Specific tools and capabilities are employed to achieve optimal design, addressing two primary challenges: cost reduction and time-to-project delivery acceleration. The conventional project development workflow typically begins with a design based on legacy designs, empirical data, experience, or literature. A prototype is then created and tested. Depending on the results, the design may meet performance metrics or require further improvements, such as cost reduction or weight optimization. This often results in an iterative cycle of revisions, contributing to nearly 75% of total development costs.

To streamline this process design exploration become essential. Virtual testing enables the optimization of a design to meet specific goals while adhering to established design constraints. Once optimal predictions are generated, the design or process can be thoroughly explored and refined. Important parameters that influence output variables can be identified, helping differentiate between significant and insignificant factors. Furthermore, performance can be assessed under various operating conditions and design points, ultimately leading to the identification of optimal conditions that align with the desired performance metrics. Additionally, the robustness of the design can be explored to ensure reliability under different scenarios.

RESPONSE SURFACE

Based on Design of Experiments

SURFACE optimization

Minimizing the pressure loss

DIRECT optimization

To achieve the desired inlet velocity without compromising pressure loss, we aim to minimize the pipe size and maximize bend radius. Direct optimization can effectively predict optimal values for these parameters. Unlike methods relying on response surface models, direct optimization involves iterative trial-and-error processes, using sample sets based on mathematical models. This continues until the design goal is met.

optimization OF DESIGN

Particle-Wall Interaction as quoted from the research paper we will find the most effective incident angle to minimize the resultant velocity.

The collision of solid particles with walls results in energy and velocity losses and transformations. Forder et al. have proposed a non-random particle-wall collision bounce model which can accurately describe and predicts particle trajectory. This model allows the velocity change of solid particles to be solved and the loss of energy to be measured using different recovery coefficients. The recovery coefficient refers to the ratio of the velocities of the particles before and after the collision which, together with the impact angle, determines the velocity of the particles after the collision. The model formula is as follows:

Ey = 0.988 − 0.78X1 + 0.19X2^2 − 0.024X3^3 + 0.027X4^4

E𝑛 = 1−0.78X + 0.84X1^2 − 0.21X2^3 + 0.028X3^4 − 0.022X4^5

where 

Ey is the tangential recovery coefficient; (denoted as y parameter below)

E𝑛 is the normal recovery factor; 

Xi are the varying incident angles of the particles, rad.

best design 

Finding the best design based on objective to minimize the velocity with only one pass of optimization using adaptive objective algorithm.

We successfully modeled the relationship between input and output parameters in our project using a combination of computational fluid dynamics (CFD) and statistical techniques.

After establishing the parameter space, we conducted a design of experiments (DOE) to efficiently sample the input variables. The resulting data was used to construct a 3D response surface model, which interpolated between discrete data points to provide a continuous representation of the input-output relationship via automation tool.

This model was then employed for optimization, identifying three candidate solutions that effectively reduced the inlet velocity coefficient by adjusting the pipe's bend radius while adhering to specified boundary conditions. 

Note: This study focused on demonstrating the feasibility of the approach and did not involve a comparative analysis of actual design options. A more comprehensive study would be required to evaluate the performance of these candidate solutions in real-world applications. Q.E.D.