Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver

Transition between free-surface and pressurized flows is a crucial phenomenon in many hydraulic systems. During simulation of such phenomenon, severe numerical oscillations may appear behind filling-bores, causing unphysical pressure variations and computation failure. This paper reviews existing oscillation-suppressing methods, while only one of them can obtain a stable result under a realistic acoustic wave speed. We derive a new oscillation-suppressing method with first-order accuracy. This simple method contains two parameters, Pa and Pb, and their values can be determined easily. It can sufficiently suppress numerical oscillations under an acoustic wave speed of 1000 ms−1. Good agreement is found between simulation results and analytical results or experimental data. This paper can help readers to choose an appropriate oscillation-suppressing method for numerical simulations of flow regime transition under a realistic acoustic wave speed.

Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver

Transition between free-surface and pressurized flows is an crucial phenomenon in many hydraulic systems, including water distribution systems, urban drainage systems, etc. During the transition, the force exerted on the structures changes drastically, thus it is meaningful to simulate this process. However, severe numerical oscillations are widely observed behind filling-bores, causing unphysical pressure variations and even computation failure. In this paper, some oscillation-suppressing approaches are reviewed and evaluated on a benchmark model. Then a new oscillation-suppressing approach is proposed to admit numerical viscosity when the water surface is at proximity of conduct roof which has first order accuracy. This approach adds numerical viscosity when water surface is at the proximity of conduct roof. It can sufficiently suppress numerical oscillations under an acoustic wave speed of 1000m/s and is simple to apply. In comparison with two experiments, the simulation results of this method show good agreement and little numerical oscillations. The results in this paper can help readers to choose an appropriate oscillation-suppressing method to improve the robustness and accuracy of flow regime transition simulations.

Reynolds Number Effects in the Flow of a Vočadlo Electrorheological Fluid in a Curved Gap

Many electrorheological fluids (ERFs) as fluids with micro-structure demonstrate a non-Newtonian behaviour. Rheometric measurements indicate that some flows of these fluids may by modelled as the flows of a Vočadlo ER fluid. In this paper, the flow of a Vočadlo fluid – with a fractional index of non-linearity – in a narrow gap between two fixed surfaces of revolution with a common axis of symmetry is considered. The flow is externally pressurized and it is considered with inertia effect. In order to solve this problem the boundary layer equations are used. The Reynolds number effects (the effects of inertia forces) on the pressure distribution are examined by using the method of averaged inertia terms of the momentum equation. Numerical examples of externally pressurized flows in the gap between parallel disks and concentric spherical surfaces are presented.

Transient Analysis of Mixed Free-Surface-Pressurized Flows With Modified Slot Model: Part 2 — Similarity Law and Eigenvalue Problem

To analyze transient free-surface-pressurized flows with entrapped air in a drainage system, a virtual slot model with ceiling has been introduced. Using this model, calculations for the reduced model and the actual size model are carried out to examine a scale effect on the transient flow. The results show that up-scaling the system causes the increase in compressibility of entrapped air so that the rate of pressure rise decreases. Next, it is confirmed that the partial differential equations for the modified slot model have real eigenvalues and then the initial value problem is well-posed when the velocity difference between air and water is not so large. The increase in the velocity difference yields a system having complex eigenvalue, however the well behaved numerical solutions can be obtained since the friction terms in the differential equations suppress the numerical instability.

Transient Analysis of Mixed Free-Surface-Pressurized Flows With Modified Slot Model: Part 1 — Computational Model and Experiment

A new computational model is developed here to analyze the influence of entrapped air on free-surface-pressurized flows in a drainage system. A virtual slot with ceiling on the top of the pipe is introduced to treat a separated gas-liquid flow. This model is a modified model of Preissmann’s and is applicable not only to open channel flow and closed conduit flow but also pressurized flow with entrapped air. Compared to experimental results using the model of 1/50 scale of actual drainage system, the calculation results show that the entrapped air in a horizontal pipe advances the time of pressure rising and makes the maximum value of pressure higher. The escape flow of entrapped air at a dropshaft is caused by long waves pushing the air in the horizontal pipe, and then the pipe slope affects the flow rate of air. The air compressibility has less effect on the transient separated air-water flow in the small-scale model.