(3 Btu/hr-ft2-F) has been assumed in the calcu-
Soil method, one pipe or conduit
lational procedure outlined by U.S. Army Corps of
This method is applicable only to the common
Engineers (1989). This heat transfer coefficient is based
conduit type of system. For the soil thermal resis-
on the outer surface area of the insulation. The valid-
tance we use the formula for an isothermal cylinder
ity of this assumption, based on some results from
buried in a semi-infinite medium having an isother-
this study, is discussed in Phetteplace (1991b).
mal surface (Holman 1972). The temperature of the
cylinder and its radius are taken as those of the
outside of the conduit. However, the isothermal soil
Method for two pipes
surface temperature is not used as prescribed by this
buried in a common conduit
This method is applicable only to the case where
formula. Instead, the temperature of the soil at the
both the supply and return pipes are in a common
depth of the pipe is used for reasons described be-
conduit. Here the same assumption as in the section
low.
above is made regarding heat transfer within the air
Soil temperatures vary with depth due primarily
space. The equations used are again those prescribed
to changes in the air temperature. The thermal prop-
by U.S. Army Corps of Engineers (1989) and are
erties of the soil damp the amplitude of the tempera-
referred to as the CEGS-02695 method here.
ture fluctuations at the surface and also cause a time
delay for a temperature disturbance at the surface to
reach the soil at some depth below. To accurately
Soil method for
model the variations in heat transfer rate from a
two direct buried pipes
For the LTHW sites, the soil method uses the
buried heat distribution system due to temperature
coupled two-pipe resistance formulation presented
variations at the surface requires a transient solution
by Phetteplace and Meyer (1990). The same assump-
to the problem. Unfortunately, no closed-form tran-
tion made above regarding soil temperatures has
sient solution is available for the case of a buried
again been made here. The thermal properties of the
pipe. Numerical methods can be used to find very
soil were estimated from published data (Kersten
good approximate solutions to such problems, but
1949) using measured soil moisture and classifica-
they require much more effort than the closed form
tion.
steady-state solutions. To account for the transient
nature of the problem an approximation can be made
by using the undisturbed soil temperature at burial
Results of heat loss measurements
Most of the results will be presented in graphical
depth instead of the ground surface temperature in
form in order to present a large amount of informa-
the steady-state solution for a buried pipe (Janson
tion within a reasonable space. Table 2 provides a
1963). We have made this substitution in the calcu-
summary of some of the more important measured
lations for the results presented here, including those
parameters and calculated results. In the graphical
made with the other methods described below where
data presented in Figures 1014, the sharp fluctua-
soil surface temperature is also required.
tions sometimes observed usually result from short-
term transients in the supply and return tempera-
Method for two buried pipes in
tures. Such transients can result from a number of
individual conduits
causes such as the startup or shutdown of pumps,
This method is a combination of the two methods
boilers, or building equipment.
outlined above, but it also accounts for the thermal
resistance of the air space and the interaction of the
two conduits. For the MTHW results presented here,
MTHW trench site
The average temperature of the supply pipe was
the method given by U.S. Army Corps of Engineers
163.6C (326.4F) and for the return pipe 107.8C
(1989), referred to as the CEGS-02695 method, has
(226.0F). The average air temperature within the
been used. This method uses steady-state conduc-
trench was 37.2C (99.0F). This temperature is the
tances for the pipe, insulation, and soil. The heat
average of four air temperatures measured within
transfer across the air space between outer surface of
the trench.
the insulation and the conduit is approximated as
During the study period the average heat loss
described below.
from the trench system was 80.5 W/m (83.8 Btu/hr-
The actual heat transfer processes within the air
ft). This value was calculated using the "insulation
space are far too complicated to warrant a complete
method" described earlier, the only method used for
treatment for the purpose of determining the heat
the trench system. Figure 10 shows the heat loss
losses from such systems. As an approximation, an
effective heat transfer coefficient of 17 W/m2-C
from the shallow trench for the entire study period.
17
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