Real-world Experiments are often multi-response. The correlation between responses and the cost of experimenting lead one to cast the problem as a multi-response model. Generation of a multi-response optimal Design is a challenging problem. There exist three general algorithms and all of them generate approximate Design and no method for multi-response n-exact Design has been cited in the literature. The existing methods have some drawbacks such as the necessity of solving many optimization problems in the process of generating an optimal Design, cumbersome manual operations and the complexity of performing sensitivity analysis. In this paper, we propose a Semi-Definite Programming (SDP) model for multi-response optimal Design. The proposed method is efficient because of solving a one shot optimization problem instead of many optimization problems, enjoying the recent advancements of interior-point solution algorithms and elimination of cumbersome manual operations. The proposed model has been tested on several test problems and proved to be very efficient since the optimal Designs were found very quickly in all cases. The robustness of the generated Designs with respect to the variance-covariance matrix is also assessed for those test problems in order to show how sensitivity analysis can be performed. The characteristics of the proposed method are also compared with those of other existing methods.

Numerical modeling of internal nozzle flow can be regarded as an essential investigation in the field of gasoline direct injection system of combustion engines since it is directly connected with fuel spray atomization and subsequently efficiency of exhaust gas emission. Internal nozzle flow can be changed and formed according to several parameters such as; system pressure, chosen fuel type, the orientation of spray holes according to injector axis, conicity of spray holes and distribution of spray holes on valve-seat, etc. The changes in these parameters also affect the formation of cavitation inside of whole domain, spray angle and create wall-wetting on the spray hole surfaces. The present work investigates the parameter and Design analysis in the valve-seat region of direct gasoline injection (GDI) injector using Computational Fluid Dynamics (CFD) and Design of Experiments (DOE). CFD is employed to study the behaviors of internal flow inside the valve-seat region according to several Design parameters, whereas a mixed-level factorial Design is used to test the significance of the effects on the response variables. In conclusion, the effects of the most significant factors on response parameters as amount of vapor formation, spray (Tau) angle, and pre-hole wall wetting are determined for further efficient Design.

The wire drawing process is an essential technique in mechanical and industrial operations in lots of applications. Therefore, the current article aims to employ different methodologies (i.e., experimental, numerical) to investigate the optimum operating conditions and lubrication type on the surface and mechanical quality of these wires. By examining the effects of die angle, drawing speed, and lubricant type on wire drawing outcomes, the research not only provides valuable insights into process optimization but also contributes to reducing defects and enhancing wire properties. Results demonstrate significant variations in tensile strength based on these parameters, highlighting the need for precise control over process variables to achieve desired outcomes consistently. Moreover, statistical analyses reveal substantial relationships between process variables and tensile strength, offering a deeper understanding of the underlying mechanisms driving wire drawing performance. Overall, this research not only advances the understanding of wire drawing processes but also offers practical insights for improving wire manufacturing techniques, ultimately bolstering product quality, reducing costs, and increasing competitiveness in the global market.