Journal of Food Engineering 61 (2004) 421–429 www.elsevier.com/locate/jfoodeng
Local surface heat transfer coefficients on a model lamb carcass Mark B. Harris, James K. Carson *, Jim Willix, Simon J. Lovatt Food Systems and Technology Group, AgResearch MIRINZ Centre, East Street, Private Bag 3123, Hamilton, New Zealand Received 30 October 2002; accepted 6 May 2003
Abstract Measurements of heat transfer coefficients (HTCÕs) at four different positions on the surface of a model lamb carcass were performed using a steady state sensor that has been described previously. The model carcass was placed in a wind tunnel and subjected to airflows at 5 C. HTCÕs were measured for free-stream air velocities between 0.5 and 8 m s1 and free-stream turbulence intensities between 1% and 8%. At the lowest turbulence intensity, the measured HTCÕs varied by as much as a factor of 5, depending on the location of the sensor on the carcass surface. When the turbulence intensity was increased, a significant increase in the HTCÕs at one position was observed, and the overall variation in heat transfer coefficients was lower. The effect of natural convection was also investigated, but was not found to be as significant as the effect of sensor position or turbulence intensity. 2003 Elsevier Ltd. All rights reserved. Keywords: Surface heat transfer coefficients; Irregular shapes; Lamb carcass; Carcass chillers
1. Introduction Several mathematical models have been developed for predicting temperature changes in meat during chilling, freezing and thawing (see Chapter 9 of ASHRAE, 1998). Such models are often used for designing meat cooling regimes, and therefore good predictions are required in order that the regimes produce meat of high quality while ensuring product safety. An important parameter used by chilling and freezing models is the heat transfer coefficient (h), which represents the complex convection and conduction processes that transport heat between the product surface and the cooling medium according to NewtonÕs Law of Cooling: q ¼ hðTs Tair Þ ð1Þ A For heat transfer surfaces commonly encountered in engineering applications, such as cylinders, tubes, fins and plane surfaces, extensive analytical and experimental work has been performed in order to determine h based on the properties of the fluid and the flow patterns around, or over the objectÕs surface (e.g. see Chapters 6– 9 of Incropera & De Witt, 1996). Due to the complex nature of fluid flow, the most convenient method of *
Corresponding author. Tel.: +64-7-838-5372; fax: +64-7-838-5625. E-mail address:
[email protected] (J.K. Carson). URL: http://www.agresearch.co.nz/fst
0260-8774/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0260-8774(03)00151-1
reporting heat convection results is in the form of empirical correlations of dimensionless heat transfer variables, i.e.: Nu ¼ f ðRe; PrÞ
ð2Þ
for forced convection, and: Nu ¼ f ðGr; PrÞ
ð3Þ
for natural convection, where Nu, Re, Gr, and Pr are the Nusselt, Reynolds, Grashof, and Prandtl numbers respectively. For regularly shaped objects, Nusselt number correlations may be found in most heat transfer texts for a wide range of fluids and flow conditions. Nusselt number correlations may also be found for selected food products (see Table 13, Chapter 8 of ASHRAE, 1998). Since air is the heat transfer fluid in the majority of food applications, Pr is not always included in the correlations and most have the following form: Nu ¼ CRem
ð4Þ
For regular geometries, such as flat plates and tubes, the exponent of Re in Nusselt number correlations ranges between 0.333 and 0.5 under laminar flow conditions, and is about 0.8 under turbulent conditions (see Tables 7.9 and 8.4 of Incropera & De Witt, 1996). Hence the nature of the flow in the boundary layer may be inferred from the value of m in Eq. (4); higher exponents imply
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Nomenclature A cp C g h k m n q Ts Tair
heat transfer surface area (m2 ) specific heat capacity of air (J kg1 K1 ) correlation coefficient (see Eq. (4)) gravitational acceleration (9.81 m s2 ) local heat transfer coefficient (W m2 K1 ) thermal conductivity of air (W m1 K1 ) correlation exponent (see Eq. (4)) number of air velocity measurements performed in the calculation of Tu heat flow through surface (W) surface temperature of carcass (C) temperature of bulk air stream (C)
turbulent conditions, lower exponents imply laminar conditions. Almost all the literature correlations for food products are for average (global) heat transfer coefficients; however, the heat transfer coefficient is inherently a local phenomenon, as shown by analyses of flows over flat plates and around cylinders and spheres (Incropera & De Witt, 1996). Very little investigative work has been carried out for highly irregular shapes such as animal carcasses. Airflow patterns in commercial air-chillers produce quite variable conditions over the surface of a carcass during cooling that, coupled with the highly irregular shape, lead to significant spatial variation in h over the surface of the carcass. As shown by Nicola€ı and De Baerdemaeker (1996), the local rate of chilling or freezing has a high dependence on h under some conditions, and, since h may vary significantly over the surface of the carcass, the local chilling rates may also vary considerably. Uneven chilling rates are undesirable, since chilling rates that are too high may cause dry-out of the carcass, while low chilling rates may produce mould growth (Missenden, Lovatt, & Amraie, 1996). Methods to improve the uniformity of chilling rates have been sought by carcass chiller designers. One approach has been to increase the turbulence of the airflows in the chiller (Missenden et al., 1996). Kondjoyan and Daudin (1997), measured heat transfer coefficients at the surface of a plaster model of a pork hind quarter suspended in a turbulent air stream, and their results showed an increase in the rate of surface heat transfer with an increase in free-stream turbulence intensity (most Nusselt number correlations available in the literature assume that the turbulence intensity of the free fluid stream is close to 0%). The aim of the research reported here was to measure local heat transfer coefficients as a function of airflow conditions over the surface of a lamb carcass shaped
Tu u x b l q Gr Nu Pr Re
turbulence intensity (%) velocity of free air stream (m s1 ) characteristic dimension (distance from tip of hind leg) (m) volume coefficient of expansion (K1 ) viscosity of air (Pa s) density of air (kg m3 ) Grashof number [gbðTs Tair Þx3 q2 =l2 ] Nusselt number [hx/k] Prandtl number [cp l=k] Reynolds number [qux=l]
object using a heat transfer coefficient sensor developed previously (Harris, Lovatt, & Willix, 1999). In particular, the influence of free-stream turbulence intensity (Tu) and the significance of natural convection were examined.
2. Heat transfer coefficient measurement method 2.1. Common approaches Methods for measuring heat transfer coefficients may be divided into two main categories: those that measure surface temperature and heat input under steady state conditions, and those that measure the transient surface temperature as the body cools or heats. The steady state method usually involves the continuous heating of a sample in a constant-temperature air stream. When the system reaches steady state, h can be computed based on the measured temperature difference between the surface of the object and the free stream, and the power input required to maintain the object at a steady temperature (see Eq. (1)). The method can involve heating an entire object to obtain an estimate of the spatially averaged h-value, or heating an insulated sensor placed into a larger object. Important factors in the design of this type of measurement are: • accounting for radiation from the heated surface to the surroundings, • eliminating any mass transfer interactions inherent in the physical set up, • minimising or correcting for any heat losses from the heated surface––particularly edge losses in the case of the insulated sensor placed into a larger object (Cleland, Cleland, & Jones, 1994). The transient method involves the back-calculation of the surface h-value from measured product and air
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temperatures during cooling or heating experiments, using a mathematical model. An alternative approach for estimating h-values is to use a combined heat and mass transfer procedure as reported by Kondjoyan and Daudin (1993) and reviewed by Harris and Willix (2000). 2.2. Customised measurement system In previous work (Harris et al., 1999), a sensor was developed for the measurement of local heat transfer coefficients on the carcass surface, based on the steady state measurement approach. The sensor was designed for installation into hollow fibreglass carcass models (or other shapes), with water pumped through the body cavity to control the surface temperature (electrical heating of the model carcass was considered, but was rejected due to the complexity of its construction and control). The sensor comprised an electrically heated, insulated disk, suitable for insertion at various positions on the model carcass. This measurement approach had the following advantages: • it enabled h-values to be measured under fixed surface and air temperature conditions; • it enabled experiments to be completed relatively quickly with simple data analysis.
Fig. 1. Schematic diagram detailing the main design features of the developed HTC sensor: (1) copper cap; (2) expanded polystyrene radiation shield; (3) acrylic sensor mast 115 mm above carcass surface to ensure air temperature measurements were performed outside the thermal and momentum boundary layers; (4) copper disk painted matt black; (5) heater pad; (6) expanded polystyrene insulation; (7) thermocouple measuring the local absolute temperature of the fibreglass carcass; (8) thermocouple measuring the absolute temperature of the copper disk; (9) heater power cable; (10) PVC cylinders glued into the fibreglass model to house the sensors; (11) thermopile (three hot and cold junctions) to measure the differential temperature between the free air stream and the copper disk.
A diagram of the sensor is shown in Fig. 1. Two waterproof polyvinyl chloride (PVC) cylinders were designed to be glued into the hollow fibreglass carcass model. The larger cylinder incorporated a copper disk whose upper surface was exposed to the air stream, while the lower surface was heated by an electrical heater pad. The high thermal conductivity of the copper ensured that the temperature distribution across the surface of the sensor was uniform and minimised temperature variation through the disk, which meant that the temperature reading of the thermocouples was not unduly sensitive to position. The exposed copper surface was painted matt black to allow accurate determination of the radiation heat loss from the surface in order that it might be deducted from the overall heat transfer (for radiation-loss calculations, see Harris et al., 1999). An expanded polystyrene (EPS) insulating ring was installed between the copper disk and the PVC sensor housing. This reduced (and fixed) the edge heat losses from the copper. Numerical analysis showed that these edge losses accounted for 12.5% of the total electrical heat supplied to the sensor unit. Correction equations were derived using the results of the numerical simulations (see Harris et al., 1999). Results obtained using the sensor could therefore be corrected for any systematic heat loss from the edges as well as any heat gain from the carcass-heating water.
The second PVC cylinder supported an acrylic mast. A 20 mm diameter copper cap, machined to fit over the top of the mast, was designed to equilibrate with the temperature of the free stream. An EPS radiation shield was inserted just below the cap to prevent measurement errors arising from radiation heat transfer from the heated copper disk and fibreglass model surface. The mast height was 115 mm, a height significantly greater than the deepest anticipated thermal boundary layer. The mast was located across or downstream from the heated surface in the carcass model so that it did not affect the boundary layers across the heated copper disk. A thermopile comprising three hot and cold junctions measured the temperature difference between the copper disk and copper cap. The power supplied to the heater pad was automatically controlled by a Hewlett PackardTM VXI data logging system to ensure that the temperature of the copper disk remained as close as possible to the temperature of the fibreglass surface. Temperature control was based on a single thermocouple inserted into the copper disk, and two thermocouples fixed to the surface of the fibreglass around the outside of the sensor. The difference between the temperatures of the copper disk and the carcass surface was maintained within the ±0.1 C uncertainty of the temperature measurements themselves (see Harris et al., 1999).
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In order to test the accuracy of the device, three sensors were placed at three different positions in a flat plate apparatus that was subjected to airflows of varying velocities. The measured h-values were compared to predictions from Nusselt number correlations for flat plates available from the literature, and there was good agreement between the predicted and measured data (see Fig. 4 of Harris et al., 1999). The overall uncertainty of the h-values measured by this device was estimated as being less than 7%, although this figure did not include possible effects the presence of the sensor may have had on the thermal and velocity boundary layers around the sensor (Harris et al., 1999). The sensor system was designed to be as modular as possible to maximise convenience. The copper disk, heater pad and surrounding insulation, as well as the mast unit were designed in such a way that they could be unplugged and removed from the PVC cylinders and used in similar experiments on different carcass shapes.
Fig. 2. Half of the fibreglass carcass model with installed sensor unit.
3. Experimental procedure The basic experimental method involved: • constructing a fibreglass model of the desired shape suitable for heating by water, • drilling two holes at the desired measurement locations and fixing the surface thermocouples, • gluing in the pre-fabricated and pre-wired PVC sensor-housing cylinders, • ducting the wires from the PVC cylinders out from the interior of the model, and connecting them to the HewlettPackard TM data logging and control system, • plugging in the disk and mast sensor components, • running the experiments––the HewlettPackard TM data logger recorded the carcass and sensor surface temperatures, controlled the power delivered to the sensors, and calculated the heat transfer coefficient based on the measured data and corrections to account for radiation heat transfer and edge losses.
Fig. 3. The lamb carcass model with four sensors units installed.
3.1. Fibreglass carcass models
3.2. Wind tunnel design and carcass suspension
A mould was made from a frozen, 16 kg lamb carcass by a local taxidermist. Using the mould, a fibreglass model was manufactured in two halves, thereby enabling installation of the sensor system (see Fig. 2). The length of the carcass was approximately 1.2 m and the maximum width was approximately 0.28 m. Four sensors were installed into the carcass model: one over the rib eye, one on the loin, one on the hind leg, and one on the shoulder (see Fig. 3).
An open-jet wind tunnel was constructed to deliver controlled longitudinal airflow conditions over the model lamb carcass. The tunnel was designed to fit within an environmental test chamber and was made from plywood and sheet metal. The tunnel comprised the following sections: • a sheet metal contraction with 2:1 area ratio, • a flow straightener and mesh screen section,
M.B. Harris et al. / Journal of Food Engineering 61 (2004) 421–429
• a 0.81 m · 0.81 m square working section 1.5 m long, resulting in a tunnel blockage of approximately 10% with the model lamb carcass installed, • a further flow straighter, • a square-to-round transition section and axial flow fan unit rated at 1.5 kW. The total length of the wind tunnel arrangement was 3 m. A schematic diagram of the experimental apparatus is shown in Fig. 4. The model carcass was suspended from three hooks; one on either side of a bar running through the neck,
425
and a third hanging a bar attached between the hind legs. Fig. 5 shows a photo of the hind portion of the carcass suspended in the wind tunnel. Faint smoke trails over the left rear leg may be seen which show that the carcass-heating water hoses did not interfere with the airflow over the sensors. The remaining attachments to the carcass (electric cables and fore-leg water hoses) were at the downstream end of the carcass. 3.3. Turbulence measurement Free-stream turbulence intensities in the wind tunnel were measured using an AirFlowTM UA6 ultrasonic anemometer. This unit measured air speed in the bulk flow direction (3840 measurements per second), and provided an estimate of the turbulence intensity (Tu) in the direction of the airflow calculated over a period of 6 s: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 1 uÞ i¼1 ðui n1 Tu ¼ 100% ð5Þ u The UA6 anemometer was not capable of measuring the remaining two components of the turbulence vector (i.e. the components orthogonal to the direction of bulk airflow). The turbulence frequency distribution and length scale were not characterised during this work. 3.4. Generation of turbulence The carcass surface heat transfer was measured under three different tunnel configurations:
Fig. 4. Schematic diagram of the assembled wind tunnel located within the environmental test chamber: (1) environmental chamber evaporator; (2) contraction section; (3) lamb carcass model; (4) flow straighteners; (5) working section of wind tunnel; (6) transition section; (7) fan; (8) HewlettPackard TM VXI data logger; (9) JulaboTM FP 65 controlled temperature water bath.
1. standard straighteners and mesh screen set in place (‘‘near laminar’’ configuration), 2. mesh screen removed (‘‘no-mesh’’ configuration), 3. flow straighteners replaced by coarse wire mesh with 25.4 mm wire spacings (‘‘coarse mesh’’ configuration).
Fig. 5. Photo of the hind portion of the model carcass suspended in the wind tunnel: (1) carcass suspension hook; (2) carcass-heating water pipes; (3) smoke trails over hind leg (velocity ¼ 1 m s1 ); (4) heat transfer coefficient sensor; (5) free air stream temperature sensor.
In order to characterise the flows resulting from the different turbulence generation configurations, measurements of velocity and turbulence intensity were performed at 27 evenly spaced positions within the working section of the wind tunnel (a 3 · 3 · 3 cubic array). Hence there was a 3 · 3 grid of measurements at three different points in the direction of the airflow, referred to respectively as the ‘‘entry’’, ‘‘midway’’ and ‘‘exit’’ points. Fig. 6 provides an indication of the turbulence profile in the direction of the bulk airflow for the three different turbulence generation configurations. Each data-point represents the average of the turbulence intensities measured at nine different positions (3 · 3 grid of positions for entry, midway and exit points) for nine different velocities between 0.5 and 8 m s1 ; hence each data-point is the mean of 81 turbulence intensity measurements.
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flow in the wind tunnel is essentially pipe-flow, while the flow in a carcass chiller is essentially that of an agitated tank, and depends greatly on the number and positions of the carcasses within the room. Accordingly, the numerical values of the measured heat transfer coefficients should be viewed as being indicative rather than definitive.
9% 8% 7%
5% 4%
4.1. Effect of sensor location and free-stream turbulence intensity
3% Entry Exit
0% near-laminar
no-mesh
coarse mesh
Fig. 6. Mean turbulence intensities for different turbulence generation configurations at different points in the direction of the bulk airflow.
Fig. 6 shows that, in general, the turbulence intensity decreased further into the working section, although the rate of decrease was small. The average Tu for the ‘‘nearlaminar’’ configuration was 1.8%, for the ‘‘no-mesh’’ configuration it was 4.7% and for the ‘‘coarse-mesh’’ configuration it was 8.1%. Other methods for turbulence generation within the wind tunnel were also attempted, including the installation of perforated plates over the front of the tunnel contraction, the installation of a tangential air injection system, and the installation of three overlapping rotating paddles at the upstream end of the working section; however, none of these arrangements could produce turbulence intensities greater than 8%. It is difficult to reproduce flow conditions prevalent in a carcass chiller inside a wind tunnel, for turbulence intensity in particular. Kondjoyan and Daudin (1997) found that the turbulence intensity generated in their wind tunnel by different turbulence promoters decreased exponentially with distance downstream from the promoter. In contrast, relatively high turbulence intensities can be encountered in industrial chillers. However, the use of a wind tunnel was necessary in order to be able to control the temperatures and flow conditions in order to isolate the effects of individual variables, which was the objective of this work.
4. Results Surface heat transfer coefficients measured at each of the four sensor positions (refer to Fig. 3) were performed over a range of velocities, free-stream turbulence intensities and carcass surface temperatures. The differences in geometry between a wind tunnel and a carcass chiller result in different types of flow: the
Figs. 7–9 show plots of h as a function of free-stream velocity (u) at the four sensor positions, for the three different average turbulence intensities. As expected, there was a definite dependence of h on the sensor position, with h-values measured at the loin being up to 5 times as great as the h-values measured at the hind leg, for a given free-stream velocity. Changes in the wind tunnel turbulence generation configurations did not appear to have a significant effect on the heat transfer coefficient measurements at the rib eye, loin or shoulder sensor positions. However, there was a clear difference between the results for Tu ¼ 8:1% and the results for Tu ¼ 1:8% and Tu ¼ 4:7% at the hind leg sensor position, as shown in Fig. 10. Eqs. (6)–(10) show Nusselt number correlations for the combined data measured at each sensor position. Since local h-values were of interest, the distance from the tip of the hind leg (upstream-most point of the carcass) to the sensor position was taken as the characteristic dimension (x). All physical properties were evaluated at the film temperature of 17.5 C. Rib eye sensor (x ¼ 0:92 m, 3 104 < Re < 4:3 105 ): Nu ¼ 0:029Re
ð6Þ
60 rib eye
50
loin shoulder
40
-1
Midway 1%
-2
2%
h (W m K )
Tu (%)
6%
hind leg 30 20 10 0 0
1
2
3
4
5
6
7
8
-1
u (m s )
Fig. 7. Heat transfer coefficients (h) as a function of free-stream air velocity (u) at the four sensor positions (refer to Fig. 3), with 1.8% freestream turbulence intensity (Tu).
M.B. Harris et al. / Journal of Food Engineering 61 (2004) 421–429 60
60 rib eye
50
hind leg Tu=1.8%
50
hind leg Tu=4.7%
loin -1
h (W m K )
shoulder
40
-2
hind leg
-2
-1
h (W m K )
427
30
hind leg Tu=8.1%
40 30 20
20
10 10
0 0
0 0
1
2
3
4
5
6
7
1
2
8
3
4
5
6
7
8
-1
u (m s )
-1
u (m s )
Fig. 8. Heat transfer coefficients (h) as a function of free-stream air velocity (u) at the four sensor positions (refer to Fig. 3), with 4.7% freestream turbulence intensity (Tu).
Fig. 10. Effect of increasing the free-stream turbulence intensity (Tu) on heat transfer coefficients (h) measured at the hind leg sensor position.
25
60 rib eye
50
20°C
20
30°C 40°C -1
h (W m K )
shoulder
40
-1
hind leg
15
-2
-1
h (W m K )
loin
30
10
20 5
10 0 0
1
2
3
4
5
6
7
8
0 0
-1
Loin sensor (x ¼ 0:61 m, 2 104 < Re < 3 105 ): Nu ¼ 0:26Re0:67
ð7Þ
Shoulder sensor (x ¼ 1:07 m, 3:5 104 < Re < 5 105 ): Nu ¼ 0:032Re
ð8Þ
Hind leg sensor (x ¼ 0:37 m, 1:2 104 < Re < 2 105 ): ðfor Tu ¼ 8:1%Þ Nu ¼ 0:037Re ðfor Tu < 8%Þ
2
3
4
u (m s )
Fig. 9. Heat transfer coefficients (h) as a function of free-stream air velocity (u) at the four sensor positions (refer to Fig. 3), with 8.1% freestream turbulence intensity (Tu).
8
1
-1
u (m s )
Fig. 11. Heat transfer coefficients measured at the rib eye sensor position with varying temperature difference between the carcass surface and the bulk air stream.
when the difference between the carcass surface and the air stream (DT ) was varied. At low air velocities (
