# [Equest-users] CHW coil model documentation

Aaron Powers caaronpowers at gmail.com
Mon Jan 27 17:33:15 PST 2014

```Erik,

I think you'll find the DOE2 documentation a little lacking as model
descriptions are concerned.  Relevant keywords can be found in the Volume
2: Dictionary reference roughly from pages 394-398 (March 2009 version).
The documentation are good at describing how to use the program and how
keywords relate to the program, but there really hasn't been an in depth
description of the models or underlying algorithms since the DOE2 Engineers
manual, which was released in 1982 for version 2.1a.  Consequently, a lot
of this document is out of date, especially with respect to the water side
equipment.

For almost all its HVAC heat transfer components, DOE2 uses empirical
curves rather than models based on the NTU method, for example.  This
empirical method has been shown to be superior to other alternatives in
many cases.

In particular, there are three main empirical curves which are used to
control cooling coil valves.  These three expressions relate the coil
capacity as a function of entering air wetbulb, entering CHW temperature,
airflow, and CHW flow.  The product of these three curves (for a given WB,
CHWST, airflow, and waterflow) multiplied by the design cooling capacity
gives each hourly operating capacity.  Mathematically, it looks like:

[image: Inline image 3]

The * in the above equations denote a normalized value with respect to
design conditions.  These together with a few extra air-side calculations
and two energy balances complete the coil model.  The entering wetbulb is
essentially imposed on the system, so, on an hourly basis, the CHWST, cfm*,
and gpm* are selected to match the hourly capacity with the hourly load.
The control scheme determines precisely how this is accomplished.  It's
important to note that these curves are normalized to compute to 1.0 at the
following values:

WBa,in = 65 deg-F (not the ARI condition)
CHWST = 44 deg-F
cfm* = 1.0   (i.e. 100% design flow)
gpm* = 1.0  (i.e. 100% design flow)

There are some details I've left out, but this is how it works from a high
level.

Now more specifically about your situation.  As you've stated, it's a CAV
system with a specified CHWST, so DOE2 has only the ability to modulate
water flow through the coil to match the load.  Another tricky part of
these curves is that they are not accurate over all inputs.  For instance,
if you were to plot the default curve for cap3* above, you'd see that the
coil still has about 25% of its capacity even with zero flow.  This is
something that would not happen if you used the NTU-effectiveness method.
Thankfully, DOE2 keeps the inputs in range, but it doesn't warn you, and
I'm not sure it's ever mentioned in the documentation.  Of importance here
is that DOE2 linearly interpolates between 30% and 0% flow for the cap3*
equation above, and it only allows wetbulbs in the range of 59 to 73 for
the cap1* equation above.

Just to have some numbers to work with, let's say your coil has a design
capacity of 100,000 Btu/hr and a design water dT of 10 deg-F, which gives a
design CHW flow of 20 gpm.  As you stated, your conditions require 60 deg-F
entering air temp (as controlled by t-stat), constant airflow, and 40 deg-F
entering water temperature.  Now let's say that you're at a very low load
like 10% of design, or 10,000 Btu/hr.  Letting the entering WB = 59 deg-F,
the first two capacity curves immediately evaluate to:

cap1* = 0.94541
cap2* = 1.0 (it's a CAV system)

So to meet the load, we need the value of cap3* to satisfy:
0.94541*cap3* = 0.1
In other words, we need to select gpm* such that cap3* = 0.10577.  This
corresponds to a gpm* of about 5.3% or a gpm of 1.06.  At 10,000 Btu/hr, a
gpm of 1.06 will produce a dT of around 18.9 deg-F across the coil.  So you
can see how large or even physically impossible dT's can happen.

I'm baffled though as to how you're able to get 80 deg-F coming off the
coil.  The only way I can create this condition is by setting the design dT
to something like 18-20 deg-F.  Maybe if you post your inp someone can find
where this is coming from.

Good luck,

Aaron

---------- Forwarded message ----------
From: Erik Kolderup <erik at kolderupconsulting.com>
To: equest-users at lists.onebuilding.org
Cc:
Date: Fri, 24 Jan 2014 12:23:53 -0800
Subject: [Equest-users] CHW coil model documentation
Anyone know where to find documentation of DOE2.2's chilled water cooling
coil model? I see keywords listed in the help system for the CHW model,
such as the CHW-CAP-FEWBEWT curve, but I haven't found any documentation
about how all the curves are used together to calculate coil performance.

I ask because my hourly outputs show physically impossible results. I have
a single CHW coil with 2-way valves. At low load the CHW flow drops, which
is expected. But it drops so much that the reported leaving water
temperature is far higher than the entering air temperature. For example, I
get 80F water leaving the coil when the entering air temperature is only
60F. The heat balance works out when comparing the air-side and water-side
loads based on the hourly outputs. But the leaving water temperature is
much too high, i.e. flow too low.

For reference, the system has 40F CHW entering the coil, 48F air leaving
the coil (hospital operating room), and constant airflow.

Thanks for any insights.

*Erik Kolderup, PE, LEED AP*
erik at kolderupconsulting.com | 415.531.5198 | www.kolderupconsulting.com
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