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Modeling moisture condensation in humid air flow in the course of cooling and heat recovery
Energy and Buildings 112 (2016) 93–100
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Modeling moisture condensation in humid air flow in the course of cooling and heat recovery G.P. Vasilyev a , Iu.A. Tabunshchikov c , M.M. Brodach c,∗ , V.A. Leskov a,b , N.V. Mitrofanova a , N.A. Timofeev b , V.F. Gornov a,b , G.V. Esaulov c a
JSC “NIIMosstroy”, Moscow, Russia JSC “INSOLAR-ENERGO”, Moscow, Russia c Moscow Architectural Institute (State Academy), Moscow, Russia b
a r t i c l e
i n f o
Article history: Received 16 June 2015 Received in revised form 30 November 2015 Accepted 1 December 2015 Available online 8 December 2015 Keywords: Condensation Phase transition Heat exchanger Defrostation Heat exchanger frosting Heat pump system Energy efficiency Heat regime Air flow
a b s t r a c t This article, written as a result of theoretical and practical research, describes a survey of condensate nucleation in heat exchangers utilizing low-potential heat of humid air. The authors conducted a series of studies aimed at developing energy-independent technical solutions to protect heat exchangers from the freezing of the moisture condensing on their exchange surfaces in the course of humid air heat recovery. There was a negative dependence of the thickness of the layer of condensate formed on the heat exchange surface, the condensation rate, and the moisture content of warm air. The article presents the outcomes of the numerical study aimed at building a model of the condensation processes that occur due to a flow of moist air when the air is cooled and heat is utilized. The study provided experimental validation for the consistency of the processes related to water vapor condensation in the flow of cooled moist air. The outcomes presented in the article can apply to both the exchange systems using the low potential heat of the atmospheric air, e.g., for room heating or snow melting, and to the exhaust air energy recovery systems of the building ventilation plant. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The widespread use of air cooled heat exchangers, recuperators, and other systems recovering waste heat of exhaust air from ventilation systems is impeded by the condensation and subsequent freezing of moisture on the surfaces of air cooled exchangers. Frost formation and icing of exchange surfaces exposed to moist air at subzero temperatures results not only in a sharp drop in the heat exchange efficiency but also in the need to use additional power to defrost the apparatuses [1,2]. The aforementioned problems are typical of air cooled systems virtually all over Russia [3]. There are two main ways to protect heat exchanger surfaces from icing: regular heating (defrosting), which means additional energy costs, and chemical protection of exchange surfaces by means of special anti-icing moisture-repellent compositions applied to the heat-exchange surface. The article [4] analyzes these two ways in detail, with emphasis on the chemical methods. The
∗ Corresponding author. Tel.: +7 916 1725736. E-mail address: [email protected] (M.M. Brodach). http://dx.doi.org/10.1016/j.enbuild.2015.12.002 0378-7788/© 2015 Elsevier B.V. All rights reserved.
condensation of water vapor in air and on cold heat-exchange surfaces clearly has a strong influence on the rate of frost formation and air cooler icing. A reasoned choice of the geometric parameters of heat exchangers, cooling air flow rates, and conditions for heat exchange with cooling surfaces can significantly reduce the energy required to defrost heat exchangers [5,6]. Hence, creating heat regime models for air cooled exchangers that provide a reasonable picture of the heat exchange process accounting for air vapor condensation in the cooling air and on cold exchange surfaces is, at the moment, an important task. Coping with the task can help to create new, energy-independent solutions to protect exchange apparatuses from frost formation. Many studies have been performed to solve this task; the work described in are most similar to the problems analyzed in our article [7]. 2. Modeling the processes of moist condensation in cooling air The purpose of the studies described herein was to develop energy-independent technical solutions protecting heat exchangers from the freezing of the moisture condensing on their exchange
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surfaces in the course of moist air heat recovery/recuperation. Numerical analyses were used to model moist condensation processes in the air flow exposed to cooling. Calculations were made using a model simulating two air canals exchanging heat via the heat-conducting wall. Fig. 1 provides a general view of the air cooler in question. To study the thickness of the condensate droplets nucleating on the heat exchange surface and the rate of nucleation, the authors solved the conjugate problem of heat conductivity and gas dynamics using the latest software platform [8] ANSYS CFX 11.0 based on the numerical solution of the Navier–Stokes equation system.
2
2
2
∂u ∂u ∂u ∂u ∂p ∂ u ∂ u ∂ u + + + u + v + w =− + ∂t ∂x ∂y ∂z ∂x ∂ x 2 ∂ y2 ∂ z 2
2
2
2
∂v ∂v ∂v ∂v ∂p ∂ v ∂ v ∂ v + + + u + v + w =− + ∂t ∂x ∂y ∂z ∂y ∂ x 2 ∂ y2 ∂ z 2
2
2
where ¯ is the average pressure, and indices i = 1,2,3 and j = 1,2,3 correspond to the coordinates x, y, z. Shear (Reynolds) tensions ui uj are six unknowns additional to the averages motion param¯ that are usually approximated using the Boussinesq eters (u¯ i , p) hypothesis:
ui uj = −t
∂u¯ i ∂u¯ j + ∂xj ∂xi
+
2 kıij , 3
(5)
where t is the additional viscosity caused by pulsations; k is the averaged eddy pulsation energy (TKE). The system is open-loop, so it requires additional conventions (“eddy models”). 2.1. First set of numerical experiments
2
∂w ∂w ∂w ∂w ∂p ∂ w ∂ w ∂ w + + + u + v + w =− + ∂t ∂x ∂y ∂z ∂z ∂x2 ∂ y2 ∂z 2
(1) Furthermore, equations of continuity and of state were to be satisfied:
∂p ∂(u) ∂(v) ∂(w) + + + =0 ∂t ∂x ∂y ∂z
(2)
p = RT
(3)
In the first sequence of numerical experiments, the authors analyzed the thermal state of the heat-conducting wall made from different materials (copper and PVC) located between two air flows (cold, −20 ◦ C, and cooling, +20 ◦ C) [9]. The areas analyzed corresponded to the exchanger simulation model shown in Fig. 1. In this set of experiments, the length of the heat exchanger was 0.3 m along the x axis (in the direction of the cooling air flow) [10,11]. Three flow modes were compared (the oncoming flow rates were 2, 1, and 0.2 m/s), and the length of the square section device was 0.3 m. The Reynolds numbers for each of the three flow modes were, respectively: 13500, 6750, 1350.
here u, v, w are the sought components of the air velocity vector (by axes x, y, z), p is the pressure, t is the time, the dynamic viscosity coefficient of air, is the density, R is the universal gas constant, T is the temperature. For the simplicity of modeling, we can assume that air is incompressible and isothermal; body forces are ignored. Direct solution of Eq. (1) taking into account the eddies of all scales (DNS, Direct Numerical Simulation) can be practically implemented only for very low flow rates. Therefore, the authors used a semi-empirical method based on velocity splitting by the time averaged component and the pulse component ui (t) = ui + ui (t) with transition to the so-called Reynolds averaged Navier–Stokes method:
∂p ∂ ∂ ∂ uj + ui · uj = + ∂t ∂xi ∂xj ∂xi ∂ui = 0, ∂xi
∂ui ∂xi
= 0,
∂ui ∂uj + ∂xi ∂xj
− ui uj , (4)
Fig. 1. Air cooler simulation model. Length: 1 m (along the X axis). Height of each of the areas of cool and cooling air (along the Y axis): 0.059 m. The area width was taken as 0.06 m (along the Z axis), and the symmetry condition was established on the border of this area. Sheet thickness is 0.002 m.
Fig. 2. Comparison of the laminar (red line) and turbulence (blue line) problem definitions. Average temperature of the heat-conducting PVC wall on the cold air side. A graph—turbulent flow mode, 2 m/s; B graph—laminar mode, 0.2 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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The computation grid consisted of 233,220 hexa-elements (264,600 nodes). 2.1.1. Boundary conditions Cooling air at the input: flow rates (2, 1, 0.2 m/s) and static temperature 20 ◦ C. Cooling air at the output: static pressure 1 atmosphere. Cold air at the input: flow rates (2, 1, 0.2 m/s) and static temperature −20 ◦ C. Cold air at the output: static pressure 1 atmosphere. The wall is considered to be heat-conducting. All other walls in the problem (lower wall, upper wall, and back wall) were considered adiabatic. To reduce the calculation time, the symmetry condition was set for the xy plane because the initial flow area was assumed to be twice as large. The first numerical experiment in this set evaluated the temperatures of the heat-conducting PVC wall for all the flow modes in two different problem definitions, the laminar and the eddy (with the SST turbulence model). Graphs in Figs. 2 and 3 show the changes to the heat-conducting wall temperature along the x axis. Based on the outcomes of the numerical experiment, it was assumed that at air flow rates exceeding 0.5 m/s, the mode was turbulent, and at lower rates, it was laminar. The second numerical experiment compared the heat regimes of the heat-conducting wall [12] made from copper and from PVC
Fig. 4. Average temperature of the wall on the cold air side. Blue line—PVC; red line—copper. A graph—turbulent flow mode, 2 m/s; B graph—laminar mode, 0.2 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Average temperature of the wall on the cold air side. Blue line—PVC; red line—copper. Turbulent flow mode – 1 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
for various air flow modes. Figs. 4–7 show the outcomes of the experiment. 2.2. Second set of numerical experiments
Fig. 3. Comparison of the laminar (red line) and turbulence (blue line) problem definitions. Average temperature of the heat-conducting PVC wall on the cooling air side. A graph—turbulent flow mode, 2 m/s; B graph—laminar mode, 0.2 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
In the second set of numerical experiments, the authors performed computations for three types of the wall dividing the flows of cold and cooling air, namely walls made of PVC, steel, and copper. The other walls of the air canals are assumed to be insulated. The dimensions of the heat exchanger were as those in the simulation
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Fig. 8. Temperature change along the x axis averaged by the cross-section of the heat-conducting PVC wall. Green line—cold air temperature −3◦ C; red line −15◦ C; blue line −28◦ C.
Fig. 6. Average temperature of the heat-conducting wall on the cooling air side. Blue line—PVC; red line—copper. A graph—turbulent flow mode, 2 m/s; B graph—laminar mode, 0.2 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
model shown in Fig. 1. To reduce the domain of computation, the flow symmetry condition was specified for the xy plane. 2.2.1. Boundary conditions Cooling air at the input is indicated with arrows in the upper part of Fig. 1; the direction of the current was along the x axis. The flow rate was 3.85 m/s); the temperature was 23 ◦ C. The static pressure of the cooling air at the exchanger output was 1 atm.
Cold air at the input is indicated with arrows in the lower part of Fig. 1. The direction of the current was against the x axis (contra flow with hot air); the flow rate was 3.85 m/s; the temperature of the cold air was changed and assumed to be −3 ◦ C (average winter temperature in Moscow), −15 ◦ C, and −28 ◦ C. Static pressure of the cold air at the exchanger output (room entrance) is 1 atm. Fig. 8 shows the outcomes of the third numerical experiment, in which graphs depicting temperature changing along the x axis are averaged by the cross-section of the heat-conducting polymer wall for the cold air temperatures −3 ◦ C, −15 ◦ C, and −28 ◦ C. Similar computations have been performed for heat-conducting walls made from steel and copper. The computation results have been consolidated in Table 1. Table 1 shows the areal temperatures on the exhaust air side for various sheet materials. As a result of the computations, the authors obtained a threedimensional temperature distribution on the cooling air side of the heat-conducting wall; this value was then used in the fourth numerical experiment as a boundary condition to solve the moisture condensation task. It should be noted that, due to the low heat conductivity of the polymer material, the three-dimensional temperature distribution on the heat-conducting wall was used in the subsequent computations. Then, only the area of the cooling air flow was taken as the domain of the computation to model water vapor condensation processes, and the obtained three-dimensional temperature distributions were stipulated as the boundary condition for the temperature on the heat-conducting wall. Fig. 9 shows the simulation model of the cooling air flow. The gravity direction was vertically downwards along the y axis. The multi flow model “Droplets with Phase Change” was selected to model the processes of fluid condensation on the wall. In this model, gas (or, to be more precise, saturated water vapor) was assumed as the carrier phase and droplets of the condensing liquid as the secondary phase. In the model, air is approximated as a continuous medium and water as drops of a small dimension of an order of 10 to 4 mm. In the process of the calculation, their diameter may be increased. Table 1 Areal temperature of the heat-conducting wall on the cooling air side.
Fig. 7. Average temperature of the heat-conducting wall on the cooling air side. Blue line–PVC; red line—copper. Turbulent flow mode – 1 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Material
Cold air temperature (◦ C)
Polymer Copper Steel
−3.1 12.1 10.75 10.8
−15 6.5 4.6 4.5
−28 −0.3 −2.3 −2.4
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Fig. 9. Simulation model of the cooling air flow used to model water vapor condensation processes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The initial concentration of the liquid both in the calculation region and at the entrance is considered as zero. The initial temperature is about 50 ◦ C. An important factor for the computation was the right selection of the time increment that would make the problem solvable. In our case, we selected a range from 10−6 s to 5 × 10−5 s. Due to a very small time increment and quite a long area (1 m), each computation took more than 24 h. The computations were performed under the same boundary conditions, and the relative moisture content of the cooling air at the exchanger input was assumed in various numerical experiments to be equal to 30%, 60%, and 80%. The calculations were considered complete at 9000 iterations. For all this, the level of discrepancies for the principal equations reached the order of 10−15 with the time spacing of 5 × 10−5 s. The temperature distribution on the lower heat-conducting wall (xz plane) was taken from the previous computations for all the three temperature modes of the cooling air supplied. In all the computation options, the moisture content in the cooling flow grew evenly toward the end of the flow, displacing the gas. The highest condensation rate was also observed on the heatconducting wall at the exchanger output. The Lagrange approach to moist droplet modeling was used to model nucleation of near-wall fluid. Non-stationary computation. The carrier phase was gas. The trajectories of fluid elements were found at the end of each time increment based on the data available about the gas flow. Fig. 10 shows the resulting fluid film that nucleated on the lower PVC wall at a cooling air moist content of 30% and an air temperature of −30 ◦ C. Fig. 11 shows the rates of liquid nucleation in a unit volume and the distribution of the liquid and gaseous phases in the median and
Fig. 10. Thickness of near-wall fluid film on the PVC heat-conducting surface and fluid element trajectories.
outflow cross-sections of the cooling air. As one can see in Fig. 5, the thickness of the condensation fluid grows at the exchanger output. The outcomes of the fourth numerical experiment with the approximate value of the resulting fluid condensate film thickness his consolidated in Table 2. The outcomes of the fourth numerical experiment are presented in Table 2. One can notice that condensation rates go down when plastic heat-exchange surfaces are used. Another important feature of the outcomes obtained is the contradiction between the change trends of the highest transition rates and the condensate film thickness at the exchanger output depending on the temperature of the cold air supplied to the exchanger. 3. Experimental validation (lab experiment) Experimental validation of the outcomes obtained during the numerical experiments was performed on a specially designed and manufactured laboratory test bench. In the course of the lab experiments, the researchers surveyed the moist regime in the air cooled heat exchanger with two reverse flow air canals divided by a wall made from the tested material, PVC. The aim of the experiment was to provide experimental validation of the outcomes obtained in
Fig. 11. Liquid nucleation rate in a volume unit and distribution of the liquid and gaseous phases in the cooling air flow. Left graph—cross-section in the middle (x = 0.5 m); right graph—outflow cross-section (x = 1 m).
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Table 2 Results of water vapor condensation modeling. Material
Cold air temperature (◦ C)
Moisture content (relative, by weight) (%)
Maximum rate of water vapor–liquid transition, kg/(m3 s)
Estimated thickness of condensate (water) film at the exchanger outflow, mm
PVC
−3.1
30 60 80 30 60 80 30 60 80
0.00038 0.00043 0.00044 0.00085 0.001 0.00114 0.00088 0.00098 0.00112
11.8 10.6 9.7 9.2 8.7 7.9 9.8 9.5 9.2
30 60 80 30 60 80 30 60 80
0.00099 0.00124 0.00137 0.0011 0.00135 0.0015 0.0012 0.0015 0.00164
9.38 9.15 9.08 9.22 9.05 8.98 9.1 8.95 8.9
30 60 80 30 60 80 30 60 80
0.001 0.0013 0.0014 0.0011 0.00139 0.00154 0.0012 0.0015 0.0017
9.5 8.8 8.8 8.95 8.78 8.68 8.9 8.7 8.6
−15
−28
Copper
−3.1
−15
−28
Steel
−3.1
−15
−28
the course of the numerical experiments and to survey condensate formation on polymeric heat-exchange surfaces [13]. The test bench virtually replicated the geometrical dimensions of the domain of computation shown in Fig. 1: there were two air canals, the exhaust canal with warm air and supply canal with cold air, that were divided by a sheet made from the tested material (PVC) so that the sheet was positioned horizontally, parallel to the air pumped by the fans through the canals. The bench had sensors recording the surface temperatures of the tested materials as well as the temperature of the air at the input to and output from the canals. Fig. 12 shows the general view of the test bench and the points where the temperature sensors were fixed. Fig. 13 shows the photo of the bench. Condensate formation was observed visually and photographed during the testing. Fig. 14 shows the photographs of the test and condensate formation. The lab experiment was carried out at the inflow cold air temperature of −3.1 ◦ C. In essence, this cold air temperature equals the average outdoor air temperature during the heating season in Moscow. Additionally, the freezing of the condensate would strongly affect lab modeling of the exchanger’s heat regime for lower temperatures. The moisture content of the cold air supplied to the exchanger was measured with the help of a vapor generator. The thickness of the condensate film was measured by the maximum height of the droplets nucleating at the exchanger outflow. Table 3 compares the outcomes obtained in the course of the
numerical analyses and laboratory experiments, which are shown in Fig. 15. The lab experiments demonstrate quite a good convergence with the numerical outcomes. The deviation of the experiment
Fig. 12. Test bench model.
Fig. 13. Test bench.
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Table 3 Comparison of the outcomes of numerical and laboratory experiments. Material
Cold air temperature (◦ C)
Moisture content (relative, by weight) (%)
Thickness of condensate (water) film at the exchanger outflow as per the numerical experiment, mm
Thickness of condensate (water) film at the exchanger outflow as per the laboratory experiment, mm
PVC
−3.1
30 60 80
11.8 10.6 9.7
8.2 7.5 6.6
Fig. 14. Photograph of condensate nucleation process on Sample No. 2 without Teflon coating.
corresponds to the thickest condensate film forming at the outflow from the exchanger. It is noteworthy that the thickest condensate film was observed on a heat-conducting wall made from PVC. Also quite interesting is the discovered inverse dependence between the thickness of the condensate film on the heat exchange wall and the moisture content of the cooling air; as the relative air humidity rises, the condensate film grows thinner. It appears that this is related to the rate of water vapor condensation in the air flow, which grows as the humidity of the air flow increases. This, in turn, results in a greater amount of condensate coming out of the exchanger with the air flow. Lowering the temperature of the cold air fed into the exchanger leads to the same result. As the temperature of the cold air drops, the rate of water vapor condensation in the cooling air flow increases, and the condensate film forming on the exchange wall at the outflow from the heat exchanger grows thinner. Another important outcome of the numerical experiments is the proximity of the condensate thickness values obtained for heat-conducting walls from PVC, copper, and steel for cold air temperatures below −15◦ C. This fact confirms that it is desirable to use polymeric heat exchangers for exhaust air energy recovery in building ventilation plants in most of Russia. The outcomes of the lab experiments have confirmed an inverse dependence between the thickness of the condensate film on the heat exchange wall and the moisture content of the cooling air; as the relative air humidity rises, the condensate film grows thinner. Acknowledgments The research presented in this article has been conducted by JSC “NIIMosstroy” with financial support from the Ministry of Education and Science of Russia. Unique project identifier is RFMEFI57914X0081. References
Fig. 15. Comparison of the outcomes of numerical and laboratory experiments.
results from the calculated ones was found in the range of 30%, which is an admissible result for a model of such complexity. The outcome of the lab experiments presented in Table 2 confirm the inverse dependence between the thickness of the condensate film on the heat exchanger wall and the moisture content of the cooling air; as the relative air humidity rises, the condensate film grows thinner. 4. Conclusion The survey presented in this article helped to gain an indepth view of the condensate droplet formation process during air flow energy recovery and to identify the most “condensate-prone” areas in the exchanger with the highest likelihood of condensate formation and subsequent freezing. As the numerical experiments have proven, the lowest water vapor condensation rate
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[8] G.P. Vasilyev, Geothermal heat supply systems and their efficiency in the Russian climate, ABOK 5 (5) (2007) 58–74 [Ventilation, Heating, Air Conditioning, Heat Supply and Construction Thermophysics, (in Russian)]. [9] Ch.Q. Tian, Sh.Q. Shao, W.X. Shi, Inverter air source heat pump, Fluid Mach. 33 (9) (2005) 67–71. [10] Y. Liu, G. Zhoua, J. Mab, Simulation of a air liquid combined heat exchanger, Procedia Eng. 15 (2011) 4052–4057, CEIS 2011.
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Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Modeling moisture condensation in humid air flow in the course of cooling and heat recovery G.P. Vasilyev a , Iu.A. Tabunshchikov c , M.M. Brodach c,∗ , V.A. Leskov a,b , N.V. Mitrofanova a , N.A. Timofeev b , V.F. Gornov a,b , G.V. Esaulov c a
JSC “NIIMosstroy”, Moscow, Russia JSC “INSOLAR-ENERGO”, Moscow, Russia c Moscow Architectural Institute (State Academy), Moscow, Russia b
a r t i c l e
i n f o
Article history: Received 16 June 2015 Received in revised form 30 November 2015 Accepted 1 December 2015 Available online 8 December 2015 Keywords: Condensation Phase transition Heat exchanger Defrostation Heat exchanger frosting Heat pump system Energy efficiency Heat regime Air flow
a b s t r a c t This article, written as a result of theoretical and practical research, describes a survey of condensate nucleation in heat exchangers utilizing low-potential heat of humid air. The authors conducted a series of studies aimed at developing energy-independent technical solutions to protect heat exchangers from the freezing of the moisture condensing on their exchange surfaces in the course of humid air heat recovery. There was a negative dependence of the thickness of the layer of condensate formed on the heat exchange surface, the condensation rate, and the moisture content of warm air. The article presents the outcomes of the numerical study aimed at building a model of the condensation processes that occur due to a flow of moist air when the air is cooled and heat is utilized. The study provided experimental validation for the consistency of the processes related to water vapor condensation in the flow of cooled moist air. The outcomes presented in the article can apply to both the exchange systems using the low potential heat of the atmospheric air, e.g., for room heating or snow melting, and to the exhaust air energy recovery systems of the building ventilation plant. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The widespread use of air cooled heat exchangers, recuperators, and other systems recovering waste heat of exhaust air from ventilation systems is impeded by the condensation and subsequent freezing of moisture on the surfaces of air cooled exchangers. Frost formation and icing of exchange surfaces exposed to moist air at subzero temperatures results not only in a sharp drop in the heat exchange efficiency but also in the need to use additional power to defrost the apparatuses [1,2]. The aforementioned problems are typical of air cooled systems virtually all over Russia [3]. There are two main ways to protect heat exchanger surfaces from icing: regular heating (defrosting), which means additional energy costs, and chemical protection of exchange surfaces by means of special anti-icing moisture-repellent compositions applied to the heat-exchange surface. The article [4] analyzes these two ways in detail, with emphasis on the chemical methods. The
∗ Corresponding author. Tel.: +7 916 1725736. E-mail address: [email protected] (M.M. Brodach). http://dx.doi.org/10.1016/j.enbuild.2015.12.002 0378-7788/© 2015 Elsevier B.V. All rights reserved.
condensation of water vapor in air and on cold heat-exchange surfaces clearly has a strong influence on the rate of frost formation and air cooler icing. A reasoned choice of the geometric parameters of heat exchangers, cooling air flow rates, and conditions for heat exchange with cooling surfaces can significantly reduce the energy required to defrost heat exchangers [5,6]. Hence, creating heat regime models for air cooled exchangers that provide a reasonable picture of the heat exchange process accounting for air vapor condensation in the cooling air and on cold exchange surfaces is, at the moment, an important task. Coping with the task can help to create new, energy-independent solutions to protect exchange apparatuses from frost formation. Many studies have been performed to solve this task; the work described in are most similar to the problems analyzed in our article [7]. 2. Modeling the processes of moist condensation in cooling air The purpose of the studies described herein was to develop energy-independent technical solutions protecting heat exchangers from the freezing of the moisture condensing on their exchange
94
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surfaces in the course of moist air heat recovery/recuperation. Numerical analyses were used to model moist condensation processes in the air flow exposed to cooling. Calculations were made using a model simulating two air canals exchanging heat via the heat-conducting wall. Fig. 1 provides a general view of the air cooler in question. To study the thickness of the condensate droplets nucleating on the heat exchange surface and the rate of nucleation, the authors solved the conjugate problem of heat conductivity and gas dynamics using the latest software platform [8] ANSYS CFX 11.0 based on the numerical solution of the Navier–Stokes equation system.
2
2
2
∂u ∂u ∂u ∂u ∂p ∂ u ∂ u ∂ u + + + u + v + w =− + ∂t ∂x ∂y ∂z ∂x ∂ x 2 ∂ y2 ∂ z 2
2
2
2
∂v ∂v ∂v ∂v ∂p ∂ v ∂ v ∂ v + + + u + v + w =− + ∂t ∂x ∂y ∂z ∂y ∂ x 2 ∂ y2 ∂ z 2
2
2
where ¯ is the average pressure, and indices i = 1,2,3 and j = 1,2,3 correspond to the coordinates x, y, z. Shear (Reynolds) tensions ui uj are six unknowns additional to the averages motion param¯ that are usually approximated using the Boussinesq eters (u¯ i , p) hypothesis:
ui uj = −t
∂u¯ i ∂u¯ j + ∂xj ∂xi
+
2 kıij , 3
(5)
where t is the additional viscosity caused by pulsations; k is the averaged eddy pulsation energy (TKE). The system is open-loop, so it requires additional conventions (“eddy models”). 2.1. First set of numerical experiments
2
∂w ∂w ∂w ∂w ∂p ∂ w ∂ w ∂ w + + + u + v + w =− + ∂t ∂x ∂y ∂z ∂z ∂x2 ∂ y2 ∂z 2
(1) Furthermore, equations of continuity and of state were to be satisfied:
∂p ∂(u) ∂(v) ∂(w) + + + =0 ∂t ∂x ∂y ∂z
(2)
p = RT
(3)
In the first sequence of numerical experiments, the authors analyzed the thermal state of the heat-conducting wall made from different materials (copper and PVC) located between two air flows (cold, −20 ◦ C, and cooling, +20 ◦ C) [9]. The areas analyzed corresponded to the exchanger simulation model shown in Fig. 1. In this set of experiments, the length of the heat exchanger was 0.3 m along the x axis (in the direction of the cooling air flow) [10,11]. Three flow modes were compared (the oncoming flow rates were 2, 1, and 0.2 m/s), and the length of the square section device was 0.3 m. The Reynolds numbers for each of the three flow modes were, respectively: 13500, 6750, 1350.
here u, v, w are the sought components of the air velocity vector (by axes x, y, z), p is the pressure, t is the time, the dynamic viscosity coefficient of air, is the density, R is the universal gas constant, T is the temperature. For the simplicity of modeling, we can assume that air is incompressible and isothermal; body forces are ignored. Direct solution of Eq. (1) taking into account the eddies of all scales (DNS, Direct Numerical Simulation) can be practically implemented only for very low flow rates. Therefore, the authors used a semi-empirical method based on velocity splitting by the time averaged component and the pulse component ui (t) = ui + ui (t) with transition to the so-called Reynolds averaged Navier–Stokes method:
∂p ∂ ∂ ∂ uj + ui · uj = + ∂t ∂xi ∂xj ∂xi ∂ui = 0, ∂xi
∂ui ∂xi
= 0,
∂ui ∂uj + ∂xi ∂xj
− ui uj , (4)
Fig. 1. Air cooler simulation model. Length: 1 m (along the X axis). Height of each of the areas of cool and cooling air (along the Y axis): 0.059 m. The area width was taken as 0.06 m (along the Z axis), and the symmetry condition was established on the border of this area. Sheet thickness is 0.002 m.
Fig. 2. Comparison of the laminar (red line) and turbulence (blue line) problem definitions. Average temperature of the heat-conducting PVC wall on the cold air side. A graph—turbulent flow mode, 2 m/s; B graph—laminar mode, 0.2 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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The computation grid consisted of 233,220 hexa-elements (264,600 nodes). 2.1.1. Boundary conditions Cooling air at the input: flow rates (2, 1, 0.2 m/s) and static temperature 20 ◦ C. Cooling air at the output: static pressure 1 atmosphere. Cold air at the input: flow rates (2, 1, 0.2 m/s) and static temperature −20 ◦ C. Cold air at the output: static pressure 1 atmosphere. The wall is considered to be heat-conducting. All other walls in the problem (lower wall, upper wall, and back wall) were considered adiabatic. To reduce the calculation time, the symmetry condition was set for the xy plane because the initial flow area was assumed to be twice as large. The first numerical experiment in this set evaluated the temperatures of the heat-conducting PVC wall for all the flow modes in two different problem definitions, the laminar and the eddy (with the SST turbulence model). Graphs in Figs. 2 and 3 show the changes to the heat-conducting wall temperature along the x axis. Based on the outcomes of the numerical experiment, it was assumed that at air flow rates exceeding 0.5 m/s, the mode was turbulent, and at lower rates, it was laminar. The second numerical experiment compared the heat regimes of the heat-conducting wall [12] made from copper and from PVC
Fig. 4. Average temperature of the wall on the cold air side. Blue line—PVC; red line—copper. A graph—turbulent flow mode, 2 m/s; B graph—laminar mode, 0.2 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Average temperature of the wall on the cold air side. Blue line—PVC; red line—copper. Turbulent flow mode – 1 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
for various air flow modes. Figs. 4–7 show the outcomes of the experiment. 2.2. Second set of numerical experiments
Fig. 3. Comparison of the laminar (red line) and turbulence (blue line) problem definitions. Average temperature of the heat-conducting PVC wall on the cooling air side. A graph—turbulent flow mode, 2 m/s; B graph—laminar mode, 0.2 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
In the second set of numerical experiments, the authors performed computations for three types of the wall dividing the flows of cold and cooling air, namely walls made of PVC, steel, and copper. The other walls of the air canals are assumed to be insulated. The dimensions of the heat exchanger were as those in the simulation
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Fig. 8. Temperature change along the x axis averaged by the cross-section of the heat-conducting PVC wall. Green line—cold air temperature −3◦ C; red line −15◦ C; blue line −28◦ C.
Fig. 6. Average temperature of the heat-conducting wall on the cooling air side. Blue line—PVC; red line—copper. A graph—turbulent flow mode, 2 m/s; B graph—laminar mode, 0.2 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
model shown in Fig. 1. To reduce the domain of computation, the flow symmetry condition was specified for the xy plane. 2.2.1. Boundary conditions Cooling air at the input is indicated with arrows in the upper part of Fig. 1; the direction of the current was along the x axis. The flow rate was 3.85 m/s); the temperature was 23 ◦ C. The static pressure of the cooling air at the exchanger output was 1 atm.
Cold air at the input is indicated with arrows in the lower part of Fig. 1. The direction of the current was against the x axis (contra flow with hot air); the flow rate was 3.85 m/s; the temperature of the cold air was changed and assumed to be −3 ◦ C (average winter temperature in Moscow), −15 ◦ C, and −28 ◦ C. Static pressure of the cold air at the exchanger output (room entrance) is 1 atm. Fig. 8 shows the outcomes of the third numerical experiment, in which graphs depicting temperature changing along the x axis are averaged by the cross-section of the heat-conducting polymer wall for the cold air temperatures −3 ◦ C, −15 ◦ C, and −28 ◦ C. Similar computations have been performed for heat-conducting walls made from steel and copper. The computation results have been consolidated in Table 1. Table 1 shows the areal temperatures on the exhaust air side for various sheet materials. As a result of the computations, the authors obtained a threedimensional temperature distribution on the cooling air side of the heat-conducting wall; this value was then used in the fourth numerical experiment as a boundary condition to solve the moisture condensation task. It should be noted that, due to the low heat conductivity of the polymer material, the three-dimensional temperature distribution on the heat-conducting wall was used in the subsequent computations. Then, only the area of the cooling air flow was taken as the domain of the computation to model water vapor condensation processes, and the obtained three-dimensional temperature distributions were stipulated as the boundary condition for the temperature on the heat-conducting wall. Fig. 9 shows the simulation model of the cooling air flow. The gravity direction was vertically downwards along the y axis. The multi flow model “Droplets with Phase Change” was selected to model the processes of fluid condensation on the wall. In this model, gas (or, to be more precise, saturated water vapor) was assumed as the carrier phase and droplets of the condensing liquid as the secondary phase. In the model, air is approximated as a continuous medium and water as drops of a small dimension of an order of 10 to 4 mm. In the process of the calculation, their diameter may be increased. Table 1 Areal temperature of the heat-conducting wall on the cooling air side.
Fig. 7. Average temperature of the heat-conducting wall on the cooling air side. Blue line–PVC; red line—copper. Turbulent flow mode – 1 m/s. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Material
Cold air temperature (◦ C)
Polymer Copper Steel
−3.1 12.1 10.75 10.8
−15 6.5 4.6 4.5
−28 −0.3 −2.3 −2.4
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Fig. 9. Simulation model of the cooling air flow used to model water vapor condensation processes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The initial concentration of the liquid both in the calculation region and at the entrance is considered as zero. The initial temperature is about 50 ◦ C. An important factor for the computation was the right selection of the time increment that would make the problem solvable. In our case, we selected a range from 10−6 s to 5 × 10−5 s. Due to a very small time increment and quite a long area (1 m), each computation took more than 24 h. The computations were performed under the same boundary conditions, and the relative moisture content of the cooling air at the exchanger input was assumed in various numerical experiments to be equal to 30%, 60%, and 80%. The calculations were considered complete at 9000 iterations. For all this, the level of discrepancies for the principal equations reached the order of 10−15 with the time spacing of 5 × 10−5 s. The temperature distribution on the lower heat-conducting wall (xz plane) was taken from the previous computations for all the three temperature modes of the cooling air supplied. In all the computation options, the moisture content in the cooling flow grew evenly toward the end of the flow, displacing the gas. The highest condensation rate was also observed on the heatconducting wall at the exchanger output. The Lagrange approach to moist droplet modeling was used to model nucleation of near-wall fluid. Non-stationary computation. The carrier phase was gas. The trajectories of fluid elements were found at the end of each time increment based on the data available about the gas flow. Fig. 10 shows the resulting fluid film that nucleated on the lower PVC wall at a cooling air moist content of 30% and an air temperature of −30 ◦ C. Fig. 11 shows the rates of liquid nucleation in a unit volume and the distribution of the liquid and gaseous phases in the median and
Fig. 10. Thickness of near-wall fluid film on the PVC heat-conducting surface and fluid element trajectories.
outflow cross-sections of the cooling air. As one can see in Fig. 5, the thickness of the condensation fluid grows at the exchanger output. The outcomes of the fourth numerical experiment with the approximate value of the resulting fluid condensate film thickness his consolidated in Table 2. The outcomes of the fourth numerical experiment are presented in Table 2. One can notice that condensation rates go down when plastic heat-exchange surfaces are used. Another important feature of the outcomes obtained is the contradiction between the change trends of the highest transition rates and the condensate film thickness at the exchanger output depending on the temperature of the cold air supplied to the exchanger. 3. Experimental validation (lab experiment) Experimental validation of the outcomes obtained during the numerical experiments was performed on a specially designed and manufactured laboratory test bench. In the course of the lab experiments, the researchers surveyed the moist regime in the air cooled heat exchanger with two reverse flow air canals divided by a wall made from the tested material, PVC. The aim of the experiment was to provide experimental validation of the outcomes obtained in
Fig. 11. Liquid nucleation rate in a volume unit and distribution of the liquid and gaseous phases in the cooling air flow. Left graph—cross-section in the middle (x = 0.5 m); right graph—outflow cross-section (x = 1 m).
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Table 2 Results of water vapor condensation modeling. Material
Cold air temperature (◦ C)
Moisture content (relative, by weight) (%)
Maximum rate of water vapor–liquid transition, kg/(m3 s)
Estimated thickness of condensate (water) film at the exchanger outflow, mm
PVC
−3.1
30 60 80 30 60 80 30 60 80
0.00038 0.00043 0.00044 0.00085 0.001 0.00114 0.00088 0.00098 0.00112
11.8 10.6 9.7 9.2 8.7 7.9 9.8 9.5 9.2
30 60 80 30 60 80 30 60 80
0.00099 0.00124 0.00137 0.0011 0.00135 0.0015 0.0012 0.0015 0.00164
9.38 9.15 9.08 9.22 9.05 8.98 9.1 8.95 8.9
30 60 80 30 60 80 30 60 80
0.001 0.0013 0.0014 0.0011 0.00139 0.00154 0.0012 0.0015 0.0017
9.5 8.8 8.8 8.95 8.78 8.68 8.9 8.7 8.6
−15
−28
Copper
−3.1
−15
−28
Steel
−3.1
−15
−28
the course of the numerical experiments and to survey condensate formation on polymeric heat-exchange surfaces [13]. The test bench virtually replicated the geometrical dimensions of the domain of computation shown in Fig. 1: there were two air canals, the exhaust canal with warm air and supply canal with cold air, that were divided by a sheet made from the tested material (PVC) so that the sheet was positioned horizontally, parallel to the air pumped by the fans through the canals. The bench had sensors recording the surface temperatures of the tested materials as well as the temperature of the air at the input to and output from the canals. Fig. 12 shows the general view of the test bench and the points where the temperature sensors were fixed. Fig. 13 shows the photo of the bench. Condensate formation was observed visually and photographed during the testing. Fig. 14 shows the photographs of the test and condensate formation. The lab experiment was carried out at the inflow cold air temperature of −3.1 ◦ C. In essence, this cold air temperature equals the average outdoor air temperature during the heating season in Moscow. Additionally, the freezing of the condensate would strongly affect lab modeling of the exchanger’s heat regime for lower temperatures. The moisture content of the cold air supplied to the exchanger was measured with the help of a vapor generator. The thickness of the condensate film was measured by the maximum height of the droplets nucleating at the exchanger outflow. Table 3 compares the outcomes obtained in the course of the
numerical analyses and laboratory experiments, which are shown in Fig. 15. The lab experiments demonstrate quite a good convergence with the numerical outcomes. The deviation of the experiment
Fig. 12. Test bench model.
Fig. 13. Test bench.
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Table 3 Comparison of the outcomes of numerical and laboratory experiments. Material
Cold air temperature (◦ C)
Moisture content (relative, by weight) (%)
Thickness of condensate (water) film at the exchanger outflow as per the numerical experiment, mm
Thickness of condensate (water) film at the exchanger outflow as per the laboratory experiment, mm
PVC
−3.1
30 60 80
11.8 10.6 9.7
8.2 7.5 6.6
Fig. 14. Photograph of condensate nucleation process on Sample No. 2 without Teflon coating.
corresponds to the thickest condensate film forming at the outflow from the exchanger. It is noteworthy that the thickest condensate film was observed on a heat-conducting wall made from PVC. Also quite interesting is the discovered inverse dependence between the thickness of the condensate film on the heat exchange wall and the moisture content of the cooling air; as the relative air humidity rises, the condensate film grows thinner. It appears that this is related to the rate of water vapor condensation in the air flow, which grows as the humidity of the air flow increases. This, in turn, results in a greater amount of condensate coming out of the exchanger with the air flow. Lowering the temperature of the cold air fed into the exchanger leads to the same result. As the temperature of the cold air drops, the rate of water vapor condensation in the cooling air flow increases, and the condensate film forming on the exchange wall at the outflow from the heat exchanger grows thinner. Another important outcome of the numerical experiments is the proximity of the condensate thickness values obtained for heat-conducting walls from PVC, copper, and steel for cold air temperatures below −15◦ C. This fact confirms that it is desirable to use polymeric heat exchangers for exhaust air energy recovery in building ventilation plants in most of Russia. The outcomes of the lab experiments have confirmed an inverse dependence between the thickness of the condensate film on the heat exchange wall and the moisture content of the cooling air; as the relative air humidity rises, the condensate film grows thinner. Acknowledgments The research presented in this article has been conducted by JSC “NIIMosstroy” with financial support from the Ministry of Education and Science of Russia. Unique project identifier is RFMEFI57914X0081. References
Fig. 15. Comparison of the outcomes of numerical and laboratory experiments.
results from the calculated ones was found in the range of 30%, which is an admissible result for a model of such complexity. The outcome of the lab experiments presented in Table 2 confirm the inverse dependence between the thickness of the condensate film on the heat exchanger wall and the moisture content of the cooling air; as the relative air humidity rises, the condensate film grows thinner. 4. Conclusion The survey presented in this article helped to gain an indepth view of the condensate droplet formation process during air flow energy recovery and to identify the most “condensate-prone” areas in the exchanger with the highest likelihood of condensate formation and subsequent freezing. As the numerical experiments have proven, the lowest water vapor condensation rate
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