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Approved for public release; distribution is unlimited / Cebeci's viscous/inviscid interaction program was applied to the analysis of steady, two dimensional, incompressible flow past four airfoils, the NACA 66₃-018, 0010 (Modified), 4412 and the Wortmann FX 63-137. Detailed comparisons with the available experimental results show that the essential features are correctly modelled, but that significant discrepancies are found in regions of flow separations. / http://archive.org/details/computationalinv00math / Lieutenant, United States Navy

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This work details a multigrid-accelerated cut-cell Cartesian mesh methodology for the solution of a single partial differential equation set that describes incompressible as well as compressible flow. The latter includes sub-, trans- and supersonic flows. Cut-cell technology is developed which furnishes body-fitted meshes with an overlapping Cartesian mesh as starting point, and in a manner which is insensitive to surface definition inconsistencies. An edge-based vertex-centred finite volume method is employed for the purpose of spatial discretisation. Further, an alternative dual-mesh construction strategy is developed and the standard discretisation scheme suitably enhanced. Incompressibility is dealt with via a locally preconditioned artificial compressibility algorithm, and stabilisation is in all cases achieved with scalar-valued artificial dissipation. In transonic flows, shocks are captured via pressure switch-activated upwinding. The solution process is accelerated by the use of a full approximation scheme (FAS) multigrid method where coarse meshes are generated automatically via a volume agglomeration methodology. The developed modelling technology is validated by application to the solution of a number of benchmark problems. The standard discretisation as well as the alternative method are found to be equivalent in terms of both accuracy and computational cost. Finally, the multigrid implementation is shown to achieve decreases in CPU time of between a factor two to one order of magnitude. In the context of cut-cell Cartesian meshes, the above work has resulted in the following novel contributions: the development of an alternative vertex-centred discretisation method; the use of volume agglomerated multigrid solution technology and the use of a single equation set for both incompressible and compressible flows. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / unrestricted

Computational fluid dynamics and heat transfer (CFD/HT) models have been employed as the dominant technique for the design and optimization of both new and existing data centers. Inviscid modeling has shown great speed advantages over the full Navier-Stokes CFD/HT models (over 20 times faster), but is incapable of capturing the physics in the viscous regions of the domain. A coupled inviscid-viscous solution method (CIVSM) for bounded domains has been developed in order to increase both the solution speed and accuracy of CFD/HT models. The methodology consists of an iterative solution technique that divides the full domain into multiple regions consisting of at least one set of viscous, inviscid, and interface regions. The full steady, Reynolds-Averaged Navier-Stokes (RANS) equations with turbulence modeling are used to solve the viscous domain, while the inviscid domain is solved using the Euler equations. By combining the increased speed of the inviscid solver in the inviscid regions, along with the viscous solver’s ability to capture the turbulent flow physics in the viscous regions, a faster and potentially more accurate solution can be obtained for bounded domains that contain inviscid regions which encompass more than half of the domain, such as data centers.

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A three dimensional viscous/inviscid interactive boundary layer method for predicting the effects of fluid viscosity on the performance of fully wetted propellers is presented. This method is developed by coupling a three dimensional low-order potential based panel method and a two dimensional integral boundary layer analysis method. To simplify the solution procedures, this method applies a reasonable assumption that the effects of the boundary layer along the span wise direction (radially outward for propeller blades) could be negligible compared with those along the stream wise direction (constant radius for propeller blades). One significant development of this method, compared with previous work, is to completely consider the effects of the added sources on the whole blades and wakes rather than evaluate the boundary layer effects along each strip, without interaction among strips. This method is applied to Propeller DTMB4119, Propeller NSRDC4381 and DTMB Duct II for validation. The results show good correlation with experimental measurements or RANS (ANSYS/FLUENT) results. The method is further used to develop a viscous image model for the cases of three dimensional wing blades between two parallel slip walls. An improved method for hydrofoils and propeller blades with non-zero thickness or open trailing edges is presented as well. The method in this thesis follows the idea of Pan (2009, 2011), but applies a new extension scheme, which uses second order polynomials to describe the extension edges. A improved simplified search scheme is also used to find the correct shape of the extension automatically to ensure the two conditions are satisfied. / text

A two-dimensional viscous-inviscid interactive boundary layer method is applied to three dimensional problems of flow around ducts and ducted propellers. The idea is to predict the effects of fluid viscosity on three dimensional geometries, like ducts, using a two-dimensional boundary layer solver to avoid solving the fully three dimensional boundary layer equations, assuming that the flow is two-dimensional on individual sections of the geometry. The viscous-inviscid interactive method couples a perturbation potential based inviscid panel method with a two-dimensional viscous boundary layer solver using the wall transpiration model. The boundary layer solver used in the study solves for the integral boundary layer characteristics given the edge velocity distribution on the geometry. The viscous-inviscid coupling is applied in a stripwise manner but by including the interaction e ffects from other strips. An important development in this thesis is the consideration of eff ects of other strips in a more rational and accurate manner, leading to improved results in the cases examined when compared to the results of a previous method. In particular, the effects of potentials due to other strips arising out of the three dimensional formulation are considered in this thesis. The validity of assuming two-dimensional flow along individual sections for application of viscous-inviscid coupling is investigated for the case of an open propeller by calculating the boundary layer characteristics in the direction normal to the assumed direction of two-dimensional flow from data obtained by RANS simulations. Also, a previous method which models the flow around the trailing edge of blunt hydrofoils has been improved and extended to three dimensional axisymmetric ducts. This method is applied to ducts with blunt and sharp trailing edges and to a ducted propeller. Correlations of results with experiments and simulations from RANS are shown. / text