Moving mesh finite difference solution of non-equilibrium radiation diffusion equations

A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves nonlinear diffusion coefficients and its solutions stay positive for all time when they are positive initially. Nonlinear diffusion and preservation of solution positivity pose challenges in the numerical solution of the model. A coefficient-freezing predictor-corrector method is used for nonlinear diffusion while a cutoff strategy with a positive threshold is used to keep the solutions positive. Furthermore, a two-level moving mesh strategy and a sparse matrix solver are used to improve the efficiency of the computation. Numerical results for a selection of examples of multi-material non-equilibrium radiation diffusion show that the method is capable of capturing the profiles and local structures of Marshak waves with adequate mesh concentration. The obtained numerical solutions are in good agreement with those in the existing literature. Comparison studies are also made between uniform and adaptive moving meshes and between one-level and two-level moving meshes.Comment: 29 page

Implementation and Validation of the Spalart-Allmaras Turbulence Model in the PMB3D Code. G.U. Aero Report 0213

The Spalart-Allmaras one-equation turbulence model has been implemented and validated in the PMB3D code, which is a parallel multi-block computational fluid dynamics (CFD) code developed at the University of Glasgow. Different test cases including turbulent flows around RAE2822 Cases 9 and 10, NLR-F5 wing, ONERA A aerofoil, AGARD Case CT2 and 18% circular arc aerofoil have been performed. In general when compared with the experimental data, the performance of the S-A model is good. For some test cases, results of this model are also compared with the k—w two-equation turbulence model. It has been observed that the S-A model is similar to the two-equation k — w model in attached flows

China has reached the lewis turning point

In the past several years, labor shortages in China have become an issue. However, there is heated debate as to whether China has passed the Lewis turning point and moved from a period of unlimited supply to a new era of labor shortage. Most empirical studies on this topic focus on estimation of total labor supply and demand. Yet the poor quality of China’s labor statistics leaves the debate open. In this paper, China’s position along the Lewis continuum is examined though primary surveys of wage rates, which offer a more reliable statistic than employment data. Our results show a clear rising trend in real wage rates since 2003. The acceleration of real wages even in slack seasons indicates that the era of surplus labor is over. This finding has important policy implications for China’s future development.dual economy, employment data, Labor market, Lewis model, Supply and demand, surplus labor, wage rates,

Implementation and Validation of the Spalart-Allmaras Turbulence Model in the PMB3D Code. G.U. Aero Report 0213

The Spalart-Allmaras one-equation turbulence model has been implemented and validated in the PMB3D code, which is a parallel multi-block computational fluid dynamics (CFD) code developed at the University of Glasgow. Different test cases including turbulent flows around RAE2822 Cases 9 and 10, NLR-F5 wing, ONERA A aerofoil, AGARD Case CT2 and 18% circular arc aerofoil have been performed. In general when compared with the experimental data, the performance of the S-A model is good. For some test cases, results of this model are also compared with the k—w two-equation turbulence model. It has been observed that the S-A model is similar to the two-equation k — w model in attached flows

Numerical study of film cooling in hypersonic flows

In this thesis, a numerical study of film cooling in hypersonic laminar and turbulent flows has been performed using an in-house Navier-Stokes solver. The aim of this computational work is to investigate the mechanism and effectiveness of film cooling in hypersonic laminar and turbulent flows. Hypersonic flow over a flat plate without film cooling was first studied to provide a reference datum to check the effectiveness of film cooling. For laminar film cooling (M¥ = 9.9), three different primary flow conditions were first used for validation. The inclusion of the development of the flow in the plenum chamber upstream of the slot was found to provide better heat prediction than a uniform boundary condition at the slot exit. Detailed information of the flow field including velocity profile, Mach contour, temperature contour and heat transfer rate was presented. The mechanism of film cooling has been revealed according to the plots of calculated velocity profiles, Mach contours and temperature contours downstream of the slot. The coolant fluid was found to affect the primary boundary layer in two ways: 1) initially a separate layer established by the coolant fluid itself in the near slot area, 2) later a mixing layer between the primary and coolant flow streams. Then five coolant injection rates between 2.95 x 10-4 and 7.33 x 10-4kg/s and three slot heights 0.8382, 1.2192, 1.6002 mm, were examined in hypersonic laminar film cooling. For turbulent film cooling (M¥ = 8.2), for the geometry used in the experiment, the injection at an angle of 20° was found to be appropriate. Different turbulence models including Wilcox's k - w model. Menter's baseline and SST model have been tested. It is concluded that the Wilcox's k - w turbulence model with dilatation-dissipation correction provides the best heat prediction. Again, five coolant injection rates varies from 5.07 x 10-4 to 30.69 x 10-4 kg/s and three slot heights (the same as studied in the laminar film cooling) were studied to check the influence on film cooling effectiveness. Both the coolant and the primary flow were air. Film cooling was found to be an effective way to protect wall surfaces that are exposed under a high heat transfer environment especially in hypersonic laminar flow. Increasing the coolant injection rate can obviously increase the film cooling effectiveness. Again, this works better in laminar flow than in turbulent flow. The coolant injection rate in turbulent flow should be considered to be high enough to give good heat protection. Slot height in both laminar and turbulent flows under the flow conditions in this study was found to be less important, which means other factors can be considered in priority when constructing film cooling systems. With the application of curve fitting, the cooling length was described using power laws according to curve fitting results. A two-equation film coating model has been presented to illustrate the relation between the film cooling effectiveness and the parameter x/(h/m). For film cooling effectiveness in log-log coordinates, a second-order polynomial curve can be used to fit the laminar flows, whilst a straight line is suitable for the turbulent flows

Visualisation and Grid applications of electromagnetic scattering from aircraft

Proceedings of the 2003 UK e-Science All Hands Meeting, 31st August - 3rd September, Nottingham UKElectromagnetic scattering behaviour plays a central role in the design of aircraft and other complex structures. This paper describes progress on visualisation tools in this area and on initial development of a web portal to enable scientists at remote locations to collaborate