Flow Pattern Map for In Tube Evaporation and Condensation

Transcription

1 Fow Pattern Map for In Tube Evaporation and Condensation Lászó Garbai Dr. *, Róbert Sánta ** * Budapest University of Technoogy and Economics, Hungary ** Coege of Appied Sciences Subotica Tech, Serbia Abstract - The aim of the artice is the review of two phase fow pattern maps for horizonta tubes. The fow pattern in evaporation and condensation section in a sma tube has been anayzed ín this artice. The two-phase fow pattern map for evaporation is proposed by Wojtan et a. whie the condensation section is proposed by Thome and E Haja. The simuation was in MathCAD and the resuts are presented in diagrams. In the simuation refrigerant R34a was used. Nomencature d diameter (m) x vapor quaity (-) G mass veocity (kg/sm ) m mass fow rate (kg/s ) p pressure (Pa) Q heat fux (W/m ) T temperature (K) f friction factor (-) A area of tube (m ) Greeks heat transfer coefficient (W/m K) therma conductivity (W/mK) void fraction (-) dynamic viscosity (Ns/m ) surface tension (-) density (m 3 /kg) Index iqued v vapor tp two phase I. INTRODUCTION For two-phase fows, the respective distribution of the iquid and vapor phases in the fow channe is an important aspect of their description. Their respective distributions take on some commony observed fow structures, which are defined as two-phase fow patterns that have particuar identifying characteristics. Heat transfer coefficients and pressure drops are cosey reated to the oca two-phase fow structure of the fuid, and thus two-phase fow pattern prediction is an important aspect of modeing evaporation and condensation. In fact, recent heat transfer modes for predicting in tube boiing and condensation are based on the oca fow pattern and hence, by necessity, require reiabe fow pattern map to identify what type of fow pattern exists at the oca fow conditions. Fow patterns have an important infuence on prediction of fow boiing and convective condensation heat transfer coefficients, and two-phase pressure drops. For horizonta tubes, the methods of Taite and Duker [] (976) and Baker [] (954), Hashizume [3], Steiner [4], are widey used. The more recent fow pattern map of Kattan, Thome and Favrat (998) and its more subsequent improvements, which was deveop specificay for sma diameter tubes typica of she-andtube heat exchangers for both adiabatic and evaporating fows. Another version of their map aso been proposed by E.Haja, Thome and Cavainni [6] (003) for in tube condensation. II. FLOW REGIMES IN HORIZONTAL PIPES When a vapor and a iquid are forced to fow together inside a pipe, there are at east seven different geometrica configurations, or fow regimes, that are observed to occur. The regime depends on the fuid properties, the size of the conduit and the fow rates of each of the phases. Vapor and iquid phases fow in horizonta tubes according to severa topoogica configurations, caed fow patterns or fow regimes that are determined by the interfacia structure between the two phases. Two-phase fow patterns in horizonta tubes are simiar to those in vertica fows but the distribution of the iquid is infuenced by gravity that acts to stratify the iquid to the bottom of the tube and the vapor to the top. Fow patterns for co-current fow of vapor and iquid in a

2 horizonta tube are show in Figure. and are categorized as foows. Bubby fow the gas bubbes are dispersed in the iquid with a high concentration of bubbes in the upper haf of the tube due to their buoyancy. When shear forces are dominant, the bubbes tend to disperse uniformy in the tube. In horizonta fows, the regime typicay ony occurs at high mass fow rates. Stratified fow At ow iquid and gas veocities, compete separation of the two phases occurs. The gas goes to the top and the iquid to the bottom of the tube, separated by an undisturbed horizonta interface. Hence the iquid and gas are fuy stratified in this regime. Stratified-wavy fow Increasing the gas veocity in a stratified fow, waves is formed on the interface and trave in the direction of fow. The waves cimb up the sides of the tube, eaving thin fims of iquid on the wa after the passage of the wave. Intermittent fow Further increasing the gas veocity, these interfacia waves become arge enough to wash the top of the tube. Large ampitude waves often contain entrained bubbes. The top wa is neary continuousy wetted by the arge ampitude waves and the thin iquid fims eft behind. Intermittent fow is aso a composite of the pug and sug fow regimes. These subcategories are characterized as foows: o Pug fow. This fow regime has iquid pugs that are separated by eongated gas bubbes. The diameters of the eongated bubbes are smaer than the tube such that the iquid phase is continuous aong the bottom of the tube beow the eongated bubbes. Pug fow is aso sometimes referred to as eongated bubbe fow. o Sug fow. At higher vapor veocities, the diameters of eongated bubbes become simiar in size to channe height. The iquid sugs separating such eongated bubbes can aso be described as arge ampitude waves. Annuar fow - At high gas fow rates, the iquid forms a continuous annuar fim around the perimeter of the tube, simiar to that in vertica fow but the iquid fim is thicker at the bottom than the top. The interface between the iquid annuus and the vapor core is disturbed by sma ampitude waves and dropets may be dispersed in the gas core. Mist fow Simiar to vertica fow, at very high gas veocities, a the iquid may be stripped from the wa and entrained as sma dropets in the now continuous vapor phase. Figure. Fow regimes in horizonta pipes [] III. FLOW REGIME MAPS To predict the oca fow pattern in a tube, a fow pattern map is used. It is a diagram that dispays the transitions boundaries between the fow patterns and is typicay potted on og-og axes using dimensioness parameters to represent the iquid and gas veocities. Fow regime maps of the sort shown in figure. are usefu when we want to gain insight into the mechanisms creating the fow regimes. Aong the horizonta axis the superficia gas veocity has been potted. Aong the vertica axis we have potted the superficia iquid veocity. Figure. Exampe of steady-state fow regime map for a horizonta pipe If the superficia gas and iquid veocities is very ow the fow is stratified. If increase the gas veocity, waves start forming on the iquid surface. Due to the friction between gas and iquid, increasing the gas fow wi aso affect the iquid by dragging it faster towards the outet and thereby reducing the iquid eve. If continue to increase the gas fow further, the gas turbuence intensifies unti it rips iquid from the iquid surface so dropets become entrained in the gas stream, whie the previousy horizonta surface bends around the inside of the pipe unti it covers the whoe

3 circumference with a iquid fim. The dropets are carried by the gas unti they occasionay hit the pipe wa and are deposited back into the iquid fim on the wa. If the iquid fow is very high, the turbuence wi be strong, and any gas tends to be mixed into the iquid as fine bubbes. For somewhat ower iquid fows, the bubbes foat towards the top-side of the pipe. The appropriate mix of gas and iquid can then form Tayorbubbes, which is the name we sometimes use for the arge gas bubbes separating iquid sugs. If the gas fow is constanty kept high enough, sugs wi not form because the gas transports the iquid out so rapidy the iquid fraction stays ow throughout the entire pipe. IV. FLOW PATTERN MAP FOR EVAPORATION IN HORIZONTAL TUBES The two-phase fow pattern map and heat transfer mode for evaporation proposed Wojtan et a.[7] (005), is a sighty modified version of Kattan, Thome and Favrat [5] map for evaporation fows in sma diameter horizonta tubes. The six principa fow patterns encountered during evaporation inside horizonta tubes are: Stratified fow(s), Stratified-wavy fow (SW), o Sug fow zone, o Sug/Stratified-Wavy zone o Stratified-Wavy zone. Intermittent fow (I), Annuar fow (A), Dryout (D), Mist fow (MF) A. FLOW PATTERN MAP OF WOJTAN ET AL. (005) The transition boundary curve between stratified fows to stratified-wavy fow is: 6. A d A vd G v strat x x 3 v g cos 3 () 3 6 A vd g D v x d Gwavy F We x 5 d Fr 50 F () Threshod ine of the intermittent to annuar fow transition at X IA is : X v v IA 0.34 The stratified-wavy region is then subdivided into three zones as foows: o G G wavy X IA gives the sug fow zone, o Gstrat G GwavyX IA and 0 x XIA give the Sug/Stratified-Wavy zone o x X gives the Stratified-Wavy zone. IA The transition boundary curve between annuar fows to dryout fow is: d n i 0.35 x g 0.37 g Gdryout g v g d i 0.7 q q DNB The transition boundary curve between dryout fows to mist fow is: d n 7 i x g g Gmist g v g d i 0.7 q q DNB (3) (4) (5) The transition boundary curve between annuar and intermittent fows to stratified-wavy fow is:

4 V. FLOW PATTERN MAP FOR CONDENSATION IN HORIZONTAL TUBES The two-phase fow pattern map for condensation proposed by E Haja, Thome and Cavaini [6] is a sighty modified version of Kattan, Thome and Favrat [5] map for evaporation and adiabatic fows in sma diameter horizonta tubes. Thome and E Haja have simpified impementation of that map by bringing a void fraction equation into the method to eiminate its iterative soution scheme. The five principa fow patterns encountered during condensation inside horizonta tubes are: Annuar fow (often referred to as shearedcontroed regime) (A), Intermittent fow (heat transfer modeed ike annuar fow), (I), Mist fow (annuar fow heat transfer mode assumed for this regime) (MF) Stratified-wavy fow (SW), Stratified fow(s), Intermittent fow refers to both the pug and sug fow regimes (it is essentiay a stratified-wavy fow pattern with arge ampitude waves that wash the top of the tube). Aso, stratified-wavy fow is often referred to in the iterature as simpy wavy fow. A. FLOW PATTERN MAP OF THOME AND EL HAJAL (003) This mode can be easiy appied and gives the void fraction as a function of tota mass fux. Hence it makes sense to use the same void fraction mode in both the fow pattern map and the fow boiing heat transfer mode for which the Rouhani-Axeson [8] mode is a better choice as a genera method. The sectiona area of the tube A and after cacuating ε, the vaues and are directy determined by: A Ad D, A A vd D The stratified ange can be cacuated from an expression evauated in terms of void fraction proposed by Biberg [9] P sin strat D The transition boundary curve between Stratified fows to Stratified-wavy fow is: (6) 6. A vd A vd G v v strat 3 x x 3 g cos The transition boundary curve between Stratified fows to Intermittent/Annuar fow is: 3 6 A vd g D v x d Gwavy F We x 5 d Fr cos 50 (7) F (8) The transition boundary curve between Annuar fows to Mist fow is: 7680 A vd g D v We Gmist x Fr ph (9) The transition boundary curve between Annuar fows to Intermittent fow is: v v X IA 0.34 V. SIMULATION OF MATHEMATICAL MODEL (0) Mathematica modes are simuated by the use of the software too MathCAD. The soution of the deterministic mathematica modes of the fow pattern and heat transfer coefficients is compex. The appied numerica simuation mode for each variabe is discretized. The input data and initia conditions in the deterministic mathematica mode ceary define the vaue of fow pattern and heat transfer coefficient i.e. is the output of the mode. The initia condition and vaues for the simuation: Refrigerant: R34a Mass veocity: G 00 kg m s Vapor quaity ranged: x = 0 [ - ]

5 Tube diameter: d 6 mm W Heat fux: q 3000 m Temperature of evaporation: t o = 5 [ C] Temperature of condensation: t c = 40 [ C] section. (Figure 3.) On the contrary, in the condensing section of the annuar fow pattern the image did not even appear. In the condensing sections the fow regime is stratified wavy. (Figure 4.) In practice, however, this is not competey the case. If the cross section of wa is considered, the condenser tube wa is the codest, hence the vapor of the two-phase refrigerant is condensed in the wa, so there a degree of annuar fow deveops. Graphs are drawn for the considered evaporation and condensation heat transfer coefficients and fow pattern in function of different quaity. VI. RESULTS AND DISCUSES The motivation for the composition of this artice was to investigate the fow pattern map and heat transfer coefficients in the horizonta tube of the condenser and the evaporator. The fow pattern is of crucia definition. With the change of fow pattern, the change of mass veocity of refrigerant occurs. The vaue of the two-phase heat transfer coefficient is determined by the mass veocity. The discrete vaue of the two-phase heat transfer coefficient is a function of the refrigerant mass veocity, the vapor quaity, the refrigerant condensing or evaporation temperature and the inner diameter of tube. α f m, x,t,d Figure 3. Fow Pattern map and Heat Transfer mode for in tube boiing Besides the heat transfer coefficients, accuracy of the pressure drop and the void fraction vaue is determined by the heat pump system of the accurate mathematica mode. The fow pattern map for boiing and fow boiing heat transfer mode for refrigerant R34a on the inside of horizonta tubes are proposed of Wojtan et a. (005). The fow pattern for condensation of refrigerant R34a on the inside of horizonta tubes are suggested by Thome and E Haja (003). The condensation heat transfer mode was used of Shah [0] correation (979). The existence of a particuar fow regime depends on a variety of parameters, incuding the thermo physica properties of the fuid, the tube diameter, orientation and geometry, force fied, mass fux, heat fux and vapor quaity. On the fow pattern maps, the vaue change of the heat transfer coefficients of evaporation and condensation can be seen. It can be seen that the added input vaues, the annuar fow is predominanty formed in the evaporating Figure 4. Fow Pattern map and Heat Transfer mode for in tube Condensation Fow patterns that occur during condensation inside horizonta tubes are simiar to those for evaporation, with the foowing exceptions: The process begins without any entrainment of iquid. There is no dryout.

6 During condensation, the condensate formed coats the tube perimeter with a iquid fim. During condensation in stratified fow regimes, the top of the tube is wetted by the condensate fim whie in evaporating fows the top perimeter is dry. REFERENCES [] Y.Taite and A.E. Duker, A mode for predicting ow regime transitions in horizonta and near horizonta gasiquid fow, AICHE Journa 3. no., [] O. Baker, Design of pipe ines for simutaneous fow of oi and gas, Oi and gas journa (954), [3] K. Hashizume, Fow pattern and void fraction of refrigerant two-phase fow in a horizonta pipe, Buetin of JSME6, no.9, [4] Verein Deutscher Ingenieure VDI-Warmeatas (VDI Heat Atas), Chapter HBB, VDI-Gesseschaft Verfahrenstechnik und Chemieingenieurwsen (GVC), Düssedorf, 993 [5] Kattan, N., Thome, J. R., and Favrat, D. (998). Fow Boiing in Horizonta Tubes. Part : Deveopment of a Diabatic Two-Phase Fow Pattern Map, J. Heat Transfer, 0, [6] E Haja, J., Thome, J.R., and Cavaini, A. (003). Condensation in Horizonta Tubes, Part : Two-Phase Fow Pattern Map, Int. J. Heat Mass Transfer, vo. 46, [7] L Wojtan, T Ursenbacher, J Thome, Investigation of fow boiing in horizonta tubes: Part I: A new diabatic two-phase fow pattern map, Internationa Journa of Heat and Mass Transfer (005) [8] Rouhani, S. Z., and Axesson, E., Cacuation of Void Voume Fraction in the Subcooed and Quaity Boiing Regions. Internationa Journa of Heat and Mass Transfer, vo. 3, no., pp , 970. [9] D. Biberg, An expicit approximation for the wetted ange in two-phase stratified pipe fow, Canadian J. Chemica Engineering (999), -4 [0] Shah MM. A genera correation for heat transfer during fim condensation inside pipes. Int. J Heat & Mass Transfer 979; : [] Dr. Ove Bratand: The Fow Assurance, Bergen Area, Norway, Oi & Energy