Direct Calculations of Cavitating Flows in Fuel Delivery Pipe by the Space-Time CE/SE Method

Abstract

In this paper, we report direct calculations of cavitating pipe flows by the method of Space-Time Conservation Element and Solution Element, or the CE/SE method for short. The tenet of the CE/SE method is treating space and time as one entity, and the calculation of flow properties is based on the local and global space-time flux conservation. As a contrast to the modern upwind schemes, no Riemann solver is used, thus the logic of the present scheme for cavitating flows is much simpler. Two numerical examples are reported in this paper: (1) a hydraulic shock problem, and (2) a cavitating pipe flow. For the hydraulic shock problem, we demonstrate the capability of the CE/SE method for capturing contact discontinuities in cavitating fluids. For the pipe flows, a two-phase homogeneous equilibrium cavitation model is employed. In both cases, numerical results compared favorably with the experimental data and analytical solution.

Isentropic one-fluid modelling of unsteady cavitating flow

“…Qin et al [21] presented a modification of Schmidt's model by multiplying a parameter (b) of O(10 À3 ) to O(10 À5 ) to the second term of (3.3) accordingly. In doing so, the ''saturated'' pressure p 0 sat can be adjusted to the physical p sat .…”

“…Schmidt's model is applicable for small size cavitation of high pressure. To extend the application of this model to the water hammer phenomenon, Qin et al [21] incorporated a model constant into Schmidt's model. However, by a strict mathematical analysis, this model constant, which was chosen to be in the range from 10 À3 to 10 À5 , should be determinable and equal to one if one requires that the equation of state developed for the cavitating flow is mathematically consistent with the formulation of sound speed used.…”

Numerical Investigation of the Interaction of Counterflowing Jets and Supersonic Capsule Flows

“…To date, the CESE based solvers have been utilized to solve a variety of problems including inviscid acoustic waves, traveling and interacting shocks, detonation waves, and cavitation flows. [17][18][19][20][21] The main objective of this study is to perform numerical computations for selected experimental configurations studied by Daso et al 16 Axisymmetric computations are carried out to study the underlying physics associated with the two modes of jet interaction. Results are compared against available experimental data, such as Schlieren images, and other details available in literature.…”

Simulations of waves in elastic solids of cubic symmetry by the Conservation Element and Solution Element method

“…Extensions to use quadrilaterals and hexahedra are also available [20]. In the past, the CESE method has been successfully applied to solve various fluid dynamics problems, including aero-acoustics [21], cavitations [22], complex shock waves [23], detonations [24], magnetohydrodynamics (MHD) [25,26], etc. Preliminary results of applying the CESE method to model electromagnetic waves [27] and elastodynamics [28] have also been reported.…”