Numerical Investigations on the Leakage Flow Characteristics of Brush Seal Based on the Three-Dimensional Staggered Tube Bundle Model

To accurately predict the leakage flow and resistance characteristics of brush seals, the multiblock structured mesh and the mesh motion technique are applied to the three-dimensional (3D) staggered tube bundle model of brush seals. The multiblock structured mesh can easily add nodes and set boundary layers in the interbristle gap between adjacent bristles, which can ensure good mesh quality (orthogonal angle and expansion ratio). The mesh motion technique realizes the overall axial compactness of the bristle pack. The effects of pressure ratio Rp, sealing clearance c, and bristle pack compactness on the leakage flow and resistance characteristics are investigated. To analyze the aerodynamic resistance of the brush seals, Euler number (Eu) is applied in this study. The numerical results are in good agreement with the experimental data. Thus, the accuracy of the presented numerical method is validated. For the contacting brush seal, ΔSx, i has a significant effect on the leakage flow rate reduction. For the clearance brush seal, ΔSx, i has little effect on the leakage flow rate reduction. The leakage flow passing through the sealing clearance keeps almost constant. As for aerodynamic resistance, the presence of the sealing clearance can effectively convert the pressure energy of the leakage flow into the kinetic energy. As a result, the leakage flow velocity exiting the bristle pack of the clearance brush seal is 1.5 to 2.0 times larger than that of the contacting brush seal. Although the existence of the sealing clearance obviously increases the leakage flow rate, it effectively reduces the aerodynamic forces acting on the bristles. The developed numerical approach based on the three-dimensional staggered tube bundle model and multiblock structured mesh can serve as a technical method for analysis of the sealing mechanisms of brush seals.

A reconstructed discontinuous Galerkin method for compressible flows on moving curved grids

A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and invalid elements near moving boundaries.

A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion

Good mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels $$t_n$$ t n and $$t_{n+1}$$ t n + 1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at $$t_n$$ t n . While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

A Reconstructed Discontinuous Galerkin Method for Compressible Flows on Moving Curved Grids

A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and elements near moving boundaries.

A Reconstructed Discontinuous Galerkin Method for Compressible Flows on Moving Curved Grids

A high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for compressible inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation on moving and deforming unstructured curved meshes. Taylor basis functions in the rDG method are defined on the time-dependent domain, where the integration and computations are performed. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. A radial basis function (RBF) interpolation method is used for propagating the mesh motion of the boundary nodes to the interior of the mesh. A third order Explicit first stage, Single Diagonal coefficient, diagonally Implicit Runge-Kutta scheme (ESDIRK3) is employed for the temporal integration. A number of benchmark test cases are conducted to assess the accuracy and robustness of the rDG-ALE method for moving and deforming boundary problems. The numerical experiments indicate that the developed rDG method can attain the designed spatial and temporal orders of accuracy, and the RBF method is effective and robust to avoid excessive distortion and elements near moving boundaries.

Structured Mesh Generation and Numerical Analysis of a Scroll Expander in an Open-Source Environment

The spread of the organic rankine cycle applications has driven researchers and companies to focus on the improvement of their performance. In small to medium-sized plants, the expander is the component that has typically attracted the most attention. One of the most used types of machine in this scenario is the scroll. Among the other methods, numerical analyses have been increasingly exploited for the investigation of the machine’s behaviour. Nonetheless, there are major challenges for the successful application of computational fluid dynamics (CFD) to scrolls. Specifically, the dynamic mesh treatment required to capture the movement of working chambers and the nature of the expanding fluids require special care. In this work, a mesh generator for scroll machines is presented. Given few inputs, the software described provides the mesh and the nodal positions required for the evolution of the motion in a predefined mesh motion approach. The mesh generator is developed ad hoc for the coupling with the open-source CFD suite OpenFOAM. A full analysis is then carried out on a reverse-engineered commercial machine, including the refrigerant properties calculations via CoolProp. It is demonstrated that the proposed methodology allows for a fast simulation and achieves a good agreement with respect to former analyses.