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Study of the drying process of wetted surfaces under conditions similar to food processing conditions
Accepted Manuscript Title: Study of the drying process of wetted surfaces under conditions similar to food processing conditions Author: L. Lecoq, D. Flick, O. Laguerre PII: DOI: Reference:
S0140-7007(17)30215-3 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.05.024 JIJR 3655
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
16-12-2016 21-5-2017 22-5-2017
Please cite this article as: L. Lecoq, D. Flick, O. Laguerre, Study of the drying process of wetted surfaces under conditions similar to food processing conditions, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.05.024. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Study of the drying process of wetted surfaces under conditions similar to food processing conditions
L. Lecoq ab*, D. Flick b, O. Laguerre a a
b
Irstea, UR GPAN, 1 rue Pierre-Gilles de Gennes, 92761 Antony, France
, UMR Ingénierie Procédés Aliments, AgroParisTech, INRA, Université Paris-Saclay, 91300 Massy, France
Highlights:
The experimental results showed the importance of relative humidity on evaporation
Influence of relative humidity was compared to air temperature and velocity
The use of a dehumidifier can double the evaporation rate of water on a wet floor
Models were developed to predict the water mass evolution
Good agreement was found between the models and the experimental data
ABSTRACT Two experiments were carried out inside a test room in order to study the drying rate of wetted surfaces under conditions similar to those encountered in food processing plants.. In the first experiment, the evaporation of water droplets on a stainless steel plate representing typical equipment was studied under different ambient conditions in the room. In the second experiment, in order to reproduce drying conditions inside a food processing plant, the floor was entirely *
Corresponding author: Tel: 33 1 40 96 90 04, Fax: 33 1 40 96 60 75, E-mail: [email protected] 1 Page 1 of 40
wetted with water, the water mass evolution was measured when the discharge air was dried by a dehumidifier, and the results were compared with those obtained without using a dehumidifier. Models predicting the evaporation rate in these two experiments were developed and the numerical results show good agreement with the experimental data. Relative humidity was the factor which exerted the greatest influence on the evaporation rate. The drying rate on the stainless steel plate increased five-fold when a dehumidifier was used. Keywords: evaporation, droplet, water film, model, drying
Nomenclature Saturated water vapor concentration kg.m-3 Water vapor concentration in the air
kg.m-3
h
Overall heat transfer coefficient
W.m-2.K-1
hc
Convective heat transfer coefficient
W.m-2.K-1
hr
Radiative heat transfer coefficient
W.m-2.K-1
k
Mass transfer coefficient
m.s-1
m
Water mass
kg
Evaporation rate
kg.s-1
M
Molar mass
kg.mol-1
mCp
Thermal inertia
J.K-1
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RH
Relative humidity
%
r
Droplet radius
m
R
Ideal gas constant
J.K−1.mol−1
S
Total surface of the plate
m²
T
Temperature
°C
t
Time
s
X
Water content in the air
kgwater.kgdry air-1
Liquid/solid contact angle
°
Receding angle
°
Wet surface compared with total surface
Dimensionless
αr
Spherical cap surface compared with total surface
ΔHv
Dimensionless
Emissivity
Dimensionless
Latent heat of water evaporation
J.kg-1
Subscripts a
air
0
initial
pl
plate
w
water
wb
wet bulb
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1. Introduction In a food processing plant, cleaning and disinfection are performed daily in order to prevent microbial growth. However, certain bacteria such as Listeria monocytogenes still persist even where best disinfection practice (Muhterem-Uyar et al. 2015, Vogel et al. 2001) is applied. In order to make this operation as efficient as possible, complete drying of the room must be performed. In practice, during cleaning and disinfection, a lot of water is used, and remaining water will allow bacteria to survive (Carpentier & Cerf 2011, Zoz et al. 2016). Several studies have been carried out with a view to improving cleaning and disinfection. However, drying is still performed empirically. The use of an air drying device (dehumidifier) in a food processing plant in order to enhance the drying process by lowering the relative humidity in the room has rarely been studied. In order to control food safety, knowledge of the evaporation phenomenon on a solid surface is necessary. Evaporation is endothermic and is therefore influenced by heat transfer in the liquid phase and at the liquid/vapor interface (Mozurkewich 1986). The evaporation rate depends on the relative humidity, the air and surface temperatures and the air velocity in the vicinity of the surface (D'agaro et al. 2006, Navaz et al. 2008, Raimundo et al. 2014, Vik & Reif 2011). The evaporation of the water droplet is also influenced by its geometry (radius, contact angle). For the same water mass, a smaller contact angle induces a larger base radius decrease, which in turn increases the exchange between the solid surface and the liquid. In the case of a heated surface, evaporation will be faster (Chandra et al. 1996). The evaporation of a droplet may be divided into two periods (Chandra et al. 1996, Yu et al. 2015) called “pinned” and “unpinned” periods. During the first (“pinned”) period, the droplet radius remains constant while the contact angle decreases and the evaporation rate is almost 4 Page 4 of 40
constant. During the second (“unpinned”) period, the opposite phenomenon can be observed: the droplet radius decreases while the contact angle remains constant. The transition from the first to the second period depends on the contact angle. Once this parameter reaches a value called the “receding angle”, the second period begins. This value depends on the combined material/liquid surface. For a water droplet on a stainless steel surface, it is about 10° (Chandra et al. 1996). Most of the models described in the literature focus on the first period alone (Hu & Wu 2015). Navaz et al. (2008) proposed a semi-empirical model to predict water mass during the evaporation of a chemical component on a solid surface. Several authors consider water vapor diffusion in stagnant air alone, while others include conjugated heat transfer and free convection (Hu & Larson 2002, Yang et al. 2014). Experimentation in a food plant is complicated. For example, the time available for the installation of sensors is short, and the number of measuring positions is limited in order to disrupt work conducted by the staff to the least possible extent. Moreover, it is usually not possible to repeat experiments, and permission from the company is necessary should it be necessary to repeat experiments. This means that interpretation of the results is more complicated and some data could be missing. The aim of this study was to reproduce the conditions (temperature, relative humidity, velocity and water mass) during the drying process inside a chilled food processing plant on a laboratory scale (test room) in which conditions are better controlled. Evaporation of water on two surfaces was studied: a non-heated stainless steel plate (to represent evaporation on equipment in a food processing plant), and the floor of the test room. The influence of an air dehumidifier on the drying rate was analyzed. The model developed in this study is based on heat and mass balances and enables prediction of the water mass evolution. This model was validated by comparing the 5 Page 5 of 40
results obtained with the experimental data, and then the model was used to predict the drying time according to room conditions, and technical solutions designed to enhance drying were proposed. 2. Experimental conditions 2.1. Test room The experiments were carried out in a test room (Figure 1a). The dimensions of this room were 3.6 m long, 3.6 m wide and 2.5 m high (32.4 m3). The temperature and relative humidity in the room were controlled using an evaporator and a dehumidifier located in the ceiling. The discharge air velocity was adjusted using a variable frequency drive. This figure also shows the locations of temperature and relative humidity measurements in the room. Two types of experiments were performed: - The first one in which the evaporation rate of water droplets deposited on a stainless steel plate exposed to different ambient conditions was measured. The position of the plate is shown in Figure 1b. This experiment represents water evaporation on equipment used in a food processing plant. - The second one in which the entire surface of the floor was wet, representing the highest water load location after the cleaning of a food processing plant. 2.2. First experiment: droplets on a stainless steel plate A stainless steel plate (the most common equipment material, 0.5 m x 0.5 m x 10-3 m) was insulated using a 10-cm layer of polystyrene placed underneath it. This insulation allows heat exchange with the air on the upper side of the plate alone, thus facilitating the interpretation of 6 Page 6 of 40
the results obtained. The plate was placed inside the test room, then 0.5 mL water droplets (average diameter ~ 0.8 cm) were deposited on this plate using a pipette. Two numbers of droplets were deposited: 50 (percentage of initial wet surface, β0, about 10%) and 100 (β0, about 20%). These percentages are usual for equipment after cleaning in the food plant (Lecoq et al. 2016). The precise percentage of initial wet surface was determined using a camera and image treatment (ImageJ software). During the experiments, the following parameters were measured: -
Weight of the wetted plate using a balance (± 0.001 g precision) and recorded by a data logger (Agilent 34970A) every 10 s until all the water evaporated.
-
Air temperature recorded every 10 s using calibrated T-type thermocouples (1 mm diameter, ± 0.2°C precision). The air temperature at different positions was measured: discharge, return air and 10 cm above the plate. The plate temperature was measured at the center and at the 4 corners of the plate, and the average value of these measurements was reported.
-
Relative humidity in the room using calibrated TESTO 174H hygrometers (± 3% precision), recorded every minute.
-
Air velocity using a hot wire anemometer (TESTO 435-2, range of measurement 0-20 m.s-1, ± 0.03 m.s-1 precision). The measurement was carried out at 3 positions at the air return of the evaporator to determine the inlet air velocity (Figure 1.b). The reported air velocity is an average value calculated from 60 measurements (recorded every 1 s over a period of 1 min).
The influence of the relative humidity of the air (from ~30% to 90%), the temperature (from 5 to 20°C), the velocity (from 2 to 4.8 m.s-1), the position of the plate in the room, the
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percentage of initial wet surface (from 7 to 28%) and the nature of the surface were studied. The experimental conditions are shown in detail in Table 2 (Section 4.1).
2.3. Second experiment: floor entirely wet The initial temperatures (air and walls) were set at 20°C in the laboratory test room. Then, the thermostat temperature was set at 5°C and the discharge air velocity at 2.0 m.s-1. The initial relative humidity measured experimentally ranged from 40 to 50%. The influence of the initial water mass on the floor was studied: -
230 g.m-² of water (total mass ~3 kg) was deposited, corresponding to approximately the amount of water remaining after cleaning inside a plant
-
80 g.m-² of water (total mass ~1 kg) was deposited, corresponding to approximately the amount of water on the surface after using a squeegee to partially remove water.
During the experiment, the following parameters were measured until all of the water was evaporated: -
Water mass. The measurements were carried out using paper towelettes to wipe the entire surface of the floor and then weighing them using an electronic balance (Sartorius, CPA34001P, ± 0.1 g). The water mass on the floor was measured at different times in order to follow its evolution during drying. In the case of 230 g.m-² water deposited initially on the floor, the experiments were carried out 5 times with the dehumidifier turned “on” by wiping the floor at 30 min, 1 h, 3 h, 5 h and 10 h after the beginning of the experiment and 7 times with the dehumidifier turned “off” by wiping the floor at 30 min, 1 h, 3 h, 5 h, 10 h , 16.33 h and 20 h. In order to avoid to the greatest possible extent 8 Page 8 of 40
variability of the results due to the modus operandi, the same procedure used for water application on the floor was performed by the same person. -
The temperature, relative humidity and velocity of the air were measured in the same manner as that used for the first experiment and the measuring positions are shown in Figure 1a.
In order to study the influence of a dehumidifier on the drying time, the experiments were performed when the dehumidifier was “on” and when it was “off”. For the experiment with the dehumidifier turned “on”, the relative humidity set value was 50% during the experiment. The characteristics of the dehumidifier are shown Table 1. 2.4. Convective heat transfer coefficient Knowledge of the heat transfer coefficient is necessary for the evaporation model development (Section 3). An experiment was carried out in order to determine its value using a fluxmeter equipped with a thermocouple (trade name Captec, width x length x depth: 4 cm x 4 cm x 450 µm, surface area = 1.6 x 10-3 m2). This fluxmeter was supplied with 10 W of heating power (Q). The fluxmeter temperature (Tf), the air temperature (Ta) measured at 5 cm from the surface of the fluxmeter and the measured flux were recorded every second until a steady state was obtained. Then, the mean values were calculated over 20 min. of a stabilization period allowing evaluation of the heat transfer coefficient h,
. It should be noted that the emissivity of
this fluxmeter is close to zero; thus, the radiative exchange can be neglected. In the first experiment, the fluxmeter was placed on the plate in 5 positions (at the 4 corners of the plate and in the center) and the average value was calculated. The different convective heat
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transfer coefficient values corresponding to different air inlet velocities from the evaporator (2.0, 3.0, 4.0, 4.8 m.s-1) or positions in the room (A, B, C, D) are presented in Table 2 (Section 4.1). In the second experiment, the fluxmeter was placed successively in 7 different locations on the floor (in the 4 corners of the room, in the center and 2 others positions in the symmetry plane). The average value was used in the model.
3. Evaporation models In order to predict the water mass evolution, models were developed for water evaporation on a stainless steel plate and for water evaporation on the floor of a test chamber. These models were validated with the experimental data. 3.1. Evaporation of water droplets on the stainless steel plate 4.1.1. Model development When a droplet deposited on a plate is exposed to air, the phenomena involved are convection, radiation and evaporation (Figure 2). The model development is based on heat/mass balances and Lewis analogy. The heat exchange between the plate and the air is related to the water evaporation ( ) and can be expressed as follows:
The evaporation rate ( ) depends on the difference between the water content in the air in equilibrium with the droplets, Csat(Tpl) and the water content in the room Cwa :
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where
is the spherical cap surface of the droplets on the surface of the plate
and Cwa =RH Csat(Ta) Because of the low thickness of the stainless steel plate (10-3 m) and the high thermal conductivity (26 W.m-1K-1), it is assumed that the thermal inertia of the plate is negligible and the thermal conductivity of the plate is infinite. The heat transfer coefficient (h) can be expressed as the sum of the convective heat transfer coefficient (hc) and the equivalent radiative heat transfer coefficient (hr). Even if the surface considered is stainless steel with a low emissivity (0.1), the water on the surface has a high emissivity (0.95) and can induce non-negligible heat transfer through radiation. Thus:
Indeed, the heat exchange by convection can be expressed as through radiation can be approximated by
and heat exchange
where
. The values of the convective heat transfer coefficient (hc) shown in Table 2 were used for the simulation.
The mass transfer coefficient k is calculated using the Lewis analogy:
with
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where
is the thermal diffusivity of air =
of water vapor in air =
m².s-1 at 0°C and
is the mass diffusivity
m².s-1 at 0°C (Bimbenet et al. 2002).
, the saturated vapor concentration, is a function of the temperature which can be estimated by a quadratic equation:
By using data in a humid air diagram to fit this equation, the values of a, b and c were identified. For 0°C
kg.m-3,
kg.m-3.°C-1 and
kg.m-3.°C-2 . It is convenient to introduce the wet bulb temperature Twb which corresponds to the case in which the plate is entirely covered by water (β=βc=1), and for negligible radiation (high hc value), Twb is defined by:
The expression of the plate temperature Tpl can be deduced from Equations 1 to 6 (the equation development is reported in the appendix):
where
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,
Using (1) and (7) the evaporation rate
can be calculated as follows:
3.1.2. Evolution of the wet surface coefficient: β The plate temperature (Tpl) and thus the evaporation rate ( ) depend on the ratio between the spherical cap surface and the total surface of the plate (βc). The evolution of this coefficient must be known in order to predict the water mass evolution during the entire evaporation process. In the case of water droplets on a stainless steel plate, the evaporation process is composed of two periods. During the first period: The ratio between the wet surface and total surface β is constant (= β0) (the droplet radius remains constant) and the contact angle between the water and the plate decreases progressively. The experimental value of β0 was obtained using a camera. The ratio between the spherical cap surface of the droplet and the plate (βc) can be calculated using Equation (9):
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In our case, the initial contact angle of water on stainless steel is rather low (α0~15°). Thus, the spherical cap surface of the droplets is close to the wet surface:
. Even in the experiment
with a stainless steel plate covered by a more hydrophobic surface (Experiment 8, see Table 2) the wet surface is close to the spherical cap surface. The initial contact angle was around 45°, which makes the spherical cap surface only 1.17 times higher than the wet surface ( ). The use of β (instead of βc) to calculate the plate temperature and the evaporation rate will not significantly impact the results.. During the second period: This period begins when the contact angle reaches the receding angle (αr =10° for water on stainless steel) which corresponds to the moment when the water mass reaches 15% of its initial value
(Doursat et al. 2016) (submitted). During this period, the contact angle
remains constant ( = 10°) and the ratio of wet surface β decreases (the droplet radius decreases). In addition, the water mass of a droplet deposited on a surface is equal to:
and the relationship between the wet surface and the droplet radius is given by:
From Equation (10), it can be seen that
is proportional to the water mass to the power of 2/3.
Therefore, from Equations (10) and (11) it can be seen that the wet surface (Sw) is also proportional to the water mass to the power of 2/3 and the evolution of β during the second period of the evaporation process can be expressed by the following equation: 14 Page 14 of 40
During the second period, the plate temperature increases because of the diminution of the wet surface and the evaporation rate decreases. This temperature reaches the air temperature when the plate is completely dried. Generalization of β equation for both the first and second periods: The
coefficient during these two periods can be expressed as follows:
Using Equations (7), (8) and (13), the water mass evolution during the entire evaporation process (periods 1 and 2) can be predicted. 3.2. Model development for the evaporation on an entirely wet floor In the case of a floor wetted by water, the heat and mass exchanges between the air and the floor can be expressed as follows:
where T is the floor temperature and m is the water mass on the floor. In this case, the thermal inertia of the surface (floor) is not negligible.
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To solve Equations (14) and (15), the numerical values of the convective coefficient h, the thermal inertia of the floor 0
and the initial percentage of wet surface over the total surface
are shown in the results (see Section 4.2.3.). The air temperature
, initially at 20°C,
decreases and tends to drop to the thermostat temperature (5°C) during the process. Its evolution, measured experimentally (at the evaporator return air inlet), is used as an input parameter of the model. Also, the evolution of the vapor concentration in the air
is
calculated from the experimental data (relative humidity and air temperature at the evaporator return air inlet). The saturated water vapor concentration
depends on the surface
temperature alone and can be calculated using Equation (5). Equations 7, 8, 13 (first experiment) or 13, 14, 15 (second experiment) were implemented using MATLAB software (vR2012a, MathWorks Inc., Natick, MA, USA, Euler method).
4. Results and discussion 4.1. First Experiment: droplets on a stainless steel plate Figure 3 shows the experimental evolution of the water mass during evaporation at 5.5°C, with a relative humidity of 31%, a convective heat transfer coefficient on the plate equal to 10.1 W.m2
.K-1 and with an initial wetted surface of 23% of the total surface (Experiment 1 in Table 2). The
two periods of evaporation can be observed in this figure: -
First period during which the evaporation rate is almost constant (decreasing contact angle, constant droplet radiuses),
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-
Second period during which the evaporation rate decreases (constant contact angle, decreasing droplet radiuses).
The evaporation rate for the first period is calculated from the slope for which the water mass evolution is linear (Figure 3). The same method was used to calculate the evaporation rate for all the studied conditions, and the values are reported in Table 2. 4.1.1. Analysis of factors that influence the evaporation rate The maximum and minimum evaporation rates under different experimental conditions (Table 2) and the ratio of these values are reported in Table 3. It can be observed that the relative humidity has the greatest impact on the evaporation rate within the ranges of conditions studied. When the relative humidity varies from 87% to 31%, the evaporation rate increases by a factor 5.2, whereas when other parameters are varied it increases by a factor 2.3 at the most. Therefore, it is obvious that reducing the relative humidity by using a dehumidifier is an efficient way of significantly increasing the evaporation rate and thus reducing the drying time. Indeed, inside a food processing plant where no dehumidifier is installed, the relative humidity is often above 85% (Lecoq et al. 2016), which is very unfavorable for drying. It can be seen from this table that when the stainless steel plate was covered with plastic film (Experiment 8 in Table 2), the wet surface was lower (β0 =10%) compared with that of the stainless steel without a plastic film (β0 ~23%) under the same conditions (initial water mass, ambient conditions and plate position in the room, Experiment 1 in Table 2). Thus, the exchange surface between the droplet and the air was lower, which induced a lower evaporation rate.
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4.1.2. Comparison between models and experimental data The experimental data for the evaporation rate during the first period were first compared with two models: -
The evaporation model based on heat and mass balances presented in Section 3 and considered as theoretical.
-
An empirical model developed in a previous study (Lecoq et al. 2017) ; the following equations are presented:
The evaporation rate comparison between the results from the empirical model and the experimental data is shown in Figure 4a. The comparison shows rather good agreement with an average relative error
of 16 %.
The evaporation rate comparison between the results from the theoretical model (Equations. 7 and 8) and the experimental data is shown in Figure 4b. The comparison shows better agreement than with the empirical model, with a relative error of 9%. The experimental water mass evolution during the entire process (periods 1 and 2) can also be compared with the prediction of the two models (using Equations (13), (7) and (8) for the theoretical model or Equations (13), (16) and (17) for the empirical model). Figure 5 presents a comparison of the water mass evolution under different air relative humidity conditions (RH =31, 70, 87%) for an air temperature of 5.5°C. 18 Page 18 of 40
The results for the water mass evolution during periods 1 and 2 of the evaporation process (first r = constant then α = constant) are in good agreement using the theoretical equations (Figure 5), whereas the empirical model tends to slightly overestimate the evaporation rate. In the configuration studied (evaporation of water on a non-heated stainless steel plate, negligible thermal inertia and very high conductivity) this model can be applied to predict the water mass evolution as a function of the ambient conditions during the entire process and therefore to predict the drying time. This model can be applied to other materials or liquids. If the values of the initial and receding angles are known, the threshold ratio (15% for stainless steel) could be estimated in order to modify Equation (13). Equations (7) and (8) can be applied if the thermal inertia of the material is negligible and the thermal conductivity is high. Of course, the convective heat transfer coefficient which depends on the ventilation and location in the room has to be known, this can be measured quite easily using a heating flux meter. 4.1.3. Optimization strategy In order to reduce the drying time of water droplets deposited on equipment, it would be interesting to quantify the influence of an increase of airflow rate, a decrease of relative humidity or a rise of air temperature on the energy cost. Therefore, for a given mass of residual water (given value of c), the relative increase of evaporation rate: (in comparison with a reference case) developed using eq. 8, can be expressed as follows:
m ref m
h
T a T pl
(18)
h ref T a . ref T pl . ref
The differentiation of eq. 18 gives:
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h d d h ref
d T a T pl T a . ref T pl . ref
(19)
By neglecting the radiation, the heat transfer coefficient can be assumed to be proportional to the square root of the local velocity (Incropera and DeWitt, 1996), which is in turn, proportional to the air flow rate (eq. 20). h 1 V d d h ref 2 V ref
(20)
Differentiation of eq. 6 after substitution by eq. 5 leads to eq. 21:
d T a T pl A .d 1 HR B .d T a
Where A=
a bT
h 2 cT a . ref / b 2 cT pl . ref k H v c
a . ref
B= b 2 cT pl .ref
HR
ref
b cT
a . ref
/
h
c k H v
(21)
b 2 cT pl . ref
By substituting eq. 20 and 21 in eq. 19, the following equation is obtained: d
1 V A d 1 RH B d T a d 2 V ref
(22)
Eq. 22 allows the estimation of the influence of V , RH and Ta as follows : For a typical reference case without air dehumidifier, T pl.ref 4 . 5 C
T a . ref 5 C ,
RH
ref
90 %,
c 0 .5,
can be defined. In this case, the value of A is 10 (dimensionless) and B is 0.044 °C-1.
This means that: -
increasing the flow rate of 1% leads to increase drying rate of 0.5%,
-
reducing the relative humidity from 90% to 89% (increasing 1-RH by 1%) increases drying rate by 10%
-
increasing air temperature by 1°C increases drying rate by 4.4% 20 Page 20 of 40
It is to be reminded that, increasing air temperature has a favorable effect not only on drying, but also on refrigeration power because the heat losses are reduced. However, air temperature has detrimental effect on bacterial growth, so Ta should not be too high to assure the sanitary requirement. One way to increase drying rate is to improve ventilation. Increasing flow rate will increase the mechanical ventilation power W v p v V with a pressure drop almost proportional to the square of the flow rate (for turbulent flow). In addition this power will be converted into heat which has to be removed from the room. This means that the improve ventilation to increase to the drying rate by 1% can leads to the increase of electric power for more than 6% compared to the reference case. The other way to increase drying rate is to reduce relative humidity, for example, by using an electric adsorption/desorption dehumidifier. The desorption enthalpy is slightly higher than the heat of vaporization. In addition, the air is heated by passing through the dehumidifier. Inversely, less water is condensed on the heat exchanger which reduces the refrigeration power. To increase by 1% the drying rate, the relative humidity needs to be reduced by only 0.1%. This leads to an additional electric power of dehumidifier which can be roughly estimated as: H vV C sat T a d HR . To summarize, the choice of improving drying rate by increasing air flow rate or using a dehumidifier can be done by comparing 6 p v with 0.1 H v C sat . Since pv is often 300 Pa, 6 p v (1800 Pa) is the same order of magnitude of 0.1 H v C sat (1700 Jm-3 or Pa) for air at 5°C. In this case, increasing ventilation or using a dehumidifier is almost equivalent. However, it should be reminded that a too high air flow rate is detrimental for the comfort of the employees. For 21 Page 21 of 40
technical reasons, it is certainly easier to reduce relative humidity from 90% to 80% than to increase the air flow rate by a factor of 4 in order to double the drying rate. This illustrates quantitatively the interest of a dehumidifier.
4.2. Second Experiment: Floor entirely wet 4.2.1. Water mass evolution Figure 6 presents the experimental evolution of the water mass on the floor when the dehumidifier was “on” and when it was “off”. It can be observed that about 80% of the initial water is evaporated after three hours in the experiment with an initial mass of 230 g.m-2 and after one hour with an initial mass of 80 g.m-2. During these periods, the evaporation rate is almost the same in both cases (with the dehumidifier “on” or “off”). The impact of the dehumidifier is more obvious for the remaining 20% of water on the floor. In the experiments during which the dehumidifier was turned off, a small amount of water (1.8 g.m-2) was still present after 20 hours during the experiment with an initial water mass of 230 g.m-2. This water was located above all in the corners of the test room where convection is lower or in areas where the floor is slightly convex and induces water accumulation. In these areas, if the relative humidity is high, which is the case when the dehumidifier is off (RH~90%), evaporation of the remaining water will take much longer, as can be seen in Figure 6. With the dehumidifier turned “on”, almost no water remains after 10 hours of drying. 4.2.2. Water content The evaporation rate evolution
(with the dehumidifier turned “on” or “off”) can be assessed by
estimating the difference between the water content of the air in contact with the floor (saturation
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value at floor temperature): inlet):
and the water content in the room (at the evaporator return air
.
Indeed, (23) Using the experimental data on the air temperature and relative humidity at the return air inlet of the evaporator and on the floor temperature,
and
were calculated (Figure 7).
The difference in water content between the air near the floor (at saturation) and the room (at the return air inlet) is a determining factor for the evaporation rate: the higher this difference, the greater the evaporation rate. This difference is quite similar at the beginning of drying (first two hours) for both cases (dehumidifier “on” and “off”) and for both the initial water masses of 80 g.m-2 and 230 g.m-2. This explains why the evaporation rate and the water mass evolution are very similar during this period. After the first two hours, the water content decreases in the case where the dehumidifier is turned “on”. For the initial mass of 230 g.m-2 of water, the water content in the air could not be reduced immediately because the dehumidification capacity of the dehumidifier is rather low (0.6 kg.h-1). During the first two hours, about 93 g.m-2 of water evaporated (a total of 1.2 kg of water). Part of this water was removed by the dehumidifier and part was removed by the evaporator. Once most of the water has evaporated, the dehumidifier was able to decrease the water content in the air, and this induced a water content difference (between the floor and the return air) twice as high as
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when the dehumidifier was turned off (Figure 7b at 10 h). This explains the higher evaporation rate when the dehumidifier was turned “on” during this period. 4.2.3. Comparison between the numerical and experimental data The water mass and the floor temperature evolution predicted by the developed model were compared with the experimental data (Figure 8). For this simulation, the following numerical values were used: h=10 W.m-2.K-1,
J.K-1,
and
It is to be highlighted that even though water was spread all over the floor, if it is not perfectly flat, and accumulates as puddles in the slightly convex locations. The initial water distribution on the floor is therefore lower than 1 (
. If the floor had been entirely flat (
,
evaporation would have been much faster (explained in Section 4.1.1.). In this model, the following equation, developed by fitting the experimental results, was used to describe its evolution:
The floor temperature is well estimated by the model considering that that the experimental temperature was measured at several locations on the surface, whereas the model considers an average value. For the water mass evolution, the numerical results are also in good agreement with the experimental data. Because of the longer evaporation time in the case of the 230 g.m-2 initial water mass, the difference between the experiments with the dehumidifier turned “on” and “off” is more obvious.
24 Page 24 of 40
4.2.4. Numerical study of the influence of the water distribution on the floor To underscore the impact of the initial water distribution on evaporation, another simulation was performed to compare the cases of
and
(with the same initial water mass: 230
g.m-2 and the dehumidifier “on”). It can be observed in Figure 9 that if the water distribution is uniform and covers the entire surface (
, low water film thickness), evaporation is faster
than in the case of water concentrated in some locations (
, higher water film thickness).
This simulation result leads to the conclusion that to enhance evaporation inside a food processing plant, particularly on the floor, its flatness and roughness are as important as the relative humidity. If the floor is damaged, water can accumulate and drying within two hours (average drying time in the food processing plant) will be impossible even when the dehumidifier is turned “on”. This remaining water can promote bacterial growth.
5. Conclusion Two experiments were performed in order to study the evaporation of water under conditions close to those encountered in a food processing plant. The first experiment represents the evaporation of water droplets on equipment (stainless steel plate). The most important parameter influencing the evaporation rate in the ranges studied is the relative humidity. When the relative humidity was reduced from 87% to 31%, evaporation rate was multiplied by a factor of 5.2. In order to enhance evaporation, relative humidity should therefore be controlled. A theoretical model was developed in order to predict the water mass evolution with good accuracy.
25 Page 25 of 40
The second experiment represents the evaporation on an entirely wet floor (with initial masses of 230 gwater.m-2 or 80 gwater.m-2) where the initial temperature (20°C) and the thermostat temperature (5°C) were set at the values used in a chilled food processing plant. The influence of a dehumidifier was studied. It was observed that without a dehumidifier, the water evaporation rate is low throughout the process, which makes complete drying impossible within an acceptable duration. When a dehumidifier is running, the water content in the air can be maintained at a rather low level which significantly enhances evaporation. In this case, complete drying can be achieved more rapidly. Because of the low capacity of vapor absorption (0.6 kg water.h-1) of the air dehumidifier used in our study, a significant influence of the dehumidifier can be observed only when 80% of the initial water has evaporated. In addition, the developed model for the evaporation of water on the floor shows that the smoothness of the surface exerts a significant influence on water distribution and thus on the evaporation rate. If water accumulates in certain locations where the floor is damaged or poorly designed, water will remain even after several hours of drying and will promote microbial growth. ACKNOWLEDGEMENT The research leading to this result has received funding from the French National Research Agency (EcoSec Project, ANR-12-ALID-0005-04). REFERENCES Bimbenet J.-J., Duquenoy A., Trystram G. 2002. Génie des procédés alimentaires : Des bases aux applications. Carpentier B., Cerf O. 2011. Review — Persistence of Listeria monocytogenes in food industry equipment and premises. International Journal of Food Microbiology 145: 1-8 Chandra S., Marzo M. d., Qiao Y. M., Tartarini P. 1996. Effect of liquid-solid contact angle on droplet evaporation. Fire Safety Journal 27: 141-58 D'agaro P., Croce G., Cortella G. 2006. Numerical simulation of glass doors fogging and defogging in refrigerated display cabinets. Applied Thermal Engineering 26: 1927–34 26 Page 26 of 40
Doursat C., Lecoq L., Laguerre O., Flick D. 2016. Droplet evaporation on a solid surface exposed to forced convection: experiments, simulation and dimensional analysis. Unpublished results, submitted to International Journal of Heat and Mass Transfer Hu D., Wu H. 2015. Numerical study and predictions of evolution behaviors of evaporating pinned droplets based on a comprehensive model. International Journal of Thermal Sciences 96: 149-59 Hu H., Larson R. G. 2002. Evaporation of a sessile droplet on a substrate. J. Phys. Chem B. 106: 1334-44 Incropera F.P., DeWitt D.P., 1996. Fundamentals of Heat and Mass Transfer, John Wiley & Sons, INC. 4ème edition, New York, Chapter 6 and 9, 886 p. Lecoq L., Flick D., Derens E., Hoang H. M., Laguerre O. 2016. Simplified heat and mass transfer modeling in a food processing plant. Journal of Food Engineering 171: 1-13 Lecoq L., Flick D., Laguerre O. 2017. Study of the water evaporation rate on a stainless steel plate under controlled conditions. International Journal of Thermal Sciences 111: 450–462 Mozurkewich M. 1986. Aerosol growth and the condensation coefficient for water: a review. Aerosol Science and Technology 5: 223-36 Muhterem-Uyar M., Dalmasso M., Bolocan A. S., et, al. 2015. Environmental sampling for Listeria monocytogenes control in food processing facilities reveals three contamination scenarios. Food Control 51: 94–107 Navaz H. K., Chan E., Markicevic B. 2008. Convective evaporation model of sessile droplets in a turbulent flow—comparison with wind tunnel data. International Journal of Thermal Sciences 47: 963-71 Raimundo A., Gaspar A., Oliveira A. V. M., Quintela D. 2014. Wind tunnel measurements and numerical simulations of water evaporation in forced convection airflow. International Journal of Thermal Sciences 86: 28-40 Vik T., Reif B. A. P. 2011. Modeling the evaporation from a thin liquid surface beneath a turbulent boundary layer. International Journal of Thermal Sciences 50: 2311–17 Vogel B. F., Huss H. H., Ojeniyi B., Ahrens P., Gram L. 2001. Elucidation of Listeria monocytogenes contamination routes in cold-smoked salmon processing plants detected by DNA-based typing methods. Appl. Environ. Microbiol. 67: 2586–95 Yang K., Hong F., Cheng P. 2014. A fully coupled numerical simulation of sessile droplet evaporation using Arbitrary Lagrangian–Eulerian formulation. International Journal of Heat and Mass Transfer 70: 409-20 Yu D. I., Kwak H. J., Doh S. W., Kang H. C., Ahn H. S., Kiyofumi M., Park H. S., Kim M. H. 2015. Wetting and evaporation of water droplets on textured surfaces. International Journal of Heat and Mass Transfer 90: 191-200 Zoz F., Iaconelli C., Lang E., Iddir H., Guyot S., Grandvalet C., Gervais P., Beney L. 2016. Control of Relative Air Humidity as a Potential Means to Improve Hygiene on Surfaces: A Preliminary Approach with Listeria monocytogenes. Plos One 11 (2): e0148418
APPENDIX: Development of Equation 7 From Equations (1), (2) and (5), it follows that:
27 Page 27 of 40
From Equations (6) (wet bulb) and (5) the following is obtained:
Eliminating
Introducing
c’
between Equations (25) and (26), Tpl can be related to
by:
, Eq. (27) becomes:
b’
a’
the solution of which is:
28 Page 28 of 40
Dehumidifier Evaporator 3.6 m Exterior 2.5 m Symmetry plane
3.6 m Airflow pattern in the room Airflow pattern from the dehumidifier Positions of the air temperature and relative humidity sensors Positions of the floor temperature sensors a 3.6 m
Evaporator
C
B
A
3.6 m
Positions of the stainless steel plate (~40cm above the floor): A (reference position), B, C and D
1m Air velocity measurements
D Top view
b
29 Page 29 of 40
Figure 1: (a)- Airflow patterns in the test room equipped with a dehumidifier (b)- Top view of the test room showing the different positions of the stainless steel plate used when the water evaporation experiments were performed
Figure 2: Schematic view of one droplet on the plate
30 Page 30 of 40
50 45
Water mass (g)
40 35 30
First period
25 20 15
Second period
10 5 0 0
100
200
300
Time (min)
400
500
Figure 3: Experimental water mass evolution during evaporation (Ambient conditions: Ta = 5.5°C, RH = 31%, h c= 10.1 W.m-2.K-1, β0 = 23%).
31 Page 31 of 40
Evaporation rate (empirical formula) (g.s-1)
0.005
20.2°C 0.004
Different RH Different air velocity
10.4°C
Different Ta 0.003
C
B A, RH=31%
Different Beta Different V and RH
D
0.002
Different RH and Ta
RH=70% 0.001 RH=90% β=7.7 % 4.8 m.s-1 4.0, 3.0 and 2.0 m.s-1 0 0
0.001
0.002
Different position with plastic cover 0.003
0.004
0.005
Experimental data evaporation rate (g.s-1)
a 20.2°C
Theorical evaporation rate (g.s-1)
0.005
Different RH
Different air velocity
0.004
10.4°C
Different Ta
0.003
Different Beta C
0.002
D
B A, RH=30%
Different V and RH Different RH and Ta
0.001
0
RH=70% β=7.7 % RH=90% 4.8 m.s-1 4.0, 3.0 and 2.0 m.s-1 0
0.001
0.002
Different position with plastic cover 0.003
0.004
0.005
Experimental evaporation rate (g.s-1)
b Figure 4: Evaporation rate comparison (1st period) between the experimental data and a- the empirical model; b- the theoretical model.
32 Page 32 of 40
Figure 5: Water mass evolution during evaporation (periods 1 and 2): comparison between the empirical model, the theoretical model and experimental data.
33 Page 33 of 40
90
250
70 60
Water mass (g.m-2)
Water mass (g.m-2)
80
dehumidifier « off »
50 40
dehumidifier « on »
30 20
200
dehumidifier « off »
150
dehumidifier r « on »
100 50
10 0
0 0
1
2 time (hours)
a
3
4
5
0
5
10
15
20
time (hours)
b
Figure 6: Experimental water mass evolution on the floor when the dehumidifier was “on” (blue curve) and when the dehumidifier was “off” (red curve) a- initial water mass: 80 g.m-2, b- initial water mass: 230 g.m-2
34 Page 34 of 40
16 14 10 8 6
X gw.kgdryair-1
air return - dehum. "on"
12
air return - dehum. "off"
10
air return - dehum. "on"
8 6
4
4
2
2
0
0 0
1
2 3 Time (hours)
4
floor
14
air return - dehum. "off"
12
X gw.kgdryair -1
16
floor
5
0
5
10 15 Time (hours)
a
20
b
Figure 7: Calculated evolution of the water content of the air in contact with the floor (saturation) and in
the
evaporator return
air,
with
the dehumidifier
turned “on” or
“off”.
a- initial water mass: 80 g.m-2, b- initial water mass: 230 g.m-2.
35 Page 35 of 40
a (1)
b (1)
a (2)
b (2)
Figure 8: Comparison between numerical and experimental results for the floor temperature (1) and the water mass evolution (2) (dehumidifier turned “on” in blue, dehumidifier turned “off” in red). a- initial water mass: 80 g.m-2, b- initial water mass: 230 g.m-2
36 Page 36 of 40
Figure 9: Comparison of the water mass evolution with
and
(dehumidifier
turned “on” and initial water mass on the floor 230 g.m-2).
37 Page 37 of 40
Table 1: Technical characteristics of the dehumidifier (Trade name Dessica DT-210): Dehumidification capacity1 [kgwater.h-1] Dry air flow rate [m3.h-1] Moist air flow rate [m3.h-1] Motor power [kW] 1 Capacity of water absorption from the air humidity
0.6 210 40 1.1 for inlet conditions of 20°C and 60% relative
38 Page 38 of 40
Table 2: Experimental conditions and evaporation rate results during the first evaporation period. Experiment number
Studied parameter
Symbol
Experimental conditions Ta Position: hc RH (%) β0 (°C) (W.m-2.K-1) ± 3% (%) ± 0.2 ± 1.1
1 RH
2
Ta
3 Air velocity which influences hc 4
Position in the room which influences
5.5
10.4 20.2
A: 10.1
31*
23
2.06
70
24
0.89
87*
23
0.40
30
28
3.09
31
25
4.68
5.5
A: 10.1
87
23
0.40
4.4
A: 11.1*
91
21
0.28
5.7
A: 12.7**
91
19
0.37
5.3
A: 14.2***
83
20
0.64
B: 10.9
33
25
2.32
C: 10.5
33
26
1.99
D: 8.5
31
23
1.79
5.8
hc 5
A: 10.1
Evaporation rate, 1st period (x g.s-1)
High Ta with intermediate RH
20.5
A: 10.1
70
18
1.78
6
High hc with low RH
5.4
A: 14.2
32
22
2.83
7
50 droplets: lower β0
5.5
A: 10.1
30
7
0.95
8
Hydrophobic surface (stainless steel covered with plastic film)
5.7
A: 10.1
29
10
1.21
All the experiments were conducted with a discharge air velocity (evaporator) of 2.0 m.s-1 with the exception of *3 m.s-1, ** 4 m.s-1 *** 4.8 m.s-1
39 Page 39 of 40
Table 3: Evaporation rate evolution within the ranges of conditions studied Evaporation rate Exp.
(1st period) (x
Conditions
g.s-1) <
1
h=10.1
Ta=5.5°C
β0 = 23-24%
31
0.40< <2.06
5.2
2
h=10.1
5.5
β0 = 22-28%
RH=29-32%
2.06< <4.68
2.3
4, 6
8.5
Ta=5.4-5.8°C
β0 = 22-26%
RH=31-33%
1.79< <2.83
1.6
1, 7, 8
h=10.1
Ta=5.5°C
7<β0<23%
RH=29-31%
0.95< <2.06
2.2
1, 8
h=10.1
Ta=5.4-5.7°C
10*<β0<23%
RH=29-31%
1.21< <2.06
1.7
* covered with plastic film
40 Page 40 of 40
S0140-7007(17)30215-3 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.05.024 JIJR 3655
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
16-12-2016 21-5-2017 22-5-2017
Please cite this article as: L. Lecoq, D. Flick, O. Laguerre, Study of the drying process of wetted surfaces under conditions similar to food processing conditions, International Journal of Refrigeration (2017), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2017.05.024. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Study of the drying process of wetted surfaces under conditions similar to food processing conditions
L. Lecoq ab*, D. Flick b, O. Laguerre a a
b
Irstea, UR GPAN, 1 rue Pierre-Gilles de Gennes, 92761 Antony, France
, UMR Ingénierie Procédés Aliments, AgroParisTech, INRA, Université Paris-Saclay, 91300 Massy, France
Highlights:
The experimental results showed the importance of relative humidity on evaporation
Influence of relative humidity was compared to air temperature and velocity
The use of a dehumidifier can double the evaporation rate of water on a wet floor
Models were developed to predict the water mass evolution
Good agreement was found between the models and the experimental data
ABSTRACT Two experiments were carried out inside a test room in order to study the drying rate of wetted surfaces under conditions similar to those encountered in food processing plants.. In the first experiment, the evaporation of water droplets on a stainless steel plate representing typical equipment was studied under different ambient conditions in the room. In the second experiment, in order to reproduce drying conditions inside a food processing plant, the floor was entirely *
Corresponding author: Tel: 33 1 40 96 90 04, Fax: 33 1 40 96 60 75, E-mail: [email protected] 1 Page 1 of 40
wetted with water, the water mass evolution was measured when the discharge air was dried by a dehumidifier, and the results were compared with those obtained without using a dehumidifier. Models predicting the evaporation rate in these two experiments were developed and the numerical results show good agreement with the experimental data. Relative humidity was the factor which exerted the greatest influence on the evaporation rate. The drying rate on the stainless steel plate increased five-fold when a dehumidifier was used. Keywords: evaporation, droplet, water film, model, drying
Nomenclature Saturated water vapor concentration kg.m-3 Water vapor concentration in the air
kg.m-3
h
Overall heat transfer coefficient
W.m-2.K-1
hc
Convective heat transfer coefficient
W.m-2.K-1
hr
Radiative heat transfer coefficient
W.m-2.K-1
k
Mass transfer coefficient
m.s-1
m
Water mass
kg
Evaporation rate
kg.s-1
M
Molar mass
kg.mol-1
mCp
Thermal inertia
J.K-1
2 Page 2 of 40
RH
Relative humidity
%
r
Droplet radius
m
R
Ideal gas constant
J.K−1.mol−1
S
Total surface of the plate
m²
T
Temperature
°C
t
Time
s
X
Water content in the air
kgwater.kgdry air-1
Liquid/solid contact angle
°
Receding angle
°
Wet surface compared with total surface
Dimensionless
αr
Spherical cap surface compared with total surface
ΔHv
Dimensionless
Emissivity
Dimensionless
Latent heat of water evaporation
J.kg-1
Subscripts a
air
0
initial
pl
plate
w
water
wb
wet bulb
3 Page 3 of 40
1. Introduction In a food processing plant, cleaning and disinfection are performed daily in order to prevent microbial growth. However, certain bacteria such as Listeria monocytogenes still persist even where best disinfection practice (Muhterem-Uyar et al. 2015, Vogel et al. 2001) is applied. In order to make this operation as efficient as possible, complete drying of the room must be performed. In practice, during cleaning and disinfection, a lot of water is used, and remaining water will allow bacteria to survive (Carpentier & Cerf 2011, Zoz et al. 2016). Several studies have been carried out with a view to improving cleaning and disinfection. However, drying is still performed empirically. The use of an air drying device (dehumidifier) in a food processing plant in order to enhance the drying process by lowering the relative humidity in the room has rarely been studied. In order to control food safety, knowledge of the evaporation phenomenon on a solid surface is necessary. Evaporation is endothermic and is therefore influenced by heat transfer in the liquid phase and at the liquid/vapor interface (Mozurkewich 1986). The evaporation rate depends on the relative humidity, the air and surface temperatures and the air velocity in the vicinity of the surface (D'agaro et al. 2006, Navaz et al. 2008, Raimundo et al. 2014, Vik & Reif 2011). The evaporation of the water droplet is also influenced by its geometry (radius, contact angle). For the same water mass, a smaller contact angle induces a larger base radius decrease, which in turn increases the exchange between the solid surface and the liquid. In the case of a heated surface, evaporation will be faster (Chandra et al. 1996). The evaporation of a droplet may be divided into two periods (Chandra et al. 1996, Yu et al. 2015) called “pinned” and “unpinned” periods. During the first (“pinned”) period, the droplet radius remains constant while the contact angle decreases and the evaporation rate is almost 4 Page 4 of 40
constant. During the second (“unpinned”) period, the opposite phenomenon can be observed: the droplet radius decreases while the contact angle remains constant. The transition from the first to the second period depends on the contact angle. Once this parameter reaches a value called the “receding angle”, the second period begins. This value depends on the combined material/liquid surface. For a water droplet on a stainless steel surface, it is about 10° (Chandra et al. 1996). Most of the models described in the literature focus on the first period alone (Hu & Wu 2015). Navaz et al. (2008) proposed a semi-empirical model to predict water mass during the evaporation of a chemical component on a solid surface. Several authors consider water vapor diffusion in stagnant air alone, while others include conjugated heat transfer and free convection (Hu & Larson 2002, Yang et al. 2014). Experimentation in a food plant is complicated. For example, the time available for the installation of sensors is short, and the number of measuring positions is limited in order to disrupt work conducted by the staff to the least possible extent. Moreover, it is usually not possible to repeat experiments, and permission from the company is necessary should it be necessary to repeat experiments. This means that interpretation of the results is more complicated and some data could be missing. The aim of this study was to reproduce the conditions (temperature, relative humidity, velocity and water mass) during the drying process inside a chilled food processing plant on a laboratory scale (test room) in which conditions are better controlled. Evaporation of water on two surfaces was studied: a non-heated stainless steel plate (to represent evaporation on equipment in a food processing plant), and the floor of the test room. The influence of an air dehumidifier on the drying rate was analyzed. The model developed in this study is based on heat and mass balances and enables prediction of the water mass evolution. This model was validated by comparing the 5 Page 5 of 40
results obtained with the experimental data, and then the model was used to predict the drying time according to room conditions, and technical solutions designed to enhance drying were proposed. 2. Experimental conditions 2.1. Test room The experiments were carried out in a test room (Figure 1a). The dimensions of this room were 3.6 m long, 3.6 m wide and 2.5 m high (32.4 m3). The temperature and relative humidity in the room were controlled using an evaporator and a dehumidifier located in the ceiling. The discharge air velocity was adjusted using a variable frequency drive. This figure also shows the locations of temperature and relative humidity measurements in the room. Two types of experiments were performed: - The first one in which the evaporation rate of water droplets deposited on a stainless steel plate exposed to different ambient conditions was measured. The position of the plate is shown in Figure 1b. This experiment represents water evaporation on equipment used in a food processing plant. - The second one in which the entire surface of the floor was wet, representing the highest water load location after the cleaning of a food processing plant. 2.2. First experiment: droplets on a stainless steel plate A stainless steel plate (the most common equipment material, 0.5 m x 0.5 m x 10-3 m) was insulated using a 10-cm layer of polystyrene placed underneath it. This insulation allows heat exchange with the air on the upper side of the plate alone, thus facilitating the interpretation of 6 Page 6 of 40
the results obtained. The plate was placed inside the test room, then 0.5 mL water droplets (average diameter ~ 0.8 cm) were deposited on this plate using a pipette. Two numbers of droplets were deposited: 50 (percentage of initial wet surface, β0, about 10%) and 100 (β0, about 20%). These percentages are usual for equipment after cleaning in the food plant (Lecoq et al. 2016). The precise percentage of initial wet surface was determined using a camera and image treatment (ImageJ software). During the experiments, the following parameters were measured: -
Weight of the wetted plate using a balance (± 0.001 g precision) and recorded by a data logger (Agilent 34970A) every 10 s until all the water evaporated.
-
Air temperature recorded every 10 s using calibrated T-type thermocouples (1 mm diameter, ± 0.2°C precision). The air temperature at different positions was measured: discharge, return air and 10 cm above the plate. The plate temperature was measured at the center and at the 4 corners of the plate, and the average value of these measurements was reported.
-
Relative humidity in the room using calibrated TESTO 174H hygrometers (± 3% precision), recorded every minute.
-
Air velocity using a hot wire anemometer (TESTO 435-2, range of measurement 0-20 m.s-1, ± 0.03 m.s-1 precision). The measurement was carried out at 3 positions at the air return of the evaporator to determine the inlet air velocity (Figure 1.b). The reported air velocity is an average value calculated from 60 measurements (recorded every 1 s over a period of 1 min).
The influence of the relative humidity of the air (from ~30% to 90%), the temperature (from 5 to 20°C), the velocity (from 2 to 4.8 m.s-1), the position of the plate in the room, the
7 Page 7 of 40
percentage of initial wet surface (from 7 to 28%) and the nature of the surface were studied. The experimental conditions are shown in detail in Table 2 (Section 4.1).
2.3. Second experiment: floor entirely wet The initial temperatures (air and walls) were set at 20°C in the laboratory test room. Then, the thermostat temperature was set at 5°C and the discharge air velocity at 2.0 m.s-1. The initial relative humidity measured experimentally ranged from 40 to 50%. The influence of the initial water mass on the floor was studied: -
230 g.m-² of water (total mass ~3 kg) was deposited, corresponding to approximately the amount of water remaining after cleaning inside a plant
-
80 g.m-² of water (total mass ~1 kg) was deposited, corresponding to approximately the amount of water on the surface after using a squeegee to partially remove water.
During the experiment, the following parameters were measured until all of the water was evaporated: -
Water mass. The measurements were carried out using paper towelettes to wipe the entire surface of the floor and then weighing them using an electronic balance (Sartorius, CPA34001P, ± 0.1 g). The water mass on the floor was measured at different times in order to follow its evolution during drying. In the case of 230 g.m-² water deposited initially on the floor, the experiments were carried out 5 times with the dehumidifier turned “on” by wiping the floor at 30 min, 1 h, 3 h, 5 h and 10 h after the beginning of the experiment and 7 times with the dehumidifier turned “off” by wiping the floor at 30 min, 1 h, 3 h, 5 h, 10 h , 16.33 h and 20 h. In order to avoid to the greatest possible extent 8 Page 8 of 40
variability of the results due to the modus operandi, the same procedure used for water application on the floor was performed by the same person. -
The temperature, relative humidity and velocity of the air were measured in the same manner as that used for the first experiment and the measuring positions are shown in Figure 1a.
In order to study the influence of a dehumidifier on the drying time, the experiments were performed when the dehumidifier was “on” and when it was “off”. For the experiment with the dehumidifier turned “on”, the relative humidity set value was 50% during the experiment. The characteristics of the dehumidifier are shown Table 1. 2.4. Convective heat transfer coefficient Knowledge of the heat transfer coefficient is necessary for the evaporation model development (Section 3). An experiment was carried out in order to determine its value using a fluxmeter equipped with a thermocouple (trade name Captec, width x length x depth: 4 cm x 4 cm x 450 µm, surface area = 1.6 x 10-3 m2). This fluxmeter was supplied with 10 W of heating power (Q). The fluxmeter temperature (Tf), the air temperature (Ta) measured at 5 cm from the surface of the fluxmeter and the measured flux were recorded every second until a steady state was obtained. Then, the mean values were calculated over 20 min. of a stabilization period allowing evaluation of the heat transfer coefficient h,
. It should be noted that the emissivity of
this fluxmeter is close to zero; thus, the radiative exchange can be neglected. In the first experiment, the fluxmeter was placed on the plate in 5 positions (at the 4 corners of the plate and in the center) and the average value was calculated. The different convective heat
9 Page 9 of 40
transfer coefficient values corresponding to different air inlet velocities from the evaporator (2.0, 3.0, 4.0, 4.8 m.s-1) or positions in the room (A, B, C, D) are presented in Table 2 (Section 4.1). In the second experiment, the fluxmeter was placed successively in 7 different locations on the floor (in the 4 corners of the room, in the center and 2 others positions in the symmetry plane). The average value was used in the model.
3. Evaporation models In order to predict the water mass evolution, models were developed for water evaporation on a stainless steel plate and for water evaporation on the floor of a test chamber. These models were validated with the experimental data. 3.1. Evaporation of water droplets on the stainless steel plate 4.1.1. Model development When a droplet deposited on a plate is exposed to air, the phenomena involved are convection, radiation and evaporation (Figure 2). The model development is based on heat/mass balances and Lewis analogy. The heat exchange between the plate and the air is related to the water evaporation ( ) and can be expressed as follows:
The evaporation rate ( ) depends on the difference between the water content in the air in equilibrium with the droplets, Csat(Tpl) and the water content in the room Cwa :
10 Page 10 of 40
where
is the spherical cap surface of the droplets on the surface of the plate
and Cwa =RH Csat(Ta) Because of the low thickness of the stainless steel plate (10-3 m) and the high thermal conductivity (26 W.m-1K-1), it is assumed that the thermal inertia of the plate is negligible and the thermal conductivity of the plate is infinite. The heat transfer coefficient (h) can be expressed as the sum of the convective heat transfer coefficient (hc) and the equivalent radiative heat transfer coefficient (hr). Even if the surface considered is stainless steel with a low emissivity (0.1), the water on the surface has a high emissivity (0.95) and can induce non-negligible heat transfer through radiation. Thus:
Indeed, the heat exchange by convection can be expressed as through radiation can be approximated by
and heat exchange
where
. The values of the convective heat transfer coefficient (hc) shown in Table 2 were used for the simulation.
The mass transfer coefficient k is calculated using the Lewis analogy:
with
11 Page 11 of 40
where
is the thermal diffusivity of air =
of water vapor in air =
m².s-1 at 0°C and
is the mass diffusivity
m².s-1 at 0°C (Bimbenet et al. 2002).
, the saturated vapor concentration, is a function of the temperature which can be estimated by a quadratic equation:
By using data in a humid air diagram to fit this equation, the values of a, b and c were identified. For 0°C
kg.m-3,
kg.m-3.°C-1 and
kg.m-3.°C-2 . It is convenient to introduce the wet bulb temperature Twb which corresponds to the case in which the plate is entirely covered by water (β=βc=1), and for negligible radiation (high hc value), Twb is defined by:
The expression of the plate temperature Tpl can be deduced from Equations 1 to 6 (the equation development is reported in the appendix):
where
12 Page 12 of 40
,
Using (1) and (7) the evaporation rate
can be calculated as follows:
3.1.2. Evolution of the wet surface coefficient: β The plate temperature (Tpl) and thus the evaporation rate ( ) depend on the ratio between the spherical cap surface and the total surface of the plate (βc). The evolution of this coefficient must be known in order to predict the water mass evolution during the entire evaporation process. In the case of water droplets on a stainless steel plate, the evaporation process is composed of two periods. During the first period: The ratio between the wet surface and total surface β is constant (= β0) (the droplet radius remains constant) and the contact angle between the water and the plate decreases progressively. The experimental value of β0 was obtained using a camera. The ratio between the spherical cap surface of the droplet and the plate (βc) can be calculated using Equation (9):
13 Page 13 of 40
In our case, the initial contact angle of water on stainless steel is rather low (α0~15°). Thus, the spherical cap surface of the droplets is close to the wet surface:
. Even in the experiment
with a stainless steel plate covered by a more hydrophobic surface (Experiment 8, see Table 2) the wet surface is close to the spherical cap surface. The initial contact angle was around 45°, which makes the spherical cap surface only 1.17 times higher than the wet surface ( ). The use of β (instead of βc) to calculate the plate temperature and the evaporation rate will not significantly impact the results.. During the second period: This period begins when the contact angle reaches the receding angle (αr =10° for water on stainless steel) which corresponds to the moment when the water mass reaches 15% of its initial value
(Doursat et al. 2016) (submitted). During this period, the contact angle
remains constant ( = 10°) and the ratio of wet surface β decreases (the droplet radius decreases). In addition, the water mass of a droplet deposited on a surface is equal to:
and the relationship between the wet surface and the droplet radius is given by:
From Equation (10), it can be seen that
is proportional to the water mass to the power of 2/3.
Therefore, from Equations (10) and (11) it can be seen that the wet surface (Sw) is also proportional to the water mass to the power of 2/3 and the evolution of β during the second period of the evaporation process can be expressed by the following equation: 14 Page 14 of 40
During the second period, the plate temperature increases because of the diminution of the wet surface and the evaporation rate decreases. This temperature reaches the air temperature when the plate is completely dried. Generalization of β equation for both the first and second periods: The
coefficient during these two periods can be expressed as follows:
Using Equations (7), (8) and (13), the water mass evolution during the entire evaporation process (periods 1 and 2) can be predicted. 3.2. Model development for the evaporation on an entirely wet floor In the case of a floor wetted by water, the heat and mass exchanges between the air and the floor can be expressed as follows:
where T is the floor temperature and m is the water mass on the floor. In this case, the thermal inertia of the surface (floor) is not negligible.
15 Page 15 of 40
To solve Equations (14) and (15), the numerical values of the convective coefficient h, the thermal inertia of the floor 0
and the initial percentage of wet surface over the total surface
are shown in the results (see Section 4.2.3.). The air temperature
, initially at 20°C,
decreases and tends to drop to the thermostat temperature (5°C) during the process. Its evolution, measured experimentally (at the evaporator return air inlet), is used as an input parameter of the model. Also, the evolution of the vapor concentration in the air
is
calculated from the experimental data (relative humidity and air temperature at the evaporator return air inlet). The saturated water vapor concentration
depends on the surface
temperature alone and can be calculated using Equation (5). Equations 7, 8, 13 (first experiment) or 13, 14, 15 (second experiment) were implemented using MATLAB software (vR2012a, MathWorks Inc., Natick, MA, USA, Euler method).
4. Results and discussion 4.1. First Experiment: droplets on a stainless steel plate Figure 3 shows the experimental evolution of the water mass during evaporation at 5.5°C, with a relative humidity of 31%, a convective heat transfer coefficient on the plate equal to 10.1 W.m2
.K-1 and with an initial wetted surface of 23% of the total surface (Experiment 1 in Table 2). The
two periods of evaporation can be observed in this figure: -
First period during which the evaporation rate is almost constant (decreasing contact angle, constant droplet radiuses),
16 Page 16 of 40
-
Second period during which the evaporation rate decreases (constant contact angle, decreasing droplet radiuses).
The evaporation rate for the first period is calculated from the slope for which the water mass evolution is linear (Figure 3). The same method was used to calculate the evaporation rate for all the studied conditions, and the values are reported in Table 2. 4.1.1. Analysis of factors that influence the evaporation rate The maximum and minimum evaporation rates under different experimental conditions (Table 2) and the ratio of these values are reported in Table 3. It can be observed that the relative humidity has the greatest impact on the evaporation rate within the ranges of conditions studied. When the relative humidity varies from 87% to 31%, the evaporation rate increases by a factor 5.2, whereas when other parameters are varied it increases by a factor 2.3 at the most. Therefore, it is obvious that reducing the relative humidity by using a dehumidifier is an efficient way of significantly increasing the evaporation rate and thus reducing the drying time. Indeed, inside a food processing plant where no dehumidifier is installed, the relative humidity is often above 85% (Lecoq et al. 2016), which is very unfavorable for drying. It can be seen from this table that when the stainless steel plate was covered with plastic film (Experiment 8 in Table 2), the wet surface was lower (β0 =10%) compared with that of the stainless steel without a plastic film (β0 ~23%) under the same conditions (initial water mass, ambient conditions and plate position in the room, Experiment 1 in Table 2). Thus, the exchange surface between the droplet and the air was lower, which induced a lower evaporation rate.
17 Page 17 of 40
4.1.2. Comparison between models and experimental data The experimental data for the evaporation rate during the first period were first compared with two models: -
The evaporation model based on heat and mass balances presented in Section 3 and considered as theoretical.
-
An empirical model developed in a previous study (Lecoq et al. 2017) ; the following equations are presented:
The evaporation rate comparison between the results from the empirical model and the experimental data is shown in Figure 4a. The comparison shows rather good agreement with an average relative error
of 16 %.
The evaporation rate comparison between the results from the theoretical model (Equations. 7 and 8) and the experimental data is shown in Figure 4b. The comparison shows better agreement than with the empirical model, with a relative error of 9%. The experimental water mass evolution during the entire process (periods 1 and 2) can also be compared with the prediction of the two models (using Equations (13), (7) and (8) for the theoretical model or Equations (13), (16) and (17) for the empirical model). Figure 5 presents a comparison of the water mass evolution under different air relative humidity conditions (RH =31, 70, 87%) for an air temperature of 5.5°C. 18 Page 18 of 40
The results for the water mass evolution during periods 1 and 2 of the evaporation process (first r = constant then α = constant) are in good agreement using the theoretical equations (Figure 5), whereas the empirical model tends to slightly overestimate the evaporation rate. In the configuration studied (evaporation of water on a non-heated stainless steel plate, negligible thermal inertia and very high conductivity) this model can be applied to predict the water mass evolution as a function of the ambient conditions during the entire process and therefore to predict the drying time. This model can be applied to other materials or liquids. If the values of the initial and receding angles are known, the threshold ratio (15% for stainless steel) could be estimated in order to modify Equation (13). Equations (7) and (8) can be applied if the thermal inertia of the material is negligible and the thermal conductivity is high. Of course, the convective heat transfer coefficient which depends on the ventilation and location in the room has to be known, this can be measured quite easily using a heating flux meter. 4.1.3. Optimization strategy In order to reduce the drying time of water droplets deposited on equipment, it would be interesting to quantify the influence of an increase of airflow rate, a decrease of relative humidity or a rise of air temperature on the energy cost. Therefore, for a given mass of residual water (given value of c), the relative increase of evaporation rate: (in comparison with a reference case) developed using eq. 8, can be expressed as follows:
m ref m
h
T a T pl
(18)
h ref T a . ref T pl . ref
The differentiation of eq. 18 gives:
19 Page 19 of 40
h d d h ref
d T a T pl T a . ref T pl . ref
(19)
By neglecting the radiation, the heat transfer coefficient can be assumed to be proportional to the square root of the local velocity (Incropera and DeWitt, 1996), which is in turn, proportional to the air flow rate (eq. 20). h 1 V d d h ref 2 V ref
(20)
Differentiation of eq. 6 after substitution by eq. 5 leads to eq. 21:
d T a T pl A .d 1 HR B .d T a
Where A=
a bT
h 2 cT a . ref / b 2 cT pl . ref k H v c
a . ref
B= b 2 cT pl .ref
HR
ref
b cT
a . ref
/
h
c k H v
(21)
b 2 cT pl . ref
By substituting eq. 20 and 21 in eq. 19, the following equation is obtained: d
1 V A d 1 RH B d T a d 2 V ref
(22)
Eq. 22 allows the estimation of the influence of V , RH and Ta as follows : For a typical reference case without air dehumidifier, T pl.ref 4 . 5 C
T a . ref 5 C ,
RH
ref
90 %,
c 0 .5,
can be defined. In this case, the value of A is 10 (dimensionless) and B is 0.044 °C-1.
This means that: -
increasing the flow rate of 1% leads to increase drying rate of 0.5%,
-
reducing the relative humidity from 90% to 89% (increasing 1-RH by 1%) increases drying rate by 10%
-
increasing air temperature by 1°C increases drying rate by 4.4% 20 Page 20 of 40
It is to be reminded that, increasing air temperature has a favorable effect not only on drying, but also on refrigeration power because the heat losses are reduced. However, air temperature has detrimental effect on bacterial growth, so Ta should not be too high to assure the sanitary requirement. One way to increase drying rate is to improve ventilation. Increasing flow rate will increase the mechanical ventilation power W v p v V with a pressure drop almost proportional to the square of the flow rate (for turbulent flow). In addition this power will be converted into heat which has to be removed from the room. This means that the improve ventilation to increase to the drying rate by 1% can leads to the increase of electric power for more than 6% compared to the reference case. The other way to increase drying rate is to reduce relative humidity, for example, by using an electric adsorption/desorption dehumidifier. The desorption enthalpy is slightly higher than the heat of vaporization. In addition, the air is heated by passing through the dehumidifier. Inversely, less water is condensed on the heat exchanger which reduces the refrigeration power. To increase by 1% the drying rate, the relative humidity needs to be reduced by only 0.1%. This leads to an additional electric power of dehumidifier which can be roughly estimated as: H vV C sat T a d HR . To summarize, the choice of improving drying rate by increasing air flow rate or using a dehumidifier can be done by comparing 6 p v with 0.1 H v C sat . Since pv is often 300 Pa, 6 p v (1800 Pa) is the same order of magnitude of 0.1 H v C sat (1700 Jm-3 or Pa) for air at 5°C. In this case, increasing ventilation or using a dehumidifier is almost equivalent. However, it should be reminded that a too high air flow rate is detrimental for the comfort of the employees. For 21 Page 21 of 40
technical reasons, it is certainly easier to reduce relative humidity from 90% to 80% than to increase the air flow rate by a factor of 4 in order to double the drying rate. This illustrates quantitatively the interest of a dehumidifier.
4.2. Second Experiment: Floor entirely wet 4.2.1. Water mass evolution Figure 6 presents the experimental evolution of the water mass on the floor when the dehumidifier was “on” and when it was “off”. It can be observed that about 80% of the initial water is evaporated after three hours in the experiment with an initial mass of 230 g.m-2 and after one hour with an initial mass of 80 g.m-2. During these periods, the evaporation rate is almost the same in both cases (with the dehumidifier “on” or “off”). The impact of the dehumidifier is more obvious for the remaining 20% of water on the floor. In the experiments during which the dehumidifier was turned off, a small amount of water (1.8 g.m-2) was still present after 20 hours during the experiment with an initial water mass of 230 g.m-2. This water was located above all in the corners of the test room where convection is lower or in areas where the floor is slightly convex and induces water accumulation. In these areas, if the relative humidity is high, which is the case when the dehumidifier is off (RH~90%), evaporation of the remaining water will take much longer, as can be seen in Figure 6. With the dehumidifier turned “on”, almost no water remains after 10 hours of drying. 4.2.2. Water content The evaporation rate evolution
(with the dehumidifier turned “on” or “off”) can be assessed by
estimating the difference between the water content of the air in contact with the floor (saturation
22 Page 22 of 40
value at floor temperature): inlet):
and the water content in the room (at the evaporator return air
.
Indeed, (23) Using the experimental data on the air temperature and relative humidity at the return air inlet of the evaporator and on the floor temperature,
and
were calculated (Figure 7).
The difference in water content between the air near the floor (at saturation) and the room (at the return air inlet) is a determining factor for the evaporation rate: the higher this difference, the greater the evaporation rate. This difference is quite similar at the beginning of drying (first two hours) for both cases (dehumidifier “on” and “off”) and for both the initial water masses of 80 g.m-2 and 230 g.m-2. This explains why the evaporation rate and the water mass evolution are very similar during this period. After the first two hours, the water content decreases in the case where the dehumidifier is turned “on”. For the initial mass of 230 g.m-2 of water, the water content in the air could not be reduced immediately because the dehumidification capacity of the dehumidifier is rather low (0.6 kg.h-1). During the first two hours, about 93 g.m-2 of water evaporated (a total of 1.2 kg of water). Part of this water was removed by the dehumidifier and part was removed by the evaporator. Once most of the water has evaporated, the dehumidifier was able to decrease the water content in the air, and this induced a water content difference (between the floor and the return air) twice as high as
23 Page 23 of 40
when the dehumidifier was turned off (Figure 7b at 10 h). This explains the higher evaporation rate when the dehumidifier was turned “on” during this period. 4.2.3. Comparison between the numerical and experimental data The water mass and the floor temperature evolution predicted by the developed model were compared with the experimental data (Figure 8). For this simulation, the following numerical values were used: h=10 W.m-2.K-1,
J.K-1,
and
It is to be highlighted that even though water was spread all over the floor, if it is not perfectly flat, and accumulates as puddles in the slightly convex locations. The initial water distribution on the floor is therefore lower than 1 (
. If the floor had been entirely flat (
,
evaporation would have been much faster (explained in Section 4.1.1.). In this model, the following equation, developed by fitting the experimental results, was used to describe its evolution:
The floor temperature is well estimated by the model considering that that the experimental temperature was measured at several locations on the surface, whereas the model considers an average value. For the water mass evolution, the numerical results are also in good agreement with the experimental data. Because of the longer evaporation time in the case of the 230 g.m-2 initial water mass, the difference between the experiments with the dehumidifier turned “on” and “off” is more obvious.
24 Page 24 of 40
4.2.4. Numerical study of the influence of the water distribution on the floor To underscore the impact of the initial water distribution on evaporation, another simulation was performed to compare the cases of
and
(with the same initial water mass: 230
g.m-2 and the dehumidifier “on”). It can be observed in Figure 9 that if the water distribution is uniform and covers the entire surface (
, low water film thickness), evaporation is faster
than in the case of water concentrated in some locations (
, higher water film thickness).
This simulation result leads to the conclusion that to enhance evaporation inside a food processing plant, particularly on the floor, its flatness and roughness are as important as the relative humidity. If the floor is damaged, water can accumulate and drying within two hours (average drying time in the food processing plant) will be impossible even when the dehumidifier is turned “on”. This remaining water can promote bacterial growth.
5. Conclusion Two experiments were performed in order to study the evaporation of water under conditions close to those encountered in a food processing plant. The first experiment represents the evaporation of water droplets on equipment (stainless steel plate). The most important parameter influencing the evaporation rate in the ranges studied is the relative humidity. When the relative humidity was reduced from 87% to 31%, evaporation rate was multiplied by a factor of 5.2. In order to enhance evaporation, relative humidity should therefore be controlled. A theoretical model was developed in order to predict the water mass evolution with good accuracy.
25 Page 25 of 40
The second experiment represents the evaporation on an entirely wet floor (with initial masses of 230 gwater.m-2 or 80 gwater.m-2) where the initial temperature (20°C) and the thermostat temperature (5°C) were set at the values used in a chilled food processing plant. The influence of a dehumidifier was studied. It was observed that without a dehumidifier, the water evaporation rate is low throughout the process, which makes complete drying impossible within an acceptable duration. When a dehumidifier is running, the water content in the air can be maintained at a rather low level which significantly enhances evaporation. In this case, complete drying can be achieved more rapidly. Because of the low capacity of vapor absorption (0.6 kg water.h-1) of the air dehumidifier used in our study, a significant influence of the dehumidifier can be observed only when 80% of the initial water has evaporated. In addition, the developed model for the evaporation of water on the floor shows that the smoothness of the surface exerts a significant influence on water distribution and thus on the evaporation rate. If water accumulates in certain locations where the floor is damaged or poorly designed, water will remain even after several hours of drying and will promote microbial growth. ACKNOWLEDGEMENT The research leading to this result has received funding from the French National Research Agency (EcoSec Project, ANR-12-ALID-0005-04). REFERENCES Bimbenet J.-J., Duquenoy A., Trystram G. 2002. Génie des procédés alimentaires : Des bases aux applications. Carpentier B., Cerf O. 2011. Review — Persistence of Listeria monocytogenes in food industry equipment and premises. International Journal of Food Microbiology 145: 1-8 Chandra S., Marzo M. d., Qiao Y. M., Tartarini P. 1996. Effect of liquid-solid contact angle on droplet evaporation. Fire Safety Journal 27: 141-58 D'agaro P., Croce G., Cortella G. 2006. Numerical simulation of glass doors fogging and defogging in refrigerated display cabinets. Applied Thermal Engineering 26: 1927–34 26 Page 26 of 40
Doursat C., Lecoq L., Laguerre O., Flick D. 2016. Droplet evaporation on a solid surface exposed to forced convection: experiments, simulation and dimensional analysis. Unpublished results, submitted to International Journal of Heat and Mass Transfer Hu D., Wu H. 2015. Numerical study and predictions of evolution behaviors of evaporating pinned droplets based on a comprehensive model. International Journal of Thermal Sciences 96: 149-59 Hu H., Larson R. G. 2002. Evaporation of a sessile droplet on a substrate. J. Phys. Chem B. 106: 1334-44 Incropera F.P., DeWitt D.P., 1996. Fundamentals of Heat and Mass Transfer, John Wiley & Sons, INC. 4ème edition, New York, Chapter 6 and 9, 886 p. Lecoq L., Flick D., Derens E., Hoang H. M., Laguerre O. 2016. Simplified heat and mass transfer modeling in a food processing plant. Journal of Food Engineering 171: 1-13 Lecoq L., Flick D., Laguerre O. 2017. Study of the water evaporation rate on a stainless steel plate under controlled conditions. International Journal of Thermal Sciences 111: 450–462 Mozurkewich M. 1986. Aerosol growth and the condensation coefficient for water: a review. Aerosol Science and Technology 5: 223-36 Muhterem-Uyar M., Dalmasso M., Bolocan A. S., et, al. 2015. Environmental sampling for Listeria monocytogenes control in food processing facilities reveals three contamination scenarios. Food Control 51: 94–107 Navaz H. K., Chan E., Markicevic B. 2008. Convective evaporation model of sessile droplets in a turbulent flow—comparison with wind tunnel data. International Journal of Thermal Sciences 47: 963-71 Raimundo A., Gaspar A., Oliveira A. V. M., Quintela D. 2014. Wind tunnel measurements and numerical simulations of water evaporation in forced convection airflow. International Journal of Thermal Sciences 86: 28-40 Vik T., Reif B. A. P. 2011. Modeling the evaporation from a thin liquid surface beneath a turbulent boundary layer. International Journal of Thermal Sciences 50: 2311–17 Vogel B. F., Huss H. H., Ojeniyi B., Ahrens P., Gram L. 2001. Elucidation of Listeria monocytogenes contamination routes in cold-smoked salmon processing plants detected by DNA-based typing methods. Appl. Environ. Microbiol. 67: 2586–95 Yang K., Hong F., Cheng P. 2014. A fully coupled numerical simulation of sessile droplet evaporation using Arbitrary Lagrangian–Eulerian formulation. International Journal of Heat and Mass Transfer 70: 409-20 Yu D. I., Kwak H. J., Doh S. W., Kang H. C., Ahn H. S., Kiyofumi M., Park H. S., Kim M. H. 2015. Wetting and evaporation of water droplets on textured surfaces. International Journal of Heat and Mass Transfer 90: 191-200 Zoz F., Iaconelli C., Lang E., Iddir H., Guyot S., Grandvalet C., Gervais P., Beney L. 2016. Control of Relative Air Humidity as a Potential Means to Improve Hygiene on Surfaces: A Preliminary Approach with Listeria monocytogenes. Plos One 11 (2): e0148418
APPENDIX: Development of Equation 7 From Equations (1), (2) and (5), it follows that:
27 Page 27 of 40
From Equations (6) (wet bulb) and (5) the following is obtained:
Eliminating
Introducing
c’
between Equations (25) and (26), Tpl can be related to
by:
, Eq. (27) becomes:
b’
a’
the solution of which is:
28 Page 28 of 40
Dehumidifier Evaporator 3.6 m Exterior 2.5 m Symmetry plane
3.6 m Airflow pattern in the room Airflow pattern from the dehumidifier Positions of the air temperature and relative humidity sensors Positions of the floor temperature sensors a 3.6 m
Evaporator
C
B
A
3.6 m
Positions of the stainless steel plate (~40cm above the floor): A (reference position), B, C and D
1m Air velocity measurements
D Top view
b
29 Page 29 of 40
Figure 1: (a)- Airflow patterns in the test room equipped with a dehumidifier (b)- Top view of the test room showing the different positions of the stainless steel plate used when the water evaporation experiments were performed
Figure 2: Schematic view of one droplet on the plate
30 Page 30 of 40
50 45
Water mass (g)
40 35 30
First period
25 20 15
Second period
10 5 0 0
100
200
300
Time (min)
400
500
Figure 3: Experimental water mass evolution during evaporation (Ambient conditions: Ta = 5.5°C, RH = 31%, h c= 10.1 W.m-2.K-1, β0 = 23%).
31 Page 31 of 40
Evaporation rate (empirical formula) (g.s-1)
0.005
20.2°C 0.004
Different RH Different air velocity
10.4°C
Different Ta 0.003
C
B A, RH=31%
Different Beta Different V and RH
D
0.002
Different RH and Ta
RH=70% 0.001 RH=90% β=7.7 % 4.8 m.s-1 4.0, 3.0 and 2.0 m.s-1 0 0
0.001
0.002
Different position with plastic cover 0.003
0.004
0.005
Experimental data evaporation rate (g.s-1)
a 20.2°C
Theorical evaporation rate (g.s-1)
0.005
Different RH
Different air velocity
0.004
10.4°C
Different Ta
0.003
Different Beta C
0.002
D
B A, RH=30%
Different V and RH Different RH and Ta
0.001
0
RH=70% β=7.7 % RH=90% 4.8 m.s-1 4.0, 3.0 and 2.0 m.s-1 0
0.001
0.002
Different position with plastic cover 0.003
0.004
0.005
Experimental evaporation rate (g.s-1)
b Figure 4: Evaporation rate comparison (1st period) between the experimental data and a- the empirical model; b- the theoretical model.
32 Page 32 of 40
Figure 5: Water mass evolution during evaporation (periods 1 and 2): comparison between the empirical model, the theoretical model and experimental data.
33 Page 33 of 40
90
250
70 60
Water mass (g.m-2)
Water mass (g.m-2)
80
dehumidifier « off »
50 40
dehumidifier « on »
30 20
200
dehumidifier « off »
150
dehumidifier r « on »
100 50
10 0
0 0
1
2 time (hours)
a
3
4
5
0
5
10
15
20
time (hours)
b
Figure 6: Experimental water mass evolution on the floor when the dehumidifier was “on” (blue curve) and when the dehumidifier was “off” (red curve) a- initial water mass: 80 g.m-2, b- initial water mass: 230 g.m-2
34 Page 34 of 40
16 14 10 8 6
X gw.kgdryair-1
air return - dehum. "on"
12
air return - dehum. "off"
10
air return - dehum. "on"
8 6
4
4
2
2
0
0 0
1
2 3 Time (hours)
4
floor
14
air return - dehum. "off"
12
X gw.kgdryair -1
16
floor
5
0
5
10 15 Time (hours)
a
20
b
Figure 7: Calculated evolution of the water content of the air in contact with the floor (saturation) and in
the
evaporator return
air,
with
the dehumidifier
turned “on” or
“off”.
a- initial water mass: 80 g.m-2, b- initial water mass: 230 g.m-2.
35 Page 35 of 40
a (1)
b (1)
a (2)
b (2)
Figure 8: Comparison between numerical and experimental results for the floor temperature (1) and the water mass evolution (2) (dehumidifier turned “on” in blue, dehumidifier turned “off” in red). a- initial water mass: 80 g.m-2, b- initial water mass: 230 g.m-2
36 Page 36 of 40
Figure 9: Comparison of the water mass evolution with
and
(dehumidifier
turned “on” and initial water mass on the floor 230 g.m-2).
37 Page 37 of 40
Table 1: Technical characteristics of the dehumidifier (Trade name Dessica DT-210): Dehumidification capacity1 [kgwater.h-1] Dry air flow rate [m3.h-1] Moist air flow rate [m3.h-1] Motor power [kW] 1 Capacity of water absorption from the air humidity
0.6 210 40 1.1 for inlet conditions of 20°C and 60% relative
38 Page 38 of 40
Table 2: Experimental conditions and evaporation rate results during the first evaporation period. Experiment number
Studied parameter
Symbol
Experimental conditions Ta Position: hc RH (%) β0 (°C) (W.m-2.K-1) ± 3% (%) ± 0.2 ± 1.1
1 RH
2
Ta
3 Air velocity which influences hc 4
Position in the room which influences
5.5
10.4 20.2
A: 10.1
31*
23
2.06
70
24
0.89
87*
23
0.40
30
28
3.09
31
25
4.68
5.5
A: 10.1
87
23
0.40
4.4
A: 11.1*
91
21
0.28
5.7
A: 12.7**
91
19
0.37
5.3
A: 14.2***
83
20
0.64
B: 10.9
33
25
2.32
C: 10.5
33
26
1.99
D: 8.5
31
23
1.79
5.8
hc 5
A: 10.1
Evaporation rate, 1st period (x g.s-1)
High Ta with intermediate RH
20.5
A: 10.1
70
18
1.78
6
High hc with low RH
5.4
A: 14.2
32
22
2.83
7
50 droplets: lower β0
5.5
A: 10.1
30
7
0.95
8
Hydrophobic surface (stainless steel covered with plastic film)
5.7
A: 10.1
29
10
1.21
All the experiments were conducted with a discharge air velocity (evaporator) of 2.0 m.s-1 with the exception of *3 m.s-1, ** 4 m.s-1 *** 4.8 m.s-1
39 Page 39 of 40
Table 3: Evaporation rate evolution within the ranges of conditions studied Evaporation rate Exp.
(1st period) (x
Conditions
g.s-1) <
1
h=10.1
Ta=5.5°C
β0 = 23-24%
31
0.40< <2.06
5.2
2
h=10.1
5.5
β0 = 22-28%
RH=29-32%
2.06< <4.68
2.3
4, 6
8.5
Ta=5.4-5.8°C
β0 = 22-26%
RH=31-33%
1.79< <2.83
1.6
1, 7, 8
h=10.1
Ta=5.5°C
7<β0<23%
RH=29-31%
0.95< <2.06
2.2
1, 8
h=10.1
Ta=5.4-5.7°C
10*<β0<23%
RH=29-31%
1.21< <2.06
1.7
* covered with plastic film
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