Module 6 Case Studies 1
Lecture 6.1 A CFD Code for Turbomachinery Flows 2
Development of a CFD Code The lecture material in the previous Modules help the student to understand the domain knowledge required for building a CFD code for turbomachinery applications. In other words, the knowledge acquired maybe used to solve turbomachinery problems through computational methods. It must be appreciated that the actual development of CFD code is a team work of several specialists. Apart from the domain knowledge experts, who are basically scientists/engineers with a good background in fluid-dynamics and other allied areas, system engineers with special programming skills are required to work in a group to develop a CFD code. 3
In Lecture 1.0, a structure has been proposed for the development of a code. Following the same structure, a methodology for developing an in-house code is narrated in the following table. Indeed, in-house codes have been developed with the help of several research students over a long period. The case studies that are illustrated from Lectures 6.2 to 6.11 are the byproducts of these efforts. The readers of this course are advised to develop their own inhouse code and verify their results following the examples in the sequence presented in Lectures 6.2 to 6.11. 4
Case Studies Using In-House Code Problem statement Mathematical formulation Available information about the problem on turbomachinery cascades; Expected outcome Typical problems of inviscid and viscous flows through stationary and rotating turbomachinery cascades with and without mutual interactions between stator and rotor are posed in Lectures 6.2 to 6.11. Initial Boundary value Problem By understanding the physics of the problem from the problem statement, the governing equations are formulated along with the initial and boundary conditions. Reference is made to lectures in Module 1, for the mathematical formulation of different problems. The sign of the Eigen values of the characteristic Jacobian of the inviscid flux vector of the governing system of equations. This sign is important of deciding as to how the inlet and outlet boundary conditions can be fed to the domain. 5
Geometry model Mesh generation Discretization of governing equations Geometry model and input conditions for flow as defined by the physics of the problem Most of the problems discussed in Lectures 6.2 to 6.11 are related to turbomachinery cascades. Other geometry models for validation and such other purposes are also given. Reference is made to Module 2 for development of geometry models. Methodology of generating nodes/cells, time instants Methods discussed in Module 3 are used to generated meshes for the geometry models developed. The cells and nodes are stored in an edge based data structure. Finite difference and finite volume methods for time and space discretizations. All the case studies are based on finite volume method using AUSM (flux vector splitting) technique given in Module 5. For time discretization Euler s method is employed where applicable. 6
Algebraic solver Implementation Solvers and knowledge of handling large discrete data Steady state solution: In a time-marching method for steady state calculation, computations are carried out using the spatially varying time steps of different cells. Unsteady state solution: the minimum of all cells from the CFL criterion is used. CFD software An in-house code is developed with the following features: (i) Multiblock grid structure. (ii) Grid transparent edge based data structure. (iii) Usage of mixed cells. (iv) Evaluation of fluxes through fictitious boundaries. (v) Scheme based on AUSM for unstructured and hybrid grids. (vi) Time-marching method for steady state calculations. The results presented in the following Lecture 6.2 to 6.11 are an outcome of the application of this in-house code. 7
Simulation run Verification Post processing Parameters, stopping criteria for stopping the iterations Convergence of numerical solution is tested by monitoring the value of an error parameter. Model validation / adjustment as required Code has been validated against benchmark solutions and literature data. Analysis of data and presentation Contours and vector plots, graphical displays. 8
Case Studies The following case studies are discussed in Lecture 6.2 to 6.11. The authors believe that the experience gained in solving these case studies elaborated in the subsequent lectures will help the reader to take up more challenging problems in turbomachinery. 1. Steady internal inviscid flows: Subsonic Flow Over a Circular Bump in Lecture 6.2. Supersonic Flow Over a Circular Bump in Lecture 6.2. Transonic Flow Over a Circular Bump in Lecture 6.2. Transonic Flow Through a NACA0012 Airfoil Cascade in Lecture 6.3. 2. Unsteady internal inviscid flows: Channel flow with a forward facing step in Lecture 6.4. 9
3. Internal viscous flows: Turbulent flow through a turbine cascade in Lecture 6.5. 4. Steady interacting flow between stator and rotor: Inviscid subsonic flow of a single stage axial turbine in Lecture 6.6. Inviscid subsonic flow of a one and half stage axial turbine in Lecture 6.7. Inviscid transonic flow of a single stage axial turbine in Lecture 6.8. Turbulent flow of a single stage transonic axial turbine in Lecture 6.9. 5. Unsteady interacting flow between stator and rotor: Unsteady turbulent flow of a single stage transonic axial turbine in Lecture 6.10. 6. Inverse design of a compressor cascade in Lecture 6.11. 10
END OF LECTURE 6.1 11