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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,)
                                                                                              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
                                                                                         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-
  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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