Spaulding and White (E17, E18) presently is being extended to Re = 200 in order to model numeri- 

 cally the drag and lift forces on a vibrating cylinder. 



Virtually all computations of the flow past bluff bodies (except for the discrete vortex model 

 described earlier) have been based upon a finite-difference approximation to the governing equations 

 where the continuum is represented by a grid of discrete points. Recently, however, the finite-element 

 method has been extended to the modeling of the time-dependent flow over a (stationary) cylinder 

 (E19). The finite element method in this case approximates the fluid continuum by some form of 

 weighted-residual average of the governing equations over elemental volumes (three dimensions) or an 

 elemental areas (two dimensions). Several finite element formulations were employed by Greshko, Lee 

 and Upson (E19) to solve the problem of flow past a stationary circular cylinder at Re = 100. Some 

 promising results were obtained, but the numerical solution was shown to be highly dependent upon 

 the choice of element (simple versus higher-order) and other considerations (lumped mass versus con- 

 ventional mass matrices). The prospect of three-dimensional computations by any of the Navier-Stokes 

 numerical methods is conceptually straightforward but is at the same time sobering financially. 



References 



El. O.M. Griffin and G.H. Koopmann, "The Vortex-Excited Lift and Reaction Forces on Resonantly 

 Vibrating Cylinders," Journal of Sound and Vibration, Vol. 54, 435-448, 1977. 



E2. O.M. Griffin, "Vortex-Excited Cross Flow Vibrations of a Single Cylindrical Tube," in Flow 

 Induced Vibrations, S.S. Chen and M.D. Bernstein (eds.), ASME: New York, 1-10 (June 1979); 

 see also Transactions of ASME, Journal of Pressure Vessel Technology, Vol. 102, No. 2, 158-166, 

 1980. 



E3. S.S. Chen, "Crossflow-Induced Vibrations of Heat Exchanger Tube Banks," Nuclear Engineering 

 and Design, Vol. 47, 67-86, 1978. 



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