Numerical Simulation Of The Cavity Flow Oscillation Based On The Fully Implicit Algorithm

Cavity flow problems exist in many aerospace applications with a great engineering value; for example, there are highly unsteady fluid motions around aircraft weapon bays and wheel wells. Additionally, there are many theoretical issues in this field, including unsteady flow, fluid dynamic instability and acoustics-vortex interaction, etc. Therefore, it is of significance to study the cavity flow in both theoretical aspects and engineering apllications. In this dissertation, a fully implicit unfactored algorithm of three-dimensional Euler and Navier-Stokes equations is firstly developed and tested on multiblock curvilinear meshes. The parallel algorithms on the multiblock grids and unstructured meshes are also developed in the thesis. The self-sustained oscillatory motion of the shear layer from the cavity flow is then numerically simulated and studied using the fully implicit unfactored methods with the revised B-L turbulent model. The main contents of the dissertation are as follows:On multiblock curvilinear meshes,a fully implicit unfactored algorithm of three-dimensional Euler and Navier-Stokes equations is developed and tested. The convective and viscous terms are discretized using the Roe's scheme and the center scheme, respectively. The large-scale sparse linear system arising from each implicit time step is solved by GMRES* method combined with the block incomplete lower-upper preconditioner. A dual time method is applied to time discretization for unsteady calculations. In order to reduce memory requirements and matrix-vector operation counts, an appropriately approximate method for the derivation of Jacobian matrix is applied in the present work, which counts to a half of the computational overheads of the exact Jacobian matrix solution.Parallel algorithm for the fully implicit unfactored method of Euler equations based on the multiblock grids is studied in the paper. A load balancing method is presented in order to increase the parallel efficiency. The statistics of wall time and parallel efficiency after the balancing demonstrates the effectiveness of the method. For the property of the large-scale parallel computers used, an estimation method for the computional and communicational time is obtained based on the least mean square approximation. The numerical results for the different flow field simulations show good agreements between parallel and serial calculations. In addition, the technique of parallel unstructured mesh generation is also proposed. Lohner's advancing front domain-splitting algorithm is improved so that the subgrids and their boundaries are more favorable for grid generation. The improved wave-front domain splitting algorithm is then applied to the domain decompositions of the flow field. According to the algorithm improved, parallel algorithms to solve Euler equations on the unstructured grids are presented. Comparisons between the multi-domain and single domain demonstrate the high efficiency of the algorithms.Using the above fully implicit unfactored methods with the revised B-L turbulent model, numerical simulations are implemented for supersonic, transonic and subsonic flows around three dimensional open cavities. The self-sustained oscillatory motion of the shear layer is displayed and the influence of the inlet boundary condition on the oscillation is discussed in detail. Comparison of numerical calculations demonstrates that the turbulent profile and characteristic boundary at the inlet can lead to better results than the laminar profile. Then, numerical simulations of supersonic flows over open cavities with a store are carried out in the paper. The flow-induced oscillation of the free shear layer is studied for this case and a comparison is made with the phenomena of the cavity without a store. The pressure fluctuation is pertinent to the store position in the cavity, which is demonstrated by the diagram of pressure and time as well as the distribution of the static pressure coefficients in the stream direction of the cavity floor and in the normal direction of the rear wall. Finally, the self-sustained oscillatory motion of the shear layer is revealed for the plates with different lengths within the cavity. The plate in the cavity isolates the shear layer and the cavity, therefore reducing the coupling between the cavity pressure fluctuations and the shear layer. The oscillation of the shear layer decreases as the plate length increases. Based on the different characteristic lengths, Heller's frequency equation is modified in the paper. The frequencies predicted by the modified equation agree with those by the close-box acoustic model. For completeness, several comparisons demonstrate the validity of the modified equation.