Clavines

For different regions in the flow field in front of an expanding piston, separate solutions in the form of asymptotic expansions may be developed. An overall solution can be constructed by matching these separate solutions. This mathematical technique was employed by several authors including Guirao et al. (1976), Gorev and Bystrov (1985), Deshaies and Clavin (1979), Cambray and Deshaies (1978), and Cambray et al. (1979). 

In addition to a near-shock and an acoustic region, Deshaies and Clavin (1979) distinguished a third—a near-piston region—where nonlinear effects play a role as well. As already pointed out by Taylor (1946), the near-piston flow regime may be well approximated by the assumption of incompressibility. For each of these regions, Deshaies and Clavin (1979) developed solutions in the form of asymptotic expansions in powers of small piston Mach number. These solutions are supposed to hold for piston Mach numbers lower than 0.35. 

Cambray, P., B. Deshaies, and P. Clavin. 1979. Solution des equations d Euler associees a I expansion d une sphere a vitesse constante. Journal de Physique. Coll. C8, 40(ll) 19-24. 

For example, ergot alkaloids produce without exception blue chromatogram zones, while clavine alkaloids primarily produce green colors [4], Urea derivatives and primary aromatic amines yield yellow chromatogram zones [28,33,34,36,37] and PR toxin and PR imine emit intense blue fluorescence on excitation with long-wavelength UV light (X = 365 nm) [44],... 

The first analytical estimation of the value of the Markstein number in the presence of realistic gas expansion was given by Clavin and Williams [8]. In the approximation of a one-step Arrhenius reaction with a high activation energy P, they found fhe following expression for Ma ... 

The Lewis number, Le, is that of the deficient species (fuel or oxidant) in the mixture. In their analysis, Clavin and Williams used the simplifying approximation that the shear viscosity, the Lewis number, and the Prandtl numbers are all temperature-independent. They also showed that, at least for weak flame stretch and curvature, the change in local flame speed due to stretch and curvature is described by the same Markstein number ... 

Clavin and Garcia [15] have obtained a more general dispersion relation for an arbitrary temperature dependence of the diffusion coefficients. Their nondimen-sional result is qualitatively the same as Equation 5.1.4, but the coefficients contain information on the temperature dependence of the diffusivities ... 

The response function in Equahon 5.1.16 has a different normalizahon to the transfer funchon defined by Clavin et al. [31]. Here Z = (Zdavin/ XQ/Cp), where M = Si/c is the Mach number of fhe flame. 

P. Clavin and F.A. Williams. Theory of premixed-flame propagation in large-scale turbulence. Journal of Fluid Mechanics, 90(pt 3) 589-604, 1979. 

G. Searby and P. Clavin. Weakly turbulent wrinkled flames in premixed gases. Combustion Science and Technology, 46 167-193, 1986. 

P. Clavin. D)mamic behaviour of premixed flame fronts in laminar and turbulent flows. Progress in Energy and Combustion Science, 11 1-59,1985. 

P. Clavin and P. Garcia. The influence of the temperature dependence of diffusivities on the dynamics of flame fronts. Journal de Mecanique Theorique et Appliquee, 2(2) 245-263, 1983. 

P. Clavin, P. Pelc and L. He. One-dimensional vibratory instability of planar flames propagating in tubes. Journal of Fluid Mechanics, 216 299-322, 1990. 

P. Clavin and J. Sun. Theory of acoustic instabilities of planar flames propagating in sprays or particle-laden gases. Combustion Science and Technology, 78 265-288, 1991. 

J.D. Buckmaster and P. Clavin. An acoustic instability theory for particle-cloud flames. Proceedings of the Combustion Institute, 24 29-36,1992. 

C. Clanet, G. Searby, and P. Clavin. Primary acoustic instability of flames propagating in tubes Cases of spray and premixed gas combustion. Journal of Fluid Mechanics, 385 157-197,1999. 

P. Clavin and G. Searby. Unsteady response of chainbranching premixed-flames to pressure waves. Combustion Theory and Modelling, 12(3) 545-567, 2008. 

R. Clavin and E.D. Siggia. Turbulent premixed flames and sound generation. Combust. Sci. Technol., 78 147-155,1991. 

Clavin, P. and Williams, F.A., Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity, /. Fluid Mech., 116, 251, 1982. 

Citrinine la 69,147,148 Citronellal la 158,159 CitroneUol la 68-70,327 Citronellyl acetate la 68 Claisen-Tischenko reaction 15 54 Clathrate complex 15 303 Clavin alkaloids 15 243 Clavine alkaloids 15 246,252 Cleanup la 119 Clemastin 15 354 Clenbuterol 15 106,107,354 Clobutinol 15 354 Cloforex 15 194,296 Clomethiazole lb 354 Clomipramine 15 352,354,355 Clonacillin lb 301 Clonidine 15 354 Clopamide 15 354 Clorexolon 15321 Clotrimazol 15 98,99,401,402 Cloxacillin 1584,188 Clozapin 15 354 Cnicin 15 290... 

A more rigorous development of wrinkled turbulent flames led Clavin and Williams [57] to the following result where isotropic turbulence is assumed ... 

This result differs from Schelkin s heuristic approach only by the factor of 2 in the second term. The Clavin-Williams expression is essentially restricted to the case of (U /SL) [Pg.233]

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