the art of air blast freezing: design and efficiency considerations

13
The art of air blast freezing: Design and efciency considerations Patrick Dempsey, Pradeep Bansal * ,1 Department of Mechanical Engineering, The University of Auckland, Private Bag e 92019, Auckland, New Zealand article info Article history: Received 16 March 2011 Accepted 6 December 2011 Available online 13 December 2011 Keywords: Blast freezer Batch Carton Refrigeration Low temperature Energy Efciency abstract Air blast freezing is a common freezing technique used throughout the world to freeze various food commodities from carcasses to packaged goods. The New Zealand Cold Storage industry identied blast freezing as the most energy intensive operation in the frozen food storage industry, consuming 8.1 GWh of electricity in New Zealand in 2005. This paper presents an overview of various types of blast freezers, their common design aws, common energy saving measures and a best practice guide. A simulation model has also been presented to predict the performance and to design an optimal system under range of operating conditions. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Air blast freezing is the process of taking a product at a temperature (usually chilled but sometimes at ambient temper- ature) and freezing it rapidly, between 12 and 48 h, to its desired storage temperature which varies from product to product (e.g. sh ¼20 C, beef ¼18 C). Typically, the evaporator tempera- ture in a blast freezer refrigeration system ranges between 35 C and 52 C. Slow freezing produces large ice crystals, which grow through cell walls, permitting an accelerated penetration of oxygen, causing rancidity and browning of meat and enhancing the danger of higher drip on thawing. Therefore, rapid freezing is required to maintain food quality as it produces small ice crystals due to a higher number of nucleation points from which ice crystals form. Air Blast freezing is classied as a forced convection phenom- enon where the use of fans increases the products surface heat transfer coefcient and produces a more uniform air temperature throughout the freezer. The air velocity, and hence heat transfer coefcient, can be altered with the use of variable speed drives (VSDs). The main detriment of forced convection in blast freezers is the use of large fans that add signicantly to the total heat load on the refrigeration system and running costs. Also, unwrapped foods are prone to moisture loss during blast freezing as the absolute humidity of the bulk air is usually lower than that of the air at the surface of the food. Although air blast freezers have been used in industry since the 1950s, limited number of technical studies have been published on specic aspects of the topic in the open literature [1,3,12,24,26, 31,42,51,52], and there is hardly any study that summarises all aspects of blast freezers at one point in a single study. Therefore, this paper presents an overview of blast freezers of their working prin- ciple, historical background, different designs, efciency issues, a modelling perspective and a best practice guide. 2. Origin of air blast freezers The early freezing rooms typically consisted of bare pipe grids in the ceiling above rails on which sheep carcasses and beef quarters were hung. These freezing rooms relied on the natural convection of cold air, typically around 15 C, and resulted in freezing times up to three days. Following World War II the world faced a serious food shortage. A major New Zealand innovation was the air blast freezer which enabled rapid freezing for high export quantities. The air blast freezer used fans to blow air at low temperatures (down to 30 C) over carcasses reducing freezing times to between 10 and 24 h. This ability to freeze and transport food to distant markets made refrigeration a highly protable trade and in fact made New Zealand one of the richest countries in the world in the 1950s and 1960s. The New Zealand company Ellis Hardie Syminton Ltd patented the A189 air-blast freezer in about 1950 [1]. The concept was to use * Corresponding author. Current address: Building Equipment Program, Oak Ridge National Laboratory, P O Box 2008, Oak Ridge, TN37831-6067, USA. Tel.: þ1 865 576 7376. E-mail address: [email protected] (P. Bansal). 1 Tel.: þ1865 576 7376. Contents lists available at SciVerse ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.12.013 Applied Thermal Engineering 41 (2012) 71e83

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Page 1: The art of air blast freezing: Design and efficiency considerations

at SciVerse ScienceDirect

Applied Thermal Engineering 41 (2012) 71e83

Contents lists available

Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

The art of air blast freezing: Design and efficiency considerations

Patrick Dempsey, Pradeep Bansal*,1

Department of Mechanical Engineering, The University of Auckland, Private Bag e 92019, Auckland, New Zealand

a r t i c l e i n f o

Article history:Received 16 March 2011Accepted 6 December 2011Available online 13 December 2011

Keywords:Blast freezerBatchCartonRefrigerationLow temperatureEnergyEfficiency

* Corresponding author. Current address: BuildinRidge National Laboratory, P O Box 2008, Oak Ridge,865 576 7376.

E-mail address: [email protected] (P. Bansa1 Tel.: þ1865 576 7376.

1359-4311/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.applthermaleng.2011.12.013

a b s t r a c t

Air blast freezing is a common freezing technique used throughout the world to freeze various foodcommodities from carcasses to packaged goods. The New Zealand Cold Storage industry identified blastfreezing as the most energy intensive operation in the frozen food storage industry, consuming 8.1 GWhof electricity in New Zealand in 2005. This paper presents an overview of various types of blast freezers,their common design flaws, common energy saving measures and a best practice guide. A simulationmodel has also been presented to predict the performance and to design an optimal system under rangeof operating conditions.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Air blast freezing is the process of taking a product ata temperature (usually chilled but sometimes at ambient temper-ature) and freezing it rapidly, between 12 and 48 h, to its desiredstorage temperature which varies from product to product (e.g.fish ¼ �20 �C, beef ¼ �18 �C). Typically, the evaporator tempera-ture in a blast freezer refrigeration system ranges between �35 �Cand �52 �C. Slow freezing produces large ice crystals, which growthrough cell walls, permitting an accelerated penetration of oxygen,causing rancidity and browning of meat and enhancing the dangerof higher drip on thawing. Therefore, rapid freezing is required tomaintain food quality as it produces small ice crystals due toa higher number of nucleation points fromwhich ice crystals form.

Air Blast freezing is classified as a forced convection phenom-enon where the use of fans increases the products surface heattransfer coefficient and produces a more uniform air temperaturethroughout the freezer. The air velocity, and hence heat transfercoefficient, can be altered with the use of variable speed drives(VSD’s). Themain detriment of forced convection in blast freezers isthe use of large fans that add significantly to the total heat load onthe refrigeration system and running costs. Also, unwrapped foods

g Equipment Program, OakTN37831-6067, USA. Tel.: þ1

l).

All rights reserved.

are prone to moisture loss during blast freezing as the absolutehumidity of the bulk air is usually lower than that of the air at thesurface of the food.

Although air blast freezers have been used in industry since the1950’s, limited number of technical studies have been published onspecific aspects of the topic in the open literature [1,3,12,24,26,31,42,51,52], and there is hardly any study that summarises allaspects of blast freezers at one point in a single study. Therefore, thispaper presents an overview of blast freezers of their working prin-ciple, historical background, different designs, efficiency issues,a modelling perspective and a best practice guide.

2. Origin of air blast freezers

The early freezing rooms typically consisted of bare pipe grids inthe ceiling above rails on which sheep carcasses and beef quarterswere hung. These freezing rooms relied on the natural convection ofcold air, typically around�15 �C, and resulted in freezing times up tothree days. Following World War II the world faced a serious foodshortage. A major New Zealand innovation was the air blast freezerwhich enabled rapid freezing forhigh export quantities. The air blastfreezer used fans to blow air at low temperatures (down to�30 �C)over carcasses reducing freezing times to between 10 and 24 h. Thisability to freeze and transport food to distant markets maderefrigeration a highly profitable trade and in factmadeNew Zealandone of the richest countries in the world in the 1950’s and 1960’s.

The New Zealand company Ellis Hardie Syminton Ltd patentedthe A189 air-blast freezer in about 1950 [1]. The concept was to use

Page 2: The art of air blast freezing: Design and efficiency considerations

Fig. 1. Schematic of a typical batch air blast freezer.

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e8372

finned surface evaporators to cool the air and large fans to directthe refrigerated air over the carcasses. During the 1950’s blastfreezing became the dominant method of freezing worldwide andthe fundamental principles of carcass freezing changed little overthe next 50 years. Prior to the 1950’s the beef trade was dominatedby quarter beef carcasses. The emergence of the hamburger inAmerica opened a newmarket for frozen boneless beef suitable fordirect processing. In response to the new boneless productdemand, Ellis Hardie Syminton Ltd in conjunction with BillFreeman constructed the world’s first continuous carton freezer for27.2 kg beef cartons near Palmerston North (New Zealand). Thefreezer blew refrigerated air as low as �40 �C at a velocity around3 m/s over the cartons and achieved freezing times of 24 h.

Over thenext 20e30years, the air-blast freezer becameuniversalin the New Zealand frozen food industry. Several variations weredeveloped, including cross flow and vertical air flow systems andthere was a move from batch to continuous production for largerthrough puts and reduced labour costs. By the 1980’s, energy effi-ciency became an important design parameter. Many potentialenergy saving initiatives were investigated in terms of both therefrigeration system and the system as a whole. Such energy savinginitiatives included: improved air flow design by altering theproduct stacking arrangement and the use of baffles and turningvanes, varying the air velocities at different times throughout thefreezing process and the effect of product packaging on freezingtimes. The easiest and most advantageous energy saving devicetoday is the use of variable speed drives (VSD’s) on evaporator fans.

3. Why blast freeze?

The killing of bacteria is largest in the range�4 �C to �10 �C dueto ‘cold-shock,’where their metabolism is disturbed, even stopped.When the freezing rate is slow, the bacteria have time to adapt tothe new conditions, hence food needs to be frozen quickly.

There are various methods available for food freezing, theseinclude: air-blast freezers (batch and continuous), fluidised bedfreezers, impingement freezers, liquid immersion freezers, platefreezers, liquid nitrogen freezers and carbon dioxide freezers. Themajor advantage of the air blast freezer is its versatility. Since air isa low viscosity fluid it has the ability to easily follow aroundirregular surface geometries, thus providing a more uniformfreezing rate over the whole product. Other freezing methods suchas plate freezing (contact freezing) offer faster cooling times [2] butcan only be used with products of a suitable geometry, i.e. a flatsurface to match the plate bed.

4. Types of air freezers

Air is the most widely used method of freezing food as it iseconomical, hygienic and relatively non-corrosive to equipment [4].Various forms of air blast freezers are used in industry [5e16].

1. Sharp freezer: or blast room freezer is a cold storage room thatrelies on natural convection and low air movement fromevaporator fans to circulate the cooling air resulting in slowfreezing times. This arrangement is sometimes used for bulkproducts like butter, beef-quarters and fish, but not for pro-cessed food products.

2. Tunnel freezers: the refrigerated air is circulated by large fansover the product confined in an insulated closed room. Meatcarcasses are supported by hooks suspended from a conveyoror specially designed racks. The trays or spacers are arranged toprovide an air space between each layer of trays. The air caneither be cross flow or counter flow, depending on the type oftunnel freezer. Various forms of tunnel freezers exist including:

2a Batch Freezers: the product is stacked on pallets, or hungfrom hooks on slide rails in the case of carcasses, andloaded into the freezer using fork hoists. This is an on/offprocess where the freezer is loaded, run until the meat isfrozen to its desired temperature, then pumped down andswitched off for unloading. Batch blast freezers are suit-able for small quantities of varied products [17]. Typically,the heat transfer coefficient is less than 50W/m2 K (Fig. 1).

2b Mechanised freezers: the pallet racks are fittedwith castersor wheels. The racks or trolleys are usually moved on railsby a pushing mechanism, usually hydraulically powered.Such mechanised tunnel freezers are known as push-through tunnels or carrier freezers which have two tiers,one on top of the other. These freezers are designedprimarily for packaged goods, as well as carcasses.Advantages of mechanised freezers over batch freezersinclude: improved air circulation over the product as itmoves at a steady rate through the tunnel; labour costsare considerably decreased as pallets are not manuallyplaced in the freezer; and there is added flexibility of thefacility by varying the freezing time with the speed of theram [18]. Heat transfer coefficients in mechanised freezersare similar to batch freezers being less than 50 W/m2 K.

2c Belt freezers: the product is loaded on a continuousconveyor belt. Modern belt freezers usually employvertical air flow to force air between the product itemscreating good contact with the product. Typically, the heattransfer coefficient of belt freezers varies between 25 and80 W/m2 K. Multi belt freezers offer the advantage ofsmaller floor space compared to single belt freezers. Thereare several forms of belt freezers:i) Multi-tier belt freezers: consist of several conveyor

systems positioned one above the other with fans andcoils positioned above the top belt. The air flow in beltfreezers can either be vertical or horizontal over theproduct. The most efficient flow is determined by theproduct characteristics, dimensions, packed orunpacked, as well as degree of processing andcomposition.

ii) Spiral belt freezers: where the belt is coiled in numerousrevolutions around one vertical central axis to optimisethe use of floor space. The belt can stack 30 tiers or

Page 3: The art of air blast freezing: Design and efficiency considerations

Fig. 3. Schematic of a fluidised bed freezer.

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e83 73

more, one above the other thus reducing floor space toa minimum. Spiral freezing is one of the most currentlyused methods in the freezing industry for largeproduction needs due to its convenience, reduced floorspace, flexibility and efficiency [19] (Fig. 2).

3. Fluidised bed freezers are used to freeze particulate foods ofuniform size and shape such as peas, cut corn, diced carrots,and strawberries. The foods are placed on a mesh conveyor beltandmoved through a freezing zone inwhich cold air is directedupward through the mesh belt and the food particulates beginto tumble and float. This tumbling exposes all sides of the foodto the cold air, thus the product is individually quick frozen(IQF). Typically, heat transfer coefficients range from 110 to160 W/m2K (Fig. 3).

4. Impingement jet freezers are straight-belt freezers involvingonly one step where the top, or more generally, both faces ofthe product receive very high velocity air at low temperaturevia uniformly distributed nozzles. The jets break the stagnantboundary layer surrounding the product, leading to a consid-erable increase in the heat-transfer coefficient, up to300 W/m2 K. The performance is comparable to cryogenicfreezers in relation to freezing time and weight, but at a muchlower cost (typically half the price).

Table 1 summarises the characteristics and operating parame-ters of the freezers described above. The cooling air temperature foreach freezers ranges between�30 and�45 �C.With similar coolingair temperatures, it is the air velocity over the product that is themain factor affecting the heat transfer coefficient.

5. Products blast frozen

Typical products frozen in air blast freezers include but are notlimited to:

� Meat e carcasses, cartons, large individually wrapped cuts,cured or processed, hamburger patties

� Poultry e whole bird or pieces, processed or breaded products� Fish e whole or eviscerated, fillets or small diced pieces, pro-cessed or breaded products, shellfish, prawns and shrimp

� Fruits e small size (whole), large size (sliced), purée or pulp� Vegetables e small and medium size, leafy� Other e Cheese and butter, dough, bread and baked products,pre-cooked ready meals

Selectingwhich freezingmethod to use is usually determined byquality specifications, economics and availability. Each foodproduct has its own unique characteristics which determine theirappropriate freezing temperature and freezing rate. Seafood, suchas prawns, requires faster freezing rates than red meat to maintaintheir texture and taste. As such, prawns are suited to Individual

Fig. 2. Schematic of a typical spiral belt freezer.

Quick Freezing (IQF) methods such as fluidised bed freezers. Redmeat however, does not require IQF freezing methods to maintainquality and can be adequately frozen in tunnel freezers.

6. Packaging

It is common practice to freeze meat or fish products in theirtransport packaging. Packaging is important in air blast freezing asit prevents dehydration, freezer burn and adherence by freezingand oxidation. The detriment of packaging is a decrease in heattransfer and hence an increase in the freezing time due to theinsulating properties of the packing material and excess enclosedair. Fig. 4 shows a typical temperature versus time graph of pack-aged and unpackaged meat products in an air-blast freezer.

Fig. 4 clearly illustrates the increased freezing time as a result ofpackaging. Stage 1 refers to the sensible cooling from the productinlet temperature (usually chilled) to freezing, stage 2 the latentheat extracted during crystallisation and stage 3 the sensiblecooling from the freezing temperature to the desired storagetemperature. Table 2 shows the heat transfer resistance of pack-aging for frozen beef and fish. It may be noted from the Table thatthe heat transfer resistance due to packaging can account for up to59% of the total resistancewhen fish is the product being frozen. Forbeef, the portion of heat transfer resistance from packaging is lessat 38%, but still significant.

Food Packaging must perform three functions: i) Control thelocal environmental conditions to enhance storage life. This isusually met by the packaging layer closest to the food. Typicalexamples include sealed plastic film and tin-plated cans. ii) Displaythe product in an attractive manner for the potential buyer.iii) Protect the product during handling and transit. Corrugatedcardboard is commonly used which unfortunately is a very goodinsulator. To reduce freezing times, cartons should use single layercardboard with a high heat transfer coefficient on the top andbottom as this is where the surface area is largest.

7. Air blast freezer operation and design

Air blast freezers are designed to supply cool air over the foodproduct with a uniform air velocity throughout the freezer [23e28].Most operation problems are related to improper positioning of thepallet or cart in the freezer [29]. Therefore, it is imperative thepallets and products are stacked in such a way that the air is free tomove over the entire product. The stacking method must enablethe cold air to circulate between the trays or boxes unhindered. Forcarton freezing, a spacer up to 70 mm should be implemented toallow sufficient air velocity between cartons [30]. Boast [18]recommends an air space equal to approximately 50% of theproduct thickness. Air temperature must be at least �35 �C, and insome cases �45 �C [31]. This equates to a refrigerant evaporationtemperature of �42 �C and �52 �C respectively.

Page 4: The art of air blast freezing: Design and efficiency considerations

Table 1Summary of forced convection freezing methods.

Freezer type Product Air velocity H.T.Ca W/m2�C Capacity Advantages Disadvantages

Batch tunnel Useful for all foods but better forbulk items, particularly carcasses

1.5-6 m/sTypically z 4 m/s

h < 50 [20] 1e80 tonnes i) Low capital costii) Versatile, can accommodatevarious product geometries

i) Long freezing timesii) Relatively low H.T.C

Continuoustunnel

Useful for all foods but better forbulk items. Mainly suited topackaged product due to hygieneissues

1.5e6 m/sTypically z 4 m/s

h < 50 [20] 1000e20,000kg/hr

i) Reduction in down time asthe freezer is not stopped forloading/unloadingii) Flexible with freezing times

i) Requires additional spaceii) Reduced freezing capacitydue to frost on evap. coils

Spiral Suitable for most foods, packaged orunpackaged e.g. poultry, red meat,sea, bakery product

3e8 m/s h z 25e80[21]

500e6000 kg/hr i) Compactii) Capable of IQFiii) Higher efficiency thantunnel

i) More expensive than tunnelfreezersii) Hygiene issues

Fluidised bed IQF small products, .5e5 cmdiameter, e.g. peas, French fries,shrimp, scallops, diced meat, meatballs

z30 m/s h z 110e160[21]

100e20,000kg/hr

i) Very fast freezing times,comparable to cryogenic onlycheaperii) High efficiency

i) Only suitable for smallproducts of fairly uniformshape and size

Impingement IQF. Meat patties, fish fillets,shrimp, French fries. Productthickness typically 0e25 mm1

10e100 m/sTypically z 40 m/s

h z 250e350[21]

Depends onapplication,can be up to1200 kg/h

i) Reduced moisture lossii) Very fast freezing times,similar to cryogenic

i) Only suitable for productsof small thickness

a Heat transfer coefficient.

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e8374

There are several optimum air velocities that are used for tunnelblast freezers in the open literature, depending upon the particularproduct being frozen; however, the generally accepted value is 4 m/s. Although increasing the air velocity will increase surface heattransfer coefficient, it does not necessarily reduce cooling time dueto the increased heat load from the fans because fan power,Wf V3.This increase in fan power increases the running cost usuallyrendering the increased fan speed uneconomical when comparedto slower speeds. Furthermore Kolbe et al [32] showed thatincreasing the air velocity above 5 m/s only barely increased thefreezing rate. This is because partway through the freezing cyclewhen the surface layers are frozen, the rate of heat transfer isincreasingly controlled by the internal conduction resistance, i.e.the Biot number becomes large.

When sizing evaporators for tunnel blast freezers, a frost build-up factor must be considered with fin spacing of no more than 4fins per inch [34]. When air coolers are mounted above a falseceiling, logarithmically spaced air deflectors can be installed to helpdeflect the air through the 90� turns and help distribute a uniformairflow over the products.

Modern spiral freezer designs eliminate any type of structureand belt support and each tier is supported directly on the previousone (self-stacking belt). The temperature of the refrigerated air is

Fig. 4. Freezing curves for packaged and unpackaged meat product in an air blastfreezer.

below �30 �C, generally being closer to �40 �C, with a circulationvelocity ranging from 3 to 8 m/s. In simple designs the air flowdirection relative to the belt can be horizontal, parallel or vertical(both upwards and downwards). Further design improvementsimplementing the use of baffles and flow dividers can provide airflow vertically upwards through the lower half of the stack anddownwards through the upper half (controlled dual flow). Thisbalances the heat transfer on the two sides of the food, and slightlydecreases freezing time and weight loss.

The current state of the art developments are focused onimpingement freezers, dual air systems [35] and improving the airflow distribution throughout air blast freezers with the aid ofcomputational fluid dynamics (CFD). Various studies [36e43] withCFD application to air blast freezers have been performed in theopen literature. CFD delivers detailed information e both in timeand space e of the flow field, the temperature and moisturedistribution, the shear forces and the heat fluxes. Furthermore,computer visualisation gives a direct insight in the process, whichallows a fast interpretation of any possible problem. Finally, themodel-based procedure allows the evaluation of many what ifscenarios at little cost compared to the process of prototyping.

8. Product geometry

Product geometry plays a significant role in determiningfreezing time. Most meat plants use a standard carton depth of160e165 mm. A reduction in carton depth can significantly reducefreezing time. The most important areas of the carton are the top

Table 2Heat transfer resistance of packaging [22].

Heat transfer resistance (m2K/W)

Source of heat transfer resistance Frozen fish Frozen beef

Convective boundary layer external tocarton

.04 .04

Carton wall .06 .02Nominal 1 mm layer of trapped air

between carton and product.04 .04

Product itself between surface andgeometric centre

.03 .06

Total .17 .16Heat transfer resistance due to

packaging system (%)59 38

Page 5: The art of air blast freezing: Design and efficiency considerations

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e83 75

and bottom as this is where the surface area and hence the heattransfer is largest.

A New Zealand meat company decided, for logistic purposes,that the base dimension of their meat cartons should be the same.To maintain a constant weight for each carton, the carton’s heightwas varied to cater for different product densities. Cleland [22]investigated the effects of the different carton heights on freezingtime and found freezing time varied between a linear anda quadratic relationship with height if the air convection heattransfer coefficient was unchanged. The tall cartons obstructed theair flow channels in the freezer more than the short cartons, thusthey had less air flow over them.

Tan et al. [44] set out to determine the factors affecting thefreezing process of tilapia fillets of different geometries. A numer-ical model based on the continuity equation, momentum equationsand energy equation was developed. Five different geometries ofequal mass were tested, three fish cakes and two spherical: slab,elliptical, disc, spherical and cylindrical respectively. The freezer’sair velocity was set at 5 m/s and temperature at �35 �C.

The three fish cakes had very similar freezing times rangingfrom 1.167 (disc) to 1.233 h (slab) due to their similar thickness andsurface area. The freezing time for the sphere was 3.7e3.9 timeslonger than that of the flat shaped fillets due to the difference insurface area and distance from surface to centre. The cylindricalshaped fillets produced the longest freezing time of 5 h.

9. Single and two stage air blast freezers

Schematic of a two-stage carton blast freezer operating in NewZealand is shown in Fig. 5. The system consists of a 63 kW VilterVMC-440 two-stage compressor with desuperheating and sub-

Fig. 5. Schematic of a two-stage carton bl

cooling, a Miller air cooled condenser with five pressurecontrolled fans, receiver, suction accumulator with sub-cooling,two 4.0 kW fixed speed evaporator fans, two custom made fourpass evaporators and seven Danfoss expansion valves. Six of theexpansion valves, rated at 10.2 kW, are used on the evaporators(three per evaporator), the remaining valve is used for the inter-cooling. The system uses refrigerant R22.

The pressure enthalpy (P-h) diagram for the two-stage blastfreezer system shown in Fig. 5, is shown in Fig. 6, with actual datataken from the site, where the advantage of two-stage compressionand sub-cooling is illustrated vividly on the P-h diagram in Fig. 6 (a)with reduced compressor work and an increased evaporatorcapacity.

The volumetric efficiency of a reciprocating compressor isinversely proportional to the compression ratio. The ability of thetwo-stage system to split the evaporating and condensing pressuredifference over two stages means the compressors are operatingwith a lower pressure ratio, thus a higher volumetric efficiencythan the single-stage system. Furthermore, by desuperheating theLSC discharge refrigerant the HSC discharge temperature is lowerthan the single-stage compressor. This means the two-stage systemis less prone to oil breakdown and fatigue on compressor compo-nents. Intercooling the liquid line enables the refrigerant to enterthe evaporator at a lower quality. Since the heat transfer coefficientof a two-phase mixture is significantly higher than the vapour,intercooling the evaporator leads to higher heat transfer coefficientthan that of the single-stage system, thereby, increasing the evap-orator efficiency.

Fig. 7 shows an older system, installed in approximately 1980.This is a single-stage system consisting of two stand alone refrig-eration units, Sub-System One (SS1) and Sub-System Two (SS2).

ast freezer operating in New Zealand.

Page 6: The art of air blast freezing: Design and efficiency considerations

Fig. 6. (a) Two-stage P-h diagram for system shown in Fig. 5 and (b) corresponding theoretical single-stage P-h diagram operating with the same suction and discharge pressures.

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e8376

Each sub-system consists of two semi-hermetic reciprocatingcompressors, oil separator, water cooled shell-and-tube condenser,thermostatic expansion valves, evaporators and a suction accu-mulator. Both systems use refrigerant R22. The freezer has eight4.0 kW evaporator fans and racks for suspending meat carcasses.

Sub-System One has two Copelametic compressors, approxi-mately 30 years old, rated at 26 kWeach operating in parallel. Thesecompressors have older reed valves. Sub-system Two has twoDWMCOPELAND compressors, approximately 10 years old, rated at20.1 kW operating in parallel. These compressors have the moremodern discus valves.

Both SS1 and SS2 have three pass water cooled shell-and-tubecondensers mounted underneath the compressor racks. Thewater cooling the condensers is fed from the mains which supplies

Fig. 7. Schematic of a single-stage carcas

water for all the water cooled systems operating at the facility. Theheated water at the outlet of the condensers is returned to themains before entering the cooling tower. The water for all systemsis driven by a single centrifugal pump. SS1 has three evaporators,one large and two small, each with different geometries. The largeevaporator is fed by twoTXV’s, the two small evaporators are fed byone TXV each. SS2 has two large evaporators each fed by twoTXV’s.

The COP for the two-stage and single-stage systems is respec-tively defined by Eqs. (1) and (2))-

Two-stage Coefficient of Performance:

COP2stg ¼ _mLSCðh2 � h1Þ_mLSCðh2 � h1Þ þ _mHSCðh4 � h3Þ

(1)

s freezer operating in New Zealand.

Page 7: The art of air blast freezing: Design and efficiency considerations

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e83 77

COP2stg ¼ 1.73

Single-stage Coefficient of Performance:

COP1stg ¼_mref ðh2 � h1Þ_mref ðh1 � h4Þ

¼ h2 � h1h1 � h4

(2)

COP1stg ¼ 1.30

Splitting the refrigeration cycle into two stages and sub-coolingresulted in 33% increase in COP from 1.30 to 1.73.

10. Simulation model of the two stage system

A steady state simulation model of the two-stage system wasdeveloped to analyse the performance of the refrigeration Systemusing the Engineering Equation Solver [33] package to optimise thesystem for maximum efficiency. The main model was based onindividual components including Compressors, condensers, evap-orators etc. using equations and correlations from the openliterature.

10.1. Compressor model

The low and high stage compressors were modelled by themethod proposed by Popovic and Shapiro (1995), where thegeometry of both the low and high stage compressors was identical(bore, stroke, rpm etc.). The refrigerant mass flow rate is calculatedby:

_m ¼ u$PD60$vsuc

�1þ C � C

�PdisPsuc

�1=n�(3)

where piston displacement (PD) is the volume actually sweptduring one cycle. The clearance volume C is the refrigerant volumeleft in the cylinder after completion of the discharge process iscalculated by:

C ¼ VdisVsuc � Vdis

(4)

The compressor work is calculated by:

_W ¼ _m

24 nn� 1

Psucvsuc

0@�

PdisPsuc

�n�1n

�1

1A35 (5)

The polytropic exponent n, in Eq. (5), is a function of thedischarge specific volume (a model output), and is calculated fromexperimental data.

n ¼ logðPdis=PsucÞlogðvdis=vsucÞ

(6)

The compressor model determines the LSC flow rate _m1 and theHSC flow rate _m2. The intercooler flow rate is calculated as thedifference between the HSC and LSC flow rates.

10.2. Condenser model

The condenser was modelled by dividing into zones corre-sponding to the refrigerant state (superheated, two-phase, sub-cooled). The condenser consisted of 46 individual tubes (Ntubes) and6 tube passes (Npasses).

The ε-NTU method is used to evaluate the heat exchangerperformance. The conductance, UA, for each zone is determined by

calculating UA for a single tube (i.e. 1 of the 46 condenser tubes),then multiplying the UAsingle tube by the total number of tubes, i.e.:

UASH;2Ph;SC ¼ Ntubes$UAsingle tube;SH;2Ph;SC (7)

The model sequence starts by guessing the fraction of the tubelength required to de-superheat the refrigerant, FSH (FSH (FSH < 1).To calculate the resistance over the superheated zone, each fullresistance, that is the each of the five resistances over the full tubelength (Rfull), is divided by the fraction of the tube length (FSH) usedfor that particular section,

The total resistance is the sum of the individual resistances. Theconductance of the superheat zone, as calculated by the model, isgiven by:

UASH;model ¼ Ntubes$1

Rtotal;SH(8)

where Rtotal,SH is the sum of the superheat resistances. In order toverify the initial guess of the superheat fraction FSH. The actual rateof heat transfer over the superheat section ( _qSH) is given by:

_qSH ¼ _m3�hin � hsat;x¼1

�(9)

The NTU conductance is calculated by:

UASH;NTU ¼ NTUSH$_Cmin (10)

The model conductance UASH,model is checked against the NTUconductance UASH,NTU. The initial guess of the fraction of the tubelength required for desuperheating, FSH, is iterated until UASH,model

and UASH,NTU converge. Upon convergence, the fraction of tubelength required for desuperheating is known and the process isrepeated for the two-phase section.

The two-phase zone analysis starts by guessing the fraction ofthe tube length required for full refrigerant condensation (latentheat), F2Ph. The resistances are solved for the tube length L2Ph cor-responding to F2Ph. The refrigerant saturation temperature and theHSC discharge pressure are used to determine the refrigerantproperties. The average heat transfer coefficient during condensa-tion in horizontal tubes, required to determine the refrigerant-sideresistance in the two-phase zone, is calculated using the correlationsuggested by Dobson and Chato [53]. The refrigerant side resistanceis determined with the area corresponding to the two-phaselength, L2Ph. The resistances are calculated in the same manner asdescribed for the superheated region using L2Ph. The conductance ofthe two-phase zone, as calculated by the model, is given by:

UA2Ph;model ¼ Ntubes$1

Rtotal;2Ph(11)

The actual rate of heat transfer over the two-phase zone, _q2Ph, iscalculated by:

_q2Ph ¼ _m3ðhx¼1 � hx¼0Þ (12)

where hx¼1 and hx¼0 refer to the vapour and liquid saturationenthalpies respectively. The air-side capacitance rate is theminimum capacitance rate in the condensing section as thecapacitance rate of the condensing refrigerant is effectively infinite.Therefore, the maximum possible heat transfer rate in thecondensing zone is:

_qmax;2Ph ¼ _Cair;sat�TR;sat � Tair;in

�(13)

The NTU conductance, UA2Ph,NTU, is calculated by:

UA2Ph;NTU ¼ Ntubes_CminNTU2Ph (14)

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P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e8378

The initial guess of the tube length required for the two-phaseregion F2Ph is iterated until UA2Ph,model and UA2Ph,NTU converge.Upon convergence, the fraction of tube length required for phase-change is knownand theprocess is repeated for the sub-cooled zone.

With FSH and F2Ph known, the fraction of tube length associatedto sub-cooling is calculated by:

FSC ¼ 1� FSH � F2Ph (15)

The six resistances are calculated using the sub-cooling tubelength given by:

Ltube;SC ¼ FSC$Ltube;total (16)

The conductance of the sub-cooled zone is calculated by:

UASC;model ¼ Ntubes$1

Rtotal;SC(17)

The NTU over the sub-cooling section is calculated by:

NTUSC ¼ UAmodel;SC_Cmin

(18)

The rate of heat transfer over the sub-cooling section is deter-mined by:

_qSC ¼ εSC_CminðTRef ;sat�Tair;inÞ (19)

The enthalpy of the refrigerant leaving the condenser is deter-mined by an energy balance across on the refrigerant side:

hout ¼ hsat;x¼0 �_qSC_m3

(20)

Finally, the total rate of heat transfer across the condenser isdetermined by:

_qcond;total ¼ _qSH � q2Ph þ _qSC (21)

If FSC (from Eq. (15)) is less than one, the refrigerant leaves thecondenser in a saturated state. Under these conditions the refrig-erant enthalpy at the condenser outlet is calculated in the samemanner as described for the sub-cooling zone.

10.3. Evaporator model

The two-stage blast freezer has two identical wavy fin-and-tubeevaporators with a staggered tube layout. Each evaporator hasthree TXV’s with a distributor further dividing the flow into 15tubes, i.e. 15 tubes per TXV. This equates to 45 tubes per evaporator.Each tube has four passes.

The evaporator is modelled in the same manner as thecondenser. The evaporator is divided into zones corresponding tothe refrigerant state. The refrigerant enters the evaporator in two-phase state and leaves superheated. The air-side heat transfercoefficient is calculated for a six row heat exchanger, same as thecondenser. The remaining resistances are calculated for four rows.

10.4. Expansion valves model

The six evaporator expansion valves and the intercoolerexpansion valve are all of the mechanically controlled thermostatictype, TXV. The throttling of the liquid refrigerant is achieved byassuming the expansion is enthalpic.

10.5. Intercooler model

The intercooler could not be modelled physically like the heatexchangers because the geometric data was unavailable. Therefore,

a thermodynamic model is used to simulate the desuperheatingand sub-cooling processes of the intercooler.

Fig. 6a shows the log P-h diagram of the two-stage systemwiththe state points used for modelling. State points 1, 2, 4, 5, 6 and themass flow rates _mevap _mcond and _mevap are calculated from thecompressor, condenser and expansion valve models coupled withthe evaporating and condensing pressures given as model inputs.The intermediate pressure is calculated as the geometric mean ofthe condensing and evaporating pressures given by:

Pint ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPevap$Pcond

q(22)

State point 3 is determined from the fraction of superheat x,given by

h3 ¼ x�h2 � hsat;Pint

�(23)

where

0 < x � 1 (24)

The fraction of superheat x is determined from the experimentaldata and can be adjusted for parametric analysis. The enthalpy atstate point 7 is determined from an energy balance across theintercooler:

Qint ¼ _mintðh3 � h6Þ ¼ _mevapðh2 � h3Þ þ _mevapðh5 � h7Þ (25)

10.6. Complete system model

The system model consists of the individual component modelslinked together. Fig. 8 shows the flow chart of the complete systemmodel. The condenser model uses two loops to determine thefraction of the tube length required for the superheat and two-phase sections according to the condenser inlet air temperature,air mass flow rate and the refrigerant condensing pressure. Theevaporator model has one loop used to determine the fraction ofthe tube required for the two-phase section according to the freezerair inlet temperature, air mass flow rate and the refrigerant evap-orating pressure. The complete model has an additional loop on thesuperheat to ensure the energy balance between the evaporator,condenser and compressors is met. The model is used as a toolto analyse the thermodynamic performance of the system(i.e. system COP).

11. Model validation and results

The two-stage compressor model consisted of two individualcompressor models, the LSC ( _m1) and HSC ( _m3). The compressormodel predicted the LSC mass flow rate to within �7% of the ninemeasured mass flow rates. Similarly, the compressor model pre-dicted the intercooler mass flow rate to within �13% of themeasured mass flow rates. The modelled condenser capacityagreed tomeasured capacity towithin�5% of the 13measured datapoints, as shown in Fig. 7.3 (Fig. 9).

The evaporator model was validated using the measuredrefrigerant mass flow rate. The outputs of the evaporator model arethe refrigerant superheat and the outlet temperature of the air. Themodelled evaporator capacity agreed with the measured capacityto within �4%. The system model was validated with the recordeddata from the unloaded freezer. The experimental data wascollected over a 4 h periodwhere the evaporator load dropped from75 kW to 45 kW. The ambient air over this period varied from17.4 �C to 19.7 �C. Fig. 7.6 shows the model predicted COP againstthe measured COP, where the model COP agreed to within �8% ofthe 11 measured data points (Fig. 10).

Page 9: The art of air blast freezing: Design and efficiency considerations

Fig. 8. System model flow diagram.

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e83 79

It was very encouraging to note that the model predicted theevaporator air outlet temperature very accurately towithin an errorof �2%. This established the accuracy and the validity of the model,which now could be used to predict performance of a blast freezeras well as a design tool for future blast freezers in order to achievehigher energy efficiency.

12. Design improvements

Odey [47] investigated performance enhancing measures ofa batch air blast freezer. He found that generalised rules of thumbhave been used for the design of air flow through blast freezers.Critical aspects of the design and implementation of the airflowcircuit are often excluded from the refrigeration contract, resultingin poorly implemented and underperforming facilities. Typically,the refrigeration contractor’s response to poor freezer perfor-mance is to increase the fan capacity and power. It was found thatsimply increasing the air flow by increasing fan speed did notnecessarily increase the air speed through the cartons in the

freezer. The higher fan speed resulted in negative velocities at thefan inlet due to the formation of a large unstable vortex. As a resultmore heat was added to the freezer from the fans thus reducingthe efficiency.

The following modifications were installed on the air blastfreezer:

� Baffling on the top and sides of the freezing chamber� Fan inlet cone and diffuser� Air inlet and discharge vanes on corners� Variable speed drive on fan

Prior to the modifications the air flow entering the fan washighly unstable with significant flow reversal. This turbulencereduced significantly with the above modifications. Most of thepressure drop in the unmodified freezer occurred at the 90� turningpoints, whereas the modified freezer had the largest pressure dropthrough the product pallets. As a result of the experiment, theexisting 11 kW fan motors drawing 8.7 kW were replaced with

Page 10: The art of air blast freezing: Design and efficiency considerations

Fig. 11. Product heat load characteristics for hot-boned and cold-boned beef cartons [47].

Fig. 9. Comparison of the condenser model capacity against measured condensercapacity.

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e8380

3.5 kW motors drawing 4.0 kW. The fans were re-pitched from 30�

to 22� to maintain drawn power within the motor capacity. Afterthe modifications satisfactory freezing was being achieved withinthe specified 48 h turnaround period.

Kemp and Chadderton [48] performed a study on the perfor-mance of batch blast freezers used to freeze beef cartons and foundthat designs seem to be based on average product heat load whichis insufficient to handle the initial peak heat load. This problem isespecially prevalent with hot-bone meat. Insufficient coolingcapacity generally occurs at the beginning of the freezing processwhen the product heat load is being released at a peak rate that farexceeds the average rate, see Fig. 5. This problem is compounded asvery few blast freezer systems manage to maintain their designcooling capacity (Fig. 11).

Bowater [34] states it is necessary to size evaporators at least50% higher than the average refrigeration load for 24 h freezes toaccount for the high initial heat load, while this requirement is notso critical for 48 h freezes. Other factors effecting cooling timeinclude overloading of the freezers that often results in highercooling loads and therefore longer freezing times. Changes inproduct packaging have to be taken into account when sizing airblast freezer throughput. Mannapperuma et al. [49] found thesurface heat transfer coefficient of whole, unpackaged chickensreduced by an order of magnitude when the chickens were wrap-ped in plastic and stored in vented boxes. Kemp and Chadderton

Fig. 10. Comparison of model COP against measured COP.

[48] surveyed a plant which changed the type of cardboard pack-aging used. As a result freezing time was increased by 8 h. Thechange of packaging was determined as the major cause of theplant’s freezing problems.

The fan load in old carcass freezers can account for up to 60%of the total refrigeration load [50]. Wee et al [51] installedvariable speed drives (VSD’s) on the fans of a 4000 lamb carcasscapacity blast freezer and reported a 44% energy saving. TheVSD was controlled by a personal computer where the programcontinuously analysed data inputs such as air temperature andcalculated the optimum air flow velocity. The VSD paybackperiod was 2.1 years. Other benefits included a more uniformproduct quality, improved power factor for the freezer fans andminimization of product weight-loss due to the lower airvelocity. Kolbe et al [32] investigated the effects of baffling andvarious fan speed control on air blast freezer performance. The8.7 tonne capacity freezer was used for 10 kg sardine cartons.The system had three 5.6 kW fans mounted in the false ceilingdownstream of the evaporator. Typical freezing times werearound 12.5 h.

The following modifications were applied to re-direct andchannel the air flow:

� Plywood on upper supply-side corners prevented air fromsweeping around the upper end of the ceiling structure

� The ceiling was lowered to 75 mm to reduce the gap betweenceiling and product

� Plastic sheeting on the supply-air side sealed the horizontalcorner where the near-vertical and horizontal ceilings meet,and at the vertical corners between wall and cartons

� Floor-to-ceiling plywood sheets, installed at the start of eachfreezing cycle, covered the ends of the racks and preventedend-around by-pass

Prior to the modifications, analysis of the flow velocities showed35% of the air went through the carton racks, 15% flowed over thetop of the racks and 50% by-passed around the two sides. Airvelocity ranged roughly from 1.5 to 4.0 m/s. After the modificationsvelocities ranged from 3.0 to 4.0 m/s, hence the average velocitythrough the product increased. The results of the baffling areshown in Table 3. The baffling reduced maximum freezing time by15%, fan energy usage by 6% and uniformity, the difference betweenmaximum and minimum freezing times of individual cartons,improved significantly.

Page 11: The art of air blast freezing: Design and efficiency considerations

Table 4Results (averages) for fan loading trials [32].

Max. time Min. time Difference Fan energy(kWh)

Total energy(kWh)

Trial 1 11.4 7.9 3.5 151 819Trail 2 11.4 7.4 4 167 873Trial 3 11.9 7.4 4.5 197 847

P. Dempsey, P. Bansal / Applied Thermal Engineering 41 (2012) 71e83 81

The second part of the experiment was to test effects of fanspeed control on both freezing time and energy use. Tests for threefan schedules were performed:

Trial 1all 3 fans come to full speed within 45 min. After 3.5 h, the fans areslowed to 75% speed for the remainder of the freezing period.

Trial 2fans came to full speed slightly faster than trial 1. Fan speed washalved after 7 h. Of these two trials, the first savedmore energy andwould be the preferred option.

Trial 3the three fans started at 30 min intervals. After 4 h the centre fanwas switched off, reducing fan power by 1/3. This method does notrequire the use of VFDs.

The results for the three trials are shown on Table 4. Trial 1performed the best reducing the maximum freezing time by anhour (8%) and reduced total energy use by 22%, based on the roomperformance prior to modifications.

Table 5Potential energy savings for industrial refrigeration systems [52].

Method Potential saving

13. Energy usage and best practice guide for blast freezing

Air blast freezing consumed8.1GWhof electricity inNewZealandin 2005 [45] and is themost energy intensive operation in the frozenstorage industry. Apparent energy use for blast freezing was calcu-lated as 133 kWh/tonne from regression analysis. This is 50% higherthan the predicted value from theoretical best practice consider-ations. The New Zealand Cold Storage Industry identified blastfreezing as an area where a 15% saving could be achieved for manysites, particularly related to reduction in fan power due to improvedairflowdesign. Comparisonwith overseas survey results showed theNZ use was similar on average. If all facilities surveyed met thetheoretical best practice energy consumption limit for blast freezing,this would represent an average energy saving of 33% per tonne ofblast frozen product. This figure is supported by a survey on energyefficiency of food refrigeration operations funded by the UKGovernment Department for Environment, Food and Rural Affairs(defra), who identified blast freezing as an area where a 20e30%energy saving could be achieved [46]. The New Zealand surveycovered13 sites that carriedout blast freezingandrecordeddata overthe duration of at least one year. These sites have a wide range ofrefrigeration systems frommulti-stagepumpcirculation ammonia tosingle-stage direct expansion fluorocarbon systems. The mostcommon refrigerant was ammonia, used at 71% of the sites.

The following measures were identified as potential energysaving solutions:

� Reduce discharge pressure set points� Raise suction pressure set points� Variable speed drives (VSD’s) for fans� Improved door protections and management

Table 3Effect of baffling on blast freezer cell [32].

Max. time Min. time Difference Fan energy(kWh)

Total energy(kWh)

Unbaffled 12.5 8.7 3.8 282 1054Baffled 10.6 9 1.6 266 924Difference 1.9 L0.3 2.2 16 130

� Optimise defrost frequency and duration

Other measures to improve blast freezing efficiency include:

� Improve air flow design to reduce fan power for the sameeffective air velocity over the product, e.g. use of air turningvanes, flat inlet and outlet cones, baffles to prevent air flowshort circuiting away from the product

� Increase the time available to freeze the product so can operatethe freezer at lower air velocities and higher air temperatures

� Once freezing is completed, reduce fan speeds and increasetemperature set points to storage temperature until unloadingcan occur

� Load product so that the air flow distribution remains uniformthroughout the freezer

� Defrost coils a short period of time after loading a batch freezerso that the coils operate lightly frosted for most of the time

Declining profit margins are forcing cold storage companies toemploy energy savings initiatives, load management strategies andmore efficient technologies. The most common energy savingmeasure is the use of off-peak electricity. Variable speed drives(VSDs) on compressors and blast freezer fans were identified as themost easily implemented energy saving new technology. Ambientair defrost systems are becoming more common rather than wateror hot gas.

Table 5 summarises the findings of a report on best practiseguide to industrial refrigeration produced by SustainabilityVictoria [52]. The report emphasised taking the “whole-system”

approach when designing new systems as this presents thegreatest opportunity to incorporate energy efficiency throughoutthe whole process, unhindered by the constraints that may beposed by existing equipment. The whole-system approach entailsconsidering the system operation as a whole rather than justfocusing on individual components as each component has flow-on effects that impact on other components, and therefore theefficiency of the system as a whole. The report recommends theuse of a control system that is responsive to the compressor headpressure. Electronic expansion valves should be used wherepossible and have their controls linked to the head pressurecontrol system.

(energy, unless stated otherwise)

Electronic expansion valves 20%VSD on compressor motors 20%VSD condenser fans 2e3% of total refrigeration costReduced temperature lift 3e4% improvement for 1 �C reductionConversion from liquid injection

to external oil coolersOver 3%

Refrigeration system replacementIf over 10 years old

Up to 30e40%

Refrigerant selection 3e10%

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14. Conclusions

This paper presented a snapshot of the use of blast freezers inthe food industry, including historical background, modellingfeatures, issues and recent advances that have enabled air blastfreezers to play a significant role in the meat industry due to theirversatility and low capital cost. There seems to be a great potentialto achieve energy savings in blast freezer industry by employingVSD’s on fans that could result in with energy savings of up to 44%.Other, cheaper and simpler energy saving measures include airbaffles, air turning vanes, fan inlet cone and outlet diffuser, andimproved user operating procedures.

When determining the heat load during the design process it isinsufficient to use the mean product load. The “peaky” nature ofmeat, particularly hot boned meat, must be taken into account toensure adequate freezing times are achieved. Evaporators shouldbe sized 50% higher for 24 h freezers and hot boned meat. Also, thedesign capacity of the freezer will deteriorate with time. It isimperative the product is stacked with adequate spacing to enableair to pass through; failure to do sowill result in localised regions oflong freezing times.

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Nomenclature

_mLSC : low stage compressor mass flow rate, kg s�1

_mHSC: high stage compressor mass flow rate, kg s�1

hLSC,in: low stage compressor suction enthalpy, kJ/kghLSC,out: low stage compressor discharge enthalpy, kJ/kghHSC,in: high stage compressor suction enthalpy, kJ/kg

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hHSC,out: high stage compressor discharge enthalpy, kJ/kgh1stgC in: single-stage compressor suction enthalpy, kJ/kgh1stgC out: single-stage compressor discharge enthalpy, kJ/kghEXVin,1st: single-stage expansion valve inlet enthalpy, kJ/kghEXVin,2nd: two-stage expansion valve inlet enthalpy, kJ/kghsat: saturation enthalpy, kJ/kgysuc: suction specific volume, m3/kgydis: discharge specific volume, m3/kgPsuc: suction pressure, kPaPdis: discharge pressure, kPa_W: work (kW)

COP2stg: two-stage coefficient of performanceCOP1stg: single-stage coefficient of performanceUA: conductance, kW/�KR: thermal resistance, �K/WT: temperature, �K_q: heat, kW_C: capacitance, kJ/�KNTU: number of transfer unitsx: qualityF: fraction, 0 � F � 1N: number of