Abstract
KEYWORDS – Master Cylinders, CFD Simulation, Parametric Models, ESC, flow
ABSTRACT - The objective of this work is the development, implementation and validation of a parametric model that helps designers do a quick estimation of the flow rate extracted by the Hydraulic Control Unit pump when the Electronic Stability Control is activated. This flow is extracted from the master cylinder reservoir into the hydraulic brake circuit, and its calculation is based on the main geometric dimensions of the cylinder, the fluid properties and the pressure and temperature conditions.
This methodology combines finite volume (CFD) models of the fluid domain and the theory of incompressible flow. Based on a detailed analysis of the results of the CFD models, a parametric model is developed for the calculation of the flow from the reservoir to the hydraulic circuit under different possible conditions of pressure generated by the HCU pump, temperature and for any type of brake fluid, characterized by its density and viscosity. From the CFD model results, the critical sections of the flow path are identified and the Reynolds number dependent loss coefficients are calculated. The parametric model divides the fluid domain in several parts, where, through an iterative procedure, the Reynolds numbers, the partial pressure drops and the mass flow rate are calculated.
The result is an advanced, parametric model that is implemented in a user friendly tool to calculate in a computationally effective way the mass flow rate demanded by the HCU pump. The calculation is based on the cylinder geometric dimensions, fluid properties and pressure and temperature conditions, thus allowing the designer to quickly adjust the dimensions for obtaining the desired flow rate. The model is validated by comparison of the flow rates predicted by the model with the ones obtained from CFD models of different master cylinders, under different pressure and temperature conditions.
The simplifications that are needed to pass from a very detailed finite volume model with one million cells to an effective model with a few DoFs makes it impossible to obtain an extremely high accuracy. Thus an accuracy of +/-15% of difference with respect to the CFD model results is allowed. If the geometry of the master cylinder is severely modified, a new set of CFD simulations must be run in order to identify the critical restrictions and characterize new discharge coefficient functions.
In summary, a parametric model for the quick calculation of the fluid flow demanded by the HCU pump from the master cylinder under ESC activation has been developed, validated and implemented. This model provides designers with a tool to adjust geometric dimensions in order to obtain the required flow under different pressure and temperature conditions.