On the structure of turbulent premixed flames in high-pressure combustors

Pergamon

Int. Comm. Heat Mass Transfer, Vol, 24, No. 4, pp. 565-568, 1997 Copyright © 1997 Elsevier Science Ltd Printed in the USA. All rights reserved 0735-1933/97 $17.00 + .00

P H S0735-1933(97)00041-9

ON THE STRUCTURE OF TURBULENT PREMIXED IN HIGH-PRESSURE COMBUSTORS

FLAMES

R.C. Aldredge Department of Mechanical & Aeronautical Engineering University of California, Davis, CA 95616-5294 Email: [email protected]

(Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT The influence of pressure on the structure of turbulent premixed flames is examined using dimensional analysis, and it is found that both reaction-sheet and distributedcombustion burning are of likely importance at high pressures characteristic of practical gas-turbine engines. © 1997 Elsevier ScienceLtd

Introduction In spark-ignition engines combustion has been found to occur in thin propagating reaction zones, f l a m e sheets, separating the cold reactants from the hot products [1]. It has not yet been estabhshed

experimentally, however, whether this is the case in rockets, ramjets, turbojets, and afterburners or whether chemical reactions in these practical configurations are widely distributed as a result of high-frequency, high-intensity turbulence fluctuations [2]. A dimensional analysis presented in the following section suggests, in fact, that chemical heat release in high-pressure gas-turbine combustors is governed by a combination of these two combustion regimes. Conditions which promote the regime of thin-flame propagation in premixed combustion are large chemical activation energies of the reactive mixture and large temporal and spatial scales of flow-field variation. When the flame thickness and the characteristic time for chemical reaction within the flame are much smaller than the length scales and time scales, respectively, characterizing fluctuations in the flow field, the flame may be modeled as an interface separating cold reactants from hot products. The interface propagates into the premixed reactants normal to itself locally at a speed which depends on the local reaction rate of the flame, which is a function of the local flame curvature, reactant concentration and flow-field strain rate. As the flame sheet propagates it is wrinkled and possibly torn by fluctuations in the flow field. A turbulent flow of reactants 565

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having a wide range of spatial and temporal scales, however, might cause distributed combustion and flame broadening by action of the small-scale fluctuations while causing flame wrinkling by action of the large-scale fluctuations. Hence, a reformulation of the flame-sheet model to account for flame-structure modification by small-scale turbulence fluctuations is a promising approach to the computational description of the combustion process in practical combustors.

High-Pressure Combustion Regime Fig. la, taken from Lifi£n and Williams [2], indicates ranges of characteristic mean flow velocity U (for example, the average volumetric flow rate divided by the cross-sectional area of the combustor) and characteristic length L (for example, the combustion chamber length) for several practical combustion devices. Constant values of the kolmogorov length scale lk are represented by straight lines on the log-log plot and are indicated for atmospheric and 10 atm (in parentheses). Dimensional analysis predicts that to within an order of magnitude lk ~. [u31/(u')3] 1/4, where u is the mean kinematic viscosity, l is the turbulence integral scale and u ~is the characteristic turbulence intensity (for example, equal to ~ , where K is the total turbulence kinetic energy). Since u ~ p-1 then lk ~ p - 3 / 4 so that practical gas turbine combustors which have operating pressures as high as 30 atm should be expected to have kolmogorov length scales well between 2 /~m and 8 ~m in size, according to Fig. la. At the center of the gas-turbine-combustor region of Fig. l a the characteristic length scale L is about 10 cm, while U ~ 1400em/s. Taking the characteristic turbulence intensity to be 30% of U and the turbulence integral length scale to be of the order of L gives RI = O(104 ) at 1 atm and Rl = O(105) at 30 atm for the turbulence Reynolds number based on the integral scale (assuming an average kinematic viscosity of 1 cm/s at 1 atm). The Damk5hler number Dt =- T/% may be estimated by taking the relevant characteristic flow time T to be l / u ~ and the characteristic chemical time as 6/UL, where 5 is the flame thickness and UL is the laminar flame speed defined by the fuel-a~r mixture. Alternatively, it may be shown that Dl = (UL/u~)2Rt. The laminar flame speed may be reduced substantially, however, by an appreciable pressure increase. For example, the laminar flame speed in a stoichiometric methane-air mixture at 320°K and 1 atm is about 40 cm/s, while UL .~ 14em/s when the pressure is increased to 30 atm [2]. As a result the Damk6hler number at 30 arm is about four times its value at 1 atm. The center of the gas-turbine-combustor region indicated in Fig. l a has been denoted on a Damk5hler-tteynolds plot, taken from Lifi£n and Williams [2], in Fig. lb for both 1 arm and 30 arm. The Damkhhler number based on the kolmogorov length scale, which may be shown to be (Ik/5) 2 and of the order 10 -1, is essentially unaffected by the pressure increase, meaning that fluctuations on the smallest length scales should have no greater or lesser effect on the flame structure as the combustor pressure in increased. On the other hand, Both Rl and Dl increase with pressure, signifying an increase in both the intensity and characteristic frequency of eddies having

Vol. 24, No. 4

STRUCTURE OF TURBULENT PREMIXED FLAMES

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Vol. 24, No. 4

length scales much larger than the flame thickness; l/6 = O(103) when /~ is interpreted as v / ~ . The characteristic combustion regime of the practical high-pressure gas-turbine combustor then likely lies closer to the reaction-sheet regime (where even the smallest scales have a negligible effect on the flame structure) than to the distributed-reaction regime. Large-scale combustion modeling based on the flame-sheet theory may therefore be a promising approach to the accurate prediction of the rates of combustion and production of key combustion products in practical combustors, as long as a submodel accounts for a modest amount of flame-structure modification by the small scales,

Summary Using dimensional analysis it has been shown that the characteristic combustion regime of highpressure gas-turbine combustors is a combination of the reaction-sheet and distributed-reaction regimes. Computational simulations based on the flame-sheet model will therefore be meaningful only if influences of flame-structure modification by small-scale turbulence fluctuations are accounted for in the model. Acknowledgements The author would like to acknowledge support of this work received from the NASA Lewis research center, grant no. NAG3-1558. Nomenclature laminar-flame thickness lk

Kolmogorov length scale

l

integral length scale

L

characteristic length scale of the combustor

uI

integral-scale turbulence intensity

UL

laminar-flame speed

U

characteristic mean combustor-fiow velocity

~-

turbulence integral time scale

T~

characteristic combustor-flow residence time

Tc

characteristic flow chemical-reaction time

u

kinematic viscosity

p

static pressure

K Rl

turbulence kinetic energy turbulence P~eynolds number

Dl

turbulence Damk5hler number References

1. P. G. Felton, J. Mantzaras and F. V. Bracco, Combustion and Flame 77,295 (1989).

2. A. Lifign, and F. A. Williams, Fundamental Aspects of Combustion, chap. 5, Oxford University Press, New York (1993).

Received November 13, 1996