Rough tubes

Severe corrosion, Rough tubing, Probe wear. Centring, Fill factor, Noise... 

An equation by Churchill Chem. Eng., S4[24], 91-92 [Nov. 7, 1977]) for both smooth and rough tubes offers the advantage of being explicit inf ... 

For very rough tubes, the flame acceleration is much more rapid as shown in the previous section. Transition to detonation is also clearly marked by a local explosion and abrupt change in the wave speed. The wall roughness controls the propagation of the wave by providing [5] ... 

Time sequences of schlieren photographs showing DDT in very rough tube stoichiometric H2/O2 mixture at 100 torr 2 ps between frames. 

In the early studies [22,24,39] on propagation of detonation in very rough tubes, the steady propagation velocities as low as 50% of the normal CJ value have been observed. Such low-velocity detonations have been referred to as quasi-detonations [4]. 

Photographic study of the structure and propagation mechanisms of quasi-detonations in rough tubes. Prog. Astr. Aeron., 138, 223, 1990. 

For rough tubes in turbulent flow (7VRc > 4000), the von Karman equation was modified empirically by Colebrook to include the effect of wall roughness, as follows ... 

Pollard (SO) found elutriation to be very successful for particles below 40 microns. The air is allowed to run for 30-minute intervals. When the sample remaining in the tube is less than 10% by weight of the previous one, the air flow is increased to remove the next size range. Excessive humidity and rough tube surfaces cause trouble. Tapping loosens the particles which might otherwise adhere to surfaces. Corcoran (20) gives a theoretical discussion of the determination of particle size, followed by a brief account of the elutriation process. 

These experiments were carried out in connectibn with Shchelkin s conception of the role of gas turbulization in the appearance of detonation. However, they simultaneously provided valuable material on the influence of external conditions on the steady propagation of detonation. The detonation velocity fell noticeably in rough tubes compared with smooth ones,... 

We referred above to experiments by Shchelkin on detonation in rough tubes spirals made of wire were inserted into glass tubes. The spirals were attached to the tube walls so that the tube surface become rough, with the magnitude of the roughness dictated by the diameter of the wire from... 

In the published experiments of Shchelkin the velocity fell to 60-50% of Dt, which is incompatible with the theory of limits developed above. The behavior of detonation in rough tubes in this respect differs from the behavior of detonation in smooth tubes. We could increase the losses in the smooth tube too by decreasing its diameter, but then, instead of steady propagation with a lower velocity, we observe termination of the propagation of detonation. 

In the normal mechanism the reaction runs simultaneously over the entire cross-section of the tube the curves presented in 11.5 illustrate the change in pressure, temperature and composition. We axe fully justified in using an approach in which we consider all quantities characterizing the state to be dependent only on the distance of the point from the shock wave front. In the case of the SM, in the mechanism which we have proposed here for rough tubes, in each intermediate cross-section part of the substance has not reacted at all (the core of the flow) and part of the substance has completely reacted (the peripheral layers) the states of the two parts— composition, temperature, specific volume—are sharply different. The only common element is the pressure, which is practically identical in a given cross-section in the two parts of the flow (in the compressed, but unreacted mixture and in the combustion products), but which changes as combustion progresses from one cross-section to another. 

The extraordinarily striking fact that transition from combustion to detonation is eased in rough tubes was discovered by Shchelkin, who was led in this by certain ideas about the role of gas turbulization. 

In order to interpret this recently discovered, but absolutely fundamental fact, we shall consider more carefully the conditions of the gas motion. The flame functions as a piston, and the dependence written above of the gas velocity on the flame velocity, w — (n—l)u, is valid insofar as the combustion products do not cool. Therefore, for detonation to occur the ratio of the drag and heat transfer is of particular importance. It is precisely in rough tubes that conditions are most favorable the increased drag accelerates the establishment of the velocity profile, while the heat transfer remains practically unchanged by the introduction of roughness. 

This effect becomes even stronger in a rough tube in which the braking increases faster than the heat transfer. 

Dipprey, D.F. and Sabersky, R.H., Heat and Momentum Transfer in Smooth and Rough Tubes at Various Prandtl Numbers , Int. /. Heat Mass Transfer, Vol. 5, pp. 329-353, 1963. 

The empirical correlations presented above, with the exception of Eq. (6-7), apply to smooth tubes. Correlations are, in general, rather sparse where rough tubes are concerned, and it is sometimes appropriate that the Reynolds analogy between fluid friction and heat transfer be used to effect a solution under these circumstances. Expressed in terms of the Stanton number,... 

For the rough-tube condition, we may employ the Petukhov relation, Eq. (6-7). The mean film temperature is... 

Rough tubes St Pr/3 = or Eq. (6-7) Fully developed turbulent flow (6-12)... 

The form and skin friction coefficients are explained in books on Fluid Flow or Transport Phenomena (for example W. J. Seek et al. Transport Phenomena, Wiley 1999). We derived that for skin friction using data for rough tubes. 

Once the friction factor is available, this equation can be used conveniently to evaluate the Nusselt number for both smooth and rough tubes. 

In turbulent flow, wall roughness increases the heat transfer coefficient h by a factor of 2 or more [Dipprey and Saber.sky (1963)]. The convection heat transfer coefficient for rough tubes can be calculated approximately from the Nusselt number relations such as Eq. 8-71 by using the friction factor determined from the Moody chart or the Colebrook equation. However, this approach is not very accurate since there is no further increase in h with/for /> 4/sn,ooih [Norris (1970)1 and correlations developed specifically for rough tubes should be used when more accuracy is desired. 

More detailed information about the structure of turbulent flows in a circular (noncircular) tube and a plane channel, as well as various relations for determining the average velocity profile and the drag coefficient, can be found in the books [138, 198, 268, 276, 289], which contain extensive literature surveys. Systematic data for rough tubes and results of studying fluctuating parameters of turbulent flow can also be found in the cited references. 

M. R. Rao, Forced Convection Heat Transfer and Fluid Friction in Fully Developed Turbulent Flow in Smooth and Rough Tubes, Indian ASI, pp. 3.8-3.23,1989. 

Y. Kawase, and A. De, Turbulent Heat and Mass Transfer in Newtonian and Dilute Polymer Solutions Flowing through Rough Tubes, Ini. J. Heal Mass Transfer, (27) 140-142,1984. 

---