What is it about?

Turbulent flow is fundamentally three-dimensional, but axisymmetric computational fluid dynamics (CFD) models of axial viscous flow over streamlined axisymmetric bodies yield quick results that are approximate but very useful for preliminary studies. This is shown by comparing the results of 2D and 3D CFD (STAR-CCM+) models of axial flow over the Defense Advanced Research Project Agency submarine model known as the DARPA SUBOFF.

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Why is it important?

The CFD community is always in search of methods to reduce the overall computational time – preferably by large factors. The detailed illustration using the much-studied DARPA SUBOFF shows that this 2D axisymmetric model, in addition to being fast by a factor of more than 300, yields results for the total drag, the wall shear stress and wall pressure coefficients, and the velocity profile within the boundary layer at various locations on the body that are very nearly the same as those obtained using 3D simulations. The difference between the 2D CFD drag at a Reynolds number of 35.35 million and experimental results is only +2.05%. Thus, the method is ideally suited for preliminary optimization studies.


The model chosen for use in any application depends on the outputs of interest. The simplest and fastest model that yields results with sufficiently low errors is the most desirable one. The model should also be robust and work well for new applications. In the preliminary design stage, a large number of options should be tried and ranked. Sub-optimal designs are often used because of the lack of time to investigate more options. A large database allows the chief designer to choose an appropriate option after considering various trade-offs. It is shown that the 2D axisymmetric model is well suited for preliminary design and the ranking of options. The error in the total drag is low and the flow in the nose and tail regions is shown to be computed with low errors. High accuracy is obtained by stating and using a few guidelines for meshing. The level of rigor in the verification and validation of the results is high and is rarely seen in recent literature. This should inspire confidence in the readers to use the method to study flows over streamlined axisymmetric bodies and new applications.

H Rahul Krishna

Read the Original

This page is a summary of: Numerical investigation of two-dimensional axisymmetric and three-dimensional flow simulations over a benchmark underwater vehicle, Physics of Fluids, January 2023, American Institute of Physics, DOI: 10.1063/5.0134985.
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