Pressure Drop for In-tube Supercritical CO 2 Cooling: Comparison of Correlations and Validation

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1 Paper No: RC-8 19 th National & 8 th ISHMT-ASME Heat and Mass Transer Conerence January -, 008 JNTU Hyderaad, India Pressure Drop or In-tue Supercritical CO Cooling: Comparison o Correlations and Validation Jahar Sarkar Department o Mechanical Engineering Institute o Technology, BHU Varanasi, UP 7 jahar_s@hotmail.com Souvik Bhattacharyya Department o Mechanical Engineering Indian Institute o Technology Kharagpur, WB 7 souvik@mech.iitkgp.ernet.in M. Ramgopal Department o Mechanical Engineering Indian Institute o Technology Kharagpur, WB 7 ramg@mech.iitkgp.ernet.in Astract The pressure drop or supercritical CO cooling in gas cooler tues or heat pump applications has een gained interest due to great variation in thermo-physical properties (specially in the pseudocritical region). This study presents a detailed comparison o pressure drop correlations availale or supercritical CO cooling in mini and micro tues. For the comparison, a general numerical model has een estalished or the gas cooler. The coniguration considered here is a counter-lo, tue-in-tue type ith CO gas loing in inner tue and the secondary luid (coolant) ater loing in the annulus. All the recommended pressure drop correlations developed or other luids or correlations specially developed or CO cooling are ased on the limited set o dimensions and operating conditions. So the correlations are required to e validated or other dimensions and conditions, ecause a more general correlation is needed or the design o an entire heat exchanger. A test acility has een developed to investigate the supercritical caron dioxide cooling in tues ith ater as coolant. Susequently the correlations have een validated ith the tested pressure drop data generated or convective gas cooling. This study is expected to help the design engineer y recommending an appropriate pressure drop correlation or actual gas cooler design to e employed in transcritical CO cycle ased cooling-heating systems. Keyords: Supercritical CO in-tue cooling, pressure drop correlations, comparison, experimental validation. Nomenclature c p Speciic heat capacity, kj kg 1 K 1 D Diameter, m Friction actor G Mass velocity, kg m s 1 h Heat transer coeicient, W m K -1 k Thermal conductivity, W m 1 K 1 L Length, m Nu Nusselt numer Pr Prandtl numer q Heat lux, kw m Re Reynolds numer R rt Relative roughness T Temperature, K p Pressure drop, ar µ Viscosity, N m s ρ Density, kg m 1

2 Suscript Bulk temperature Inside all temperature 1. Introduction Within last decade, natural rerigerant CO ased transcritical cycle has gained special interest in rerigeration, heat pump and air-conditioning applications due to various advantages such as loer pressure ratio, higher rerigerant capacity, easy availaility and superior heat transer properties along ith zero ODP and negligile GWP compared to synthetic rerigerants. Due to lo critical temperature (1.1 o C), supercritical heat rejection is taking place or CO in the gas cooler instead o condenser or conventional cycle. The temperature proile o cooled CO thus can e matched up ith temperature proile o cooling medium ith single-phase heat transer such as ater. This gives reduced thermodynamic losses in single-phase heating. Thus, single-phase heat transer in gas cooler leads various application possiilities o transcritical CO heat pumps in ater heating and other simultaneous process heating and cooling applications such as in ood and agricultural industries [1]. Optimum design o gas cooler is an important parameter or designing a CO ased rerigeration or heat pump system. Supercritical CO gas cooling operates very close to the critical point o CO, hich means large variation in the properties o CO ith temperature and precisely due to this it is very diicult to predict heat transer characteristics o supercritical CO during tue cooling process using various turulent models. The great variation in thermo-physical properties (specially in the pseudo-critical region) cause the heat transer coeicient and pressure drop o caron dioxide to e greatly dependent on oth the local temperature and the heat lux in gas cooler tues. Hence detail study on supercritical CO gas cooling pressure drop or dierent operating conditions such as pressure and mass lo rates, dimensional parameters is required or rigorously understanding the processes and optimum design o gas cooler. Pitla et al. [] and Fang [] have revieed the supercritical heat transer and pressure drop characteristics o caron dioxide in-tue lo primarily including eects o physical actors on supercritical heat transer and riction actor correlations. Almost all the general single-phase pressure drop correlations availale in the open literature are unsuitale near the pseudo-critical region due to arupt variation o thermophysical properties. Hence, ne or modiied pressure drop correlation or in-tue supercritical CO cooling is required to take care o the variation o properties in oth radial and longitudinal direction o lo. Literature search shos very limited riction actor correlations ased on the constant thrmophysical properties oth or smooth tue (Blasius equation & Filonenko s equation [4]) and rough tue (Colerook s equation & Althul s modiied equation [], Churchill s equation []). Petrov & Popov [6] proposed the riction actor correlation or supercritical CO cooling ased on the numerical calculation. They have also proposed another correlation hich as calculated asically or cooling o supercritical ater [7]. Although there is no such correlation availale, it as developed ased on the experiment on the supercritical CO cooling. To take care o the great variation o thermophysical properties, validation o availale correlation is required. Recently e experimental validations on riction actor correlations or supercritical CO cooling ere conducted (Yoon et al. [8], Dang et al. [9], Son et al. []) ut recommended correlations are not common. So, still need the validation o the correlations or other dimensions and lo rates, ecause e need a more general correlation or the design o an entire heat exchanger. In the present ork a detailed comparison o availale riction actor correlations or the pressure drop calculation oth in smooth tue and rough tue and validation ith experimental results or supercritical caron dioxide cooling in mini and micro tues have een carried out. For the comparison, a general numerical model has een estalished or the gas cooler. The coniguration considered here is a counter-lo, tue-in-tue type ith CO gas loing in inner tue and the secondary luid (coolant) ater loing in the annulus. A test acility has een developed to investigate the supercritical caron dioxide cooling in tues ith ater as coolant. Susequently, pressure drop have een measured across the gas cooler or various operating conditions and the correlations have een validated.. Theoretical Analysis Total pressure drop in the gas cooler can e calculated y, G L p h ρ D λ = + Where, λ is the local pressure drop coeicient, hose recommended value is 1.. Hydraulic drag, h [4] is given y, h = + i. Where, the inertia actor as in one dimensional approximation is expressed as: 8q 1 ρ i = Gcp ρ t p m For incompressile luid lo, the value o inertia actor is 0. So, or in-tue CO cooling in supercritical region, or simplicity, it is recommended to neglect inertia actor; i.e, =. h (1) ()

3 .1 Friction actor correlations Large numers o riction actor correlations have een developed ased on constant thermophysical property oth or smooth tue and rough tue. Blasius equation and Filonenko s equation are the idely used in riction actor calculation or turulent lo in smooth tue and constant thermo-physical property [4]. Blasius equation is given y, 1/4 4 = 0.16 Re or Re () 1/ 4 = 0.184Re or Re Filonenko s equation or riction coeicient is given y, = [0.79 ln(re) 1.64] (4) Aove equation is only valid or smooth tue ith ully turulent lo ( Re > 8 ). Althul s modiied equation [] or the riction actor or rough tue or the range o Re > 8 and R 0.001: rt ( ) 0. ' = 0.11 R rt + 68/Re ' i ' = ' i ' > () Churchill [] proposed a more complicated equation or all lo regimes & all relative roughness, hich agrees ith Moody diagram: = ln 0.9 Re ( 7 / Re) 0.7R + rt / 1/ (6) Re Thermophysical property variations in the cooling conditions at supercritical pressures signiicantly aect the pressure drop characteristics. No CO speciic experimental correlations are ound or the riction actor in the cooling condition at supercritical pressures. Petrov and Popov [6] solved governing equations numerically using the Prandtl mixing length o turulence and proposed olloing ormulas or the riction actor o CO cooled in supercritical conditions 4 in the range o Re = and Re = : s ( 1.8 ln(re ) 1.64) ρ µ = ρ µ (7) 0.4 q here, s = 0.0 G Later in 1988, they [7] calculated the riction actor or cooling o supercritical ater in range o 4 Re < and 4 Re <..0 as ollos: m 1/4 1/ µ ρ = µ ρ 0m m m 0m They claimed that this equation is also applicale or helium and caron dioxide. The riction actors 0 and 0m are calculated y Filonenko s equation at T and T m respectively, and Filonenko s equation is only used or the ully developed turulent lo in smooth tues. In order to extend the use o equations 7 and 8 to transitional regime and rough tue, Churchill s equation 4 is recommended instead o Filonenko s equation to calculate 0 and 0m. Fang et al. [] recommended that since the equation 8 is derived rom calculation o ater supercritical cooling; it is etter to use equation 7 or supercritical CO cooling.. Comparison o correlations A simple computer code has een developed or comparison o various riction actor correlations, presented in the aove section, or dierent comination o operating and dimensional parameters. For thermophysical and transport properties o CO, an exclusive property suroutine has een developed ased on seminal ork y Span ad Wagner [11], Vesovic et al. [1] and Feghour et al. [1] and incorporated in the code. Fang et al. [] have done a comparison study o Blasius equation (), Filonenko s equation (4), Althul s modiied equation () and Churchill equation (6) ith respect to Re and shoed that Blasius equation can e valid or Re < 1. and Filonenko equation can e used or Re > 8. Figure 1 shos the variation o riction actor along the SS tue rom inlet to outlet or in-tue CO cooling. Counter-lo heat exchanger ith inner tue diameters 4.7 mm/ 6. mm and outer tue diameters mm/ 1 mm, has een assumed. Folloing input parameters have een taken or generated data: Gas cooling pressure = 0 ar, inlet and outlet temperature o CO are 9 K and 08 K, mass lo rate o CO is 0.04 kg/s, inlet and outlet temperatures o secondary luid ater are 98 K and K. For the simulation ork, the heat exchanger has een discretized to consider the lengthise property variation and energy conservation equations have een applied to each i (8)

4 segment. For rerigerant side heat transer calculation, Pitla et al. [14] correlation employing the mean Nusselt numer concept ased on a numerical and experimental study has een used to account or the property variation in the perpendicular direction o lo: Nu + Nu k Nu Nu = h= k (9) k D Nu and Nu are Nusselt numers ased on the thermophysical properties at the all and ulk temperature respectively, evaluated rom the Gnielinski correlation, as shon elo: ( / 8)(Re 00) Pr Nu0 = () 1/ / ( / 8) (Pr 1) Result shos that oth the riction actors increase due to decrease in Reynolds numer ith the decrease in rerigerant temperature along the gas cooler. Petrov-Popov correlation or riction actor, hich is ased on the calculation o supercritical CO cooling considering the property variation overpredicts y aout 7.% than the constant property ased Filonenko s equation. Friction actor Petrov-Popov Filonenko Along the tue (m) Reynolds numer Figure 1. Comparison o riction actor calculation in the gas cooler Figure. Design layout o the CO heat pump test acility. Experimental Validation.1 Experimental methodology To study the pressure drop characteristics in the gas cooler, the test acility or the prototype o a transcritical CO heat pump or simultaneous ater cooling and heating, developed in IIT Kharagpur has een used. Figure shos a design layout o the test acility and the Figure shos the photograph o the prototype ith accessories and instrumentation. Saturated or superheated vapour rom separator (item 11) is compressed to high pressure through compressor (item 4) and the compressed hot CO gas is cooled as it los through gas cooler (item 6). Then the cooled CO luid is expanded to evaporation pressure through expansion device (item 9) and the resulting to-phase CO passes through evaporator (item ) to give the cooling eect. To-phase, saturated vapour or superheated vapour o CO exits rom the evaporator and enters the separator. A receiver (item 7) is used eteen gas cooler and expansion device to store the CO liquid or control the pressures. A Coriolis mass lo meter (item ) is installed eteen the separator and the compressor to measure the mass lo rate and temperature o CO vapour entering the compressor. To Sagelok saety valves (item ) are used in oth lo and high pressure sides to control the higher limit o pressure. Four pressure gauges (item ) have een used in dierent locations. One dierential pressure gauge (item 8) is used to measure the rerigerant side pressure drop in the gas cooler. CO cylinder (item 1) is used or external charging o CO. A W-end is provided eore compressor to provide superheating o CO vapour, i required. A temperature-controlled ath is used in hich W-end is immersed. But this as never used, ecause the outlet o evaporator as already suiciently superheated at operating conditions. Hoever, this provision or heating the rerigerant could e requisitioned during cooler ater inlet amient temperatures in inter. A separate air-cooled condensing unit is used to supply ater at required temperature and lo rate to the gas cooler. For ater inlet to evaporator at required lo rate and temperature, a separate heating unit as used (not shon in igure). Thermocouples ere itted in dierent sections to measure various temperatures; the sensors ere susequently connected to the data acquisition system (DAS), hich is interaced ith a computer as shon in Figure 4. A Dorin CO compressor (model TCS11) as chosen or the experimental investigation. On the asis o minimum and maximum pressure ratios o 80/0 and /6 (ar/ar), respectively, a Sagelok integral onnet needle valve (model SS-1RS4) as used as the expansion device. The separator and receiver ere designed or a total volumetric capacity o 8 L and L, respectively. A condensing unit including a an and a storage tank as employed or a heat transer rate o 6 kw to cool the arm ater to its initial temperature at the inlet to the gas cooler. A ater ath ith heater and pump as incorporated in the evaporator to supply 4

5 ater at constant temperature and lo rate, so that a cooling capacity o. kw can e otained. The evaporator and the gas cooler are counter-lo tue-intue heat exchangers, here CO los in the inner tue and ater in the outer annulus. Once aricated, oth the heat exchangers ere tested up to ar pressure or leak detection and pressure sustainaility. Figure 6. Insulated gas cooler Figure. Prototype o transcritical CO heat pump Figure 4. Experimental setup ith ull instrumentation Figure. Design layout gas cooler Due to single-phase lo in the gas cooler, pressure drop is very lo compared to that o evaporator or the same conditions and the same diameter (as discussed in chapter ). For 1/4 inch OD, the maximum pressure drop is around 1 ar accompanied y excellent heat transer rate as is evident rom the simulation. Hence or the present system design condition, 1/4 inch (6. mm) OD as chosen or the gas cooler. The tue thickness as taken as 0.8 mm (leading to 4.7 mm ID), hich is suicient to ithstand the expected rerigerant pressure in the gas cooler. For the ater side (tue annulus), standard stainless tue o 1 mm OD ith 1 mm thickness ( mm ID) as taken. Mass lo rate o ater as in the range o 1.-. L/min or design conditions. The crosssectional area ratio o ater to rerigerant as.64. Total designed heat transer length or the gas cooler as taken as 14 m. Figure shos the layout o tue-intue counter-lo gas cooler, hich as designed or the experiment. Rerigerant los through inner tue hereas the ater los through the annulus. For the sake o simplicity o arication, only to ros ere considered. Gas cooler contains 14 parallel segments in to ros, each 1 m long, here the rerigerant tues are connected y 180 o circular ends having the same diameter and the ater tues are connected y 90 o straight tues o 9. mm OD. Suicient gap eteen the to parallel segments as maintained in arication or proper insulation and handling. The gas cooler arication closely olloed that o the evaporator and similar practices ere implemented in oth the arication processes. Ater the arication, the gas cooler as tested up to a pressure o ar or leak detection and pressure sustainaility. The aricated gas cooler, as shon in Figure 6, has an eective total heat transer length o aout 1.6 m. The gas cooler as properly insulated y glassire insulation to reduce the heat transer ith the amient. The thermocouples ere connected to each segment or detailed study o heat transer through the gas cooler.

6 Ater leak testing o the individual components, they ere assemled ith suitale instruments. The assemled system as again tested or leaks under high pressure. All the measuring devices ere calirated as per standard procedure (or example, thermocouple y thermostatic ath). Then the system as purged and then charged ith CO. Beore sitching on the compressor, condensing unit or the gas cooler and heating unit or the evaporator ere started to stailize the temperature in the system and total rerigerant charge present in the system as estimated. Ater recording initial reading and starting the data scan o the DAS, the compressor as sitched on. Control o discharge pressure as achieved y simultaneous control o the total mass o CO in the system and degree o opening o the expansion device. The total rerigerant mass in the system as controlled y adding CO rom a high pressure cylinder or y venting it through the saety valve. The operating parameters ere varied independently olloing a test matrix. Temperatures ere monitored at all required locations. The principal system perormance parameters under steady state, namely, poer input to the compressor, rerigeration capacity and cooling output in evaporator, heat rejection rate o rerigerant and heating output in gas cooler, cycle COP and actual COP have een computed rom the measured data. Detailed calculation procedures and experimental uncertainty analyses have een reported elsehere [1]. Repeataility tests or to sets o operating parameters shoed that most o the data points or cooling COPs are ithin the uncertainty ranges ( ± 6% ) o the test loop measurements in oth cases. The Sagelok dierential pressure gauge has een used or measurement o the pressure drop in the gas cooler, hich has the range o 0-4 ar ith the accuracy o ±1.%. The pressure drop has een calculated or the dierent operating conditions.. Results and discussions Only Petrov-Popov equation has een developed ased on the numerical analysis o supercritical CO cooling and this equation has een validated ith the experimental data. Although compressiility aect part is neglected due to use o mini-tue as it is important or micro-tue. Using the operating condition recorded in the experiment, the pressure drop has een calculated using the numerical model presented aove y using Equations (1) & (7). Figure 7 shos the measured and predicted trend o pressure drop using the correlation used or simulation or dierent pressure and mass lo rates o CO. Pressure drop due to tue ending has also een considered or estimating the predicted data. Comparison shos that the measured values are higher (up to % deviation) than predicted values. One reason may e due to tue roughness, hich as neglected or pressure drop estimation or the predicted data. Use o Churchill equation instead o Filonenko equation gives less deviation. Measured pressure drop (ar) (90, (11, (, (0, 0.4 (Pressure in 0. (8, ar, mass lo rate in Predicted pressure drop (ar) Figure 7. Predicted versus measured pressure drop o CO in gas cooler. Other experimental validations Based on the experimental data, Yoon et al. [8] recommended Blasius correlation (Equation ) or the prediction o pressure drop in the supercritical region o caron dioxide. Previous experimental results y Dang et al. [9] shoed that Filonenko s equation (Equation 4) gives reasonale prediction under small diameter tue conditions. Son et al. [] conducted test or horizontal tue and compared the experimental data ith the prediction y Blasius and Petrov Popov [4] correlations. The correlation, hich is proposed y Blasius agreed quite ell ith the experimental data. The mean deviation o the measured and predicted pressure drop is 4.6%, hereas or Petrov Popov mean deviation is 64% Thereore, they recommended Blasius s correlation or the prediction o pressure drop during gas cooling process o CO in the supercritical region. 4. Conclusion Detailed comparison o riction actor correlations to calculate the pressure drop or supercritical caron dioxide cooling in mini and micro tues has een done y estalishing a simulation code or counter-lo, tue-in-tue gas cooler. A test acility has een developed to investigate the supercritical caron dioxide cooling in tues ith ater as coolant and the pressure drop correlation has een validated ith the experimental data generated. Comparison clearly shos that Blasius equation can e valid or Re < 1. and Filonenko equation can e used or Re > 8 and Petrov-Popov correlation or riction actor overpredicts y aout 7.% than the constant property ased Filonenko s equation. The variation o riction actor along the tue is not signiicant. The asolute value o inertia drag, hich is negative in cooling conditions, is commensurate ith the riction drag. Hence the gas cooler pressure drop is less compared ith the evaporator pressure drop. Experimental results 6

7 sho that the percentage o pressure drop in the gas cooler tue is very less compared to other rerigerant. This results lead to design possiilities o eective gas cooler. Experimental validation o Petrov-Popov correlation implies that the measured values are higher (up to % deviation) than predicted values. This deviation can e reduced y using Churchill equation instead o Filonenko equation. Acknoledgement The inancial support extended to Ministry o Human Resource and development, India is grateully acknoledged. Reerence 1. M.H. Kim, J. Pettersen, and C.W. Bullard, Fundamental process and system design issues in CO vapor compression systems, Prog Energy Com Sc, 0(), , S.S. Pitla, D.M. Roinson, E.A. Groll, and S. Ramadhyani, Heat transer rom supercritical caron dioxide in tue lo: a critical revie, HVAC & R Research, 4(), 81, X. Fang, C.W. Bullard, and P.S. Hrnjak, Heat Transer and Pressure drop o gas coolers, ASHRAE Transactions, -66, F.P. Incropera, and D.P. DeWitt, Introduction to heat transer, rd Ed. John Wiley & Sons, Ne York, S.W Churchill, Friction actor equation spans all luid regimes. Chemical Engg 7, 91-9, N.E. Petrov, and V.N. Popov, Heat transer and resistance o caron dioxide eing cooled in supercritical region. Thermal Engg (), 11-14, N.E. Petrov, and V.N. Popov, Heat transer and hydraulic resistance ith turulence lo in a tue in a tue o ater under supercritical parameters o state. Thermal Engg (), 77-80, S.H. Yoon, J.H. Kim, Y.W. Hang, M.S. Kim, K. Min, and Y. Kim, Heat transer and pressure drop characteristics during the in-tue cooling process o caron dioxide in the supercritical region, Int J Rerigeration, 6(8), , C Dang, and E. Hihara, In-tue cooling heat transer o supercritical caron dioxide. Part 1. Experimental measurement, Int J Rerigeration, 7(7), , C.H. Son, and S.J. Park, An experimental study on heat transer and pressure drop characteristics o caron dioxide during gas cooling process in a horizontal tue, Int J Rerigeration 9(4), 9 46, R. Span, and W. Wagner, A ne equations o state or Caron dioxide covering the luid region rom triple point temperature to 10 K at pressure up to 800 MPa, J. Phys. Chem. Re. Data, 9-196, V. Vesovic, W.A. Wakeham, G.A. Olchoy, J.V. Sengers, J.T.R. Watson, and J. Millat, The transport properties o caron dioxide, J. Phys. Chem. Re. Data, 19, , A. Fenghour, W.A. Wakeham, and V. Vesovic, The viscosity o caron dioxide, J. Phys. Chem. Re. Data, 7, 1-44, S.S. Pitla, E.A. Groll, and S. Ramadhyani, Ne correlation to predict the heat transer coeicient during in-tue cooling o turulent supercritical CO ; Int J Rerigeration, (7), , J. Sarkar, Transcritical caron dioxide heat pumps or simultaneous cooling and heating, Ph.D. Thesis, IIT Kharagpur, India,