Coil icing and other opportunities within freezer/anteroom complexes.

ABSTRACT

This treatise concerning moisture precipitation under freezing conditions proceeds from similarity between the coil-frost formations of a recent coil-frost testing program and coil-frost formations frequently found in freezers coincident with frost accumulations around doorways or elsewhere within the room. Calculated data involving dehumidification alternatives applicable to the two (or more) temperature/humidity environments typical of freezer/anteroom complexes are presented, which reveal the paramount role of applied psychrometrics with respect to air-side engineering at freezer temperatures and which, in conjunction with modern control-system technology, prepare the way for a future treatise that promises significant logistics-related benefits through the integration of all refrigeration loads of these high-usage facilities into an overall refrigeration-system design within which coil-frosting need not occur.

BACKGROUND--CONVENTIONAL DEHUMIDIFICATION

ASHRAE Technical Committee 10.8, Refrigeration Load Calculations, was formed from a Task Group circa 1983. Coincident with its formation, the ASHRAE director of technology directed questions to the new TC of contradictory refrigeration-system performance where snowlike coil frost was seen regardless of the location at which the ice-crystals first appeared. All questions involved freezer/anteroom complexes. Contradictory instances occurred where the addition of artificial sensible-heat load--with no other change--was accompanied by significantly lowered freezer temperature. Other contradictory instances of lowered freezer temperature occurred simply in response to raised suction temperature, sometimes dramatically, typically a week or so following the change. Such observations in conjunction with one member (Cole 1989) having recently published a paper describing aerosol emissions commonly seen during coildefrosting, which had expanded upon earlier coil-icing research (Stoecker et al. 1983), promrted an early decision by the new TC to prepare and ask the society to fund a testing program for the measurement of freezer heat gain due to coil defrosting under the various circumstances of coil design and operation customarily found in industry. Following forums, seminars, and symposia considering such a program, a Work Statement was eventually approved in 1997 that became ASHRAE RP-1094, "A Study to Determine Heat Loads Due to Coil-Defrosting--Phase II."

Coincident with the contradictory performance described above, Technical Committee 10.5, Refrigerated Distribution and Storage Facilities, sponsored an infiltration-air study for which the 1984 Work Statement read as follows:

  In recent years the size and number of refrigerated distribution and
  storage facilities have grown significantly and it is now estimated
  that refrigerated warehouses use 1 x [10.sup.14] Btu's of energy per
  year. In spite of this large use of energy and the fact that
  infiltration represents 50% or more of the refrigeration load, the
  method of calculation for this load is fundamentally left to the
  experience [emphasis added] of the design engineer.

However, the resulting study (Hendrix and Henderson 1988) produced data that fell far short of corroborating the 50% or more conclusion of TC 10.5, which was seen to not only reinfo[R.sub.C]e reasons for the TC 10.8 coil-frost study but to lend confirmation as well to the great harm to frosted-coil cooling performance that had been surmised.

Omitted Psychrometric Analysis

The coil-frost studies of RP-1094 experienced discord stemming from differences in perspective throughout most of the undertaking. To explain this circumstance, it was apparent in 1983 at the time of TC 10.8's formation that refrigeration air-side engineering was universally lacking throughout the low-temperature dry-surface-coil refrigeration sector of the industry. Unlike customary engineering practice at air-conditioning levels, consideration of phenomena associated with moist-air precipitation on dry-surface-type coils at freezer temperatures was simply being omitted.

This omission, a quirk among an otherwise demanding category of highly proficient engineers, was found to consist of tacit agreement throughout the low-temperature industry--established in earlier days--that applied psychrometrics, the authoritative engineering basis for the efficient sensible and latent conditioning of moist air to any particular need, could be safely ignored at freezer temperatures. However, originating without wide-scale problems in the pre-computerized age of low-doorway-usage freezers, the omission had resulted, with the introduction of computerized warehousing and associated high-usage doorways, in the exceedingly large tonnage increases (de facto because of very sizable refrigeration-equipment additions found necessary with no other explanation), which prompted the 1984 Work Statement of TC 10.5. The omission had similarly resulted in moisture precipitation at freezer doorways in quantities that not only created safety hazards due to fog, frost, and ice at those locations but in serious warehousing productivity interference as well. Clearly, the high-usage doorways that coincided with the computerization of food storage-and-retrieval operations underway in the 1970s, and with logistical improvements generally, had resulted in moist-air infiltration well into the range where psychrometric effects and their overall consequence on good refrigeration-system design could no longer be ignored. These refrigeration-related consequences, typical of the early 1980s, are illustrated by Figures 1 through 4. Figure 5 contains an additional refrigeration-related element to be addressed later.

Addressing Psychrometric Principles

The RP-1094 testing program was guided by the straight-line principle of applied psychrometrics as expounded in the US government-financed manual GRP-158 (ASHRAE 1978) and its successors (e.g., Pedersen et al. [1998]). (1) A hoped-for testing outcome of value to system-design engineers was establishment of a dry-bulb/wet-bulb, coil-entering-air demarcation representable on the psychrometric chart between the formation of favorable (icelike) and unfavorable (snowlike) coil frost, which, prior to the efforts of RP-1094, had been postulated for freezers generally by Smith (1989) and tested, though at high freezer temperatures only, by Cleland et al. (1993). Although achieving the hoped-for demarcation during either program did not occur, a more useful visualization for refrigeration-system designers (and operators) was observed to be the light to very dense frosting that occurred on the test coil's inlet face but not within the coil.

The same light to very dense inlet-face frosting of the test coil had been consistently observed in the industry during the early 1980s at the time of TC 10.8's formation and the ad hoc 50% or more observation of TC 10.5 quoted above. However, simply on the basis of attention to cause and effect on the part of most refrigeration-system operators by the end of the 1980s, it had become customary practice (1) to introduce sensible heat to ice-crystal-laden doorway infiltration by means of large electric heaters--amazingly so because of usable, hot-gas waste heat generally available nearby--and (2) to limit coil TD (coil entering-air temperature minus coil-refrigerant temperature) to approximately 10[degrees]F(5.6[degrees]C) maximum, each action independently having been found contributory, if not singularly effective, toward the formation of coil icing rather than coil frosting. The phenomena at play are readily demonstrated by means of the two lines drawn on Figure 12 and discussed later under "Comparisons Generally." These phenomena were expanded upon earlier by Smith (1992, 1998).

The Ambiguity of Coil-Frost Testing

Regarding the failure to establish demarcation mathematically, reference is made to Chung and Algren (1959) who wrote with respect to coil performance: "the density and the thermal conductivity of the frost vary unpredictably and through a wide range. It is clear that no mathematical solution to the problem is possible ...." Consistent therewith, it was written 43 years later by Sherif et al. (2002) with respect to the RP-1094 coil-frost testing: "In the middle section of the coil ... significant deviations (up to 34%) between the calculated and the straight-line paths were observed." Three companion references by Mago and Sherif (2005a, 2005b, 2005c) further expand upon this topic. Thus, a sufficiently clear-cut, comprehensive demarcation between icelike and snowlike coil-frosting conditions was found realistically unattainable, but the testing is seen to have confirmed industry's current practice of (1) limiting coil TD (see Figure 12 in this respect) and (2) eliminating airborne ice crystals by means of sensible-heat addition wherever ice crystals appear.

BACKGROUND--DESICCANT DEHUMIDIFICATION

Coincident with the coil-defrosting study, TC 10.5 sponsored a seminar with a view toward ascertaining to what extent desiccant dehumidification should be recommended in its chapter of the ASHRAE Handbook--Refrigeration. Very simply, with freezer-doorway and related frosting problems increasing at the time, desiccant dehumidification was increasingly serving as corrective. Thus, with over-cooling-Plus-reheat dehumidification of freezer anterooms being customary textbook-wise where latent-heat ratio (LHR) of room load exceeds LHR of the evaporator-unit selection (i.e., where sensible-heat ratio [SHR] of room load is less than SHR of the air-cooling process), gas-heat-reactivated desiccant dehumidification was contrasted, in discourse-style at the seminar, against the textbook solution and against employment of a freezer vestibule in each case. The loading-dock analyses included herein, comparing tonnage, electrical demand, energy cost, and primary-energy consumption for the two methods of dehumidification, with and without freezer vestibules, were the basis of the earlier discourse. Although the analyses were made available at the seminar, for technical committee response, the analyses require formal presentation as shown and discussed below.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

COMPARATIVE ANALYSES

Commercial scale unit (CSU), a designation borrowed from the United States Department of Energy as shown in Figure 6, depicts a typical freezer-doorway situation assumed for four loading-dock refrigeration system alternatives. A ratio of eight truck load-out doors to one freezer doorway is assumed, and 3 tons (10.6 kW) per load-out door is used in accordance with a common loading-dock equipment-sizing practice of industry.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Figure 7 depicts, for the four alternatives, tons of refrigeration capacity required per ton of basic heat gain as a function of room SHR ranging between 1.00 and 0.60. The graphical depictions are as follows:

* Table 1, Analysis NC, denotes a normally high room-design humidity and conventional dehumidification.

* Table 2, Analysis ND, denotes a normally high room-design humidity and desiccant dehumidification.

* Table 3, Analysis LC, denotes a psychrometrically correct, lowered room-design humidity and conventional dehumidification.

* Table 4, Analysis LD, denotes a psychrometrically correct, lowered room-design humidity and desiccant dehumidification.

Thus, the four alternatives are compared for a 45[degrees]F (7.2[degrees]C) loading dock opening to a -5[degrees]F (-20.6[degrees]C) freezer. Analyses NC and ND for conventional and desiccant dehumidification, respectively, assume a normal design RH of 80% in both cases. Analyses LC and LD, also for conventional and desiccant dehumidification, respectively, assume a lowered design RH of 41% as dictated by the "squall line" shown and explained in Figure 8.

All calculated data for conventional dehumidification analyses NC and LC stem from formulae accompanying the data for air-refrigerating processes depicted in Figures 9, 10, and 11. All aspects of the calculating procedures are in accordance with ASHRAE's Cooling and Heating Load Calculation Principles (Pedersen et al. 1998).

All calculated data for desiccant-dehumidification analyses ND and LD stem from the rating data of a representative manufacturer of gas-heat-reactivated desiccant-dehumidification equipment (Munters 1995).

Freezer Vestibule

The term freezer vestibule, employed for analyses NC and ND and depicted functionally in Figure 8 by means of line [N.sub.O]V, denotes a moisture step-down chamber at the entrance to an otherwise open freezer doorway. Other freezer-vestibule features, essential to the minimizing of freezer doorway air exchange and to the prevention of airborne ice-crystal precipitation while satisfying logistical requirements at that location, are recommended for a treatise in the very near future.

Coefficients of Performance

Table 5, Comparative COPs for Alternative Loading-Dock Refrigeration Systems, was prepared from Tables 1, 2, 3, and 4. One should note that Table 3 for the LC system could be realistically omitted because of excessive over-cooling-with-reheat through most of its operating range; see comparative curve 3 on Figure 7 in this regard. Therefore, analysis NC for conventional dehumidification (Curve 1 of Figure 7) employing a nonstop pass-through freezer vestibule is the most energy-efficient choice of the four. One should note in this regard that the 4.21 kW electrical demand shown for the vestibule is a matter of conventional field engineering rather than a manufacturer's rating.

Thus, comparing COP for conventional system NC to either of the two desiccant systems as shown in Table 5, the authoritatively calculated values reveal for a typical refrigerated loading dock that primary energy required of desiccant-based refrigeration is approximately double that of properly designed, conventional refrigeration.

Comparisons Generally

In addition to the squall-line limit for anteroom moisture-level control, Figure 8 also depicts (by the dashed line) the result of air-mixing between Point [N.sub.o] (a normally found design-humidity level for freezer-anterooms) and Point [F.sub.o] (a typical freezer condition). Figure 1, taken just within the freezer, shows in actuality the airborne ice crystals predicted by infiltration along the squall line. Figure 2 shows, as labeled, "Psychrometric effects Complete," a common sight throughout the 1980s, a significantly less common sight ever since, but at the expense of large electric heaters installed within an industry procedure quite void of refrigeration engineers. Line VT[F.sub.o] on the chart represents an on-the-verge-of-precipitation air-mixing path for moist-air infiltration entering the freezer. Line VT, terminating at T (tangency with the saturation curve), represents, for an anteroom air-cooling process, the coldest coil-surface temperature beyond which airborne ice-crystal precipitation within the coil, though not necessarily on the coil, is predictable.

Figure 9 shows (1) the squall line as defined on Figure 8; (2) Points [N.sub.o], [L.sub.o], and [F.sub.o] denoting normal, lowered, and freezer coil-entering-air conditions; and (3) [N.sub.T], [L.sub.T], and [F.sub.T] denoting Points of tangency for "ideal" air-cooling processes terminating on the saturation curve (except for the air-bypassed portion), where "ideal" refers to cases in which SHR of "air-warmup" (as labeled on Figures 10 and 11) is equal to or lower than SHR of the air-cooling paths terminating at [N.sub.T], [L.sub.T], or [F.sub.T].

Figures 3 and 4, showing frost-clogged coils (from the 1980s), depict frosting conditions similar to the recent RP-1094 test results referred to earlier. The ceiling accumulations seen in the case of Figure 4 are due, quite expectedly, to the aerosol emissions associated with snowlike frost defrosting, also as referred to earlier.

Figure 5 can be seen to demonstrate profoundly the overall consequence of omitted air-side engineering at freezer temperatures. Obviously, from the "avalanche" after-effects to be seen, "wind-driven snow" had to have been present in the coil-inlet airstream. This photograph was taken a few weeks after the coil was switched from a -27[degrees]F(-33[degrees]C) suction line to a -45[degrees]F (-43[degrees]C) suction line. (The change in saturated suction temperature had been recommended, enigmatically, by someone as part of an "energy management" program!) The type of frosting seen coincided with a several-degree rise in freezer temperature. The coil, after two months, was returned to the -27[degrees]F line, following which the freezer temperature returned to its setting and the coil again iced and deiced normally.

Figure 12 deserves special engineering attention where desiccant dehumidification is seen advantageously as a corrective to coil, doorway, and other frosting locations in freezer/anteroom complexes. Line [F.sub.o] [F.sub.T] (well within the subsaturated, no-precipitation region of the Psychrometric chart) versus Line [F.sub.o] [F.sub.x] (well within the supersaturated, airborne ice-crystal region of the chart) is the engineering matter to note: Line [F.sub.o] [F.sub.x] represents the snow-making process of Figure 5 while Line [F.sub.o] [F.sub.T] represents the ideal coil-icing condition to which the system had finally been returned. Had desiccant dehumidification been provided instead, doing so would have constituted a "fix" with the strange [F.sub.o] [F.sub.x] air-cooling process remaining, which, based on Table 5, would have constituted frost correction at approximately double the primary energy cost of a correctly engineered retrofit.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

CONCLUSIONS

1. Field experience, which has observed that coil inlet-face frosting is eliminated as a consequence of airborne ice-crystal prevention at doorways or elsewhere, is seen to have been confirmed in the course of the RP-1094 frost-testing program.

2. The snowlike coil-frost concerns of the recent past are seen to have quite totally disappeared where design coil TD is limited in accordance with the straight-line principle of applied psychrometrics as authoritatively expounded by Pedersen et al. (1998).

3. Inattention to the straight-line principle of applied psychrometrics at freezer temperatures is seen to be the root cause of, not only coil-frosting rather than coil icing, but of frosted doorways, iced or wet floors, and fog in the doorway vicinity as well. In the case of modern-day computerized warehousing, these effects are particularly adverse to productivity and energy consumption.

4. The frost-corrective role seen for desiccant-based refrigeration, while possibly valid where inappropriately designed conventional refrigeration has been irredeemably installed, is shown to be extremely inefficient, and generally absolutely unnecessary, when compared against conventional refrigeration of appropriate design. First-cost of the latter as a retrofit should expectedly be more advantageous as well.

5. Authoritative calculating procedures for freezer/anteroom complexes affirmed by the recent RP-1094 testing program show that the optimum air-cooling path for the anteroom and the optimum ice-crystal-free exfiltration-air path to the freezer are, in each case, along the "squall line."

6. Refrigeration system design engineers, in the best interest of their employers (and national energy policy), should stand against the procedure of their voice not being included with respect to door selection, other doorway treatment, and the management of freezer doorways generally.

7. Any motivation toward future frosted-coil testing with the intention of mathematical modeling should consider the unpredictable nature of frost growth due to its varying insulating effect and resistance to airflow.

Special Observation and Conclusion

8. For high doorway-usage freezer/anteroom complexes designed and operated in accordance with the straight-line principle of applied psychrometrics, keen management of doorway-usage time-periods, frequency, and duration is seen to offer great potential for energy savings additionally: (1) no-usage time far outweighs actual-usage time of these doorways and (2) modern-day control technology and related devices are available to capitalize on the large disparity without infringing upon safety, productivity or other logistical concern.

9. Thus, consistent with the long-established calculating procedures of ASHRAE, and in keeping with modern-day logistics, major consideration should be given to the integration of all refrigeration loads of freezer/anteroom complexes into an overall refrigeration-system design. Microprocessor-regulated control systems and associated controller technology in this regard should become mandatory discourse between industrial-refrigeration engineers and their control-system counterparts. Discussing the elements of such discourse with respect to control-system functions should be the objective of a treatise soon to follow.

ACKNOWLEDGMENT 

The author wishes to thank Mr. William G. Acker, president, Acker & Associates, Green Bay, Wisconsin, for his assistance and review of the Psychrometric calculations in this paper. His many years of experience in this area were invaluable.

REFERENCES

ASHRAE. 1978. GRP-158, Cooling and Heating Load Calculation Manual. Prepared under HUD Contract No. H-2303. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Chung, P.M., and A.B. Algren. 1959. Frost formation and heat transfer on a cylinder surface in humid air cross flow. ASHRAE Transactions 65:232.

Cleland, A.C., A.N. O'Hagan, and D.J. Cleland. 1993. Air cooling coil performance under frosting conditions, Part I: Performance measurement and results and Part II: Modeling. Refrigeration Science and Technology 1993-3:345-362.

Cole, R.A. 1989. Refrigeration loads in a freezer due to hot gas defrost and their associated costs. ASHRAE Transactions 95(2):1149-54.

Gameiro, W. 2000. Cutting and boning room design. 2000 IIAR Convention, Nashville, Tennessee.

Hendrix, W.A., D.R. Henderson, and H.Z. Jackson. 1989. Infiltration heat gains through cold storage room doorways. ASHRAE Transactions 95(2):1158-68.

Mago, P.J., and S.A. Sherif. 2005a. Coil frosting and defrosting issues at low freezer temperatures near saturation conditions. ASHRAE Transactions 111(1):3-17.

Mago, P.J., and S.A. Sherif. 2005b. Frost formation and heat transfer on a cold surface in ice fog. International Journal of Refrigeration 27(5):538-46.

Mago, P.J., and S.A. Sherif. 2005c. Psychrometric charts and property formulations of supersaturated air. HVAC & R research 11(1):147-63.

Munters. 1995. Bulletin 400. Honeycombe[R] Industrial Dehumidifier Performance.

Pedersen, C.O., D.E. Fisher, J.D. Spitler, and R.J. Liesen. 1998. Cooling and Heating Load-Calculation Principles, chapter 8 and Appendix D. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

Sherif, S.A., P.J. Mago, and R.S. Theen. 2002. A study to determine heat loads due to coil defrosting--Phase II, Final Technical Report No. UFME/SEECL-200201, ASHRAE Project No. 1094-RP. Department of Mechanical Engineering, University of Florida, Gainesville, January 2002 (Revised May 2002). "Conclusions," p. 105.

Smith, G.R. 1989. Theoretical cooling coil calculations at freezer temperatures to avoid unfavrable coil-frost. ASHRAE Transactions 95(2):1138-52.

Smith, G.R. 1992. Latent heat, equipment related load, and applied psychrometrics at freezer temperatures. ASHRAE Transactions 98(2):649-57.

Smith, G.R. 1998. applied psychrometrics for high-usage freezers. ASHRAE Transactions 104(1):1717-21.

Stoecker, W.F., J.J. Lux, Jr., and R.J. Kooy. 1983. Conserving energy in industrial refrigeration systems by reducing condensing temperatures--Effect on hot gas defrost. Final report, ASHRAE RP-193. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

George R. Smith, PE

Life Member ASHRAE

George R. Smith is president of Industrial Air Conditioning Company, Lewistown, MT.

(1). As GRP-158 is out of print, all subsequent references herein will refer readers to Pedersen et al. (1998)--this publication provides all of the information from GRP-158 with relatively no changes.

Table 1. Loading-Dock Refrigeration--Analysis NC (Note A); Conventional
Dehumidification--Commercial-Size Unit (Note B); 45[degrees]F
Dock--80%RH; Normal Design Humidity; Electrically Heated "Freezer
Vestibule" Employed (Note C)

Symbol      Item                                     Unit

-           Percent moisture gain                    %
[R.sub.R]   Room sensible heat ratio (RSHR)          -
[P.sub.V]   Vestibule power (Note E)                 kW
[T.sub.S]   Coil surface temperature (Note F)        [degrees]F
[Q.sub.TG]  Loading-dock total design heat gain (1)  ton
[Q.sub.LG]  Loading-dock total latent heat gain (2)  ton
[R.sub.C]   Coil sensible heat ratio                 -
[Q.sub.D]   Coil defrosting heat gain (3)            ton
[Q.sub.C]   Hot-gas returned to compressor (3)       ton
[Q.sub.RA]  Reheat added load (4)                    ton
[Q.sub.V]   Vestibule load (5)                       ton
[Q.sub.TL]  Total refrigeration load (6)             ton
[R.sub.P]   Refrigeration power ratio (7)            kW/ton
[P.sub.D]   Total electrical demand (8)              kW
HYEU        Half-year energy usage (9)               therm/yr
HYEC        Half-year energy cost (10)               $/yr

Symbol      Calculated Data

-                0         10         20         30
[R.sub.R]        1.00       0.90       0.80       0.70
[P.sub.V]        4.21       4.21       4.21       4.21
[T.sub.S]       39.5       38.0       36.5       31.5
[Q.sub.TG]      24         24         24         24
[Q.sub.LG]       0.00       2.40       4.80       7.20
[R.sub.C]        1.00       0.90       0.80       0.70
[Q.sub.D]        0.00       0.00       0.00       5.54
[Q.sub.C]        0.00       0.00       0.00       1.30
[Q.sub.RA]       0.00       0.00       0.00       0.00
[Q.sub.V]        1.20       1.20       1.20       1.20
[Q.sub.TL]      25.20      25.20      25.20      32.04
[R.sub.P]        0.81       0.84       0.87       0.97
[P.sub.D]       24.62      25.38      26.14      35.29
HYEU        11,041     11,380     11,719     15,824
HYEC        $6,471     $6,670     $6,869     $9,274

                             Break
Symbol      Calculated Data  (Note D)

-                40               34
[R.sub.R]         0.60             0.66
[P.sub.V]         4.21             4.21
[T.sub.S]        23.0             23.0
[Q.sub.TG]       24               24
[Q.sub.LG]        9.60             8.16
[R.sub.C]         0.66             0.66
[Q.sub.D]         7.39             6.28
[Q.sub.C]         1.73             1.47
[Q.sub.RA]        4.24             0.00
[Q.sub.V]         1.20             1.20
[Q.sub.TL]       38.55            32.95
[R.sub.P]         1.14             1.14
[P.sub.D]        48.16            41.78
HYEU         21,596           18,732
HYEC        $12,658          $10,979

Formulae

 (1)  [Q.sub.TG] = (24) tons (Note B)
 (2)  [Q.sub.LG] = ([Q.sub.TG])(1 - [R.sub.R])
 (3)  If ([T.sub.S] > 32), then ([Q.sub.D] = 0) and ([Q.sub.C] = 0);
        If (TS [less than or equal to] 32), then ([Q.sub.D] = 0.77)
        ([Q.sub.LG]) and ([Q.sub.C] = 0.18)([Q.sub.LG]). (Note G)
 (4)  [Q.sub.RA] = ([Q.sub.TG])([R.sub.C] - [R.sub.R]) /
        (1 - [R.sub.C]) (Note H)
 (5)  [Q.sub.V] = ([P.sub.V])(3412/12000)
 (6)  [Q.sub.TL] = ([Q.sub.TG]) + ([Q.sub.D]) + ([Q.sub.C]) +
        ([Q.sub.RA]) + ([Q.sub.V])
 (7)  [R.sub.P] = (0.02)(30 - [T.sub.S]) + (1.0) (Note I)
 (8)  [P.sub.D] = ([P.sub.V]) + ([R.sub.P])([Q.sub.TL])
 (9)  HYEU = ([P.sub.D])(3412) / ([10.sup.5])(0.3333)(8760hr/yr)(0.5) =
        449[P.sub.D] (Note J)
(10)  HYEC = ([P.sub.D])(CE)(8760)(0.5) (Note J)

(A) This analysis is intended for preliminary judgment purposes.
(B) One "Commercial Scale Unit" (CSU, a DOE term) is taken to
consist of one freezer doorway and eight truck load-out doors. For total
heat gain, 3 tons per truck load-out door times 8 = 24 tons in
accordance with an industry approximation customarily employed.
(C) See Figure 10 for the psychrometric basis and graphical depiction of
these calculations. Cost of electricity, CE = $0.06 per kWh. Reheat not
required for RSHRs 0.66 and larger. Coil icing is predicted to occur for
all RSHRs less than 0.66.
(D) "Break" denotes the point on the psychrometric chart where tangency
occurs between the air-cooling path and the saturation curve. For any
[T.sub.S] below this point, sensible overcooling occurs and reheat is
required.
(E) [P.sub.V] denotes heat gain to the freezer vian an 8 x 12 freezer
vestibule subjected to 20 pass-throughs per hour of 5 seconds door-open
time each. This heat gain, as regularted by means of modern control
systems technology, is essentially entirely independent of all heat
transfers throughout the freezer/anteroom complex. All calculations are
in accordance with Pedersen et al. (1998).
(F) See psychrometric depiction.
(G) The factors shown in Formula 3 were determined from the coil
defrosting heat gain data of Cole (1989).
(H) Reheat assumed to be free hot-gas heat reclaim. Formula 4 is
determined from the geometry of the psychrometric depiction for
the air-cooling, air-reheating, and air-warmup paths or by equating
[R.sub.R] to [R.sub.C] in their breakdown values.
(I) Assumed [R.sub.P] provides average power input to compressor,
condenser, evaporator, and their ancillary devices for modern,
efficiently designed, water or evaporative condenser-cooled systems.
This relationship was derived from Gameiro (2000). Specifically
determined values of [R.sub.P] should be used if available.
(J) Formulae 9 and 10 assume constant operation wherein full-load energy
consumption half the time is assumed to be representative, annually, of
the accumulated variations that actually occur.

Table 2. Loading-Dock Refrigeration--Analysis ND (Note A); Desiccant
Dehumidification--Commercial-Size Unit (Note B); 45[degrees]F
Dock--80%RH; Normal Design Humidity; Electrically Heated "Freezer
Vestibule" Employed (Note C)

Symbol            Item                                  Units

-                 Percent moisture gain                 %
[R.sub.R]         Room sensible heat ratio (RSHR)       -
[P.sub.V]         Vestibule power (Note D)              kW
[Q.sub.TG]        Loading-dock total heat gain          ton
[Q.sub.LG]        Loading-dock total latent heat        Btu/h
                    gain (2)

Determination of Desiccant Dehumidification Model
[T.sub.PI]        Process inlet temperature             [degrees]F
[M.sub.PI]        Process inlet moisture                gr/lba
[M.sub.PO.sup.1]  Preliminary process outlet            gr/lba
                    moisture (Note E)
[V.sub.PI.sup.1]  Preliminary process air quantity (3)  [ft.sup.3]/min
-                 Manufacturers model (Note E)          -
[V.sub.PI]        Process air quantity (Note F)         [ft.sup.3]/min
PFA               Process Face Area (Figure 1)          ft[.sup.2]
PFV               Process face velocity (4)             ft/min
[V.sub.R.sup.o]   Maximum reactivation air              [ft.sup.3]/min
                    quantity (Figure 1)
[M.sub.PO]        Process outlet moisture (Figure 2)    gr/lba
K                 Factor based on PFA and [M.sub.PO]    -
                    (Figure 3)
[T.sub.PO]        Process outlet temperature (5)        [degrees]F
[V.sub.R]         Reactivation air quantity (6)         [ft.sup.3]/min

Energy Input Required for the Latent Heat Gain
[P.sub.DR]        Drier reactivation-air                kW
                    blower power (7)
[P.sub.DP]        Drier process-air blower power (8)    kW
[Q.sub.DP]        Drier process-air blower heat (9)     ton
[Q.sub.DA]        Drier process-air after-cooling (10)  ton
[T.sub.S]         Coil surface temperature (11)         [degrees]F
[R.sub.P]         Refrigeration power ratio (12)        kW/ton
[P.sub.L]         Latent heat refrigeration power (13)  kW
[Q.sub.R]         Reactivation heat (14)                therm/h
[Q.sub.V]         Vestibule load (15)                   ton

Energy Input Required for the Sensible Heat Gain
[Q.sub.SG]        Sensible heat gain (16)               ton
[P.sub.S]         Refrigeration power (17)              kW

Summation
[Q.sub.TL]        Total refrigeration load (18)         ton
[P.sub.T]         Total electrical demand (19)          kW
HYEU              Half-year energy usage (20)           therms/yr
HYEC              Half-year energy cost (21)            $/yr

Symbol                     Calculated Data

-                      0         10           20
[R.sub.R]              1.00       0.90         0.80
[P.sub.V]              4.21       4.21         4.21
[Q.sub.TG]            24         24           24
[Q.sub.LG]             0     28,800       57,600

Determination of  Desiccant Dehumidification Model
[T.sub.PI]            45         45           45
[M.sub.PI]            35.5       35.5         35.5
[M.sub.PO.sup.1]      -           3.0          3.0
[V.sub.PI.sup.1]      -        1303         2606
-                     -      HCD-2250    HCD-4500
[V.sub.PI]             0       1300         2600
PFA                   -           3.75         7.50
PFV                   -         347          347
[V.sub.R.sup.o]       -         600         1300
[M.sub.PO]            -           1.8          1.8
K                     -           0.080        0.080
[T.sub.PO]            -          82.5         82.5
[V.sub.R]              0        375          749

Energy Input Required for the Latent Heat Gain
[P.sub.DR]             0.00       0.69         1.38
[P.sub.DP]             0.00       1.85         3.69
[Q.sub.DP]             0.00       0.52         1.05
[Q.sub.DA]             0          4.5          8.9
[T.sub.S]             35         35           35
[R.sub.P]              0.9        0.9          0.9
[P.sub.L]              0.00       4.49         8.98
[Q.sub.R]              0.00       0.57         1.14
[Q.sub.V]              1.20       1.20         1.20

Energy Input Required for the Sensible Heat Gain
[Q.sub.SG]            24.0       21.6         19.2
[P.sub.S]             21.60      19.44        17.28

Summation
[Q.sub.TL]            25.2       27.8         30.4
[P.sub.T]             25.81      30.68        35.55
HYEU              11,574     16,244       20,914
HYEC              $6,784     $9,630      $12,476

Symbol                     Calculated Data

-                      30           40
[R.sub.R]               0.70         0.60
[P.sub.V]               4.21         4.21
[Q.sub.TG]             24           24
[Q.sub.LG]         86,400      115,200

Determination of  Desiccant Dehumidification Model
[T.sub.PI]             45           45
[M.sub.PI]             35.5         35.5
[M.sub.PO.sup.1]        3.0          3.0
[V.sub.PI.sup.1]     3910         5213
-                 HCD-4500     HCD-6800
[V.sub.PI]           3900         5200
PFA                     7.50        11.25
PFV                   520          462
[V.sub.R.sup.o]      1300         2200
[M.sub.PO]              3.2          2.8
K                       0.065        0.070
[T.sub.PO]             78.5         79.8
[V.sub.R]            1005         1392

Energy Input Required for the Latent Heat Gain
[P.sub.DR]              1.85         2.57
[P.sub.DP]              5.54         7.38
[Q.sub.DP]              1.57         2.10
[Q.sub.DA]             12.0         16.6
[T.sub.S]              35           35
[R.sub.P]               0.9          0.9
[P.sub.L]              12.20        16.81
[Q.sub.R]               1.52         2.11
[Q.sub.V]               1.20         1.20

Energy Input Required for the Sensible Heat Gain
[Q.sub.SG]             16.8         14.4
[P.sub.S]              15.12        12.96

Summation
[Q.sub.TL]             31.6         34.3
[P.sub.T]              38.92        43.93
HYEU               24,128       28,939
HYEC              $14,435      $17,367

Formulae

 (1)  [Q.sub.TG] = 24 tons (Note B)
 (2)  [Q.sub.LG] = (1 - [R.sub.R])([Q.sub.TG])(12,000)
 (3)  [V.sub.PI.sup.1] = ([Q.sub.LG]) / (0.68)([M.sub.PI] -
        [M.sub.PO.sup.1])
 (4)  PFV = ([V.sub.PI]) / (PFA) (Note G)
 (5)  [T.sub.PO] = ([T.sub.PI]) + (0.625)([M.sub.PI] - [M.sub.PO]) +
        (K)(250 - [T.sub.PI])
 (6)  [V.sub.R] = ([V.sub.PI])([T.sub.PO] - [T.sub.PI]) / (250 - 120)
        (Note H)
 (7)  [P.sub.DR] = (2.17 / 1000)([V.sub.R])(0.85kW/hp) (Note I)
 (8)  [P.sub.DP] = (1.67 / 1000)([V.sub.PI])(0.85kW/hp) (Note I)
 (9)  [Q.sub.DP] = ([P.sub.DP], kW)(3412 Btu/kWh) / (12,000 Btuh/ton)
(10)  [Q.sub.DA] = ([V.sub.PI])(1.1)([T.sub.PO] - [T.sub.PI]) /
        (12,000)
(11)  [T.sub.S] = ([T.sub.PI]) - (10[degrees]F) typically. A smaller
        temperature difference may be dictated by proximity of the
        saturation curve.
(12)  [R.sub.P] = (0.02)(30 - [T.sub.S]) + (1.0) (Note J)
(13)  [P.sub.L] = ([Q.sub.DP] + [Q.sub.DA])([R.sub.P])
(14)  [Q.sub.R] = ([V.sub.R])(1.1)(250 - 95)([10.sup.-5]) - ([P.sub.DR])
        (3412) / ([10.sup.5])(0.333) (Note K)
(15)  [Q.sub.V] = ([P.sub.V])(3412/12000)
(16)  [Q.sub.SG] = ([Q.sub.TG])([R.sub.R])
(17)  [P.sub.S] = ([R.sub.P])([Q.sub.SG])
(18)  [Q.sub.TL] = ([Q.sub.DP]) + ([Q.sub.DA]) + ([Q.sub.SG]) +
         ([Q.sub.V])
(19)  [P.sub.T] = ([P.sub.V]) + ([P.sub.DR]) + ([P.sub.DP]) +
        ([P.sub.L]) + ([P.sub.S])
(20)  HYEU = (([P.sub.T])(3412) / ([10.sup.5])(0.3333) + (Q))(4380)=
        449[P.sub.D] + 4380[Q.sub.R] (Note L)
(21)  HYEC = ([P.sub.T])(CE) + ([Q.sub.R])(CG)(4380) (Note L)

(A) This analysis is intended for preliminary judgment purposes.
(B) One "Commercial Scale Unit" (CSU, a DOE term) is taken to
consist of one freezer doorway and eight truck load-out doors. For
total heat gain, 3 tons per truck load-outdoor times 8 = 24 tons in
accordance with an industry approximation customarily employed.
(C) See Manufacturer's Rating Data for the basis of these calculations.
Cost of electricity, CE = $0.06 per kWh. Cost of gas, CG = $0.63 per
therm.
(D) [P.sub.V] tabulated above is from freezer-vestibule engineering data
for an 8 x 12 doorway subjected to 20 pass-throughs per hour of 5
seconds duration each. The values include freezer refrigeration power
corresponding to the vestibule's heat loss to the freezer.
(E) Using [T.sub.PI] and [M.sub.PI], read [M.sub.PO.sup.1] from Figure 2
of the Manufacturer's Rating Data at 500 fpm process face area for a
preliminary selection.
(F) Using [V.sub.PI.sup.1], record preliminary model size selection from
Figure 1 of the Manufacturer's Rating Data.
(G) Guided by [V.sub.PI.sup.1] (and [V.sub.R] later), select [V.sub.PI]
within the selected model's rated range.
(H) See "Note 10" of the "Instructions" on Manufacturer's Rating Data
regarding model size selection.
(I) The values 1.67 and 2.17 are motor horsepower per 1000 cfm, for
process and reactivation-air blowers, respectively, based on the
architectural design drawings for a recent installation.
(J) Assumed [R.sub.P] provides average power input to compressor,
condenser, evaporator, and their ancillary devices for modern,
efficiently designed, water or evaporative condenser-cooled systems.
This relationship was derived from Gameiro (2000).Specifically
determined values of [R.sub.P] should be used if available.
(K) 95[degrees]F reactivation inlet air, as shown, is assumed.
(L) Formulae 20 and 21 assume constant operation wherein full-load
energy consumption half the time is assumed to be representative,
annually, of the accumulated variations that actually occur.

Table 3. Loading-Dock Refrigeration--Analysis LC (Note A); Conventional
Dehumidification--Commercial-Size Unit (Note B); 45[degrees]F
Dock--41%RH; Lowered Design Humidity; Unheated "Traffic Door" Employed
(Note C)

Symbol      Item                                     Units

-           Percent moisture gain                    %
[R.sub.R]   Room sensible heat ratio (RSHR)          -
[T.sub.S]   Coil surface temperature (Note E)        [degrees]F
[Q.sub.TG]  Loading-dock total design heat gain (1)  ton
[Q.sub.LG]  Loading-dock total latent heat gain (2)  ton
[R.sub.C]   Coil sensible heat ratio                 -
[Q.sub.D]   Coil defrosting heat gain (3)            ton
[Q.sub.C]   Hot-gas returned to compressor (3)       ton
[Q.sub.RA]  Reheat added load (4)                    ton
[Q.sub.TL]  Total refrigeration load                 ton
              including reheat (5)
[R.sub.P]   Refrigeration power ratio (6)            kW/ton
[P.sub.D]   Total electrical demand (7)              kW
HYEU        Half-year energy usage (8)               therms/yr
HYEC        Half-year energy cost (9)                $/yr

Symbol      Calculated Data

-                0         10          20          30
[R.sub.R]        1.00       0.90        0.80        0.70
[T.sub.S]       23.5       17.2         0.1         0.1
[Q.sub.TG]      24         24          24          24
[Q.sub.LG]       0.00       2.40        4.80        7.20
[R.sub.C]        1.00       0.90        0.85        0.85
[Q.sub.D]        0.00       1.85        3.70        5.54
[Q.sub.C]        0.00       0.43        0.86        1.30
[Q.sub.RA]       0.00       0.00        8.00       24.00
[Q.sub.TL]      24.00      26.28       36.56       54.84
[R.sub.P]        1.13       1.26        1.60        1.60
[P.sub.D]       27.12      33.01       58.42       87.63
HYEU        12,160     14,800      26,196      39,294
HYEC        $7,127     $8,674     $15,354     $23,030

Symbol      Calculated Data  Break (Note D)

-                40               15
[R.sub.R]         0.60             0.85
[T.sub.S]         0.1              0.1
[Q.sub.TG]       24               24
[Q.sub.LG]        9.60             3.60
[R.sub.C]         0.85             0.85
[Q.sub.D]         7.39             2.77
[Q.sub.C]         1.73             0.65
[Q.sub.RA]       40.00             0.00
[Q.sub.TL]       73.12            27.42
[R.sub.P]         1.60             1.60
[P.sub.D]       116.85            43.82
HYEU         52,391           19,647
HYEC        $30,707          $11,515

Formulae

(1)  [Q.sub.TG] = (24) tons (Note B)
(2)  [Q.sub.LG] = ([Q.sub.TG])(1 - [R.sub.R])
(3)  If ([T.sub.S] > 32), then ([Q.sub.D] = 0) and ([Q.sub.C] = 0);
       If (TS [less than or equal to] 32), then ([Q.sub.D] =
       0.77) ([Q.sub.LG]) and ([Q.sub.C] = 0.18)([Q.sub.LG]). (Note F)
(4)  [Q.sub.RA] = ([Q.sub.TG])([R.sub.C] - [R.sub.R]) / (1 - [R.sub.C])
       (Note G)
(5)  [Q.sub.TL] = ([Q.sub.TG]) + ([Q.sub.D]) + ([Q.sub.C]) +
       ([Q.sub.RA])
(6)  [R.sub.P] = (0.02)(30 - [T.sub.S]) + (1.0) (Note H)
(7)  [P.sub.D] = ([R.sub.P])([Q.sub.TL])
(8)  HYEU = ([P.sub.D])(3412) / ([10.sup.5])(0.3333)(8760h/yr)(0.5) =
       449[P.sub.D] (Note I)
(9)  HYEC = ([P.sub.D])(CE)(8760)(0.5) (Note I)

(A) This analysis is intended for preliminary judgment purposes.
(B) One "Commercial Scale Unit" (CSU, a DOE term) is taken to consist of
one freezer doorway and eight truck load-out doors. For total heat gain,
3 tons per truck load-outdoor times 8 = 24 tons in accordance with an
industry approximation customarily employed.
(C) The above loading-dock condition provides optimum infiltration to a
-5[degrees]F/95% RH freezer without need for a freezer vestibule but an
exceptionally large energy consequence results. Reheat not required for
RSHRs 0.85 and larger. Coil icing is predicted to occur for all RSHRs
less than 0.85. See Figure 11 for the basis of these calculations. Cost
of electricity, CE = $0.06 per kWh.
(D) "Break" denotes the point on the psychrometric chart where tangency
occurs between the air-cooling path and the saturation curve. For any
[T.sub.S] below this point, sensible overcooling occurs and reheat is
required.
(E) See psychrometric depictions.
(F) The factors shown in Formula 3 were determined from Cole (1989).
(G) Reheat assumed to be free hot-gas heat reclaim. Formula 4 is
determined from the geometry of the psychrometric depiction for the air-
cooling, air-reheating, and air-warmup paths or by equating [R.sub.R] to
[R.sub.C] in their breakdown values.
(H) Assumed [R.sub.P] provides average power input to compressor,
condenser, evaporator, and their ancillary devices for modern,
efficiently designed, water or evaporative condenser-cooled systems.
This relationship was derived from Gameiro (2000). Specifically
determined values of [R.sub.P] should be used if available.
(I) Formulae 8 and 9 assume constant operation wherein full-load energy
consumption half the time is assumed to be representative,
annually, of the accumulated variations that actually occur.

Table 4. Loading-Dock Refrigeration--Analysis LD (Note A); Desiccant
Dehumidification--Commercial-Size Unit (Note B); 45[degrees]F
Dock--41%RH; Lowered Design Humidity; Unheated "Traffic Door"
Employed) (Note C)

Symbol            Item                                  Units

-                 Percent moisture gain                 %
[R.sub.R]         Room sensible heat ratio (RSHR)       -
[Q.sub.TG]        Loading-dock total design heat gain   ton
[Q.sub.LG]        Loading-dock total latent             BTU/h
                    heat gain (2)

Determination of Desiccant Dehumidification Model
[T.sub.PI]        Process inlet temperature             [degrees]F
[M.sub.PI]        Process inlet moisture                gr/lba
[M.sub.PO.sup.1]  Preliminary process outlet moisture   gr/lba
                    (Note D)
[V.sub.PI.sup.1]  Preliminary process air quantity (3)  [ft.sup.3]/min
-                 Manufacturers model (Note E)          -
[V.sub.PI]        Process air quantity (Note F)         [ft.sup.3]/min
PFA               Process face area (Figure 1)          ft[.sup.2]
PFV               Process face velocity (4)             ft/min
[V.sub.R.sup.o]   Maximum reactivation air quantity     [ft.sup.3]/min
                    (Figure 1)
[M.sub.PO]        Process outlet moisture (Figure 2)    gr/lba
K                 Factor based on PFA and [M.sub.PO]    -
                    (Figure 3)
[T.sub.PO]        Process outlet temperature (5)        [degrees]F
[V.sub.R]         Reactivation air quantity (6)         [ft.sup.3]/min

Energy  Input Required for the Latent Heat Gain
[P.sub.DR]        Drier reactivation-air blower         kW
                    power (7)
[P.sub.DP]        Drier process-air blower power (8)    kW
[Q.sub.DP]        Drier process-air blower heat (9)     ton
[Q.sub.DA]        Drier process-air after-cooling (10)  ton
[T.sub.S]         Coil surface temperature (11)         [degrees]F
[R.sub.P]         Refrigeration power ratio (12)        kW/ton
[P.sub.L]         Latent heat refrigeration power (13)  kW
[Q.sub.R]         Reactivation heat (14)                therms/h

Energy Input Required for the Sensible Heat Gain
[Q.sub.SG]        Sensible heat gain (15)               ton
[P.sub.S]         Refrigeration power (16)              kW

Summation
[Q.sub.TL]        Total refrigeration load (17)         ton
[P.sub.T]         Total electrical demand (18)          kW
HYEU              Half-year energy usage (19)           therms/yr
HYEC              Half-year energy cost (20)            $/yrD

Symbol                     Calculated Data

-                      0          10           20
[R.sub.R]              1.00        0.90         0.80
[Q.sub.TG]            24          24           24
[Q.sub.LG]             0      28,800       57,600

Determination of Desiccant Dehumidification Model
[T.sub.PI]            45          45           45
[M.sub.PI]            18          18           18
[M.sub.PO.sup.1]      -            2.3          2.3
[V.sub.PI.sup.1]      -         2698         5395
-                     -      HCD-4500     HCD-6800
[V.sub.PI]             0        2700         5400
PFA                   -            7.50        11.25
PFV                   -          360          480
[V.sub.R.sup.o]       -         1300         2200
[M.sub.PO]            -            0.5          1.2
K                     -            0.080        0.060
[T.sub.PO]            -           72.3         67.8
[V.sub.R]              0         568          947

Energy  Input Required for the Latent Heat Gain
[P.sub.DR]             0.00        1.05         1.75
[P.sub.DP]             0.00        3.83         7.67
[Q.sub.DP]             0.00        1.09         2.18
[Q.sub.DA]             0           6.8         11.3
[T.sub.S]             35.0        35.0         35.0
[R.sub.P]              0.9         0.9          0.9
[P.sub.L]              0.00        7.07        12.12
[Q.sub.R]              0.00        0.86         1.44

Energy Input Required for the Sensible Heat Gain
[Q.sub.SG]            24.0        21.6         19.2
[P.sub.S]             21.60       19.44        17.28

Summation
[Q.sub.TL]            24.0        29.5         32.7
[P.sub.T]             21.60       31.39        38.81
HYEU               9,685      17,845       23,691
HYEC              $5,676     $10,624      $14,161

Symbol                     Calculated Data

-                      30           40
[R.sub.R]               0.70         0.60
[Q.sub.TG]             24           24
[Q.sub.LG]         86,400      115,200

Determination of Desiccant Dehumidification Model
[T.sub.PI]             45           45
[M.sub.PI]             18           18
[M.sub.PO.sup.1]        2.3          2.3
[V.sub.PI.sup.1]     8093        10791
-                 HCD-9000     HCD-15000
[V.sub.PI]           8100        10800
PFA                    15.00        25.00
PFV                   540          432
[V.sub.R.sup.o]      2800         7500
[M.sub.PO]              2.0          1.0
K                       0.055        0.070
[T.sub.PO]             66.3         70.0
[V.sub.R]            1326         2075

Energy  Input Required for the Latent Heat Gain
[P.sub.DR]              2.45         3.83
[P.sub.DP]             11.50        15.33
[Q.sub.DP]              3.27         4.36
[Q.sub.DA]             15.8         24.7
[T.sub.S]              35.0         35.0
[R.sub.P]               0.9          0.9
[P.sub.L]              17.16        26.18
[Q.sub.R]               2.01         3.15

Energy Input Required for the Sensible Heat Gain
[Q.sub.SG]             16.8         14.4
[P.sub.S]              15.12        12.96

Summation
[Q.sub.TL]             35.9         43.5
[P.sub.T]              46.22        58.29
HYEU               29,527       39,915
HYEC              $17,693      $23,999

Formulae

 (1)  [Q.sub.TG] = 24 tons (Note B)
 (2)  [Q.sub.LG] = (1 - [R.sub.R])([Q.sub.TG])(12,000)
 (3)  [V.sub.PI.sup.1] = ([Q.sub.LG]) / (0.68)([M.sub.PI] -
        [M.sub.PO.sup.1])
 (4)  PFV = ([V.sub.PI]) / (PFA)
 (5)  [T.sub.PO] = ([T.sub.PI]) + (0.625)([M.sub.PI] - [M.sub.PO]) +
        (K)(250 - [T.sub.PI])
 (6)  [V.sub.R] = ([V.sub.PI])([T.sub.PO] - [T.sub.PI]) / (250 - 120)
        (Note G)
 (7)  [P.sub.DR] = (2.17 / 1000)([V.sub.R])(0.85kW/hp) (Note H)
 (8)  [P.sub.DP] = (1.67 / 1000)([V.sub.PI])(0.85kW/hp) (Note H)
 (9)  [Q.sub.DP] = ([P.sub.DP], kW)(3412 Btu/kWh) / (12,000 Btuh/ton)
(10)  [Q.sub.DA] = ([V.sub.PI])(1.1)([T.sub.PO] - [T.sub.PI]) / (12,000)
(11)  [T.sub.S] = ([T.sub.PI]) - (10[degrees]F) typically. A smaller
        temperature difference may be dictated by proximity of the
        saturation curve.
(12)  [R.sub.P] = (0.02)(30 - [T.sub.S]) + (1.0) (Note I)
(13)  [P.sub.L] = ([Q.sub.DP] + [Q.sub.DA])([R.sub.P])
(14)  [Q.sub.R] = ([V.sub.R])(1.1)(250 - 95)([10.sup.-5]) -
        ([P.sub.DR])(3412) / ([10.sup.5])(0.333) (Note J)
(15)  [Q.sub.SG] = ([Q.sub.TG])([R.sub.R])
(16)  [P.sub.S] = ([R.sub.P])([Q.sub.SG])
(17)  [Q.sub.TL] = ([Q.sub.DP]) + ([Q.sub.DA]) + ([Q.sub.SG])
(18)  [P.sub.T] = ([P.sub.DR]) + ([P.sub.DP]) + ([P.sub.L]) +
        ([P.sub.S])
(19)  HYEU = (([P.sub.T])(3412) / ([10.sup.5])(0.3333) + (Q))(4380) =
      449[P.sub.D] + 4380[Q.sub.R] (Note K)
(20)  HYEC = ([P.sub.T])(CE) + ([Q.sub.R])(CG)(4380) (Note K)

(A) This analysis is intended for preliminary judgment purposes.
(B) One "Commercial Scale Unit" (CSU, a DOE term) is taken to consist of
one freezer doorway and eight truck load-out doors. For total heat gain,
3 tons per truck load-out door times 8 = 24 tons in accordance with an
industry approximation customarily employed.
(C) See Manufacturer's Rating Data for the basis of these calculations.
Cost of electricity, CE = $0.06 per kWh. Cost of gas, CG = $0.63 per
therm.
(D) Using [T.sub.PI] and [M.sub.PI], read [M.sub.PO.sup.1] from Figure
2 of the Manufacturer's Rating Data at 500 fpm process face area for a
preliminary selection.
(E) Using [V.sub.PI.sup.1], record preliminary model size selection from
Figure 1 of the Manufacturer's Rating Data.
(F) Guided by [V.sub.PI.sup.1] (and [V.sub.R] later), select [V.sub.PI]
within the selected model's rated range.
(G) See "Note 10" of the "Instructions" on Manufacturer's Rating Data
regarding model size selection.
(H) The values 1.67 and 2.17 are motor horsepower per 1000 cfm, for
process and reactivation-air blowers, respectively, based on the
architectural design drawings for a recent installation.
(I) Assumed [R.sub.P] provides average power input to compressor,
condenser, evaporator, and their ancillary devices for modern,
efficiently designed, water or evaporative condenser-cooled systems.
This relationship was derived from Gameiro (2000). Specifically
Determined values of [R.sub.P] should be used if available.
(J) 95[degrees]F reactivation inlet air, as shown, is assumed.
(K) Formulae 19 and 20 assume constant operation wherein full-load
energy consumption half the time is assumed to be representative,
annually, of the accumulated variations that actually occur.

Table 5. Comparative COPs for Alternative Loading-Dock Refrigeration
Systems (Note A); -5[degrees]F/95%RH Freezer and 45[degrees]F Loading
Dock Assumed. (See notations in Figure 6.)

Table and System Number                             1
System Analyzed (Note A)                            NC

Design humidity level                               Normal (Note B)
  Relative humidity (RH) %                          80
Dehumidification means                              Conventional
                                                      refrig.
Freezer doorway equipment                           Freezer vestibule
                                                      (Note E)
Room Sensible Heat Ratio (SHR) (Note B)
Refrigeration Benefit
  Basic total heat gain (BTHG)             ton
  Basic sensible heat gain (BSHG)          ton
  Basic latent heat gain (BLHG)            ton

Extracting BLHG
  Reactivation energy                      therm/h  -
  Drier fans power input                   kW       -
  Drier after-cooling heat loads
    Process drier                          ton      -
    Process blower                         ton      -
Refrigeration for BLHG                     ton       4.80
  Refrigeration for BSHG                   ton      19.20
  Refrigeration for the vestibule heat     ton       1.20
Total refrigeration load                   ton      25.20
  Refrigeration power ratio                kW/ton    0.87

Electrical Demand
  Refrigeration                            kW       21.92
  Vestibule heater                         kW        4.21
  Drier fans                               kW       -
  Total electrical demand                  kW       26.13
Primary Energy Input
  Refrigeration (Note F)                   therm/h   2.19
  Vestibule heater (Note F)                therm/h   0.42
  Drier fans (Note F)                      therm/h  -
  Desiccant reactivation                   therm/h  -
  Total primary energy input               therm/h   2.61
Therms per Hour Energy Benefit for 24      therm/h
  Tons of Refrigeratio
COP = energy benefit/primary energy input  -         1.10
Excess input compared to system 1          percent  -

Table and System Number                    2
System Analyzed (Note A)                   ND

Design humidity level                      Normal (Note B)
  Relative humidity (RH) %                 80
Dehumidification means                     Desiccant based
                                           (Note D)
Freezer doorway equipment                  Freezer vestibule
                                           (Note E)

Room Sensible Heat Ratio (SHR) (Note B)            0.80
Refrigeration Benefit
  Basic total heat gain (BTHG)                    24.00
  Basic sensible heat gain (BSHG)                 19.20
  Basic latent heat gain (BLHG)                    4.80
Extracting BLHG
  Reactivation energy                       1.14
  Drier fans power input                    5.07
  Drier after-cooling heat loads
    Process drier                           8.90
    Process blower                          1.05
Refrigeration for BLHG                      9.95
  Refrigeration for BSHG                   19.20
  Refrigeration for the vestibule heat      1.20
Total refrigeration load                   30.35
  Refrigeration power ratio                 0.90
Electrical Demand
  Refrigeration                            27.32
  Vestibule heater                          4.21
  Drier fans                                5.07
  Total electrical demand                  36.60
Primary Energy Input
  Refrigeration (Note F)                    2.74
  Vestibule heater (Note F)                 0.42
  Drier fans (Note F)                       0.51
  Desiccant reactivation                    1.14
  Total primary energy input                4.81
Therms per Hour Energy Benefit for 24              2.88
  Tons of Refrigeratio
COP = energy benefit/primary energy input   0.60
Excess input compared to system 1          83

Table and System Number                    3              4
System Analyzed (Note A)                   LC             LD

Design humidity level                      Lowered        Lowered
                                           (Note C)       (Note C)
  Relative humidity (RH) %                 41             41
Dehumidification means                     Conventional   Desiccant
                                           refrig.        based (Note D)
Freezer doorway equipment                  Unheated       Unheated
                                           traffic door   traffic door

Room Sensible Heat Ratio (SHR) (Note B)     0.80
Refrigeration Benefit
  Basic total heat gain (BTHG)             24.00
  Basic sensible heat gain (BSHG)          19.20
  Basic latent heat gain (BLHG)             4.80
Extracting BLHG
  Reactivation energy                              -        1.44
  Drier fans power input                           -        9.42
  Drier after-cooling heat loads
    Process drier                                  -       11.30
    Process blower                                 -        2.18
Refrigeration for BLHG                             17.36   13.48
  Refrigeration for BSHG                           19.20   19.20
  Refrigeration for the vestibule heat             -      -
Total refrigeration load                           36.56   32.68
  Refrigeration power ratio                         1.60    0.90
Electrical Demand
  Refrigeration                                    58.42   29.41
  Vestibule heater                                 -      -
  Drier fans                                       -        9.42
  Total electrical demand                          58.42   38.81
Primary Energy Input
  Refrigeration (Note F)                            5.86    2.95
  Vestibule heater (Note F)                        -      -
  Drier fans (Note F)                              -        0.95
  Desiccant reactivation                           -        1.44
  Total primary energy input                        5.86    5.34
Therms per Hour Energy Benefit for 24       2.88
  Tons of Refrigeratio
COP = energy benefit/primary energy input           0.49    0.54
Excess input compared to system 1                 125     105

(a) See "Comparative Analyses" and Tables 1, 2, 3, and 4 for the
    calculating basis of all tabulations shown.
(b) "Normal" industry practice has been to select anteroom air-cooling
    units on the basis of 20[degrees]F coil-refrigerant temperature or
    higher, for which a resultant 80% room RH, as assumed herein, is
    typical.
(c) "Lowered" indicates room RH is maintained on the "squall line" as
    explained by means of Figure 7.
(d) "Desiccant based" refers to refrigeration systems in which all
    dehumidification is by means of a desiccant.
(e) "Freezer vestibule" denotes a freezer air-lock in which air density
    is maintained essentially identical to air density in the anteroom
    proper.
(f) Primary energy input = (electrical demand kW)(3412 Btu/kWh)/(100,000
    Btu/therm)(0.34), where 0.34 is average decimal equivalent of 34%
    electrical generating efficiency assumed on the basis of Diagram
    5, Electricity Flow 2001 of the Energy Information Administration.