Low Temperature Heat Exchanger Research Articles

Research on shell-side heat and mass transfer with multi-component in LNG spiral-wound heat exchanger under sloshing conditions

The spiral-wound heat exchanger (SWHE) is the primary low-temperature heat exchanger for large-scale LNG plants due to its high-pressure resistance, compact structure, and high heat exchange efficiency. This paper studied the shell-side heat and mass transfer characteristics of vapor-liquid two-phase mixed refrigerants in an SWHE by combining a multi-component model in FLUENT software with a customized multicomponent mass transfer model. Besides, the mathematical model under the sloshing condition was obtained through mathematical derivation, and the corresponding UDF code was loaded into FLUENT as the momentum source term. The results under the sloshing conditions were compared with the relevant parameters under the steady-state condition. The shell-side heat and mass transfer characteristics of the SWHE were investigated by adjusting the component ratio and other working conditions. It was found that the sloshing conditions enhance the heat transfer performance and sometimes have insignificant effects. The sloshing condition is beneficial to reduce the flow resistance. The comprehensive performance of multi-component refrigerants has been improved and the improvement is more significant under sloshing conditions, considering both the heat transfer and pressure drop. These results will provide theoretical support for the research and design of multi-component heat and mass transfer enhancement of LNG SWHE under ocean sloshing conditions.

Heterogeneous nucleation condensation of methane gas on the wall-A molecular dynamics study

Methane is condensed in a low-temperature heat exchanger, a critical step in the liquefaction of natural gas. Currently, the microscopic mechanism regarding the heterogeneous condensation of methane on the heat exchanger wall remains unclear. This lack of understanding is of scientific importance in advancing the development of natural gas liquefaction processes. Therefore, molecular dynamics simulation is used in this paper to study the process of methane heterogeneous nucleation and core growth during the early stage of condensation, and analyze the influence mechanism of wall energy and cold source temperature on nucleation kinetics. The results show that the high-energy wall can enhance the interaction between cold wall atoms and methane molecules, facilitate heat transfer, accrete methane molecules to condense and adsorb on the wall to form a core, thus increasing the condensation rate of methane. Whereas, the low-temperature cold source promotes the condensation nucleation and growth process by increasing the supersaturation of methane. This study investigates the process and kinetic characteristics of heterogeneous nucleation of methane from a microscale perspective, providing guidance for the development of natural gas liquefaction in low-temperature heat exchangers, with the aim of enhancing the diversity and reliability of energy supply.

Evaluation of Pressure, Surface Characteristics, and Fluid Properties Effect on Pool Boiling Heat Transfer Over Plain and External Micro-Finned Cylindrical Surfaces

Abstract Pool boiling is extensively used in high- and low-temperature heat exchangers as it results in a high heat transfer coefficient compared to natural and single-phase forced convection. Pool boiling experimental study conducted over a plain cylindrical surface (PS) and four external micro-finned cylindrical surfaces (MFCSs), with R123 and R141b at different pressures in the heat flux range 20–100 kW/m2, is presented in this paper. The objective of the present study is to explore the effect of pressure, surface characteristics, and fluid properties on pool boiling heat transfer over plain and micro-finned cylindrical surfaces. The boiling performance improved at a higher pressure, irrespective of the working fluid used for all the test surfaces. It was found that, with the rise in pressure, the boiling heat transfer coefficient (BHTC) for the MFCSs increases at a higher rate than the PS. In comparison with PS, the average rise in the BHTC with pressure, for the MFCS-1, MFCS-2, MFCS-3, and MFCS-4 with R123 were 69.3% to 84.3%, 3.3% to 9.9%, 16.9% to 22.4%, and 29.4% to 40.2%, respectively. The higher BHTC over micro-finned cylindrical surfaces results due to more nucleation site results from lower surface wettability and micro-finned geometry. It was observed that the pool boiling over the plain surface with R123 results in higher BHTC compared with R141b at all tested pressures, whereas the pool boiling characteristics over MFCSs varied based on the combined effect of micro-finned surface geometry, surface wettability, heat flux, pressure and fluid properties. The bubble departure diameters over all the surfaces were measured at 30 W, 60 W, and 90 W at different pressures, and a new model of bubble departure diameter was proposed based on dimensionless terms. The total mean absolute error (MAE) of the proposed bubble departure diameter model was about 6.79% for the whole range of data points.

Dynamic artificial neural network model for ultralow temperature prediction in hydrogen storage tank

Hydrogen fuel cell vehicles are gaining popularity as an alternative to electric vehicles. To support their use, research on hydrogen-storage devices and charging stations is being conducted actively. However, high-pressure hydrogen dispensing can lead to a temperature increase and potential explosion hazards. Therefore, maintaining safe hydrogen temperatures during charging is crucial. However, accurately predicting temperature changes in hydrogen heat exchangers is challenging owing to rapidly changing operating conditions and large temperature differences. In this study, we adopt a deep-learning-based artificial neural network for predicting temporal temperature variations in low-temperature hydrogen heat exchangers. Two networks, namely, the deep neural network (DNN) and recurrent neural network (RNN), are constructed with Bayesian optimization based on the experimentally measured data from an ultralow-temperature hydrogen heat exchanger to predict temperature. Both models showed superior prediction accuracies of temperature within 3.11 % of mean absolute error (MAE) and heat transfer rates of the heat exchanger within 2.53 % of MAE. In particular, DNN modeling is recommended as a universal method for predicting the temperature when previous data are known, and RNN modeling is recommended for predicting the temperature for successive actions in a compressed-hydrogen system.

Experimental investigation on heat transfer and pressure drop of brazed plate heat exchanger using LiBr solution

To improve the performance and miniaturization of the absorption system, it is required to use a plate heat exchanger as a solution heat exchanger and to predict its performance accurately. In this study, the thermal performance of solution heat exchangers was investigated under operating conditions of the solution heat exchanger in the double-effect absorption system and new correlations of Nu and Fanning friction factor were developed and compared. As a result, the hot-side Nu of the high-temperature solution heat exchanger was 6.3–23.1, which was higher than that of the low-temperature solution heat exchanger (4.8–20.1). The thermal properties of the LiBr solution depending on the temperature were significantly sensitive. The developed Nu correlation (Nu = 0.273Re0.693Pr1/3) had a high accuracy with experimental results. In addition, the Fanning friction factor correlation was proposed as f = 1.601/Re0.123. The developed Fanning friction factor was lower than in other literature because the Fanning friction factor was affected by geometry parameters (chevron angle, pitch, height, and size).

Multicomponent numerical model for heat pump control with low-temperature heat storage: A benchmark in the conditions of Central Europe

This paper presents a computational parametric study on increasing the Seasonal Coefficient of Performance for residential heat pumps, utilizing an enhanced computational model and comparing it to previous research. The model computes a system that consists of a heat pump, low-temperature heat storage, heat exchanger and circulation pump, and a control unit which allows the heat pump to choose either low-temperature heat storage or ambient air as the favorable heat source. A parametric study is conducted to obtain results from a numerical model describing in detail the heat storage, surrounding soil, and the behavior of a water tank with and without temperature stratification and with two different geometries. These are combined into three different systems. Each system uses an algorithm for heat pump control that combines equithermal regulation and deferred heat storage discharging based on long-term temperature trends. Python is used to transform the numerical model into a computational model, and the assessment of heat pump operation is made based on meteorological data from the years 2012–2021 recorded in the city of Brno, Czech Republic, Central Europe. Previous studies have suggested that this combination for heat pump control and a more detailed numerical model of the system should result in a SCOP increase. In this study, heat losses of an actual occupied building with floor area of 140 m2 without considering heat radiation are used. The results show that stratification cannot be omitted for numerical modelling, and that the geometry of the storage influences how the storage should be designed. For a wide and shallow storage, it is better to insulate the system and increase the SCOP from 3.8 to 4.65, but non-insulated deep and narrow storage can increase the from 3.8 to 4.95. Flow rate is also an important parameter with a local maximum between 0.01 and 0.02 kg/s for every cubic meter of the storage. When a system consisting of parts readily available on the market is used at optimal conditions, the resulting increase can be from 11.8% up to as high as 25.7% with low-temperature heat storage ranging from 9 to 25 cubic meters.

Thermodynamic analysis and multi-objective optimization of a waste heat recovery system with a combined supercritical/transcritical CO2 cycle

This study firstly develops a novel combined cycle system consisting of a supercritical CO2 recompression Brayton cycle and a transcritical CO2 refrigeration cycle to recover waste heat from a marine turbine for both power generation and refrigeration. The pressure drop of the total heat exchanger in the whole cycle is considered in the thermodynamic and economic modeling process. Then, the influence of crucial system parameters on the system performance and economics is investigated through parametric sensitivity analysis. Finally, the system is optimized parametrically by multi-objective optimization. The results show that the higher inlet pressure of the high-pressure compressor helps to improve the thermal efficiency but reduces the exergy efficiency; the low-temperature heat exchanger plays a decisive role in the overall system exergy destruction; the HRHE accounts for a more significant proportion of the system cost, and the pressure drop has the most significant impact on the network of the system. The optimal solution is COP = 3.059, LCOE = 18.348$/(kW/h), and ηWhr = 0.651 when waste heat recovery efficiency, COP, and LCOE are considered optimization objectives.

Performance assessment and comparative study on novel carbon dioxide based power cycles for the cascade engine waste heat recovery

• Two novel CO 2 based power cycles for waste heat recovery are proposed. • Thermodynamic and exergoeconomic models are established for these systems. • Comparative studies and optimizations for these thermal systems are performed. • The novel systems show the better overall performance in exhaust heat extraction. Exploiting waste heat from engine could greatly alleviate current severe energy and environmental situation. Carbon dioxide (CO 2 ) based power cycle is considered as a type of competitive and promising energy utilization system for engine waste heat recovery (WHR) due to its high efficiency, compact design and environmentally friendly property. However, a large space is left for CO 2 -based power cycle to improve the thermodynamic and economic performance. To more efficiently and thoroughly utilizing engine waste heat, two novel CO 2 -based power cycles are proposed. Mathematical models are developed based on the software MATLAB to conduct quantitative thermodynamic and exergoeconomic analysis, parametric analysis, system optimization, and exergy analysis on the proposed systems and two traditional systems. The results show that the first proposed system can enhance net power output by 57.95% and 4.31% and meanwhile reduce total product unit cost by 14.96% and 20.74%, respectively, compared with two traditional systems. As well, the improvement of 61.61% and 6.73% for net power output and 4.11% and 10.62% for total product unit cost can be achieved by the second proposed system. Exergy analysis indicates that the cooler and low-temperature waste heat exchanger have the first and second highest exergy destructions for two proposed systems.

Dual fluid trigeneration combined organic Rankine-compound ejector-multi evaporator vapour compression system

This article evaluates the energy and exergy performance of a novel dual fluid combined organic Rankine-compound ejector multi evaporators vapour compression system (ORCEMES) for power, cooling and heating purposes. Six working fluids with ultra-low global warming potential: R1234ze(E), R1243zf, R1234yf for the CEMES and R1234ze(Z), R1336mzz(Z) and R1224yd(Z) for the ORC were selected, resulting in nine combinations. The system can work in two operating modes: power-cooling and power-heating modes. The combination of R1234ze(Z) and R1234ze(E) results in the highest overall system energy performance. The proposed system increases power generation from 21% to 75% at high geothermal and low geothermal temperatures, respectively, compared with separated basic ORC and multi-evaporator systems at the same operating conditions and cooling capacity. The proposed CEMES reduces compressor power consumption to 85% of the basic system, increasing COP remarkably. Concerning the exergy analysis, the low-temperature recapture heat exchanger shows the highest exergy destruction compared to the rest of the components, followed by the turbine. Besides, the second expansion valve presents the lowest exergy destruction percentage.

Effect of Adsorbent on the Performance of Double Effect Adsorption Refrigeration Cycle with Adsorption Heat Recovery

This study investigates the performance of double effect adsorption refrigeration cycle that utilizes the adsorption heat of a high-temperature adsorbent heat exchanger for desorption of a low-temperature one. Because there is a freedom to select an adsorbent for each adsorbent heat exchanger, the combination of adsorbents such as silica gel, FAM-Z01, FAM-Z02 and FAM-Z05 were examined. The temperature of an external heat source was assumed to be 90°C. Dynamic cycle simulation was employed to estimate the performance in terms of coefficient of performance (COP) and specific cooling power (SCP). The results show that the combination of the adsorbents FAM-Z01 and FAM-Z02 for the low-temperature heat exchanger and high-temperature one, respectively, is the most effective to achieve high COP as well as high SCP. The results also indicate that the COP=1.0 is attainable when the mass allocation of the adsorbents and the cycle time are selected appropriately. From the viewpoint of maximizing the cooling power, COP=0.9 is suggested for the best design, where the mass of high-temperature side is equal to the mass of low-temperature side.

Distributed Thermal Response Multi-Source Modeling to Evaluate Heterogeneous Subsurface Properties.

A thorough assessment of thermal properties in heterogeneous subsurface is necessary in design of low-temperature borehole heat exchangers (BHEs). A distributed thermal response test (DTRT), which combines distributed temperature sensing (DTS) with a conventional thermal response test (TRT), was conducted in a U-bend geothermal loop installed in an open borehole at the University of Illinois at Urbana-Champaign to estimate thermal properties by analyzing the thermal response of different geologic materials while applying a constant heat input rate. Fiber-optic cables in the DTRT were deployed both inside the U-bend geothermal loop and in the center of the borehole to improve the accuracy of calculated heat-loss rates and borehole temperature profile measurements. To assess the subsurface thermal conductivity during the heating phase of the DTRT, a single-source model and a multi-source model, both based on the infinite line source method, were developed using the borehole temperature data and temperatures inside and along the outside of the loop, separately. The two models returned similar thermal conductivity values. The multi-source modeling has the advantage of predicting the thermal conductivity of heterogeneous geologic materials from borehole temperature profiles during the DTRT heating phase. In addition, based on the distributed thermal conductivity measured in the borehole, estimates were made for both radial thermal impacts and the rate of heat loss in the BHE.

Thermodynamic Evaluation of a Direct Expansion Ground-Sourced Heat Pump with Horizontal Ground Heat Exchangers Using Advanced Exergy Analysis

This paper deals with the advanced exergetic analysis of a horizontal direct-expansion ground sourced CO2 heat pump operating in a transcritical cycle. The cycle is thermodynamically modeled in Engineering Equation Solver (EES) considering the pressure drops in both high and low temperature heat exchangers, and the system is to provide a fixed heating load. Conventional exergy analysis orderly suggests a compressor, expansion valve, gas cooler and ground heat exchanger to be considered for system improvement, while tracing exergy destruction of all components in detail demonstrates true improvement potential of each and all components and the system as a whole and offers a different order. Advanced exergy analysis points out that the compressor is directly and indirectly responsible for 56% of the overall exergy destruction generated in the cycle, confirming the detrimental role of this component in the system. The second influential component is recognized to be a ground heat exchanger accounting for 20% exergy destruction of the compressor as well as submitting 89% avoidability in its own exergy destruction, and expansion valve proves to be the last option for system improvement according to this analysis.

Numerical investigation on serrated fin of sub-atmosphere plate-fin heat exchanger used in superfluid helium system

A mathematical model is developed to investigate the effects of working media, operating conditions and fin structural parameters on the flow and heat transfer performance of sub-atmospheric and low-temperature helium in serrated fin. For helium, nitrogen and air, when the Reynolds number (Re) is less than 2500, the Colburn heat transfer factor (j factor) of helium is in the middle, while that is the lowest when Re is higher than 2500. The Fanning friction factor (f factor) of helium under the working condition is much higher than those of air and nitrogen under corresponding working conditions. The results show that short fin height is selected for high Re and high fin height is selected for low Re. The overall performance can be improved by increasing the fin spacing and decreasing the fin thickness. Small fin length can improve the overall performance, but the effect is poor at high Re. The Kriging response surface is used to fit the flow and heat transfer correlations of serrated fin. The fitting degrees of j and f factors are 0.963 and 0.978 respectively, and the average relative errors are 4.31% and 8.79% respectively. The two correlations have good prediction performance, which can provide a theoretical reference for the design of sub-atmospheric and low-temperature plate-fin heat exchanger.

Design and Performance Analysis of a Biomass Fueled Mono-Tube Boiler for Humid Air Turbine Cycle

Externally fired gas turbine (EFGT) is one of the few power generation configurations capable of utilizing biomass in its solid form without any additional equipment to convert it to liquid or gas. Due to its high thermal output capability for drying applications, EFGT is one of the most suitable configurations for the off-grid rural areas in Malaysia with abundant biomass waste and high demand of heat for crops drying. The main downside of EFGT is the necessity for high temperature heat exchanger which compromises the system feasibility due to the high cost and other technical challenges. This can be eliminated by the addition of steam in a configuration known as humid air turbine (HAT), thus, limiting the required temperature and allowing for the use of common low-temperature heat exchanger types. Several mono-tube steam boiler designs were compared to fulfil the required steam flow rate of 2 kg/min for the available EFGT system. Counter-flow design was found to be more suitable with its higher efficiency. The boiler was characterized experimentally at output steam flow rate range of 0.4-2 kg/min using off-cut waste wood from furniture industry. Maximum achieved boiler efficiency and specific fuel consumption were 73% and 0.29 kg/kWh, respectively.

Feasibility research on the novel experimental solar-assisted CO2 based Rankine cycle integrated with absorption refrigeration

In this paper, a feasibility analysis of the novel solar-assisted transcritical carbondioxide (tCO2) based Rankine cycle (RC) with an absorption refrigeration system (ARS) is performed. The experimental investigations are conducted on the test rig of the solar-assisted tCO2-RC for a typical day in the spring season. The unique experimental facility consists of evacuated tube type solar collectors, a high-temperature heat exchanger, a low-temperature heat exchanger, and a pump. In addition, an expansion valve is employed instead of the turbine in order to simulate the turbine operation. The proposed ARS is a single-stage type, and it is supposed to be driven by the rejected thermal energy from the experimental RC cycle. The performance of the integrated system is analyzed in terms of energy and exergy. The ARS analysis is made for water-lithium bromide (H2O-LiBr) and ammonia-water (NH3-H2O) refrigerant pairs for comparison purposes. According to the results, the power generation rate of CO2 based RC reaches up to 0.385 kW. The ARS working with H2O-LiBr presents higher refrigeration capacity with 1.413 kW while the energy and exergy efficiencies of the integrated power-refrigeration system are determined as 29.62% and 5.36% respectively. For the integrated system with NH3-H2O, the energy efficiency is 21.51% and the exergy efficiency is 4.99%. From the results, it is concluded that the ARS working with H2O-LiBr can be successfully integrated with the solar-assisted tCO2-RC for sustainable power generation and refrigeration applications. Future research should, therefore, concentrate on integrating an actual ARS with the experimental power cycle.

Fundamental Analyses and Observations of Liquid Droplet on Aluminum Surface for Heat Exchangers

Aluminum is one of the most popular materials in the industry because of lightweight Furthermore, the heat exchanger is using more aluminum rather than cumbersome and costly copper inside the system. Nowadays, all of the low-temperature heat exchanger fins are aluminum. However, when the heat exchanger is used for a long time the fin of the heat exchanger will accumulate contamination inside such as dust. The existence of contamination has strongly effect heat exchanger system performance. In this study, the physical of the water droplet with the different surface roughness (Ra) on the aluminum surfaces were studied. Hence, in this experiment, the liquid water droplet behaviors on the aluminum surfaces were observed by the contact angle. The interaction between liquid droplets and solid surface on the flat plate affect the contact angle of the water droplet. Liquid water droplet movements were analyzed by considering the change of the contact angle, were used to explain liquid droplet behaviors on the aluminum surface. Consequently, in this study, the liquid droplet behaviors on the aluminum surface can be used to improve the self-cleaning surface of the heat exchanger such as the air-conditioning system

THERMO-ENVIRONMENTAL ANALYSIS AND MULTI-OBJECTIVE OPTIMIZATION OF PERFORMANCE OF ERICSSON ENGINE IMPLEMENTING AN EVOLUTIONARY ALGORITHM

This paper makes attempt to optimize a high-temperature differential Ericsson engine with several conditions. A mathematical approach based on the finite-time thermodynamic was proposed with the purpose of gaining thermal efficiency, the output power and the entropy generation rate throughout the Ericsson system with regenerative heat loss, finite rate of heat transfer, finite regeneration process time and conductive thermal bridging loss. In this study, an irreversible Ericsson engine is analyzed thermodynamically in order to optimize its performance. In addition, three Scenarios in multi-objective optimization are presented and the results of them are assessed individually. The first strategy is proposed to maximize the Ecological function, the thermal efficiency and the Exergetic performance criteria. Furthermore, the second strategy is suggested to maximize the Ecological function, the thermal efficiency and Ecological coefficient of performance. The third strategy is proposed to maximize the Ecological function and the thermal efficiency and Dimensionless ecological based thermo-environmental function.  Multi-objective evolutionary algorithms based on NSGA-II algorithm was applied to the aforementioned system for calculating the optimum values of decision variables. Decision variables considered in this paper including the regenerator’s effectiveness, the high-temperature heat exchanger’s effectiveness, the low-temperature heat exchanger’s effectiveness, the working fluid temperature in the low-temperature isothermal process and the working fluid temperature in the high-temperature isothermal process. Moreover, Pareto optimal frontier was achieved and an ultimate optimum answer was chosen via three competent decision makers comprising LINMAP, fuzzy Bellman-Zadeh, and TOPSIS approaches. The results from scenarios shown that third scenario is the best scenario.

Thermal Performance of a Low-Temperature Heat Exchanger Using a Micro Heat Pipe Array

Domestic heat exchangers, even though widely used in industry, are not adequate for studies on low-temperature flue-gas use technologies. Despite spite their limitations, very few theoretical models have been investigated based on practical applications. Moreover, most of the existing studies on heat exchangers have focused particularly on one-dimensional and two-dimensional heat transfer models, while limited studies focus on three-dimensional ones. Therefore, this study aims at investigating the thermal performance of a low-temperature flue-gas heat recovery unit in the cold regions. Specifically, this study was conducted in the context of Changchun of Jilin Province, China, a city with the mean ambient temperature of −14 °C and mean diurnal temperature of −10 °C during winter. Experimental results showed that the thermal efficiency of the heat exchanger was higher than 60%. Through assessing the heat exchange coefficient and heat exchange efficiency of the heat exchanger, it is found that the thermal efficiency had been improved up to 0.77–0.83. Furthermore, the ICEPAK software and the standard k-ε RNG turbulence model were used to carry out simulations. The velocity and outlet temperature of fresh airflow and polluted airflow were simulated through setting different inlet temperatures of fresh air and polluted air inlet. Numerical results further indicated that the flow state was laminar flow. The micro heat pipe array side had small eddies and the heat transfer was significantly improved due to the flow of air along the surface of the micro heat pipe.

Performance Evaluation of an Industrial Absorption System

The Absorption systems have a wide range of the potential employing thermal processes to obtain both chilled water and hot water for cooling and heating applications. The performance of absorption chiller system has been extensively investigated. The absorption chiller type is (Li-Br/H2O) double-effect, parallel-flow and it is capable of providing a cooling capacity [500 R.T], [1750 kW] using natural gas as a fuel to separate refrigerant in the high pressure generator. A thermodynamic analysis for an absorption system has been analyzed based on the principle of mass conservation and the first and the second laws of thermodynamics of each component of the absorption system. The fouling effect of low and high temperature heat exchangers on the performance of absorption system has been investigated. Measurements has been recorded in two years (2015 and 2016).The temperature sensors and infrared device is used to measure specific points on the cycle components which permits to predict the COP and the second law efficiency behavior for a long time of operation. Results showed that the COP of the absorption chiller system in 2015 is higher than obtained in 2016 by average percentage 22%. The effectiveness of the low and high temperature heat exchangers decreased by 2.89% and 0.5%, respectively. Consequently, it was clear that the second law efficiency decreased by 14.04% from 2015 to 2016. Due to the fouling effect of low and high temperature heat exchangers it is recommended that doing periodic maintenance to these components of the absorption chiller systems.

Effect of operating variables on performance of an absorption chiller driven by heat from municipal solid waste incineration

This study presents an experimental analysis for a lithium-bromide/water waste steam driven parallel flow double effect absorption chiller evaluation. The absorption chiller analyzed is allocated at Bali refuse incineration plant for air conditioning system. This unit can supply a cooling capacity [400 USRT], [1406 kW]. A set of mathematical equations have been developed to estimate coefficient of performance (COP) of the chiller for each component. Theoretical analysis shows that increasing of the low temperature and high temperature heat exchangers effectiveness, decreasing temperature of absorber and condenser, increasing temperature of high pressure generator, and increase loading factor of the system improved the COP. The entire cycle is optimized by Engineering Equation Solver (EES) software from the standpoint of maximizing the COP via applying the direct experimental method. The optimization result of COP is obtained by the thermodynamic cycle.