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106 designer also can investigate the influence of more than one parameter at the same time. Lastly, a novel MOC is integrated to explore the performance of the turbine at different operating conditions while the geometry is fixed. 5.2 Optimisation Algorithm Although DoEC can be used to optimise the turbine, it is a time-consuming technique because the user is required to manually change the input parameters for each single run. However, DoEC is a helpful technique when applied as a parametric study to explore the effects of a single or a combination of variables on the geometry and performance of the turbine. An optimisation technique is developed and coupled to the design procedure. The OC is essential because it is used to optimise the turbine and eventually to achieve better ORC performance. This code is a genetic optimisation technique that eliminates the manual iterative procedure. The MATLAB optimisation ToolboxTM® [236] is used to optimise the geometry and performance of the turbine under specified design conditions. This toolbox provides functions to maximise objectives and satisfy the user- defined constraints. It includes solvers for linear programming, mixed- integer linear programming, quadratic programming, nonlinear optimisation and nonlinear least squares. Fmincon, which is a constrained nonlinear minimisation or maximisation algorithm, is the solver used in this study. This algorithm finds the constrained minimum of a scalar function of several variables at an initial estimate. The objective function is shown in equation (5-1). (5-1) 𝛾=𝑎𝜂 +𝑎𝑊 +𝑎 𝑜𝑢𝑡. 0 𝑡𝑠 0 𝑜𝑢𝑡 2𝑑𝑚𝑎𝑥 𝑊 The multipliers 𝑎0 , 𝑎1 and 𝑎2 are used to define the objective function. Turbine total to static efficiency 𝜂𝑡𝑠, expander power output 𝑊𝑜𝑢𝑡 and the expander power over the turbine size 𝑊𝑜𝑢𝑡 are the important objective 𝑑𝑚𝑎𝑥 functions of the turbine. For example, if the turbine total to static efficiency 𝜂𝑡𝑠 is selected as the objective function, then the multipliers become asPDF Image | Automotive Radial Turbine Expander Design WHR
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