MIT1_204S10_assn6 - Computer Algorithms in Systems...

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Computer Algorithms in Systems Engineering Spring 2010 Problem Set 6: Building ventilation design (dynamic programming) Due: 12 noon, Wednesday, April 21, 2010 Problem statement Buildings require exhaust systems to remove waste gases from processes conducted in a manufacturing, medical or research facility, as well as those from human activity in the building. The system must handle the required exhaust volume. Air velocity must be within given limits, primarily to limit noise and vibration. Pressure balance must be maintained at junctions between ducts; duct size must fit within the available space, and costs should be minimized while meeting all the other criteria. As an example, smaller ducts are less expensive in capital costs, but require higher fan pressure to move the required air flow, which increases the operating costs. Existing manual design methods either too simple to produce a good design, or are very difficult to use. A dynamic programming approach can be used as the basis of a design tool for engineers or architects. You will write the basic portion of such a tool in this assignment. A building exhaust system is shown below. There are 56 duct segments and 28 junctions in the network. You are given a tree representation of this network in There is only one duct segment between nodes in; for example, segments 52, 53 and 54 are just one segment whose length is the sum of all three. Nodes 1 through 14 are where the exhaust air enters the system; it then flows through nodes 15 through 27, to the fan (node 28, which you may model separately). There is just a single fan that draws the exhaust volume out from the top of the system. The length of each duct segment and the design of the entire system depend on the building layout. Nodes 1 through 14 have data on the exhaust volume that enters the system. This is the flow through the duct segment immediately upstream (toward the fan) from the node. The ducts upstream from nodes 15 through 28 have a flow that is the sum of the flows entering from earlier ducts (flow conservation). We assume the ducts are round; each duct (segment between nodes) has a minimum and maximum diameter, and it has a minimum and maximum air velocity. For simplicity, the minimum diameter= 0.3 meters and the maximum diameter= 1.5 meters for all ducts. These size constraints are imposed by the building design. The minimum velocity= 1 m/sec and the maximum velocity= 10 m/sec, except at the duct upstream of node 27 (on the roof), where the maximum velocity= 30 m/sec. If the velocity is too low, granular material may not be carried out through the system; if the velocity is too high, noise and vibration occur. When two ducts join at a node, the pressure of the incoming air must be the same in both ducts.
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This note was uploaded on 12/04/2011 for the course ESD 1.204 taught by Professor Georgekocur during the Spring '10 term at MIT.

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MIT1_204S10_assn6 - Computer Algorithms in Systems...

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