In this article, loop-like planar networks are studied to supply the required amount of isothermal water within the optimal time and through the shortest path. The network is formed by circular cross sectioned conduits with possibly different geometric measurements viz. diameter and length. The wall of each conduit is rigid and adiabatic in nature.

The flow governing equation is first locally solved for a single conduit by analytical method and an ordinary differential equation model is developed in term of flow rate, pressure and time, along with constant fluid properties. This model is converted into analogous electrical circuit having lump parameters: flow resistance and inertance of conduit, together they are termed as flow impedance. This approach helps in developing a global model for each possible accessible path between source and destination node and each such path is rated on the basis of equivalent flow impedance. This sets a multi-objective dynamic flow optimization algorithm and the same is executed under the assumption of fully developed and laminar flow.

The demand of water is generated by demanding nodes of network and supply is done by a single source node having fixed amount of water. The pressure valves situated at junctions points of network are control variables and will be varied after the path having minimum impedance is picked. This variation is bounded by pressure values at source and demanding node. A set of pressure values at junction points will make water to flow through a particular path. Thus, using graph theory concepts each such node will be labeled by source, destination and particular pressure value which will give access to flow from source and destination. The case of infinite looping is also possible and will be detected to avoid the energy wastage. 

Since the aim is to supply the water within optimal time and through the shortest possible path, all the possible flow accessible paths between source and destination node are studied to measure the amount of flow impedance (resistance). Thus to give access to flow between source and destination for particular set of pressure values, each path will have finite impedance, after avoiding looping. The aim is to pick out the minimum impedance value over the derived set of pressure values.

The optimum flow impedance is further used to measure the pumping power as the cost of flow of a particular path. The method can be extended to reduce the water wastages by controlling pressures efficiently.


Optimal Flow Strategy to Distribute Water Through Loop-Like Planar Networks

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
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