Mathematical Description of Vortex Separators for the Purpose of Optimization and Determination of

The mathematical description of a hydrodynamic vortex separator is based on the analysis of multiphase flow, where balancing the forces acting on a particle in the vortex field is crucial. In the Ansys environment (especially in the Fluent module), the mathematical description and optimization of a vortex separator are implemented using computational fluid dynamics (CFD). This allows for the precise determination of the parameters necessary to maintain similarity between the model and the actual device. Ansys allows for the validation of dimensionless numbers, which are crucial for maintaining hydrodynamic similarity. This is accomplished in two ways:
1. Verification of the velocity field through simulations of different scales (e.g., 1:10 vs. 1:1 model) to check whether the tangential and radial velocity distributions scale with the Reynolds number.
2. Stokes number similarity. Ansys Fluent allows monitoring of the particle relaxation time relative to the residence time in the device, which is fundamental for the transferability of results." For different device sizes.
This will be accomplished through hydrodynamic similarity analysis. Simulations will be performed at various scales: (a) comparing the results for the laboratory and industrial models; (b) verifying the dimensionless parameters – checking whether the constancy of the Stokes and Reynolds numbers guarantees the same separation efficiency when changing the dimensions.
Next, the separator design will be optimized. The objective function will be defined: a trade-off between separation efficiency and pressure losses.
A sensitivity analysis will be performed. The impact of inlet and outlet geometry on the device's efficiency will be analyzed. The fractional efficiency curve will be determined, and then the cut-off diameter for the optimized model will be determined.
As part of the research, design guidelines for a series of separators will be formulated. The reliability of the ANSYS model will be assessed against the similarity theory.