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Engineering Tribology Episode 2 Part 1

Tham khảo tài liệu 'engineering tribology episode 2 part 1', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Computational Hydrodynamics 225 Figure 5.12 Coded mesh of the control volume used in thermohydrodynamics 8 . T ae The parameter E is used to enforce flow directionality or convection into the controlling finite difference equation 5.52 . There are two values of E and the selection is based on the difference between lubricant flow in and out of the control volume. E E1 if E1 0 and E 0 if E1 0 5.59 E1 laEl laW laNl lasl - lapl 5.60 The inequality in equation 5.59 allows for reversal of flow which otherwise causes numerical instability. The subscripts for all the mass flow terms e.g. pw n are lower case denoting that an average between velocities at the central and peripheral node is taken for example wn 0.5 wN wP . Sp and Sc are terms representing viscous heating where allowance is made for the strong influence of temperature on viscosity. These two quantities are derived from the basic expression for viscous heating which is caused by the shearing of the lubricant s n ẫ 5.61 where s is the intensity of viscous heating W m3 The controlling equation for Sp and S is based on the assumption of a linear dependence of the heat source term on temperature s Sc SpTp 5.62 The precise forms of Sp and S are given by s s dn Sp np dTp oid 5.63 TEAM LRN 226 Engineering Tribology S. s 1 - Tp dn I dTp o d 5.64 where all terms are as calculated from the previous sweep of iteration for temperature and are referred to as old values. The exponential viscosity law can be written as Table 2.1 hp Te Tp 5.65 where np is the predicted dynamic viscosity of the lubricant Pas n0 is the dynamic viscosity of the lubricant at some reference temperature T0 Pas Y is an exponent of viscosity-temperature dependence typically Y 0.05 K-1 . or rearranged as dn _ dTp -Yhp 5.66 Substituting 5.66 into 5.63 and 5.64 yields Sp -YS 5.67 S. s 1 - T dT J S 1 Yt Ip dlp old Ì 5.68 Treatment of Boundary Conditions in Thermohydrodynamic Lubrication As mentioned already the boundary conditions necessary when viscous