this study, a simple heat transfer model, appropriate for such an exchanger, was used to estimate what values of effectiveness might be obtainable while keeping the size of the exchanger as compact as possible. The effects of channel length and spacing, liquid specific heat and viscosity and block material conductivity on exchanger effectiveness are considered and results reported. The model predicts that for a cubic exchanger of side length 8.25 cm with 50 channels per side at a diameter of 3.0 mm each, for a particular high temperature situation using molten salts, with an inlet and outlet temperature difference of around 170 K, an effectiveness of 0.4 can be achieved with a total mass flow rate of 0.5 kg $$\cdot$$ s $$^{-1}$$ along with a Reynolds number of less than 2000.

Carnot Battery Based on Brayton Supercritical CO2 Thermal Machines Using Concentrated Solar Thermal Energy as a Low-Temperature Source

Carnot batteries store surplus power as heat. They consist of a heat pump, which upgrades a low-temperature thermal energy storage, a high-temperature storage system for the upgraded thermal energy, and a heat engine that converts the stored high-temperature thermal energy into power. A Carnot battery is proposed based on supercritical CO2 Brayton thermodynamic cycles. The low-temperature storage is a two-tank molten salt system at 380 °C/290 °C fed by a field of parabolic trough collectors. The high-temperature storage consists of another two-tank molten salt system at 589 °C/405 °C. Printed circuit heat exchangers would be required to withstand the high pressure of the cycles, but shell and tube heat exchangers are proposed instead to avoid clogging issues with molten salts. The conventional allocation of high-temperature molten salt heat exchangers is then modified. Using solar energy to enhance the low-temperature thermal source allowed a round-trip efficiency of 1.15 (COP of 2.46 and heat engine efficiency of 46.5%), thus increasing the stored power. The basic configuration has a levelised cost of storage of USD 376/MWh while replacing the shell and tube heat exchangers with hybrid printed circuit heat exchangers is expected to lower the cost to USD 188/MWh.

UNITY: Kyoto Fusioneering’s Unique Integrated Testing Facility for Fusion Power Generation

One of the major research and development challenges on the critical path to achieving a fusion pilot plant is demonstrating the viability of power production from fusion. In August 2022, Kyoto Fusioneering launched the construction of the world’s first integrated testing facility for fusion power generation. The primary testing loop of the facility will initially adopt PbLi, with the prospect of adding an additional molten salt loop, with dimensions of around 5 × 5 × 3 m with a coolant inventory of approximately 100 L. To be completed in 2025, this facility will demonstrate (1) heat extraction from a mock-up blanket, (2) high-temperature heat transfer and exchange, (3) electricity generation from blanket heat, and (4) hydrogen isotope extraction under commercially relevant conditions—to be completed in time for the first-generation demonstration fusion plants. This facility is named UNITY, standing for Unique Integrated Testing facilitY to symbolize the integration of all critical components.

Operational characteristics of a free-piston Stirling generator with resonant self-circulating heat exchangers

Heat transfer is one of the most critical issues faced by free-piston Stirling generators (FPSGs) during power amplification, and the emergence of resonant self-circulating heat exchangers offers an alternative solution. In this study, a high-power FPSG with resonant self-circulating heat exchangers has been numerically studied using commercial software SAGE and thermoacoustic post-processing. The principle feasibility and operational characteristics of the proposed system with different loop lengths are verified based on comparative analysis with the Component Test Power Convertor. Results show that introducing a self-circulating heat exchanger can achieve high-power heat transfer through a steady flow. However, it results in a significant degradation in the performance of the FPSG, where the acoustic power loss in the loop is the most critical cause. The pump used to generate the steady flow also requires additional power consumption. Furthermore, systems with shorter loops of non-integer multiples of wavelength have higher system efficiency and lower pump power consumption. For example, the output electric power can achieve 9.9 kW (corresponding to a thermal-to-electric efficiency of 18.8%) when the loop length is 2 m, where the power consumption of the pump is only 0.19 kW. Meanwhile, the pipe diameter of the loop and the temperature difference between the inlet and outlet of the high-temperature heat exchanger should be determined by considering both the performance of the FPSG and the power consumption of the pump.