Proceedings of the Eighth GAMM-Conference on Numerical Methods in Fluid Mechanics pp 79-88 | Cite as

# Unsteady Viscous Flow Calculations Including Surface Heating and Cooling Effects

## Abstract

A fully implicit solution technique is applied to study the unsteady flow characteristics including surface heating and cooling effects of an infinite circular cylinder at a Reynolds number of 100. The fluid flow problem is governed by the Boussinesq approximation of the Navier-Stokes equations. The equations in the finite-difference form are linearized using Newton’s method and the resulting system of equations including the boundary conditions are solved simultaneously using a direct solution technique. In a previous paper, the solution technique was presented and results (coarse grid) were discussed. Here, results are presented for higher grid densities, different boundary conditions, and various angles between the freestream velocity vector and the gravitational acceleration vector.

## Preview

Unable to display preview. Download preview PDF.

## References

- [1]Wigton, L. B., “Application of MACSYMA and Sparse Matrix Technology to Multielement Airfoil Calculations,” AIAA Paper 87-1142, June 1987.Google Scholar
- [2]Van Dam, C. P., Hafez, M. and Ahmad, J., “Calculation of Viscous Flows with Separation Using Newton’s Method and Direct Solver,” AIAA Paper 88-0412, Jan. 1988; also AIAA Journal, in print.Google Scholar
- [3]Roache, P. J., and Ellis, M. A., “The BID Method for the Steady-State Navier-Stokes Equations,” Computers and Fluids, Vol. 3, 1975, pp. 305–320.MathSciNetADSzbMATHCrossRefGoogle Scholar
- [4]Tuann, S. Y., and Olson, M. D., “Numerical Studies of the Flow Around a Circular Cylinder by a Finite Element Method,” Computers and Fluids, Vol. 6, 1978, pp. 219–240.ADSzbMATHCrossRefGoogle Scholar
- [5]Cebeci, T., Hirsh, R. S., Keller, H. B., and Williams, P. G., “Studies of Numerical Methods for the Plane Navier-Stokes Equations,” Computer Methods in Applied Mechanics and Engineering, Vol. 27, 1981, pp. 13–44.ADSzbMATHCrossRefGoogle Scholar
- [6]Walter, K. T., and Larsen, P. S., “The FON Method for the Steady Two-Dimensional Navier-Stokes Equations,” Computers and Fluids, Vol. 9, 1981, pp. 365–376.ADSzbMATHCrossRefGoogle Scholar
- [7]Schreiber, R., and Keller, H. B., “Driven Cavity Flows by Efficient Numerical Techniques,” Journal of Computational Physics, Vol. 49, 1983, pp. 310–333.MathSciNetADSzbMATHCrossRefGoogle Scholar
- [8]Schütz, H., and Thiele, F., “An Implicit Method for the Computation of Unsteady Incompressible Viscous Flows,” GAMM Workshop on Numerical Methods in Fluids, Vieweg, 1987.Google Scholar
- [9]Van Dam, C. P., Hafez, M., and Brucker, D., “Unsteady Navier-Stokes Calculations Using Biharmonic Formulation and Direct Solver,” AIAA Paper 89-0465, Jan. 1989.Google Scholar
- [10]Lecointe, Y., and Piquet, J., “On the Use of Several Compact Methods for the Study of Unsteady Incompressible Viscous Flow Round a Circular Cylinder,” Computers and Fluids, Vol. 12, 1984, pp. 255–280.zbMATHCrossRefGoogle Scholar
- [11]Schlichting, H., Boundarv-Laver Theory, 7th ed., McGraw-Hill, 1979.Google Scholar
- [12]Noto, K., “Computation on Disappearance of the Karman Vortex Street past Heated Cylinder Submerged in Horizontal Main Flow,” Proceedings of ISCFD Nagoya, Aug. 1989, pp. 605-610.Google Scholar
- [13]Gray, D. D., and Giorgini, A., “The Validity of the Boussinesq Approximation for Liquids and Gases,” International Journal of Heat and Mass Transfer, Vol. 19, 1976, pp. 545–551.zbMATHCrossRefGoogle Scholar
- [14]Dongarra, J. J., Moler, C. B., Bunch, J. R., and Stewart, G. W., “LINPACK User’s Guide,” SIAM, Philadelphia, 1979.CrossRefGoogle Scholar
- [15]Fornberg, B., “A Numerical Study of Steady Viscous Flow past a Circular Cylinder,” Journal of Fluid Mechanics, Vol. 98, 1980, pp. 819–855.ADSzbMATHCrossRefGoogle Scholar