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Title: The calculation by finite differences of steady two-dimensional laminar flow in a T-junction
Author: Blowers, Roger Martyn
ISNI:       0000 0001 3468 3397
Awarding Body: University of Surrey
Current Institution: University of Surrey
Date of Award: 1973
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This thesis describes the development of a computer program to study the steady two-dimensional laminar incompressible flow in a T-junction, at which one fully-developed channel flow impinges at right angles upon another. The calculation is made by finite differences on a non-uniform mesh. Solutions are presented for varying inlet velocity ratios, and for Reynolds numbers in the range 10[2] to 10[4]. Two further flow problems are also considered briefly using the same program. In the first the side channel is transformed to a square cavity. This allows a direct comparison with the work of previous authors, and good agreement is found. In the second the side channel is transformed to an outlet. The computational problem proves unusually awkward because it is surprisingly difficult to find a method of iteration which converges with a viable expenditure of computer time, and, more importantly, because the flow pattern proves very sensitive to the numerical treatment of the immediate neighbourhood of the 270-degree corners. The convergence difficulty is substantially overcome after a great deal of experimentation. The corner-flow difficulty is treated by a novelmesh configuration. Nevertheless the separated flow proves sensitive to the mesh size at the corner. This sensitivity is investigated, with the aid of analytical solutions, and it is concluded that the mesh size at the corner needs to be of the order of the Stokes radius, which in turn is inversely proportional to the Reynolds number. Considerable attention is given to the accuracy of the finite difference solutions, both theoretically, and practically by duplicating solutions using alternative finite difference equations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available