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High-Order Unsteady Heat Transfer with the Harmonic Balance Method

Knapke, Robert
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1427962937

Abstract Details

2015, PhD, University of Cincinnati, Engineering and Applied Science: Aerospace Engineering.
Despite the significant advancements in computational fluid dynamics, modeling turbomachinery flows remains extremely difficult. The challenges include complex unsteady blade row interactions, large thermal gradients, and complex geometries. During the design process, simplifications and approximations are necessary to reduce the computational cost. Two common simplifications are the use of adiabatic boundary conditions and steady methods for resolving the flow field in multistage turbomachinery. The Harmonic Balance (HB) method is an efficient way to simulate periodic unsteady phenomena. Compared to traditional time-marching methods, the HB method reduces the computational cost by considering only the dominant frequencies of the solution field. Using a Fourier series representation of the solution variables, an unsteady governing equation transforms into a series of steady-like equations. The cost is further reduced when considering multistage turbomachinery. Unlike a time-marching method, which requires periodic boundaries, the HB method models a single blade passage per blade row. A phase lag condition is applied instead of a periodic condition. At the junction between blade rows, an interface resolves the relative motion and any passage mismatch. Assuming the heat transfer of wall boundary conditions is, by definition, non-physical. Assuming no heat transfer (an adiabatic wall) is certainly wrong for turbomachinery flows because of the large thermal gradients. An constant temperature wall can provide a better approximation, but for complex geometries, the temperature is not known a priori. The most accurate approach involves modeling both the fluid and solid domains, which is called Conjugate Heat Transfer (CHT). This can be performed in several ways, but the most stable method is one in which the fluid and solid are strongly coupled. This strong coupling is achieved by using the same discretization in both domains. This dissertation details an approach for accurately and efficiently simulating the unsteady heat transfer in turbomachinery flows. The HB and CHT methods are developed within a framework that uses a high-order Discontinuous Galerkin (DG) spatial discretization and a versatile Chimera overset scheme. The implemented HB method is fully linearized, allowing the use of an efficient Quasi-Newton solver. The HB equations are coupled within a linear system that includes the linearized HB pseudo-spectral operator. Phase lag and relative motion interfaces are included, hence the computational domain of multistage turbomachinery simulations is reduced to one passage per blade row. Modeling turbulent flows is achieved with the Spalart-Allmaras turbulence model. A strongly coupled CHT method is introduced. The solid and fluid domains are both discretized with the DG method. The fluid to solid interface enforces a consistent wall temperature and heat flux. The Harmonic Balance method, the Conjugate Heat Transfer method, and the Spalart-Allmaras turbulence model are independently verified using a series of test cases. In addition, CHT on curved 3D geometries is performed for the first time. Lastly, unsteady heat transfer is simulated using the combination of the HB and CHT methods. These test cases demonstrate the fast convergence and accurate modeling of the implemented methods. This work provides the basis for the accurate and efficient simulation of turbomachinery flows.
Mark Turner, Sc.D. (Committee Chair)
John Benek, Ph.D. (Committee Member)
Shaaban Abdallah, Ph.D. (Committee Member)
Paul Orkwis, Ph.D. (Committee Member)
241 p.
Aerospace Materials
harmonic balance; conjugate heat transfer; discontinuous galerkin

Recommended Citations

Citations

  • Knapke, R. (2015). High-Order Unsteady Heat Transfer with the Harmonic Balance Method [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1427962937

    APA Style (7th edition)

  • Knapke, Robert. High-Order Unsteady Heat Transfer with the Harmonic Balance Method. 2015. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1427962937.

    MLA Style (8th edition)

  • Knapke, Robert. "High-Order Unsteady Heat Transfer with the Harmonic Balance Method." Doctoral dissertation, University of Cincinnati, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1427962937

    Chicago Manual of Style (17th edition)

ucin1427962937
1,035
© 2015, some rights reserved.Creative Commons License High-Order Unsteady Heat Transfer with the Harmonic Balance Method by Robert Knapke is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.