Assessing the causes of combustion-driven oscillations in boilers using a feedback-loop stability model. - propane gas grill with stainless steel control panel

Introduction when a new boiler is developed, there may be a tone noise that is neither normal nor objectionable.This tone noise comes from the unstable sound of heat, called combustion-Drive oscillation.When sound is reflected from the combustion chamber to the supply chamber of the mixture or more to the air valve, the oscillation driven by combustion occurs.Sound is a transparent pressure that causes the flow or composition of the mixture (I.e., Equivalent ratio) fluctuations.This leads to a fluctuating rate of heat release or volume, which is an acoustic interference in the combustion chamber.Baade (1978) pointed out that this phenomenon is a positive feedback loop that leads to higher feedbackUntil the behavior is no longer a linear amplitude combustion oscillation.At present, boiler manufacturers have solved these problemsand-Wrong way and different way.Typical solutions include modifying the geometry of the combustion chamber, adding acoustic absorption, switching burners and gas valves, and setting up boiler controls to avoid certain operating conditions.However, the industry usually does not solve the problem in a systematic way.The purpose of the work recorded in this paper is to help the boiler industry move towards a more systematic approach.Specifically, low.The sequential model of combustion oscillation phenomenon was recorded and then demonstrated on two boilers showing oscillation.The goal of the model proposed by Baade (1978,2007) more than 30 years ago was combustion oscillation caused by fluctuating mixed flow.Because fluctuations can also cause oscillation.Mixturecomposition, developed a supplementary model based on the work of sattelmayer (2003.Higgins (1802) seems to be the first to prove the existence of combustion oscillation.In his classic, Lord rayleighlord explained the phenomenon, saying: "If the heat is regularly transmitted to the air quality of the vibration in the cylinder bound by the piston (for example ), the effect produced will depend on the stage of vibration in which the transfer takes place.Vibration is encouraged if it is heated to the air at the maximum condensation moment, or if heat is taken away from the air at the maximum sparse moment "(Riley 1945 ).Lord Ray noted that one of the main requirements for amplification of instability through the feedback process is the phase relationship between acoustic pressure and heat transfer.In 1950 s, Putnam (1971) mathematically describes the criteria for and suggests that thermal acoustic instability may occur if [integral.sup.T.sub.0] p (t) q (t) dt> 0 (1) where ep (t) = acoustic pressure q (t) = pulsating part of heatThe release rate assumes that the acoustic particle velocity (v (t) is proportional to the pulsating part (q (t) of the flame heat release.Therefore, the left side of equation 1 is also proportional to the acoustic energy generated by a cycle (I.e.The power of sound ).In order for thermal acoustic instability to occur, the left side must be positive and greater than the dissipated acoustic energy.The disturbance of the combustion rate is inevitable.However, these disturbances may not necessarily result in a thermal-acoustic effect, unlessThere are exciting mechanisms.Instability occurs when a small modulation of the flow rate or composition of the mixture causes a thermal release oscillation.Reduction in volume velocity due to thermal release oscillation (I)e.Sound interference) causes acoustic oscillation fed back into the mixture.LOW-The sequential model of the mixture flow oscillation feedback loop stability model baade (1978,2007) is reformulated by (1) The putnam equation in the form of a feedback loop and (2) defines this relationship in the frequency domain.In the process, Baade determines three transfer functions that need to be determined.The two transfer functions (Z and H) are acoustic and can be determined by experiment or simulation.Other transfer functions (G) are flame-related and, although some models are available, it is better to determine by experiment.Figure 1 shows a schematic diagram of the Baade feedback loop stability model (Baade 1978, 2004) used to predict combustion oscillation.[Indicates a disturbance to the volume velocity of the external flame of the feedback loop??].sub.ext].The driving point (Z) of the combustion chamber is the oscillating pressure ([??]) The volume speed to the combustion chamber ([??].sub.tot] or [??]).H is the transfer function about the disturbance of mixed logistics ([[??].sub.I) the sound pressure to the combustion chamber ([??]).[Figure 1 omitted] for the closed loop, a transfer function describing the flame is required, and Baade (1978) is represented by the flame transfer function (G.In a supporting paper for Baade's work, Goldschmidt and others.(1978) define G as the ratio of the volume flow oscillation ([??]) The volume speed of the flow of the mixture ([[??].sub.i]).Thus,G = [??]/[[??].sub.I] (2) the flame transfer function can also be defined as the ratio of the fluctuating part of the combustion mass flow rate to the injected mass flow rate (Goldschmidt et al ).1978).This transfer function is usually measured and will be described in a more detailed description.After defining three transfer functions (Z, H, and G), it is very simple to derive expressions for stability criteria based on feedback loops (Baade 1978.If all three transfer functions are multiplied, if [[The] mathematical expression is not reproducible in ASCII] (3??].sub.Ext] assuming zero, the ratio on the right side of the equation is unit.Therefore, the H x G x Z = 1 (4) equation 4 defines the customThe excited oscillation kept itself but did not grow (Baade 1978 ).Note that Z, H, and Gare are each complex function of the frequency.However, right-The hand side of 4 is real.This means that instability can only occur at frequencies where the sum of phases of Z, H, and G is equal to a multiple of 0 [degree] or 360 [degree.Therefore, under the left-hand side of equation 4 which exceeds 1 and is the true frequency, the conditions for thermal acoustic instability are favorable.For the sake of simplicity, Baade (2004;Baade and Tomarchio 2008) recasting equation 4 as an absolute value of inequality [Z x H]> 1/[G] (5) at a frequency more than the right on the left side of equation 5, combustion oscillation is more likely to occur.In the following discussion, we chose to follow the reasoning route in Elsari and Cummings (2003) to describe the acoustic model.The model assumes that there is * plane wave propagation in the pipeline, * low Mach number flow, and * the length of the flame is small compared to the acoustic wavelength.Figure 2 shows a schematic diagram of the pipe with heat release.Assume that the flame is a volume velocity source with volume source strength (Q.Q = [S] Requirements for conservation of mass.sub.1] [[??].sub.1] + [S.sub.2] [[??].sub.2] (6)where[[??].sub.1] = sonic particle velocity of upstream pipeline??].sub.2] = acoustic particle velocity in downstream pipeline [S.sub.1] = cross-Cross section of upstream pipeline [S.sub.2] = cross-The cross-sectional area of the downstream pipeline particle velocity refers to the vibration of particles in the fluid medium, where particles refer to a large number of molecular collections occupying a small volume.It is assumed that [Delta] is very small compared with the wavelength of sound waves ,[??].sub.1] and [[??].sub.2] (as shown in Figure 2) due to the continuity of acoustic pressure, it should be equal to each other (I.e., The sound pressure does not change suddenly in the space ).[Z.sub.u] and [Z.sub.D] upstream and downstream acoustic impedance (sound pressure specific volume velocity), respectively ).[Figure 2] as shown in figure 3, an acoustic circuit can be constructed.The circuit constructed is similar to a circuit in which the pressure and volume velocity correspond to the voltage and current respectively.Please note that the upstream and downstream impedance ([Z]sub.u] and [Z.sub.D) parallel to each other.Next, Z is the equivalent acoustic impedance of the acoustic circuit shown in figure 3, which can be written as [mathematical expression, not reproducible in ASCII] (7) Baade (1978) notice [??].sub.tot] and [??] Not the input and output of the combustion chamber, but the corresponding input and output of the dynamic process in the combustion chamber.The disturbance of the flow volume speed of the mixture is indicated??].sub.I] is equal to the negation.sub.1][[??].sub.1] in Figure 2.Therefore, he is a negative access to the burner port that observes the supply of the mixture (Baade 1978) (access is the reciprocal of the acoustic impedance) and can be used in ASCII] (8) is the [Mathematical expression] that cannot be reproduced in??].sub.i] and [??Not the input and output of the hybrid supply, but the dynamic process that occurs when the hybrid supply occurs.The prediction and measurement of the flame transfer function is the ratio of fluctuating combustion mass flow to injected mass flow (Goldschmidt et al ).1978).Goldschmidt and others.(1978) The Flame transfer function is measured using an acoustic method.The speaker is used as an incentive below the burner to fluctuate the burner inlet flow and to measure the sound pressure with or without a flame.[Figure 3 omitted] Figure 4 shows a schematic diagram of the method suggested by Goldschmidtet al.(1978) oscillate the inlet flow and measure the flame oscillation.Please note that the speakers are placed in the fuel air mixing room.Measure the sound pressure in the mixing chamber (microphone 1) and after combustion (microphone 2.Turn off the flame ([[?) The sound pressure at the time (measured at the microphone 2 )??].sub.Off]) with the inlet of the burner ([[??].sub.i]).Again, with the opening of the flame, the sound pressure ([??].sub.On]) is proportional to the volume flow oscillation ([??) The flame itself.Microphone 1 is used to monitor input to ensure consistency between the two tests.Korov ov et al then defined the flame transfer function Gis as [mathematical expression, not reproducible in ASCII] (9.(2006, Kornilov 2005) and Khanna (2001) detection of OH using chemical LEDsWhat can be directly related to the release rate indicator??].In the case of kornilov, the flow velocity oscillation is measured using a hotline anemometer ([[??].sub.I) as the flame goes out.By taking the ratio of the Fourier transform amplitude of [I], the gain of the flame transfer function is foundsub.Oh] the signal of the amplitude of the sound wave speed signal measured by the hotline anemometer.Like Goldschmidt and others.(1978), the flow is disturbed by the excitation of the speaker.[Figure 4 omitted] Kornilov (2006) developed an empirical formula modified by Baade (2008), expressed as a [Mathematical expression] for the flame transfer function of Bunsen burnerexpress, not reproduced in ASCII] (10) where []sub.0] = the offset term of the flame transfer function, defined as [tau].sub.0] = time-Delay parameters of the flame transfer function [tau.sub.1] = attenuation parameter of flame transfer function [ω] = angle frequency [[ρ.sub.U] = density of unburned mixture [[p.sub.D] = density of combustion product [tau.sub.0] is defined as [tau ].sub.0] = 2[pi][V.sub.0]/[T.sub.0] H (11) where [V.sub.0] = average gas speed h = flame height [T.sub.0] = empirical constant [[TAO].sub.1] is defined as [head ].sub.1] = [T.sub.1]/[H] square root of [Ssub.L] (12)where[S.sub.L] = flame propagation speed [T.sub.1] = the model of empirical constantKornilov should be useful as an estimate.The model was developed for Ben Sheng lamps, and most commercial burners can be considered as arrays of Ben Sheng lamps.However, the model does not take into account the actual burner geometry, the presence of different control flows, and the impact of metal or ceramic grids on burnersurface.LOW-Order model of equivalent ratio oscillation feedbackThe combustion oscillation of the cyclic stability model can also pass the fluctuation equivalent ratio (Sattelmayer 2003;Lieuwen et al.2001).Sattelmayer (2003) developed a model that combines the effects of the equivalence ratio and the flow fluctuation of the mixture.However, the model assumes that the geometry of the burner and the flatbed burner is simple.In addition, the model is considered too complex for the ASHRAE community as it needs to solve 16 equations.Decided to develop a feedback-Similar to the loop model shown earlier.Although Sattelmayer suggests that combustion oscillation may be a combination of two mechanisms (mixture flow and equilibrium ratio fluctuation), one mechanism is more likely to dominate.In addition, the solution of burningThe oscillation problem in the boiler will target one mechanism or another, not a combination of the two.Therefore, a separate feedback loop for equivalent fluctuations was developed and no attempt was made to merge the two models into a unified model.Sattelmayer (2003) proves that a unified model is non-linear.The model is shown in figure 5.Z and [H.sub.1] All are pure acoustic transfer functions.Z is burning-The chamber impedance is the same as the one used in the mixture flow model.[H.sub.1] The relevant fluctuation speed ([??].sub.V) to the fluctuation pressure ([??) In the burner.[H.sub.2] the equivalent ratio is described ([??]) The fluctuation speed to the gas valve.Flame transfer function ([G.sub.[Phi]) should also be defined according to the equivalent ratio fluctuation.Therefore, [mathematical expressions are not reproducible in ASCII] (13) Where is??) = Heat release of fluctuations.In this case, if [absolute value Z] x [absolute value [H.sub.Absolute value of [H] xsub.2] absolute value of x [G]sub.[Phi]> 1 (14), which can be reformulated as the absolute value of [Z] x [H]sub.1]> [1/[absolute value [H.sub.2] absolute value of x [G]sub.[phi]]].(15) if [angle] Z [angle] [Hsub.1] + [angle][H.sub.2] +[angle][G.sub.[Phi] = 0 (16) [Figure 5 Slightly] The acoustic model of the intake system under the equivalent ratio perturbation, Z is the same as described in the section "system acoustic model."However, the acoustic model of the intake system now uses the transfer function [H.sub.1], this is related to the level of particles that fluctuate ([[??].sub.V]) to fluctuating pressure at the gas valve ([??) At the flame.Figure 6 shows the variables considered.This transfer function ([H.sub.Month]) The mufflertransfer matrix can be calculated.The transfer matrix between the flame and the gas valve is defined as [T.sub.1] and between the gas valve and the inlet opening, as [T.sub.2], as shown in figure 6.Impedance of the pipeline at the gas valve ([Z]sub.Uv]) is defined as a gas valve ([[??].sub.V) to volume speed ([[??].sub.v]).It can be determined from the transfer matrix between the valve and the inlet opening [T2] and the impedance at the inlet opening ([Z]sub.rad]).[Z.sub.Uv] can be represented as A [mathematical expression, which cannot be reproduced in ASCII] (17), where [.sub.2], [B.sub.2], [C.sub.2], and [D.sub.2] it's [T.sub.2]].This impedance is parallel to that of the gas valve.However, it can be assumed that the impedance of the gas body valve is much larger than [Z.sub.Uv] because the opening of the gas valve is much smaller than the area of the inletpipe.The transfer function ([H.sub.1]), the volume velocity fluctuation of the gas valve is associated with the sound pressure in the flame, which can be expressed in ASCII non-reproducible [Mathematical expression] (18) details on the determination and use of the transfer matrix can be found in supporting papers by Zhou et al.(2013).[Figure 6 omitted] the combustion intensity between the volatile equivalent ratio fuel and the oxidation agent at the gas price depends on their relative molar (or volume) concentration.When their concentration ratio is chemically positive, all the reactants can be completely consumed by the reaction, so that the combustion intensity is as high as possible.This method of combustion is called chemical metering combustion.The product with the highest heat generated by chemical metering combustion.In the CHON system, these products are water (gas phase or liquid phase), carbon dioxide and nitrogen.In order to measure the relative molarity concentration of the fuel and oxidation mixture, we define the fuel/oxidation ratio, [m]sub.f]/[m.sub.A] The ratio of the quality of the fuel to the quality of the oxidation agent in the mixture.Similarly, if the air is an oxidation, then [m.sub.A) is the quality of the air.To illustrate the deviation between the actual combustion and the chemometric combustion, the equivalent ratio [phi] is defined as [phi] = [[m]sub.f]/[m.sub.a]).sub.act]/[([m.sub.f]/[m.sub.a]).sub.(19) in which the subtext function and stoi specify the actual and chemical metering status.(1) Actual fuel and oxidation agent.e., Air) obtain the molar concentration from the measurement.From equation 19, [phi] = 1 corresponds to chemometric combustion, and [phi] 1 correspond to fuel-lean and fuel-Burning rich.Attention, air-to-Sometimes the fuel equivalent ratio is used, which is only the penultimate of the current definition of [phi.The oscillation of air and fuel leads to fluctuations in the equivalent ratio.The equivalent ratio can be decomposed into a constant part ([right.[Phi] and the fluctuation part (【??]).The equivalence relation can therefore be expressed as [phi] = [bar.[phi]] + [??] (20) the fluctuation part of the equivalence ratio is [Mathematical expression] that cannot be reproduced in [ASCII] (21) of [column.m].sub.F] = constant mass of fuel [BA.m].sub.A] = constant mass air??].sub.F] = fluctuating quality of fuel??].sub.A] = the fluctuating quality of airIt is reasonable because of the CrossCompared with the main pipe, the cross-sectional area of the injection port is very small.There is no fuel fluctuation in this case, which means that the fuel mass flow is constant.In addition, the fluctuation part of air quality is small compared to the total air mass flow.Therefore, the denominator in equation 21 is about 1.Equation 21 can then be reduced to [mathematical expression, where [[ASCII] (22) is not reproducible??].sub.V] = fluctuation part of mass flow [Rod.q].sub.V] = constant part of the mass flow rate, resulting in a transfer function related to the fluctuation of the equivalence ratio to the velocity of the acoustic particles ([H]sub.2) can be expressed as [mathematical expression, not reproducible in ASCII] (23) Please note, [H.sub.2] constant as the frequency changes and is defined as the interval between the equivalent ratio and the constant part of the mass flow rate, which is easy to measure.Prediction of the flame transfer function in the case of an equivalent ratio fluctuation ([G.sub.[Phi]) is defined as the ratio of fluctuating heat release to fluctuating equivalent ratio.Sattelmayer (2003) represents the flame transfer function as [G.sub.[phi]] =[e.sup.-[Omega] [TAO] [United States]sub.b]/[bar.[phi]]([[[rho].sub.u]/[[rho].sub.d]] -1) (24)where[u.sub.B] = the average flow rate at the burner [[p.sub.U] = gas density upstream of the burner [[ρ.sub.D] = the gas density downstream of the burnerA time delay parameter ([tau) is defined as [tau] = L/u (25) whereL = distance from the gas valve to the surface of the burner = average velocity equation 22 assume that the fluctuation equivalent ratio of the gas valve and the surface of the burner is the same.However, Sattelmayer (2003) shows that the fluctuation equivalent ratio changes due to the air convection effectThe fuel mixture is transmitted from the valve to the burner.These changes are minimal at a lower frequency.Feedback loop stability model results furnace No. 1 is a propane gas boiler with a capacity of 58 KW (200,000 Btu/hour) representing relatively large and rigid firestube boilers.Heat exchangers cast aluminum with countless fingers in the lower chamber to facilitate heat transfer.The combustion-When the boiler operates at about 2100Hz, there is an oscillation problem.If the equivalent ratio is increased, there will be no instability.Switching burners ease instability.Figure 7 shows the chemical properties of typical burners, and Table 1 shows the main dimensions of burners 1 and 2.Under the action of Burner 1, combustion oscillation occurs in the boiler.Burner 1 consists of perforated metal cylinders with ceramicsfabric sock.Ring diffuser for positioning 12.5cm (5 in.) Base from the burner.The Burner 2 has a higher flow resistance, consisting of three layers: a two-story perforated cylinder with a small gap between themMetal socks for outer tubes.The diameter of the two burners is similar, but the Burner 1 is 5 cm (2 ).) longer.In Burner 2, there is a distributor panel at the connection point.The panel merged 5mm (0.2 in.) and 11 mm (0.43 in.) Round holes.If there is no connection to the entrance or ventilation pipe, burn-No driving oscillation was generated.However, if the intake or exhaust opening is partially blocked by the masking tape, an oscillation is caused.The tape is of low quality and therefore does not significantly affect the acoustic effect.However, clogging reduces the flow rate.A similar reduction in inflow rate is achieved by increasing the length of the intake and/or exhaust pipes.By adding additional lengths on the intake and exhaust channels (or covering the intake or exhaust openings with tape), it can be determined that the combustion oscillation mainly occurs at about 6 intake flow.5 m/s (21.3 ft/s).Measure the flow rate using a speedometer.The feedback-The loop stability model of boiler 1 was determined using the calculated downstream and upstream impedance and the measured flame transfer function (Herrin et al ).2013).Impedance was determined using the methods discussed in the companion paper (Zhou et al ).2013).The impedance of the burner is added to the upstream impedance at the attachment of the burner.Plane wave propagation is assumed inside the burner.This seems reasonable because the sound speed inside and outside the burner is very different due to the high temperature.So there is a difference between the highand lower-Temperature Gas medium.Since the oscillation occurs above 2000Hz, the acoustic wavelength will be on the order of magnitude of 15 cm (6 in.).At high frequencies, the size of the burner itself will be important (I.e., Is substantial compared to the sound wave wavelength ).Figure 7 shows the schematic diagram of aburner.[L.sub.B] is the distance from burnerbase to the opening of the lower burner port, and [L]sub.C] is the distance from the opening of the lower burner port to the approximate center of the surface of the burner port (the approximate center of the flame, that is, the sound source.No visualization technology is used, so the dimension of [L]sub.C) is an estimate.For burner 1,12.5 cm (5 in.) Is assumed to be [L.sub.C].Combined length ([L.sub.B] + [L.sub.C) can be considered as aduct with cross functionEqual to the area of the burner.Use the methods described in the companion paper (Zhou et al )., 2013), can be combined for length and four-Parameters A, B, C, and D.The burner can be considered as a transfer impedance ([Z]sub.Tr]), can be measured according to Wu et al.(2003) Liu et al.(2013).In this case, the total upstream impedance can be expressed as [Z.sub.u] = (A + [Z.sub.tr]C) [Z.sub.att] + B +[Z.sub.tr]D/C[Z.sub.Att] D (26), where [Z.sub.Att] = burner attachment [impedance omitted in figure 7] the length of the burner from the bottom of the burner to the center of the burner Port mode using a simulation model ([L]sub.B] +[L.sub.C]) was varied.Figure 8 compares the absolute values of [Z x H] for various selected lengths.Note that the change is around 2100Hz.In the work not shown here, the effect of switching from one burner Port mode to another on the [absolute value] of Z x H was also studied, but it was found to be less significant.The results show that the geometry of the burner is more important than the burner Port mode or the material selected for the sock (I.e., Sintering metal or ceramic fibers placed on the burner port cylinder ).The size and phase of the Z x H and 1/G of the burner 1 are shown in Figure 9.When the size of Z x H exceeds 1/G, thermal acoustic instability is possible when Z x H and 1/Gare equivalent phases.The results show that for the selected ([L.]) it is possible to burn an oscillation at 2100Hzsub.B] + [L.sub.C]).However, the length of this selection is somewhat arbitrary, so the validation of the model is uncertain.As mentioned earlier, the geometry difference between Burner 1 and 2 (see table 1) the results of Figure 8 show that at high frequencies, small changes in the overall geometry can greatly affect the [absolute value] of Zx H.Therefore, the model shows that the difference in the geometry of the burner may ease the instability.However, the validation of the model is uncertain and further experimental work is recommended to investigate the effect of burnergeometry on combustion oscillation.Boiler 2 is a propane gas boiler with a much larger capacity of 147 KW (500,000 Btu/hour) with stainless steel heat exchanger.In the upper and lower parts of the heat exchanger, the coils are arranged in a cylindrical shape.The reason for the oscillation is the equivalent ratio of a fluctuation.This is blocked in the following ways.The manufacturer increases the distance between the gas supply and the burner until the combustion oscillation is eliminated.In doing so, since the gas valve has a small effect on the acoustic impedance, there should not be a significant change in the acoustics of the air inlet.However, according to equations 24 and 25, the flame transfer function associated with fluctuating heat release will change significantly.In particular, please note the relationship between [TAO] and the distance (L) from the gas valve to the burner.In the end, the manufacturer chooses to change the intake system and the air valve to eliminate instability.[Figure 8] [Figure 9] the oscillation frequency is about 10 hz, and the whole unit vibrates violently.The oscillation frequency is determined by measuring the vibration of the boiler with an accelerometer.Increasing the length of the vent has the greatest effect on the oscillation frequency, which reduces the instability frequency.For boiler 2, the feedback stabilization model takes into account the fluctuation of mixing flow and equivalent ratio.The downstream impedance is modeled and the high temperature in the combustion chamber is taken into account.In this case, the length from the bottom of the burner to the center of the cylinder at the burner port ([L]sub.B] + [L.sub.C) is not included because it is very short compared to the wavelength of sound waves of 34.3 m (112.5 ft) at low frequency (I.e., 10 Hz).In addition, it is found that the burner transfer impedance is not important at low frequency.Using equations 10 and 24, the flame transfer function of the fluctuation mixture and the equivalent ratio fluctuation was found, respectively.The values used in equation 10 and 24 are shown in Table 2 and table 3, respectively.Table 4 compares the frequency of combustion instability identified using the mixture flow and equivalent ratio model with the measured frequency.The results show that the main reason for instability is the fluctuation of equal efficiency.There are some differences between prediction and measurement.However, these differences can be expected for several reasons.First of all, the boiler vibrates violently, which means that the structural resonance is coupled with more resonance sound.This coupling can change the acoustic resonance frequency slightly.In addition, the phase of the flame transfer function of the equivalent ratio fluctuation is very sensitive to the input (see equation 24), which is the estimated value.Therefore, the model believes that improving the fuel intake system is the best way to solve this problem.The results also show that equivalence is more likely to cause concern than fluctuations at low frequencies.Figure 10 shows the size and phase of Z x [H]sub.1] and1/([H.sub.2] x [G.sub.[Phi] of case 2 in Table 4 (equivalent ratio oscillation ).It is possible if the combustion of Z x [H] is unstablesub.1] More than 1/([H.sub.2] x [G.sub.[Phi]) and the time when the phase is equal.Figure 11 shows a similar size and phase diagram for Z x H and 1/G of mixture flow fluctuations.Low summary and conclusionThe order model originally developed by Baade (1978) for the identification and prevention of combustion oscillation was applied to two boilers.The original model was enhanced by introducing a feedback loop to handle the equivalent ratio fluctuation.In each case, the model determines the possible causes and possible solutions.(Zhou et al ).2013) the measurement and simulation of the downstream impedance of the two boilers are described in detail.[Figure 10] [Figure 11] 1 the furnace adopts a switch burner to solve the unstable problem.By applying this model, it is determined that the higher acoustic resistance of the new burner can provide some benefits.However, the main reason why the second burner solves the problem may be the difference in geometry.The model shows that minor changes in the geometry of the burner have a significant effect on the upstream impedance.For boiler 2, the problem of instability is solved by switching the gas valve.The model identifies the equivalent ratio fluctuation as the main cause of instability.However, the model also shows that, at a higher frequency, oscillation also occurs due to fluctuations in the flow of the mixture.This study proves the usefulness of feedback --Loop stability model as a diagnostic tool.In each case, the model points out the possible causes of instability.However, feedback-The model of loop instability proposed in this work is by no means exhaustive.Additional enhancements are required to include other important factors such as flow and flue gas recycling.This paper is based on the research results of the ASHRAE research project RP-1517.The work reported in this article has been RP-1517.The author thanks the help of TC 6.10, especially the valuable guidance and guidance of the DoctorPeter Baade.Reference baade, P.K.1978.Design standards and models to prevent combustion oscillation.ASHRAE deal 84 (1): 449-65.Baade, P.K.2004.How to solve the problem of abnormal combustion noise.Sound and Vibration July, 22-7.Baade, P.K., and M.J.Tomarchio.2008.Tips and tools to solve the problem of abnormal combustion noise.Journal of Sound and Vibration July, 12-7.Elsari, M., and A.Cummings.2003.Combustion oscillation in gas applications.Applied Acoustics 64 (6): 565-580.Goldschmidt, V.W., R.G.Leonard, J.F.Riley, G.Wolf Rand and p.K.Baade.1978.Transfer function of gas flame: measurement 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at the University of Kentucky in Lexington, Kentucky.