an investigation of instability in a domestic gas boiler by simulatio

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Proceedings of the Institution of Mechanical

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DOI: 10.1243/09576509JPE162

2006 220: 869Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy X Tauzia, T Etchebarne, P Chesse, J-F Hetet and D Chalet

An investigation of instability in a domestic gas boiler by simulation

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An investigation of instability in a domesticgas boiler by simulation X Tauzia , T Etchebarne, P Chesse, J-F Hetet, and D Chalet

Ecole Centrale de Nantes, UMR CNRS 6598, Nantes Cedex 3, France

The manuscript was received on 7 February 2005 and was accepted after revision for publication on 31 July 2006.

DOI: 10.1243/09576509JPE162

Abstract: The experimental investigation of a domestic gas boiler revealed an unstable oper-

ation mode under certain circumstances and geometry. This paper presents the development,validation, and analysis of the modelling of a complete sealed gas boiler. The modelling usesa non-dimensional/one-dimensional non-linear solution of the mass, momentum, andenergy conservation equations. The sealed vessel is divided into three zones separated by theburner and the heat exchanger. A special focus is placed on the burner which was determinedto play a major role in the occurrence of instabilities. The comparison between measured andsimulated results shows a good agreement at steady state. The investigation of unstable con-gurations reveals the ability of the simulation model to locate unstable zones in a qualitativemanner and provides the inuence of the control parameters over the systems stability. Anattempt is made at explaining the differences observed in the quantitative results. Finally, a few potential solutions to prevent or reduce unstable zones are evaluated with the simulationmodel.

Keywords: domestic boiler, instabilities, thermodynamic modelling, system approach, controlparameters

1 INTRODUCTION

A study published by the Energy Observatory inOctober 2001 shows that 80 per cent of Frenchhomes rely on gas for domestic heating, despite theclosing of the price gap between gas and electricity.To satisfy an increasing demand, domestic gasboilers have been the subject of new developmentsin the objective of increasing the heating powerusing premixed burners. In addition, a new type of boilers known as sealed boilers has been developedto satisfy the new safety requirements related to airrenewal in boiler rooms.

The development of these new technologiesresults in a few faulty operation modes. Under cer-tain weather conditions and depending on the heat-ing power and geometric conguration, the structureof the boiler may vibrate. These vibrations are

combined with low-frequency pressure oscillations.In addition to noise problems, this type of operationis not acceptable for the customers and may end upbeing dangerous.

This paper presents a model based on a systemapproach aimed at describing the gas boiler behaviourand analysing the faulty operations that are observed.First, the investigated system is briey presented.Then, the proposed modelling is presented, including the main sub-models. Finally, somesimulation resultsare compared with experimental measurements and a few predictive results are provided.

2 DESCRIPTION OF THE SYSTEM AND ITSFAULTY OPERATION

2.1 Investigated system: a combination of sealedboiler

The water system being investigated is used for pro-

ducing heat and hot water (combination boiler) foran apartment or a house. The various experiments were conducted with a combination of sealed

Corresponding author: Laboratoire de Me canique des Fluides,

Equipe Energe tique des Moteurs a ` Combustion Interne, Ecole Centrale de Nantes, BP 92101, Nantes 44321, France. email: [email protected]

869

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The main variables that are measured are thetemperature and pressure variations at variouslocations, the air mass ow, and the speed of thefan, as shown in Fig. 1. Five control parameters areselected to test their inuence on the boiler oper-ation: exhaust pipe and air pipe lengths, gas compo-sition, gas mass ow, injector diameter, andinjector/ame stabilizer distance (the later is studiedusing a modied burner as explained in Fig. 2). Thedetailed description of the experimental setup isavailable in reference [ 2], including the location of the sensors, their type, and the data acquisition

module. As an example, Fig. 3 shows the boiler stab-ility domain as a function of inlet and exhaust pipesgeometry and the gas composition, all other vari-ables being constant. Figure 4 shows the pressurevariations in the vessel in the case of stable andunstable operations.

The experimental investigations resulted in a pre-cise characterization of the system behaviour. In par-ticular, the stable domain was identied as well asthe oscillation amplitude of the various ow

variables. In addition, the inuence of the controlparameters was evaluated.

The observed instability is a combustion instability of the system type involving the entire appliance. Theunsteady acoustic mode is the Helmholtz mode(vibration at the resonance frequency of the systemcomposed of a vessel and two pipes). Analysis of the results shows the predominant role played by the premixture transfer delay between the injectorand the ame front. An explanation of the processleading to the systems instability was established.It is mainly based on the presence of uctuations

in the mixture composition transferred to the ameat the average speed of the premixture. This canexplain the different behaviour between methaneand propane (Fig. 2). Indeed, several differencesexist between the two congurations: injectionpressure, injector diameters, lower heating value,stiechiometric coefcient are different. Rayleigh cri-terion [ 1] says that the system is stable when J T F n and the system is unstable when J T F n 1/2, where n is an integer, T the

Fig. 2 Burner overview and details

Fig. 3 Comparison of the system stability zones in the exhaust pipe length versus air pipe lengthdomain with methane and propane rated power

An investigation of instability in a domestic gas boiler 871



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delay between gas injection and combustion heatrelease, and F Helmholtz resonance acoustic fre-quency. The conjunction of these modicationsmust lead to a different delay between gas owrateat the burner inlet and heat release at the burneroutlet. These variations of T modify the value of J ,and thus the stability of the system.

The experimental analysis is rather tedious andshould be repeated for each boiler and eachconguration. As a result, it was decided to takeadvantage of the experimental results to develop a

simulation code in the objective of characterizing a boilers behaviour and predicting the potentialoccurrence of instabilities.

3 BOILER MODELLING

3.1 Assumptions and fundamentals

A survey of the numerous combustion instability models available in the literature was conducted[3 14 ]. In addition to the modelling of the combus-tion, the prediction of instability domains must takeinto account the dynamics of the internal ows. Thegreat diversity of the instability characteristics as wellas the systems being considered is not compatible with a single approach. A literature survey showsnumerous modelling methods with respect to theow dynamics. A summary and a classication of the models were established to determine the bestpossible approach depending on general criteria, asshown in Fig. 5.

Two criteria are required to determine the bestpossible method:

(a) the natural frequencies of the unstable modes(level 1);

(b) the research objectives (level 2).

The rst criterion compares the characteristicpressure wave length associated with the instability and the equipment geometry. When the oscillationfrequency is low, the parameters vary in phase within the appliance around the average value.The dynamics of the instability is properly simulated

by a model resulting from a system approach(non-dimensional compressible approach forvolumes and one-dimensional uncompressible

Fig. 4 Comparison between stable and unstable gasows rated power propane.

Fig. 5 Algorithm for choosing the modelling of the ow dynamics

872 X Tauzia, T Etchebarne, P Chesse, J-F Hetet and D Chalet

Proc. IMechE Vol. 220 Part A: J. Power and Energy JPE162 IMechE 2006 by guest on June 25, 2011pia.sagepub.comDownloaded from


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assumption for pipes). The calculated values areonly dependent on time. The quasi-steady assumption is acceptable since the characteristictime of the instability is rather large. This type of

approach is used for low frequency combustioninstabilities (instability mode on volume or rst-order longitudinal). Even though the instability dynamics are properly modelled, this type of approach does not provide the spatial distributionof the ow variables.

When the instability wave length is similar orsmaller than the appliance characteristic length,the pressure does not vary in phase within thesystem. The spatial discretization of the system(one-dimensional, two-dimensional, or three-dimensional) is required to take into account theinstability dynamics [ 10 15 ].

For both these approaches, two resolutionmethods are detailed in the literature. Some authorspropose a linear analysis of the equations describing the system, whereas others solve the equations whilekeeping the non-linear terms. The non-linear resol-utions are replacing the linear approach. Solving the NavierStokes equations in non-linear mode isnow possible with the latest performance of compu-ters. These non-linear models provide the amplitudeof the limit cycles; however, the linear approach canbe sufcient when the objective is to locate the limitof the system instability, the propagation of faulty

conditions or the efciency of a control parameter.The instabilities identied through the experimen-tal investigations are characterized by very low fre-quencies ( , 10 Hz). The analysis seems to indicatea system instability. These observations along withthe research objectives (which include the calcu-lation of instabilities amplitude) led to the selectionof a non-linear model.

Regarding time considerations, it is assumed thatthe systems behaviour is a non-stationary modecomposed of a succession of stationary states(quasi-stationary assumption). This assumptionauthorizes the use of steady state equations for thefollowing:

(a) regular and singular pressure losses;(b) operating characteristics of the fan;(c) gas thermodynamic properties.

From a spatial perspective, the wave length charac-terizing the pressure wave propagation with a fre-quency of , 7 Hz is rather large in comparison withthe boiler dimensions. This leads the following assumptions:

(a) the thermodynamic values vary simultaneously

in the vessel (capacitive aspect);(b) the uid can be assumed to be uncompressible

within the pipes (inertial aspect).

3.2 Spatial discretization

A model based on a system approach is proposedusing the assumptions presented in the previous sec-tion. The system is divided into control volumes in which the variables (pressure, mass, temperature,and ow) are only dependent on time.

The gas feeding system shown in Fig. 6 is modelledas a manifold, maintained at constant pressure(capacitive element) followed by a pipe (inertialelement). The injector rail is modelled with a capaci-tive element corresponding to the rail volume. Theinjectors are modelled through an orice with a discharge coefcient.

The vessel in which the heat exchanges takes placeis divided into three distinct volumes to account forsevere temperature differences, as shown in Fig. 7.

This discretization leads to boundary equationsrelated to mass and energy transfers between the var-ious zones. The ow between volumes 1 and 2 isobtained using the motion quantities. A constantequivalent section is calculated for the sectionthrough which the secondary air passes betweenthe burner arms. The ow between volumes 2and 3 is obtained using Bernoullis equation. An equivalent section is calculated for the heatexchanger section through which the exhaust gascirculates.

3.3 Calculations for the capacitive elements

An energy balance is obtained by applying the rstprinciple of thermodynamics in open systems. Thefollowing equation is obtained by neglecting kineticand potential energy terms and assuming that thegas is perfect and homogeneous

dT dt

1

Mc v dQdt

dW dt

_Q Xlin,out _m lh l ! T

M

d M

dt

(1)

Fig. 6 Modelling of the gas feeding system




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Assuming that the gas is homogeneous, the massequilibrium in a given volume is the following

d M dt

Xlin,out _m l (2)The pressure is obtained using Mayers relation forperfect gas as follows

P MRT

V (3)

3.4 Calculations for inertial elements

The instantaneous mass ow through the pipes isobtained using the momentum equation for a non-compressible uid while modelling the frictionforces with a pressure loss. The rate of change of the mass ow as a function of time is the following

d _mdt

S L

(P in D P P out ) (4)

where DP represents the pressure variations relatedto resistive elements (regular or singular pressurelosses) or driving elements (fan).

Assuming a quasi-stationary variation of thesystem variables, the pressure losses can beexpressed as follows

D P j r 2

D 2

S 2 (5)

The various discharge coefcients were evaluatedusing the tables provided by Idlcik [ 16 ]. They were

modied using the experimental measurements of the pressure losses through the various elements of the system.

3.5 Air and exhaust gas thermodynamicproperties

Variation of the excess air within a volume isobtained using the mass equilibrium of each specieassuming that the volume is homogeneous

e M a

M g R sto1 (6)

The air and exhaust gas mass enthalpy and thespecic heat at constant pressure are computedusing the molar specic heat and enthalpy of O 2 ,N2 , CO2 , and H 2 O provided by polynomialregressions obtained from the tables available inreference [ 17 ]. The equilibrium equation of thechemical reaction describing the combustion of gas with excess air is obtained assuming that thecombustion is complete.

3.6 Determination of the fan operating point

The operation map of the fan obtained from exper-imental measurements is stored in matrix form.Interpolation is used to determine the pressure vari-ations as a function of the mass ow and speed. Thevariations are transposed to take into account the

difference between reference and actual conditions.Newtons second law applied to the fan providedthe fan speed as a function of time.

Fig. 7 Spatial discretization of the system using capacitive and inertial elements




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3.7 Mass ow through a section

The mass ow through a real or equivalent oriceis provided by Bernoullis equation for a non-compressible uid and Barre Saint-Venantsequations for a compressible uid. Barre Saint- Venants equation for a subsonic ow is the following

_m C d S P inR k T in

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 g k g k 1 P inP out 2=g k P in

P out g k 1=g k " #vuut

(7)

Bernoullis equation is expressed as follows

_m C d S ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP in P outp (8)3.8 Exchangers heat exchange

The water to be heated takes the energy contained inthe combustion products by going through a coun-ter-ow heat exchanger, as shown in Fig. 8. Refer-ences [ 18 ] and [ 19 ] provide little information ontransient heat exchanges (non-stationary conductionduring the establishment of a steady state) and noinformation on the convective exchanges during

transients.The following assumptions are proposed.

1. The instantaneous heat exchange, assumed to bequasi-stationary, is provided by the steady stateequations.

2. Given the thermal inertia associated with the water mass, the water inlet temperature is only dependent on the systems average conditions.

Balancing the power provided by the exhaust gas with the power gained by the water allows for theevaluation of the average water temperature at theheat exchanger outlet (Fig. 9)

T ch eau C p f _m f

(T ch f T fr f )C p eau r eau _m eau

T fr eau

(9)

The global exchange coefcient per square metre is

obtained, assuming that the tube thickness is smalland the copper conductive coefcient is signi-cantly larger than the uid/wall convective coef-cients. The evaluation of the convective exchangecoefcients is semi-empirical [ 18 ]. The forcedconvective exchange coefcient is obtained fromHilperts table in the case of an air ow that isperpendicular to a pipe [ 18 ].

A similar formulation is derived for the convectiveexchange coefcient within the tubes using exper-imental data. In addition, the speed of the waterow within the tube is assumed to be constant.The instantaneous thermal power is expressed asfollows

c a 1 a 2 v 0:5

a 1 a 2 v 0:5S ech F ech

T ch f T fr eau T ch eau T fr f ln[( T ch f T ch eau )=(T fr f T fr eau )] (10)

where F ech is a corrective coefcient to account forthe heat exchanger type (counter ow). This coef-cient depends on the temperature gradient and canbe assumed to be equal to 1 in the case being inves-tigated. a 1 and a 2 are derived from the experimentusing the mass ow of the exhaust gas, the powerbeing exchanged, and the measured temperaturesfor two steady states.

3.9 Modelling of the unsteady heat exchangeassociated with the combustion

The analysis of experimental results showed thepredominant role played by the unsteady heat releasein the occurrence of instabilities [ 1]. As a result,a special focus was placed on the heat exchange.

A rst investigation was conducted with a Compu-

tational uid dynamics (CFD) code in the objectiveof characterizing a partially premixed burner and,in particular, the transfer of the various species as

Fig. 8 Schematic diagram of an heat exchanger withtwo passes

Fig. 9 Schematic diagram of the heat exchange




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well as the variations of composition [ 1]. The analysisof the ow inside a burner arm which was achieved with the Fluent CFD code [ 20 ] showed a reductionof the unsteady gas ow signal between the inlet

and outlet. Consequently, the following modelling based on two parameters was selected:

(a) a damping coefcient linking the amplitude of the composition uctuations at the inlet and atthe outlet;

(b) a delay associated with the transfer time of thecomposition uctuations.

The mass ow of the gas reaching the ame is thenthe following

_m g f l _m g in amor [ _m g in (t t )

_m g in ] (11)

A phenomenological model of the delay is alsoproposed. The selected control parameters areassociated with the gas velocity (injector diameterand average mass ow), the air velocity (averagetotal volume ow), and the burner arm geometry (length and equivalent section). The coefcients b 1 ,b 2 , and a are evaluated through a parametric investi-gation comparing computed and experimentalresults for specic operating points

t a

Diam 2inj4 p

L S bras

_m

b 1g D

b 2a (12)

Finally, a fundamental study of the ame kinetic was performed in order to evaluate the relationshipbetween the composition uctuations at the amesource (at the burner arm outlet) and the unsteady heat release. The objective was to determine undercertain assumptions the transfer function linking heat release and variation of composition using an approach similar to Ducruixs approach [ 21 ]regarding speed uctuations. The heat release wasdetermined to be directly proportional to the instan-taneous gas ow at the ame

_Q _m gfl PCI (13)

3.10 Resolution

A simulation language called Advanced ContinuousSimulation Language (ACSL) was selected to modelthe system being investigated [ 22 ]. This language was specically developed for the simulation of time-dependent processes described by differential

equations or transfer functions. An explicitdescription of the model as a function of time isnot required to solve the differential equations. The

selected integration algorithm is the Runge Kutta fourth-order algorithm.

4 VALIDATION

4.1 Steady state

The model validation was performed by comparing simulated and experimental results for the following ve variables:

(a) pressure within the sealed vessel;(b) air ow;(c) boiler efciency;

(d) heat exchanger outlet temperature;(e) fan average speed.

The objective is the determination of the variationtrend and amplitude rather than the exact value of the variable being considered, which would behardly achievable given the proposed assumptions.

The simulation runs are conducted by setting theinjection pressure in order to reach the boilersrated power. Figure 10 shows the simulated andmeasured relative pressure of the sealed vessel,heat exchanger outlet temperature, fan speed, and

air ow as a function of the exhaust pipe length.The remaining control parameters and, in particular,the air pipe length are kept constant.

A fairly good agreement is achieved from a quali-tative and quantitative perspective. As shown by the experimental results, the pressure in the sealedvessel increases with the exhaust pipe length.The temperature decreases when the exhaustpipe length increases. The amplitude of thetemperature variation is of the same order as theexperimental observations. The model underesti-mates the experimental value by 20 K. This appearsto be acceptable given the temperatures averagevalue.

Qualitatively, the model properly estimates the fanspeed variation trends when the exhaust pipe lengthincreases. Quantitatively, the differences that areobserved between simulation and experiment canbe partially explained by the lack of an accurate cali-bration of the speed measuring device. In particular,the speed of the asynchronous motor fan cannotactually exceed 3,000 r/min.

Similar results were obtained for different variablesof the air piping system. The series of experimentsaimed at evaluating the inuence of the air pipe

length and the boiler power showed a good quanti-tative and qualitative agreement between simulatedand measured results [ 1].




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4.2 Unsteady state

The initial focus of the model validation is on theinuence of the geometry (exhaust and air pipelengths) on the systems behaviour at the rated con-ditions. Figure 11 shows a comparison betweensimulated and experimentally observed stability

domains. This gure shows a sufcient agreementbetween numerical and experimental results. In par-ticular, the presence of an exhaust pipe length rangefor which the system is unstable is properly predictedfor all unstable lengths of the air pipe. Furthermore, a good agreement between simulated and experimen-tal results is achieved with respect to the existence of an air pipe length limit beyond which no instabilitiesare observed across the range of exhaust pipe lengthsthat were experimentally tested. This length limit isslightly underestimated by the model. For a givenair pipe length, the predicted range of exhaust pipelengths for which the system is unstable is higherthan the experimentally observed range; however,the range width is properly evaluated by the model.

Figure 12 shows the computed pressure oscillationcharacteristics in terms of amplitude and frequency.Even though a comparison for a given exhaust pipelength is not signicant since predicted andmeasured stability domains are different, a compari-son between the amplitudes of simulated andmeasured pressure oscillations shows that they are

of the same order of magnitude.Calculated frequencies are similar to the frequen-

cies obtained after treating the measured pressure

Fig. 10 Model validation for the inuence of the exhaust pipe length on the sealed vessel relativepressure, exchanger outlet temperature, fan speed, and air ow at the rated conditions

Fig. 11 Comparison between simulation and

experiment at the rated conditions for thestability domain as a function of the exhaustand air pipe lengths




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signal. Again, the poor agreement between themeasured and predicted stability domains makes itdifcult to compare the results for a given exhaustpipe length. The simulated frequency is slightly over-estimated; however, the variation amplitudes of observed and calculated frequencies are similar fora given variation amplitude of the exhaust pipelength in the narrow range being investigated.

A comparison for the oscillation amplitudes of thegas mass ow and air volume ow shows a goodqualitative agreement between calculated andmeasured values. As an example, Fig. 13 shows thegas mass ow and air volume ow oscillation ampli-tudes as a function of the exhaust pipe length for anair pipe length of 10 m. Similar results were obtainedfor other air pipe lengths [ 1]. For a given length, thesimulation results show the existence of a maximumoscillation amplitude located near the middle of theinstability zone.

From a quantitative perspective, the oscilla-tions order of magnitude for the gas mass ow

(10 per cent) and air volume ow (20 per cent) isproperly estimated by the model; however, the com-parison of the maximum amplitudes shows an overes-timation that reaches 30 per cent for the gas ow and45 per cent for the air ow.

Finally, the variations of the fan speed are around30 r/min for the most critical congurations. Thisresult is similar to what is experimentally observed.The temperature oscillations are very small as indi-cated by the lack of signicant temperature oscil-lations in the experimental measurements [ 1].

Another control parameter of interest is the injec-tor diameters, as illustrated by Fig. 14. The modelshows a good agreement with experimental obser-vations. The oscillation amplitude increases withthe injectors diameter. Quantitatively, the modelappears to be very reactive with respect to modi-cations of the injector diameter. This results in anoverestimation of the oscillation amplitudes. Theincrease of the oscillation amplitude with the injec-tors diameter can be explained by a reduction in

Fig. 12 Comparison between simulation and experiment for the oscillation frequency andamplitude as a function of the exhaust pipe length

Fig. 13 Gas mass ow and air volume ow oscillation amplitudes versus exhaust pipe length comparison between simulation and experiment




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the pressure difference between the combustionchamber and the gas rail. Reducing the injectionpressure is indeed necessary to make up for theincrease of the injectors diameter in order to main-tain the rated power. Consequently, for given oscil-lations of the combustion chamber pressure, thedecrease of the injection pressure boost results in a higher variation of the gas ow and thus a largerunsteady heat release. On the contrary, a reductionof the injectors diameter decreases the gas massow sensitivity with respect to interferences in thecombustion chamber pressure and thus contributesto a better stability of the system.

4.3 Predictive investigations

The model was used as a predictive tool for testing the inuence on the system stability of certain par-ameters such as the ambient air temperature andthe inlet pipe diameter, as shown in Fig. 15. Signi-cant modications of the instability zone can be

observed in the air pipe length versus exhaust pipelength domain. The effect of the air temperaturecan be linked to a modication of the systemsaero-acoustic balance through the variation of the

air density.The instability zone in the air pipe length versusexhaust pipe length domain decreases with theinlet pipe diameter. For a given diameter of 0.07 m,all congurations are stable.

5 CONCLUSION

The proposed model for the simulation of a domesticsealed boiler achieved the following signicantresults.

1. The model properly estimates the inuence of theexhaust and air pipe lengths even though differ-ences are observed in the location of the simu-lated and observed stability domains.

2. Experimentally observed trends regarding theinuence of the injection system (injectorsdiameters, equivalent burner arm length) areconrmed by the simulation.

3. The computed amplitudes and frequencies are inagreement with the measured values.

These results show that the model is able to predict

the existence of low-frequency instabilities, thusvalidating the approach being used. In addition, themodel can globally provide the system sensitivity with respect to the investigated control parameters;however, the differences that are observed regarding the stability domain and the inuence of the appli-ance power show the need for improving the model-ling of the ow in the burner arm using experimentaland numerical investigations specically developedfor a burner arm. This is a required condition for

Fig. 14 Pressure signal amplitude versus injectordiameter at rated power

Fig. 15 Variation of the stability domain as a function of the ambient air temperature and inletpipe diameter




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S surface (m 2 )S ech heat exchange surface (m 2 )t time (s)T temperature (K)

V volume (m3

)W total mechanical work of the system (J)

a 1 , a 2 coefcientsg specic heat ratior density (kg/m 3 )t delay (s)c exchanged thermal power (W)j discharge coefcient

Subscripts

a airbras burner armch warmeau waterf exhaust gas amefr coldg gasin inletinj injection systemk specie k out outlet


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an investigation of instability in a domestic gas boiler by simulatio

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