Electron temperatures in hydrocarbon flames

Electron Temperatures in Hydrocarbon. Flames The cxpcrimcntal findings ot’ Porter [I] that in some hydroWbon-air flames the elwrron tcmpcraturc, itt the rryian kforc thg peak gasi tcmpcrature, is highcx Lhutt tlac @ls tcmpcraturc is also supported by studios of zthylenc-s.ir and methane-air flames avcc a wide range of equivalence ratios [Z], In the httcr wsrk, it was found that the peak electrcrn tempcraturcs occurred ahead of the peak gas trmpcraturc. The present authors agree with l%rtcr*s attributioxl of the elevated eIectron tempratures to collisions of the second kind. The question arises as to whether the electron temperature at a given point is a measure of extraequiiibriam excitation at that point or whether the relaxation rate for electron energy is such that the value of electron temperature is r&ted to previous electron history. It is possible to construct curves of electron energy hYss rate apinst clcctron tcmpcrnture for a given gas composition and temperature [3]. The electron temperature is that temperature at which the net rate of gain of electron energy from the species with extra-equilibrium excitatron is balanced by the net rate of hs of electron energy to all other species, The authors have computed the equiiibrium composition of a methane-air flame with an equivalence ratio of 1.0, at a gas temperature of 1213°K and a pressure of 38 torr. This is an approximation to the composition at the poinl in an cxperimental flame where the peak electron t.emperature occurs. For the purposes of the prcsecnt

Y Tea = 2360aK

I;igurt

1. Relaxation

of electron

temperature.

try EM1 asd Bradley [33. Values of electron ~itr~ion cross sections for C02, CO, and N, w~rr t;rken I’rom the same sources as were used try thcs~ wmkm-s. The eiectron collision cross sections for 02, I-I,, and El,0 were taken from Rcfs. 4, 5 and 6. respectivciy. The equilibrium prr~~~~i,io;~s of other species, such as 0, H, tick ;rnrdof;, iotaled less than 0.005 %, and t&~x cl*f~ct trin the net loss rate would be rrt_%i&nr&ant. Ccyrxuidcran idealized situation in which the &ctr~ temperature is T,, and the supply of cnsr~~ to electrons due to extra-equilibrium e~irarinu is instantaneousIy reduced to zero ;rl zero time. The relaxation of electron tem.JWKIXEWG, ?;. in time, t, toward the gas tem$~~tr.~a CM be found from the energy loss r:UWQ WH itr I:ig, 1. The mean energy of an &%IPi!!kIs iJIS)kY&,and the energy equation is

The integral has been evakated by ph~:ing I/ffT,) against T,, as shown in Fig. 1If and integrating the curve with respect to Y&.+I% resulting relaxation af T,, from a peak vakz of 236O”K, wirh respect to rime. Is sho~rr in Fig. 2. The relaxation is almost compla~e ~i#kr:: 10m8 sec. Similar results wnuM be sbtnairrei4for other flame gases. As a consequence of the very short relaxaticm time the value of T, at a point ia a #ame, when considered in relation to the value o1 the gas temperature, gives a rnea~ure of the extra-equilibrium excitation at that point. Thus there should be a point-by-point correlation between chemiluminescent emission and elevation of electror? temperature. The authors wish to thank the Science Research Council for suppuptr’ng this hark and also Dr. A. V. Phelps for furnishing a consisrennrset uf cross-sectior! data, sclm~ unpublishad.

References I. 2.

3. 4. 5. 6.

Mechanical Engineering University of Leeds Leeds, England

Department

(Received

July,

19701