Tom Peterson

February 25, 2000

Analysis of the JT Heat Exchanger in the Heat Exchanger Test Feedbox for
CERN

[Description.]{.underline}

The drawing "JTX Heat Exchanger, Main Assembly" (1650-ME-250550) shows
the heat exchanger design. It consists of two layers of finned, copper
tubing, helically wound on a polyethylene "mandrel", or inner core, and
contained in a stainless pipe. An identical heat exchanger was provided
to the TESLA Test Facility at DESY in 1996 as part of the feedbox for
the TTF string. (I hear that it works fine, but I do not have
quantitative data about the heat exchanger performance. Data from a
similar, single layer heat exchanger have been used to refine the
model.)

[Modeling.]{.underline}

The heat exchanger was modeled using Engineering Equation Solver (from
F-Chart Software, Middleton, Wisconsin) as two parallel counterflow heat
exchangers. Although the two "shell" (flow outside the tubes) layers are
separated by a screen in order to obtain some mixing between the flows,
the two tube passes are entirely parallel and not the same length, so
the result of the analysis should include a conservative estimate of the
effects of unbalanced flows. The total tube and return flows are equal,
but the two parallel tube and two parallel shell flows all differ from
one another. The analysis is analytical, with average properties used to
obtain heat transfer coefficients. The heat transfer coefficients with
surface areas are used to find overall heat transfer and a Log Mean
Delta-T based on end temperatures. Inlet, exit and average helium
properties are found from calls to HEPROP (Cryodata, Niwot, Colorado).

A pressure drop coefficient ("friction factor") for the shell side is
found from measurements of pressure drops in a similar, single layer
heat exchanger with identical finned tubing.

The thermal properties of superfluid are ignored, and some inlet
conditions result in calculation of sublambda temperatures at the tube
exits. In reality, the tube exit temperature will probably never go
below T-lambda due to the relatively large channel size (7.7 mm ID) and
influx of heat from the normal zone.

[Results.]{.underline}

The following plots summarize the analytical results as a function of
mass flow. Inlet conditions are 4.58 K, 1.40 bar, (except for figure 4,
which used 4.45 K, 1.25 bar) and 1.77 K, 14.5 mbar.

Figure 1. Tube and shell side exit temperatures versus total mass flow

![](media/image1.wmf){width="6.1506944444444445in"
height="3.734722222222222in"}

Figure 2. JT valve exit quality versus total mass flow

![](media/image2.wmf){width="5.829861111111111in" height="3.76875in"}

Figure 3. Shell side pressure drop versus total mass flow

![](media/image3.wmf){width="5.948611111111111in"
height="3.8472222222222223in"}

Figure 4. Exit temperatures versus flow imbalance at 18 g/s, 4.45 K tube
inlet

![](media/image4.wmf){width="6.147916666666666in"
height="3.9743055555555555in"}

[Conclusions.]{.underline}

The design mass flow was 10 g/s. At 18 g/s the shell side pressure drop
is about 2.8 mbar, corresponding to about 50 mK higher temperature in
the saturated bath than without the heat exchanger flow resistance.
Figure 4 shows that the optimal mass flow balance, in terms of matching
temperatures, would be 42% of the mass flow in the inner tube. However,
because the inner helix is shorter, we actually will have about 52% of
the mass flow in the inner tube. The outer tube exit will actually
probably not go below T-lambda, but heat will be transferred into the
outer tube from the inner tube flow where they merge. The overall effect
might not be much less total cooling than with the optimal flow balance.
In any case, as Figure 4 shows, the flow balance will probably have only
a small effect on the exit enthalpy.