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Fundamentals to frontiers Expansion tanks By WILLIAM J. COAD afid sizing of a closed expansion the temperature limits, and the tank since the article "Compression pressure limits, but also t o how the Tank Selection for Hot Watet Heat- t systrm! trulk is dc~sigi7rdi t ~ t o l ~ e ing Systems," by H. A. Lockhart The derivation of the formulas for The fundamental components of a and 6 . F. Carlson, appeared in the sizing tanks is rather fundamental if hydronic system a r e the heat A S H R A E Journal Section of it can be assumed that the air cush- source, load, circulator, piping, and Hecrtir~glPi~~rngiAir Co~lditioilingin ion behaves as a perfect gas. For expansion tank. Strangly enough, April 1953! Yet, since that time, such equations, all the necessary the most complex device of the five there have been immense strides in values that are not established as is probably the one that would ap- the application of hydronic sys- design parameters are readily avail- pear to be the least complicated - tems. able from any steam table. The only the expansion tank. Considering the The correct sizing of expansion complications are those relative to fundamentals, the expansion tank tanks is becoming ever more critical how the tank is employed in the sys- serves a dual purpose. It allows for as larger volume systems are being tem. As an example, if it is assumed the volumetric changes in the flu- employed. Not only are large vol- that the water in the tank always id, resulting from temperature umes a result of large capacity sys- remains at its initial temperature, changes, to occur between planned tems, but they are also an integral that compression and expansion of pressure limits; and it establishes part of solar systems and other the air in the tank are isothermal, the point of constant or known pres- power conserving systems that and that the air in the tank was ini- sure in the system. In many cases. utillze thermal storage through liq- tially compressed from atmospheric the tank serves the additional pur- uid phase temperature changes. The pressure in the tank, Equation 1 (see pose of being an integral part of the very important observation made in table) can be readily derived. Thus, air control subsystem. the article cited above was that the if a designer uses this equation and It appears that very little has sizing of a tank relates not only to anticipates the system performance been published regarding the design the volume of water in the system, to be in accordance with his design, Equations f o r expansion t a n k siztng -- -- - - - - - - - -- - --- -- Equation Example tank No Equation Assumptions size gal Air compresses isothermally ( t l ) * Water in tank is at temperature tl Initial air charge is atmospheric Air comDresses isothermallv it11 V liv2 v1 1) - 3ult1 2 v = .- -L - --- * Water in tank is at temperature t 2 lo,lp, - P,,/Pz)- (vzIv1 I ) (I - p JP,) air lnit~al charge IS atmospheric Air compresses isothermally ( t ~ ) Initial air charge is at pressure pl where, with volumes in consistent units: V,, = volume of water in system t2 - highertemperature F (piping heat exchangers etc )' V, - volume of expansion tank vl v2 - speciftc volume of water at temperature t l specific volume of water at temperature t7 p,, - atmospher~cpressure psia (2 - linear coefficient of thermal expansion 1 deg F pl - pressure at lower temperature, psia St hignei temperature minus lower teiriperature F p2 pressure at higher temperature psia tl lower temperature F *At t , and not including water in the tank Fundamentals to frontiers tank is used to provide the expan- as possible. sion cushion. From the standpoints of ther- If the initial air charge in the tank modynamics and hydraulics, these is not compressed from atmos- equations can be used to size ex- he must take all possible steps to pheric pressure in the tank itself pansion tanks with an equal degree asbure that his design will satisfy the but rather is forced into the tank at a of accuracy for heating water sys- assumptions. This might include design operating pressure (either tems, chilled water systems, and leaving the tank uninsulated and in- from a compressed air system or as dual temperature systems. When a stalled in such a way that thermal with a precharged diaphragm type tank with a liquid-gas interface is circulation between the piping and tank) and the air is assumed to com- used in a chilled water system, the tank will be minimal. press and expand isothermally, however, unless extreme pre- If, on the other hand, the assump- Equation 3 results. The significance cautions are taken there is a con- tions are that the initial charge of of recognizing the differences in tinual pumping effect that removes water in the tank changes tempera- these assumptions can be illustrated air from the tank by absorption in ture with the main volume of water, with an example. Assume that a sys- the water, thus causing the small that the air in the tank is at its initial tem contains 10,000 gal of water, tanks designed by these relation- charge temperature and compresses has a fill pressure of 15 psig at the ships to water log frequently. One and expands isothermally, and that tank with a maximum limit set at 25 option is to provide oversized tanks the air in the tank was initially com- psig, and is designed to operate over t o minimize t h e frequency of pressed in the tank from atmos- a temperature range of 70 F (fill) to needed air charging; another is to pheric pressure, Equation 2 re- 220 F. design such systems to prevent the sults. The equation becomes a bit The calculated tank sizes for the absorption phenomenon, which has more complex if the air in the tank is three different conditions are shown numerous other detrimental effects assumed to increase in temperature in t h e table along with the on system performance. R with the liquid (it must be remem- equations. The differences among bered that the total pressure of the these sizes are seen to be signifi- O n this page errch m o n t h , the airrhor gas in the tank is the sum of the cant, indicating that in the selection shares his engineering philosophy by explor- partial pressures of the air and water of the tank, the designer must: ing ( I wide vurieiy o f topics ranging ,from vapor and that a saturated condition 1) Determine what operating as- .fzrndamentals to new frontier:, , ns tliey relate always exists). Although not totally sumptions are to be employed in t o bitilding rnvirorimental s y s t e m s . MI.. Cond is vice president o f Charles J . R . accurate, this equation would be a selecting the tank sizing equation. McClrtre & Associates cind qffiliuie prcges- fair approximation of the condition 2 ) Design the system to achieve sor. o ~nechnnicalengineering at Washing- f where a portion of a thermal storage the assumed conditions as closely rorr Unii,ettriiy, St. Lo~ris,1Mo. HeatingIPipinglAir Conditioning, May 1980

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