Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 17

Search results for: regenerator

17 Experimental Study on Friction Factor of Oscillating Flow Through a Regenerator

Authors: Mohamed Saïd Kahaleras, François Lanzetta, Mohamed Khan, Guillaume Layes, Philippe Nika

Abstract:

This paper presents an experimental work to characterize the dynamic operation of a metal regenerator crossed by dry compressible air alternating flow. Unsteady dynamic measurements concern the pressure, velocity and temperature of the gas at the ends and inside the channels of the regenerator. The regenerators are tested under isothermal conditions and thermal axial temperature gradient.

Keywords: friction factor, oscillating flow, regenerator, stirling machine

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16 Comparison between Post- and Oxy-Combustion Systems in a Petroleum Refinery Unit Using Modeling and Optimization

Authors: Farooq A. Al-Sheikh, Ali Elkamel, William A. Anderson

Abstract:

A fluidized catalytic cracking unit (FCCU) is one of the effective units in many refineries. Modeling and optimization of FCCU were done by many researchers in past decades, but in this research, comparison between post- and oxy-combustion was studied in the regenerator-FCCU. Therefore, a simplified mathematical model was derived by doing mass/heat balances around both reactor and regenerator. A state space analysis was employed to show effects of the flow rates variables such as air, feed, spent catalyst, regenerated catalyst and flue gas on the output variables. The main aim of studying dynamic responses is to figure out the most influencing variables that affect both reactor/regenerator temperatures; also, finding the upper/lower limits of the influencing variables to ensure that temperatures of the reactors and regenerator work within normal operating conditions. Therefore, those values will be used as side constraints in the optimization technique to find appropriate operating regimes. The objective functions were modeled to be maximizing the energy in the reactor while minimizing the energy consumption in the regenerator. In conclusion, an oxy-combustion process can be used instead of a post-combustion one.

Keywords: FCCU modeling, optimization, oxy-combustion, post-combustion

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15 Thermo-Exergy Optimization of Gas Turbine Cycle with Two Different Regenerator Designs

Authors: Saria Abed, Tahar Khir, Ammar Ben Brahim

Abstract:

A thermo-exergy optimization of a gas turbine cycle with two different regenerator designs is established. A comparison was made between the performance of the two regenerators and their roles in improving the cycle efficiencies. The effect of operational parameters (the pressure ratio of the compressor, the ambient temperature, excess of air, geometric parameters of the regenerators, etc.) on thermal efficiencies, the exergy efficiencies, and irreversibilities were studied using thermal balances and quantitative exegetic equilibrium for each component and for the whole system. The results are given graphically by using the EES software, and an appropriate discussion and conclusion was made.

Keywords: exergy efficiency, gas turbine, heat transfer, irreversibility, optimization, regenerator, thermal efficiency

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14 Thermal Performance of Reheat, Regenerative, Inter-Cooled Gas Turbine Cycle

Authors: Milind S. Patil, Purushottam S. Desale, Eknath R. Deore

Abstract:

Thermal analysis of reheat, regenerative, inter-cooled gas turbine cycle is presented. Specific work output, thermal efficiency and SFC is simulated with respect to operating conditions. Analytical formulas were developed taking into account the effect of operational parameters like ambient temperature, compression ratio, compressor efficiency, turbine efficiency, regenerator effectiveness, pressure loss in inter cooling, reheating and regenerator. Calculations were made for wide range of parameters using engineering equation solver and the results were presented here. For pressure ratio of 12, regenerator effectiveness 0.95, and maximum turbine inlet temperature 1200 K, thermal efficiency decreases by 27% with increase in ambient temperature (278 K to 328 K). With decrease in regenerator effectiveness thermal efficiency decreases linearly. With increase in ambient temperature (278 K to 328 K) for the same maximum temperature and regenerator effectiveness SFC decreases up to a pressure ratio of 10 and then increases. Sharp rise in SFC is noted for higher ambient temperature. With increase in isentropic efficiency of compressor and turbine, thermal efficiency increases by about 40% for low ambient temperature (278 K to 298 K) however, for higher ambient temperature (308 K to 328 K) thermal efficiency increases by about 70%.

Keywords: gas turbine, reheating, regeneration, inter-cooled, thermal analysis

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13 A Multi-Objective Optimization Tool for Dual-Mode Operating Active Magnetic Regenerator Model

Authors: Anna Ouskova Leonteva, Michel Risser, Anne Jeannin-Girardon, Pierre Parrend, Pierre Collet

Abstract:

This paper proposes an efficient optimization tool for an active magnetic regenerator (AMR) model, operating in two modes: magnetic refrigeration system (MRS) and thermo-magnetic generator (TMG). The aim of this optimizer is to improve the design of the AMR by applying a multi-physics multi-scales numerical model as a core of evaluation functions to achieve industrial requirements for refrigeration and energy conservation systems. Based on the multi-objective non-dominated sorting genetic algorithm 3 (NSGA3), it maximizes four different objectives: efficiency and power density for MRS and TMG. The main contribution of this work is in the simultaneously application of a CPU-parallel NSGA3 version to the AMR model in both modes for studying impact of control and design parameters on the performance. The parametric study of the optimization results are presented. The main conclusion is that the common (for TMG and MRS modes) optimal parameters can be found by the proposed tool.

Keywords: ecological refrigeration systems, active magnetic regenerator, thermo-magnetic generator, multi-objective evolutionary optimization, industrial optimization problem, real-world application

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12 All-Optical Function Based on Self-Similar Spectral Broadening for 2R Regeneration in High-Bit-Rate Optical Transmission Systems

Authors: Leila Graini

Abstract:

In this paper, we demonstrate basic all-optical functions for 2R regeneration (Re-amplification and Re-shaping) based on self-similar spectral broadening in low normal dispersion and highly nonlinear fiber (ND-HNLF) to regenerate the signal through optical filtering including the transfer function characteristics, and output extinction ratio. Our approach of all-optical 2R regeneration is based on those of Mamyshev. The numerical study reveals the self-similar spectral broadening very effective for 2R all-optical regeneration; the proposed design presents high stability compared to a conventional regenerator using SPM broadening with reduction of the intensity fluctuations and improvement of the extinction ratio.

Keywords: all-optical function, 2R optical regeneration, self-similar broadening, Mamyshev regenerator

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11 Efficient Liquid Desiccant Regeneration for Fresh Air Dehumidification Application

Authors: M. V. Rane, Tareke Tekia

Abstract:

Fresh Air Dehumidifier having a capacity of 1 TR has been developed by Heat Pump Laboratory at IITB. This fresh air dehumidifier is based on potassium formate liquid desiccant. The regeneration of the liquid desiccant can be done in two stages. The first stage of liquid desiccant regeneration involves the boiling of liquid desiccant inside the evacuated glass type solar thermal collectors. Further regeneration of liquid desiccant can be achieved using Low Temperature Regenerator, LTR. The coefficient of performance of the fresh air dehumidifier greatly depends on the performance of the major components such as high temperature regenerator, low temperature regenerator, fresh air dehumidifier, and solution heat exchangers. High effectiveness solution heat exchanger has been developed and tested. The solution heat exchanger is based on a patented aluminium extrusion with special passage geometry to enhance the heat transfer rate. Effectiveness up to 90% was achieved. Before final testing of the dehumidifier, major components have been tested individually. Testing of the solar thermal collector as hot water and steam generator reveals that efficiency up to 55% can be achieved. In this paper, the development of 1 TR fresh air dehumidifier with special focus on solution heat exchangers and solar thermal collector performance is presented.

Keywords: solar, liquid desiccant, dehumidification, air conditioning, regeneration, coefficient of performance

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10 Design Optimization and Thermoacoustic Analysis of Pulse Tube Cryocooler Components

Authors: K. Aravinth, C. T. Vignesh

Abstract:

The usage of pulse tube cryocoolers is significantly increased mainly due to the advantage of the absence of moving parts. The underlying idea of this project is to optimize the design of pulse tube, regenerator, a resonator in cryocooler and analyzing the thermo-acoustic oscillations with respect to the design parameters. Computational Fluid Dynamic (CFD) model with time-dependent validation is done to predict its performance. The continuity, momentum, and energy equations are solved for various porous media regions. The effect of changing the geometries and orientation will be validated and investigated in performance. The pressure, temperature and velocity fields in the regenerator and pulse tube are evaluated. This optimized design performance results will be compared with the existing pulse tube cryocooler design. The sinusoidal behavior of cryocooler in acoustic streaming patterns in pulse tube cryocooler will also be evaluated.

Keywords: acoustics, cryogenics, design, optimization

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9 Solar Liquid Desiccant Regenerator for Two Stage KCOOH Based Fresh Air Dehumidifier

Authors: M. V. Rane, Tareke Tekia

Abstract:

Liquid desiccant based fresh air dehumidifiers can be gainfully deployed for air-conditioning, agro-produce drying and in many industrial processes. Regeneration of liquid desiccant can be done using direct firing, high temperature waste heat or solar energy. Solar energy is clean and available in abundance; however, it is costly to collect. A two stage liquid desiccant fresh air dehumidification system can offer Coefficient of Performance (COP), in the range of 1.6 to 2 for comfort air conditioning applications. High COP helps reduce the size and cost of collectors required. Performance tests on high temperature regenerator of a two stage liquid desiccant fresh air dehumidifier coupled with seasonally tracked flat plate like solar collector will be presented in this paper. The two stage fresh air dehumidifier has four major components: High Temperature Regenerator (HTR), Low Temperature Regenerator (LTR), High and Low Temperature Solution Heat Exchangers and Fresh Air Dehumidifier (FAD). This open system can operate at near atmospheric pressure in all the components. These systems can be simple, maintenance-free and scalable. Environmentally benign, non-corrosive, moderately priced Potassium Formate, KCOOH, is used as a liquid desiccant. Typical KCOOH concentration in the system is expected to vary between 65 and 75%. Dilute liquid desiccant at 65% concentration exiting the fresh air dehumidifier will be pumped and preheated in solution heat exchangers before entering the high temperature solar regenerator. In the solar collector, solution will be regenerated to intermediate concentration of 70%. Steam and saturated solution exiting the solar collector array will be separated. Steam at near atmospheric pressure will then be used to regenerate the intermediate concentration solution up to a concentration of 75% in a low temperature regenerator where moisture vaporized be released in to atmosphere. Condensed steam can be used as potable water after adding a pinch of salt and some nutrient. Warm concentrated liquid desiccant will be routed to solution heat exchanger to recycle its heat to preheat the weak liquid desiccant solution. Evacuated glass tube based seasonally tracked solar collector is used for regeneration of liquid desiccant at high temperature. Temperature of regeneration for KCOOH is 133°C at 70% concentration. The medium temperature collector was designed for temperature range of 100 to 150°C. Double wall polycarbonate top cover helps reduce top losses. Absorber integrated heat storage helps stabilize the temperature of liquid desiccant exiting the collectors during intermittent cloudy conditions, and extends the operation of the system by couple of hours beyond the sunshine hours. This solar collector is light in weight, 12 kg/m2 without absorber integrated heat storage material, and 27 kg/m2 with heat storage material. Cost of the collector is estimated to be 10,000 INR/m2. Theoretical modeling of the collector has shown that the optical efficiency is 62%. Performance test of regeneration of KCOOH will be reported.

Keywords: solar, liquid desiccant, dehumidification, air conditioning, regeneration

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8 Investigation of the Working Processes in Thermocompressor Operating on Cryogenic Working Fluid

Authors: Evgeny V. Blagin, Aleksandr I. Dovgjallo, Dmitry A. Uglanov

Abstract:

This article deals with research of the working process in the thermocompressor which operates on cryogenic working fluid. Thermocompressor is device suited for the conversation of heat energy directly to the potential energy of pressure. Suggested thermocompressor is suited for operation during liquid natural gas (LNG) re-gasification and is placed after evaporator. Such application of thermocompressor allows using of the LNG cold energy for rising of working fluid pressure, which then can be used for electricity generation or another purpose. Thermocompressor consists of two chambers divided by the regenerative heat exchanger. Calculation algorithm for unsteady calculation of thermocompressor working process was suggested. The results of this investigation are to change of thermocompressor’s chambers temperature and pressure during the working cycle. These distributions help to find out the parameters, which significantly influence thermocompressor efficiency. These parameters include regenerative heat exchanger coefficient of the performance (COP) dead volume of the chambers, working frequency of the thermocompressor etc. Exergy analysis was performed to estimate thermocompressor efficiency. Cryogenic thermocompressor operated on nitrogen working fluid was chosen as a prototype. Calculation of the temperature and pressure change was performed with taking into account heat fluxes through regenerator and thermocompressor walls. Temperature of the cold chamber significantly differs from the results of steady calculation, which is caused by friction of the working fluid in regenerator and heat fluxes from the hot chamber. The rise of the cold chamber temperature leads to decreasing of thermocompressor delivery volume. Temperature of hot chamber differs negligibly because losses due to heat fluxes to a cold chamber are compensated by the friction of the working fluid in the regenerator. Optimal working frequency was selected. Main results of the investigation: -theoretical confirmation of thermocompressor operation capability on the cryogenic working fluid; -optimal working frequency was found; -value of the cold chamber temperature differs from the starting value much more than the temperature of the hot chamber; -main parameters which influence thermocompressor performance are regenerative heat exchanger COP and heat fluxes through regenerator and thermocompressor walls.

Keywords: cold energy, liquid natural gas, thermocompressor, regenerative heat exchanger

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7 The Effect of Mean Pressure on the Performance of a Low-Grade Heat-Driven Thermoacoustic Cooler

Authors: Irna Farikhah

Abstract:

Converting low-grade waste heat into useful energy such as sound energy which can then be used to generate acoustic power in a thermoacoustic engine has become an attracting issue for researchers. The generated power in thermoacoustic engine can be used for driving a thermoacoustic cooler when they are installed in a tube. This cooler system can be called as a heat-driven thermoacoustic cooler. In this study, low heating temperature of the engine is discussed. In addition, having high efficiency of the whole cooler is also essential. To design a thermoacoustic cooler having high efficiency with using low-grade waste heat for the engine, the effect of mean pressure is investigated. By increasing the mean pressure, the heating temperature to generate acoustic power can be decreased from 557 °C to 300 °C. Moreover, the efficiency of the engine and cooler regenerators attain 67% and 47% of the upper limit values, respectively and 49% of the acoustical work generated by the engine regenerator is utilized in the cooler regenerator. As a result, the efficiency of the whole cooler becomes 15% of the upper limit value.

Keywords: cooler, mean pressure, performance, thermoacoustic

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6 Improving Fluid Catalytic Cracking Unit Performance through Low Cost Debottlenecking

Authors: Saidulu Gadari, Manoj Kumar Yadav, V. K. Satheesh, Debasis Bhattacharyya, S. S. V. Ramakumar, Subhajit Sarkar

Abstract:

Most Fluid Catalytic Cracking Units (FCCUs) are big profit makers and hence, always operated with several constraints. It is the primary source for production of gasoline, light olefins as petrochemical feedstocks, feedstock for alkylate & oxygenates, LPG, etc. in a refinery. Increasing unit capacity and improving product yields as well as qualities such as gasoline RON have dramatic impact on the refinery economics. FCCUs are often debottlenecked significantly beyond their original design capacities. Depending upon the unit configuration, operating conditions, and feedstock quality, the FCC unit can have a variety of bottlenecks. While some of these are aimed to increase the feed rate, improve the conversion, etc., the others are aimed to improve the reliability of the equipment or overall unit. Apart from investment cost, the other factors considered generally while evaluating the debottlenecking options are shutdown days, faster payback, risk on investment, etc. A low-cost solution such as replacement of feed injectors, air distributor, steam distributors, spent catalyst distributor, efficient cyclone system, etc. are the preferred way of upgrading FCCU. It also has lower lead time from idea inception to implementation. This paper discusses various bottlenecks generally encountered in FCCU and presents a case study on improvement of performance of one of the FCCUs in IndianOil through implementation of cost-effective technical solution including use of improved internals in Reactor-Regeneration (R-R) section. After implementation reduction in regenerator air, gas superficial velocity in regenerator and cyclone velocities by about 10% and improvement of CLO yield from 10 to 6 wt% have been achieved. By ensuring proper pressure balance and optimum immersion of cyclone dipleg in the standpipe, frequent formation of perforations in regenerator cyclones could be addressed which in turn improved the unit on-stream factor.

Keywords: FCC, low-cost, revamp, debottleneck, internals, distributors, cyclone, dipleg

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5 Gas Sweetening Process Simulation: Investigation on Recovering Waste Hydraulic Energy

Authors: Meisam Moghadasi, Hassan Ali Ozgoli, Foad Farhani

Abstract:

In this research, firstly, a commercial gas sweetening unit with methyl-di-ethanol-amine (MDEA) solution is simulated and comprised in an integrated model in accordance with Aspen HYSYS software. For evaluation purposes, in the second step, the results of the simulation are compared with operating data gathered from South Pars Gas Complex (SPGC). According to the simulation results, the considerable energy potential contributed to the pressure difference between absorber and regenerator columns causes this energy driving force to be applied in power recovery turbine (PRT). In the last step, the amount of waste hydraulic energy is calculated, and its recovery methods are investigated.

Keywords: gas sweetening unit, simulation, MDEA, power recovery turbine, waste-to-energy

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4 Environmental Catalysts for Refining Technology Application: Reduction of CO Emission and Gasoline Sulphur in Fluid Catalytic Cracking Unit

Authors: Loganathan Kumaresan, Velusamy Chidambaram, Arumugam Velayutham Karthikeyani, Alex Cheru Pulikottil, Madhusudan Sau, Gurpreet Singh Kapur, Sankara Sri Venkata Ramakumar

Abstract:

Environmentally driven regulations throughout the world stipulate dramatic improvements in the quality of transportation fuels and refining operations. The exhaust gases like CO, NOx, and SOx from stationary sources (e.g., refinery) and motor vehicles contribute to a large extent for air pollution. The refining industry is under constant environmental pressure to achieve more rigorous standards on sulphur content in the fuel used in the transportation sector and other off-gas emissions. Fluid catalytic cracking unit (FCCU) is a major secondary process in refinery for gasoline and diesel production. CO-combustion promoter additive and gasoline sulphur reduction (GSR) additive are catalytic systems used in FCCU to assist the combustion of CO to CO₂ in the regenerator and regulate sulphur in gasoline faction respectively along with main FCC catalyst. Effectiveness of these catalysts is governed by the active metal used, its dispersion, the type of base material employed, and retention characteristics of additive in FCCU such as attrition resistance and density. The challenge is to have a high-density microsphere catalyst support for its retention and high activity of the active metals as these catalyst additives are used in low concentration compare to the main FCC catalyst. The present paper discusses in the first part development of high dense microsphere of nanocrystalline alumina by hydro-thermal method for CO combustion promoter application. Performance evaluation of additive was conducted under simulated regenerator conditions and shows CO combustion efficiency above 90%. The second part discusses the efficacy of a co-precipitation method for the generation of the active crystalline spinels of Zn, Mg, and Cu with aluminium oxides as an additive. The characterization and micro activity test using heavy combined hydrocarbon feedstock at FCC unit conditions for evaluating gasoline sulphur reduction activity are studied. These additives were characterized by X-Ray Diffraction, NH₃-TPD & N₂ sorption analysis, TPR analysis to establish structure-activity relationship. The reaction of sulphur removal mechanisms involving hydrogen transfer reaction, aromatization and alkylation functionalities are established to rank GSR additives for their activity, selectivity, and gasoline sulphur removal efficiency. The sulphur shifting in other liquid products such as heavy naphtha, light cycle oil, and clarified oil were also studied. PIONA analysis of liquid product reveals 20-40% reduction of sulphur in gasoline without compromising research octane number (RON) of gasoline and olefins content.

Keywords: hydrothermal, nanocrystalline, spinel, sulphur reduction

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3 The Role of Fluid Catalytic Cracking in Process Optimisation for Petroleum Refineries

Authors: Chinwendu R. Nnabalu, Gioia Falcone, Imma Bortone

Abstract:

Petroleum refining is a chemical process in which the raw material (crude oil) is converted to finished commercial products for end users. The fluid catalytic cracking (FCC) unit is a key asset in refineries, requiring optimised processes in the context of engineering design. Following the first stage of separation of crude oil in a distillation tower, an additional 40 per cent quantity is attainable in the gasoline pool with further conversion of the downgraded product of crude oil (residue from the distillation tower) using a catalyst in the FCC process. Effective removal of sulphur oxides, nitrogen oxides, carbon and heavy metals from FCC gasoline requires greater separation efficiency and involves an enormous environmental significance. The FCC unit is primarily a reactor and regeneration system which employs cyclone systems for separation.  Catalyst losses in FCC cyclones lead to high particulate matter emission on the regenerator side and fines carryover into the product on the reactor side. This paper aims at demonstrating the importance of FCC unit design criteria in terms of technical performance and compliance with environmental legislation. A systematic review of state-of-the-art FCC technology was carried out, identifying its key technical challenges and sources of emissions.  Case studies of petroleum refineries in Nigeria were assessed against selected global case studies. The review highlights the need for further modelling investigations to help improve FCC design to more effectively meet product specification requirements while complying with stricter environmental legislation.

Keywords: design, emission, fluid catalytic cracking, petroleum refineries

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2 Study on the Integration Schemes and Performance Comparisons of Different Integrated Solar Combined Cycle-Direct Steam Generation Systems

Authors: Liqiang Duan, Ma Jingkai, Lv Zhipeng, Haifan Cai

Abstract:

The integrated solar combined cycle (ISCC) system has a series of advantages such as increasing the system power generation, reducing the cost of solar power generation, less pollutant and CO2 emission. In this paper, the parabolic trough collectors with direct steam generation (DSG) technology are considered to replace the heat load of heating surfaces in heat regenerator steam generation (HRSG) of a conventional natural gas combined cycle (NGCC) system containing a PG9351FA gas turbine and a triple pressure HRSG with reheat. The detailed model of the NGCC system is built in ASPEN PLUS software and the parabolic trough collectors with DSG technology is modeled in EBSILON software. ISCC-DSG systems with the replacement of single, two, three and four heating surfaces are studied in this paper. Results show that: (1) the ISCC-DSG systems with the replacement heat load of HPB, HPB+LPE, HPE2+HPB+HPS, HPE1+HPE2+ HPB+HPS are the best integration schemes when single, two, three and four stages of heating surfaces are partly replaced by the parabolic trough solar energy collectors with DSG technology. (2) Both the changes of feed water flow and the heat load of the heating surfaces in ISCC-DSG systems with the replacement of multi-stage heating surfaces are smaller than those in ISCC-DSG systems with the replacement of single heating surface. (3) ISCC-DSG systems with the replacement of HPB+LPE heating surfaces can increase the solar power output significantly. (4) The ISCC-DSG systems with the replacement of HPB heating surfaces has the highest solar-thermal-to-electricity efficiency (47.45%) and the solar radiation energy-to-electricity efficiency (30.37%), as well as the highest exergy efficiency of solar field (33.61%).

Keywords: HRSG, integration scheme, parabolic trough collectors with DSG technology, solar power generation

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1 The Numerical Model of the Onset of Acoustic Oscillation in Pulse Tube Engine

Authors: Alexander I. Dovgyallo, Evgeniy A. Zinoviev, Svetlana O. Nekrasova

Abstract:

The most of works applied for the pulse tube converters contain the workflow description implemented through the use of mathematical models on stationary modes. However, the study of the thermoacoustic systems unsteady behavior in the start, stop, and acoustic load changes modes is in the particular interest. The aim of the present study was to develop a mathematical thermal excitation model of acoustic oscillations in pulse tube engine (PTE) as a small-scale scheme of pulse tube engine operating at atmospheric air. Unlike some previous works this standing wave configuration is a fully closed system. The improvements over previous mathematical models are the following: the model allows specifying any values of porosity for regenerator, takes into account the piston weight and the friction in the cylinder and piston unit, and determines the operating frequency. The numerical method is based on the relation equations between the pressure and volume velocity variables at the ends of each element of PTE which is recorded through the appropriate transformation matrix. A solution demonstrates that the PTE operation frequency is the complex value, and it depends on the piston mass and the dynamic friction due to its movement in the cylinder. On the basis of the determined frequency thermoacoustically induced heat transport and generation of acoustic power equations were solved for channel with temperature gradient on its ends. The results of numerical simulation demonstrate the features of the initialization process of oscillation and show that that generated acoustic power more than power on the steady mode in a factor of 3…4. But doesn`t mean the possibility of its further continuous utilizing due to its existence only in transient mode which lasts only for a 30-40 sec. The experiments were carried out on small-scale PTE. The results shows that the value of acoustic power is in the range of 0.7..1.05 W for the defined frequency range f = 13..18 Hz and pressure amplitudes 11..12 kPa. These experimental data are satisfactorily correlated with the numerical modeling results. The mathematical model can be straightforwardly applied for the thermoacoustic devices with variable temperatures of thermal reservoirs and variable transduction loads which are expected to occur in practical implementations of portable thermoacoustic engines.

Keywords: nonlinear processes, pulse tube engine, thermal excitation, standing wave

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