Heat transfer systems contain many sources of nonlinearity including temperature dependent material properties, radiation boundary conditions, and internal source terms. Despite progress in numerical simulations, producing accurate models that can predict these complex behaviors are still encumbered by lengthy processing times. Accurate models can be produced quickly by utilizing projection Reduced Order Modeling (ROM) techniques. For discretized systems, the Singular Value Decomposition technique is the preferred approach but has had limited success on treating nonlinearities. In this research, the treatment of nonlinear temperature dependent material properties was incorporated into a ROM. Additional sources of nonlinearities such as radiation boundary conditions, temperature dependent source heating terms, and complex geometry were also integrated. From the results, low conductivity, highly nonlinear material properties were predicted by the ROM within 1% of full order models, and additional nonlinearities were predicted within 8%. A study was then done to identify initial snapshots for use in developing a ROM that can accurately predict results across a wide range of inputs. From this, a step function was identified as being the most accurate and computationally efficient. The ROM was further investigated by a discretization study to assess computational gains in both 1D and 3D models as a function of mesh density. The lower mesh densities in the 1D and 3D ROMs resulted in moderate computational times (up to 40 times faster). However, highly discretized systems such as 5000 nodes in 1D and 125000 nodes in 3D resulted in computational gains on the order of 2000 to 3000 times faster than the full order model. / Ph. D. / Heat transfer systems contain many sources of nonlinearity including temperature dependent material properties, radiation boundary conditions, and internal source terms. Despite progress in numerical simulations, producing accurate models that can predict these complex behaviors are still limited by the time it takes to compute meaningful results. Accurate models can be produced quickly by utilizing some mathematical techniques whereby the original problem is projected into a smaller sub-space and solved with fewer variables. The full space results are then determined by undoing the projection on the results. This is one approach from a larger knowledge base called Reduced Order Modeling (ROM) techniques. For discretized systems, the Singular Value Decomposition technique is the preferred approach but has had limited success on treating nonlinearities. In this research, the treatment of nonlinear temperature dependent material properties was incorporated using the projection approach, tailored to treat the specific material property nonlinearity as well as radiation boundary conditions, temperature dependent source heating terms, and complex geometry. While the approach presented here is specific to the heat transfer application, other problems of a similar form can be handled in the same manner. From the results, low conductivity, highly nonlinear material properties were predicted by the ROM within 1% of full order models, and additional nonlinearities were predicted within 8%. A study was then done to identify initial snapshots for use in developing a ROM that can accurately predict results across a wide range of inputs. From this, a step function was identified as being the most accurate and computationally efficient. The ROM was further investigated by a discretization study to assess computational gains in both 1D and 3D models as a function of mesh density. The lower mesh densities in the 1D and 3D ROMs resulted in moderate computational times (up to 40 times faster). However, highly discretized systems such as 5000 nodes in 1D and 125000 nodes in 3D resulted in computational gains on the order of 2000 to 3000 times faster than the full order model.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/74885 |
| Date | 01 February 2017 |
| Creators | Free, Jillian Chodak |
| Contributors | Mechanical Engineering, Lattimer, Brian Y., Diller, Thomas E., Huxtable, Scott T., Ekkad, Srinath, Staples, Anne E. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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