- Email: [email protected]
Heat transfer with freezing in a scraped surface heat exchanger
Applied Thermal Engineering 25 (2005) 45–60 www.elsevier.com/locate/apthermeng
Heat transfer with freezing in a scraped surface heat exchanger Mohamed Ben Lakhdar a, Rosalia Cerecero b, Graciela Alvarez b, Jacques Guilpart b, Denis Flick c,*, Andre Lallemand d a
b
LGL France Refrigerating Division, 42, rue Roger Salengro BP 205, 69741 Genas, France UMR Genie industriel alimentaire––Food process engineering Ensia/Cemagref/INAPG/INRA, Cemagref, UR Genie des procedes frigorifiques, BP 44, 92163 Antony cedex, France c UMR Genie industriel alimentaire––Food process engineering, Ensia/Cemagref/INAPG/INRA, Institut National Agronomique, Paris-Grignon, 16, rue Claude Bernard, 75231 Paris cedex 05, France d Centre de Thermique––UMR A CNRS 5008, Institut National des Sciences Appliquees de Lyon, 20, avenue Albert Einstein, 69621 Villeurbanne cedex, France Received 12 February 2004; accepted 9 May 2004 Available online 25 June 2004
Abstract An experimental study was carried out on a scraped surface heat exchanger used for freezing of water– ethanol mixture and aqueous sucrose solution. The influence of various parameters on heat transfer intensity was established: product type and composition, flow rate, blade rotation speed, distance between blades and wall. During starting (transient period) the solution is first supercooled, then ice crystals appear on the scraped surface (heterogeneous nucleation) and no more supercooling is observed. It seems that, when blades are 3 mm far from the surface, a constant ice layer is formed having this thickness and acting as a thermal resistance. But when the blades rotate at 1 mm from the surface, periodically all the ice layer is removed despite the surface is not really scraped. This could simplify ice generator technology. An internal heat transfer coefficient was defined; it depends mainly on rotation speed. Correlations were proposed for its prediction, which could be applied, at least as a first approach, for the most common freezing applications of scraped surface heat exchanger i.e. ice creams (which are derived from sucrose solutions) and two-phase secondary refrigerants (which are principally ethanol solutions). 2004 Elsevier Ltd. All rights reserved. Keywords: Scraped surface heat exchanger; Freezing; Sucrose; Ethanol; Correlation; Heat transfer coefficient
*
Corresponding author. Tel.: +33-1-4408-7239; fax: +33-1-4408-1666. E-mail address: fl[email protected] (D. Flick).
1359-4311/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.05.007
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
Nomenclature A cp D Dr Dh e h h Lf N_ Nu ¼ hD k Pr ¼ Q_
heat exchange area, m2 specific heat capacity, J kg1 K1 scraped wall inner diameter, m rotor diameter, m external hydraulic diameter, m gap between the blades extremity and the wall, m heat transfer coefficient, W m2 K1 specific enthalpy, J kg1 K1 specific latent heat of fusion for ice at 0 C, J rotor rotation speed, s1 Nusselt number
lCp k
Prantdl number heat flux, W rÞ Rea ¼ quðDD axial Reynolds number l _
2
Rer ¼ qNlD rotational Reynolds number h external Reynolds number Reext ¼ qvD l R heat transfer resistance K m2 W1 T temperature, K or C V_ 1 u ¼ pðD2 D 2 Þ=4 mean axial velocity, m s r v mean velocity of pure ethanol V_ volume flow rate, m3 s1
Greek symbols k l q um uv x x0
thermal conductivity, W m1 K1 dynamic viscosity, Pa s density, kg m3 mass fraction of ice volume fraction of ice solute mass fraction in the solution; mass of solute/mass of solution global mass fraction of solute; mass of solute/mass of solution and ice
Subscripts eth ext f i int 0 p s w cri
pure ethanol external freezing point ice internal initial product solution wall critical value
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47
1. Introduction Scraped surface heat exchangers (SSHE) are often used to produce ice creams and ice slurries. The interest of SSHE for ice creams, is the production of a lot of small crystals before hardening the product in cold rooms, which improves its unctuousness. Recently, many studies have been reported about ice slurries used as two-phase secondary refrigerant, SSHE are used to generate them continuously. In both applications, the objective is to produce the maximal amount of ice without exceeding a viscosity threshold to insure pumpability. Therefore heat transfer performances have to be predicted taking into account ice crystallisation. Many studies are devoted to fluid flow and heat transfer in SSHE without phase change. Fluid flow is similar to the Couette–Poiseuille configuration: annular channel between two cylinders, the inner rotating [1,2]. Flow pattern depends on two Reynolds numbers. The axial Reynolds number (Rea ) is based on the mean axial velocity (volumetric flow rate divided by the cross section) and the rotational Reynolds number (Rer ) on the tangential velocity of inner cylinder or of blades extremity. When rotating speed increases, toro€ıdal vortices (called Taylor vortices) appear at a critical rotational Reynolds number for which Becker and Kaye [3] propose a value depending on the ratio between rotor diameter (Dr ) and tube diameter (D). When rotating speed is further increased, the vortices become perturbed and finally turbulence appears. The presence of blades modifies the appearance of the vortices and increases locally the shear rate [4], but the order of magnitude of the critical rotational Reynolds number is the same. Various correlations are proposed to predict heat transfer coefficient for monophasic fluids. [2,5]. They have generally the following form: Nu ¼ aReba Recr Prd
ð1Þ
Prandtl number exponent is often fixed at 1/3. The rotational Reynolds number exponent is generally small for laminar flow and ranges from 1/2 to 1 for vortical and turbulent flow. Harriot [6] proposed a theoretical approach where the limiting phenomenon is the heat penetration from the wall to the product between two scrapings, he found that the Nusselt number is proportional to the square root of rotational Reynolds number. The axial Reynolds number is often omitted, as the tangential velocity is much higher than the axial mean velocity. Some correlations take account of the number of blades [7]. Some others propose a correction factor for viscosity near the heated wall [8]. Moreover, the axial dispersion can be taken into account by including a residence time distribution model [9]. Relations are also proposed for non-newtonian fluids; this is of interest because food products often exhibit such behaviour [10]. Only few studies deal with crystallisation in SSHE. Weisser [11] and Dinglinger [12] studied freezing of sucrose solution. The latter proposes a correlation with a correction factor (depending on freezing temperature, inlet and outlet temperature of product) because in their experiments the product is cooled down and frozen at once in the same SSHE. More recently, crystallisation of other substances where studied in SSHE: p-xylene by De Goede and De Jong [13], brine by Kawaji et al. [14]. Bel and Lallemand [15] studied freezing of water–ethanol slurries using an ice generator where the exchange surface was not scraped but brushed. They propose a correlation where the axial and the rotational Reynolds number are added. Numerical simulations of fluid flow and heat transfer were also reported, for example by Baccar and Abid [16], Hong et al. [17] and Ben Lakhdar et al. [18]; but they do not consider any phase
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
change for the product. Such simulations can predict qualitatively the flow pattern (dead zones, vortices) but are not able to predict heat intensity when freezing occurs. The aim of the present work is to characterise experimentally the influence of various parameters (flow rate, blade rotation speed, distance between blades and wall, product concentration) on heat transfer for two products (water–ethanol mixture and aqueous sucrose solution) and to propose correlations able to predict the heat transfer at a scraped surface when freezing of water occurs. 2. Material and methods 2.1. Experimental device The experimental device is presented in Fig. 1. The heat exchanger (build in the lab) included a scraped surface tube, made of stainless steel, which had 100 mm inner diameter, 2.5 mm thickness and 520 mm length. A countercurrent turbulent flow of chilled pure ethanol circulated around this tube inside an annular jacket with a radial gap of 3 mm. This ensured a quite uniform and high external heat transfer coefficient (at the outer side of the wall). The aqueous solution circulated in a closed loop through a variable speed volumetric pump (PCM 4I10). The flow rate, measured by a Coriolis flowmeter (ABB K40), could vary from 0.1 to 0.3 kg/s. At the outlet of SSHE, the ice slurry was heated with an electric device (Vulcanic 10745) in order to melt all the ice. The heating power was adjusted so that the temperature at the SSHE inlet was just above the equilibrium freezing temperature (Tf < T < Tf þ 1:5 K) when steady state was reached. This protocol allowed to minimise the enthalpy needed to cool down the solution before freezing, so that it was negli-
Fig. 1. Experimental device.
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
49
gible compared to the phase change enthalpy. Otherwise, it would be difficult to estimate which part of the heat exchanging surface was involved for crystallisation. The wall temperature was measured at 6 positions along the scraped surface by thermocouples brazed on the external side of the tube (which is in contact with pure ethanol). Solution or ice slurry temperature was also measured at different position in the loop by thermocouples or platinum sensors. Two blades made of stainless steel were rigidly fixed on the rotor, which had an external diameter of 40 mm. Their position could be modified so that their extremity was between 1 and 3 mm far from the tube inner surface. The blades never really scraped the surface as in SSHE used for the heating of sensitive food products, which would otherwise brown on the heated surface. In our case, at first sight, a permanent ice layer will form in the gap between the wall and the blades extremity; ice crystals grow on this layer and are detached by the blades. The rotation speed could vary from 100 to 800 rpm. The rotational Reynolds number was always higher than the critical value, calculated from Becker’s and Kaye’s relation [3] (Eq. (2)), which was 166 in our case. Rercri
"
,
ðD Dr Þ 0:0571 1 0:652 Dr !# 1 1=2 ðD Dr Þ þ 0:00056 1 0:652 Dr
pD2 ¼ ðD Dr ÞDr
D þ Dr 2 D Dr
ð2Þ
2.2. Estimation of heat flux density The heat flux exchanged at the surface was estimated by the following steps. First we calibrated the external heat transfer coefficient (at the outer side of the wall) versus flow rate of pure ethanol. For this calibration, the solution entered the SSHE at ambient temperature so that no crystallisation occurred and the exchanged heat flux was obtained from inlet/outlet temperature difference and flow rate of the solution. Then, for the other experiments with crystallisation, this calibration was used to deduce the heat flux from ethanol flow rate, ethanol temperature (mean value between inlet and outlet) and wall temperature (mean value of the 6 thermocouples). For the external heat transfer characterisation, the solution flow rate ranged from 0.02 to 0.08 kg s1 and the pure ethanol flow rate from 0.75 to 2.41 kg s1 . The correlation proposed by Gnielinsky [19] for annular flow, in the transition zone between laminar and turbulent regime, was used (Eq. (3)) as it fits the experimental results with an accuracy of 5% (Fig. 2). The Dittus– Boelter’s [20] correlation underestimates the heat transfer intensity probably because the Reynolds number for the annular flow of ethanol ranges between 3000 and 10000. 2=3 ! 0:059Re0:25 1000ÞPr ðRe Dh ext ext ext 1þ Nuext ¼ 1:03 0:5 2=3 L 1 þ 12:7 0:059Re0:25 Prext 1 ext annular gap ¼ 0:05 ð3Þ external diameter
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60 External heat transfer coefficient (W/(m².K))
50
4500 4000 3500 3000 2500 2000 1500 1000 500 0 0
2000
4000
6000
8000
10000
External Reynolds number
Fig. 2. External heat transfer coefficient vs. external Reynolds number (experiment and Gnielinski correlation).
2.3. Thermophysical properties To define the dimensionless numbers, which are involved in the correlations, we used the thermophysical properties of ice slurry estimated at the outlet of the SSHE. The diphasic properties (ice slurry) were obtained from the monophasic ones (solution, ice). For ice and water– ethanol mixtures, a detailed description is given by Guilpart et al. [21]. For sucrose solution, the relations recommended by Mathlouthi and Reiser [22] were used for the density and those recommended by Bubnik et al. [23] were used for thermal conductivity, specific heat, viscosity and freezing point temperature. The liquidus curve is given by Eq. (4) where x (kg solute/kg solution) is the solute mass fraction in the solution. Tf ðxÞ ¼ ð5:176x þ 13:27x2 24:16x3 þ 75:5x4 Þ
ðT in CÞ
ð4Þ
Local thermodynamical equilibrium was assumed except during supercooling periodðT ¼ Tf ðxÞ () x ¼ xf ðT ÞÞ. There is no solute in the ice crystals (temperature is always higher than the eutectic one). The global mass fraction of solute in the slurry x0 (kg solute/kg solution + ice) remains constant and equal to the value of x before freezing. Thus, the mass fraction of ice in the slurry can be calculated versus temperature x0 ð5Þ um ¼ 1 xf ðT Þ The slurry density is obtained by addition of ice and solution volume. 1 um ð1 um Þ ¼ þ ð6Þ q qs qi The volume fraction of ice in the slurry is then q ð7Þ uv ¼ um qi The thermal conductivity is obtained by the Maxwell lower bound relation [24] for dilute solid/ liquid suspensions
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
k ¼ ks
2ks þ ki 2uv ðks ki Þ 2ks þ ki þ uv ðks ki Þ
51
ð8Þ
where ks and ki are the thermal conductivities of solution and ice and uv can be obtained from the temperature by the previous relations. The specific enthalpy of slurry is obtained by adding those of ice and solution Z T Z T 0 0 cpi ðT ÞdT þ ð1 um Þ cps ðT 0 ÞdT 0 ð9Þ h ¼ um Lf þ 0 C
0 C
For a given global solute mass fraction, the specific enthalpy is only function of temperature, so an apparent specific heat can be defined for the slurry (needed energy to increase by 1 K, 1 kg of slurry following liquidus curve) which was used to calculate the Prandtl number. cp ¼
dh dT
ðwhere h is obtained from Eq:ð9ÞÞ
ð10Þ
The slurry was supposed to remain newtonian. Experiments (not presented here), obtained by tubular rheology showed that the flow behaviour index remains near unity for an ice volume fraction less than 7%; which was the case in the present work. The relation proposed by Thomas [25] for solid/liquid suspensions which is an extension of Einstein’s law was used l ¼ ls ð1 þ 2:5uv þ 10:05u2v þ 2:73103 expð16:6uv ÞÞ
ð11Þ
2.4. Operating conditions Table 1 presents the operating conditions used for heat transfer characterisation. Table 1 Operating conditions Product
Ethanol or sucrose mass fraction
Gap between blades and wall (mm)
Product mass flow rate (kg/s)
Rotation speed (rpm)
Water + ethanol
0.10
1 and 3
0.16
1 and 3
0.20
1
0.14 0.20 0.30 0.14 0.20 0.30 0.14 0.20 0.30
300–500–700 300–500–700 300–500–700 300–500–700 300–500–700 300–500–700 100–200 . . . 600–700 100–200 . . . 600–700 100–300–500–700
0.15
1
0.30
1
0.10 0.12 0.14 0.10 0.12 0.14
200–300 . . . 700–800 200–300 . . . 700–800 200–300 . . . 700–800 200–300 . . . 700–800 200–300 . . . 700–800 200–300 . . . 700–800
Water + sucrose
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3. Results and discussion 3.1. Supercooling Fig. 3 presents an example of temperature evolution of the product at the outlet of SSHE before steady state was reached and without heating the product with the electric device. The product aspect was also visualised trough a Pyrex tube. The temperature decreased first below the freezing temperature by a few degrees while the product remained transparent: the solution was supercooled and was not at thermodynamical equilibrium. Then, temperature rose abruptly and the product became suddenly opaque: nucleation appeared. The sensible heat accumulated during supercooling was transformed into latent heat by formation of a multitude of ice crystals. Just after the temperature jump, its value was slightly below the freezing temperature, and then it decreased slowly (because, in the loop, inlet temperature also decreased) whereas the ice fraction increased. Local thermal equilibrium (between remaining solution and ice) was then probably reached at the SSHE outlet. All the results further presented were obtained after this transient period (without supercooling).
3.2. Heat transfer resistances Fig. 4 presents an example of the measured temperatures when steady state was reached. It appeared that the wall and product temperature variations along the SSHE were small compared to their difference. Thus, a simple arithmetic average was used to characterise the mean temperature difference between the wall and the product (average of the 6 thermocouples for the wall, average between inlet and outlet for the product). An internal heat transfer resistance Rint (between wall and product) has been calculated from the measured temperatures, knowing the wall
15 13 11 9 7 5 3 1 -1 -3 -5 -7 -9
T (°C)
freezing temperature : -4.2 °C -4.5°C
-6.4°C 0
5
10
15
20
25
30
35
Time (min)
Fig. 3. Example of product temperature evolution at the outlet of SSHE (before steady state was reached and without heating the product) (solute: ethanol 10%, mass flow rate: 0.14 kg/s, rotation speed: 100 rpm).
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
53
Fig. 4. Example of wall and product temperature when steady state is reached (time averaged values over one hour) (solute: sucrose 15%, mass flow rate: 0.14 kg/s, rotation speed: 800 rpm).
resistance Rw and the external resistance Rext (between wall and pure ethanol) from Gnielinsky’s correlation [19] with an accuracy of 5%. Rint þ Rw ¼
Tp Tw Tp Tw ðthe wall temperature is measured on the external side ¼ Rext _Q=A Tw Teth in contact with pure ethanolÞ ð12Þ
Typically (Fig. 4) the temperature differences between wall and product or between wall and pure ethanol were about 4 C, they were estimated with a precision of 0.1 C. Thus the relative precision of Rint was typically 10%. Nevertheless, the external flow rate of pure ethanol was always the same; this reduced the influence of the uncertainty of Rext . Figs. 5–8 show the internal heat transfer resistance versus rotation speed for different flow rates, different aqueous solution (ethanol and sucrose) and different concentration. The influence of the gap between the blade extremity and wall is also presented in the case of 10% ethanol solution. Increasing the rotation speed lowered the internal heat transfer resistance; the influence was particularly noticeable below about 500 rpm. Different effects resulting from the rotation of the blades could explain this. • Similarly to the penetration theory proposed by Harriot [6] for monophasic fluids, it can be assumed that an ice layer is formed between two scrapings, which acts as a thermal resistance. Reducing the time between successive scraping reduces this resistance. • The blades scrap the new formed ice crystals and mix them with the rest of the product. Some of these ice crystals will melt if the product enters the SSHE at a temperature much higher than the freezing point. The blades rotation enhances this mixing effect which tends to cool the product quickly down to freezing temperature. When the product reaches the wall, it is then faster frozen. This effect is small in our case because the product entered the SSHE near its freezing point. • When ice is produced near the wall, the remaining solution is concentrated and its freezing point temperature decreases, this reduces freezing front progression. The blades replace this
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
concentrated solution by solution taken far from the wall. This radial mixing effect is more efficient when blades rotate more rapidly.
Heat trasnfer resistance (Km²/W)
Increasing the product flow rate decreased slightly the internal heat transfer resistance (except for 30% sucrose solution). Two effects could be involved. A higher flow rate leads to higher axial velocities and thus to better mixing and transfer. This effect is certainly negligible because the mean axial velocity was always small compared to the tangential velocities (at blade extremity for example). A higher product flow rate leads also in our experiments to a smaller ice amount at the outlet because the extracted heat (refrigerating power) is roughly constant. Reducing the amount of ice in the SSHE, lowers the mean values of ice slurry viscosity and conductivity which have indirect effects. Raising the concentration had a minor effect in the case of ethanol but increased the internal heat transfer resistance in the case of sucrose especially for low rotating speed. A higher concentration leads to a higher viscosity in the case of sucrose (this tends to reduce the transfer) and amplifies the cryo-concentration phenomena of the solution (this tends to reduce the freezing front progression). Enlarging the gap between the blade extremity and the wall increased the internal heat transfer resistance. At first sight, this could be explained by the resistance of a permanent ice layer (of 1 or 3 mm), which forms between the blade extremity and the wall. Thus, the internal heat transfer resistance could be considered as the sum of the permanent ice layer resistance and an additional resistance, which holds for heat, ice crystals and solute transfer between the product and its interface with the permanent ice layer. But it seems that a permanent ice layer forms only when the gap between blades and wall is large enough (e ¼ 3 mm), otherwise (e ¼ 1 mm) the ice layer is not strong enough and is periodically removed from the wall. This assumption is supported by several observations.
0.0025 0.002 0.0015 0.001 0.0005 0 0
200
400
600
800
Rotation speed (rpm)
e=3mm 0.14 kg/s
e=3mm 0.20 kg/s
e=3mm 0.30 kg/s
e=1mm 0.14 kg/s
e=1mm 0.20 kg/s
e=1mm 0.30 kg/s
1mm ice
3mm ice
Fig. 5. Internal heat transfer resistance vs. rotation speed (10% ethanol).
Heat transfer resistance (Km²/W)
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
55
0.0025 0.002 0.0015 0.001 0.0005 0 0
200
400
600
800
Rotation speed (rpm) e=1mm 0.14 kg/s
e=1mm 0.20 kg/s
e=1mm 0.30 kg/s
1mm ice
Heat transfer resistance (Km²/W)
Fig. 6. Internal heat transfer resistance vs. rotation speed (20% ethanol).
0.0025 0.002 0.0015 0.001 0.0005 0 0
200
400
600
800
Rotation speed (rpm) e=1mm 0.10 kg/s
e=1mm 0.12 kg/s
e=1mm 0.14 kg/s
1mm ice
Fig. 7. Internal heat transfer resistance vs. rotation speed (15% sucrose).
• The internal heat transfer resistance for e ¼ 1 mm (without taking account of a permanent ice layer) had almost the same value as the gap between the internal heat transfer resistance for e ¼ 3 mm and the thermal resistance of an ice layer of 3 mm (Fig. 5). This is coherent with the fact that the additional internal resistance normally only depends on the internal conditions (blades rotation speed, product type, concentration and flow rate). • The internal heat transfer resistance was sometimes smaller than a hypothetical permanent ice layer of 1 mm (cf. sucrose solution at high rotation speed). • The ice slurry appeared as fluffy with some relatively large flakes.
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
• The periodical formation and removal of an ice layer could explain the measured evolution of the wall temperature (Fig. 9). The ice layer formation leads to an increasing resistance until its thickness reaches about 1 mm, thus wall temperature becomes more distant from product one. Then the rotating blades limit the ice thickness and sometimes remove a thick flake (of about 1 mm). After removal of an ice flake, the ice layer resistance disappears and the wall temperature becomes suddenly closer to the product one.
3.3. Correlation for internal heat transfer coefficient estimation
Heat transfer resistance (Km²/W)
In order to predict the internal heat transfer coefficient (inverse of internal resistance) in SSHE used for freezing of aqueous solution, independently of wall diameter and possibly of solute type and concentration, the experimental results were converted in term of dimensionless numbers (Nu, Rer , Rea , Pr, x0 ). For experiment with a blade-wall gap of 3 mm, the permanent ice layer resistance was deduced from the internal heat transfer resistance. The physical properties used in the dimensionless numbers were those of the diphasic product at the outlet of the SSHE. Prandtl number, in particular, takes into account the phase change, because the latent heat of fusion appears in the apparent heat capacity. Table 2 gives the variation ranges of these properties and of the dimensionless numbers. Logarithmic multiple regressions were performed to express Nu versus Rer , Rea , Pr and x0 with a power law function. According to the Student test, it appeared that Prandtl number had no significant effect, both for sucrose and ethanol. This means that taking apparent diphasic properties in the same dimensionless numbers as for one-phase flow is not sufficient to explain hydrodynamic/thermal behaviour during the crystallisation of a solution. For our experiments with sucrose, the axial Reynolds number had no significant effect either. This can be due to the small range of flow rate variation in this case. 0.0025 0.002 0.0015 0.001 0.0005 0 0
200
400
600
800
Rotation speed (rpm) e=1mm 0.10 kg/s
e=1mm 0.12 kg/s
e=1mm 0.14 kg/s
1mm ice
Fig. 8. Internal heat transfer resistance vs. rotation speed (30% sucrose).
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
57
1 0
Temperature (°C)
-1
product wall
-2
pure ethanol
-3 -4 -5 -6 -7 -8 -9 0
10
20
30
40
50
Time (min)
Fig. 9. Example of wall temperature evolution (6th position) (solute: sucrose 15%, mass flow rate: 0.14 kg/s, rotation speed: 700 rpm) (product and pure ethanol temperatures are the inlet-outlet mean values). Table 2 Variation ranges of the diphasic physical properties at the outlet of SSHE and of the dimensionless numbers Product
q kg m3
Ethanol Sucrose
960–980 6–15 1070–1110 3–10
l mPa s
k W m1 K1
cpðapparentÞ kJ kg1 K1
Pr
Rer
Rea
0.6–0.8 0.5–0.6
15–50 80–250
220–620 1400–1800
1700–24000 4000–34000
130–560 90–270
The following correlations were finally proposed ethanol:
0:38 0:80 Nu ¼ 4:47Re0:27 a Rer x0
sucrose:
0:34 Nu ¼ 0:63Re0:61 r x0
ðR2 ¼ 0:82Þ
ðR2 ¼ 0:67Þ
ð13Þ ð14Þ
Fig. 10 presents a comparison between experimental and calculated Nusselt number values. The correlation was less accurate for sucrose than for ethanol. A common correlation for ethanol and sucrose could not be obtained. Applying the correlation identified for ethanol to operating conditions and thermophysical properties of the sucrose experimentation led to overestimation of the heat transfers up to 250%. This is not surprising because ice crystal growth and removal depends on solute type [26] and the nature of the two mixtures is different: sucrose is a solid dissolved in a liquid whereas ethanol is a liquid totally miscible with water. Other correlations from the literature were also tested. Applying Harriot’s correlation [5] based on the penetration theory, with Prandtl number calculated from apparent diphasic properties, led to predicted heat transfer coefficients up to hundred times higher than the measured ones.
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60 250 200 150
10% ethanol
Nucal
16% ethanol
100
20% ethanol 50
correlation ± 15 %
0 0
50
100
150
200
250
Nuexp (a)
250 200 150 Nucal
15% sucrose
100
30% sucrose correlation +/- 20%
50 0 0
50
100
150
200
250
Nuexp (b)
Fig. 10. Comparison between experimental and calculated (from Eqs. (11) and (12)) Nusselt number values.
Dinglinger’s correlation [12] was not applicable because the correction factor, involving the difference between inlet and freezing temperatures, tends to zero in our case. The correlation proposed by Bel and Lallemand [15] for ethanol solution freezing inside a brushed surface heat exchanger underestimated about 8 times our results obtained with ethanol solution freezing inside a scraped surface heat exchanger. Therefore it appeared that only the specific correlations proposed can be used to design scraped surface heat exchangers for freezing of ethanol-water mixtures (widely used as secondary diphasic refrigerant) or sucrose solutions (major component of ice creams). 4. Conclusion Different parameters influence the heat transfers inside a scraped surface heat exchanger used for freezing of aqueous solutions: blade rotation speed and solute concentration have the major effect. A permanent ice layer is formed between the blade extremity and the wall only when the
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59
gap is high enough (more than 1 mm). The phenomena complexity (water crystallisation inside a solution, ice crystal removal from the wall, mixing effect of the blades) explains certainly that specific correlations have to be used for each kind of exchanger (brushed vs. scraped) and solute (ethanol vs. sucrose). Nevertheless, the proposed correlations can be used, at least as a first approach, for the most common freezing applications of scraped surface heat exchanger i.e. ice creams (which are derived from sucrose solutions) and two-phase secondary refrigerants (which are principally ethanol solutions).
References [1] G. Cognet, Les etapes vers la turbulence dans l’ecoulement de Couette-Taylor entre cylindres coaxiaux, J. de mecanique theorique et appliquee, numero special (1984) 7–44. [2] M. Harr€ od, A literature survey of flow patterns, mixing effects, residence time distribution, heat transfer and power requirements, J. Food Process. Eng. 9 (1986) 1–62. [3] K.M. Becker, J. Kaye, Measurement of diabatic flow in annulus with an inner rotating cylinder, J. Heat Transfer 84 (1962) 97–105. [4] E. Dummont, F. Fayolle, J. Legrand, Flow regims an wall shear rates determination within scraped surface heat exchanger, J. Food Eng. 45 (2000) 195–207. [5] J.F. Maingonnat, G. Corrieu, Etude des performances thermiques d’un echangeur a surface raclee: revue des principaux modeles decrivant le transfert de chaleur et la consommation de puissance, Entropie 111 (1983) 29–36. [6] P. Harriot, Heat transfer in scraped-surface exchangers, Chem. Eng. Progr. Symp. Ser. 55 (1959) 137–139. [7] S. Sykora, B. Navratyl, O. Karasek, Heat transfer on scraped walls in the laminar and transitional regions, Collection Czech. Chem. Commun. 33 (1968) 518–528. [8] V. Ramdas, V.W. Uhl, M.W. Osborne, J.R. Ort, Heat transfer to viscous materials in a continuous-flow, scraped wall, commercial-size heat exchanger, A. I. Ch. E. Nat. Heat Transfer Conf. (1977) 24–31. [9] J.F. Maigonnat, G. Corrieu, Etude des performances thermiques d’un echangeur de chaleur a surface raclee: influence de la diffusion axiale de chaleur sur les performances thermiques, Entropie 111 (1983) 37–48. [10] J.F. Maingonnat, T. Benezech, G. Corrieu, Performances thermiques d’un echangeur de chaleur a surface raclee traitant des produits alimentaires newtoniens et non-newtoniens, Rev. Gen. Therm. 279 (1985) 299–304. [11] H. Weisser, Untersuchung zum W€arme€ ubebergang im Kratzkuhler, Ph.D. thesis, 1972, University of Karlsruhe. [12] G. Dinglinger, Die W€arme€ ubertragung im Kratzk€ uhler, K€ altetechn 16 (1964) 170–175. [13] R. De Goede, E.J. De Jong, Heat transfer properties of scraped-surface heat exchanger in the turbulent flow regime, Chem. Eng. Sci. 48 (1993) 1393–1404. [14] M. Kawaji, E. Stamatiou, R. Hong, J.J. Xu, D.Y. Shang, V. Goldstein, Experimental and numerical investigation of ice-slurry generator performance, in: 2nd Workshop on Ice slurries of Int. Inst. of Refrigeration, Paris, France, 2000. [15] O. Bel, A. Lallemand, Etude d’un fluide frigoporteur diphasique. (1) caracteristiques thermophysiques intrinseques d’un coulis de glace (2) analyse experimentale du comportement thermique et rheologique, Int. J Refrig. 22 (1999) 164–187. [16] M. Baccar, M.S. Abid, Numerical analysis of three-dimensional flow and thermal behaviour in a scraped surface heat exchanger, Rev. Gen. Therm. 36 (1997) 782–790. [17] R. Hong, M. Kawaji, V. Goldstein, Numerical investigation of ice-slurry flow and heat transfer in a scraped ice generator and a storage tank, in: 3rd Workshop on ice slurries of Int. Inst. of Refrigeration, Lucerne, Switzerland, 2001. [18] M. Ben Lakhdar, J. Moureh, D. Flick, W. Guatherin, A. Lalllemand, Simulation numerique des ecoulements et des transferts dans un echangeur de chaleur a surface raclee, Recents progres en genie des procedes 11 (1997) 139–144. [19] V. Gnielinski, Neue Gleichungen f€ ur den W€arme-und den Stoff€ ubergang in turbulent durchstr€ omten Rohren und Kan€alen, Forsch. Ing.-Wes. 41 (1975) 8–16. [20] W.M. Rohsenow, J.P. Hartnett, Y.I. Cho, Handbook of Heat Transfer, McGraw Hill, 1998.
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[21] J. Guilpart, L. Fournaison, Ben M.A. Lakhdar, Methode de calcul des proprietes thermophysiques des coulis de glace: application au melange eau-ethanol, in: 20th Int. Congress of Refrigeration, Sydney, Australia, 1999. [22] M. Mathlouthi, P. Reiser, Le saccharose: proprietes et applications, Polytechnica (1995). [23] Z. Bubnik, P. Kadlec, D. Urban, M. Bruhns, Sugar technologists manual, 8th edition Verlag Dr. A. Bartes, Germany, 1995. [24] R.H. Perry, D. Green, Perry’s Chemical Engineer’s Handbook, fifth edition, McGraw-Hill, New York, 1973. [25] D.G. Thomas, Transport characteristics of suspension, J. Colloid. Sci. 20 (1965) 267–277. [26] R.J.C. Vaessen, C. Himawan, G.J. Witkamp, Scale formation of ice from electrolyte solutions on a scraped surface heat exchanger plate, J. Cryst. Growth 237–239 (2002) 2172–2177.
Heat transfer with freezing in a scraped surface heat exchanger Mohamed Ben Lakhdar a, Rosalia Cerecero b, Graciela Alvarez b, Jacques Guilpart b, Denis Flick c,*, Andre Lallemand d a
b
LGL France Refrigerating Division, 42, rue Roger Salengro BP 205, 69741 Genas, France UMR Genie industriel alimentaire––Food process engineering Ensia/Cemagref/INAPG/INRA, Cemagref, UR Genie des procedes frigorifiques, BP 44, 92163 Antony cedex, France c UMR Genie industriel alimentaire––Food process engineering, Ensia/Cemagref/INAPG/INRA, Institut National Agronomique, Paris-Grignon, 16, rue Claude Bernard, 75231 Paris cedex 05, France d Centre de Thermique––UMR A CNRS 5008, Institut National des Sciences Appliquees de Lyon, 20, avenue Albert Einstein, 69621 Villeurbanne cedex, France Received 12 February 2004; accepted 9 May 2004 Available online 25 June 2004
Abstract An experimental study was carried out on a scraped surface heat exchanger used for freezing of water– ethanol mixture and aqueous sucrose solution. The influence of various parameters on heat transfer intensity was established: product type and composition, flow rate, blade rotation speed, distance between blades and wall. During starting (transient period) the solution is first supercooled, then ice crystals appear on the scraped surface (heterogeneous nucleation) and no more supercooling is observed. It seems that, when blades are 3 mm far from the surface, a constant ice layer is formed having this thickness and acting as a thermal resistance. But when the blades rotate at 1 mm from the surface, periodically all the ice layer is removed despite the surface is not really scraped. This could simplify ice generator technology. An internal heat transfer coefficient was defined; it depends mainly on rotation speed. Correlations were proposed for its prediction, which could be applied, at least as a first approach, for the most common freezing applications of scraped surface heat exchanger i.e. ice creams (which are derived from sucrose solutions) and two-phase secondary refrigerants (which are principally ethanol solutions). 2004 Elsevier Ltd. All rights reserved. Keywords: Scraped surface heat exchanger; Freezing; Sucrose; Ethanol; Correlation; Heat transfer coefficient
*
Corresponding author. Tel.: +33-1-4408-7239; fax: +33-1-4408-1666. E-mail address: fl[email protected] (D. Flick).
1359-4311/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.05.007
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
Nomenclature A cp D Dr Dh e h h Lf N_ Nu ¼ hD k Pr ¼ Q_
heat exchange area, m2 specific heat capacity, J kg1 K1 scraped wall inner diameter, m rotor diameter, m external hydraulic diameter, m gap between the blades extremity and the wall, m heat transfer coefficient, W m2 K1 specific enthalpy, J kg1 K1 specific latent heat of fusion for ice at 0 C, J rotor rotation speed, s1 Nusselt number
lCp k
Prantdl number heat flux, W rÞ Rea ¼ quðDD axial Reynolds number l _
2
Rer ¼ qNlD rotational Reynolds number h external Reynolds number Reext ¼ qvD l R heat transfer resistance K m2 W1 T temperature, K or C V_ 1 u ¼ pðD2 D 2 Þ=4 mean axial velocity, m s r v mean velocity of pure ethanol V_ volume flow rate, m3 s1
Greek symbols k l q um uv x x0
thermal conductivity, W m1 K1 dynamic viscosity, Pa s density, kg m3 mass fraction of ice volume fraction of ice solute mass fraction in the solution; mass of solute/mass of solution global mass fraction of solute; mass of solute/mass of solution and ice
Subscripts eth ext f i int 0 p s w cri
pure ethanol external freezing point ice internal initial product solution wall critical value
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
47
1. Introduction Scraped surface heat exchangers (SSHE) are often used to produce ice creams and ice slurries. The interest of SSHE for ice creams, is the production of a lot of small crystals before hardening the product in cold rooms, which improves its unctuousness. Recently, many studies have been reported about ice slurries used as two-phase secondary refrigerant, SSHE are used to generate them continuously. In both applications, the objective is to produce the maximal amount of ice without exceeding a viscosity threshold to insure pumpability. Therefore heat transfer performances have to be predicted taking into account ice crystallisation. Many studies are devoted to fluid flow and heat transfer in SSHE without phase change. Fluid flow is similar to the Couette–Poiseuille configuration: annular channel between two cylinders, the inner rotating [1,2]. Flow pattern depends on two Reynolds numbers. The axial Reynolds number (Rea ) is based on the mean axial velocity (volumetric flow rate divided by the cross section) and the rotational Reynolds number (Rer ) on the tangential velocity of inner cylinder or of blades extremity. When rotating speed increases, toro€ıdal vortices (called Taylor vortices) appear at a critical rotational Reynolds number for which Becker and Kaye [3] propose a value depending on the ratio between rotor diameter (Dr ) and tube diameter (D). When rotating speed is further increased, the vortices become perturbed and finally turbulence appears. The presence of blades modifies the appearance of the vortices and increases locally the shear rate [4], but the order of magnitude of the critical rotational Reynolds number is the same. Various correlations are proposed to predict heat transfer coefficient for monophasic fluids. [2,5]. They have generally the following form: Nu ¼ aReba Recr Prd
ð1Þ
Prandtl number exponent is often fixed at 1/3. The rotational Reynolds number exponent is generally small for laminar flow and ranges from 1/2 to 1 for vortical and turbulent flow. Harriot [6] proposed a theoretical approach where the limiting phenomenon is the heat penetration from the wall to the product between two scrapings, he found that the Nusselt number is proportional to the square root of rotational Reynolds number. The axial Reynolds number is often omitted, as the tangential velocity is much higher than the axial mean velocity. Some correlations take account of the number of blades [7]. Some others propose a correction factor for viscosity near the heated wall [8]. Moreover, the axial dispersion can be taken into account by including a residence time distribution model [9]. Relations are also proposed for non-newtonian fluids; this is of interest because food products often exhibit such behaviour [10]. Only few studies deal with crystallisation in SSHE. Weisser [11] and Dinglinger [12] studied freezing of sucrose solution. The latter proposes a correlation with a correction factor (depending on freezing temperature, inlet and outlet temperature of product) because in their experiments the product is cooled down and frozen at once in the same SSHE. More recently, crystallisation of other substances where studied in SSHE: p-xylene by De Goede and De Jong [13], brine by Kawaji et al. [14]. Bel and Lallemand [15] studied freezing of water–ethanol slurries using an ice generator where the exchange surface was not scraped but brushed. They propose a correlation where the axial and the rotational Reynolds number are added. Numerical simulations of fluid flow and heat transfer were also reported, for example by Baccar and Abid [16], Hong et al. [17] and Ben Lakhdar et al. [18]; but they do not consider any phase
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
change for the product. Such simulations can predict qualitatively the flow pattern (dead zones, vortices) but are not able to predict heat intensity when freezing occurs. The aim of the present work is to characterise experimentally the influence of various parameters (flow rate, blade rotation speed, distance between blades and wall, product concentration) on heat transfer for two products (water–ethanol mixture and aqueous sucrose solution) and to propose correlations able to predict the heat transfer at a scraped surface when freezing of water occurs. 2. Material and methods 2.1. Experimental device The experimental device is presented in Fig. 1. The heat exchanger (build in the lab) included a scraped surface tube, made of stainless steel, which had 100 mm inner diameter, 2.5 mm thickness and 520 mm length. A countercurrent turbulent flow of chilled pure ethanol circulated around this tube inside an annular jacket with a radial gap of 3 mm. This ensured a quite uniform and high external heat transfer coefficient (at the outer side of the wall). The aqueous solution circulated in a closed loop through a variable speed volumetric pump (PCM 4I10). The flow rate, measured by a Coriolis flowmeter (ABB K40), could vary from 0.1 to 0.3 kg/s. At the outlet of SSHE, the ice slurry was heated with an electric device (Vulcanic 10745) in order to melt all the ice. The heating power was adjusted so that the temperature at the SSHE inlet was just above the equilibrium freezing temperature (Tf < T < Tf þ 1:5 K) when steady state was reached. This protocol allowed to minimise the enthalpy needed to cool down the solution before freezing, so that it was negli-
Fig. 1. Experimental device.
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
49
gible compared to the phase change enthalpy. Otherwise, it would be difficult to estimate which part of the heat exchanging surface was involved for crystallisation. The wall temperature was measured at 6 positions along the scraped surface by thermocouples brazed on the external side of the tube (which is in contact with pure ethanol). Solution or ice slurry temperature was also measured at different position in the loop by thermocouples or platinum sensors. Two blades made of stainless steel were rigidly fixed on the rotor, which had an external diameter of 40 mm. Their position could be modified so that their extremity was between 1 and 3 mm far from the tube inner surface. The blades never really scraped the surface as in SSHE used for the heating of sensitive food products, which would otherwise brown on the heated surface. In our case, at first sight, a permanent ice layer will form in the gap between the wall and the blades extremity; ice crystals grow on this layer and are detached by the blades. The rotation speed could vary from 100 to 800 rpm. The rotational Reynolds number was always higher than the critical value, calculated from Becker’s and Kaye’s relation [3] (Eq. (2)), which was 166 in our case. Rercri
"
,
ðD Dr Þ 0:0571 1 0:652 Dr !# 1 1=2 ðD Dr Þ þ 0:00056 1 0:652 Dr
pD2 ¼ ðD Dr ÞDr
D þ Dr 2 D Dr
ð2Þ
2.2. Estimation of heat flux density The heat flux exchanged at the surface was estimated by the following steps. First we calibrated the external heat transfer coefficient (at the outer side of the wall) versus flow rate of pure ethanol. For this calibration, the solution entered the SSHE at ambient temperature so that no crystallisation occurred and the exchanged heat flux was obtained from inlet/outlet temperature difference and flow rate of the solution. Then, for the other experiments with crystallisation, this calibration was used to deduce the heat flux from ethanol flow rate, ethanol temperature (mean value between inlet and outlet) and wall temperature (mean value of the 6 thermocouples). For the external heat transfer characterisation, the solution flow rate ranged from 0.02 to 0.08 kg s1 and the pure ethanol flow rate from 0.75 to 2.41 kg s1 . The correlation proposed by Gnielinsky [19] for annular flow, in the transition zone between laminar and turbulent regime, was used (Eq. (3)) as it fits the experimental results with an accuracy of 5% (Fig. 2). The Dittus– Boelter’s [20] correlation underestimates the heat transfer intensity probably because the Reynolds number for the annular flow of ethanol ranges between 3000 and 10000. 2=3 ! 0:059Re0:25 1000ÞPr ðRe Dh ext ext ext 1þ Nuext ¼ 1:03 0:5 2=3 L 1 þ 12:7 0:059Re0:25 Prext 1 ext annular gap ¼ 0:05 ð3Þ external diameter
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60 External heat transfer coefficient (W/(m².K))
50
4500 4000 3500 3000 2500 2000 1500 1000 500 0 0
2000
4000
6000
8000
10000
External Reynolds number
Fig. 2. External heat transfer coefficient vs. external Reynolds number (experiment and Gnielinski correlation).
2.3. Thermophysical properties To define the dimensionless numbers, which are involved in the correlations, we used the thermophysical properties of ice slurry estimated at the outlet of the SSHE. The diphasic properties (ice slurry) were obtained from the monophasic ones (solution, ice). For ice and water– ethanol mixtures, a detailed description is given by Guilpart et al. [21]. For sucrose solution, the relations recommended by Mathlouthi and Reiser [22] were used for the density and those recommended by Bubnik et al. [23] were used for thermal conductivity, specific heat, viscosity and freezing point temperature. The liquidus curve is given by Eq. (4) where x (kg solute/kg solution) is the solute mass fraction in the solution. Tf ðxÞ ¼ ð5:176x þ 13:27x2 24:16x3 þ 75:5x4 Þ
ðT in CÞ
ð4Þ
Local thermodynamical equilibrium was assumed except during supercooling periodðT ¼ Tf ðxÞ () x ¼ xf ðT ÞÞ. There is no solute in the ice crystals (temperature is always higher than the eutectic one). The global mass fraction of solute in the slurry x0 (kg solute/kg solution + ice) remains constant and equal to the value of x before freezing. Thus, the mass fraction of ice in the slurry can be calculated versus temperature x0 ð5Þ um ¼ 1 xf ðT Þ The slurry density is obtained by addition of ice and solution volume. 1 um ð1 um Þ ¼ þ ð6Þ q qs qi The volume fraction of ice in the slurry is then q ð7Þ uv ¼ um qi The thermal conductivity is obtained by the Maxwell lower bound relation [24] for dilute solid/ liquid suspensions
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
k ¼ ks
2ks þ ki 2uv ðks ki Þ 2ks þ ki þ uv ðks ki Þ
51
ð8Þ
where ks and ki are the thermal conductivities of solution and ice and uv can be obtained from the temperature by the previous relations. The specific enthalpy of slurry is obtained by adding those of ice and solution Z T Z T 0 0 cpi ðT ÞdT þ ð1 um Þ cps ðT 0 ÞdT 0 ð9Þ h ¼ um Lf þ 0 C
0 C
For a given global solute mass fraction, the specific enthalpy is only function of temperature, so an apparent specific heat can be defined for the slurry (needed energy to increase by 1 K, 1 kg of slurry following liquidus curve) which was used to calculate the Prandtl number. cp ¼
dh dT
ðwhere h is obtained from Eq:ð9ÞÞ
ð10Þ
The slurry was supposed to remain newtonian. Experiments (not presented here), obtained by tubular rheology showed that the flow behaviour index remains near unity for an ice volume fraction less than 7%; which was the case in the present work. The relation proposed by Thomas [25] for solid/liquid suspensions which is an extension of Einstein’s law was used l ¼ ls ð1 þ 2:5uv þ 10:05u2v þ 2:73103 expð16:6uv ÞÞ
ð11Þ
2.4. Operating conditions Table 1 presents the operating conditions used for heat transfer characterisation. Table 1 Operating conditions Product
Ethanol or sucrose mass fraction
Gap between blades and wall (mm)
Product mass flow rate (kg/s)
Rotation speed (rpm)
Water + ethanol
0.10
1 and 3
0.16
1 and 3
0.20
1
0.14 0.20 0.30 0.14 0.20 0.30 0.14 0.20 0.30
300–500–700 300–500–700 300–500–700 300–500–700 300–500–700 300–500–700 100–200 . . . 600–700 100–200 . . . 600–700 100–300–500–700
0.15
1
0.30
1
0.10 0.12 0.14 0.10 0.12 0.14
200–300 . . . 700–800 200–300 . . . 700–800 200–300 . . . 700–800 200–300 . . . 700–800 200–300 . . . 700–800 200–300 . . . 700–800
Water + sucrose
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
3. Results and discussion 3.1. Supercooling Fig. 3 presents an example of temperature evolution of the product at the outlet of SSHE before steady state was reached and without heating the product with the electric device. The product aspect was also visualised trough a Pyrex tube. The temperature decreased first below the freezing temperature by a few degrees while the product remained transparent: the solution was supercooled and was not at thermodynamical equilibrium. Then, temperature rose abruptly and the product became suddenly opaque: nucleation appeared. The sensible heat accumulated during supercooling was transformed into latent heat by formation of a multitude of ice crystals. Just after the temperature jump, its value was slightly below the freezing temperature, and then it decreased slowly (because, in the loop, inlet temperature also decreased) whereas the ice fraction increased. Local thermal equilibrium (between remaining solution and ice) was then probably reached at the SSHE outlet. All the results further presented were obtained after this transient period (without supercooling).
3.2. Heat transfer resistances Fig. 4 presents an example of the measured temperatures when steady state was reached. It appeared that the wall and product temperature variations along the SSHE were small compared to their difference. Thus, a simple arithmetic average was used to characterise the mean temperature difference between the wall and the product (average of the 6 thermocouples for the wall, average between inlet and outlet for the product). An internal heat transfer resistance Rint (between wall and product) has been calculated from the measured temperatures, knowing the wall
15 13 11 9 7 5 3 1 -1 -3 -5 -7 -9
T (°C)
freezing temperature : -4.2 °C -4.5°C
-6.4°C 0
5
10
15
20
25
30
35
Time (min)
Fig. 3. Example of product temperature evolution at the outlet of SSHE (before steady state was reached and without heating the product) (solute: ethanol 10%, mass flow rate: 0.14 kg/s, rotation speed: 100 rpm).
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
53
Fig. 4. Example of wall and product temperature when steady state is reached (time averaged values over one hour) (solute: sucrose 15%, mass flow rate: 0.14 kg/s, rotation speed: 800 rpm).
resistance Rw and the external resistance Rext (between wall and pure ethanol) from Gnielinsky’s correlation [19] with an accuracy of 5%. Rint þ Rw ¼
Tp Tw Tp Tw ðthe wall temperature is measured on the external side ¼ Rext _Q=A Tw Teth in contact with pure ethanolÞ ð12Þ
Typically (Fig. 4) the temperature differences between wall and product or between wall and pure ethanol were about 4 C, they were estimated with a precision of 0.1 C. Thus the relative precision of Rint was typically 10%. Nevertheless, the external flow rate of pure ethanol was always the same; this reduced the influence of the uncertainty of Rext . Figs. 5–8 show the internal heat transfer resistance versus rotation speed for different flow rates, different aqueous solution (ethanol and sucrose) and different concentration. The influence of the gap between the blade extremity and wall is also presented in the case of 10% ethanol solution. Increasing the rotation speed lowered the internal heat transfer resistance; the influence was particularly noticeable below about 500 rpm. Different effects resulting from the rotation of the blades could explain this. • Similarly to the penetration theory proposed by Harriot [6] for monophasic fluids, it can be assumed that an ice layer is formed between two scrapings, which acts as a thermal resistance. Reducing the time between successive scraping reduces this resistance. • The blades scrap the new formed ice crystals and mix them with the rest of the product. Some of these ice crystals will melt if the product enters the SSHE at a temperature much higher than the freezing point. The blades rotation enhances this mixing effect which tends to cool the product quickly down to freezing temperature. When the product reaches the wall, it is then faster frozen. This effect is small in our case because the product entered the SSHE near its freezing point. • When ice is produced near the wall, the remaining solution is concentrated and its freezing point temperature decreases, this reduces freezing front progression. The blades replace this
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
concentrated solution by solution taken far from the wall. This radial mixing effect is more efficient when blades rotate more rapidly.
Heat trasnfer resistance (Km²/W)
Increasing the product flow rate decreased slightly the internal heat transfer resistance (except for 30% sucrose solution). Two effects could be involved. A higher flow rate leads to higher axial velocities and thus to better mixing and transfer. This effect is certainly negligible because the mean axial velocity was always small compared to the tangential velocities (at blade extremity for example). A higher product flow rate leads also in our experiments to a smaller ice amount at the outlet because the extracted heat (refrigerating power) is roughly constant. Reducing the amount of ice in the SSHE, lowers the mean values of ice slurry viscosity and conductivity which have indirect effects. Raising the concentration had a minor effect in the case of ethanol but increased the internal heat transfer resistance in the case of sucrose especially for low rotating speed. A higher concentration leads to a higher viscosity in the case of sucrose (this tends to reduce the transfer) and amplifies the cryo-concentration phenomena of the solution (this tends to reduce the freezing front progression). Enlarging the gap between the blade extremity and the wall increased the internal heat transfer resistance. At first sight, this could be explained by the resistance of a permanent ice layer (of 1 or 3 mm), which forms between the blade extremity and the wall. Thus, the internal heat transfer resistance could be considered as the sum of the permanent ice layer resistance and an additional resistance, which holds for heat, ice crystals and solute transfer between the product and its interface with the permanent ice layer. But it seems that a permanent ice layer forms only when the gap between blades and wall is large enough (e ¼ 3 mm), otherwise (e ¼ 1 mm) the ice layer is not strong enough and is periodically removed from the wall. This assumption is supported by several observations.
0.0025 0.002 0.0015 0.001 0.0005 0 0
200
400
600
800
Rotation speed (rpm)
e=3mm 0.14 kg/s
e=3mm 0.20 kg/s
e=3mm 0.30 kg/s
e=1mm 0.14 kg/s
e=1mm 0.20 kg/s
e=1mm 0.30 kg/s
1mm ice
3mm ice
Fig. 5. Internal heat transfer resistance vs. rotation speed (10% ethanol).
Heat transfer resistance (Km²/W)
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55
0.0025 0.002 0.0015 0.001 0.0005 0 0
200
400
600
800
Rotation speed (rpm) e=1mm 0.14 kg/s
e=1mm 0.20 kg/s
e=1mm 0.30 kg/s
1mm ice
Heat transfer resistance (Km²/W)
Fig. 6. Internal heat transfer resistance vs. rotation speed (20% ethanol).
0.0025 0.002 0.0015 0.001 0.0005 0 0
200
400
600
800
Rotation speed (rpm) e=1mm 0.10 kg/s
e=1mm 0.12 kg/s
e=1mm 0.14 kg/s
1mm ice
Fig. 7. Internal heat transfer resistance vs. rotation speed (15% sucrose).
• The internal heat transfer resistance for e ¼ 1 mm (without taking account of a permanent ice layer) had almost the same value as the gap between the internal heat transfer resistance for e ¼ 3 mm and the thermal resistance of an ice layer of 3 mm (Fig. 5). This is coherent with the fact that the additional internal resistance normally only depends on the internal conditions (blades rotation speed, product type, concentration and flow rate). • The internal heat transfer resistance was sometimes smaller than a hypothetical permanent ice layer of 1 mm (cf. sucrose solution at high rotation speed). • The ice slurry appeared as fluffy with some relatively large flakes.
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
• The periodical formation and removal of an ice layer could explain the measured evolution of the wall temperature (Fig. 9). The ice layer formation leads to an increasing resistance until its thickness reaches about 1 mm, thus wall temperature becomes more distant from product one. Then the rotating blades limit the ice thickness and sometimes remove a thick flake (of about 1 mm). After removal of an ice flake, the ice layer resistance disappears and the wall temperature becomes suddenly closer to the product one.
3.3. Correlation for internal heat transfer coefficient estimation
Heat transfer resistance (Km²/W)
In order to predict the internal heat transfer coefficient (inverse of internal resistance) in SSHE used for freezing of aqueous solution, independently of wall diameter and possibly of solute type and concentration, the experimental results were converted in term of dimensionless numbers (Nu, Rer , Rea , Pr, x0 ). For experiment with a blade-wall gap of 3 mm, the permanent ice layer resistance was deduced from the internal heat transfer resistance. The physical properties used in the dimensionless numbers were those of the diphasic product at the outlet of the SSHE. Prandtl number, in particular, takes into account the phase change, because the latent heat of fusion appears in the apparent heat capacity. Table 2 gives the variation ranges of these properties and of the dimensionless numbers. Logarithmic multiple regressions were performed to express Nu versus Rer , Rea , Pr and x0 with a power law function. According to the Student test, it appeared that Prandtl number had no significant effect, both for sucrose and ethanol. This means that taking apparent diphasic properties in the same dimensionless numbers as for one-phase flow is not sufficient to explain hydrodynamic/thermal behaviour during the crystallisation of a solution. For our experiments with sucrose, the axial Reynolds number had no significant effect either. This can be due to the small range of flow rate variation in this case. 0.0025 0.002 0.0015 0.001 0.0005 0 0
200
400
600
800
Rotation speed (rpm) e=1mm 0.10 kg/s
e=1mm 0.12 kg/s
e=1mm 0.14 kg/s
1mm ice
Fig. 8. Internal heat transfer resistance vs. rotation speed (30% sucrose).
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57
1 0
Temperature (°C)
-1
product wall
-2
pure ethanol
-3 -4 -5 -6 -7 -8 -9 0
10
20
30
40
50
Time (min)
Fig. 9. Example of wall temperature evolution (6th position) (solute: sucrose 15%, mass flow rate: 0.14 kg/s, rotation speed: 700 rpm) (product and pure ethanol temperatures are the inlet-outlet mean values). Table 2 Variation ranges of the diphasic physical properties at the outlet of SSHE and of the dimensionless numbers Product
q kg m3
Ethanol Sucrose
960–980 6–15 1070–1110 3–10
l mPa s
k W m1 K1
cpðapparentÞ kJ kg1 K1
Pr
Rer
Rea
0.6–0.8 0.5–0.6
15–50 80–250
220–620 1400–1800
1700–24000 4000–34000
130–560 90–270
The following correlations were finally proposed ethanol:
0:38 0:80 Nu ¼ 4:47Re0:27 a Rer x0
sucrose:
0:34 Nu ¼ 0:63Re0:61 r x0
ðR2 ¼ 0:82Þ
ðR2 ¼ 0:67Þ
ð13Þ ð14Þ
Fig. 10 presents a comparison between experimental and calculated Nusselt number values. The correlation was less accurate for sucrose than for ethanol. A common correlation for ethanol and sucrose could not be obtained. Applying the correlation identified for ethanol to operating conditions and thermophysical properties of the sucrose experimentation led to overestimation of the heat transfers up to 250%. This is not surprising because ice crystal growth and removal depends on solute type [26] and the nature of the two mixtures is different: sucrose is a solid dissolved in a liquid whereas ethanol is a liquid totally miscible with water. Other correlations from the literature were also tested. Applying Harriot’s correlation [5] based on the penetration theory, with Prandtl number calculated from apparent diphasic properties, led to predicted heat transfer coefficients up to hundred times higher than the measured ones.
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M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60 250 200 150
10% ethanol
Nucal
16% ethanol
100
20% ethanol 50
correlation ± 15 %
0 0
50
100
150
200
250
Nuexp (a)
250 200 150 Nucal
15% sucrose
100
30% sucrose correlation +/- 20%
50 0 0
50
100
150
200
250
Nuexp (b)
Fig. 10. Comparison between experimental and calculated (from Eqs. (11) and (12)) Nusselt number values.
Dinglinger’s correlation [12] was not applicable because the correction factor, involving the difference between inlet and freezing temperatures, tends to zero in our case. The correlation proposed by Bel and Lallemand [15] for ethanol solution freezing inside a brushed surface heat exchanger underestimated about 8 times our results obtained with ethanol solution freezing inside a scraped surface heat exchanger. Therefore it appeared that only the specific correlations proposed can be used to design scraped surface heat exchangers for freezing of ethanol-water mixtures (widely used as secondary diphasic refrigerant) or sucrose solutions (major component of ice creams). 4. Conclusion Different parameters influence the heat transfers inside a scraped surface heat exchanger used for freezing of aqueous solutions: blade rotation speed and solute concentration have the major effect. A permanent ice layer is formed between the blade extremity and the wall only when the
M.B. Lakhdar et al. / Applied Thermal Engineering 25 (2005) 45–60
59
gap is high enough (more than 1 mm). The phenomena complexity (water crystallisation inside a solution, ice crystal removal from the wall, mixing effect of the blades) explains certainly that specific correlations have to be used for each kind of exchanger (brushed vs. scraped) and solute (ethanol vs. sucrose). Nevertheless, the proposed correlations can be used, at least as a first approach, for the most common freezing applications of scraped surface heat exchanger i.e. ice creams (which are derived from sucrose solutions) and two-phase secondary refrigerants (which are principally ethanol solutions).
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