PARAMETRIC STUDIES FOR HEAT EXCHANGERS

Transcription

1 Chapter 3 PARAMETRIC STUDIES FOR HEAT EXCHANGERS 3.1 INTRODUCTION This chapter discusses in detail the methodology considered for the thermal design of the heat exchangers: an evaporator, a suction line heat exchanger and a gas cooler in three separate parts. The operating parameters of the heat exchangers are determined using transcritical CO 2 vapour compression cycle. The equations are solved using Engineering Equation Solver (EES) [Kli 10]. Primarily, the heat exchangers are designed through parametric study in EES. Further IMSTA ART based on finite volume technique has been used to evaluate the performance of the heat exchangers. At the end, the heat exchangers are optimized using IMST ART. The finalized geometric configurations were then released for manufacturing. The first part deals with a fin and tube evaporator, the second part discusses a suction line heat exchanger (SLHX) and third part describes a gas cooler for the CO 2 transcritical air conditioning system. 3.2 EVAPORATOR The evaporator is the heat absorbing fin and tube type heat exchanger used for the cooling and dehumidification of room air. The effectiveness-ntu method has been employed for the thermal design of the plain-fin and tube evaporator. For the better understanding of CO 2 evaporation heat transfer, the two-phase flow pattern based phenomenological boiling heat transfer and frictional pressure drop models have been used. The analytical modeling of the plain-fin and tube evaporator is explained in details below. The CO 2 refrigerant flows through tubes expanded against the fins and air flows over the tube-bank and fins assembly in cross-flow arrangement. Following are assumptions considered in parametric analysis of heat exchangers. steady state heat transfer between the fluids CO 2 is considered as a pure substance pressure drop is assumed negligible for thermal design calculations no internal heat generation in the evaporator heat loss to or from the surroundings is negligible uniform distribution of refrigerant and air flows 53

2 condensation of water vapor in ambient air on evaporator surface is negligible tube-to-tube conduction through fins is neglected longitudinal heat conduction is not considered Mathematical model description The simulation has been done for plain and fin tube type evaporator using EES. The onedimensional equations are solved in EES. The geometry of the plain and fin type evaporator has been defined in the program. The thermo-physical properties of refrigerant and air are calculated with the help of in-built fluid property database REFPROP [LHM 07]. For parametric evaluation, the Effectiveness-NTU method is employed. The overall conductance (UA) has been evaluated through finding out individual thermal resistance in the heat flow path. From knowledge of UA and minimum heat capacity rate, number of transfer units (NTU) are calculated, which is in turn give the evaporator effectiveness. The actual evaporator capacity has been estimated from the effectiveness and maximum heat transfer units possible between both fluids. For constant evaporator capacity, the evaporator geometry is finalized iteratively such that the superheated refrigerant (CO 2 ) temperature at evaporator exit does not exceed 20 o C over a range of ambient air temperatures. Finally, the refrigerant (CO 2 ) side two-phase and ambient air-side pressure drops are calculated. The overall conductance UA of the evaporator is inverse of the total thermal resistance between refrigerant (CO 2 ) and air, R total, which can be found by summing all of the thermal resistances in series as follows, where, R in is the convection resistance between refrigerant CO 2 and inner tube surface, R f,in is refrigerant side fouling resistance, R cond is the tube-wall conduction resistance, and R out is resistance between air and the outer surface of the plain-fins and tubes. The resistance between refrigerant (CO 2 ) and tube inside surface can be represented as, Where, is the average heat transfer coefficient of refrigerant. The refrigerant side heat transfer coefficient calculation procedure is explained in section 3.8. D i is the tube inner diameter found as, 54

3 D o is the tube outer diameter, is the tube wall thickness, W c is the length of heat exchanger normal to air flow direction, and N t is total number of tubes found as, Where, N t,c is number of tube columns, and N t,r is number of tube rows. The tube wall conduction thermal resistance is found as, Where, k tube is the tube material thermal conductivity. The resistance between air and the outer surface of the heat exchanger R out can be expressed in terms of an overall surface efficiency,, as follows, Where, A t,2 is total heat transfer surface area available on air side which is the sum of finned i.e. secondary surface area A s, and un-finned tube surface i.e. primary surface area A p. These areas are found as follows, Where, is fin thickness, and N fin is the number of fins found as, Where, P fin is fin spacing (or fin pitch). Where, H c and L c are the height and depth of heat exchanger core respectively and are calculated by equation 3.10 and Where, P t and P l are the transverse and longitudinal tube spacing respectively. The average heat transfer coefficient on air-side is found as follows, 55

4 Where, j c is Colburn j-factor - the dimensionless heat transfer coefficient of air, cp h is specific heat of air, Pr h is Prandtl number of air. The air-side heat transfer coefficient calculation procedure is given in section 3.9 of this chapter. In equation (3.12), is the mass flux of air, which is found as, Where, is the mass flow rate of air, and is the minimum free flow area available on air side determined by equation The overall surface efficiency is related to the fin efficiency and calculated by equation The fin efficiency calculation procedure is outlined in detail, in section The refrigerant side fouling resistance is found as, Where, F foul is the refrigerant side fouling factor. Once, an overall conductance UA of the evaporator is found from equations (3.1), (3.2), (3.5), (3.6), and (3.16) then number of transfer units NTU is calculated by equation Where, C min is the minimum heat capacity rate. 56

5 In evaporation heat transfer, heat capacity rate of the hot fluid is usually taken as the minimum. Also, for evaporative heat transfer, the heat capacity rate ratio (C r = C min /C max ) becomes equal to zero. Hence, effectiveness of the evaporator is found as, Once effectiveness is found, the capacity of evaporator is calculated as follows, Where, T h,i and T c,i are the inlet temperatures of hot and cold fluids respectively. Then, outlet temperature of hot fluid T h,o is found from following heat balance, The enthalpy of refrigerant at outlet h c,o is found from the knowledge of heat balance on refrigerant side as follows, Now the enthalpy of CO 2 at outlet is compared with the saturation enthalpy h c, sat of refrigerant. If ( ), CO 2 is still in the two-phase region. In such a case mass flow rate of CO 2 and/or volume flow rate of air is adjusted till the refrigerant at outlet is in superheated vapor condition. If ( ), the refrigerant (CO 2 ) is in superheat region. The temperature of superheated refrigerant CO 2 at an evaporator exit is calculated from equation below, In equation 3.22, h c,sat and T c,sat are enthalpy and temperature of refrigerant vapor, and the only unknown is the outlet temperature of refrigerant T c,o. In this way, the capacity of an evaporator for given geometry and thermo-physical properties of fluids, is calculated using the effectiveness-ntu method of heat exchanger design. The details of thermal design of evaporator are briefly explained in form of a flowchart given in Figure

6 Start Read known geometry of evaporator: D o, δ tube, P t, P l, N t,r, N t,c, W c, δ fin, P fin Calculate remainder geometry of the evaporator: D i, N t, H c, L c, L t, N fin Calculate: A fr, A t, and A mf on both fluid sides, and β Hx of evaporator Read upstream air parameters: T h,i, P h,i, rh h,i, cp h,i, ρ h,i, μ h,i, k h,i, Pr h,i, Read refrigerant inlet parameters: T c,i, P c,i, x c,i, cp c,i, ρ c,i,, h c,i, h c,sat Adjust Calculate: Ġ h, Ġ c, Adjust and/or NO Is, 50 Ġ c 1500 kg/s-m 2? Calculate: R cond, R in, u h,f, u h,c, Re Do, Re Pl, j c,, η fin, η out, R out, R f,in, R total, UA, NTU, ε, T h,o, T c,o Is, 9 T c,o 20 o C? No Display Results End Figure 3.1: Flowchart for thermal design of an evaporator Flow patterns during co 2 evaporation Flow patterns are very important in understanding the very complex two-phase flow phenomena and heat transfer trends in flow boiling. To predict the local flow patterns in a channel, a flow pattern map is used. Cheng et al. [CRQT 08] has developed flow boiling 58

7 heat transfer model based on the Cheng Ribatski Wojtan Thome CO 2 flow pattern map [CRWT 06]. This model accurately predicts changes of trends in flow boiling data, which indicates the flow patterns such as onset of dry-out and onset of mist flow. In the present study, the physical properties of CO 2 have been obtained from built-in fluid property function of EES. Based on the quality of CO 2 at evaporator inlet (x c,i ) and the mass flux (Ġ c ), the flow patterns in the flow passage are first determined from the updated flowpattern map. In this model accurately accounted the transitions in flow patterns such as annular flow to dryout (A D), dryout to mist flow (D M) and intermittent flow to bubbly flow (I B) transition curves. The void fraction ε and dimensionless geometrical parameters A LD, A VD, h LD and P id used in the flow pattern map are defined in the equations 3.23 to equation Here, A LD is dimensionless cross-sectional area occupied by liquid phase [-], A VD is dmensionless crosssectional area occupied by vapor phase [-], h LD is dimensionless vertical height of liquid phase of refrigerant [-] and P id is dimensionless perimeter of interface of vapour and liquid phase. Where, the stratified angle, θ strat (which is the same as θ dry of Figure 3.2) is calculated using the equation (3.28) proposed by Biberg, [CRQT 08], 59

8 Figure 3.2: Stratified two-phase flow in a horizontal channel The stratified-wavy to intermittent and annular flow (SW I/A) transition boundary has been calculated with the Kattan Thome Favrat criterion [CRQT 08] as, Where, the liquid Froude number Fr L and the liquid Weber number We L are defined by equation Then, the stratified-wavy flow region is subdivided into three zones according the criteria by Wojtan et al. [CRQT 08], Ġ c > Ġ wavy (x IA ) gives the slug zone; Ġ strat < Ġ c < Ġ wavy (x IA ) and x < x IA give the slug/stratified-wavy zone; x x IA gives the stratified-wavy zone. The stratified to stratified-wavy flow (S SW) transition boundary is calculated with the Kattan Thome Favrat criterion [CRQT 08], For the new flow pattern map: Ġ strat = Ġ strat (x IA ) at x < x IA. 60

9 The intermittent to annular flow (I A) transition boundary is calculated with the Cheng Ribatski Wojtan Thome criterion [CRWT 06] as, Then, the transition boundary is extended down to its intersection with Ġ strat. The annular flow to dryout region (A D) transition boundary is calculated with the new modified criterion of Wojtan et al. [CRQT 08] based on the dryout data of CO 2 in this study as, Which, is extracted from the new dryout inception equation in the study as, The vapor Weber number We V, vapor Froude number Fr V,Mori defined by Mori et al. [MYOK 00], and the critical heat flux q crit as per Kutateladze correlation [CRQT 08] are calculated, The dryout region to mist flow (D M) transition boundary is calculated with the news criterion developed by Cheng et al. [CRQT 08] based on the dryout completion data for CO 2 as, 61

10 Which, is extracted from the dryout completion equation developed by Cheng et al. [CRQT 08] for Ġ mist calculation from, The intermittent to bubbly flow (I B) transition boundary is calculated with the criterion, which arises at very high mass velocities and low qualities as shown in equation If Ġ c > Ġ B and x < x IA, then the flow is bubbly flow (B). The following conditions are applied to the transitions in the high vapor quality range, If Ġ strat (x) Ġ dryout (x), then Ġ dryout (x) = Ġ strat (x) If Ġ wavy (x) Ġ dryout (x), then Ġ dryout (x) = Ġ wavy (x) If Ġ dryout (x) Ġ mist (x), then Ġ dryout (x) = Ġ mist (x) CO 2 - side heat transfer coefficient Once the flow patterns present along the flow path are identified, the local heat transfer coefficients for respective flow patterns are calculated by the procedure outlined below. An updated general flow boiling heat transfer model based on flow patterns developed by Cheng et al. [CRT 08] has been used to calculate the local and average heat transfer coefficients for evaporation heat transfer of CO 2. The detailed procedure is given below. The Kattan Thome Favrat general equation for the local flow boiling heat transfer coefficients h tp in a horizontal tube is used as the basic flow boiling expression which is as, Where, θ dry is the dry angle as shown in Figure 3.3 as follows, 62

11 Figure 3.3: Schematic diagram of liquid film thickness δ, and dry angle θ dry [CRT 08] The dry angle θ dry defines the flow structures and the ratio of the tube perimeter in contact with liquid and vapor. In stratified flow, θ dry equals the stratified angle θ strat calculated from equation (3.28). In annular (A), intermittent (I) and bubbly (B) flows, θ dry = 0. For stratified-wavy flow, θ dry varies from zero up to its maximum value θ strat. Stratifiedwavy flow is subdivided into three subzones (slug, slug/stratified- wavy and stratifiedwavy) to determine θ dry. For slug zone (slug), the high frequency slugs maintain a continuous thin liquid layer on the upper tube perimeter. Thus, similar to the intermittent and annular flow regimes, one has θ dry = 0 [CRT 08]. For stratified-wavy zone (SW), the following equation is proposed, For slug-stratified wavy zone (Slug + SW), the following interpolation between the other two regimes is proposed for x < x IA, The vapor phase heat transfer coefficient on the dry perimeter h V is calculated with the Dittus Boelter correlation assuming tubular flow in the tube as follows, Where, the vapor phase Reynolds number Re V is defined as follows, 63

12 The heat transfer coefficient on the wet perimeter h wet is calculated with an asymptotic model that combines the nucleate boiling and convective boiling heat transfer contributions to flow boiling heat transfer by the third power as follows, Where, h nb, S and h cb are respectively nucleate boiling heat transfer coefficient, nucleate boiling heat transfer suppression factor and convective boiling heat transfer coefficient and are determined in the following equations. The nucleate boiling heat transfer coefficient h nb is calculated with the Cheng Ribatski Wojtan Thome [CRWT 06] nucleate boiling correlation for CO 2 which is a modification of the Cooper correlation, as follows, The Cheng Ribatski Wojtan Thome [CRWT 06] nucleate boiling heat transfer suppression factor S for CO 2 is applied to reduce the nucleate boiling heat transfer contribution due to the thinning of the annular liquid film. Furthermore for non-circular channels, if D eq > 7.53 mm, then set D eq = 7.53 mm (use instead of D i for non-circular channels in the equations). The liquid film thickness δ shown in Figure 3.3 is calculated with the expression proposed by El Hajal et al. [CRT 08] as follows, Where, the cross sectional area occupied by liquid phase of refrigerant, A L = A (1-ε), based on the equivalent diameter (D i for circular channels) as shown in Figure 3.2. When the liquid occupies more than one-half of the cross-section of the tube at low vapor quality, equation 3.51 would yield a value of δ > D eq /2, which is not geometrically realistic. 64

13 Hence, whenever equation 3.51 gives δ > D eq /2, δ is set equal to D eq /2 (occurs when ε < 0.5). The liquid film δ IA is calculated with equation 3.51 at the intermittent (I) to annular flow (A) transition. (Note: D eq for non-circular channels, D i for circular channels) The convective boiling heat transfer coefficient h cb is calculated with the following correlation, Where, the liquid film Reynolds number Re δ is defined as, The void fraction ε is calculated from equation The heat transfer coefficient in mist flow is calculated by a new correlation developed as a result of modification of the correlation by Groeneveld [CRT 08], with a new lead constant and a new exponent on Re H according to CO 2 experimental data as follows, Where, the homogeneous Reynolds number Re H and the correction factor Y are calculated as follows, The heat transfer coefficient in the dry-out region is calculated by a linear interpolation proposed by Wojtan-Ursenbacher-Thome as follows [CRT 08], Where, h tp (x di ) is the two-phase heat transfer coefficient calculated with equation 3.42 at the dry-out inception quality x di and h M (x de ) is the mist flow heat transfer coefficient calculated with equation 3.54 at the dry-out completion quality x de. Dry-out inception quality x di and dry-out completion quality x de are respectively calculated from equation 3.35 and equation

14 The vapor Weber number We v and the vapor Froude number Fr V,Mori defined by Mori et al. [MYOK 00] are calculated from equation 3.36 and equation 3.37, and the critical heat flux q crit is calculated with the Kutateladze correlation from equation If x de is not defined at the mass velocity being considered, it is assumed that x de = A heat transfer model for bubbly flow was added by Cheng et al. [CRT 08] to the model for the sake of completeness. In absence of any data, the heat transfer coefficients in bubbly flow regime are calculated by the same method as that in the intermittent flow Air-side heat transfer coefficient The work of McQuiston and Parker [Ste 03] is used to evaluate the air-side convective heat transfer coefficient for a plain-fin and tube heat exchanger with multiple depth-rows of staggered tubes. The model is developed for dry coils. The heat transfer coefficient is based on the Colburn j-factor, which is defined as, Substituting the appropriate values for the Stanton number, St h, gives the following relationship for the air-side convective heat transfer coefficient, Where, cp h is the specific heat of air, and Ġ air is the mass flux of air through the minimum flow area which is expressed as, The minimum free flow area, A mf,2, is calculated from equation McQuiston and Parker used a plain-fin and tube heat exchanger with 4 depth-rows as the baseline model, and for this model defined the Colburn j-factor as, and the parameter JP is defined as, Where, A t is the tube outside surface area, and A t,2 is the total air side heat transfer surface area (fin area plus tube area). The Reynolds number, Re Do in the above expression is based 66

15 on the tube outside diameter, D o, and the mass flux of air, Ġ air. The area ratio can be expressed as, where P l is the tube spacing parallel to the air flow (longitudinal), P t is the tube spacing normal to the air flow (transverse), L c is the depth of the evaporator in the direction of the air flow, D h is the hydraulic diameter defined as, and ζ is the ratio of the minimum free-flow area to the frontal area, The j-factor for heat exchangers with four or fewer depth-rows can then be found using the following correlation, Where, z is the number of depth-rows of tubes, and Re Pl is the air-side Reynolds number based on the longitudinal tube spacing, Fin analysis to determine fin efficiency The plain-fin and tube heat exchangers are widely used in several domains such as heating, ventilating, refrigeration and air conditioning systems. In practical application of air-torefrigerant heat exchangers, the dominant resistance is on the air-side and improving the accuracy of the analysis of the air-side heat transfer is required by the growing demand of high performance heat transfer surfaces [PC 03]. The fin performance is commonly expressed in terms of heat transfer coefficient and fin efficiency, which is defined as the ratio of the actual fin heat transfer rate to the heat transfer rate that would exist if the entire fin surface was at the base temperature. This case is the one providing the maximum heat transfer rate because this corresponds to the maximum driving potential (temperature difference) for the convection heat transfer. Many 67

16 experimental studies are available in the open literature to characterize the air-side heat transfer performance for several types of fins used in finned tube heat exchangers. The established correlations are used for design, rating and modeling of heat exchangers. What is observed in nearly all published papers is that, whatever the fin type (plain, louvered, slit), the fin efficiency calculation is always performed by analytical methods derived from circular fin analysis [PC03]. The analytical circular fin analysis involves a number of assumptions, known as ideal fin assumptions, which need to be addressed. These assumptions are: one-dimensional radial conduction, steady state conditions, radiation heat transfer negligible, constant fin conductivity, constant heat transfer coefficient over the entire fin, fin base temperature is assumed to be constant, thermal contact resistance between the prime surface and the fin is negligible, the surrounding fluid is assumed at constant temperature. Among the ideal fin assumptions, the first one should be carefully considered because the actual fin geometry used in plain-fin and tube heat exchanger differs significantly from the plain circular fin shape. Fin efficiency equations for dry plain circular fins under the aforementioned assumptions are reported in many handbooks [PC 03]. The analytical solution for a circular fin, which is the same as for an angular sector of circular fin with adiabatic fin tip is given by following equation, Where, In and K n are the modified Bessel functions of first and second kind. Several studies have been performed in order to simplify this circular fin efficiency formulation by avoiding the use of modified Bessel functions. Among all the approximations, the Schmidt approximation is the most widely used one. Hong and Webb [PC 03] propose to slightly modify the Schmidt equation (equation 3.69 and 3.70) by using a modified φ parameter φ m (equation 3.71) in equation 3.69, in order to obtain better accuracy. 68

17 With this modification, the error between the analytical solution (equation 3.68) and the approximation does not exceed 2% over the practical range of conditions r f /r o 6 and m(r f r o ) 2.5. Figure 3.4: Unit cells for inline and staggered tube layouts with plain fins. Plain-fin and tube heat exchangers are generally composed of continuous flat plate fins. The fins are metal sheets pierced through the tube bank. The tube lay-out is either inline or staggered configuration. In order to express the fin efficiency of the continuous plain fins, the fin is divided in unit cells. Considering that all the tubes are at the same temperature, the adiabatic zones of the fins determine the unit cells, as presented in Figure 3.4. The considered fin shape is rectangular for the inline configuration and hexagonal for the staggered lay-out. Two methods are used in order to calculate the efficiency of these rectangular or hexagonal fins from the circular fin efficiency with adiabatic fin tip condition. The most accurate method is the sector method. Nevertheless, being simpler and more widely used, the equivalent circular fin method is used in this thesis. 69

18 Gardner and Schmidt [PC 03], in their respective studies, have shown that in the case of rectangular and hexagonal fins, the fin efficiency could be treated as a circular fin, by considering an equivalent circular fin radius. For the calculation of the equivalent circular radius, two approaches are possible. The first one consists in considering a circular fin having the same surface area as the rectangular or hexagonal fin. The other method is the Schmidt method in which correlations are developed in order to find an equivalent circular fin having the same fin efficiency as the rectangular fin (equation 3.72) or the hexagonal fin (equation 3.73). Equations 3.69), equation 3.71, and equation 3.73 are used to calculate the fin efficiency of plain-fins for staggered tube layout CO 2 - side two-phase pressure drop A new two-phase frictional pressure drop model for CO 2 is developed by Cheng et al. [CRQT 08] This model has incorporated the updated CO 2 flow pattern map, which is used to calculate two-phase pressure drop during evaporation of CO 2. This is a phenomenological two-phase frictional pressure drop model, which is intrinsically related to the flow patterns. Based on quality and mass flux of CO 2 refrigerant at the evaporator inlet, first the two-phase flow patterns possible along the flow path are decided as aforementioned in section 3.7. The total pressure drop is the sum of the static pressure drop (gravity pressure drop), the momentum pressure drop (acceleration pressure drop) and the frictional pressure drop, For horizontal channels, the static pressure drop equals zero. The momentum pressure drop is calculated as, 70

19 CO 2 frictional pressure drop model for annular flow (A) [CRQT 08]: The basic equation is the same as that of the Moreno Quibén and Thome pressure drop model as, Where, the two-phase flow friction factor of annular flow fa is calculated by equation This correlation is thus different from that of the Moreno Quibén and Thome pressure drop model. The mean velocity of the vapor phase u c,v is calculated by equation The void fraction ε is calculated using equation The vapor phase Reynolds number Re V and the liquid phase Weber number We L are based on the mean liquid phase velocity u c,l. CO 2 frictional pressure drop model for slug and intermittent flow (Slug + I) [CRQT 08] To avoid jump in the pressure drops between these two flow patterns, the Moreno Quibén and Thome pressure drop model is updated as given in equation Where, Δp A is calculated with equation 3.76 and the single-phase frictional pressure drop considering the total vapor liquid two-phase flow as liquid flow Δp LO is calculated by equation

20 The friction factor is calculated with the Blasius equation as, Where, Reynolds number Re LO is calculated as, CO 2 frictional pressure drop model for stratified-wavy flow (SW) [CRQT 08]: The equation is kept the same as that of the Moreno Quibén and Thome pressure drop model as, Where, the two-phase friction factor of stratified-wavy flow f SW is calculated with the following interpolating expression (a modification of that used in the Moreno Quibén and Thome pressure drop model) based on the CO 2 database as, and the dimensionless dry angle θ * dry is defined as, For θ dry in the stratified-wavy regime (SW), the following equation is proposed, The single-phase friction factor of the vapor phase f V is calculated as, Where, the vapor Reynolds number is calculated with equation (3.79). CO 2 frictional pressure drop model for slug-stratified wavy flow (Slug + SW) [CRQT 08]: The authors propose to avoid any jump in the pressure drops between these two flow patterns and to updated the Moreno Quibén and Thome pressure drop model as, 72

21 Where, Δp LO and Δp SW are calculated with equation 3.83 and 3.86 respectively. CO 2 frictional pressure drop model for mist flow (M) [CRQT 08]: The following expression is kept the same as that in the Moreno Quibén and Thome pressure drop model as, The homogenous density ρ c,h is defined as, Where, the homogenous void fraction ε h is calculated as, And the friction factor of mist flow f M was correlated according to the CO 2 experimental data, which is different from that in the Moreno Quibén and Thome pressure drop model by equation The mist flow Reynolds number is defined as, Where, the homogenous dynamic viscosity is calculated as proposed by Cicchitti et al. [CLSS 60] in equation The constants in equation (3.95) are quite different from those in the Blasius equation. According to Cheng et al. [CRQT 08], the reason is possibly because there are limited experimental data in mist flow in the database and also perhaps a lower accuracy of these experimental data. Therefore, Cheng et al. [CRQT 08] feel the need for more accurate 73

22 experimental data in mist flow to further verify this correlation or modify it if necessary in the future. CO 2 frictional pressure drop model for dryout region (D) [CRQT 08]: The linear interpolating expression is kept the same as that in the Moreno Quibén Thome pressure drop model as, Where, Δp tp (x di ) is the frictional pressure drop at the dryout inception quality x di and is calculated with equation 3.76 for annular flow or with equation 3.86 for stratified-wavy flow, and Δp M (x de ) is the frictional pressure drop at the dryout completion quality x de and is calculated with equation x di and x de are calculated with equations 3.35 and 3.40 respectively. CO 2 frictional pressure drop model for stratified flow (S) [CRQT 08]: The Cheng et al. [CRQT 08] found that no data fell into this flow regime but for completeness, they kept the method the same as that in the Moreno Quibén and Thome pressure drop model as, Where, the mean velocity of the vapor phase u c,v is calculated with equation 3.78 and the two-phase friction factor of stratified flow is calculated as, The single-phase friction factor of the vapor phase f V and the two-phase friction factor of annular flow f A are calculated with equation 3.90 and equation 3.77 respectively, and the dimensionless stratified angle θ * strat is defined as, Where, the stratified angle θ strat is calculated with equation Where, Δp LO and are calculated with equation 3.83 and 3.99 respectively. 74

23 CO 2 frictional pressure drop model for bubbly flow (B) [CRQT 08]: In their study, the authors found no data available for this regime but keeping consistency with the frictional pressure drops in the neighboring regimes and following the same format as the others without creating a jump at the transition (there is no such a model in the Moreno Quibén and Thome pressure drop model), the following expression is proposed as, Where, Δp LO and Δp A are calculated with equation 3.83 and 3.76 respectively. According to Cheng et al. [CRQT 08], further experimental data are needed to verify or modify this model for bubbly flow regime Air-side pressure drop According to Rich, the air-side pressure drop can be divided into two components, the pressure drop due to the tubes, Δp tubes, and the pressure drop due to the fins, Δp fin. The work of Rich [Wri 00] is used to evaluate the air-side pressure drop due to the fins, which is expressed as, where, f fins is the fin friction factor, v m is the mean specific volume of air, Ġ h is mass flux of air, A s is the finned (secondary) surface area, and A mf,2 is the air-side minimum free flow area. In experimental tests, Rich found that the friction factor is dependent on the Reynolds number, but it is independent of the fin spacing for fin density between 3 and 14 fins per inch. In this range of fin density, Rich expresses the fin friction factor as, Where, the Reynolds number Re Pl is based on the tube longitudinal spacing, P l, To determine the pressure drop over the tubes, the relationships developed by Kim-Youn- Webb [Jia 03] are used. The tube-side friction factor and pressure drop is expressed as, 75

24 where, P t is tube transverse pitch, D o is tube outside diameter, A t,o is tube outside surface area, and Re Do is air-side Reynolds number based on tube outside diameter found as, Modification in IMST ART for evaporator The geometry of an evaporator finalized using Engineering Equation Solver (EES) [Kli 10] is further modified in IMST ART [CGMB 02]. The geometry and performance parameters of individual components have an effect on the system energy performance. In case of an evaporator, the parameters like air side pressure drop, refrigerant pressure drop, refrigerant flow circuits, tube longitudinal and lateral pitch, overall refrigerant charge, refrigerant side pressure drop etc. have effect on the system overall performance parameters. The geometry of an evaporator is further fine tuned through the parametric simulation study to achieve maximum energy performance of the system for the rated conditions. 3.3 SUCTION LINE HEAT EXHANGER (SLHX) A SLHX is used to transfer heat from supercritical high pressure and temperature CO 2 to subcritical low pressure and low temperature CO 2. The transfer of heat results in the cooling of the supercritical gas or liquid and heating of the subcritical CO 2 vapor. This transfer of the heat has impact on the performance of the transcritical CO 2 cycle. The literature review has shown that a SLHX in the cycle increases the Coefficient of Performance (COP) of the cycle in the range 5% to 10%. This part focuses on developing the mathematical iterative method to predict the heat transfer coefficient as well as pressure drop for a straight tube in tube type heat exchanger. Further, the CFD model to predict the heat transfer as well as pressure drop between the subcritical and supercritical CO 2 in a straight tube in tube type heat exchanger has been discussed. 76

25 The actual flow arrangement of a SLHX is shown in Figure 3.5. The SLHX is a straight tube in tube counter flow type heat exchanger. The subcritical CO 2 refrigerant flows in the core and supercritical CO 2 refrigerant flows in the annulus. from receiver/evaporator (subcritical CO 2 inlet) from gas cooler (supercritical CO 2 inlet) to compressor (subcritical CO 2 outlet) to expansion valve (supercritical CO 2 outlet) Figure 3.5: Tube in tube type suction line heat exchanger For simulation of SLHX, the available data are inlet temperatures sides supercritical and subcritical, mass flow rates on both the sides, working pressure on both the sides and standard sizes of the diameters. Following assumptions are considered for the evaluation of various parameters of SLHX. CO 2 is considered as a pure fluid. Negligible pressure drop Heat exchanger operates under steady state conditions. No heat generation in the heat exchanger. Heat losses to or from the surroundings are negligible. Longitudinal heat conduction in the fluid and in the wall is not considered Mathematical model A computer code has been developed in Engineering Equation Solver (EES) to study effects of geometry and operating parameters on the thermal performance of a SLHX. EES calculates the thermo-physical properties with respect to pressure and temperature using inbuild fundamental equations of state for CO 2. EES solves equations by Newton - Raphson iterative method [Kli 10]. To consider the variation of thermo-physical properties, the entire length of a SLHX has been divided equally into several discrete segments ( L) as shown in Figure 3.6. At each segment, outlet temperature is calculated based on the outlet temperature and pressure of the previous segment. The outlet temperature of first segment is considered as the inlet temperatures to the next segment, in this manner it repeats until the 77

26 last segment of the tube. This has helped in grabbing accurately the fast changing properties of CO 2 in the computer program. supercritical co 2 inlet temperature supercritical co 2 flow (annular side) assume subcritical co 2 outlet temperature subcritical co 2 flow (inner side) inner tube thickness Fig. 3.6: Mathematical model of a SLHX Simulation Figure 3.7 provides an algorithm that needs to provide input parameters: inner diameter of core tube and outer tube, outer diameter of core tube, operating mass flow rates and pressures of both the sides, inlet temperature of supercritical CO 2. An algorithm is required to guess outlet temperature of subcritical CO 2 to begin the iterations of the program. This program first calculates the length of the each segment and then it calculates fluid properties, Reynolds numbers, friction factors, heat transfer coefficients and overall heat transfer coefficient with respect to temperatures and pressures for each segment. Finally, it calculates the overall heat transfer for the entire length of a SLHX. This program differs in working out Nusselt numbers for the subcritical and supercritical CO 2. The research work has evaluated different correlations for Nusselt numbers for both the subcritical and supercritical CO Petukhov and Kirillov et al. correlation for subcritical region Equation [Petukhov and Kirillov et al] predicts the heat transfer coefficient for singlephase, forced convective, turbulent flow in a smooth pipe in the range of 0.5< Pr < 2000 and 3000 < Re < with 10% accuracy [K03]. Where, 78

27 Input for IHE: Dimensions (d i, d o, D i ), Mass Flow Inlets (m c, m h ), Operating Pressures (P c, P h ), Temperatures (T c,i, T h,i, T w ), Length Spacing ( L) Calculate: Areas (A, A c, A h ), duplicate i = 1, n Length [i] = (i-1)* L Calculate: Fluid Properties (i.e. µ c,i, µ h,i, µ w,i,ρ c,i, ρ h,i,ρ w,i,cp c,i, Cp h,i, Cp wi, Pr c,i, Pr h,i ) for i=1 to i= n Calculate: Vel c,i, Vel h,i, Vel w,i,re c,i, Re h,i,re w,i,f c,i, f h,i,nu c,i, Nu h,i, Nu w,i, h c,i, h h,i, U,i for i=1 to i= n Calculate Outlet Temperatures using LMTD: T c, i+1, T h, i+1 for i=1 to i= n Stop If T c, i+n = 283 K No Guess T c,i Yes End Loop Figure 3.7: Flow chart for thermal calculations 79

28 2. Pitla et al. correlation for supercritical region The correlation of Pitla et al. [PGR 01] has been used to predict the heat transfer coefficient of supercritical CO 2 during in-tube cooling. The correlation is given in Equation Where, Gnielinski correlation is used to calculate both Nusselt numbers Nu wall and Nu bulk. Here, subscripts wall and bulk represent that properties are evaluated at wall temperature and bulk flow temperature respectively. Where, 3. Chang et al. correlation for supercritical region The correlation of Chang et al. [SP 05] has been used to evaluate the heat transfer coefficient and pressure drop during gas cooling process of CO 2 in supercritical region. The authors have provided the separated correlations for region above and below the pseudocritical temperature (T b /T pc >1 and Tb/Tpc 1) on the thermodynamic property chart for CO 2. The predicted heat transfer coefficient by new proposed correlation is within the accuracy of 10% with the experiment data. The outlet temperatures of each segment are calculated by equating LMTD and energy balance equations as shown by equations and respectively. The outlet temperatures of first segment are considered as inlet temperature to the next segment. In this manner, calculation repeats until the n th segment and finally at segment i = n, the gives the outlet temperature of the supercritical CO 2 and inlet temperature of the subcritical CO 2. If temperature of the subcritical CO 2 at i = n is equal to the guess 80

29 temperature of the subcritical CO 2, then solution stops else need to adjust the guess value of the outlet temperature of the subcritical CO 2 at i = 1. Inputs: Dimensions (d i, d o, D i ), Mass Flow Inlets (m c, m h ), Operating Pressures (P c, P h ), Inlet, Outlet & wall Temperatures (T c,i, T c,o, T h,i, T h,o, T w ), Length (L) Calculate: Heat Transfer & cross sections Areas (A, A c, A h ), Calculate: Fluid & Solid Properties Calculate: Vel c, Vel h, Vel w, Re c, Re h, Re w, c, h Calculate Pressure Drop ( ) Stop Figure 3.8: Flow chart for the pressure drop calculations Pressure drop in a SLHX An algorithm shown in Figure 3.8 provides the basic structure of the program to calculate Reynold number and friction factor at bulk temperatures on the entire length of a SLHX. This program uses Filonenko friction factor correlation for subcritical region and Petrov - Popov friction factor correlation for supercritical region. 1. Filonenko's friction factor for subcritical region Filonenko friction factor correlation is widely used for the turbulent gas flow in smooth tubes. 2. Petrov and Popov friction factor for supercritical region 81

30 Petrov and Popov calculated the friction factor of CO 2 cooled in the supercritical conditions in the range of Re wall = and Re bulk = Petrov and Popov obtained an interpolation equation of the friction factor. ρ ρ Where f w, the friction factor is calculated by Filonenko Eqution [Fil 48] at tube wall temperature and the exponent s is given by, (3.118) Numerical model A SLHX is numerically modeled using Computation Fluid Dynamic (CFD) technique. CFD is a technique to solve the set of nonlinear highly coupled partial differential equations to governing the fluid flow and associated phenomenon like heat transfer, combustion, particle interaction etc. Geometry Mesh Physics Solve Reports Post- Processing Select Geometry Unstructured Heat Transfer ON/OFF Steady/ Unsteady Forces Report Contours Geometry Parameters Domain Shape and Size Structured Compressible ON/OFF Flow properties Iterations/ Steps Convergent Limit XY Plot Verification Validation Vectors Streamlines Viscous Model Precisions (single/ double) Boundary Conditions Numerical Scheme Initial Conditions Figure 3.9: CFD Process 82

31 Figure 3.9 shows in detail the process of CFD. First the geometry has to be created with the consideration of some CFD modeling constraints. This geometry then needs to be meshed. Meshing or grid generation is a process in which the domain of interest is discretized in the finite volumes. Appropriate models, such as the k turbulence models, boundary conditions and solver parameters are assigned as per the analysis requirements. Solver solves the various governing equations iteratively to attain the defined convergence criteria. The continuity, energy and momentum balance equations basically solved using CFD algorithm Numerical simulation for a SLHX For this study, the geometric model was created in commercial CAD software - Ideas. The tubes having inner diameters of core and outer tubes are 5 mm and mm respectively with 0.5 mm wall thickness. The length of a SLHX was used 1 m. The pre-processing software Gambit was used to mesh the computational model of a SLHX. The unstructured non-uniform mesh with cells are used to discretize the main computational model as shown in Figures 3.10 and The boundary conditions are define as follows, 1. Mass flow inlet for both subcritical and supercritical refrigerant inlets 2. Pressure outlet for both subcritical and supercritical refrigerant outlets 3. Fluid domain for both subcritical and supercritical refrigerants 4. Solid domain for thickness of the inner pipe 5. Wall with no slip rest of the surfaces Figure 3.10: Isometric view of enlarged CFD model 83

32 Figure 3.11: Side view of CFD model The double precision solver scheme was used for simulations. The convection term in the governing equations was modeled with the bounded second-order upwind scheme. The SIMPLE scheme is used for coupling the pressure and the velocity field. The thermophysical properties of the subcritical and supercritical CO 2 were taken as a function of temperature and pressure in the form of polynomial equations. Under turbulent flow conditions, the standard k ε model was employed with standard wall functions. The numerical solution converged when the residuals for all equations below the 1e-05. Simulations were done at operating pressures ranging from 95 to 115 bar and the mass flow rate ranging from kg/s to kg/s to find out the outlet temperatures and pressure drops of a SLHX. 3.4 GAS COOLER The fin and tube gas cooler is used to reject heat to the atmosphere in CO 2 air conditioning system. This chapter discusses in detail the methodology adopted for the simulation and design of the fin and tube gas cooler. The simulation is worked out for predicting the heat transfer as well as pressure drops for a plain fin and tube gas cooler using different correlations. Finally, IMST ART for further fine tuning the geometrical configuration of the gas cooler. The simulation has been carried for parametric simulation of a fin and tube gas cooler with analytical correlations for refrigerant CO 2 and air. Further, optimization of the geometry of a gas cooler for maximum heat rejection capacity by single parameter at one time marching method has been worked out. 84

33 3.4.1 ANALYTICAL MODEL The parameters of a fin and tube gas cooler are evaluated in Microsoft Office Excel Spreadsheet program. The actual flow arrangement of the fin and tube gas cooler for air conditioning system with CO 2 as a refrigerant is shown in Figure 3.12, which is single pass, unmixed-unmixed, four pass three circuit staggered tube arrangement fin and tube gas cooler. The transcritical CO 2 refrigerant flows through the tubes and it is cooled by the atmospheric air. The schematic arrangement of fin spacing and frontal plain fin and tube gas cooler view is as shown in Figure Figure 3.12: Staggered tube layout of a gas cooler (a) Fin spacing arrangement (b) Four pass - three circuit staggered tube gas cooler arrangement Figure 3.13: Frontal view of a fin and tube gas cooler 85

34 Input parameters: P GC ; L 1 ; L 2 ; L 3 ; ID; OD; P t ; P l ; N t ; m air ; m ref ; F d ; F s ; t f Estimate thermo physical Properties for CO 2 and air Calculate surface geometric properties for air side: Core volume; A o ; A min air ; A t Calculate surface geometric properties for fin side: Core volume; A sf ; N f ; L f ; M; ɸ; Re/rt Evaluate: η Fin ; η o Estimate: V air ; G air : Re air ; D h ; V ref ; G ref ; Re ref Determine: Colburn j factor and Nusselt number Calculate: HTC and OHTC Evaluate: U o ; NTU; ɛ Figure 3.14: Flow chart for simulation of heat transfer coefficient The assumptions made are: CO 2 is considered as a pure fluid, a gas cooler is a four pass with three-circuit cross flow, both fluids unmixed, staggered tube heat exchanger, steady state processes in the gas cooler, no internal heat generation in the heat exchanger and NTU-ε method is considered for the thermal design. The algorithms of evaluation of heat transfer coefficient and pressure drop in gas cooler are shown in Figure 3.14 and Figure 3.15 respectively. Microsoft Office Excel spread sheets are used to carry out the 1-D calculation for fin and tube gas cooler. The Thermo-physical 86

35 properties for transcritical CO 2 are taken from NIST database [LHM 07]. The operating conditions considered for the base line gas cooler are as per Table 6.1 and the geometry of the base case gas cooler model is given in Table 6.2. Table 6.3 provides the summary of different correlations with their range for geometrical parameter to which they are applicable. This study has provided evaluation of different correlations for geometrical parameters namely tube diameter, longitudinal tube spacing, transverse tube spacing, fin spacing and number of tube rows with respect to present simulation study as shown in Figure To calculate the overall air side fin surface efficiency for a plain-fin and tube heat exchanger with multiple rows of staggered tubes arrangement, hexagonal fin into circular shape to avoid cumbersome numerical conversion required to solve the equations. Input parameters: P GC ; L 1 ; L 2 ; L 3 ; ID; OD; P t ; P l ; N t ; m air ; m ref ; F d ; F s ; t f Estimate thermo physical Properties for CO 2 and air Calculate surface geometric properties for air side: Core volume; A o ; A min air ; A t Calculate surface geometric properties for refrigerant side: Core volume; A i ; A min ; A s Estimate: V air ; G air : Re air ; D h ; V ref ; G ref ; Re ref Determine friction factor f and Nusselt number Calculate: p Figure 3.15: Flow chart for simulation of pressure drop Fin Analysis For calculation of the overall air side fin surface efficiency (η o ), for a fin and tube heat exchanger with multiple rows of staggered tubes the correlation of Creed Taylor [Tay 04] 87

36 has been used and hexagonal shaped fins as shown in Figure The shape of fin has been modified from hexagonal to circular as shown in Figure 3.17 to avoid cumbersome numerical correlation required to solve the equations. Fig Configuration for staggered tube along with hexagonal fins P diag Figure 3.17 Cross section for continuous circular fins The air side fin efficiency calculated by equation A η o = 1- A fin o 1- η fin The fin efficiency of a circular fin is calculated using equation tanh mrt φ η fin = mrφ t (3.126) (3.127) 88

37 Where, m is the standard extended surface parameter, which is defined as, 2ho m= k.t fin f (3.128) The fin efficiency parameter for a circular fin, φ is calculated using equation R R e e φ= ln r t rt Where, the equivalent circular fin radius, R e, is calculated using equation X t e Xl = X t r t t R r 2 P 2 t 2 P diag = + Pl (3.129) (3.130) (3.131) Rich correlation [Ric 73] is considered to work out air side heat transfer coefficient for the simulation of air side plain fin and tube gas cooler.... (3.132) j R = 0.195* R e air Air side Nusselt number is calculated by using most familiar Colburn s equation N = j.r.p u e r Colburn (3.133) Based on the experimental data on gas cooling of supercritical carbon dioxide, Yoon et al. suggested an empirical correlation using the modified form of Dittus-Bolter s correlation. The correlation (equation 3.133) suggested by Yoon have an average deviation of 1.6%, the absolute average deviation of 12.7% and the RMS deviation of 20.2%. n b c pc N u = a.re. Pr a 0.14, b 0.69, c 0.66, n 0... T T a 0.013, b 1.0, c 0.05, n T T pc pc (3.134) Rich developed plain fin coil correlations for Fanning friction factor based on data from eight coil configurations (equation 3.135). f = 1.70.R -0.5 r e...3 N 14fins/in (3.135) L f 89