PARTIALLY PREMIXED COMBUSTION SUPPORTED BY PLASMA
*1Topina A.A., 2Shneider M.N., 2Miles R.B.
1 Kharkov National Automobile and Highway University, Ukraine, 
2Princeton University, USA 

There are a lot of papers devoted to the problems of combustion assisted by the different discharges plasma. A review of the recent experimental data at this area is presented in [1]. The great scientific interest to these problems is caused by a necessity to organize a clean combustion process with a low level of toxic emissions. One of the ways of the problem solution is an organization of the ultra-lean mixture combustion. In that case additionally to the difficult problem of the ultra-lean mixture ignition a problem of the flame stabilization appeared. A corresponding energy input by the discharge plasma in the flame recirculation zone can stabilize the flame as it was shown in [2]. To create a plasma area authors in [2] used a nanosecond pulsed discharge. It is well known that this discharge creates a nonequilibrium plasma due to a very short pulse duration. 
We consider a premixed jet of propane-air mixture discharging into a quiescent atmosphere with an additional energy input by the nanosecond pulsed discharge. To test the proposed model the problem geometry was chosen coinciding with the burner geometry in the experiments [2] with the cylindrical gas mixture inlet and the cylindrical bluff body for the flame stabilization.   A source term in the energy equation that models a plasma input was calculated using 1D model of the nanosecond pulsed discharge [3] and then tabulated as a function of the time and space. To model turbulent combustion we used an assumption of the very rapid chemical kinetics in the flame. A progress variable was defined as a normalized sum of product species , where  is the mass fraction of species ,is the mass fraction of species after adiabatic combustion. As a closure for the chemical reaction rate in the premixed turbulent combustion is still challenging, a choice of the closure model for the considered case of the V-shaped flame was chosen in the frame of the eddy-dissipation model, as for the diffusion combustion. 
It was shown that this assumption is quite satisfactory and could describe the experimental flame pattern with different flame regimes because of the intermittency factor . Ahead of the flame front it was supposed that a chemical reaction rate was controlled by the mixing process and turbulence, so all the species distribution could be derived from the calculated Zeldovich variable (the mixture fraction) distribution. It was also supposed that a propane-air mixture consists of 53 components according to the GRI 3.0 mechanism of the hydrocarbons combustion. It should be noted that in the recirculation zone the stretch effect of the flame could be significant so the source term in the progress variable equation was additionally multiplied by a stretch factor in the form of the complementary error function for the turbulent dissipation rate distribution. Parameters of the nanosecond pulsed discharge were as follows: a pulse width -10 ns, an interelectrode gap – 3 mm, a maximum voltage – 10 kV. We considered a lean propane-air mixture with equivalence ratio . 

Fig.1. V-shaped flame stabilized by plasma: a)a progress variable distribution for the case of  , b)stream lines at without plasma (flame extinction) and with plasma( flame stabilization)

It was obtained that for the considered range of the Re number     the V-shaped flame is formed, with the transition to the flame extinction at high Re  and for the lean mixture limit. It was also shown that the V –shaped flame can be stabilized by the nanosecond plasma discharge, if the discharge plasma was located in the recirculation zone under the bluff body (zone 1 in the Fig.1a) with a very low power input. Main effect of the formed plasma column is thermal and can be modeled as a heat source with the source term intensity, which is proportional to the discharge power averaged on the plasma volume from the experimental data. 

LITERATURE
1. Starikovskii A.Yu. Plasma supported combustion. // Proc. Comb. Inst.  2005.  v.30.  P.2405–2417
2. Pilla G., Galley D., Lacoste D.A., Lacas F., Veynante D., Laux C.O. Stabilization of a turbulent premixed flame using a nanosecond pulsed plasma. // IEEE Trans. Plasma Sci.  2006.  v.34.   P.2471–2477.
3. Tropina А.А.,  Uddi M.,  Ju Y. Non-equilibrium plasma influence on the minimum ignition energy. Part 1: Discharge model// IEEE Trans. on Plasma Sci. – 2011. – v.39. – P.615–623.