PREDICTION OF ICE AND FROST FORMATION IN THE FIN TUBE EVAPORATORS FOR AIR/WATER HEAT PUMPS

Transcription

1 - 1 - PEDICTION OF ICE ND FOST FOMTION IN THE FIN TUE EVPOTOS FO I/WTE HET PUMPS M. lbert,. Sahinagic, L. Gasser,. Wellig and K. Hilfiker Lucerne Uniersity of pplied Sciences and rts Engineering & rchitecture, CC Thermal Energy Systems & Process Engineering, Technikumstrasse 1, CH-648 Horw, Switzerland. In the next few years, the seasonal performance factor of air/water heat pumps will be greatly increased. Success in doing this will depend on two factors: The adaptation of the operating characteristic of the heat pump by the use of continuous power control and the reduction of ice and frost formation. Frost leads to a considerable reduction of the airflow through the eaporator and, therefore, of heat and mass transfer. The formation of ice and frost is influenced by a complex interaction between eaporator, fan characteristic and the characteristic of the heat pump itself. In order to further improe the efficiency of the oerall system, a precise prediction of the operation behaiour is required. ased on the theory of simultaneous heat and mass transfer, a mathematical-physical simulation program was deeloped in the course of the LOEF project. This program allows forecasts of the non-stationary the operation behaiour of the air/water heat pump during ice and frost formation in the eaporator to be made. Here, the greatest challenge was to deelop a physical correlation for the properties of the ice and frost deposits during this non-stationary process. Numerous experiments allowed four fields to be distinguished with different characteristics - dependent on the temperature on the boundary layer between air and ice or frost. Comparison with the results of measurements made show that the simulation program deeloped represents the processes inoled in an air/water heat pump during its operation with a high degree of accuracy. Key Words: air/water heat pump, ice and frost formation, simulation 1 INTODUCTION ir/water heat pumps (/W-HP) extract heat energy from ambient air when this is cooled down in an eaporator in the form of a fin tube heat-exchanger. t low ambient temperatures, the surface temperature of the eaporator falls below the freezing point of water resulting in the water apour contained in the air being deposited on the fins and tubes in the form of ice or frost. The building up of ice or frost layers leads to an obstruction of the free cross-section in the eaporator and thus reduces the air flow rate; this leads in turn to a degradation of heat transfer and, therefore, of the efficiency of the whole heat pump. The growth of a frost layer leads to nonstationary processes during operation, meaning that process ealuations are heaily impeded; in order to erify the effects of measures taken to optimise the /W-HP, complex experiments are often unaoidable. In the LOEF project (erlinger et al. 8), a mathematical-physical simulation program was deeloped which allowed the calculation of the non-stationary operating behaiour of /W-HP with ice and frost formation in the eaporator for any geometries. The core of the calculation program is a model for simultaneous heat and mass transfer along with an empirically deeloped correlation for the calculation of the effectie thickness of the frost layer

2 - - formed and the air-side heat transfer coefficient. eliable statements on the behaiour of the entire heat pump process can only be made if it is possible to correctly calculate both the growth of the frost layer and the associated air-side pressure drop across the eaporator. STTE OF THE T layer of frost on the fins of the eaporator has a negatie effect on the thermal resistance between ambient air and eaporating working fluid as a result of two different effects. ecause of its limited thermal conductiity, the frost represents - together with that of the fin and tube material - an additional thermal resistance between the boundary layer of the air and the eaporating refrigerant. The thermal conductiity of frost is heaily dependant on its density as the air trapped in the pores exhibits a considerably lower thermal conductiity than solid ice. From measurements, it is known that the thermal conductiity of frost can be calculated for the releant temperature range using λf.15 W/mK (Sahinagic et al. 4). The obstruction of the free cross-section has, howeer, a much greater influence than the higher thermal resistance of the frost layer (Sahinagic et al. 4). s a result of the increased pressure drop, the air flow rate decreases in accordance with operating characteristics of the fan; the output temperature of the air falls and the simultaneous heat and mass transfer is impaired. s a result, the eaporation temperature drops and, along with it, the efficiency of the heat pump. Therefore, the eaporator can be optimised by proiding for a more een distribution of the frost deposited. Most studies concerning frost formation in eaporators are concerned with the direct cooling systems in refrigerated warehouses, i.e. concerning de-sublimation at low temperatures. Inestigations in the temperature range of -1 C to 15 C releant to /W-HP are ery seldom. For the definition of a model, howeer, one can reert to the examination of selected works on the subject. Sanders, for example, has applied Merkel s main equation (Merkel 196) to heat and mass transfer in a fin tube heat-exchanger (Sanders 1974). Using this approach, the temperature and humidity gradients can be united in an enthalpy gradient, which allows a considerable simplification of the equations for simultaneous heat and mass transfer. With the calculation method for heat transfer circuits introduced by Strelow, a non-iteratie calculation of the input and output states for the eaporator is possible (Strelow 1997). In this case, the characteristics of the heat exchangers are described on the basis of the operating characteristics according to ošnjakoić (ošnjakoić et al. 1997). The calculation of the pressure drop in the dry eaporator according to Glass simple empirical equation proides ery precise results (Glass 1988). Fahlén extended Glass equation with the effectie frost thickness, which means that the pressure drop in an iced-up eaporator can also be ealuated (Fahlén 1996). In this case, the effectie frost layer is defined as the thickness of a flat layer which would result in the same pressure drop as the real layer of frost with all its irregularities. 3 MODEL 3.1 Simultaneous heat and mass transfer The principal equations for simultaneous heat and mass transfer were deried using the example of a duct of infinitesimal length cooled on one side. It must be noted that different states can occur in the eaporator depending on ambient conditions. If the surface temperature of the fins is aboe the dew point temperature of moist ambient air, the air will be chilled without being dehumidified. t surface temperatures below the dew point temperature, the water apour in moist air condenses and a latent heat flow occurs in addition to the sensible heat flow obtained from the cooling of the air. Surface temperatures below the freezing point of water lead to direct de-sublimation of water apour in the air or to the freezing of any condensate present; the latent heat flow is, compared with condensation, increased by the amount of heat released during

3 - 3 - solidification. ϑ x i i ϑ x o o ϑi x dx i moist air ϑ ϑ x ϑ x ice / frost cooling surface / fin x d dl a d Q & s d Q & d Q & l x x x i x o dx ϑ ϑ ϑ i ϑ o abs. humidity abs. humidity at the boundary layer abs. humidity at the inlet abs. humidity at the outlet infinitesimal change in abs. humidity air temperature temperature at the boundary layer air temperature at the inlet air temperature at the outlet infinitesimal change in air temperature Figure 1: Surface area of infinitesimal length The entire heat flow transmitted to the cooling surface area d Q & consists of, in total, the sensible heat proided by the cooling of moist air d Q & s (conectie heat transfer) and the latent heat flow d Q & l of the condensation and/or solidification of the water apour precipitated from the air d m& (mass transfer): spv s α ( ϑ ϑ ) d (1) r dm& l i spv r β ρ i ( x x ) d () The ariable r i corresponds to the specific enthalpy of eaporation of water r during condensate formation and, for frost formation, the specific enthalpy of sublimation r s. In accordance with Lewis analogy, the mass transfer coefficient β and the heat transfer coefficient α are proportional to each other. If the Lewis number Le is known, β can be calculated from α. For the present application with moist air, one can calculate β using Le 1 (Sahinagic et al. 4). β α ρ 1 c p 1 Le / 3 (3) Consequently, it follows for the entire transmitted heat flow that: α s + l α i cp ( ϑ ϑ ) + ( x x ) r d (4) For the calculation of the simultaneous heat and mass transfer, both the temperature and humidity gradients must be considered. Merkel showed that the two gradients can be formulated in a combined way as an enthalpy gradient (Merkel 196). The equations for the calculation of simultaneous heat and mass transfer are simplified considerably by the use of enthalpy gradients and a clear oeriew results. Moreoer, the entry state of the air can also be expressed in just one expression, i.e. the specific enthalpy of moist air. Merkel starts with equation (4) as the basis of his deriation. In this case, assumptions were made that the Lewis number is one ( Le 1) and the specific heat capacities of moist and dry air are approximately identical.

4 - 4 - ssuming c c the specific enthalpy of moist air is: p p d h c p ϑ + x r (5) ccordingly, the specific enthalpy gradient between the air and the boundary layer (with saturated air at the boundary layer) is: h s c p ( ϑ ϑ ) + r (x x ) (6) Using (6) in (4), the heat flow d Q & results in the case of partial condensation: α (h s ) d (7) c p In aboe equation, the heat flow from the solidification of the water apour must additionally be added during ice and frost formation. So that the entire calculation can be made using only enthalpies, all temperatures (internal/external tube surface temperature, eaporation temperature of the working fluid) must also be expressed in terms of their corresponding specific enthalpies. This is done by the use of the specific saturation enthalpy of moist air as the enthalpy in the case of saturation is only dependent on the temperature. The sensitie heat flow d Q & s can be calculated in accordance with (1), or by means of the energy balance oer the surface area d (temperature change of moist air while flowing oer d ). Thus the following is obtained for α : α m& ϑ c ϑ p d (8) For the entire heat flow, with (8) in (7), the following results: (h s m d ϑ ϑ & ) ϑ (9) The heat flow d Q & is therefore proportional to the quotient of the driing enthalpy and temperature gradients to the boundary layer as well as to the temperature decrease of moist air in the direction of flow. The heat flow d Q & can also be calculated using the air-side energy balance with the infinitesimal change in specific enthalpy of the moist air dh : m dh & (1) Using (1) in (9) it follows that: dh h s ϑ ϑ (11)

5 - 5 - ssuming that the moist air in the air cooler of the heat pump is saturated, the following is alid: h s dh s s s ϑ ϑ s (1) If the air is saturated with water apour, its specific enthalpy only depends on its temperature. For simplification, the saturation cure for moist air (Mollier - diagram) is linearised for the releant temperature range: h s a + b ϑ s (13) The relationship between the gradient of the specific saturation enthalpy and the temperature gradient in the direction of flow is then: dh s s b (14) y differentiation of the specific enthalpy of moist air against saturation temperature, the following results: dh s s c p + c p V x s + (r + c p V ϑ s dx ) s s (15) Since x x ( p ( ϑ )) s it follows that: s s dx s s dx dp s dp s (16) From the calculation of the mass loading of the air with water apour one obtains dx dp s V 1 p (17) where is the gas constant for air and V the gas constant of water apour, respectiely. From the Clausius-Clapeyron equation for the apour pressure cure we obtain: dp s r V p T s (18) y the introduction of (16), (17) and (18) in (15) one obtains: dh s s c p + c p V x s (r + c p V ϑ s ) V p p r T s (19)

6 - 6 - c pv x s and c pv ϑs can be neglected in comparison to the specific enthalpy of eaporation r. For the gradient b the following clear relationship can be formulated: dh b s s c p + V p p r T s () 3. Calculation method for fin tube air coolers (operating characteristic) For the calculation of the heat exchanger configuration, a method based on coupled matrix equations is applied which allows an iteration-free calculation method to be used that can be applied to any configuration ariants. This method was already proposed by ošnjakoić and later further deeloped by Strelow (ošnjakoić et al. 1997, Strelow 1997). With the operating characteristics of the moist air and the working fluid (refrigerant) deried below, it is possible to describe the connection between specific entry and exit enthalpies of both flows in the heat exchanger using a linear approach. With the aid of the factor b (equation 14), the temperature gradient between the internal surface area of the tube and the eaporating working fluid ( ϑ T ϑ ) can be expressed using the gradient of specific enthalpies hst s (specific saturation enthalpies). Using the heat transfer coefficient α on the working fluid side, the following is alid: dq & α α ( ϑt ϑ ) d (hst s ) d b (1) The heat transfer between the moist air and the eaporating working fluid can be calculated with the gradient of specific enthalpies: k(h s ) d () For the oerall heat transfer coefficient k the following is alid: c p δt b k + + α λt α 1 (3) The entire heat flow d Q & can also be calculated using the energy balances of the two mass flows oer the surface area d. In this case, the changes in the apour quality x V and temperature Δ T on the working fluid side must be considered due to the temperature glide and the flow-dependent pressure drop. The energy balances of the two fluid flows gie for the transferred heat flow: m& d dh m& r dx V m& ~ c b p dh s (4) With the corrected specific heat capacity: ~ c p r ( 1 x ) ΔT V (5)

7 - 7 - The factor X / indicates the relationship between a part-surface area to the total air-side heat transfer surface area. Using this together with Y ( h s ), it follows that: & dh k Y dx and & dh k Y dx (6) U With corrected mass flows U & and U & : U s U & m ~ c m& d and U& p & (7) b y rearranging the equations in (6) one obtains: dh dx k dhs k Y and Y U & dx U & (8) The aboe equations are subtracted from each other: dy k + dx U& k U& Y (9) For a counter-flow heat exchanger with X one obtains the exit state ( h ho ) for the specific enthalpy of moist air along with the entry state ( h s hsi ) for the working fluid on entry into the eaporator. The integration of (9) then yields: Y (h s ) (h o si ) e k k X U U& & (3) For X 1 the following is alid: h i so (h o si ) e The total transferred heat flow is: k k U U& & (31) Q& U& (h ) U& (h i o so h si ) (3) From (31) and (3), one obtains the dimensionless change in specific enthalpy of the two streams: φ h (h (h i i o si ) 1 e ) U& L 1 U& F k k U& F U& L e k k U& U& and φ h U& φ U& h (33) Using the same method, the operational characteristics for a finned tube element with a finite surface area were subsequently deried. In this case, a fin efficiency must be taken into account

8 - 8 - during the consideration of heat transfer from moist air to the fins of a tube element, which is calculated according to Sanders (Sanders 1974). The calculation of the air-side heat transfer coefficient is carried out using an empirical correlation obtained from measurements on the dry eaporator (VDI-Wärmeatlas 6). y stringing seeral tube elements together, one finally obtains a complete fin tube eaporator. The combination of the tube elements that are considered as being single units is done in the calculation program using a so-called structure matrix. 3.3 Empirical correlations s already mentioned, the main effect of a frost layer is the obstruction of the free cross-section for air-flow in the eaporator, which leads to a reduction of the air flow rate account of the fan characteristic. For this reason, the precise calculation of the pressure drop is especially important for the correct simulation of the whole process. the pressure drop for a dry fin tube eaporator (Fahlén 1996) is: Δp n T 5 ρ w sfin (34) This equation contains only the number of the tube rows n T in the direction of air flow, the fin spacing s Fin, the density of moist air ρ and the air elocity between the fins w. n ealuation of the equation for air elocities between 1 and 3 m/s yielded a maximum deiation of 1% (erlinger et al. 8). Using the continuity equation, the pressure drop can be expressed as a function of the air flow rate V & (alid for a dry eaporator). In this case, the number of the fins n and the height of the eaporator H are required as additional factors. Fin Δp nt V 3 5 ρ 1 3 nfin H sfin & (35) eduction of the flow cross-section by the effectie thickness of the frost layer δ F : Δp nt V 3 F 5 ρ fl 1 3 n (s Fin H Fin δf ) & (36) Soling equation (35) for s Fin, inserted in (36) and soled for the effectie frost thickness: δ F nt ρ V& 3 V& 1 nfin H Δp 3 Δp F 1 3 (37) In order to be able to determine the effectie frost thickness from the frost mass deposited, an empirical correlation was deeloped on the basis of an extensie set of measurements of the effectie frost thickness as a function of the frost mass loading. In this case, the effectie frost thickness is calculated from measured alues for the pressure drop Δ pf and the air flow rate V & using equation (37). y simultaneous measurement of humidity at the input and output of the eaporator, the frost mass m F, and, by diiding by the eaporator surface area, the frost mass loading maf can be calculated. The results of the measurements are shown in figure for arious fin temperatures.

9 Effectie frost thickness [m] ange IV: frost formation experimental data correlation ange III: ice/frost formation experimental data correlation ange II: ice formation experimental data correlation (experimental data for arious fin temperatures, cf. erlinger et al. 8) Frost mass loading [kg/m ] Figure : Effectie frost thickness as a function of the frost mass loading in different ranges Since the frosting process depends strongly on the fin temperature, four different ranges can be distinguished for which a separate correlation is necessary. The different correlations are summarised in table 1. Table 1: Correlations for the effectie frost thickness for arious temperature ranges ange ϑ Fin Correlation Illustration I Condensate formation > -3 C Δp C [Pa] Δp m ac [Pa] [kgm ] II Ice formation C δf m.8 [m] [kgm af ] III Ice/frost formation C δf m.51 m] [kgm af [ ]

10 - 1 - IV Frost formation < -5.5 C For m af.3 kgm δf m.9 m] [kgm af [ For m af >.3 kgm δf maf.51 m] [kgm ].65 [. ] In area I, the water apour is just condensed without any freezing occurring. The condensate forms a film or indiidual drops on the fins through which the air-side flow pressure drop is increased. s the condensate flows off continuously, a steady state is achieed after a certain period of time. t the somewhat lower fin temperatures occurring in area II, the condensate no longer flows off but, with a slight delay, freezes to a compact ice layer. The transitional area between ice and frost formation is coered in area III. s a result of small local temperature differences, both ice and frost can result. rea IV applies to ery low fin temperatures where a frost layer is formed from the beginning as a result of pure de-sublimation. s the increase in the effectie frost thickness is not linear (figure ), two different correlations are used depending on the frost mass loading. For the calculation of the oerall heat transfer coefficient in (3), the air-side heat transfer coefficient α is required. The empirical correlation created for this is based on a calculation method for ribbed surfaces (VDI-Wärmeatlas 6). The equation for calculation of the apparent heat transfer coefficient α is: app 1 1 k α app + Ti 1 α C δ + λ T T (38) The oerall heat transfer coefficient k was determined by measurement on a brine cooled fin tube heat-exchanger under dry conditions. The heat conduction through the tube wall is calculated from the wall-thickness δ T and the thermal conductiity λ T of the tube material. The heat transfer coefficient of the cold brine α C can be taken from literature (VDI-Wärmeatlas 6). The heat transfer relation of the cold brine and the heat conduction through the tube wall are weighted by the surface area ratio between the air-side surface and the internal surface area of the tube wall Ti. For the calculation of the actual heat transfer coefficient, the fin efficiency must be considered. The following relationship between α and α app is alid: α app α Te + η Fin Fin (39) For the air side heat transfer coefficient the following empirical correlation is alid (erlinger et al. 8): α 45 w.78 (4)

11 ESULTS The pressure drop represents the main factor in simulations since the course of the process oer time is significantly determined by it. Especially in the case of a flat fan characteristic, a small deiation in the calculation of pressure drop has a strong effect on the air flow rate and therefore on the heat transfer in the eaporator too. Moreoer, the air flow rate influences frost growth, thus leading to an oer-proportionate error in the simulated pressure drop. s an example, figure 3 shows a comparison between measurements and simulation for air temperatures of 6 C and - C and a relatie humidity of 8%. detailed description of the heat exchanger and the experiments can be found in erlinger et al. (8). 1 1 ir-side pressure drop [Pa] Experiment ϑ 6 C Simulation ϑ 6 C ir-side pressure drop [Pa] Experiment ϑ - C Simulation ϑ - C Time [min] Time [min] Figure 3: ir-side pressure drop oer time at 6 C and - C with 8% rh In all operating states, the air-side pressure drop can be simulated with a high degree of accuracy. The maximum discrepancy in comparison to measured alues is around 8%. The simulated pressure drops are tendentially somewhat too low. The measured and simulated alues for heat flows in the eaporator oer time are shown in figure 4 at air temperatures of 6 C and - C and a relatie humidity of 8%. Heat flow in the eaporator [W] Experiment ϑ 6 C Simulation ϑ 6 C Heat flow in the eaporator [W] Experiment ϑ - C Simulation ϑ - C Time [min] Time [min] Figure 4: Heat flow in the eaporator oer time at 6 C and - C with 8% rh The alidation of the simulation program was carried out using the results of measurements made in experiments with a commercial /W-HP (Sahinagic et al. 8).

12 - 1-5 CONCLUSIONS ND OUTLOOK Using the simulation program described, the non-stationary operating behaiour of an /W-HP can be represented with a high accuracy. s a result, the effects of optimisation measures taken on the heat pump can be estimated with little effort and, consequently, the number of measurement series required can be greatly reduced. Especially during the deelopment of control concepts for continuously power-controlled /W-HP, a simulation program can be of great benefit since the icing-up of the heat pump also aries on account of changing operating characteristics. Here, new control concepts can be tested in a irtual way and any possible weaknesses can be recognised at an early stage. Moreoer, plant-specific control system parameters can be determined in adance. 6 EFEENCES erlinger L., M. Imholz, M. lbert,. Wellig, K. Hilfiker 8. LOEF: Optimierung des Lamellenluftkühlers/Verdampfers on Luft/Wasser-Wärmepumpen, Teil 1: Theoretische und experimentelle Untersuchungen, Swiss Federal Office of Energy, erne. ošnjakoić F, K.F. Knoche Technische Thermodynamik,. Teil, 6. uflage, Dr. Dietrich Steinkopff Verlag, Darmstadt. Fahlén P Frosting and Defrosting of ir Coils, Doctoral Thesis, Document D36, Department of uilding Serices Engineering, Chalmers Uniersity of Technology, Göteborg. Glas L.O. 1988/1989. Operation experience from air-water heat pumps Operational comparisons. Merkel F Verdunstungskühlung, VDI-Zeitschrift 7, S Sahinagic., M. Imholz, L. erlinger, H. Huber, K. Hilfiker 4. LOEF: Untersuchung der Frostbildung für Lamellenluftkühler on Wärmepumpen, Swiss Federal Office of Energy, erne. Sahinagic., L. Gasser,. Wellig, K. Hilfiker 8. LOEF: Optimierung des Lamellenluftkühlers/Verdampfers on Luft/Wasser-Wärmepumpen, Teil : Mathematischphysikalische Simulation des Lamellenluftkühlers mit Kondensat- und Frostbildung, Swiss Federal Office of Energy, erne. Sanders C.Th Frost Formation: The influence of frost formation and defrosting on the performance on air coolers, Dissertation WTHD 63, Delft Uniersity of Technology, Delft. Strelow O Eine allgemeine erechnungsmethode für Wärmeübertragerschaltungen, Forschung im Ingenieurwesen, Vol. 63, Part 9, S VDI-Wärmeatlas 6. Verein Deutscher Ingenieure, 1. bearbeitete und erweiterte uflage, Springer-Verlag, erlin, Heidelberg, New York.