Friction calculations

Where there is doubt as to the adequacy of restraint friction, calculations shall be made and indicated anchoring shall be installed. 

The total frequency-dependent friction calculated from the MCT, (z), is plotted against the Laplace frequency (z) in Fig. 14. In the same figure the Enskog friction (e and the binary contribution (z) are also shown. Note here that in the high-frequency regime the frequency-dependent total friction is much less than the Enskog friction and is dominated entirely by the binary... 

Further empirical methods are required to account for the additional frictions effects resulting from bends, valves, changes in pipe size, etc. The detailed treatment of friction calculations is beyond the scope of thermodynamics.t... 

The annealed sample that was not treated by friction has been used as a standard one. Dislocation density caused by friction process was investigated using the sample treated in Ar-gas medium at 823K during 60 min. For the sample treated by friction calculated dislocation density was determined in the range from 1010 to 10 cm 2 whereas that for the annealed sample was obtained in the range 106to 10s cm 2. Thus, plastic deformation occurred due to friction causes the increase of total dislocation density. 

Analogy between heat and momentum transfer The analogy coupled with wall-friction calculations or measurements provides the heat transfer coefficient. In Section 5.1 we develop this analogy for a particular problem which leads, in terms of the wall-friction coefficient of this problem, to the heat transfer coefficient. 

Hu and Zwanzig (1974) have performed hydrodynamic calculations of the rotational friction coefficents of prolate and oblate ellipsoids as a function of the axial ratio using slip boundary conditions. The ratio of the friction calculated with slip to that calculated with stick boundary conditions is shown in Fig. 7.8.3 as a function of the axial ratio p. 

Before the computer age, the friction factor plot and the convenience plots made from it were the only means that engineers had of solving fluid friction problems in pipes. For an occasional such calculation or a problem outside the normal range of the engineer s experience, they are probably still the best way. However, for routine pipe friction calculations, engineers use computers. To do so, they need equations equivalent to the friction factor plot. 

FIGURE 183. When two solid surfaces of differing hardness make contact, asperities in the harder material may cut into or plow the softer surface. Such a process will increase the apparent friction between the two surfaces. The plowing contribution can be estimated using a cone model in which the angle of the plow cut is taken as 20 and the coefficient of friction calculated according to Equation (18.5). 

Certain reference books show a roughness of steel of 0.045-0.05 mm. This is difficult to maintain in steel pipes carrying slurries as they are often subject to erosion and corrosion. For this reason, the author recommends the use of a slightly higher roughness of the order of 0.06 mm in friction calculations. 

This simple surface feature enables insight to some important effects within mixed lubrication regime. After these results three different real surface topographies are compared with each other. Finally the friction calculation will be explained and two Stribeck curves are presented. 

Since it is expected that the friction coefficient in the boundary regime is also above the hydrodynamic friction coefficient, it shows that the assumptions which are made concerning the friction calculation are not sufficient yet. It is supposed to be the temperature calculation which must be introduced to... 

The last section describes the friction calculation with fluid and solid friction. The new model enables the calculation of Stribeck curves over several orders of magnitude. But it has proven that the assumptions concerning solid friction calculation are not sufficient yet. Since it could be shown that solid contact spots cannot be calculated by Reynolds equation but rather must be identified by a... 

Reply by the Authors In the case of pure elastic conditions we assume that a certain part of the elastic deformation - the hysteresis - gets lost and therefore must be taken into account for friction calculation. The authors know that this assumption is not sufficient because additional mechanisms must be taken into consideration as well. The most important point for future work will be the temperature calculation at these contact spots, to check whether the molecular thin film between the asperities still exists or not. If there is no more oil film available in the micro contact area, adhesive forces are assumed between the two surfaces. The authors believe that the temperature calculation will play a decisive role in the Iriction calculation. 

For both sides of the gas cooler, wall friction is turned off in order to provide direct control over the friction calculations. For the NaK side of the gas cooler, the Reynolds number dependent form loss coefficient option In RELAP5-3D is used to accurately represent the Kays and London compact heat exchanger 1/10-19.35 (Reference 12-10). The friction factor data is fit to the exponential format required by the code resulting in the following relation ... 

---