Bin Data for Air Conditioning CalculationsBarry M. Cohen, P.E.
Douglas R. Kosar
The issue of weather design data for humidity has recently been addressed in the ASHRAE Handbook of Fundamentals by the tabulation of a new group of design conditions which are based upon extremes of humidity ratio and mean coincident values of dry bulb temperatures. However, differing coincidences of cooling and dehumidification loads is actually problematic across the range of all weather conditions that exist in a given climatic region, and can lead to erroneous conclusions about the efficacy of air conditioning throughout a cooling season, as well as the anticipated energy consumption and cost of operation. This is a summary of information that will appear soon in detail in the ASHRAE Journal. The deficiencies of conventional single-parameter bin data are demonstrated and the superiority of joint frequency bins is described.
The issue of weather design data for humidity has recently been addressed in the ASHRAE Handbook of Fundamentals(1) by the tabulation of a new group of design conditions which are based upon extremes of humidity ratio and mean coincident values of dry bulb temperatures. Typically, in the design tables, extremes of humidity are accompanied by milder mean summer conditions, while the temperature extremes are accompanied by moderate mean humidities. The high humidity, mild temperature conditions are especially difficult to handle with conventional cold-coil air conditioning units. Fresh air typically carries in a disproportionate humidity load.
This has been highlighted in several papers that were presented at the Eleventh Symposium on Improving Building Systems in Hot and Humid Climates(2,3). Calculations were done using various methods which indicated that indoor humidities in many applications in humid climates would climb to uncomfortable levels for a high percentage of the cooling season when conventional air conditioning was used to control indoor conditions.
Calculations may be done using weather bins, which are created by accumulating all hourly occurrences of closely related weather as if they had the same weather. Hours that fall into a certain range of some parameter, most often dry bulb temperature are collected, and then characterized by the mid-point of the range.
The way to deal with other parameters is to calculate the average value of all of these parameters in each individual bin, which it referred to as the "mean coincident" value. That average value is then used for energy calculations. The most common second parameter, and one that is often tabulated only for summer conditions is the ambient humidity.
A computer application, known as BinMaker(4), has become available recently which can provide the engineer with various types of bin weather representations. BinMaker produces binned weather data from the TMY-2 data set, which is only one of a number of options for obtaining hourly weather data. Recent studies reported at the ASHRAE 1998 Annual Meeting in Toronto(5,6) indicate that TMY-2 data is equal to or superior to any other option for weather data to be used for estimation of seasonal energy consumption.
Using the BinMaker software, one can then create bin weather data. But, what is the best form of bin data to use? There are several ways to organize weather data into bins. Figure 1 compares dry bulb bins (with mean coincident humidity ratio) to humidity ratio bins (with mean coincident dry bulb) for Savannah, Georgia.
As Figure 1 shows, dry bulb bins do not contain hours where the coincident humidity ratio exceeds 127.5 gr/lb, even though the humidity ratio can approach 150 gr/lb in the extreme. Similarly, humidity ratio bins do not contain hours where coincident dry bulb temperature exceeds 85F, even though dry bulb temperatures can approach 96F in the extreme
Bin Weather Data Options for Air Conditioning
Calculations have been done here for ventilation loads, which are fully dependent upon the temperature and humidity weather conditions, so they can easily illustrate the effect of the method employed. Many people are now using equipment which will treat ventilation separately from space loads because ASHRAE Standard 62-1989 has raised the recommended ventilation rates for buildings(7).
The weather parameters are used to calculate HVAC loads which lead to equipment energy consumptions. Ventilation loads are proportional to the difference between ambient conditions and indoor conditions. Recently, a comparison standard was developed which indicates the absolute and relative magnitudes of the latent and sensible loads introduced by ventilation air. This is called a set of Ventilation Load Indexes. Climates are characterized by the annual loads in ton-hours carried in by one scfm of ventilation air. These indexes indicated the dominance of latent load in ventilation air for most climates in the US, a phenomenon which is usually lost in conventional building analyses.
Consider the following options for bin representation:
Figure 3 is a contour map of hours of occurrence of weather conditions in Savannah, Georgia based upon a joint frequency bin distribution. Extreme low temperatures and humidities are excluded. Nearly all the data falls between about 40% relative humidity and 100% relative humidity (the saturation line) and there is a high occurrence of data between 80% and 100% relative humidity over the whole range.
In Figure 4, one can also find an overlay of plots of the data in bin representations of dry bulb temperature bins with mean coincident humidity ratios, and humidity ratio bins with mean coincident dry bulb temperatures. Dry bulb bins include the entire range of dry bulb temperatures, but do not show the full range of humidities, and vice versa with the humidity ratio bins.
Note also the ASHRAE 1% design conditions from the 1997 Handbook of Fundamentals(8). As with bins, they tend to underpredict the humidity when the dry bulb design point is used, and to underpredict the temperature when the dew point design point is used.
Up to about 73F and 105gr/lb, the two lines are similar. After that, they are quite different. The humidity ratio bins form an almost vertical line, de-emphasizing the range of dry bulb temperatures (maximum value of 83F where a reasonable number of hours occur), while the dry bulb bins form an almost horizontal line, de-emphasizing the range of humidity (maximum value of 112.5 where a reasonable number of hours occur). Neither format shows that many hours at high relative humidity will occur.
This information loss in single-parameter bin data is common, but especially problematic in the Eastern United States where humidity issues can become an HVAC design problem. This can lead to errors regarding the sensible and latent loads that need to be handled and their effect on the air conditioner performance.
Ventilation Air Conditioning Loads
The same indexes have been developed using bin data instead of hour-by-hour calculations. The annual loads are reduced to ton-hours/scfm rather than Btu/lb/hr (or kJ/kg/hr) in order to achieve a direct sense of the impact of the loads on the energy consumption of air conditioning equipment.
For all forms of weather data, the VLIís are calculated as follows:
where Ni or Nj are the number of hours in a particular bin. The indoor conditions used, Ti and Wi, were 75 F and 60% relative humidity. Only positive loads are used in the calculations.
One approach, which was used for all the bin representations, was to sum the latent load for all the bins where positive latent load exists for the latent component of the VLI, and to sum the sensible load for all the bins where positive sensible load exists for the sensible component of the VLI.
Another approach is more the way engineers would use a bin analysis. For this, temperature bins are used, but only to the neutral temperature point of the space (or a balance point of the engineerís choosing). This does not recognize humidity loads that occur when temperatures are below that. This humidity must be removed at some point, but it creates a great degree of discomfort until then, and will cause material degradation as well. Consider the graph in Figure 5 of the cumulative VLI as a function of the cut-off point for the analysis, using dry bulb bins referenced to indoor conditions of 75F and 60% relative humidity.
At 75F, where the sensible load no longer exists, the latent VLI has a less-than-complete value of 4.32 which is 81% of itís correct value of 5.36 for the year. By 69F or so for Savannah, the VLI would be about its correct seasonal value.
Now look at the comparisons of the methods used. The ventilation load is always dominated by the latent load, but temperature bin calculations are 17% too low. Were the bin analysis stopped at 75F, the error relative to the full VLI, a value of 6.52 would have been 33%. Similarly, the humidity bins underestimates the sensible load by about 43%, but this not a significant ventilation load anyway. The joint frequency method gives almost the same results as the hour-by-hour approach.
Figure 7 tabulates the results for the fourteen cities shown, which are scattered throughout the US, except for the less humid West Coast.
The first two rows are the VLIís based upon a full 8760 hours of a year. These values are the most accurate since they are independently calculated for every hour of the year.
The second two rows contain results calculated using joint frequency bins. Far fewer hours, or calculations, are required, yet the answers are quite close.
Next are VLIís calculated using dry bulb bins with mean coincident humidity, followed by the VLIís calculated using humidity ratio bins with mean coincident dry bulb.
The use of dry bulb bins produces erroneous latent loads, because of the use of mean coincident humidity values, which range from 6% to 82%. The use of humidity ratio bins produces erroneous sensible loads, because of the use of mean coincident temperatures, which range from 18% to 98%.
Using the more traditional calculation of bin loads, using dry bulb bins, down to the space neutral temperature, the sensible VLIís would be the same as when all dry bulb bins are used, but the latent VLIís are even more in error, ranging from 15% to 88%. For Savannah, the percent error rises to 33% from 17%. In Baltimore, it rises to 53% from 33%. In New Orleans, it rises to 24% from 10%. In Little Rock, it rises to 33% from 18%. In Miami, it rises to 15% from 6%. Since the dominant ventilation load is the latent load, these errors can cause severe problems.
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