Effect of reactant-surface stretching on chemical laser performance

Abstract

High-pressure DF chemical lasers use gas trip jets to increase the laser cavity reactant mixing rate. The trip jets can improve the laser efficiency by about 100% when compared to the laminar mixing value. It is postulated that the trip jets create a secondary flow which increases the mixing rate by stretching the contact surface between the reactant streams. The surface stretching rate can be described in terms of a strain rate s 0 . A qualitative explanation for the performance characteristics of trip-nozzle lasers is provided herein by developing flow and laser models which can define the effect of strain on the reactant burning rate and laser efficiency. Strain affects laser performance via a single parameter 7 = 2s 0 /k c , where k c is a characteristic collisional deactivation rate for the lasing specie. Strain levels of 7 = 2-3 appear to be consistent with trip nozzle data. The model also indicates the efficiency of low-pressure laminar mixing (7 = 0) lasers could be increased significantly for strain rate levels in the 7 = 3-5 range. Nomenclaturefusivity fiJ 2 ~ functions in amplifier solution, Eq. (22) F = (y// w) 2 , normalized flame location 8>8o = S ain P er unit length, g 0 = o [F] 7 G = integrated gain across flow channel, Eq. (16) G* = G/(g0W), normalized integrated gain G; = -^rjr 2 )/(4NggW) 9 threshold gain / = radiation intensity k**k* = kinetic rates for collisional deactivation and pumping, cmVmole-s k c ,k p = [ ] k* 9 kinetic rate concentration product, Kj = k p /k c , (pumping/deactivation) rate ratio K 2 = 2a/(eA: c ), (stimulated emission/deactivation) rate ratio K 3 = 1+K 2 L,L 0 = fluid element length scale, see Fig. 2 M i = /'th specie molecular weight N A = Avagadro's number p = pressure P = laser power, Eq. (17) P* = ^ r/, normalized power per channel r =yf/w 9 volume fraction of oxidizer burned rj, r 2 -mirror reflectivities s(x) = dw/dz, axially varying linear strain rate 50 = characteristic constant linear strain rate t = x/ «, flow time t b = strained flow oxidizer element burnout time t d =0.25 (w/Bj) 2 /D, laminar burnout time T = temperature u -constant axial flow velocity V =(u,v,w), velocities for coordinates fixed in fluid element, see Fig. 2 w } (x), w 2 (x) = oxidizer and fuel element widths w = w ; (0), initial oxidizer element width x b ,x d =ut b ,ut d , characteristic distances X i = /th specie mole fraction y f = flame location, Eq. (9) and Fig. 2 y* = wr(x), effective flame location for strained flow Y it Yf = /th specie mass fraction, initial values 7 = 2s 0 /k c , (strain/deactivation) rate ratio e = hvN A , energy per mole of photons f =*/: c /«, normalized axial distance fj,, £ d = x b k c /u, x d k c /u, characteristic distances f,., l e = start and end of lasing region in oscillator solution f0 = axial location of flame with penetration y f $ dj = value of f rf for which r e (£ d ) = ! 9 i.e., when frf = £dj> £e ~ f 6T\ = transverse coordinate, see Eq. (3), or normalized laser efficiency (vi c /ri 0 ) 9 see Eq. (18) r] 0 = efficiency for a premixed saturated ...

Flowfield experiments on a DF chemical laser

“…Further discussion of this aspect of the problem is given by Driscoll. 10 While our understanding of the mixing augmentation mechanism induced by the gas jet injection is less than satisfactory, it is still possible to model this flow empirically. Figure 10 shows a comparison of the measured axial distribution of small-signal gain on six DF lines for the m/A = 2.0 g/s-cm 2 , /* = 3% condition and the results calculated using the BLAZE-II computer code.…”

“…In fact, the recent nonreacting flow visualization studies of Cenkner and Driscoll 9 suggest another mechanism based on the jets distorting the reactant interface so ajs to increase the contact area between the reactant streams. Flow and laser performance models based on this reactant-surface stretching mechanism have recently been developed by Driscoll 10 and it is found that these models can provide a qualitative explanation for the faster mixing and increased laser performance obtained from these lasers. An understanding of the gas jet mixing mechanism is essential if one is to develop models which can accurately predict the media gain distributions for the different lasing lines.…”

“…They do not attempt to model a physical mixing mechanism as does the more recent model proposed by Driscoll. 10 The shortcomings of earlier models can be traced, in part, to the lack of reacting flow data against which such models can be tested. In this paper, we present photographic data for a DF laser operating in both the laminar and augmented mixing mode.…”

Mixing enhancement in chemical lasers. II - Theory

“…(6a) and (6b), r? can be rewritten as (8) The first integral in Eq. (8) can be written as where (9) The second integral can be evaluated analytically and Eq.…”