Form Approved
REPORT DOCUMENTATION PAGE
OMB No. 0704-0188
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1. AGENCY USE ONLY (Leave blank)
2. REPORT DATE
3. REPORT TYPE AND DATES COVERED
August 1995
4. TITLE AND SUBTITLE
5. FUNDING NUMBERS
Optimal Design of Piping Systems for District Heating
6. AUTHORS
Gary Phetteplace
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
8. PERFORMING ORGANIZATION
REPORT NUMBER
CRREL Report 95-17
U.S. Army Cold Regions Research and Engineering Laboratory
72 Lyme Road
Hanover, N.H. 03755-1290
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
10. SPONSORING/MONITORING
AGENCY REPORT NUMBER
11. SUPPLEMENTARY NOTES
12a. DISTRIBUTION/AVAILABILITY STATEMENT
12b. DISTRIBUTION CODE
Approved for public release; distribution is unlimited.
Available from NTIS, Springfield, Virginia 22161
13. ABSTRACT (Maximum 200 words)
First, a method for determining the optimal size for a single pipe segment in a district heating system is developed.
The method is general enough to allow for any set of economic or physical parameter values. In addition, any form
of load management, i.e., temperature or flow modulation, or both, can be accommodated by the integral form of
the coefficients in the cost equation. An example is presented that shows a 17% savings in life cycle costs over a design
based on a common rule of thumb. Next the heat consumer and his effects on the piping system are studied. A new
model is developed for the consumer's heat exchanger that uses the geometric mean temperature difference as an
approximation for the logarithmic mean temperature difference. The new consumer model is integrated into the
previous single pipe model and, for a sample case, its effect is determined. For systems having multiple pipes and
consumers, the constraints are first developed and then the general solution strategy. The method makes use of the
solution to the unconstrained problem as a starting point for the constrained solution. Monotonicity analysis is then
used to prove activity of some of the constraints, and thus simplify the problem. Finally, the branch-and-bound
technique is shown to be suitable for finding a design with discrete values for all the pipe diameters. A simple
example is provided. In addition, a method is also demonstrated for further refinement of the pipe network to
eliminate excessive throttling losses in the consumer's control valves. The method developed here should be feasible
for designing the piping networks for district heating systems of moderate size, and its major advantage is its
flexibility.
14. SUBJECT TERMS
15. NUMBER OF PAGES
Applied optimization
Heat distribution systems
103
Branch-and-bound method
Heat transfer
16. PRICE CODE
District heating
Optimal design
17. SECURITY CLASSIFICATION
18. SECURITY CLASSIFICATION
19. SECURITY CLASSIFICATION
20. LIMITATION OF ABSTRACT
OF REPORT
OF THIS PAGE
OF ABSTRACT
UNCLASSIFIED
UNCLASSIFIED
UNCLASSIFIED
UL
Standard Form 298 (Rev. 2-89)
NSN 7540-01-280-5500
Prescribed by ANSI Std. Z39-18
298-102
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