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Thermodynamic analysis of Stirling engine systemsAdhemar Araoz, PhD studentSupervisors : Prof. Torsten Fransson Marianne Salomon, PhD.

KTH ROYAL INSTITUTEOF TECHNOLOGY1Outline2Background-MotivationResearch ObjectivesMethodologyTechnology OverviewThermodynamic Analysis of Stirling enginesThermodynamic analysis of SE-CHP systemsConclusionsFuture work2Motivation3The need for the development of different energy technologies

Different technologies Particular research challengesSource: International Energy Agency3

Stirling systems4

Definition : A Stirling engine is a thermal machine that transforms heat into work to produce electricity. The engine operates on a thermodynamic cycle, with compression and expansion of the working fluid at different temperature levels

Attractive Stirling PropertiesStirling engine Technological Needs1. Multi-fuel capability2. Waste heat recovery3. High Theoretical efficiency4. Modular systems suitable to access isolated regions.5. Lower noise levelsThere are needs to:Reduce the mechanical and thermal losses in prototypes. Increase the power to heat ratio.Improve the engine efficiency.Increment the reliability of the system(long life, long service intervals).Reduce the manufacturing costs.Source : D.G. Thombare, S.K. Verma, Technological development in the Stirling cycle engines, Renewable and Sustainable Energy ReviewsResearch challenge: Improve the design of Stirling engine systems4Research Objectives5Main objective

Assess the design of Stirling engine systems with emphasis on applications for small scale CHP systems

Specific objectives

Assess the design of Stirling engine prototypes

Develop an adequate design tool for Stirling engines.Determine the effect that different design and operational parameters have on the engine performance

Propose design guidelines to increase the thermodynamic performance of CHP-SE systems

Evaluate the integration of the engine into Combined Heat and Power SystemsDetermine the main parameters that affect the system performance

5Methodology6Modelling approachModel Development(Articles 1,2)Model Validation(Articles 1,2)Parametric Analysis for a Prototype(Article 3)Integration of SE into CHP systems(Article 4)Literature Review67Technology Overview

7Technology overviewStirling engine components8The pistons, the cylinder volumes, the heat exchangers and the crank mechanism. These are arranged in different configurations

Piston-Displacer ConfigurationsAlpha BetaGamma

8Technology OverviewHeat exchangers in Stirling engines9

Heater heads

Cooler

RegeneratorThe main heat exchangers are the heater, cooler and regenerator.

HeaterCoolerInternal regenerator

9Thermodynamic Analysis of Stirling engines(Articles 1, 2,3)1010

Ideal Stirling cycle11The Ideal Stirling cycle consists on four thermodynamic processes

1-2: Isothermal compression. 2-3 :Constant Volume heating.3-4:Isothermal expansion. 4-1 :Constant volume cooling.

Real cycle largely differs from the ideal description.

11Thermodynamic analysis12Second order analysis were chosen, considering a compromise between accuracy and computational requirements

12Proposed second order model (Article 1) 13

Engineering thermodynamic approach

Coupling thermodynamic and heat transfer analysis

13

Ideal adiabatic model 14AssumptionsThe engine is divided into 5 characteristic control volumes The expansion and compression spaces are adiabatic Sinusoidal volume variations Ideal gas inside the engine No heat, no mechanical losses Ideal Regenerator Source: Urieli, I.; 1977, A computer simulation of Stirling engine machines Ph. D Thesis, University of the Witwatersrand, Johannnesburg.

Mass balanceEnergy balanceEquation of stateVolume variationsGoverning equations

14Heat transfer model15

External combustion systemDependent on appropriate correlations15Energy losses module 16Pressure drop through the regeneratorSource: B. Thomas, D. Pittman, Update on the evaluation of different correlations for the flow friction factor and heat transfer of Stirling engine regenerator, American Inst. Aeronaut. & Astronautics, 2000: pp. 7684.sPressure drop through heater and cooler

f : Estimated considering one dimensional flow and cyclic steady state conditions Shuttle conduction

Oscillating flow of the displacer across a temperature gradientInternal conduction losses

Qlk

16Numerical solution17Set of algebraic differential equations for the engine and the heat transfer modulesIterative initial value numerical method until cyclic state conditions are reachedFourth order Runge Kutta scheme for the time discretization

17The GPU-3 engine is a single cylinder displacer engine, with rhombic and sliding rod seals

Capable to produce approximately 7.5 kW with hydrogen working fluid at 6.9 MPa and 3600 rpm rotational speed

The engine was studied by NASA-Lewis Research Centre (LeRC) and is well documented

In addition, the NASA-Lewis Research Centre developed a computational model which was also compared with the model proposed

Simulation of GPU-3 Stirling Engine18

Brake Power Th=704 C

Brake Power at Mean Pressure=2.76 MPa - Good capability of the model for the prediction of the brake power at different conditions - The results reflect the effect that different pressure levels and temperatures on the brake power

P=1.38 MPaP=2.76 MPa P=4.14 MPaFrequencyBrake Power kWFrequencyBrake Power kWT=583 CT=704 C18Simulation of Genoa Stirling engine19

The experimental measurements presented very low power output (55 W). But the thermal performance corresponded with the calculated with the model. For this reason the evaluation of the mechanical efficiency was included

Heat ExchangersCooler

Regenerator

Balancing flywheel

CrankcaseCrankshaftGenerator19

Mechanical efficiency of the system20 The mechanical efficiency is evaluated with Senft efficiency theorem.

W- is the forced work in the systemHypothesis: The model attributed the main losses to the forced work

20Parametric Analysis21ParameterOperational parametersCharge pressure (Pch)Temperature ratio (Tr=Twater/Tad )Design parametersCrankmechanismPhase angle Mechanism effectiveness HeaterTubes internal diameterLength of tubesCoolerTubes internal diameter LengthRegeneratorHousing internal diameterRegenerator length Porosity ()Wire diameterTypeMaterial

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ResultsInfluence of the charging pressure and temperature ratio

22Improve brake power by increasing the pressure but considering the limits determined by the temperature ratioCritical pointCritical point

Improvements on the brake power may be reached with increments on the charge pressure and reductions on the temperature ratio (high temperatures). The brake power increases until a critical pressure is reached, and after this point the brake power decreases drastically

At higher temperature ratios(low temperature operation) the break point is found at lower pressures

Therefore, in order to improve the engine brake power, both the flame temperature, which affects the temperature ratio and the charged pressure, must be increased.

2223 ResultsInfluence of the crank mechanism on the engine performanceA crank mechanism with low effectiveness will drastically reduce the brake power and thus the efficiency of the enginePhase angles closer to 70 degrees represent the optimum design values

Brake power

23Results24 Heat exchangers sizingThe curves reflect a balance between the positive effect of the increased heat transfer area and the negative influence of the dead volume and pressure drop

Brake powerBrake EfficiencyHeater

24Regenerator analysis (Housing diameter)25Regenerator capacity vs negative increment of dead volume and pressure dropHousing diameter influence on the engine brake powerBrake power start to decrease, around dihous=0.095 m

25Thermodynamic analysis for small scale Stirling engine CHP systemsArticle 42626

Description and Modelling of the system27

Generic CHP systemCombustion system (conventional fuels, renewable fuels)Stirling engine (Alpha, beta,gamma,free piston)Boiler heat exchanger

27Simulation Results28Energy Balance CHPEnergy Balance Stirling engineThe power output of the SE corresponds only to 1.2% of the heat input and the main output is the heated waterThe main losses correspond to the heat lost to the surroundings through the connections and the interface box

28Combustion analysisDifferent Biomass fuels-Overall EfficiencyAir Excess Ratio (wood pellets as fuel )Fuel humidity (wood pellets)Large and negative effectHigher chemical losses(Ash +UHC) Maximum thermal power around 1.9

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Efficiency Analysis30Overall efficiencyExergy efficiency3 Parameters: -Heat transfer to surroundings-Heat transfer to the engine-Heat transfer to the boiler hexLarge sensitivityHeat to surroundingsHeat to the engineHeat to the boilerIncrement electrical out Small reductionHeat t recoveredVery low exergyIncreasing the size of the engineIncreasing the engine size would increment the exergy efficiency

30Conclusions 31Objective: Design assessment of Stirling engine prototypesA mathematical model that included the integration of thermodynamic, heat transfer and mechanical efficiency was developed and probed adequate for the design assessment of Stirling engine systemsFrom the different curves:

Pressure and temperatures Energy Balance

Design crank mechanism Reduce the forced work.

Design of heat exchangers Dead volumes vs heat transfer area.

- Design of regenerator Pressure drop vs heat transfer

31Conclusions 32Objective: Propose design guidelines to increase the thermodynamic performance of CHP-SE

.

Identify and reduce Energy lossesCombustion parameters Operating parameters Engine designHeat Transfer SEHeat Transfer Boiler-HEXThe study allowed to propose and evaluate design improvements by using the thermodynamic analysis of the system32Future work33Model DevelopmentPropose low cost engine prototypesExtend the analysis to Free piston enginesOptimization routines33Future work34Analysis of the SE-CHP system

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Thanks

KTH ROYAL INSTITUTEOF TECHNOLOGY35Team TitleCompany NameCompany NameDepartment NameMethod of characteristics

Stirling engine analysis

0th order

1st order

2nd order

3rd order

Empirical correlations (Beale equation)

Isothermic modelsSchmidth analysis

Decoupled approach

Coupled approach

Nodal models

4th order

CFD models

Adiabatic models

Modified adiabatic models

Ideal Adiabatic Module

Internal Heat Transfer Module

External Heat Transfer Module

Energy Losses Module

Design variables

Outputs

External Heat Transfer

External Cooling

Outputs

Qh

Qk

Inputs: Design variables

Regenerator Space

Hot Source (Tflame)

External Wall of the Heater(Twoh)

Internal Wall of the heater(Twih)

Radiation + Convection

Conduction

Working FluidHeater (Th)

Convection

Qh

Qh

Qh

Convection

Convection

Working Fluid inside the cooler(Tk)

Internal Wall of The cooler (Twik)

External wall of the cooler (Twok)

Conduction

Cooling Fluid Temperature(Tek)

Heater

Qk

Cooler

Qk

Qk

Ideal Adiabatic Module

Internal Heat Transfer Module

External Heat Transfer Module

Energy Losses Module

Model outputs

Mechanical Efficiency

Lh

Cooling passages

Lk

Combustion

Fuel