Corrsin

A Prandtl number of 0.7 has been suggested for nonisothermal jets by Not-tage fro Porstall and Shapiro,Corrsin and Uberoi, - and Grimitlyn. Abramovich suggested a Prandtl number for a compact jet of 0.75, and for a linear jet, 0.5. 

Corrsin, S. 1943. Investigation of Flow in an Axially Symmetric Heated Jet of Air. NAC.A Wartime Report W-94. 

The characteristic time constant for mesomixing by the inertial-convective process (Corrsin, 1964) is given by... 

In a RANS simulation of scalar mixing, a model for i ,/, must be supplied to compute (4>a). In fully developed turbulence, t,p can be related to tu by considering the scalar energy spectrum, as first done by Corrsin (1964). 

Despite the progress in CFD for inert-scalar transport, it was recognized early on that the treatment of turbulent reacting flows offers unique challenges (Corrsin 1958 Danckwerts 1958). Indeed, while turbulent transport of an inert scalar can often be successfully described by a small set of statistical moments (e.g., (U), k, e, (, and (scalar fields, which are strongly coupled through the chemical source term in (1.28). Nevertheless, it has also been recognized that because the chemical source term depends only on the local molar concentrations c and temperature T ... 

Correa, S. M., A. Gulati, and S. B. Pope (1994). Raman measurements and joint pdf modeling of a nonpremixed bluff-body-stabilized methane flame. In Twenty-fifth International Symposium on Combustion, pp. 1167-1173. Pittsburgh, PA The Combustion Institute. Corrsin, S. (1951a). The decay of isotropic temperature fluctuations in an isotropic turbulence. Journal of Aeronautical Science 18,417 -23. 

This problem has been addressed by Corrsin (1974) for several simple hypothetical cases. Many qualitative and, in some instances, semiquanti-... 

Corrsin, S. (1974). Limitations of gradient transport models in random walks and in turbulence. Adv. Geophys. 18A, 25-59. 

General discussions of several aspects concerning the treatment of chemical reactions with diffusion are given by Damkohler (D2), Horn and Kiichler (H12), Prager (P7), Schoenemann and Hofmann (SlO), and Trambouze (Til). Corrsin (C21) has discussed the effects of turbulence on chemical reactions from the fundamental point of view of turbulence theory. We will first discuss the application of each type of model to chemical reactors. Then a short comparison will be made between the different approaches. 

The second general approach is based on extension of the creeping flow result, as in earlier sections. Corrsin and Lumley s modification (Cll) of the equation proposed by Tchen (Tl) allows Eq. (11-43) to be generalized as... 

The pressure gradient term has been extended to its full form from the Navier-Stokes equation. Equation (11-70) has been discussed by Corrsin and Lumley (Cll), Hinze (H5), and Soo (S7). It is applicable only if a particle is small compared to the scale of velocity variations in the fluid (L8), i.e., if... 

Reynolds (Rl, R2) was one of the earlier investigators to appreciate the random nature of turbulence. The dimensionless parameter bearing his name is widely used as a measure of the physical characteristics of steady, uniform flow. Such a measure is essentially macroscopic and does not describe the local or transient behavior at a point in the stream. In recent years much effort has been devoted to understanding the basic mechanism of momentum transport by turbulence. The early work of Prandtl (P6), Taylor (Tl), Karmdn (Kl), and Howarth (K4) laid a basis for the statistical theory of turbulence which is apparently in reasonable agreement with experiment. More recently Onsager (03), Corrsin (C6), and Kolmogoroff (K10) extended the statistical theory of turbulence to describe the available experimental data in terms of kinetic-energy... 

C7. Corrsin, S., Natl. Advisory Comm. Aeronaut. Tech. Notes 2124 (1950). 

David J. Corrsin, General Counsel/Exec. VP Joseph P. DeManche, Exec. VP-Oper. 

It is suggested that the pressure gradient may be estimated from the Navier-Stokes equation of a single-phase fluid by [Corrsin and Lumley, 1956]... 

The general equations for chemical reaction in a turbulent medium are easy to write if not to solve (2). In addition to those for velocities (U = U + uJ and concentrations (Cj = Cj + Cj), balance equations for q = A u, the segregation ( , and the dissipations e and eg can be written (3). Whatever the shape of the reactor under consideration (usually a tube or a stirred tank), the solution of these equations poses difficult problems of closure, as u S, 5 cj, cj, and also c cj, c Cj in the reaction terms have to be evaluated. The situation is even more complicated when the temperature and the density of the reacting mixture are also fluctuating. Partial solutions to this problem have been proposed. In the case of instantaneous reactions (t << Tg) the "e-quilibrium assumption" applies the mixed reactants are immediately converted and the apparent rate of reaction is simply that of the decrease of segregation, with Corrsin s time constant xs. For instance, with a stoichiometric proportion of reactants, the extent of reaction X is given by 1 - /T ( 2), a simple result which can also be found by application of the IEM model (see (33)). 

Among experimental studies of chemical reactions in turbulent media, fast reactions in tubular reactors with multijet injection of reactants are very popular, since the first experiments of Mao and Toor (34) and Vassiliatos and Toor (35). Their data have been (and are still) extensively exploited for testing theoretical models, although one may ask if homogeneous isotropic turbulence was perfectly controlled in these experiments. In order to rule out this objection, a new series of experiments was recently performed by Bennani et al. (28, 29, 30, 36) in a 0.29 m i.d. tube eliminating the influence of boundary layers. Turbulence was created by a grid and carefully controlled by velocity fluctuation measurements. Previous studies (2) had confirmed that the decrease of Ig with a non-reacting species (passive scalar) obeys Corrsin s equation ... 

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