CHARACTERISTICS OF CHAMBER TEMPERATURE CHANGEDURING VACUUM COOLING

RUI ZHAO1, ERTONG CHEN1,3, MEIYING LIN1, DA-WEN SUN2,3

and BINKAI XU1

1Institute of Cryobiology and Food FreezingShanghai University of Science and Technology

Shanghai, China

2Biosystems EngineeringUniversity College Dublin

National University of IrelandEarlsfort Terrace, Dublin 2, Ireland

Accepted for Publication October 5, 2007

ABSTRACT

In order to investigate the dynamic changing pattern of the chambertemperature with chamber pressure during vacuum cooling, 10 repeatedexperiments were conducted to evaluate the time-dependent temperature andpressure in the vacuum chamber during vacuum cooling of water. Water waschosen in the experiment as it is the main component of most foods. The resultsshowed that the temperature in the vacuum chamber significantly depended onvariation in pressure at different pumping stages. The temperature changes inthe chamber generally followed a certain pattern. In the early stage of vacuumcooling, the chamber temperature dropped very quickly (0.26 K/s), while atthe end of vacuum cooling, it increased rapidly (0.22 K/s), and was about11.8 K higher than the ambient temperature when the vacuum was releasedwith ambient air flowing back to the chamber.

PRACTICAL APPLICATIONS

Vacuum cooling is a rapid cooling method for the food industry; furtherunderstanding of the vacuum cooling mechanism can help to control andimprove this cooling process. Temperature changing pattern and distributionaffects the quality of the food product in vacuum cooling process. As the maincomponent of most foods is water, it is necessary to investigate the dynamic

3 Corresponding authors. TEL: 86 21 55274687; FAX: 86 21 55276049; EMAIL: chenetong@163.com (E. Chen); dawen.sun@ucd.ie (D.-W. Sun); Web sites: www.ucd.ie/refrig; www.ucd.ie/sun

Journal of Food Process Engineering 32 (2009) 177–186. All Rights Reserved.© Copyright the AuthorsJournal Compilation © 2008 Wiley Periodicals, Inc.DOI: 10.1111/j.1745-4530.2007.00208.x

177

temperature changing pattern and distribution with vacuum pressure duringvacuum cooling of water so that the information obtained could be used as areference for vacuum cooling of food products.

INTRODUCTION

Vacuum cooling uses a vacuum system to rapidly evacuate the air andmoisture in a vacuum container which contains fresh agricultural or foodproduct, causing moisture evaporation in the product and rapid temperaturereduction (McDonald and Sun 2000; McDonald et al. 2000). The vacuumcooling rate is faster than normal cooling that is based on heat conduction andconvection, and the shelf life of vacuum-cooled vegetables can be significantlyextended; therefore, vacuum cooling has been successfully applied to coolvegetables and cut flowers since the 1950s (Brosnan and Sun 2001; Briley2004). In recent years, as a rapid cooling treatment, vacuum cooling has alsobeen used to minimize the growth of surviving microorganisms for cookedfoods (James and James 2000; Wang and Sun 2004). The trend of integratingvacuum cooling into the processing procedures of some prepared consumerfoods, e.g., cooked meats and ready meals, has recently become popular in thefood industry (Wang and Sun 2001; Zheng and Sun 2004; Sun and Zheng 2006).

However, despite extensive studies in vacuum cooling technology, nostudy has been specifically conducted to examine the temperature changecharacteristics in the vacuum chamber. Therefore, in the current study, water isused in vacuum cooling equipment to investigate the variation of vacuumpressure and temperature. Thus, results from this study will further facilitatethe understanding of the vacuum cooling mechanism.

MATERIALS AND METHODS

An experimental vacuum cooler was designed and used in the currentstudy. Figure 1 shows the configuration of the vacuum cooler. The vacuumchamber is a stainless steel cylinder, whose diameter is 400 mm and height is470 mm, with a Stalinite (silica base glassware) (Yaojing Glass Ltd., Shang-hai, China) cover. The cover has a diameter of 500 mm and thickness of10 mm. An O-shaped rubber seal is placed between the vacuum chamber andthe cover. The evacuation rate of the vacuum pump is 4 L/s. Four thermo-couples with an accuracy of �0.5C and response time of 100 ms (PinganAutomation Instruments Ltd, Shanghai, China) and a pressure transducer(Ns-B, TM Automation Instruments Ltd, Shanghai, China) were installed inthe vacuum chamber, which were calibrated before experiments.

178 R. ZHAO ET AL.

During the experiment, 100 g water with an initial temperature of 28Ccontained in a plastic container (height: 31.3 cm; bottom area: 13.2 ¥ 12.4 cm)was placed on the tray. The four thermocouples were arranged respectively onthe water surface (floating on the surface), near the bottom of the vacuumchamber, in the middle of the vacuum chamber and underneath the chambercover, and were respectively marked with T1, T2, T3 and T4. Figure 1 also showsthe arrangement of the thermocouples, which were 20, 15, 10 and 3 cm,respectively, underneath the chamber cover. A refrigeration system was used tocool the vacuum chamber first, then the vacuum pump (2XZ-4, Kangjia Ltd,Shanghai, China) was switched on when the condensing unit temperaturedropped to 5C. Vacuum cooling continued until the water surface temperatureT1 dropped to 2C. Experiments were repeated 10 times and mean data werereported.

RESULTS AND DISCUSSION

According to the experimental results, it was observed that the changepattern of each temperature (T2, T3 and T4) in the chamber was similar in eachindividual experiment; however, each temperature change pattern was differ-ent from the others, i.e., the chamber base temperature T2 was a little lowerthan the middle T3, mainly because of the effect of the condensing unit;however, T4 underneath the chamber cover only changed slightly, as T4 wasfar away from the water sample. Therefore, only sample temperature T1 and

1

2

3

4

5

10

9

8

7

6

T2

11 T4

T3

T1

FIG. 1. SCHEMATIC DIAGRAM OF THE VACUUM COOLING EQUIPMENT1, chamber cover; 2, vacuum chamber; 3, pressure sensor; 4, vacuum pump; 5, pressure-releasing

valve; 6, condensing unit; 7, water sample; 8 to 11, thermocouples.

CHARACTERISTICS OF CHAMBER TEMPERATURE CHANGE 179

chamber temperature T3 were chosen as representative for a detailed discus-sion. Figure 2 shows the change patterns of T1 and T3, and the chamberpressure p. Table 1 lists the corresponding mean values with SDs at key pointsA, B, C, D and E in Fig. 2. As it can be seen from Fig. 2, the changes in thechamber temperature during vacuum cooling can be divided into four stages.

Vacuum Process

Stage A-B. Figure 2 shows that with the rapid reduction of pressure(103.2–20.4 kPa) in vacuum chamber in stage A-B, the temperature T3 (29.4–20.1C) in the chamber also decreased rapidly to be lower than the watertemperature T1 (29.3–28.5C). Although in this period a large volume of gaswas evacuated by the vacuum pump, it only took about 34 s. This can beexplained by the following thermodynamic analysis.

According to the first law of thermodynamics, the heat flux equation ofthe gas in the vacuum chamber can be expressed as (Holman 1980)

45

40

35

30

25

20

15

10

5

00 150 300 450 600 750

20

40

60

80

100

120

0

Pre

ssur

e (k

Pa)

Tem

pera

ture

(° C

)

P

A B C D E

T1

T3

FIG. 2. THE AVERAGE TEMPERATURE AND PRESSURE CURVES DURINGVACUUM COOLING

TABLE 1.THE AVERAGE VALUES AT THE KEY POINTS IN FIG. 2

Parameters A B C D E

p (kPa) 103.2 � 1.3 20.4 � 0.6 3.7 � 0.6 102.5 � 1.2 102.9 � 1.4T1 (C) 29.3 � 0.8 28.5 � 1.0 2.7 � 0.3 4.3 � 0.6 9.6 � 0.8T3 (C) 29.4 � 1.4 20.1 � 1.4 27.2 � 1.3 40.8 � 2.8 29.6 � 1.9

180 R. ZHAO ET AL.

δ δQ h dm W h dm dU+ = + +in in out out (1)

Supposing at a given time t after starting the vacuum pump, the chambertemperature was Tt, its mass m1 and its pressure p1, Dt later, the chambertemperature became Tt+Dt, mass m2 and pressure p2. In the limited time periodof Dt, as there was very limited heat exchange with the environment, thisprocess could be considered an adiabatic expansion process, therefore dQ = 0.Meanwhile the volume of the system remained constant, therefore dW = 0.

The first law of thermodynamics can be then expressed as

− + =hdm dU 0 (2)

i.e.,

mdu udm hdm= − = 0 (3)

Assuming the gas in the chamber as an ideal gas (Holman 1980), Eq. (3) canbe expressed as

mc dT c c Tdmv p v= −( ) (4)

By integrating Eq. (4), the mass ratio can be found as

m

m

T

T

k2

1

11

= ⎛⎝⎜

⎞⎠⎟

+ −τ τ

τ

Δ (5)

And the mass of the gas is given by the ideal gas equation:

mp V

RT11=

τ(6)

mp V

RT22=

+τ τΔ(7)

Therefore the temperature Tt+Dt can be described as

T Tp

p

k

k

τ τ τ+

−

= ⎛⎝⎜

⎞⎠⎟Δ

2

1

1

(8)

CHARACTERISTICS OF CHAMBER TEMPERATURE CHANGE 181

According to Eq. (8), it can be calculated that the temperature of the gas Tt+Dt

is lower than the gas temperature Tt. Table 2 shows two calculated examples,confirming the decrease of theoretical T3 during this stage. Table 2 also showsthat the experimental T3 agreed with the calculated values, indicating thevalidity of the aforementioned analysis. Therefore T3 in the chamber decreasedrapidly in stage A-B.

Stage B-C. In the earlier period of stage B-C, with the slow reduction ofpressure (20.4–13.8 kPa) in the vacuum chamber, T3 increased (20.1–26.0C),while the water temperature T1 had a small drop (28.5–28.2C) because ofthe evaporation of the surface water. Then T1 increased (28.2–28.5C) again,which might be caused by air bubbles in the water rushing to the water surface.This process was not an adiabatic expansion process, but a process of the gasobtaining energy in the vacuum chamber. As the chamber wall surface tem-perature was higher than T3, the gas molecules obtained some energy fromthe chamber wall by convection and radiation. Moreover, the gas obtainedthe extra massive energy from water; therefore, T3 increased quickly to watertemperature T1.

It can be seen from Fig. 2 that the chamber temperature T3 shows a slighttemperature drop (26.0–24.9C) in the middle period of stage B-C. While witha small reduction of the pressure in the chamber (13.8–4.0 kPa), the sampletemperature T1 shows a rapid reduction (28.5–5.8C). In this period the partialvapor pressure of air in the chamber was lower than the saturation pressurebecause of evacuation by the vacuum pump; therefore, the water boiledfiercely, even splattering outside the vessel. Massive evaporation and ebullitionof the water caused rapid reduction of the water temperature T1. As a result ofthe rapid temperature decrease, vapor rushed into the chamber and causeda reduction in the chamber temperature T3.

After the reduction of T3, the chamber pressure remained almostunchanged (4.0–3.8 kPa); therefore, the water stopped boiling, and littleevaporation occurred, causing little change in water temperature T1 (5.8–2.7C). Therefore, there was less influence on the gas in the chamber by

TABLE 2.EXAMPLES OF THEORETICAL T3 AS COMPARED WITH

MEASURED DATA IN STAGE A-B

Example p (kPa) Measured T3 (K) Calculated T3 (K)

1 71.6 301.1 � 1.260.2 299.5 � 1.5 299.5

2 43.5 296.1 � 1.937.2 295.0 � 1.3 295.8

182 R. ZHAO ET AL.

low-temperature vapor molecules. However, heat transfer by convection andradiation still occurred between the chamber wall and the gas in the chamber.As the result, the temperature T3 increased (24.9–27.2C) in the later period ofstage B-C.

Pressure-releasing Stage

Stage C-D. Figure 2 also shows that when the vacuum was interruptedby ambient air flowing back to the vacuum chamber, the chamber pressurerapidly increased (3.7–102.5 kPa) in a very short time, and T3 in the chambercontinued to increase (27.2–40.8C) to an even higher value than the ambienttemperature of about 32C, which can be explained by the following thermo-dynamic analysis.

In stage C-D, a large amount of gas at a constant pressure and tem-perature flowed into the vacuum chamber, which could be considered anadiabatic process. If the gas in the vacuum chamber was considered asystem, with this process taking relatively longer time (approximately 60 s),and the height of the chamber being 6 mm shorter than the diameter, thesystem could be considered uniform. In this process, Eq. (1) can beexpressed as

h dm dU0 = (9)

By integrating Eq. (9), the following equation can be obtained:

m u m u m m h2 2 1 1 2 1 0= + −( ) (10)

As the gas in the chamber is assumed to be an ideal gas, Eq. (10) can beexpressed as

m c T m c T m m c T

p V

RTT

p V

RTT

p

v v p2 1 2 1 0

2 1

τ τ τ

τ ττ τ

ττ

+

++

= + −( )

= +

Δ

ΔΔi e. ., 22 1

0

V

RT

p V

RT

c

cTp

vτ τ τ+

−⎛⎝⎜

⎞⎠⎟Δ

(11)

The gas temperature in the vacuum chamber can be expressed as

TkT

T

Tk

T

T

p

p

τ ττ

τ τ+ =

+ −⎛⎝⎜

⎞⎠⎟

Δ

0 0

1

2

(12)

CHARACTERISTICS OF CHAMBER TEMPERATURE CHANGE 183

According to Eq. (12), in stage C-D, the gas temperature is related to theadiabatic exponent k, pressure ratio p1/p2 and temperature ratio Tt/T0 (T0 beingambient temperature). It can be shown by Eq. (12) that Tt+Dt is higher than Tt.Table 3 shows two examples comparing the experimental T3 and those calcu-lated by Eq. (12), confirming the increase of theoretical T3 during this stage.The difference between the experimental and calculated T3 is due to theassumption made in the calculation. Therefore, T3 in the chamber increased instage C-D.

Stage D-E. In this stage, the pressure in the chamber remained the sameas the atmospheric pressure, and the gas temperature T3 in the chamberdecreased (40.8–29.6C). Because the gas temperature in the vacuum chamberwas higher than that of the chamber wall surface, heat was transferred from thegas to the wall surface, resulting in the decrease of T3 until reaching theambient temperature. In the meantime, the water surface temperature T1

increased gradually.

CONCLUSIONS

In the vacuum cooling process, the chamber temperature did not remainconstant, but changed following some patterns.

At the beginning of the vacuum cooling, the chamber temperaturedropped quickly in general, and then was followed by a gradual increase in theremaining period of vacuum cooling.

In the pressure-releasing stage, the gas temperature in the vacuumchamber increased rapidly to even higher than the ambient temperature, thendecreased gradually to ambient temperature.

TABLE 3.EXAMPLES OF THEORETICAL T3 AS COMPARED WITH MEASURED DATA

IN STAGE C-D

Example p (kPa) T0 (K) Measured T3 (K) Calculated T3 (K)

1 35.7 304.7 � 2.0 305.8 � 1.239.3 304.6 � 1.5 306.2 � 1.4 313.9

2 82.9 304.4 � 1.2 312.6 � 1.385.3 304.4 � 1.8 313.1 � 1.5 314.9

184 R. ZHAO ET AL.

NOMENCLATURE

cv specific heat at constant volume (J/m3K)cp specific heat at constant pressure (J/m3K)E gas energy (kJ)h0 atmospheric enthalpy (kJ/kg)hin enthalpy of gas into a control volume (kJ/kg)hout enthalpy of gas out of a control volume (kJ/kg)

k adiabatic exponent kc

cp

v

= ≈ 1 4.

m1 mass of the gas in the chamber at t (kg)m2 mass of the gas in the chamber at t + Dt (kg)p1 air pressure in vacuum chamber at t (Pa)p2 air pressure in vacuum chamber at t + Dt (Pa)Q heat transfer rate (W)R gas constant kJ/(kg K)T0 ambient temperature (K)T1 water temperature (C)T2 gas temperature near the bottom of the vacuum chamber (C)T3 gas temperature in the middle of the vacuum chamber (C)T4 gas temperature underneath the chamber cover (C)Tt gas temperature in vacuum chamber at t (K)Tt+Dt gas temperature in vacuum chamber at t + Dt (K)u1 gas internal unit energy in vacuum chamber at t (kJ/kg)u2 gas internal unit energy in vacuum chamber at t + Dt (kJ/kg)U gas internal energy in vacuum chamber (kJ)W work (W)t time (s)Dt time step (s)

ACKNOWLEDGMENT

The authors would like to thank the Education Commission of Shanghaifor its financial support (Program T0503).

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CHARACTERISTICS OF CHAMBER TEMPERATURE CHANGE 185

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