See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/329566051 Theoretical Parametric Study of Wrap-Around Heat Pipe (WAHP) in Air Conditioning Systems Article · December 2018 DOI: 10.1142/S2010132519500044 CITATIONS READS 0 62 1 author: Mridul Sarkar Integrated Environmental Solutions, Pune, India 8 PUBLICATIONS 15 CITATIONS SEE PROFILE All content following this page was uploaded by Mridul Sarkar on 02 January 2019. The user has requested enhancement of the downloaded file. International Journal of Air-Conditioning and Refrigeration World Scientific Publishing Company Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems Mridul Sarkar Integrated Environmental Solutions India Pvt. Ltd. Pune-411021, India. [email protected]; [email protected] Warp around heat pipes (WAHP) belong to a special class of recuperative heat exchangers that transfer heat from inlet to outlet locations via thermal gradient, without using any energy. In the present work, effects of various mechanical parameters on the performance of a WAHP dehumidifier system that are based on the underlying principles of heat and mass conservation are presented primarily from a theoretical point of view. A simplified methodology pertaining to wet cooling coils is applied here for defining the case of moisture condensation during precooling process at WAHP evaporator. Inlet air temperature, inlet humidity ratio, air mass flow rate, dehumidifier outlet temperature and effectiveness are the main operational parameters considered in this study. On the other hand, comparative performance study of the WAHP system is done through other set of thermodynamic parameters like the supply air temperature, supply humidity ratio, specific coil load and recovered enthalpy. The subtle variations in these factors against the operational parameters not only help in stipulating functional characteristics of the WAHP, but also allow HVAC designers to make informed decisions for system design and performance without relying entirely on manufacturer’s equipment data. Keywords: Wrap-around heat pipe (WAHP), dehumidification, humidity, coil load, recovered enthalpy, effectiveness higher than many conductors of comparable dimensions4-5. Performance investigations of heat pipe heat exchangers (HPHX) and WAHP applied in HVAC systems for heat recovery are important topics of research. El-Baky et al. performed experimental investigation6 on the effect of return to fresh air mass flow ratios and fresh air temperatures on the effectiveness of HPHX system. Experimental study on a 2-Row copper HPHX7 charged with R-134a refrigerant by Yau et al. is aimed towards the investigation of the influence of evaporator inlet temperatures and face velocity on heat pipe performance. From the results, they concluded that the sensible effectiveness of HPHX actually decreased as the evaporator face velocity is increased. However, in the temperature range considered for the study, the sensible effectiveness stayed almost constant. Noie- 1. Introduction Due to global rise in energy prices and demand, it becomes very important that the energy sources be used and managed in an efficient and prudent way. Almost, 10-30% of annual energy consumption in building sector is due to air conditioning equipment1. In recent years, serious strides are taken in the field of energy recovery for cooling and dehumidification applications, which is a major requirement from HVAC systems particularly for hot, humid and temperate climates. The usage of heat pipes in air conditioning equipment for air-to-air heat recovery and efficient dehumidification is becoming more popular in recent time due to its ease of integration, less maintenance and no supplementary energy requirement for operation2-3. In fact, thermal conductivity of heat pipes is reported to be several times 1 2 Mridul Sarkar Baghban et al. presented theoretical and experimental investigations of a methanol-based HPHX system8 for hospital surgery rooms. Yau showed the impact of heat pipes on the energy efficiency of dehumidification systems9 through transient simulation model of an HVAC system installed with two 8-row HPHX for an operating theater in tropical climate of Malaysia. Ahmadzadehtalatapeh investigated the performance of an air conditioning system with a HPHX10 and verified that it met the comfort criteria recommended by ASHRAE through TRNSYS simulation. Experimental study of an air handling unit with 7looed WAHP11 by Jouhara et al. is aimed towards the investigation of the effect of heat loads and face velocities on the overall resistance of the heat pipe loops. They also concluded that the overall effectiveness of WAHP decreases as the face velocity increases. Ezzuddin et al. presented an experimental investigation of WAHP charged with R-134a refrigerant12 and two-pass evaporator and condenser sections to characterize the thermal performance of the system in terms of overall thermal resistance. Many researchers have also evaluated the economic potential of heat pipes for building air conditioning. Jouhara conducted a detailed study on the energy performance13 of WAHP and reported an annual saving of 134 MWh for a ventilation system supplying 3m3/s of outdoor air. Zhang et al. presented simulation results14 showing the energy conservation potential of heat pipes for dedicated outdoor air handling units serving office buildings in Hong Kong. From the literature review, it is quite evident that the application of heat pipes for air conditioning and building HVAC services is an active area of research and development. Despite all of these, lack of simplified methodologies for analyzing the performance of heat pipes forces designers and engineers to depend on various manufacturer selection software and catalogs. The present work is aimed towards bridging this knowledge gap. The primary twofold objective of the present work is outlined as follows: • Establishing basic formulations for defining psychrometric process through a WAHP enhanced Fig. 1. Schematic of heat pipe systems used in HVAC: (a) Wrap-Around Heat Pipe (WAHP), (b) Heat Pipe Heat Exchanger (HPHX). Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems dehumidifier system, including the limiting case of moisture condensation during precooling. • Depicting theoretical variation of characteristic parameters of a WAHP against the operating parameters like inlet air temperature, inlet humidity ratio, dehumidifier coil outlet temperature, air mass flow rate and WAHP effectiveness. WAHP t4 t3 t1 t3 3 (1) Energy balance across the evaporator and condenser in terms of air enthalpy is expressed as: 2. Basic Heat Pipe systems A heat pipe system does not utilize any mechanical component or consume electricity to transfer energy from one point to another. Heat pipes used for air conditioning applications are closed loop systems, where a difference in density and temperature between the two phases of refrigerant fluid drives its movement inside the tubes and creates a pulsating effect. The working fluid evaporates by absorbing heat at one point and rejects heat at the other by condensing back to liquid as per Ref.2. Figure 1 shows the two basic configurations of heat pipes used prevalently in air conditioning systems. In wrap-around heat pipe (WAHP) system, front and rear sides of the dehumidifier coil are covered by the evaporator and condenser sections, respectively. The evaporator section precools the incoming air before the dehumidifier coil cools it further. The cooled and dehumidified air is subsequently reheated as it passes through the condenser section and supplied to the space. In heat pipe heat exchanger (HPHX) system, the supply and exhaust streams pass through the evaporator and condenser sections, respectively, which allows air-toair heat recovery between the two streams. The connecting tubes enable transport of the refrigerant fluid between the evaporator and condenser sections of the heat pipe system during the whole cycle. The operating temperature range of WAHP and HPHX for air conditioning systems depends upon the required supply conditions for intended space application and refrigerant used in heat pipes. Literature sources [Ref. 6, 8] suggest 15-550C to be appropriate temperature range for heat pipes in air conditioning applications. m q1 q2 m q4 q3 If recovered heat at the evaporator is entirely sensible, then the effectiveness is also defined by: WAHP The sensible effectiveness of WAHP from fig.1 is given by: t1 t2 t1 t3 (3) which gives: t2 t1 WAHP t1 t3 (4) The evaporator exit temperature from Eq. (4) is compared with the dew point temperature (DPT) at inlet (point 1) to check whether condensation occurs at the evaporator. The DPT can be expressed in terms of humidity ratio and absolute pressure as per Ref.15: tadp B kT0 B kT0 2 4 A AT0 2 BT0 2A T0 (5) Where, C plv A 2R P k ln t ln P0 B 3. Basic underlying equations (2) l0 C plvT0 R Based on the comparison between evaporator exit temperature and the inlet dew point temperature, two 4 Mridul Sarkar different cases can be shown as per the proceeding subsections. The unit for temperature in Eq. (10) is Kelvin. Hence, here ‘T’ implies T0+t. The saturation humidity ratio corresponding to this temperature is given by: 3.1.1. Case 1: No condensation If the temperature at evaporator exit (t2) is greater than or equal to the inlet DPT, moisture condensation does not occur at the evaporator and unsaturated air passes through the coil. So in case 1: t2 DPT1 (6) In this case, the absolute humidity at point 2 will be: 2 1 (7) On a psychrometric chart, the cooling-dehumidification process through the coil can be simply depicted by a straight line from the coil inlet to outlet conditions that intersects the saturation curve at coil ADP (apparatus dew point) on extending further16. In terms of the ADP and coil bypass factor (BF), coil outlet temperature is: t3 tadp 1 BF t2 BF (8) adp PTadp Pt PTadp (11) Humidity ratio at the coil exit is obtained by substituting the value of ωadp into Eq. (9). It should be noted that the relative humidity of air at coil exit can not exceed 100%. If air reaches the saturation condition inbetween coil inlet and exit temperatures, it follows the 100% RH curve on a psychrometric chart for rest of the process. In that case, ω3 will be simply equal to saturation humidity ratio corresponding to the coil exit temperature. Since, heat addition to the air stream at condenser is entirely sensible, humidity ratio remains unchanged after leaving the condenser: 4 3 However, due to an increase in temperature through the condenser, relative humidity of the supply air reduces. The condenser exit (supply) temperature is obtained by: Similarly the absolute humidity ratio at coil exit is: 3 adp 1 BF 1 BF (9) Since, ADP condition corresponds to the lowest saturation limit of air passing through the coil, the vapor pressure at this temperature (tadp) is determined from the modified Clausius-Clapeyron equation17-18 as: PTadp C plv T adp R P0 T 0 l0 C plv T0 1 1 exp R T0 Tadp (10) t4 t3 WAHP t1 t3 (12) 3.1.2. Case 2: With Condensation If the evaporator exit temperature calculated from Eq. (4) is lower than the inlet DPT, condensation of water vapor occurs during precooling. Since heat absorbed at the evaporator is not entirely sensible in this case, the effectiveness given by Eq. (3) is not valid. From conservation of energy, heat released at the condenser section is expressed in terms of air enthalpy difference by: Qc ma q4 q3 (13) Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems Since, humidity ratio at the condenser inlet and exit are unknown and heat transfer to air at condenser side is entirely sensible, Eq. (13) can be written as: (14) Qc ma c pm t4 t3 The term cpm is the specific heat of moist air and can be approximated within the limits of workable accuracy by a constant value ~ 1.02 kJ/kg-K for a wide range of humidity ratios encountered in air conditioning systems. Using Eq. (2), (13) and (14): q2 q1 c pm t4 t3 q1 c pa t1 1 l0 c pv t1 NTUWAHP 1 NTUWAHP UAWAHP Re Rc 2 Re NTU e 2 (19) From Eq. (17) and (19): NTU e 2WAHP 1 WAHP (20) (16) BFe exp NTU e qe q2 BFe q1 1 BFe (22) The saturation enthalpy (qe) determined above could also be approximated by a quadratic equation in terms of the evaporator effective surface temperature (te) reported in literature as per Ref. 21-22 as: (18) qe a te 2 b te c The above equation is based on the assumption that the heat pipe has infinite thermal mass because the vapor (23) Typical values of the coefficients a, b, and c for wet coils at different barometric pressures by considering a Table 1 Regression coefficients of saturation enthalpy function Coefficients of trend line function: Coefficient of determination (R2) qe a te 2 b te c Pt (kPa) (21) Analogous to cooling coils, enthalpy of wet surface of the evaporator is given by: (17) Overall resistance of the WAHP is given in terms of external resistances at the evaporator and condenser by: 1 NTUWAHP As with cooling coils, bypass factor of the evaporator section can be similarly defined in terms of NTU as: The effectiveness of a WAHP with equal flow rates through its evaporator and condenser sections is written in terms of the number of heat transfer units (NTU)19- 20 as: WAHP inside has almost a uniform temperature throughout its length and its overall thermal resistance is due to external fluid flow at the evaporator and condenser sections3, 5. In terms of NTU on evaporator side, the overall NTU of WAHP module is give by: (15) where, the inlet enthalpy (q1) is given by: 5 a b c 108.386 0.0774 0.1988 19.484 0.9998 106 0.0793 0.1797 19.895 0.9998 101.325 0.0838 0.1036 21.24 0.9998 100 0.0849 0.1004 21.383 0.9998 99 0.0859 0.0838 21.677 0.9998 6 Mridul Sarkar saturation temperature band of 4-25oC is shown in Ref. 21. The same theory can be applied here for wet evaporator surface of the heat pipe. However, taking the operational parameters of the WAHP into account, these regression coefficients are modified for a relatively wider dew point band of 10-35oC. Table 1 shows typical values of the coefficients at different atmospheric pressures encountered in air conditioning problems. The logical solution of Eq. (23) is given by: te b b2 4 a (c qe ) (24) 2a By determining qe from Eq. (15), (16) and (22) and substituting into Eq. (24), the value of te is obtained. Temperature of air at the evaporator exit is given by: t2 BFe t1 (1 BFe ) te (25) and the corresponding humidity ratio is: 2 BFe 1 1 BFe e The humidity ratio (ωe) at the evaporator surface is determined by replacing Tadp with Te in Eq. (10) and (11). From above, it is clear that moisture condensation occurs during precooling if effective temperature of the evaporator is lower than the DPT of air at WAHP inlet. The psychrometric condition at evaporator exit is determined by applying Eq. (25) and (26), which require evaporator BF and saturated conditions corresponding to the effective evaporator surface temperature. This is analogous to the methodology for determining exit conditions through a cooling coil using the coil BF and ADP conditions. Now air that enters the dehumidifier coil is at near saturated condition (t2 and ω2). Similar to case 1, air will exit the coil (required coil outlet temperature t3 and corresponding humidity ω3) at saturated state, if the line that is joining coil inlet and coil ADP conditions intersects the 100% RH curve (saturation) in between. Eq. (27) and (28), given below shows the saturation vapor pressure and relative humidity (RH) corresponding to the coil exit temperature (t3), respectively: (26) Fig. 2. Parametric variation with evaporator inlet temperatures at coil outlet temperature: 12oC, coil bypass factor: 0.1, inlet humidity ratio: 0.018 kg/kg-DA of: (a) WAHP exit humidity ratio, (b) WAHP exit temperature, (c) Recovered enthalpy, (d) Coil load. Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems 7 Fig. 3. Psychrometric plots at different inlet temperatures - (a) Evaporator inlet temperature: 41oC, inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. (b) Evaporator inlet temperature: 29oC, inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. with each of the operating parameters while holding all the remaining parameters constant. C plv T3 R PT P0 3 T0 l0 C plv T0 1 1 exp R T0 T3 RH 3 3 Pt 100% PT 3 3 4.1. Inlet temperature (27) (28) The RH from Eq. (28) will be equal to 100% in case condensation occurs during precooling. 4. Parametric variation This section presents a comparative performance study of WAHP based dehumidifier systems by defining the effects of various operating parameters on key performance parameters like WAHP supply humidity, supply temperature, recovered enthalpy and dehumidifier coil load. The proceeding subsections depict the variation in these performance parameters Inlet air temperature affects the supply condition, coil load and recovered heat through a WAHP system. For a WAHP operating at a particular effectiveness, increasing the evaporator inlet temperature leads to an increase in the coil inlet temperature. Due to this, a lower coil ADP is required for cooling and dehumidifying air to a fixed coil outlet temperature thereby increasing the dehumidifier coil load and may result in reduction of supply humidity ratio, when air exiting the dehumidifier is not 100% saturated. Although, the recovered energy increases with an increase in inlet temperature through the evaporator, it leads to reheating of air to a higher temperature through the condenser. With WAHP operating at higher effectiveness, the precooling and reheating can be increased through the evaporator and condenser, respectively at a fixed inlet condition and coil outlet temperature. This leads to an increase in recovered energy and supply temperature, but reduces the net dehumidifier coil load. It should be noted that moisture 8 Mridul Sarkar condensation occurs at the evaporator, if difference between the inlet air DBT and effective evaporator temperature exceeds the entering air dew point depression (DPD). Now this scenario arises either when the effectiveness of WAHP is higher, which enables the evaporator to precool air below its DPT or when the air temperature entering the WAHP itself is lower, which results in comparatively lower DPD. Figure 2 shows variations of thermodynamic parameters of the WAHP system with the evaporator inlet temperatures at varying sensible effectiveness and typical psychrometric processes through a WAHP system at different inlet temperatures are depicted in Figure 3. 4.2. Inlet humidity ratio Contrary to inlet temperature, an increase in inlet humidity ratio does not affect the condenser outlet temperature or recovered heat as long as dehumidifier coil has enough capacity to cool and dehumidify air up to the required level. However, both the condenser outlet temperature and recovered heat will increase with the operating effectiveness of WAHP. As the humidity ratio rises, DPT also increases. This leads to a sharp decrement in the DPD. As the DPD reduces, the net sensible load ratio (SLR) of the coil also decreases. As a result, dehumidification efficiency of the dehumidifier coil increases. Water vapor in moist air will condense off at the evaporator, if its effective temperature is low enough to precool the air below its inlet DPT. With an increment in the inlet humidity ratio, the supply DPT also increases until further reduction in DPD causes moisture condensation during precooling and fully saturated air exits the dehumidifier coil. Beyond this point, a further increase in inlet humidity ratio does not change the supply humidity ratio and remains constant at the saturated humidity ratio corresponding to the coil outlet temperature. For a fixed coil outlet temperature, increasing the inlet humidity ratio directly affects the net coil load. In this case, predominant portion of the coil load will be the latent part. Due to elevated air moisture content entering the dehumidifier, net coil load increases and more energy is expended for dehumidification. However, operating a WAHP at a higher effectiveness results in greater temperature differential across the evaporator thereby reducing net coil loads. Figure 4 shows the variation of different parameters of a WAHP system with inlet humidity ratios and Figure 5 depicts psychrometric plots at different inlet humidity ratios. 4.3. Coil outlet temperature DPT of the supply air through a wrap-around dehumidifier heat pipe can be controlled by modulating the coil outlet temperature. This is done by either Fig. 4. Parametric variation with inlet humidity ratios at coil outlet temperature: 12oC, coil bypass factor: 0.1, evaporator inlet temperature: 35oC of: (a) WAHP exit humidity ratio, (b) WAHP exit temperature, (c) Recovered enthalpy, (d) Coil load. Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems 9 Fig. 5. Psychrometric plots at different inlet humidity ratios - (a) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. (b) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.012 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. controlling the opening and closing of chilled water valve to vary the water flow rate through the coil or bypassing air around the coil by using face and bypass dampers (FBD). At fixed inlet humidity ratio and temperature, air exits the condenser at a slightly elevated temperature on increasing the coil outlet temperature. This results in marginal reduction of recovered heat, since the maximum theoretical heat transfer reduces with an increase in coil outlet temperature. However, to achieve a lower coil outlet temperature, the coil ADP needs to be reduced that not only increases the latent load ratio and net coil load, but also results in reduction of supply humidity ratio. In addition to this, increased dehumidification load at a lower coil outlet temperature leads to saturation of air leaving the coil. Operating a WAHP at a higher effectiveness leads to increased precooling and reheating through evaporator and condenser. As a result, recovered enthalpy and condenser exit temperature increases, but reduction in dehumidifier coil load is observed. Figure 6 and 7 shows the parametric variation and psychrometric plots at different coil outlet temperatures, respectively. 4.4. Air mass flow rate Air mass flow rates drastically affect the performance of heat pipes. The face velocity through a WAHP dehumidifier increases as the airflow rate is increased. Due to this, higher fraction of air bypasses the WAHP and dehumidifier coil leading to reduction in the contact time with heat pipe and coil surfaces. Hence, as airflow rate is increased, sensible effectiveness of the WAHP and contact factor (1 - BF) of the dehumidifier coil decreases. The effectiveness of a WAHP at any airflow rate in terms of a reference airflow rate and effectiveness is given by: WAHP x WAHP r ef 1 x 1 WAHP r ef Where, x is expressed in terms of the ratio of air mass flow rate to the reference air mass flow rate as: m x a ma ref 0.534 10 Mridul Sarkar Fig. 6. Parametric variation with coil outlet temperatures at evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, coil bypass factor: 0.1 of (a) WAHP exit humidity ratio, (b) WAHP exit temperature, (c) Recovered enthalpy, (d) Coil load. A detailed derivation of the correlations for sensible effectiveness of WAHP and HPHX in terms of the reference effectiveness and corresponding airflow rates are presented in Appendix A and B, respectively. With respect to the reference airflow rate, the effectiveness of a WAHP decreases as the airflow ratio exceeds 1 and vice-versa. Due to this, higher energy recovery and higher condenser outlet temperature are expected by a WAHP operated at a higher effectiveness or reduced airflow rate. As airflow rate increases, distribution energy from fans also increases due to an increase in pressure drop through the WAHP dehumidifier unit, which indirectly affects dehumidifier coil loads. However, in this paper only the explicit effect of air flow rate on the coil bypass factor and WAHP effectiveness are considered. The pressure drop across Fig. 7. Psychrometric plots at different coil outlet temperatures - (a) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. (b) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 11oC, coil BF: 0.1, sensible effectiveness of WAHP: 0.4. Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems a WAHP module depends primarily on its geometrical configuration (fin dimensions, number of heat pipe rows, tube diameter and fin spacing) and flow rate of air stream passing through it [Ref. 4]. As per literature study [Ref. 21, 23] the bypass factor of a coil can be expressed entirely as a function of air mass flow rate by: X BF exp 0 ma (29) The term X0 shown in Eq. (29) above is derived from a reference air mass flow rate and the coil bypass factor corresponding to this reference air mass flow rate. For a given configuration, the coil BF increases with an increment in the face velocity and must be operated at a lower ADP to supply at the required DPT. As a result, the specific coil load actually increases with an increase in air mass flow rate. As the ADP or effective temperature of the coil is reduced, air gradually moves towards the saturated condition during the coolingdehumidification process and exits the coil at 100% RH. On the other hand, as heat recovery increases with a reduction in airflow ratio, more precooling occurs at the evaporator that reduces air DPD. This allows it to reach the saturated condition even at a relatively higher coil ADP. Based on the above arguments, the variations in 11 the thermodynamic parameters of a WAHP with air mass flow rate ratios are shown in Figure 8. Typical psychrometric plots of the processes through a WAHP enhanced dehumidifier at a reference airflow rate and at reduced airflow rate is depicted in Figure 9. 5. Conclusions The present work showed the variation of characteristic factors of a WAHP enhanced dehumidifier system with operational parameters. Basic mathematical formulations are derived here for theoretically deducing the operational characteristics of WAHP system including the limiting case of moisture condensation at the evaporator. The operating effectiveness of a WAHP system played a pivotal role in the variation of system supply temperature, recovered enthalpy and dehumidifier coil load. Even though, a fixed effectiveness is assumed while deriving the variation of characteristic parameters with operating parameters, this operating effectiveness is shown to be inversely correlated with external air flow rates at the condenser and evaporator sections. Based on the variation trends in supply conditions, coil load and recovered energy by applying these formulations, it can be concluded that the specific dehumidifier coil load is directly dependent on the inlet air temperature, inlet humidity ratio and air mass flow rate and tends to increase with an increment in each of these operating Fig. 8. Parametric variation with air mass flow rate ratio at evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, reference coil bypass factor: 0.1, dehumidifier coil outlet temperature: 12oC. of: (a) WAHP exit humidity ratio, (b) WAHP exit temperature, (c) Recovered enthalpy, (d) Coil load. 12 Mridul Sarkar parameters. However, the same coil specific load showed a decreasing trend with an increase in coil outlet temperature and operating effectiveness of WAHP. The WAHP supply temperature and recovered enthalpy, increased as the WAHP is operated at a higher effectiveness. The supply temperature also showed considerable increment as inlet air temperature is increased. The inlet humidity ratio does not affect the recovered enthalpy or supply temperature, but directly influenced the net coil load. The supply DPT and humidity ratio depended explicitly on the required coil outlet temperature, inlet dew point depression (DPD) and coil ADP, but indirectly affected by the WAHP effectiveness and coil bypass factor during operation. If condensation occurs during precooling, the supply DPT will be equal to the coil outlet temperature. These simple conclusions aided in defining the performance characteristics of the WAHP system in terms of each operational parameter in consideration and allowed making informed decision regarding system design and control. Appendix A. WAHP effectiveness in terms of reference effectiveness and mass flow ratio Sensible effectiveness is identified as the main characteristics to define the performance of heat pipes. Researchers have assumed infinite thermal mass for a heat pipe because the vapor inside it has almost a uniform temperature throughout its length3. Hence, the effectiveness of heat pipes prominently depends upon the external flow conditions that affect the transport of heat in and out of evaporator and condenser sections, respectively5,11. So, in this paper, the overall heat transfer efficiency of heat pipe is assumed to vary only with external airflow rates, without considering the influence of other thermodynamic parameters like heat load and operating temperature. Several assumptions are made here to simplify the methodology of deriving theoretical correlation for sensible effectiveness at any airflow rate in terms of the reference effectiveness and corresponding airflow rate ratio: Fig. 9. Psychrometric plots at different air mass flow rate ratio - (a) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, reference coil BF: 0.1, reference sensible effectiveness of WAHP: 0.4, air mass flow rate to reference air mass flow rate ratio: 1, (b) Evaporator inlet temperature: 35oC, inlet humidity ratio: 0.018 kg/kg-DA, dehumidifier coil outlet temperature: 12oC, reference coil BF: 0.1, reference sensible effectiveness of WAHP: 0.4, air mass flow rate to reference air mass flow rate ratio: 0.6. Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems • Steady state analysis. • Density and heat transfer coefficient of air are assumed to be constant throughout the process. • Thermal resistances of the heat pipe tube and wick are neglected. Fouling resistance is also neglected. • Internal resistance due to pulsating flow of refrigerant is considerably lower than the external resistance and hence neglected here. • The fins are assumed to be 100% efficient. The face velocities over evaporator and condenser are determined by the fin height and width. • Geometrical configurations of evaporator and condenser sections are assumed to be identical. • The analysis is simplified by considering the condenser and evaporator sections as single circular tubes. The whole procedure can be simplified and categorized into following steps: a) Simplifying the external resistance by heatexchanger ε-NTU relation: For a heat exchanger with equal mass flow rates at the hot and cold ends, the net effectiveness in terms of NTU is shown in section 3.1 as: WAHP NTUWAHP 1 NTUWAHP The number of heat transfer units (NTU) for the heat pipe shown in the equation above is given by: NTUWAHP UAWAHP (A-1) Cmin Where, Cmin Ce Cc (A-2) The overall thermal resistance of WAHP is given by: 1 UAWAHP Re Rc 2 Rc 13 (A-3) The resistance at condenser side in terms of corresponding NTU is given by: Rc 1 NTU c Cmin (A-4) Overall NTU of the WAHP is written in terms of the condenser side NTU as: NTUWAHP NTU c 2 (A-5) b) Expressing the heat transfer coefficient as a function of flow rate for WAHP: The Nusselt number for flows over circular tubes as per Hilpert correlation19 is given by: Nuc hc D a Rec m Pr 0.33 kf (A-6) For typical heat pipes, the hydraulic diameter of the exposed tube does not exceed 0.5 inch and the face velocities prescribed by manufacturers for enhanced dehumidification does not exceed 500 fpm24. In this range, the external Reynold’s number remains below 4000, for which, m and a takes the value 0.466 and 0.683, respectively19. Hence, for flow around heat pipe tubes: hc ma 0.466 (A-7) c) Expressing the ratio of NTU as a function of airflow rate ratio: In terms of the reference airflow rate, the ratio of heat transfer coefficients can be written as: m hc a hc ma ref ref 0.466 (A-8) 14 Mridul Sarkar Similarly in terms of the overall thermal conductance from ε-NTU relation: effectiveness and manufacturer’s effectiveness is lower than ±5%. Appendix B. NTU c Cmin h c NTU c Cmin ref hc Effectiveness of HPHX in terms of the reference effectiveness and mass flow ratios (A-9) ref From Eq. (A-8) and (A-9): m NTU c a NTU c ref maref 0.466 maref ma m a ma ref 0.534 (A-10) d) Expressing the effectiveness in terms of the reference effectiveness and flow ratio: By applying Eq.(A-5) and (A-10): 2 2WAHP x WAHP 1 WAHP 1 WAHP ref documented Unlike WAHP, the airflow rates through the condenser and evaporator in a HPHX system vary freely. Hence, effectiveness of HPHX at any supply flow rate not only depends on the supply flow rate but also on the condenser to evaporator flow rate ratio too. With all the assumption made earlier, the whole derivation can be simplified into following steps: a) Simplifying the external resistances at the evaporator and condenser by heat-exchanger ε-NTU relation: The effectiveness of HPHX from Fig. 1(b) is given by: (A-11) HX C T T Ce T1 T2 c 4 3 Cmin T1 T3 Cmin T1 T3 (B-1) The effectiveness of a counter flow heat exchanger as reported in literature19-20 is given by: Where, m x a ma ref 0.534 HX Hence, the effectiveness of WAHP in terms of its reference performance can be written as: WAHP 1 exp NTU HX 1 Cr 1 Cr exp NTU HX 1 Cr The net heat capacity ratio Cr in Eq. (B-2) is defined as: Cr x WAHP r ef 1 x 1 WAHP (A-12) r ef Eq. (A-12) derived above should be applied on a caseby-case basis for every unique constructional configuration of WAHP. The accuracy of the derived equation is tested against the manufacturer’s data obtained from selection software25 for two different WAHP configurations. Figure A1 shows the comparison of results at mass flow rate ratios over a wide range around the reference ratio (equal to 1). The results show that the error between estimated (B-2) Cmin Cmax (B-3) Defining a new parameter ‘r’ as: r Condenser mass flow rate mc Evaporator mass flow rate me (B-4) From Eq. (B-3) and (B-4), one can deduce: Cmin mc c pa if mc me Cr r (B-5) Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems Cmin me c pa if me mc 1 Cr r (B-6) and in this case: Considering the first case, when Cr = r, Eq. (B-2) can be written as: HX 1 exp NTU HX 1 r 1 r exp NTU HX 1 r (B-7) NTU HX 1 r HX 1 ln 1 r 1 HX (B-8) 1 Re Rc 1 1 r NTU c NTU e where: Re (B-13) (B-9) he me hc mc Rc (B-12) Cc b) Expressing the evaporator to heat pipe NTU ratio as a function of the condenser to evaporator air mass flow ratio: Since the evaporator and condenser sections are assumed to have identical geometrical configuration: In terms of the net resistance: UAHX UA HX From Eq. (B-4) and (B-9)-(B-12): NTU HX which gives: NTU HX 15 1 NTU c Cc (B-10) 1 NTU e Ce (B-11) 0.466 (B-14) The ratio of heat transfer coefficients shown above is due to Eq. (A-7) applicable for external flows over circular tubes of heat pipes. Hence: Fig. A-1. Comparison of effectiveness for two different WAHP configurations: (a) Qref = 9.5 m3/s, heat pipe dim.: 6 rows, 10 fpi, 0.5 inch OD, fin dim. 2540 x 1580 mm2, Refrigerant: R-410a, Evaporator inlet: 42oC, 35% RH, Condenser inlet: 12oC, 95% RH. (b) Qref = 3 m3/s, heat pipe dim.: 6 rows, 10 fpi, 0.5’ OD, fin dim. 762 x 1260 mm2, Refrigerant: R-410a, Evaporator inlet: 42oC, 35% RH, Condenser inlet: 12oC, 95% RH. . 16 Mridul Sarkar NTU e me NTU c mc 0.534 1 r 0.534 (B-15) NTU HX NTU HX ref And from Eq. (B-13) and (B-15): 1 r 0.466 NTU e 0.534 NTU HX r (B-16) 1 r 0.466 r 0.534 (B-17) HX 1 r 1 1 r HX 1 HX ref 1 rref 0.466 (B-18) rref 0.534 z r (B-21) z x 1 r ref 1 r ref Reiterating the steps shown above for the case when r >1 and: me mc As shown earlier in Eq. (A-10) for WAHP, similar expression can be written for evaporator of HPHX as: m NTU e e NTU e me ref ref (B-20) where, the exponent ‘z’ is a function of mass flow ratio and is given by: At a reference condenser to evaporator flow ratio, Eq.(B-17) takes the form as: ref Eliminating the LHS of the above equation by substituting corresponding variables from Eq. (B-13), (B-15), (B-16) and (B-19), the effectiveness of HPHX in terms of its reference performance can be written as: In conclusion, the evaporator to heat pipe NTU ratio is shown to be a direct function of the condenser to evaporator air mass flow rate ratio. c) Expressing effectiveness in terms of the reference performance and condenser to evaporator air mass flow ratio: Defining the evaporator to heat pipe NTU ratio as parameter ‘γ’, Eq.(B-16) can be rewritten as: 1 r HX 1 ln 1 r 1 HX 1 rref HX 1 ref ln 1 HX ref 1 rref The effectiveness at any supply flow rate can be expressed in terms of the reference effectiveness as: 0.534 x (B-19) HX Taking the ratio of heat pipe NTU from Eq. (B-8) into account, one can write: 1 1 r 1 y 1 HX r 1 1 HX r ref (B-22) Theoretical parametric study of Wrap-Around Heat Pipe (WAHP) in air conditioning systems 17 Fig. B-1. Comparison of effectiveness for HPHX configuration 1: Qe-ref = 9.5 m3/s, rref = 0.999, heat pipe dim: 6 rows, 10 fpi, 0.5 inch OD, fin dim: 2540 x 1580 mm2, Refrigerant: R-410a, evaporator inlet: 42oC, 35% RH, condenser inlet: 24oC, 50% RH at (a) constant condenser side airflow rate and variable evaporator side air flow rates, (b) constant evaporator side airflow rate and variable condenser side airflow rates Fig. B-2. Comparison of effectiveness for HPHX configuration 2: Qe-ref = 3.0 m3/s, rref = 0.999, heat pipe dim: 6 rows, 10 fpi, 0.5 inch OD, fin dim: 762 x 2025 mm2, Refrigerant: R-410a, evaporator inlet: 42oC, 35% RH, condenser inlet: 24oC, 50% RH at (a) constant condenser side air flow rate and variable evaporator side airflow rates, (b) constant evaporator side air flow rate and variable condenser side airflow rates Where the exponent ‘y’ is: 1 1 r ref y x 1 1 r ref and evaporator to heat pipe NTU ratio ‘λ’ for this case is given by: NTU e 1 r 0.466 NTU HX (B-23) Figures B-1 and B-2 show the comparison of results from the derived correlation and manufacture’s performance data25 for two different configurations of HPHX. It should be noted that both Eq. (B-21) and (B22) can’t be defined for equal reference flow rates at condenser and evaporator sections (i.e. flow ratio equal to 1). Hence, for mathematically approximating the results, a reference condenser to evaporator flow ratio of 0.999 is applied here to derive the sensible effectiveness at different evaporator and condenser flow rates. The data are plotted for two different scenarios: first scenario, where condenser flow rate is kept constant and second scenario, where evaporator flow rate is kept constant. Comparison of results shows that the error between the two data does not exceed ±5%, which affirms the validity of the derived correlations. 18 Mridul Sarkar Nomenclature Symbols A BF C Surface area (m2) Bypass factor Heat capacity rate (kW/K) cpa Specific heat capacity of dry air (1.006 kJ/kg-K) cpm Specific heat capacity of moist air (1.02 kJ/ kg-K) cpv D DPT h Specific heat capacity of vapor (1.86 kJ/kg-K) Hydraulic diameter (m) Dew point temperature (oC) Convective heat transfer coefficient (W/m2-K) kf Thermal conductivity of fluid (W/m-K) l0 NTU Specific latent heat of vaporization of water at 273 (2501 kJ/kg) Air mass flow rate (kg/s) Number of heat transfer units Nuc P Pr Nusselt number Saturation vapor pressure (kPa) Prandtl number Pt Q Ambient pressure (kPa) Volume flow rate Heat transfer rate (kW) Specific enthalpy of air (kJ/kg) m Q q qe R Specific saturation enthalpy of air at effective surface temperature of evaporator (kJ/kg) Gas constant for water vapor (0.4618 kJ/kg-K) Rc External thermal resistance at condenser (K/W) Re External thermal resistance at evaporator (K/W) Rec RH r t te U Reynold’s number Relative humidity Condenser to evaporator mass flow ratio Air temperature (oC) Effective surface temperature of evaporator (oC) Overall heat transfer coefficient (W/m2-K) Greek symbols α ε Ratio of molecular mass of water vapor and dry air (0.622) Effectiveness of WAHP Humidity ratio (kg moisture/kg DA) Subscripts 0 1 2 Reference state (273.15 K) Evaporator inlet Evaporator outlet / dehumidifier coil inlet 3 4 a adp c e HX min. ref WAHP Dehumidifier coil outlet / condenser inlet Condenser outlet Of air Apparatus Dew Point At condenser At evaporator Heat pipe heat exchanger Minimum Reference performance Wrap-around heat pipe Acknowledgments The author acknowledges no conflict of interest. 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