Parametric study of economical energy usage in freezing tunnels

Parametric study of economical energy usage in freezing tunnels M. A. Harrison and P. J. Bishop Keywords: freezing tunnels, energy, mathematical models

Etude param6trique de I'utilisation 6conomique de 1'6nergie dans les tunnels de cong61ation En raison du coot #lev& de I'#lectricit# consomm&e par les tunnels de cong61ation on a effectu& une #tude d~taill#e pour voir comment on pourrait r~duire ces coots sans augmenter fortement le coot d'investissement. II s "agissait de congeler des boites de 340 g de concentr&s d'agrumes dans un grand tunnel ~ bande transporteuse. On a #tabfi un module d'ordinateur dont les principales variables #taient la temperature et la vitesse de /'air de refroidissement,

I'espacement des boites et le temps de s#jour, la puissance du ventilateur et les besoins du compresseur frigorifique. La difficult# du calcul du bilan frigorifique Iors de la cong#lation du concentr& est raise en #vidence dans le tableau 1 et une r#capitulation des charges frigorifiques est donn#e dans le tableau 2. On effectue une ~tude param~trique en s "appuyant sur le coefficient K qui est I'&nergie du ventilateur divis#e par la chaleur retiree au chargement. Le coefficient de performance du tunnel est analys# en fonction du nombre de Nusselt, de la temperature clans le tunnel et des valeurs de K. On analyse aussi le coot en tenant compte de la consommation d'&nergie et du coot d'investissement du tunnel. Les coOts de fonctionnement les plus bas apparaissent aux temp6ratures de I'air les plus basses, parce que cela augmente le d#bit sans augmenter la puissance du ventilateur.

Large amounts of electricity are consumed in food freezing tunnels. An actual freezing tunnel at a citrus processing plant was studied experimentally to determine its operating characteristics. A computer model was also developed, and predicted temperature profiles were compared to experimental data. A parametric study was performed to determine

the effect of the bad velocity, ambient temperature, internal fan loads, and can spacing on the tunnel bad. Methods for improving the effectiveness of t h e freezing tunnels are discussed. It is concluded that a factor, K, the ratio of fan work divided by the useful refrigeration effect, was the best indicator of economical energy usage in the freezing tunnel.

Because of the alarming rise in energy costs in recent years, studies have been undertaken to find ways to minimize energy usage. This study investigated energy usage in freezing tunnels in citrus plants where it may account for ,--25% of the total energy costs (Porter and Bishop1; Bishop et al.2). The primary objective of this investigation was to determine the effect of the important design and operating parameters on energy consumption in a freezing tunnel (Harrison3). The parametric study was accomplished with a computer model of a freeze tunnel, based upon

observations made at an actual unit. After validating temperature profiles predicted by the model, important parameters were varied from the actual conditions measured for the observed tunnel. The effect of these parametric variations on the freezing tunnel's effectiveness was then evaluated. In any freezing tunnel, energy is consumed primarily by the fans and the refrigeration compressors. Fig. 1 is a simple sketch of the observed freezing tunnel with approximate dimensions. The closely packed cans stand upright on a conveyor belt; refrigerated air is blown between the cans by large fans to maintain a high rate of heat transfer and short freezing times.

PJB is Associated Professor,atthe Universityof Central Florida, Orlando, Florida. USA. MAH is Senior Engineer,at the BettisAtomic Power Laboratory,West Mifflin, Pennsylvania, USA. Paperreceived 20 March 1984. This paper was first published in ASHRAE Transactions 1984, V. 90, Pt. 1. It is reproduced here with the permission of the American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1791 Tullie Circle NE, Atlanta, GA 30329. Opinions, findings conclusions, or recommendations expressed in this paper are those of the author(s) and do not necessarily reflect the views of ASHRAE.

Volume 8 Number 1 January 1985

Experimental measurements A variety of measurements was necessary to determine the tunnel's typical operating conditions. Measurements were only made on a 1 2 oz (340 g) can size. An average conveyor belt speed was obtained by noting the time required for a given can to go from

0140-7007/85/010029-0853.00 © 1985 Butterworth 8 Co (Publishers) Ltd and IIR

29

Nomenclature A

cross-sectional area packing surface area per unit volume av Avoid void area surface area As cfm cubic feet per minute COP coefficient of performance of refrigerating unit COP~ tunnel coefficient of performance specific heat of air Cp effective specific heat of concentrate Ceff hourly cost d D unit cost h heat-transfer coefficient HP fan horsepower Ah enthalpy difference between inside and outside air k thermal conductivity of air K ratio of fan work divided by useful refrigeration effect L length of can of concentrate L* characteristic length of packed bed rhc mass flow rate of concentrate rate through tunnel Nusselt number Nu Pr Prandtl number q total rate of heat transfer from packing bed heat removed per unit food product O AOc nominal heat removed from the concentrate in a full freezing tunnel

4S.7m

L C~C~

I

:o o BELT

FAN

heat removal rate from concentrate fan heat gain infiltration heat gain cooling load transmission heat gain cost per unit energy Reynolds number Rh hydraulic radius of packed bed T temperature Ta air temperature upstream of concentrate in tunnel ATa temperature rise of air in tunnel T, initial average concentrate temperature TO outside air temperature Ts can surface temperature Too air temperature log mean temperature difference ~T~n t time to reference time At freezing time U overall heat transfer coefficient u local air velocity u* packed bed velocity Ul,U2 peak air velocities between cans in each region V total volume of packed bed volume flow rate of air through fan "V-fa n compressor work Wc fan work W~ fraction of void volume in bed kinematic viscosity v qc

qf qinf qL qtrans R Re

measured using a styrofoam-ball-type flow detector. The void area was essentially an equilateral triangle such that the void fraction of the bed in the tightly packed regions was 0.09, while in the void areas it was 1.0. The characteristic packed bed velocity u* was then calculated using

EVA~A~R

"%\ ;

*

1

(2)

u =Avoi---~J A1 p - -

Fig. 1

6.t~

- - - I

Freeze tunnel sketch

Fig. 1 Schema du tunnel de cong#lation

entrance to exit of the tunnel. Void fraction was calculated from data obtained from counters. Fan flow rate was calculated by measuring the pressure changes radially across the fan and graphically integrating

"M"fan= 1 u d A

(I)

A

A pitot-static tube was connected to an oil well manometer to obtain the radial pressure readings. The peak air velocity between cans, both in the tightly packed region (subscript 1) and in the void regions (subscript 2) of the conveyor belt, was

,30

Avoid A2

where ul and u2 were the peak air velocities between the cans in each region. Air temperature upstream and downstream of the cans was measured as a function of tunnel position. Precision-grade mercury thermometers, either partial or total immersion, were used as required. Automatic evaporator defrosting with hot gas occurred for a single evaporator every 3 h. Louvres to isolate the evaporator during its defrost cycle did not operate properly. Although it was attempted to avoid taking data during defrosting periods, this was not possible due to the large time period needed to establish typical operating conditions. The average concentrate temperature was measured as a function of time and position in the freezing tunnel. Two methods were used to approximate typical average concentrate temperatures. Large radial temperature gradients resulted from the rapid freezing process so that part way down the tunnel the concentrate was solidly frozen near the can surface with liquid in the middle.

Revue Internationale du Froid

(because of the variation of c~ as a function of temperature) between the average concentrate temperatures at the tunnel entrance and exit. (The effective specific heat of concentrate varies in this equation with temperature, according to Table 1; since temperature was measured as a function of time through the tunnel, the specific heat variation through the tunnel is also known.) The heat-transfer coefficient was then estimated from Newton's law of cooling as:

0.8

0,6

0°4

OoZ

o

I 0,2

I 0.~

I 0.6

I 0.8

t.O

hFig. 2 Averagetemperatureof concentrateversus time in the freeze tunnel. O. Mixing-cup method; A computer-aided method Fig. 2 Temperature moyenne du concentr~ en fonction du temps clans le tunnel de cong#lation

The mixing cup method, where concentrate was emptied into pre-chilled thermos bottles and mechanically mixed to a uniform temperature, was one method used to determine an average concentrate temperature. Data were collected by removing cans from specific locations in the tunnel, measuring the temperatures, and recording the time of travel. Thus, average concentrate temperatures were measured at various times in the freezing process. A second method, the computer-aided method, was used to obtain average temperatures as a function of time based upon measuring centerline concentrate temperatures only. This avoided the mixing problem of the previous method. The computer-aided method will be explained in the analytical section, where the radial temperature distribution is numerically obtained. The average concentrate temperatures with time traversed in the tunnel are shown for both methods in Fig. 2. The computer-aided curve is longer because the average conveyor belt speed was slower when centreline temperatures were recorded and the cans were in the tunnel longer. The largest temperature difference between methods occurred when the cans were near the tunnel exit. Du ring periodic checks of the temperature of concentrate exiting the tunnel, temperature differences this large were observed as a result of the routine operation of the tunnel. However, another possible factor in this discrepancy is that when data were recorded for the mixing cup curve, the freeze tunnel door was open longer when thermos bottles were passed in and out than when thermos bottles were not used. The freeze tunnel door was large and, when open, could increase somewhat the cooling load, resulting in generally higher temperatures. Information about the concentrate temperature variation with time was used to obtain an estimate of the heat-transfer coefficient, h, in the tunnel. The heatremoval rate from the concentrate to the tunnel can be estimated by integrating: Te

qc=rh~ce.(T)dT

(3)

T,

where Te is the concentrate temperature at the final time. The integrations were accomplished graphically

Volume 8 Numero 1 Janvier 1985

qc A(T,-Ta)

(4)

The heat-transfer coefficient obtained from Equation (4) was later compared to the heat-transfer coefficient obtained analytically using Equation (8) for a packed bed freezing tunnel.

M o d e l description A computer model of the freezing tunnel was developed to perform a parametric study of factors influencing energy use. The experimental measurements taken on the tunnel were necessary to evaluate the accuracy of the model. The temperature distributions in each can of concentrate were determined to calculate the can's average temperature, heat content and surface temperature. The cylindrical heat-conduction equation for variable thermal properties is:

la/

aT\

(:3/ tiT\

8T

(5)

The four boundary conditions are: dT --=0 dr

at r=O

- E aT ~r,=R=h[T,=A - Too(z)] at the surface radius

_Kam T =h[T,=0.L-T(z)] at the top and ~3zlz=oz bottom of the cans An explicit numerical finite-differencing technique was employed to solve this equation with the convective boundaries (Holman4). Discontinuities in the effective thermal properties around the freezing point of concentrate required a small time step to assure a stable solution. The cylinder was divided into three sets of concentrate rings for a total of nine volume elements and nodes, as shown in Fig. 3. The width of the outermost elements in either the axial or radial direction is half that of the inner elements. This arrangement improved the stability of the solution compared to the case where nodes are equally spaced. At the top of the can, an air gap exists that tends to insulate the concentrate. The size of this air gap was measured, and its thermal resistance was calculated and summed to the convective thermal resistance to yield an effective resistance to heat flow from the top surface. It was assumed that the thermal resistance of the can material was negligible. An additional concern

31

was that the air temperature was not uniform and would change as the air flowed around the cans. The effect was accounted for by calculating the temperature rise of the air: Ta - q ai, _ hay Tro rh rhcp

(7)

The air temperature near the surface of each volume element was estimated by assuming the air temperature over the upstream elements was equal to the initial air temperature. The air temperature near the surface of the downstream elements was assumed equal to the initial air temperature plus the temperature rise calculated from Equation 7. The air temperature at the middle surfaces was the average of the air temperatures at the ends. The results of these assumptions agreed well with experimental observations. The surface temperature, TS, was assumed to be uniform over the can's surface. The computer program estimated Ts by averaging the temperature of the outer elements, weighted relative to their surface areas at each time step. Methods exist to predict temperature distribution changes in freezing problems in general (Saitoh~; r I

I

I

I

I

I

I

I

I

I "t--

I L. t

I

-

I

I

I I

X --

I -

. . . . . . .

LaudauB; Keller and BallardT; ChenS). Common methods involve assuming a boundary exists between regions of frozen and unfrozen liquids. Each region has appropriate thermal properties, and the latent heat is assumed to evolve at the boundary as it moves through the freezing material. However, as pointed out by Keller and Ballard 7, the freezing process in fruit juice has freezing properties of a typical two-phase system of ice and solution. In equilibrium, at a given temperature below the freezing point, a given amount of ice exists with a given amount of solution at a certain concentration. Any change in equilibrium temperature alters the amount of ice and solution, with a corresponding change in solution concentration. As the amount of ice and solution changes with temperature, the thermal properties change. Keller and Ballard 7 calculated values of effective thermal properties over a range of temperatures and citrus juice concentrations. Data used in the calculations correspond to a Brix (sugar content) of 44.8 ° which is currently the legal standard for Florida orange juice concentrate. Table 1 presents the effective thermal properties for orange juice concentrate as obtained from Keller and Ballard 7. The convective heat-transfer coefficient, h, was determined analytically by assuming the tunnel to be a packed bed. Although most cans stood upright and were packed tightly, empty gaps and a few cans on their sides were scattered between regions of tightly packed cans. According to Whitaker 9, the N u can be obtained by: N u = ( 0 . 5 R e l / 2 + 0.2Re2/3)pr 1/3

I

J

I

I

I

t I

I

I

I

I

I

(8)

where:

I

I I

Re =

I I

J

I

I

I

I

I

I

i

I

I

~

I

,

I

I

u'L*

v

, h-

NuK

L*

and:

1 [

~D

L*=-, u*-udAvoid av A voie,]

VIEW

SIDE V I ~ WITH CAN

From the experimental measurements, the characteristic velocity and void fraction were obtained. Equation (8) predicts, for a 12oz (340g) can size (1.26in (320mm) in radius, 4.4in (1140mm) in

UPRIGHT Fig.

Volume element and nodal arrangement

3

Fig. 3 Element de volume et disposition nodale

Table

1. Effective

thermal

properties

for

Brix

44.8 ° citrus

concentrate

7

Tableau 1. Propri~t6s t h e r m i q u e s p o u r un c o n c e n t r ~ d ' a g r u m e ~ 4 4 , 8 ~ B r i x 7

Specific heat capacity

Temperature

Thermal conductivity

Density

(°F)

(°c)

(Btu Ibm -1 °F-~)

(kJ kg -1 K-1)

(Btu h -1 ft -1 °F -1)

(W m -1 K-1) (Ibm ft -3)

(kg m -3)

16.0 15.0 10.0 5.0 +0.0 -5.0 -10.0 -15.0 -20.0

- 8.9 - 9.4 - 12.2 - 15.0 - 17.8 - 20.6 - 23.3 - 26.1 - 28.9

0.72 5.13 3.86 2.81 2.00 1.41 1.06 0.94 1.00

3.06 21.47 16.16 11.76 8.37 5.90 4.44 3.93 4.19

0.18 2.00 0.72 0.36 0.35 0.35 0.47 0.60 0.65

0.31 3.46 1.25 0.62 0.61 0.61 0.81 1.04 1.12

1205 1204 1191 1179 1170 1163 1157 1154 1149

32

75.2 75.1 74.4 73.6 73.0 72.6 72.2 72.0 71.7

International Journal of Refrigeration

t,o

o.8

or in metric units:

0,6

qi,f(kW) = 1.202 (cms)*&h 0.~"

0,2

0

'.2

o'.,

01, T;]~

18

,.o

t/t o

Fig. 4 Comparisonof measured ( - - ) and computer-predicted (---) valuesof the averagetemperatureof concentrateversustime in the freeze tunnel. O, Nu=86; /k Nu=101: I-I, Nu=126. Ta=- 28.9°C; T~=-2.2°C; to=2.5 h

Fig. 4 Comparaison des valeurs mesur~es et calculg,es par ordinateurde la temperaturemoyennedu concentr#en fonctiondu tempsde s~jourdensle tunnelde cong~lation

(*cubic meters per second volume flow rate) where infiltration occurs from door openings and from the conveyor belt. The volume flow rate due to door openings was calculated using procedures in the ASHRAE Handbook 1°. The fans are entirely enclosed in the tunnel, and the heat addition 1~ is in I-P units, qf,,=2995 HP, or more generally: q,,n, = Wt

(11 )

The heat removal from the concentrate can be obtained by integrating:

(1 2)

q~=rh~f c., dT=hA (T,- T,) height) a Nu of ,-, 1 26. The accuracy of the correlation is better than _+25% (Whitakerg). This value of Nu determined from Equation (8) was compared to the value obtained from the temperature measurements, as explained earlier. The mixing cup curve predicts a Nu of 86. These curves are shown in Fig. 4. Based upon the measurements within the tunnel, the tunnel was analysed as being composed of three regions because of the uneven fan distribution, with higher heattransfer coefficients at the tunnel ends than in the middle. The evaporator defrosting was modelled by assuming that after 1 h of cooling, the upstream air temperature increased to 30"F ( - 1.1°C) for ~ 10 min and then returned to its original value of -20~F

(- 28.8°c). As seen from Fig. 4, the averageNu over the tunnel length was close to a curve resulting from a Nu of 101. To conduct the parametric study of the tunnel, aNu of 101 was assumed typical of its operating conditions. This value was 20% lower than the value predicted by the packed bed correlation. The measurements can now be used to estimate the relative contributions of heat losses to the tunnel energy balance. The coefficient of performance (COP) is used to estimate the effectiveness of the tunnel. It is defined as: Refrigeration effect qc COPt- - Net work input We+ Wf

The equation forCOP,, Equation (9) can be put in a more convenient form for the parameter study. Recalling that the compressor work can be written as q,oAo/COP, and that the heat load is the sum of energy transfer from the concentrate to the tunnel (qc) plus the energy from the fans (qf) the equation for COPt becomes:

COPt-

(10)

qc

COP qLOAO I qf + W__!COP~ CO----P4-Wf 1 + qc /

where q,oAD=qc+qf. Substituting Equation (11), qf=2995 HP (2.2 kW) and the work done by the fans, Wf=2545 HP (1.9 kW) yields:

(9)

Infiltration heat gains are calculated using I-P units as:

Volume 8 Number 1 January 1985

P a r a m e t e r study - results and discussion

COPt =

The value of qc, the heat-removal rate from concentrate, is obtained by calculating the rate of change of concentrate enthatpy. Fan ratings are used to determine Wf. Compressor work, W c. is estimated by an energy balance on the tunnel, since the refrigeration plant supplies several loads besides the freeze tunnel. The energy balance consists of accounting for the transmission, infiltration, energy addition due to fans, and the heat removal from the concentrate. Transmission heat gains are calculated using:

q,,,,,=UA,(To- T~)

where the thermal properties of the concentrate are effective properties that account for the latent heat of fusion, and thermal property changes with temperatu re7. A summary of the cooling loads on the freezing tunnel was calculated and is summarized in Table 2.

COP

COP

(2995+ 2545COP)HP~1 +K(1 +COP) 1+ qc (13)

Table 2. Summary of cooling Imxl$ Talbeau 2. R#capitulation des bilans frigorifiques Heat gain Souse

(HP)

(kW)

Percentageof total

Concentrate Transmission Infiltration Fans Total

244 18.6 1.7 117.8 382.0

181.7 13.9 1.3 87.9 284.9

63.8 4.9 0.5 30.9 100.0

1,0

and, for a given tunnel size, decreases the freezing time. The price of the increased .capacity is a decrease in COP t Values of COPt, Nu, Ta, K, and freezing time, &t, have already been estimated for a variety of computersimulated operating points. Since &Qc is fixed, and a relationship between COP, and At has been established, values of COP: versus qc can be generated from:

~. 0°.5

0

qc=AQc/At

501

t~00 Nu

I 150

200

Fig. 5 Freezetunnel coefficient of performance divided by the refrigeration unit coefficient of performanceversus Nusseltnumber. O, Ta=-23.3"C; I-I. Ta=-28.9°C; A, Ta=-34.4°C; O, Ta= - 40.0"C Fig. 5 Coefficientde performance du tunnel de cong~lation divis~ par le coefficient de performance du groupe frigorifique en fonction du hombre de Nusselt

where: qc = & Q J & t

(14)

K = 2545 HP &t/AQc

(1 5)

and: K is a dimensionless number, providing a ratio of fan energy added to the tunnel divided by the heat removed from the concentrate. The COP and COP: were calculated for each value of h and Ta. Fig. 5 is a graph of COPt/COP versusNu. The ratio of COPt/COP has a maximum value of 1.0. When COPt=COP, the least energy is expanded for a given useful refrigeration effect, qc. Freeze tunnels are operated with lower efficiencies when it is necessary to provide a high qc and/or a short freezing time, &t. When heat transfer is increased by using fans to increase Nu and the ratio of fan work divided by useful refrigeration effect K increases, then COPt < COP. This relationship is displayed in Equation (1 3) as well as Fig. 5. At very low Nu, an increase in T~ also increases the COPt. This is because at low Nu, the system is closer to a refrigerated space than a freeze tunnel, and the dominant effect of increasing T, is the corresponding increase in COP. But at high Nu, the dominant effect of an increase in T, is increased freezing time, and the COP: actually decreases. This suggests that while maintaining a higher T. in a refrigerated space results in a higher COP and lower energy consumption in a refrigeration problem, maintaining a higher T, in a freeze tunnel problem results in a lower COPt and higher energy consumption. Also, the COPt decreases rapidly as K increases, as expected. The result of adding fans to a refrigerated space is to increase the rate of heat transfer. This increase in the rate of heat transfer increases the tunnel's capacity (q~)

34

Fig. 6 is a graph of COP: versus qc for the range of Nu and Ta investigated. Again, the highest COP: is obtained for the lowest values of K and Nu, and for high values of the Nu, the highest COPt is obtained for the lowest value of Ta. But it also shows that large values of K restrict the tunnel to relatively low COPt's for any value of T,. The highest COPt's exist at the lowest Nu, as expected. But relatively large capacities appear possible, even for the lowest Nu investigated. The COPt of the tunnel is high for IowNu, primarily because K is so low. K was calculated using the fan power predicted by the fan laws. For N u = 4 6 , the fan law predicts a power level of 1.5 kW, relative to 75 kW for N u = 1 0 1 . Actually producing a significant cooling airflow in a freeze tunnel similar to the one observed with only 1.5 kW may not be achievable because of the physical size and flow characteristics of the evaporators and packed bed. Careful experimental analysis using system and fan curves would be necessary to predict accurately behaviour for any conditions significantly different from the measured conditions. It is important to consider the effects of various values ofNu, T,, and K on the COPt because the COP: is a measure of the tunnel's effectiveness. But a more obvious method of judging freezing tunnel performance is to consider its energy consumption per

5

"

•

o 1,0

2°0

qc FREEZE TUNNEL CAPACITY ( x 293 KW )

Fig. 6 Freeze tunnel coefficient of performance versus tunnel capacity. - - - , Nu value; . . . . . . K value. O. Ta=-23.3°C; F1, Ta=28.9°C; A. Ta=- 34.4°C; C), Ta=- 40.0"C Fig. 6 Coefficient de performance du tunnel de congeletion en fonction de la puissance frigorifique du tunnel

Revue Internationale du Froid

3O

2o

v

Constructing a freeze tunnel is one of the largest initial expenses when building a food processing plant 1. It is obvious that minimizing K will reduce the operating expenses of the tunnel, but the design must take into account trade-offs between the initial investment capital and final operating expenses. However, many important trends that apply to freezing 12 ounce (340g) cans of citrus concentrate will have some relevance to any freeze tunnel where the needed useful refrigeration effect is large. The lowest operating costs occur at the coldest air temperatures, because the freezing times are shorter and the tunnel's capacity is greater. However, for a g iven air tem peratu re, the lowest operating costs occur for the lowest Nu and, consequently, the longest freezing time. This means the freeze tunnel should be designed to provide an adequate freezing time, but no shorter than necessary. The fans should be chosen to provide this freezing time with the lowest reasonable producable air temperature. If the capacity varies, the fans should be operated selectively to maintain the lowest effective value of K.

Conclusions :

qc

, 1.0

,

, 2.0

I

FREEZE TUNNEL CAPACITY ( x 293 KN )

Fig. 7 Freeze tunnel electricity cost versus freeze tunnel capacity. Key as in Fig. 6

The major results of this investigation are the trend and the relationships between energy consumption, Nusselt number, air temperature, and the ratio of fan

Fig. 7 CoDt de r@lectricit~ consommde par le tunnel de cong~lation en fonction de la puissance frigorifique du tunnel de cong~lation

\

\

unit of of processed food. The energy consumed, or equivalently the net work expended, is related to qc by the definition of COP, from Equation (13): Wc + Wf=qc/COP,

\ \

The monetary cost of the electricity to operate the tunnel is related to the work performed by: d= RqJCOPt

(18)

where D = u n i t cost; At=freezing time; and Q=heat removed per unit food product. Fig. 7 is a graph of hourly energy costs and rate of energy assumption versus capacity. Once again, except at low capacities, the least energy is expended for a given production rate at the lowest achieable values of Nu, K, and Ta. As the capacity is increased by lowering Ta or increasing Nu, the costs increase. However, increased unit energy costs may be acceptable, or even desirable, if the increased capacity results in a decreased total unit cost. The unit costs, both in energy and money, are graphed versus capacity in Fig. 8. It is interesting to observe that the ratio of fan work divided by tunnel capacity, K, can be related directly to the unit cost of the product. Also, the unit cost and K can be substantially reduced, for a given Nu, by lowering Ta. In the particular tunnel observed, K=0.33-0.48 for typical operating conditions.

Volume 8 Num6ro 1 Janvier 1985

\ \

(17)

where d = hourly cost; and R = cost per unit energy. The unit monetary cost, or cost per unit of food processed is: D = dAt = RQ/COP,

\

(16) k k

\

\

o

K = 0.8

\ v

\ K=0.6 Nu =

129

K=

K

Nu = 97

K=

Nu

=

68

=46 0

i

.

! 1,0

I

qc' FREEZE TUNNEL CAPACITY

I 2,0

I

(x 293 KW !

Fig. 8 Freeze tunnel electricity cost per unit processed versus freeze tunnel capacity. Key as in Fig. 6

Fig. 8 CoOt de I'@lectncit~ consomm~e par le tunnel de congdlation par unit~ trait~e en fonction de la puissance frigorifique du tunnel de

cong6lation

35

work divided by useful refrigeration effect. In review, the most economical energy consumption occurs, for large freeze tunnels, when the freezing times are no shorter than required, the air temperature is the lowest achievable value, and the ratio of fan work divided by useful refrigeration effect is the lowest achievable value. Although some efficiency of the refrigerating unit is lost by producing a low air temperature, this is more than offset by the increased freeze tunnel capacity and freeze tunnel coefficient of performance. The significance of the ratio of fan work divided by the useful refrigeration effect, K, is also important. The energy expended to produce the desired cooling effect per unit of food product is determined predominantly by the value of K for the freeze tunnel. The minimum achievable values of K depend on the freeze tunnel design, the required refrigeration effect, and properties of the food product. The range of values f o r k measured for the observed freeze tunnel are reasonably accurate and could be used to compare the effectiveness of the observed tunnel to another. The equation for the freeze tunnel's coefficient of performance, Equation (1 3), can be used by freeze tunnel operators and designers to estimate the freeze tunnel effectiveness. The heat content of the food product and the amount of food product in the tunnel would have to be determined. The freezing times can be estimated for a variety of products, and should be known by the tunnel operator. The power requirements of the fans are fixed, or determinable, so K may be calculated frequently without any other knowledge than that of the freeze tunnel design and the thermal

properties of the food product. If the C O P can be estimated, the COPt can also be estimated.

References 1

2

3 4 5

6 7 8 9

10 11

Porter, W. A., Bishop, P. J. Analysis of energy use and recommendationsfor potential savingsat a citrus concentrate plant in Florida, EIESReport,Universityof Central Florida, 15 August (1979) Bishop, P. J., Doering, R. D., Minardi, A. Potential for cogeneration and waste heat recovery in Florida, Governor's energy office star report 79.065, Stateof Florida, Sept (1980) Harrison, M. A. A parametric study of economical energy usage in freezetunnels, Master'sThesis, University of Central Florida, Orlando, 12 August (1980) Holman, J. P. Heat transfer, 4th ed., McGraw-Hill Book Company, New York, (1976) p. 130 8aitoh, 1". Numerical method for multidimensional freezing problems in arbitrary domains,ASMEJoumalofHeat Transfer 100 May (1978) 294-299 LaLKlau,H. G. Heat conduction in a melting solid. Quarterly Journal of Applied Mathematics 81 April (1950) 81-94 Keller, G. J., Ballard, H. Predictingtemperaturechanges in frozen liquids, Industrial and Engineering Chemistry 48 Feb. (1956) 188-196 Chen, C. S. Specific heat of citrus juice and concentrate Proceedings of the Florida State Horticultural Society92 June (1 979) 154-156 Whitaker, S. Forcedconvection heattransfercorrelation for flow in pipes, pastflat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles, American Institute of Chemical Engineering Journal 18 March (1972) 361-371 ASHRAE ASHRAE Handbook Fundamentals volume, American Society of Heating, Refrigerating, and Air Conditioning Engineers. New York, (1977) p. 273 ASHRAE ASHRAE Handbook Fundamentals volume, American Society of Heating, Refrigerating and Air Conditioning Engineers. New York (1981)

International Journal of Refrigeration