Instantaneous Cooling Loads by Computer Based on ASHRAE's Time Averaging Method

Instantaneous Cooling Loads by Computer based on ASHRAE'S time averaging method

R. V. THOMAS 1

Naval Facilities Engineering Command Washington, D.C. 20390

Variables affecting cooling load calculations are numerous, often difficult to define precisely, and always intricately interrelated. Many of the components of the cooling load vary in magnitude over a wide range during a 24 hour period, and as the cyclic changes in load components are not usually in phase with each other careful analysis is required to establish the resultant maximum cooling load for a building or zone. There may be an appreciable difference between the net instan taneous rate of heat gain and the total cooling load at any instant. This differene is caused by the storage and subsequent release of heat by the structure and its con tents. This thermal-storage effect may be quite important in determining an economical cooling equipment capacity. This computer program uses the ASHRAE method of calculating cooling loads. It takes the instantaneous heat gain and breaks it into radiation and convection components. Convection components are added directly to the room space and instantaneous cooling load. The radiation components are summed and averaged over a given time period (dependent on building construction) up to and including the time of the desired load~ They are then changed into convected components and added back into the room space as part of the instantaneous cooling load (See figure 1). Therefore, a cooling load calculation at any given time is actually taking into account the radiation build up that has been taking place several hours earlier. The program will print out a building's cooling load, at any location, room by room, for any hour between 8 AM and 5 PM and contains a psychrometric routine for calculating moisture content, latent heat and relative humidity. The building itself can also be rotated to find the optimum orientation. Built into the program are eleven types of roofs, eight types of walls, six activity levels of people and six room lighting levels.

Key Words: Convection, direction cosines, fenestration, heat lag, latent heat, radiation, relative humidity, sensible heat, solar heat gain factor, thermal-storage, total equivalent temperature differentials, "U" factor.

1. Introduction

Calculation of a cooling load by hand using ASHRAE'S methods becomes very tedious and lengthy, especially when the process has to be repeated to find the hour of the maxium load or the orientation for minimum load. Lengthy and repetitious calculations such as these lend themselves very well to solution by computer and in this case the problem was programmed in fortran for a Burroughs 5500 time sharing computer.

2. Basic Considerations

Heat lag should be carefully considered in the cooling load calculations. In certain types of buildings the effect of solar radiation is still apparent several hours after the sun has shifted from that exposure. In other types having a much lighter construction, the heat gain due to solar radiation decreases markedly with the passing of the sun. Some walls, war~ed by the sun, may radiate heat long after the passing of the sun. In these cases the greater mass may be used to your advantage by pre-cooling it below the room design conditions prior to the hour of peak load and much of the sun's radiant energy will go into raising the temperature of the walls. (see figure 1).

1 Mechanical Engineer, mechanical design.

225 2.1 Fenestration Areas

Solar heat gain factors were used in calculating heat gain through fenestration area~, These solar heat gain factors were developed from the equations found in Chapter 28 of [~ which locate the sun's position in the sky with respect to the surface in question, These equations express the radiation from the sun on a surface as a function of the date, time of day, latitude, and direction cosine of the surface receiving the radiation. To further simplify the input and eliminate the need for putting in direction cosines of building surface, direction cosines for the most commonly used directions (N, NE, E, SE, S, SW, W, and NW) were built in to the program so the user need only supply the direction ("N", ''NE", ... etc) the surface is facing. By using a looping method and advancing the hour each loop, the sun's position is advanced across the sky and the result ing solar heat gain to each building surface is calculated, In the early stages of development, the solar heat gain factors thus calculated were then checked with the standard ASHRAE solar heat gain tables for various latitudes.

The program then time averages these factors (length of time hg average depends on building con struCtion)and breaks them into convected and radiant components. It then multiplies them by the fenestration area and adds the resultant heat gain to the room load. Shading devices such as drapes, blinds, sun screens, etc. are handled by inputing the proper shade factor,

2.2. Walls and Roof

Heat gain through the walls and roof is calculated by using total equivalent temperature differ entials (heat gain divided by "U" value), These quantities have dimensions of temperature and take into account the solar radiation heat gain and heat gain from the difference between inside and outside design temperatures.

(Heat coefficient) Total hea~ t:ansmission from ~ (Total equival~nt _ ~ transm~ssio~ 1 solar radLatLon and temperature = temperature dLfferentLal * Btu hr-1 ft 2 °F difference between outside and ( room air, Btu hr-1 ff2

Total equivalent temperature differentials for eight types of walls and eleven types of roofs from [1)? have been stored in permanent files in order to reduce the amount of input data required. Since these differentials are based on a daily outdoor temperature range of 20 degrees, a routine for correcting these equivalent temperature differentials for daily ranges other than 20 degrees has been built in,

Heat transmitted through the walls and roof is broken down into components similar to the method used above for glass. The convected portion is obtained by multiplying the total temperature differ ential of the time of the desired load by the "U" Value and the area. The radiant portion is obtained by averaging the total equivalent temperature differential several hours leading up to and including the hour of the desired cooling load (the exact number of hours time lag is determined by the program depending on the type of construction). These values are then multiplied by the "U" value and the area.

Following the methods of ASHRAE, 40% of the convected and 60% of the radiant heat gain are added to the instantaneous cooling load.

2,3. Latent Heat

Heat and moisture are given off by humans at different rates depending on their level of activity sensible and latent heats can, in many instances, become a large fraction of the total load, and these 2 Six different activity levels of occupants with their associated lighting Watts ft- and ventilation requirements were built into the program so the user need only specify the type and number of persons who will be occupying the space. An exception code was also built in which allows the user to insert any values of sensible and latent heat, lighting or ventilation CFM which differ from the standard values.

A subroutine using computer developed equations from [3] was then written to express relative humidity and moisture content as a function of the dry bulb and wet bulb temperature, This routine is used to calculate the moisture content of the ventilation air, the resulting latent load, and the relative humidities of the air at indoor and outdoor design conditions.

The daily outdoor temperature is varied from morning to night by a routine based on a "time" versus "outdoor temperature" chart from [2].

2 Figures in brackets indicate the literature references at the end of this paper.

226 3. Output

A sample of the prograrris output (see figure 2) shows a typical search for a building's peak load, The following is an explanation of headings over the printout:

RM ID -This is the ID. No. of the various rooms for which the cooling load is being solved, The entire building may be looked at as one room for a quick analysis of a building cooling load.

RSH - This is the room sensible heat. It is composed of radiation and convected heat through the glass, doors, wall, roof, lights and the sensible gain from the people plus the sensible load from the ventilation air that by passes the coil plus any miscellaneous load,

RTH - This is the room Total heat. It is composed of RSH plus the latent load from the people and the latent load from the ventilation air that by-passes the coil,

OA SH - This is sensible heat of the outside air that is not by-passing the coils, It is calculated for the given time of day,

OA TH - This is the OA SH plus the latent heat of the outside air that is not by passing the coils. It is calculated for the given time of day.

OA CFM- This is the amount of outside air that is being supplied to the room. Usually based on local codes and ordinances on ventilation requirements.

GTH - This is the grand total heat and is the sum of RTH plus the OA TH.

BUILDING TOTAL- This is the sum of all the GTH 1 s from each room, In the case where the building is treated as a single room, GTH will equal BUILDING TOTAL.

4. References

1 ASHRAE, Handbook of Fundamentals 1967. 3. Fairfax, J, P. and Tung, J, S-T "Construction of a psychrometric 2 Trane, Solar Tables for heat gain table by use of a digital computer", calculations, 1966. ASHRAE JOURNAL, March 1968, 59-61.

INTERIOR FURNISHINGS RADIATION CONVECTION AND STRUCTURE, VARIABLE HEAT STORAGE

INSTANTANEOUS (DELAYED IN TIME) ~ HEAT GAIN 1

AIR IN SPACE AND CONVECTION INSTANTANEOUS CONDITIONING COOLING LOAD 'EQUIPMENT

THE RADIATION ABSORBED BY THE INTERIOR FURNISHINGS AND STRUCTURE REACHES THE GONDITIONING EQUIPMENT AFTER A CONSIDERABLE TIME DELAY

Figure 1. Origin of the Difference Between the Magnitudes of the Instantaneous Heat Gain and Instantaneous Cooling Load

2Z7 ***BUILDING COOLING LOAD AT TIME= 1500 OUTS IDE DSGN DB & WB TE"MP= 95,0 78,0 RH'l"o= 47.4 INSIDE DSGN DB & WB TEMP= 75,0 60,5 RR%= 43.2

OACFM GT!I RM ID RSH RTH OA SH OATH 14859, 10798. 12117. 935. 2741. so. 1 40, 20911. 16563, 18718. 748. 2193. 2 80, 20084. 3 13588, 15698, 1496. 4386. 50. 14503, 4 10442. 11761. 935. 2741.

BUILDING TOTAL= 70357.

WHAT TIME NEXT ?1600

***BUILDING COOLING LOAD AT TIME= 1600 OUTSIDE DSGN DB & WB TEMP= 95,0 78,0 RH%= 47,4 INSIDE DSGN DB & WB TEMP= 75.0 60.5 RH'l"o= 43.2

OA CFM GTH RM ID RSH RTH OA SH OA TH 15483, 11450, 12769, 907. 2713. so. 1 40. 20950, 16625. 18780, 726. 2171. 2 80, 20225. 13774, 15884, 1451. 4341. 3 so. 14847 . 4 10815. 12134. 907. 2713.

BUILDING TOTAL= 71505.

WHAT TIME NEXI' ?1700

***BUILDING COOLING LOAD AT TIME= 1700 OUTSIDE DSGN DB & WB TEMP= 95.0 78.0 RH%= 47.4 INSIDE DSGN DB & WB TEMP= 7 5.0 60.5 RR']"o= 43.2 OA CFM GTH RM ID RSH RTH OA SH OA TH 15460, 1 11493. 12812, 842. 2648. so. 2118. 40. 20598. 16325 0 18480, 673. 2 20157. 13810. 15920, 1346. 4237. 80, 3 14939. 4 10973, 12292. 842. 2648. so.

BUILDING TOTAL= 71154.

Figure 2. Building Cooling Load at Time 1500

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