Computational Fluid Dynamics Worked Examples
List of the Examples in the Book
All the problems are extracted from our publication" Computational Fluid Dynamics Recipes - Outline & Worked Examples" and all formulae references are from the book. To order our publications, please visit our page here.
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Creeping Flow Past a Square Block
Example 13.2 - Creeping Flow Past a Square Block
Consider a two-dimensional low Reynolds number flow of an incompressible fluid on a stationary plate with a two-dimensional square block fixed to it, as shown in Figure 13.9. The flow field away from the plate is a parallel flow given by the velocity U = 1. The block has the dimensions of 1 × 1. We want to find the fluid flow pattern in the front and at the back of the block.
The Grid
Similar to Example 13.1, we use the simplified staggered grid. The grid for vorticity is indexed by i and j, and the grid for stream function by I and J. The computational domain is selected large enough, such that the farfield flow is parallel. In our case, we use a 5H × 5H domain, as shown in Fig, 13.10, assuming a uniform grid with Δx = Δy = h.
Detailed solution is provided in the Book
Results
The stream lines are shown Figure 13.13
Comparing the computational result of Figure 13.13 with the experimental result*, Figure 13.14, shows that the symmetric recirculating regions in the front and at the back of the block have been resolved clearly. The discrepancy between the size of the recirculating areas in the experimental and the computational results are caused by the creeping flow approximation as well as the computational errors.
* - Milton Van Dyke. An Album of Fluid Motion. The Paraboic Press, Stanford, California 1982.