Mixing diffusional

The burning rate of propellants is one of the important parameters for rocket mo-tordesign. As described in Section 7.1.2, the burning rate of AP composite propellants is altered by changing the particle size of the AP used. The diffusional mixing process between the gaseous decomposition products of the AP particles and of the polymeric binder used as a fuel component determines the heat flux feedback from the gas phase to the condensed phase at the burning surface. - This process is a... 

When AP particles are added to GAP-AN pyrolants, a number of luminous flame-lets are formed above the burning surface. These flamelets are produced as a result of diffusional mixing between the oxidizer-rich gaseous decomposition products of the AP particles and the fuel-rich gaseous decomposition products of the GAP-AN pyrolants. Thus, the temperature profile in the gas phase increases irregularly due to the formation of non-homogeneous diffusional flamelets. 

Fig. 12.11 shows the structure of a rocket plume generated downstream of a rocket nozzle. The plume consists of a primary flame and a secondary flame.Fil The primary flame is generated by the exhaust combustion gas from the rocket motor without any effect of the ambient atmosphere. The primary flame is composed of oblique shock waves and expansion waves as a result of interaction with the ambient pressure. The structure is dependent on the expansion ratio of the nozzle, as described in Appendix C. Therefore, no diffusional mixing with ambient air occurs in the primary flame. The secondary flame is generated by mixing of the exhaust gas from the nozzle with the ambient air. The dimensions of the secondary flame are dependent not only on the combustion gas expelled from the exhaust nozzle, but also on the expansion ratio of the nozzle. A nitropolymer propellant composed of nc(0-466), ng(0-369), dep(0104), ec(0 029), and pbst(0.032) is used as a reference propellant to determine the effect of plume suppression. The burning rate characteristics of the propellants are shown in Fig. 6-31. Since the nitropolymer propellant is fuel-rich, the exhaust gas forms a combustible gaseous mixture with the ambient air. This gaseous mixture is ignited and afterburning occurs somewhat downstream of the nozzle exit. The major combustion products in the combustion chamber are CO, Hj, CO2, N2, and HjO. The fuel components are CO and H2, the mole fractions of which at the nozzle throat are co(0.47) and iH2(0.24).

Ottino (1989,1994) discuss the whole problem of intermixing of fluids A and B in terms of stretching, folding, thinning, and finally diffusional mixing of fluid elements. Figure 16.8 tries to illustrate this mechanism however, we must now leave this fascinating subject. 

Compared with the AP decomposition flame thickness, the fuel-oxidant redox flame extends a much greater distance from the propellant surface and depends on the rate of both chemical reaction and diffusional mixing. 

The relative roles played by diffusional mixing and chemical reaction in determining the reaction rate of the O/F flame are difficult to analyze. Consequently, as was done in the original formulation (92), expressions... 

As in Ref. 92 for a second-order gas-phase reaction where the prevailing pressure is sufficiently low for the O/F flame (Zone II of Figure 1) to be chemical-reaction rate controlled (high diffusional mixing rate), the chemical mass conversion rate in a zone of length LIIt ck at temperature Tg may be expressed as ... 

Such diffusional mixing tends to keep the composition and temperature uniform within the reactor. 

As an illustration, consider the isothermal, isobaric diffusional mixing of two elemental crystals, A and B, by a vacancy mechanism. Initially, A and B possess different vacancy concentrations Cy(A) and Cy(B). During interdiffusion, these concentrations have to change locally towards the new equilibrium values Cy(A,B), which depend on the local (A, B) composition. Vacancy relaxation will be slow if the external surfaces of the crystal, which act as the only sinks and sources, are far away. This is true for large samples. Although linear transport theory may apply for all structure elements, the (local) vacancy equilibrium is not fully established during the interdiffusion process. Consequently, the (local) transport coefficients (DA,DB), which are proportional to the vacancy concentration, are no longer functions of state (Le., dependent on composition only) but explicitly dependent on the diffusion time and the space coordinate. Non-linear transport equations are the result. 

For very dilute solid solutions of B in A, the basic physics of diffusional mixing is the same as for (A, A ). An encounter between VA and BA is necessary to render the B atoms mobile. But B will alter the jump frequencies of V in its surroundings and therefore numerical values of the correlation factor and cross coefficient are different from those of tracer A diffusion. Since the jump frequency changes also involve solvent A atoms, in addition to fB, the numerical value of fA must be reconsidered (see next section). 

In this case, the electrogenerated R will encounter Z as it diffuses away from the electrode and will react to form P. This diffusional mixing of two reactants (R and Z in this example) is the basis for chronoabsorptometry (and other electrochemical techniques) as a kinetic method. The homogeneous chemical reaction of R will perturb its accumulation by a magnitude that is proportional both to k and to the concentration of Z. The influence of this perturbation is apparent from the concentration-distance profiles for R, which are illustrated for a rate constant of 107 L/(mol s) in Figure 3.9. 

The distributor plate is sandwiched against the catalyst wafer using a gasket of polymer or graphite and the volume above each catalyst patch defines a reaction volume. A cross-section view of one of the 256 reaction/detection channels is shown below (Fig. 3.8). Feed gas enters the reaction volume from the side. For residence times greater than 100 ms the reactor behaves as a difFusionally mixed... 

The quadratic dependence between chaimel dimensions and diffusional mixing times in equation (1) might serve as a stimulus to manufactme channels with small diameters (<50nm) enabling complete mixing in microseconds. 

We have considered the situation of only one phase for any mixture composition this means that there is no surface tension and the fluid behavior is completely characterized by the turbulent flow described by the mass and momentum balance equations. To solve these equations, one needs to model the diffusional mixing of the species present in the system and to identify local values of the thermodynamic and transport properties, as considered in Section 3.2. Here we just point out that once the methods for predicting local values of fluid density and viscosity have been worked out, one should be able to integrate Eqs. (10) and (11). 

Mixing of chemical differences in fluids through diffusion has been dealt with in some detail previously, for example, England et al. (1987) for oil and gas, and Smalley et al. (1995) for water. A general equation that gives an order of magnitude estimate of diffusional mixing times is... 

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