Alan Kruizenga
Mark Anderson
University of Wisconsin,
商务车英文
Madison,WI53711
Roma Fatima
Texas A&M University, College Station,TX77843 Michael Corradini
Aaron Towne
University of Wisconsin,
Madison,WI53711 Devesh Ranjan
Texas A&M University, College Station,TX77843Heat Transfer of Supercritical Carbon Dioxide in Printed Circuit Heat Exchanger Geometries
The increasing importance of improving efficiency and reducing capital costs has led to significant work studying advanced Brayton cycles for high temperature energy conver-sion.Using compact,highly efficient,diffusion-bonded heat exchangers for the recupera-tors has been a noteworthy improvement in the design of advanced carbon dioxide Brayton cycles.The heat exchangers will operate near the pudocritical point of car-bon dioxide,making u of the drastic variation of the thermophysical properties.This paper focus on the experimental measurements of heat transfer under cooling condi-tions,as well as pressure drop characteristics within a prototypic printed circuit heat exchanger.Studies utilize type-316stainless steel,nine channel,mi-circular test c-tion,and supercritical carbon dioxide rves as the workingfluid throughout all experi-ments.The test ction channels have a hydraulic diameter of1.16mm and a length of 0.5m.The mini-channels are fabricated using current chemical etching technology,emu-lating techniques ud in current diffusion-bonded printed circuit heat exchanger manu-facturing.Local heat transfer values were determined using measured wall temperatures and heatfluxes over a large t of experimental parameters that varied system pressure, inlet temperature,and massflux.Experimentally determined heat transfer coefficients and pressure drop data are compared to correlations and earlier data available in litera-ture.Modeling predictions using the computationalfluid dynamics(CFD)package FLUENT are included to supplement experimental data.All nine channels were modeled using know
n inlet conditions and measured wall temperatures as boundary conditions.The CFD results show excellent agreement in total heat removal for the near pudocritical region,as well as regions where carbon dioxide is a high or low densityfluid.
[DOI:10.1115/1.4004252]
Introduction
Minimizing capital costs and increasing plant operation allows power to become more affordable.As traditional energy sources in the United States,such as coal,natural gas,and petroleum,con-tinue to ri in price and become scarce,it is clear that we must employ alternative sources of energy to ensure affordable eco-nomic growth in the future.Solar,wind,and nuclear are among the leading alternative energy sources.
The Department of Energy’s program for next generation nu-clear reactors establishes and defines broad goals to help increa nuclear’s role in national and global production of energy[1]. Several of the designs employ a liquid metal or molten salt as the moderator and primary coolant and,therefore,necessitate a condary power conversion cycle.
The supercritical carbon dioxide(S-CO2)Brayton cycle is one of the recommended power cycles for u with the potential reactors.This Brayton cycle us CO2in a supercritical state,at pressures above thefluid’s critical pressure.As single pha is maintained throughout the cycle,it significantly contributes to simplified plant design.In addition,one can take advantage of the high power densities inherent with supercritical power conversion cycles.Highly efficient power conversion(>40%)at moderate temperatures provides additional incentive for cloly investigat-ing the cycles.
Many of the cycle designs u a recuperator and a heat exchanger to pre-cool the S-CO2directly before the compressor. As the S-CO2decreas in temperature at a given pressure;the thermophysical properties transition sharply at a specific tempera-ture termed the pudocritical temperature(T pc).The pudocriti-cal temperature is so named,becau it mimics the critical temperature,and exhibits a maximum in specific heat as illus-trated in Figure1.
Heat transfer augmentation and deterioration occur under cer-tain conditions in this region of drastic property variations for the heating mode[2].While much work investigating heat transfer in heating modes for supercriticalfluids has been done,compara-tively less work exists in the cooling mode;only a few experi-ments to date exist using pure CO2[3–9].Many existing heat transfer correlations tend to capture qualitative effects,but quanti-tatively disagree with each other,especially in the near critical
region[10].This work strives to supplement current heat transfer and pressure drop databas,evaluate heat transfer and pressure drop correlations,benchmark current models,and explore proto-typic heat exchanger designs.
Experimental Facilities
Figure2shows a schematic reprentation of the experimental apparatus ud during the heat transfer and pressure drop investi-gations.The heat transfer facility consists of two loops:one loop for the recirculation of CO2and another for the heat exchanger test ction.The CO2loop contains veral critical components: the main pump forfluidflow,the inverter for pump control,and the HPLC pump ud to control system pressure.
The main pump is a ChemPump(Model GCT-1.5K-20S),capa-ble offlow rates up to14m3/h,dynamic head up to15m,and sys-tem pressures up to20MPa.The pump is ud in conjunction with a throttle valve to generateflow to the test ction.Once the
Contributed by the Heat Transfer Division of ASME for publication in the J OUR-
NAL OF T HERMAL S CIENCE AND E NGINEERING A PPLICATIONS.Manuscript received May
11,2010;final manuscript received May17,2011;published online August10,
2011.Assoc.Editor:Bengt Sunden.
Journal of Thermal Science and Engineering Applications SEPTEMBER2011,Vol.3/031002-1
Copyright V C2011by ASME
throttle valve is t,the pump speed is varied to maintain a con-stant flow to the test ction.
The pump speed is controlled with a Danfoss adjustable fre-quency inverter.The frequency inverter is controlled by a propor-tional-integral-derivative (PID)control scheme implemented in
LABVIEW TM
8.5[11].This allows for the preci control of mass flow rates,þ/À0.1kg/h,during experiments.Loop conditions are monitored to provide feedback necessary for system stability.
Monitoring takes place using thermocouples and a pressure transducer.One K-type thermocouple monitors loop temperature (calibrated within 0.5 C from 5to 75 C).The absolute pressure of the recirc
ulation loop is monitored with a Siemens pressure transducer (Model 7MF4432-1GA10-1NC1-Z),and is recorded during experiments.The pressure transducer has operating limits of 0–40MPa,with an accuracy of better than 0.1%.The pressure and temperature are monitored and controlled to ensure that the fluid density remains high enough to achieve the desired flow rates.
The system pressure is adjusted and controlled with a S-CO 2pump capable of pumping CO 2at pressures up to 60MPa.A port-able cooling bath,using water as the working fluid,is ud to remove excess heat generated during experiments in the heat exchanger test loop.
The heat exchanger test loop consists of a Coriolis flow meter,heater,and test ction.The flow rate is measured accurately with the Coriolis flow meter (Siemens Model 7ME4100-1DM11-1DA1),which has a maximum error of 0.3%for low flow conditions with typical errors of 0.1%of the measured value.The flow meter is placed before the heater to ensure cool CO 2flows through it.
The test ction consists of veral pieces:the heat exchanger plate,the mating plate,and the cooling blocks.The heat exchanger plate is designed to be interchangeable with other pro-totypic designs,with flow paths fabricated by chemically etching into type 316stainless steel.On each end of the plate,there are entrance and exit manifolds,with a distance from manifold to manifold of 500mm.
The channel configuration ud in this study consists of nine mi-circular,parallel channels of 1.9mm diame-ter.The heat exchanger plate is bolted to its mating plate to com-plete the prototypic heat exchanger (Fig.3).
The mating plate consists of a flat plate with an O-ring groove machined into the surface,along with three holes at each end;two for thermocouples and one for a pressure tap.The O-ring is made from 1/16”Viton cord stock,cut to length,and glued together with Cyanoacrylate Adhesives to form the al.In addition to the bolt holes in the mating plate and heat exchanger plate,a t of ten thermocouples are implanted into each plate.
Thermocouples measure the axial variation in wall temperature.Holes needed for the thermocouples,as shown in Fig.4,have a large L/D ratio ($33),so electrical discharge machining was nec-essary.Each hole is 1mm in diameter and 33mm deep,spaced axially by 50mm.Thermocouples are thermally coupled to the wall using 63/37tin/lead solder as gap filler,due to 63/37’s excel-lent thermal conductivity (40.9W/m-K)and low melting point (183 C).
Attached to the top of the mating plate and bottom heat exchanger plate are ten individual aluminum water blocks ud to provide cooling,while also measuring local heat removal by per-forming an energy balance on each cooling block (Fig.5).
The
Fig.2Schematic of experimental facility at the University of
Wisconsin
images什么意思Fig.3Top and bottom of heat transfer test
ction
Fig.1Thermophysical property variations for CO 2with both pressure and temperature.Maximum in specific heat reprents pudocritical temperature (T pc ).The critical pressure for car-bon dioxide is 7.377MPa.
031002-2/Vol.3,SEPTEMBER 2011
Transactions of the ASME
inlet and outlet temperatures,and the volumetric flow rate of water for each cooling block are measured.Using the quantities,the local heat flux is calculated.
Data Reduction
One of the primary goals of this work is to obtain local heat transfer coefficients (HTCs)along the axial position of the test ction.Prior to data reduction,it is necessary to ensure experi-ments are performed at steady state.
Experiments were found to be in steady state once the energy balance between the heat removed fr
om the CO 2was within 10%of the heat added to the cooling water.Heat for each fluid is calcu-lated by the following equations:
Q CO 2¼_m ði in Ài out Þ(1)Q H 2O ¼
X 20i ¼1
_v
i q i C p Ài T 1Ài ÀT 2Ài ðÞ(2)
where _m
is the mass flow rate of CO 2and i is the inlet and outlet enthalpy,determined from the measured temperature and pres-sure._v
i is the volumetric flow rate of the cooling water,q i is the density,C p Ài the specific heat of water,and T is the inlet or outlet temperature of the water,where properties are determined by measured temperatures.
The local HTCs were obtained using values measured in each subction,as illustrated in Fig.6.Within each of the ten subctions,the local wall temperature and power removal are
彩虹的拼音measured.An energy balance is employed to find the outlet enthalpy,清华大学 在职研究生
i CO2½j þ1 ¼i CO2½j À
Q j _m
(3)
Using this balance,the temperature at j þ1is calculated and,there-fore,the local bulk temperature is known for each subction.The local wall temperature in contact with the fluid is calculated as expresd in the following:
T w j ½ ¼0:5T top ½j þ
q top ½j z kA þT bottom ½j þq bottom ½j
kA z
nominal(4)where q is the power removal on the top or bottom cooling blocks
(as indicated),k is the thermal conductivity of the stainless steel,A is the perpendicular area available for heat transfer,z is the dis-tance between the thermocouple and the fluid,and T is the top or bottom temperature measured in the stainless wall.
The local HTC is then calculated,with the appropriate quanti-ties known,by
h ½j ¼
q top ½j þq btm ½j A tube T b ½j ÀT w ðÞ½j
(5)
where A tube is the area of the nine parallel channels over one sub-ction,which is 50mm in length.All the HTC data shown will
be derived from this analysis for local values.
日语谐音Results
All experiments were performed at steady state conditions,
which were found to be conditions when the heat balance between water and CO 2was less than 10%,and after all temperatures (wall and fluid)were unchanging after 10min.Data was taken at a rate of one point per cond for 8min.Then,all recorded values were averaged.
Heat Transfer
Several experiments were performed examining the effect of the bulk temperature on heat transfer.As shown in Fig.8,
which
Fig.4Mixing manifold on test ction.Also shown is the wall
thermocouple implanted into the stainless
steel.
Fig.5Test ction asmbled with water cooling
block
Fig.6One of the ten subctions for the test ction
Journal of Thermal Science and Engineering Applications SEPTEMBER 2011,Vol.3/031002-3
has constant inlet pressure and massflow rate,inlet temperature significantly changes the heat transfer profile.Many previous S-CO2cooling mode studies failed to show bulk temperature and wall temperature[10],so this was an important consideration for this work.Literature shows that as the bulk temperature approaches T pc the heat transfer increas rapidly[10].This occurs due to the increasing specific heat of thefluid(Fig.11). However,the peak in the heat transfer appears to occur sli
ghtly before the bulk temperature reaches T pc(Fig.9),which may indi-cate the importance of using afilm temperature to predict the heat transfer.However,when considering error in the bulk temperature measurement,it is difficult to establish what the properfilm tem-perature weighting should be between the wall and the bulk. Previous investigations indicated that decreasing pressure, while remaining above the critical pressure,also increas the heat transfer[10].This was found to occur,as reprented in Fig.10,which shows the heat transfer to increa with decreasing pressure,likely due to the increasing Prandtl number,as shown in Fig.11.The Reynolds number is nearly equivalent over the nor-malized temperature span for the7.5and8.1MPa cas,which leaves the large variation in the Prandtl number driving the heat transfer coefficient peaks in the HTC.It should be noted that due to entrance and exit effects,resulting in heat transfer augmenta-tion,thefirst and last axial locations were not plotted.
There has been some question as to what the most appropriate heat transfer correlation is for cooling.While many have been suggested,it is of interest to compare various correlations[10]. Established single pha correlations are suggested for super-criticalfluids when temperature gradients are low within theflow [2].One of the most widely ud single pha correlation is Gnie-linski’s[12]given by
Nu b¼
ðf=8ÞRe bÀ1000
ðÞPr b
1þ12:7
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðf=8ÞðPr2=3bÀ1Þ
q
2
64
3
75(6)
石家庄英语口语
where Re is the Reynolds number and Pr is the Prandtl number,both evaluated at bulk conditions,and f is the friction factor given by
f¼
1
0:79lnðReÞÀ1:64
ðÞ2
(7)
Fig.8Bulk and wall temperatures(top)for experiments with a massflux of762kg/m2s and
system pressure of7.5MPa.The bottom plot shows how the heat transfer coefficient
changes as a function of length and inlet condition.Heatflux listed is the average heatflux
over the test
length.
Fig.7Diagram of water cooling block.Each cooling block
(20in total)is bolted to the heat exchanger.Thermocouples to
measure water temperature are placed at the inlet and
outlet.Fig.9Heat transfer coefficient as a function of bulk
temperature
031002-4/Vol.3,SEPTEMBER2011Transactions of the ASME
Through the Nuslt number the HTC can be calculated,rechina
Nu b ¼
h d hyd b
(8)
where d hyd is the hydraulic diameter and k b is the thermal conduc-tivity of CO 2.Another widely accepted single pha correlation is
the Dittus Boelter correlation [13],evaluated at the film tempera-ture,which is defined below,
Nu f ¼0:023Re 0:8f Pr 0:3
f
(9)T f ¼
T b þT w
2
(10)
A well known correlation ud in supercritical fluids for the heat-ing mode is the Jackson correlation [2],which corrects for the dif-ferences in temperature in the flow with variables evaluated at wall conditions,
Nu b ¼0:0183Re 0:82b Pr 0:5
b
q w
q b
0:3 C p C p ;b
n
eal(11)
where n is bad on
n ¼0:4for T b <T w <T pc or 1:2T pc <T b <T w ;
n ¼0:4þ0:2T w
T pc À1 for T b <T pc T w ;
n ¼0:4þ0:2T w T pc À1 1À5T b
T pc
À1 for T pc <T b <1:2T pc and T b <T w ;
The average specific heat is bad on the enthalpy and tempera-ture differences,
C
p ¼i w Ài b T w ÀT b
(12)
There has been a recent correlation developed to predict in-tube cooling,where the Nuslt number is calculated at the wall and at bulk conditions using the Gnielinski correlation [14
],
Fig.12Comparison of calculated Nuslt numbers to experi-mentally determined Nuslt numbers for veral established correlations.Percentages indicate difference from a y 5x of再见了母校
1.
Fig.13Distribution of pressure loss between the local,acceleration,and frictional
effects
Fig.11Reynolds and Prandtl numbers evaluated under bulk conditions for low mass flux tests.Differences in HTC are due to changes in the Prandtl
number.
Fig.10Decreasing pressure results in significant increas in
HTC
Journal of Thermal Science and Engineering Applications SEPTEMBER 2011,Vol.3/031002-5
