On modeling of pulse combustors

Twentieth

Symposium (International) on Combustion/The Combustion Institute, 1984/pp. 2019-2024

ON

MODELING

OF

PULSE

COMBUSTORS

BOGDAN PONIZY Warsaw Technical University STANISLAW WOJCICKI Washington State University Experimental investigations of reignition and combustion in a pulse combustor were performed to establish a realistic physical model useful in numerical simulation of these processes. The model takes into consideration all phenomena observed during a working cycle, including weak reignition by recirculation of combustion products, low temperature burning at the boundary layer of entering air, initiation of explosive combustion and fast flame spreading through the combustor chamber. Results of these experimental investigations were applied to determine some simplifying assumptions for simulation of the combustion process in a mathematical model. One-dimensional flow through the pulse combustor was assumed and two methods of simulation of the combustion process were examined. The first method, based on a plug flow reactor with a space-time distribution of heat release rate, was unable to take into consideration mixing processes affecting temperature variations in the combustor. The second method, applying a set of two well-stirred reactors, was the one that effectively imitated the operation of actual pulse combustors.

Introduction

Pulsating combustion is characterized by a very strong intrinsic feedback mechanism completely controlling the periodic behavior of the process. This mechanism is based on a cyclic reignition and combustion fulfilling the Rayleigh criterion related to such a heat release that sustains the pressure oscillations in the flow~l The analysis presented here is aimed at a simple pulse combustor with an aerodynamic valve. Such a device offers a number of attributes (like intense burning, enhanced heat transfer, capability of boosting pressure) and has, in addition, some potential for improvements with respect to both efficiency and effectiveness in various applications from water heating and coal gasification to aircraft propulsion. 2'3 It seems that numerical simulations based on experiments capable of revealing some substantial physical details of the process may contribute to the origin of a new generation of pulse-combustors in which all the uncontrolled phenomena wilt be excluded. In the experimental part of the paper, a model of ignition and combustion consistent with main observed phenomena is proposed. To adapt this model for numerical analysis, two methods are presented. In the first method, the combustion process is simulated by a space-time distribution of experimentally determined heat release rates. In the second method, a set of two well-stirred reactors is sub-

stituted for the analyzed combustion process. Some results obtained from the calculations are compared with experimental measurements and, on this basis, the validity of the proposed models is discussed.

Experimental

The geometry of the investigated combustor (Fig. 1) is typical for a pulsejet with an aerodynamic valve, but the combustion chamber itself is slightly longer in order to retain the whole combustion process in the visualization area. This area is determined by three quartz windows located at both sides of the combustion chamber. The windows refer to the three sections of the combustion chamber: inlet section (c), central section (b) and outlet section (a). The principle of operation of such a pulse combustor based on inertia effects of unsteady flow is well known, 1'4 but some questions regarding the mechanism of ignition and the character of combustion remain open. All experiments performed were concentrated on these two problems. During the experiments the following measurements were taken (Fig. 1):

2019

pressure fluctuations P (by means of piezoelectric transducers) recorded at five points from Xi to Xv, - - temperature fluctuations at inlet and at outlet ends of the pulsejet, (T,, and Tex, respectively) --

PRACTICAL COMBUSTION DEVICES

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FIG. 1. Experimental apparatus: AV--acoustic valve; B--combustion chamber, OT--outlet tube, SP--spark plug; a,b,c--sections of the combustion chamber, outlet section, central section and inlet section, respectively, SA--starting air; Xi-Xsmpoints of measurement of pressure fluctuations; T~,, T~-points of measurement of temperature fluctuation at inlet and at outlet of the pulse jet, respectively; T, F--points of spectroscopic measurements of temperature and chemical reaction rate variation, respectively.

by means of resistance thermometers made of 0.01 mm platinum wire, -temperature variations, T, and chemical reaction rate variations, F, at each of three sections of the combustion chamber. The last measurements were based on registration of the thermal radiation of excited Na atoms (as in the sodium line reversal method) and of the radiation of CH radicals spectral band which is characteristic for hydrocarbon combustion and corresponds to the chemical reaction rate F. To insure a proper Na concentration in the combustion chamber, NaOH seeding was introduced through the inlet tube of the combustor. The amplification of the temperature registration system was adjusted to record only the values above the average temperature of the combustion products (about 1500 K). Thus, the results of measurements are of a qualitative character and correspond mainly to the temperature variations in the reaction region. Both the temperature variation T and the chemical reaction rate variation F were synchronized with the high speed camera taking the Schlieren picture of the flow at the inlet to the combustor and with the pressure variation P measured at the point Xnl. This allowed the determination of the beginning (X~n) and the end (Xs) of the fresh air inflow into the combustion chamber (marked in Fig. 2). Analyzing the oscillograms of measurements shown in Fig. 2, one can notice that the chemical reactions F of moderate intensity start first in the inlet section (c) of the combustion chamber (even at a negative pressure value). But they do not cause any significant temperature rise T. The considerable increase in the chemical reaction rate associated with a similar increase in temperature occurs only in the central section of the combustion chamber (b). The

process is finished by the relatively uniform afterburning in outlet section (a). Some details of the combustion process are better seen on the streak picture (Fig. 3) taken also with sodium seeding. The picture is synchronized with the pressure variation Pin, the temperature variation Ti, at the inlet end and the temperature variation Tex at the outlet end of the pulsejet. The schematic interpretation of the process shown beneath the photograph brings out some phenomena which are characteristic for the process: - - a trace of entering fresh air (Ain) and a reversal movement of combustion products (R) that confirms the formation of the recirculation zone during the intake period; - - weak ignition (WI) and low temperature combustion (LT) which were noted by the previous measurements presented in Fig. 2. -strong ignition (SI) and high temperature combustion (HT) expanding both upstream (Te) and downstream along the trace of entering fresh air (Ai.).

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FIG. 2. Temperature and chemical reaction rate distribution correlated with pressure variation in three sections of the combustion chamber and with air inflow, recorded by means of the schlieren motion picture: a-outlet section, b-central section, c-inlet section, T-intensity of Na spectral line radiation (hN,) corresponding to gas temperature distribution, F-intensity of CH spectral line radiation (hcn) corresponding to chemical reaction rate, X,,beginning of fresh air inflow into the chamber, P-pressure variation (at point Xnl in Fig. 1).

ON MODELING OF PULSE COMBUSTORS Taking into account all these results, the following model of the ignition and combustion process can be presented (Fig. 4).

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ture is rather lean, the temperature increase is small. The strong ignition occurs at the contact surface between the frontal portion of the entering air and the combustion products where the heat and mass exchange is most intensive. This initiates the explosive combustion which spreads through the central and inlet sections of the chamber. The combustion is completed by the afterburning following the motion of expanding combustion products moving to the outlet of the combustor.

At the beginning the chamber is filled with combustion products mixed with the gaseous fuel supplied continuously. The entering air causes the gases to move backward and then to recirculate. Simultaneously the weak ignition appears at the boundary layer of the air stream. As the layer is relatively thin and the combustion mix-

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FIG. 3. Streak photograph and schematic interpretation of the process in combustion chamber correlated with pressure variation Pm at point X~n and temperature variations T~, and T~x at inlet and outlet of the pulse jet, respectively: A~,-trace line of the entering fresh air, R-recirculating flow, Te-trace line of the explosion, LT-low temperature reaction zone, HT-high temperature reaction zone, WI-weak ignition, SIstrong ignition, Pat-atmospheric pressure.

2022

PRACTICAL COMBUSTION DEVICES

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FIG. 4. Schematic interpreation of reignition and combustion processes: 1-fresh air, 2-hot combustion products from the preceeding cycle, 3-weak ignition on the outer boundary of the air stream, 4strong ignition, 5-expanding explosion, 6-discharge of combustion products through the inlet tube, 7afterburning.

Thus, the combustion process consists of two stages: - - the low temperature burning at the boundary layer of air entering the combustion chamber, - - the explosion initiated by a strong ignition in the central part of the combustion chamber9 In the existing methods of modeling of pulse combustors,6'7's'~r the combustion process is represented either by a flame front traveling through the combustion chamber (from the outlet to the inlet) or by a gradual (or even instantaneous) increase in pressure. It seems, however, that the process described above requires instead, the application of more fundamental phenomena.

Numerical

Model

The results of the above experimental investigations were applied to determine some assumptions for the reignition and combustion processes in the mathematical model9 Basic equations adapted to the mathematical model are typical for one-dimensional unsteady compressible flow with friction, heat release and heat exchange. 4 The set of equations consist of:

where s is entropy, % is specific heat at constant pressure, T is temperature, qv is heat released in chemical reaction, and q~ is heat transfer through the walls. d) equation of state p = 9RT where R is a gas constant. Numerical simulation of the process was made using a method of characteristics.5 For this purpose, a constant time technique 6 has been chosen. In this technique a grid is formed of constant time lines and particle paths that correspond to the llIrd order characteristics. In the plug flow reactor, a spacetime distribution of heat release rate in the combustion chamber was assumed, according to the diagram presented in Fig. 5. The diagram was built on the basis of the experimental results shown in Fig. 2 (hcll lines) and the weak ignition point was synchronized with fresh air inflow into the combustion chamber. To insure the stability of the numerical solution, the time interval in the combustion chamber was reduced in comparison with that in the remaining regions of the pulsejet. The calculated solution is shown in Fig. 6, where it is compared with the results of experimental measurements. A qualitative agreement may be noticed in essential features, such as the length of the cycle and a relative position of characteristic points of pressure and temperature variations. The slope, however, of the temperature curve during the outflow of the combustion gases through the inlet tube is much steeper for the experiment than for the simulation (compare the Ti, curves in Figs. 6a and 6b). It denotes that mixing processes (neglected by the assumption of one-dimensional flow in the plug reactor and the inlet tube) are, in the actual combustor, of great consequence. It is, therefore, pos-

ON MODELING OF PULSE COMBUSTORS I I

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FIG. 5. Space-time distribution of heat release rate assumed in numerical simulation correlated with pressure variation: a, b, c-points of measurements corresponding to the outlet, central and inlet sections of the combustion chamber, respectively; hcHCH spectral line radiation corresponding to the heat release rate, d-level of the atmospheric pressure, Pin-pressure distribution in time measured at point b. sible by manipulation of some coefficients to fit the calculated pressure curves to those obtained from experiment, but it is impossible, using this method, to improve the shape of the temperature curve. To introduce mixing, a set of two well-stirred reactors was applied (Fig. 7). The heat release (according to the time distribution of the reaction rate corresponding to the point "b" in Fig. 5) proceeds in the first reactor (I). In the second reactor (II), the combustion process is neglected (there is only mixing). This assumption is justified for long combustion chambers, which is the case. The thermodynamic parameters existing in the reactors are represented by points J1 and J2 (Fig. 7), which are fixed with respect to the combustion chamber. The a) ~

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2023

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FIG. 6. Measured pressure and temperature variations (a) compared to calculated values: (b) in plug flow reactor, (c) in stirred reactor; T~,-gas temperature at the inlet of the combustor, T,x-gas temperature at the outlet of the combustor.

results of the simulation are presented in Fig. 6c, which shows a good qualitative agreement with experiment (compare the Ti, curves in Figs. 6a and 6c). Application of well-stirred reactors for simulation seems to be particularlv helpful for pulse cornbustors with muhiple inlets.l~ Conclusions

The following conclusions may be drawn from this work:

(i) The assumed mechanism of reignition and combustion in a pulse combustor takes into consideration all the facts observed in the experiments performed: - - recirculation of combustion products,

- - weak ignition and low temperature combustion in the boundary layer of the entering air, - - strong ignition occuring at the contact surface between the frontal portion of the entering air and the combustion products, - - explosive combustion expanding both upstream and downstream; (ii) The time-space distribution of heat released in a pulse combustor resulting from the experimental investigations does exclude the application of simplifications, usually accepted in numerical simulations, which are based on assumptions such as an instantaneous heat addition in the whole combustion chamber or a constant rate of heat release with advancing flame. (iii) The one-dimensional numerical model with plug flow reactor is not able to take into consideration all the phenomena (particularly mixing) essential for the full analysis of the pulse combustor operation. It is believed, however, that the same one-dimensional model cooperating with a wellstirred reactor may correctly simulate the actual process. REFERENCES 1. PUTNAM,A. A. AND BROWN, D. J.: Combustion Technology (H. B. Pahner and J. M. Beer, Eds.), p. 128, Academic Press, 1974. 2. CORLISS, J. M., PUTNAM, A. A. AND LOCKLIN,

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PRACTICAL COMBUSTION DEVICES

D. W.: Status of a Gas-Fired Aerovalved Pulse Combustion System for Steam Raising, Symposium on Pulse-Combustion Application, Atlanta, 1982. 3. LOCKWOOD, R. M.: Guidelines for Design of Pulse-Combustion Devices Particularly Valveless Pulse Combustors, Symposium on PulseCombustion Applications, Atlanta, 1982. 4. SERVANTY, P.: Some Comments on Pulsating Combustion, E n t r o p i e , Not. 22, 1968 (in French). 5, RUDINGER, G.: Wave Diagrams for Nonsteady Flow in Ducts, D. Van Nostrand Company, 1955.

6. HAm~EE, D. R.: Numerical Analysis, Oxford University Press, 1958. 7. WINIARSKI, L. D.: First International Symposium on Pulsating Combustion, Sheffield, 1971. 8. KENTFILED, J. A. C., REHMAN, M., CRONJE, J.: Performance of Pressure-Gain C o m b u s t o r Without Moving Parts, Journal of Energy, Vol. 4, 1980. 9. SCHULTZ-GRUNOW, F.: Gasdynamics Investigation of the Pulse-Jet Tube NASA TMI131, 1947. 10. KENTFmLD, J. A. C.: Valveless Pulse Combustors with Multiple Inlets, Symposium on Pulsecombustion Application, Atlanta, 1982.

COMMENTS R. Levine, N.B.S., USA. Is it difficult to maintain a constant mixture ratio in the burned gas? There is little opportunity for mixing after the gas enters the discharge duct. Authors" Replft. Fuel and air are usually supplied

to the combustion chamber separately and fluctuating flow rates. They additionally mix combustion products from the previous cycle contain oxygen) in various proportions. Thus it is rather impossible to maintain a stant mixture ratio in the burned gas.

with with (that con-