Enfoque Pedagógico de la materia de Artes

B.LEISENHEIMER and W.LEUCKEL Universität Karlsruhe, Engler-Bunte-Institut, Lehrstuhl und Bereich Feuerungstechnik, Germany

Introduction

Optical measuring technique with very high resolution allows transient records of flame front positions and thus supply new possibilities of evaluating laminar and turbulent burning velocity (Palm-Leis et al., 1969, Dowdy et al., 1990). Therefore effort and good progress has been made in investigating laminar deflagrations in closed vessels especially in the early stage of explosion after ignition. Subject of this paper is the investigation of laminar and turbulent flame front behaviour in the later stage of an explosion process, where experimental data of burning velocity and knowledge about the effect of self-generated turbulence in a spherical propagating flame front are still limited.

It will be shown that laminar explosion experiments led to a radial range of the propagating flame front in which the influence of stretch due to the overall spherical shape as well as compression of the unburnt gas can be neglected, so that the burning velocity S is mainly influenced by self-generated acceleration processes. In this particular regime of flame front radius also turbulent flame fronts are accelerated by additional self-generated turbulence, and the flame front propagation is based on the effective turbulence intensity (u’/SL,p)eff resulting from superposition of fan-generated (u’/S”d. and flame-generated (u’/SL,p)gen turbulence intensity. Finally, a linear increase of reduced turbulent burning velocity ST/SL,p with increasing effective turbulence intensity (u’/SL,p)eff can be deduced.

Experimental

The pressure/time histories of premixed lean and rich fuelgas/air-mixture flame fronts (p0= 1.013 bar, T0=298K) ignited by spark discharge (E=50mJ) in the centre of a closed spherical explosion bomb (volume V=1.16m³, radius R=0.651m) were recorded by piezoelectric pressure transducers (Piezotronics) in order to evaluate laminar and turbulent burning velocity as function of radius (Fig. 1). By using different fuel gases (CH4, H2,

Fire Engineering and Emergency Planning. Edited by R.Barham.

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CH4/H2, C2H2/N2), the laminar burning velocity of a theoretical one-dimensional planar flame front SL,P was varied in a wide range between 0.2<SL,p<3.4m/s. In order to generate a homogeneous mixture prior to ignition as well as to induce different scales of turbulence, 2, 4 and 8 small (d=0.25m, 500<n<2500rpm) or 8 large (250<n< 1300rpm) ventilation fans were mounted symmetrically inside the explosion vessel, and were run in wide ranges of the rotational speed n.

Fig. 1: Experimental set-up

To determine the influence of turbulent velocity fluctuation amplitude and integral length scale on flame shape, binarized images of laminar and turbulent propagating flame fronts were recorded by a CCD-camera (Nanocam Proxitronic) in the early stage of combustion, using laser light sheet illumination from a 4.5W Argon/lon laser (Innova 70).

An advanced method of measuring turbulence characteristics in the isothermal system is introduced combining a 5-hole Pitot-probe sonde providing the ū values (ū=time averaged mean value and spatial direction of velocity vector) with hot-wire anemometry providing the u’ values (u’=RMS-value of velocity fluctuation). The single hot wire probe was orientated towards negative direction with respect to the mean velocity vector

Fire engineering and emergency planning 34

ū, which leeds to the representative turbulence intensity u’. The integral length scale LT

was obtained calculating the cross-correlation function (inverse Fourier Transformation of cross power density spectra) of the signal of two hot-wire probes using a 16 bit signal analyzer (Tectronix).

Calculation of burning velocity

Based on theoretical considerations using the base principles of mass and energy conservation, and introducing several justified simplifications such as ideal gas law, spherical flame propagation, isentropic compression of fresh and burnt mixture (isentropic exponent κ= 1.4) and no heat loss to the vessel wall, it can be deduced (Lewis et al., 1934) that pressure p increases proportionally to the increasing mass fraction of burnt mixture M in the vessel (p~Mb), finally reaching the theoretical maximum pressure pe at the end of explosion, corresponding to the final state of isochoric combustion.

Dissociation processes in the burnt gas were taken into account.

Although the experimental maximum pressure at the end of the combustion process (inflection point) is actually lower than the theoretical one due to heat loss and reaction quenching near to the wall, the simplifying considerations made above are justified in the early stage of explosion. In addition to the geometrical assumption of spherical flame propagation and neglect of the flame front volume compared to the fresh and burnt gas volume, one obtains an analytic relation between motion of the flame dx relative to the fuelgas/air-mixture and the pressure rise dp

(1)

Hence, introducing the dimensionless pressure p’=(p/p0−1) and the reduced time t’=(pe1/3/R)t and replacing the flame motion dx by dx=S dt one arrives at:

(2)

In order to get an expression of S(p’), it is suitable to plot the pressure/time record p’^1/3 as a function of t’ in order to avoid a mathematical singularity at t=0 (dp=0) for numerical integration. Transforming the first derivative of this function, which represents the integrand of eq. 2, the burning velocity S can be evaluated as function of (p’) in the range p>1.02 bar respectively r>0.1m.

Self-generated turbulence of laminar and turbulent transient flame fronts 35

Results and Discussion

In order to define a radial regime during a deflagration process in which the flame front is predominantly influenced by acceleration, laminar stoichiometric methane/air explosions were investigated from the point of ignition up to the end of combustion. Taking into account the experimental data of flame velocity in the very early stage of explosions in a closed vessel (Bradley et al., 1993) the typical behaviour of burning velocity S, (Fig. 2) is represented by three main zones, where SL is predominantly influenced by different effects: Stretch, Acceleration and Compression.

Fig. 2: Reduced laminar burning velocity S

/S

as a function of reduced vessel radius r/R

For spherical flame propagation with increasing radius the influence of flame front stretch (flame curvature and straining, hydrodynamic effects) reduces the one-dimensional planar laminar burning velocity SL,P linearly with the stretch factor k (Markstein, 1951, Clavin, 1985): SL=SL,P −Lk, where k=(1/A)(dA/dt)=(2/r)(dr/dt)and L=Markstein lenght scale (Stretch).

Above a certain radius r/R≈0.02 of a spherically propagating flame front, stretch effect due to the overall spherical shape of the flame front can be neglected compared with the instantaneous local flame curvature due to flame instabilities or turbulence motion. In this regime of Acceleration we determined an approximately linear increase of SL with vessel radius r: SL/SL,p~r/R. During laminar deflagration, hydrodynamic flame instabilities due to thermal expansion of the gas and transport effects implies an initial wrinkling of the

Fire engineering and emergency planning 36

flame front (Sivashinsky, 1977). Under those conditions of diffusional-thermal instability, Sivashinsky (1977) emphasized that the flame front spontaneously becomes turbulent characterized by a constant increase in its mean propagation velocity, which is in good aggreement with our experimental results (laser light sheet images, burning velocity SL) of spherical laminar flame propagation (Fig. 2).

The following exponential increase of SL (Compression) can be described by a function SL ~(p/p0)^z, (p/p0)^z, where z represents pressure (SL~p^−0.47) and temperature (SL~T²) dependency of the laminar burning velocity SL of stoichiometric methane/air flames (Andrews et al., 1972) which leads to z=0.1 and is also in good agreement with the experimental behavior of SL (Fig. 2). In the last stage of combustion the flame front is close to the wall, and the quenching of combustion process due to heat losses causes a sharp decrease of SL.

Introducing the commonly used Markstein number Ma=L/δL(L=0.15mm; Bradley et al. 1993) and Karlovitz number Ka=kδL/SL(δL= laminar flame thickness), the typical behaviour of SL for laminar deflagration of stoichiometric methane/air-mixtures in closed vessels can be described in a wide radial range (r/R<0.9) by superposition of stretch, acceleration and compression:

(3)

Concluding these results there is a region of the propagating flame front between 0.02<

r/R<0.6, in which the influence of stretch due to the overall spherical shape as well as compression of the unburnt gas can be neglected, hence the burning velocity is mainly influenced by acceleration processes and further evaluation in this direction is promising.

In order to study the acceleration of various fuel gases during turbulent explosion experiments, turbulence parameters of the fan-generated turbulent flow field were measured. In the region of evaluation of turbulent burning velocity ST, turbulent macro length scale is fairly constant LT≈24 mm and independent of the number, size and speed of the fans. Turbulence intensity u’ increases approximately linearly from 1.4m/s (r/R=0.1) up to the maximum value 2.4m/s (r/R 0.5) and followed by a weak decrease to 2.3m/s around r/R= 0.65.

Moreover, variation of the orientation of the hot wire probe in the explosion bomb has shown, that the fan induced turbulent flow field in this inner region of the vessel can be regarded as isentropic but not homogeneous. These destributions are linear functions between the centre of the explosion bomb and half of radial distance to the wall, which represents the regime of detailed evaluation.

Self-generated turbulence of laminar and turbulent transient flame fronts 37

Fig. 3: Reduced turbulent burning velocity S

/S

as a function of vessel radius r[m]

As a consequence of these turbulence conditions a strong increase of turbulent burning velocity ST during turbulent flame front propagation in the vessel was obtained (Fig. 3).

Hence, assuming the preservation of the isotropic turbulent flow field during each explosion experiment, ST can be correlated with turbulence intensity u’ at each respective radial posi-tion, and it became obvious that ST increases progressively.

On the other hand, under moderate turbulence conditions like in the present case, linear increase of ST with increasing u’ must be assumed (Abdel-Gayed et al., 1984, Fansler et al., 1990, Leuckel et al., 1990).

Therfore, as could be expected from the laminar experiments described above, it can be deduced that the turbulent flame front is accelerated by self-generated additional to the fan-generated turbulence, i.e. the propagation of the flame front is based on the effective turbulence intensity (u’/SL,p)eff resulting from superposition of fan-generated (u’/SL,p)eff

and self-generated (u’/SL,p)meas turbulence. This generated part of turbulence increases in direct proportion to the increasing overall flame front surface (u’/SL,P)gen~(r/R)²

Fire engineering and emergency planning 38

Fig. 4: Reduced turbulent burning velocity S

/S

as a function of effective turbulence intensity (u’/S

)

Taking into account additional self-generated turbulence for all fuelgas/air mixtures and turbulence conditions investigated, the reduced turbulent burning velocity ST/SL,P plotted against effective turbulence intensity (u’/SL,p)eff demonstrates the expected linear behaviour (Fig. 4).

Conclusions

Based on the evaluation of laminar burning velocity SL as well as on fan-generated turbulent burning velocity ST of premixed transient fuelgas/air explosions inside a constant volume spherical vessel as a function of various turbulence characteristcs of flow field—namely turbulence intensity u’ and macro length scale LT—the following results can be concluded:

- Fan-generated turbulence intensity u’ increases approximately linearly with increasing vessel radius and fan speed.

- Turbulent macro lenght LT=24±2mm is constant along the vessel radius and independent of number, diameter and speed of the fans generating turbulence.

- Self-generated turbulence causes linear increase of SL/SL,p~(r/R)² during the laminar explosion process in good agreement with theorical predictions.

Self-generated turbulence of laminar and turbulent transient flame fronts 39

- Self-generated turbulence causes a progressive increase of ST/SL,p~(r/R)² during an explosion process with initial fan-generated turbulence.

- With respect to additional self-generated turbulence the reduced turbulent burning velocity ST/SL,p increases linearly with increasing effective turbulence intensity (u’/SL,p)eff.

References

Abdel-Gayed, R.G., Al-Khishali, K.J. and Bradley, D. (1984). Turbulent Burning Velocities and Flame Straining in Explosions. Proc. R. Soc. Lond. A391, p. 393.

Andrews, G.E. and Bradley, D. (1972). Ihe Burning Velocity of Methane-Air Mixtures. Comb.

Flame 19, p. 275.

Bradley, D., Ali, Y., Lawes, M. and Mushi, E.M.J. (1993). Problems of the Measurement of Markstein Lengths with Explosion Flames. Joint Meeting of the British and German Sections of the Combustion Institute, Queens College, Cambridge, p. 404.

Clavin, P. (1985). Dynamic Behaviour of Premixed Flame Fronts in Laminar and Turbulent Flows.

Prog. Energy Combust. Sci. 1 1, p. 1.

Dowdy, D.R., Smith, D.B. and Taylor, S.C. (1990). The Use of Expanding Spherical Flames to Determine Burning Velocities and Stretch Effects in Hydrogen/Air Mixtures. Twenty-third Symposium (International) on Combustion, p. 325, the Combustion Institute.

Fansler, T.D. and Groff, E.G. (1990). Turbulence Characteristics of a Fan-Stiffed Combustion Vessel. Comb. Flame 80, p. 350.

Leuckel, W., Nastoll, W. and Zarzalis, N. (1990). Experimental Investigation of the Influence of Turbulence on the Transient Premixed Flame Propagation Inside Closed Vessels. Twenty-third Symposium (International) on Combustion, p.729, the Combustion Institute.

Lewis, B. and Von Elbe, G. (1934). Determination of the Speed of Flames and the Temperature Distribution in a Spherical Bomb from Time-Pressure Explosion Records. Jour. Chem. Phys. 2, p. 283.

Markstein, G.H. (1951). Experimental and Theoretical Studies of Flame-Front Stability. J. Aero.

Sci. 18, p. 199.

Palm-Leis, A. and Strehlow, R.A. (1969). On the Propagation of Turbulent Flames. Comb. Flame 13, p. 111.

Sivashinsky, G.I. (1977). Nonlinear Analysis of Hydrodynamic Instability in Laminar Flames-I.

Derivation of Basic Equations. Acta Astronautica 4, p. 1177.

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ALGORITHMS FOR THE CALCULATION