High‐Pressure Reverse Osmosis for Industrial Water Recycling: Permeate‐Sided Pressure Drop as Performance‐Limiting Factor

The objective of this study is to design spacers using fluid topology optimization in 2D crossflow Reverse Osmosis (RO) membrane channel to improve the performance of RO processes. This study is an initial attempt to apply topology optimization to designing spacers in RO membrane channel. The performance was evaluated by the quantity of permeate flux penetrating both upper and lower membrane surfaces. A coupled Navier-Stokes and Convection-Diffusion model was employed to calculate the permeate flux. To get reliable solutions, stabilization methods were employed with standard finite element method. The nine reference models which consist of the combination of circle, rectangular, triangle shape and zigzag, cavity, submerge configuration of spacers were simulated. Such models were compared with new model designed by topology optimization. The permeate flux at both membrane surfaces was determined as an objective function. In addition, permissible pressure drop along the channel and spacer volume were used as constraints. As a result of topology optimization as the permissible pressure drop changes in channel, characteristics of spacer design development was founded. Spacer design based on topology optimization was reconstructed to a simple one considering manufactuability and characteristics of development spacer design. When a simplified design was compared with previous 9 models, new design has a better performance in terms of permeate flux and wall concentration at membrane surface.

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Influence of Different Parametrizations on the Optimum Design of a High Pressure Turbine Blade Firtree

Volume 7A: Structures and Dynamics ◽

10.1115/gt2016-56749 ◽

2016 ◽

Author(s):

Frank Wagner ◽

Arnold Kühhorn ◽

Thomas Weiss ◽

Dierk Otto

Keyword(s):

High Pressure ◽

Turbine Blade ◽

Complex Geometry ◽

Three Dimensional ◽

Parametric Models ◽

Limiting Factor ◽

High Pressure Turbine ◽

The Creation ◽

High Flexibility ◽

Critical Regions

Today the design processes in the aero industry face many challenges. Apart from automation itself, a suitable parametric geometry setup plays a significant role in making workflows usable for optimization. At the same time there are tough requirements against the parametric model. For the lowest number of possible parameters, which should be intuitively ascertainable, a high flexibility has to be ensured. Within the parameter range an acceptable stability is necessary. Under these constraints the creation of such parametric models is a challenge, which should not be underestimated especially for a complex geometry. In this work different kinds of parametrization with different levels of complexity will be introduced and compared. Thereby several geometry elements will be used to handle the critical regions of the geometry. In the simplest case a combination of lines and arcs will be applied. These will be replaced by superior elements like a double arc construct or different formulations of b-splines. There will be an additional focus on the variation of spline degree and control points. To guarantee consistency a set of general parameters will be used next to the specific ones at the critical regions. The different parameter boundaries have a influence on the possible geometries and should therefore be tested separately before an optimization run. The analysis of the particular parametrization should be compared against the following points: • effort for the creation of the parametrization in theory • required time for the implementation in the CAD software • error-proneness/robustness of the parametrization • flexibility of the possible geometries • accuracy of the results • influence of the number of runs on the optimization • comparison of the best results Even though this assessment matrix is only valid for the considered case, it should show the general trend for the creation of these kinds of parametric models. This case takes a look at a firtree of a high pressure turbine blade, which is a scaled version of the first row from a small to medium aero engine. The failure of such a component can lead to a critical engine failure. For that reason, the modeling/meshing must be done very carefully and the contact between the blade and the disc is of crucial importance. It is possible to use scaling factors for three dimensional effects to reduce the problem to a two dimensional problem. Therefore the contact description is shortened from face-to-line to line-to-point. The main aim of the optimization is the minimization of the tension (notch stress) at the inner bends of the blade respectively at the outer bends of the disc. This has been the limiting factor in previous investigations. At this part of the geometry the biggest improvement are expected from a superior parametrization. Another important constraint in the optimization is the pressure contact (crushing stress) between blade and disc. Additionally the geometry is restricted with measurements of the lowest diameter at specific fillets to fulfill manufacturing requirements.

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