Notes on Predicting Off-Design
Based on the Type of Modeling to be Done and Available Information:
To determine off-design performance in a vapor compression cycle, one must either specify
1) the condenser exit subcooling, flow control specifications, or refrigerant charge, and
2) evaporator exit superheat or refrigerant charge.
The ambient control option under Parametrics can be used to specify compressor inlet superheat and/or condenser exit subcooling (if either are known or can be reasonably estimated) as a function of ambient temperature. This option can be used with outdoor ambient as the parametric to predict off-design performance once the heat pump is properly setup for off-design analysis -- by specifying appropriate combinations of the above settings.
The rest of this note discusses possible approaches to modeling systems with differing amounts of information on flow control and accumulator hardware specifications and/or design refrigerant conditions.
The most suitable approach also may depend on whether:
1) you are trying to predict performance at other conditions for a specific unit, or a family of units of quite similar HX design, where you already know some expected subcooling and superheat trends from lab data, or
2) you want to predict performance in a new system design based on hardware
specifications and design subcooling and superheat levels alone.
General Recommendations Based On
Available Equipment Information
For Capillary Tubes or Short Tube Orifices
1) If the fixed flow control hardware specifics are known,
1a) an accumulator is present, but details aren't known,
if you want to simulate an accumulator designed to operate dry in cooling mode up to a certain ambient above design point, use the ambient control option to assume design superheat at design conditions and 10F more superheat (or a measured superheat level) at SEER rating conditions,
if you want to simulate an accumulator designed to operate wet throughout cooling mode, set the superheat level at a constant value of 5F or less,
if you want to use the default accumulator geometry, proceed to 1b) below.
1b) an accumulator is present, and details are known,
determine the required charge at design cooling conditions and superheat, and specify this to predict performance, superheat, and subcooling over the full range of ambients for both wet and dry accumulator conditions.
2) If the fixed flow control hardware specifics are known,
an accumulator is not present,
specify refrigerant charge required to give design superheat at design conditions
specify estimated superheat vs ambient trend over desired operating range.
For Thermal Expansion Valves (TXVs)
If the TXV hardware specifics are not known (or the user doesn't want to simulate at this level of hardware detail), design subcooling and superheat must be determined or estimated. The charge balance method with fixed superheat level is recommended in this case (where the design charge is calculated by the model based on the design subcooling).
If the TXV hardware specifics are known (or those determined by the model are to be used), then design (rated opening) superheat is also known.
1st Choice. If subcooling trends with ambient are known or reasonable estimates are available, then the required superheat trends with ambient that best match the subcooling data can be determined from the model. These superheat trends can then be specified with the ambient control option for the specified TXV hardware to predict performance.
2nd Choice. If only superheat trends with ambient are known or reasonable estimates are available, then these can be specified with the ambient control option for the specified TXV hardware to predict performance. (Superheat trends with ambient should be consistent with the minimum, rated, and maximum opening superheat specifications of the valve.)
3rd Choice. If neither subcooling or superheat trends with
ambient are known, then one must determine or estimate the design subcooling
level and calculate the required charge. Given charge and TXV hardware
specifications, the model will seek the required operating superheat levels. If
these superheat levels remain within the expected operating range of the TXV,
the results should be a reasonable estimate of system performance. If not, or if
the model fails to converge, one must revert to the case where the TXV hardware
details are not used. (See more discussion below and in the
online report ORNL/CON-343 (pp. 27-37) regarding the limitations of the
model when specifying TXV and charge directly.)
General Recommendations Based on the
Range of Equipment Designs To Be Modeled
In the following section, we discuss the various off-design modeling
approaches starting with those that are likely to be most accurate for specific
equipment, but the least general in applying to modified designs, followed by
those that may be less accurate in an absolute sense, but more physically based
and thus more able to predict changes in superheat or subcooling trends with
ambient as the flow control or HX designs are changed.
Basic Cycle Balance Approaches
The solution approach used by the model for the basic cycle balance can be
(A PDF version for printing is also available.)
Use of Ambient Control Option
The most accurate approach for specific equipment, but probably the least general (or predictive) for other HX or compressor combinations, especially with fixed flow control devices, is to specify the subcooling and superheat trends with ambient as determined from experiments with test units where the flow controls are sized for desired superheat and subcooling at design conditions. By specifying these trends directly, interpolation and extrapolation of system performance for these tested models to higher or lower ambients outside the test range should give more accuracy than with the other methods discussed below (at least until the limit of maximum opening superheat is reached in the case of a TXV or until two-phase HX exit conditions are reached with fixed flow controls).
TXVs tend to maintain fairly constant levels of evaporator exit superheat and condenser exit subcooling for an air-conditioning application with a properly sized, cross-charged, TXV flow control device. Because of this, use of the ambient control option to apply small linear corrections to the design superheat and subcooling levels should allow one to simulate the cycle effect of a TXV control quite well until the limit of TXV control is reached. (In heating mode, the subcooling levels vary more than in cooling but still much less than with fixed flow controls.)
The superheat and subcooling variations with ambient for systems with fixed
flow controls are larger, generally more nonlinear, and often the HX exit
conditions go into the two-phase region at the more off-design conditions.
Because of this, extrapolations of experimental superheat and subcooling trends
for these controls are limited to the point at which refrigerant two-phase exit
conditions are predicted. However, if you mainly want to predict the performance
of a given system over a range of ambients where the subcooling and superheat
levels are known (and nonzero) at the upper and lower limits of operation, the
ambient control option would be a suitable way of predicting performance at all
intermediate conditions (within the limits of the linear trend approximation).
Fixed Flow Control with Accumulator
The next most accurate approach and more general in predicting trends with
other HX sizings or designs would be for the case of a specified fixed opening
flow control (capillary tube or short tube orifice), with an accumulator, where
the compressor inlet superheat would remain fairly constant at a low value with
ambient, as long as there were some liquid in the accumulator. Here a low
superheat value would be specified and the levels of subcooling would be
determined by the system balance where the mass flow through the flow control
matches that through the compressor.
Fixed or TXV Flow Control w/o Accumulator
A bit lower in accuracy and generality would be the case of a specified flow control (cap tube, short-tube-orifice, or TXV) with no accumulator, where the superheat trend with ambient was specified from tests on a similar design. In these cases, an engineering model of the flow control device (flow as a function of upstream and downstream conditions) replaces a linear assumption of subcooling trend with ambient that would be used with the ambient control option.
The accuracy of this approach is certainly less for a TXV than for a fixed flow control, because the TXV opening is directly proportional to the specified superheat level. The accuracy of the experimentally measured superheat levels strongly impacts the valve setting at different ambients. The recommended approach for modeling TXVs without a charge balance would be, instead, to find the calculated superheat trend that matches the measured subcooling trend with ambient for a TXV system (as measurements of subcooling levels are more stable). This model-calculated required superheat trend would then be specified with the ambient control option along with the TXV hardware specifications. (Note that the superheat that controls the TXV is the evaporator exit value rather than the compressor inlet levels specified by the user, so any suction line heat transfer rate or delta-T needs to be accounted for here appropriately in any case.)
Occasionally, one sees in the literature a discussion of a "TXV" model where
the superheat level is fixed and a simple fixed opening orifice model of some
type is used. Similar results can be obtained in our model by selecting TXV
hardware characteristics and specifying a fixed superheat level. This results in
simulating a fixed opening TXV and is probably the least accurate representation
of the system performance trends with a TXV over a range of operating
Charge Balance Approaches
The solution approach used by the model for the change balance approach can
be viewed here
to see how it adds an additional iteration loop to the basic cycle balance, or
to see all of the solution options together. (PDF versions for printing are
also available for the added
and the full
solution logic diagrams.)
Fixed Flow Control or TXV Superheat Trend with Fixed Charge
The next most accurate approach and most general in predicting trends with other HX sizings or designs would be for the case of a fixed opening flow control and charge or in the case of a TXV, a fixed superheat or superheat trend with ambient and fixed charge. Here the required charge is calculated at design conditions of subcooling and superheat. This calculated design charge is then specified as constant and off-design superheat (for cap tubes and short-tube orifices) or subcooling (for TXVs) is adjusted by the model to maintain this fixed charge.
This approach, while theoretically sound, does not generally predict subcooling or superheat trends with ambient as accurately as does the basic cycle balancing method discussed above, most likely due to the limitations of the HX and charge models in tracking changes in charge with ambient in the heat exchangers and two-phase distributors. This is because the charge inventory accounting in the system, especially the heat exchangers, is only approximate due to the simplified heat flux and void fraction integration assumptions. The heat exchanger circuitry simplifications used in the model contribute further approximation. (See the online documents related to charge inventory modeling -- the 1987 ASHRAE paper and the 1991 ORNL/CON-343 report, for more discussion of these issues.)
These modeling errors, especially in predicting the HX regions occupied by subcooled liquid in the condenser and superheated gas in the evaporator, would be expected to be the largest in our model in cases where the subcooling and/or superheat levels are the highest. Since the charge calculation errors can be similar for the different flow controls (until higher levels of subcooling or superheat occur), the charge balance approach is still useful in comparing relative performance of different flow controls with ambient until the superheat or subcooling levels rise to where the HX models to become invalid based on the specific HX circuiting of the units to be modeled. (Cases with fixed flow controls where the HXs have two-phase exit conditions should not be a problem for the model.)
These trends might be expected to change the least as HX designs are varied for systems with TXVs, where the flow control can adjust to maintain similar superheat at off-design conditions (assuming that the TXV is resized for the same level of design subcooling). For fixed opening devices, the off-design trends of superheat and subcooling might be expected to deviate more for HX designs with different HX volumes or heat transfer distributions. However, we do not have sufficient experience with enough data sets to say that this is the case.
Because of the above-mentioned potential for charge balance errors, off-design superheat and subcooling and resultant performance trends predicted with the charge balance approach should be viewed with caution until they have been validated for a specific design.
The modeling of a TXV by use of fixed superheat (or superheat trend with ambient based on laboratory testing as discussed above) and a charge balance is recommended over use of the explicit TXV hardware model and charge balance. We have found the former to be a much simpler, more stable, and generally more accurate, approach for off-design prediction for TXV systems.
For the explicit TXV hardware model with charge balance to work well, the charge inventory model must quite accurately predict changes in superheat with ambient. This is a significant modeling challenge as small differences in charge usually result in rather large changes in superheat. As TXV opening is very sensitive to superheat level (usually less than a 10F change in superheat to change the valve from fully open to fully closed), small errors in superheat trend prediction have a large effect on TXV opening and thus high-side pressure and subcooling level.
If one needs to model off-design performance in a new system design with a
fixed flow control (capillary tube or short-tube orifice control) with or
without an accumulator, the charge inventory model with specified flow control
size is recommended. While one could use the ambient control option to specify
expected superheat and/or subcooling trends with ambient based on existing
models, these are less likely to remain valid in general as HX design changes
are made than for a TXV control where its variable opening can adjust to some
degree for these differences.
In summary, the model provides a variety of ways in which one can model
off-design cooling or heating performance. Which method is most appropriate
depends in part on whether one is trying to simulate existing equipment or
develop a new design and further on what kind of component information is
available. While it is important that all off-design predictions be validated
against some test data, this is especially the case when a charge balance is