H. Magnus Andersson, T. Staffan Lundström and B. Rikard Gebart
The focus is set on the development and evaluation of a numerical mgodel describing the impregnation stage of a method to manufacture fibre reinforced polymer composites, namely…
Abstract
The focus is set on the development and evaluation of a numerical mgodel describing the impregnation stage of a method to manufacture fibre reinforced polymer composites, namely the vacuum infusion process. Examples of items made with this process are hulls to sailing yachts and containers for the transportation industry. The impregnation is characterised by a full 3D flow in a porous medium having an anisotropic, spatial‐ and time‐dependent permeability. The numerical model has been implemented in a general and commercial computational fluid dynamic software through custom written subroutines that: couple the flow equations to the equations describing the stiffness of the fibre reinforcement; modify the momentum equations to account for the porous medium flow; remesh the computational domain in each time step to account for the deformation by pressure change. The verification of the code showed excellent agreement with analytical solutions and very good agreement with experiments. The numerical model can easily be extended to more complex geometry and to other constitutive equations for the permeability and the compressibility of the reinforcement.
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Jörgen Burman and B. Rikard Gebart
The overall pressure drop in an axisymmetric contraction is minimised using two different grid sizes. The transition region was parameterised with only two design variables to…
Abstract
The overall pressure drop in an axisymmetric contraction is minimised using two different grid sizes. The transition region was parameterised with only two design variables to make it possible to create surface plots of the objective function in the design space, which were based on 121 CFD calculations for each grid. The coarse grid showed to have significant numerical noise in the objective function while the finer grid had less numerical noise. The optimisation was performed with two methods, a Response Surface Model (RSM) and a gradient‐based method (the Method of Feasible Directions) to study the influence from numerical noise. Both optimisation methods were able to find the global optimum with the two different grid sizes (the search path for the gradient‐based method on the coarse grid was able to avoid the region in the design space containing local minima). However, the RSM needed fewer iterations in reaching the optimum. From a grid convergence study at two points in the design space the level of noise appeared to be sufficiently low, when the relative step size is 10–4 for the finite difference calculations, to not influence the convergence if the errors are below 5 per cent for this contraction geometry.
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John Bergström and Rikard Gebart
The potential for overall efficiency improvements of modern hydro power turbines is a few percent. A significant part of the losses occurs in the draft tube. To improve the…
Abstract
The potential for overall efficiency improvements of modern hydro power turbines is a few percent. A significant part of the losses occurs in the draft tube. To improve the efficiency by analysing the flow in the draft tube, it is therefore necessary to do this accurately, i.e. one must know how large the iterative and the grid errors are. This was done by comparing three different methods to estimate errors. Four grids (122,976 to 4,592 cells) and two numerical schemes (hybrid differencing and CCCT) were used in the comparison. To assess the iterative error, the convergence history and the final value of the residuals were used. The grid error estimates were based on Richardson extrapolation and least square curve fitting. Using these methods we could, apart from estimate the error, also calculate the apparent order of the numerical schemes. The effects of using double or single precision and changing the under relaxation factors were also investigated. To check the grid error the pressure recovery factor was used. The iterative error based on the pressure recovery factor was very small for all grids (of the order 10–4 percent for the CCCT scheme and 10–10percent for the hybrid scheme). The grid error was about 10 percent for the finest grid and the apparent order of the numerical schemes were 1.6 for CCCT (formally second order) and 1.4 for hybrid differencing (formally first order). The conclusion is that there are several methods available that can be used in practical simulations to estimate numerical errors and that in this particular case, the errors were too large. The methods for estimating the errors also allowed us to compute the necessary grid size for a target value of the grid error. For a target value of 1 percent, the necessary grid size for this case was computed to 2 million cells.