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Additional info for Advanced methods for practical applications in fluid mechanics
3-D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 2. " Journal of Non-Newtonian Fluid Mechanics 127(2-3): 95-106. Tatum, J. , M. V. Finnis, et al. (2007). "3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. " Journal of Non-Newtonian Fluid Mechanics 141: 99-115. Westerweel, J. (1997). " Measurement Science and Technology 8: 1379-1392. , D. Dabiri, et al. (1997). " Experiments in Fluids 23: 20-28. Westerweel, J.
The figure shows that increasing the subsonic zones (smaller M∞ ) degrades the convergence. Apparently, numerical simulation with smaller of M∞ will need optimization in order to provide better convergence. (a) (b) 42 Advanced Methods for Practical Applications in Fluid Mechanics (c) Fig. 8. Dimensionless residual norm for the gas density vs. the number of iterations (a)k − ε model, (b)–B-L model, (c)- k − ε compressibility model. The influence of the pressure ratio on the upstream flow structure was also studied.
2 u z ln − ψ m zo (18) Where the similarity function ψm (z/L) in Eq. (15) or (18) is given as ψ m = ψ h = −5 z L for z/L ≥ 0 1 + x2 π 1+ x −1 for z/L<0 − 2 tan ( x ) + + ln 2 2 2 ψ m = 2 ln (19) (20) Modification of the Charnock Wind Stress Formula to Include the Effects of Free Convection and Swell 53 and the function ψh (z/L) in Eq. (16) is given as 1 + x2 for z/L<0 2 ψ h = 2 ln (21) where z x = 1 − 16 L 1/4 for z/L < 0 Under neutral conditions, that is when z/L approaches 0, the transfer coefficients in Eqs.