Oil pipes are indispensable to a hydraulic circuit. The linear model of pipe based on the Hagen-Poiseuille law is commonly used and very convenient in the analyses. However, real oil passages, such as in manifolds and oil passages in an automatic transmission in a car, have complex configurations. As they are quite three-dimensional and have various kinds of pressure drops on the inside, it is sometimes unsuitable to represent the real oil passages using the linear model. As the result of applying it to the real oil passage, the equivalent pipe length would sometimes be very long unrealistically. Moreover, the inertia effect of oil column in the passage is sometimes non-negligible.
This study represents a way to model real oil passages into a dynamically-equivalent pipe model using its CAD data and CFD results. The pressure drop is represented by the non-linear model of pipe and the coefficients are calculated from ΔP-Q curve of the passage which is obtained by CFD steady flow analysis. The inertia effect of oil column is calculated by CFD unsteady flow analysis and its coefficient is obtained from the solution of the differential equation which is expressed by a correlation coefficient. As a result, a new model of pipe is successfully obtained with the same effects of resistance and inertia as the real oil passage. The simulation using the new model of pipe agrees well with the experimental results. This modeling way is applicable to all oil passages with any 3-D configuration.