Numerical Simulations of Two-Dimensional Laminar Flow Over Bluff Bodies Using the Immersed Boundary Method with Cartesian Grids

Open Access
Author:
Stergiou, Jonathan Chris
Graduate Program:
Aerospace Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
December 15, 2008
Committee Members:
  • Philip John Morris, Thesis Advisor
  • Sue Ellen Haupt, Thesis Advisor
Keywords:
  • fluid
  • computational
  • cylinder
  • immersed boundary
  • cfd
  • dynamics
  • bluff body
Abstract:
The details of flow past bluff bodies are investigated with two computational fluid dynamics solvers. The first computational code is the NPHASE-PSU code, a face-based, fully unstructured, second order discretized, implicit, finite volume fluid dynamics solver. The second is the CARIBOU code, a node based, structured, fourth order discretized, explicit, finite element fluid dynamics solver. The implementation of the immersed boundary method is assessed within the framework of NPHASE-PSU through comparisons of flowfields modeled both with and without the use of the immersed boundary method. The initial test case consists of steady state two-dimensional laminar flow past a circular cylinder (Re=1). The flowfield is solved initially by using a standard boundary approach on a body-fitted grid. A subsequent study uses a similar body-fitted grid with the immersed boundary method. Finally, a uniform Cartesian grid is coupled with the immersed boundary method. The three flow solutions are compared and their velocity fields and flowfield symmetries are examined in detail. The result of the investigation shows that these three test cases yield nearly identical solutions, indicating that all approaches correctly calculate flow in this regime. The second experimental case involves transient calculation of two-dimensional laminar flow past a circular cylinder (Re=100). This experimental setup is examined using a body-fitted grid and standard boundary, body-fitted grid and immersed boundary, and two separate analyses of uniform Cartesian grids and immersed boundaries (the second analysis here is performed in CARIBOU). The solutions are compared to eachother and to experimental data by analyzing velocity fields, drag and lift coefficients (viscous, pressure, and total), and vortex shedding frequency. All cases possess closely matching velocity fields and Strouhal numbers. The standard boundary case matches experimental data regarding lift and drag coefficients with high accuracy. The two immersed boundary cases run in NPHASE-PSU, as well as the CARIBOU case also agree closely with experimental data, indicating that all numerical models correctly represent the physical flowfields. The final experimental case involves transient calculation of two-dimensional laminar flow past a square cylinder (Re=100). This experiment, like the previously discussed cases, involves solutions that use both standard and immersed boundary methods, both in NPHASE-PSU and CARIBOU. All cases possess accurate velocity fields and Strouhal numbers. The standard boundary case matches the CARIBOU immersed boundary case with close accuracy. The two immersed boundary cases run in NPHASE-PSU, as well as the CARIBOU case, also agree closely with each other, indicating that all numerical models correctly represent the physical flowfields.