Turbulence in EPRs

The above theoretical analysis of penetrable roughnesses and their interaction with the flow was based on the introduction of a distributed momentum sink (i.e. the force) and heat and mass sources, and was sufficient for discovering some important features of the phenomenon under consideration. It was a simplified consideration with mainly constant coefficients. However, in order to be applied to real environmental and engineering problems, realistic exchange coefficients are to be known. 

The coefficient of turbulent viscosity vr is the most important among them. A number of scientific efforts were spent for estimating it with respect to the whole wide spectrum of problems of fluid mechanics and heat and mass exchange. Thousands of lengthy papers have been devoted to the problem of turbulence . However, we still have no any sufficiently grounded and generally accepted theory. Turbulence still remains to be the most serious challenge to theoretical physics. 

In the study of the penetrable roughnesses of any kind, it seems reasonable to issue from the already known facts and the theories of roughness-associated turbulence. However, the turbulence in EPRs has its own pronounced features. Learning it can give a new light to old problems and researches. 

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It makes clear after the experimental experience that two Reynolds numbers (3.30) should be responsible for the turbulence in EPRs, global and local ones, correspondingly ... 

Some paradoxes of the turbulence in canopies, or EPRs, were pointed out by Raupach and Thom in their state-of-art review of 1981, [522], The first phenomenon is the value of the drag coefficient of elements that constitute the EPR. The highly precise measurements in aerodynamic tubes brought values that depend on the obstacle shape, the flow turbulence level, and the mutual disposition of obstacles but vary near cf 0.5 for spheres and cf 1 for cylinders in the working range of the local Reynolds number 103 < Re < 105. The same coefficient determined from the field measurements in forests turned out to be several times less (in this case, the indirect calculations were performed). A similar paradox takes place for the exchange coefficients. 

It can thus be thought that the intensive turbulence within EPRs, i.e. canopies, reveals some features that are very distinguishing from the common unobstructed turbulence. Such kind of the turbulence attracted an increased attention of researchers in last years, [81, 155, 186, 187, 305, 318, 410, 462, 500, 522], Despite the simplified first-order turbulence closures (algebraic models) or second-order ones (with differential equations for vr) turned useful and lead to some plausible results in practical areas, many its phenomena remains unexplained. Further information about basic turbulence laws is provided in Chapters 2, 4 to 9 along with further practical applications. 

Inside the EPR, many works issue from the gradient representation of the effective turbulent shear in the flow... 

The turbulent shear (3.130) is often taken constant in the approximate performances of boundary layers in fact, Fig. 3.31,C highlights that it is constant over a significant depth H of the main EPR region. The flow obeys the following equation ... 

The numerical results for the flow characteristics jj1- and j have been presented in Fig. 3.29 as functions of the EPR dimensionless density A. The calculations were also performed for the empirical turbulence constant vro = 0.03U h. The shear velocity [/, (A) and the displacement height d(A) turned out to increase, but t/,(A) and Z0(A) decrease with increase in the EPR density. It is possible to vary vro in order to fit these theoretical profiles to experimental data, thus determining the empirical constant. 

However, the most fundamental problem for the theory of EPR is the amendment of the exchange coefficients by means of the in-depth study of the turbulence within the EPR. 

It can be seen from the above consideration that the theory of EPR flows based on the introduction of the distributed force and sources of substances agrees well with experimental data, at least qualitatively. At the same time, the notable scattering can motivate looking for a refined theory, especially as concerned to the algebraic turbulence model (3.131). Second-order turbulence models that are expressed in terms of the differential equations for vT and the associated quantities should certainly fit better,... 

To estimate the efficiency of using tubular turbulent divergent-convergent-type reactors for the preparation of a uniform liquid-gas mixture with a developed phase contact surface, in the case of EPR production, it is advisable to study the quality of dispersion systems obtained in these types of reactors compared with stirred tank reactors. 

Calculations show that the average dispersed particle size throughout the volume of the tubular turbulent reactor, intended for specific conditions of EPR (EPDM) commercial production, is about 0.127 mm, whereas in the case of using conventional stirred tank reactors, in bubbling mode, this value is 10-fold higher at 1.2 mm. 

Thus, using small-scale tubular turbulent divergent-convergent-type reactors at the stage of uniform gas-liquid mixture formation, prior to feeding this mixture into a stirred tank polymerisation reactor, results in a notable (virtually hy one order of magnitude) increase in the phase contact surface. A developed phase interface facilitates the uniform saturation of liquid products with monomers and hydrogen. In this case, it allows improved performance characteristics of the EPR in contrast to stirred tank reactors. 

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