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Assessing the Degree of Unsteadiness in Flow Modeling: From Physics to Numerical Solution

Abstract

From a long-term perspective all flows in a water system are unsteady in the sense that no single value persists throughout; all flows continuously change or adjust, either suddenly or gradually, over the system's life. From first filling to final decommission, the flow rate routinely changes from near zero to other, possibly quite high, values. Yet from either a performance or modeling perspective, a detailed or complete consideration not only of all flows, but of all possible transitions in flows, is both impossible and excessive. Thus, it is necessary to restrict attention to specific and targeted design regimes that capture in a reasonable way the key system performance issues in terms of cost effectiveness, hydraulic capacity, structural strength, as well as the system's overall reliability, robustness, vulnerability, and resilience. Yet even this is a tall order and immediately raises three key and intensely practical questions for the analyst: (i) How important is the unsteadiness inflow conditions to understand the system response? (ii) What mathematical models should be used to capture this unsteadiness? And (iii) what spatial and/or temporal discretization is needed to accurately simulate the selected model? A whole host of intriguing considerations arise from these questions that interconnect with issues including the purpose of the analysis, the physical and economic consequences of both conservatism and risk, and both the experiences and biases of the analyst. This paper briefly explores the related questions of modeling intent, physical and numerical approximations, and how these issues map to the physical behavior of the system. Several specific modeling options are overviewed including nearly steady (or extended period) approaches, rigid water column models, (i.e., including inertia effects), and water hammer models (i.e., also including small compressibility effects). This paper provides a brief summary of these considerations and attempts to provide some tentative and preliminary guidance into how these questions of unsteadiness need to be framed or posed. There are clearly issues of physics at stake, in terms of whether certain phenomena are dominant or trivial, but even this evaluation is contingent on the context of the modeling exercise and what specific questions are being answered. A couple of indices are helpful, at least in a limited way, for characterizing the system response, and should perhaps be routinely computed to help analysts gauge or judge the unsteadiness in a system. These include the time scale of boundary and flow adjustments relative to the water hammer time scale, and the size of two unsteady head terms (the acceleration head and the Joukowski head) relative to predicted pressure and flow changes. However, in complex systems the rules must always be supplemented with more detailed numerical explorations and exercises in grid refinement. This paper was presented at the 8th Annual Water Distribution Systems Analysis Symposium which was held with the generous support of Awwa Research Foundation (AwwaRF).

Authors

Karney BW; Jung B; Alkozai A

Pagination

pp. 1-16

Publisher

American Society of Civil Engineers (ASCE)

Publication Date

March 13, 2008

DOI

10.1061/40941(247)56

Name of conference

Water Distribution Systems Analysis Symposium 2006

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