Loading...

Development of discontinuous Galerkin method on Unstructured Grids for simulation of cavitating Flows

Haji Hassanpour, Mahya | 2019

549 Viewed
  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 52684 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Hejranfar, Kazem
  7. Abstract:
  8. In this work, a high-order nodal discontinuous Galerkin method (NDGM) is applied and assessed for the simulation of the non-cavitating/cavitating flows. At first, the basic formulation of the NDGM is explained and the properties of the solution method of the NDGM are studied by solving the one-dimensional wave equation. Then, the one-fluid approach with the thermal effects is used to properly model the cavitation phenomenon. Here, the spatial and temporal derivatives in the system of governing equations are discretized using the NDGM and the third-order TVD Runge–Kutta method, respectively. Various numerical fluxes such as the Roe, Rusanov, HLL, HLLC and AUSM+-up and two discontinuity capturing methods, namely, the generalized MUSCL limiter and a generalized exponential filter are formulated and implemented in the solution algorithm of the NDGM and their accuracy and performance are examined by simulating different one-dimensional non-cavitating and cavitating flow problems. The high-order NDGM is also developed and assessed for the simulation of the 2D incompressible flows on triangle elements. The governing equations are the 2D incompressible Navier–Stokes equations with the artificial compressibility method. The discretization of the spatial derivatives in the resulting system of equations is made by the NDGM and the time integration is performed by applying the implicit dual-time stepping method. Three numerical fluxes, namely, the local Lax–Friedrich, Roe and AUSM+-up are formulated and applied to assess and compare their accuracy and performance in the simulation of incompressible flows using the NDGM. Several steady and unsteady incompressible flow problems are simulated to examine the accuracy and robustness of the proposed solution methodology. Indications are that the NDGM applied for solving the incompressible Navier–Stokes equations with the artificial compressibility approach and the implicit dual-time stepping method is accurate and robust for the simulation of steady and unsteady incompressible flow problems. In addition, the NDGM is also extended in three-dimensions and its accuracy and robustness are verified by solving different non-cavitating problems. Then, the NDGM is applied and examined for the simulation of the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier‐Stokes equations on the triangle/tetrahedral elements. The formulation used here is based on the homogeneous equilibrium model considering the continuity and momentum equations together with the transport equation for the vapor phase with applying appropriate mass transfer terms for calculating the evaporation/condensation of the liquid/vapor phase. The spatial derivative terms in the resulting system of equations are discretized by the NDGM and an implicit dual‐time stepping method is used for the time integration. An artificial viscosity approach is implemented and assessed for capturing the steep discontinuities in the interface between the two phases. The accuracy and robustness of the proposed method in solving the preconditioned multiphase Euler/Navier‐Stokes equations are examined by the simulation of different axisymmetric, two‐ and three-dimensional cavitating flows. A sensitivity study is also performed to examine the effects of different numerical parameters on the accuracy and performance of the solution of the NDGM. Indications are that the solution methodology proposed and applied here based on the NDGM with the implicit dual‐time stepping method and the artificial viscosity approach is accurate and robust for the simulation of the inviscid and viscous cavitating flows
  9. Keywords:
  10. Discontinuous Galerkin ; Numerical Flux ; Artificial Compressibity Method ; Cavitation Flow ; Perconditioned Equations ; Discontinuity Capturing Method

 Digital Object List

 Bookmark

No TOC