Modeling the dynamics of flow in gas pipelines
The description of nonstationary one-dimensional flow of a nonideal gas in a pipe is treated with the goal of developing a mathematical description of flow and pressure (density) dynamics adequate for creating a simulation model of large pipeline networks, the analysis starts from Newton's equation of motion. The continuity equation, and the energy equation. The authors determine the relationships among: space discretization, terms of Newton's equation, and frequency of the dynamic processes occurring in the system. The resulting dynamic description of a pipe is discussed for two different modes of space discretization, and quantitative rules for space discretization are given.
A universal dynamic simulation model of gas pipeline networks
A model for simulating the dynamic behavior of gas distribution pipeline networks is developed. A new implicit integration method and a special crossing-branch method are presented. The first method can accommodate systems exhibiting both slow and fast responses and prevents numerical oscillations in the solution. In the crossing-branch method, the solution of very large systems described by sparse matrices is provided, based upon special properties of the matrix. On the basis of these methods, a universal model for simulating the network of any structure of arbitrary size is created. Examples of model testing and use are given.
Experimental observation of a strange nonchaotic attractor.
Evidence is presented for the existence of a strange nonchaotic attractor in a two-frequency quasi-periodically driven, buckled, magnetoelastic ribbon experiment. Scaling behavior in the Fourier amplitude spectrum is observed in agreement with predicted scaling behavior for strange nonchaotic attractors. Dimension measurements also support the existence of a strange nonchaotic attractor