Exchangers”, Journal Of Heat Transfer, 136, 081703 (May
Y. Ito, N. Inokura, T. Nagasaki, “Conjugate Heat Transfer in Air-to-Refrigerant Airfoil HeatExchangers”, Journal of Heat Transfer, 136, 081703 (May 2014)(The American Society ofMechanical Engineers: ASME)
Yu ItoTokyo Institute of Technology,4259-G3-33-402, Nagatsuta-cho,Midori-ku, Yokohama,Kanagawa 226-8502, Japane-mail: itoyu110@00.alumni.u-tokyo.ac.jpNaoya InokuraTokyo Institute of Technology,4259-G3-33-402, Nagatsuta-cho,Midori-ku, Yokohama,Kanagawa 226-8502, JapanTakao NagasakiTokyo Institute of Technology,4259-G3-33-402, Nagatsuta-cho,Midori-ku, Yokohama,Kanagawa 226-8502, Japane-mail: tnagasak@es.titech.ac.jpConjugate Heat Transferin Air-to-Refrigerant AirfoilHeat ExchangersA light and compact heat exchange system was realized using two air-to-refrigerant airfoil heat exchangers and a recirculated heat transport refrigerant. Its heat transfer performance was experimentally investigated. Carbon dioxide or water was used as arefrigerant up to a pressure of 30 MPa. Heat transfer coefficients on the outer air-contactand inner refrigerant-contact surfaces were calculated using an inverse heat transfermethod. Correlations were developed for the Nusselt numbers of carbon dioxide andwater on the inner refrigerant-contact surface. Furthermore, we proposed a method toevaluate a correction factor corresponding to the thermal resistance of the airfoil heatexchanger. [DOI: 10.1115/1.4027554]Keywords: Nusselt number, supercritical carbon dioxide, gas turbine, airfoil heatexchanger, intercooler, recuperatorIntroductionIntercooled, recuperated aviation gas turbines (IR gas turbines)have the strong potential to reduce fuel consumption in aviation.Intercoolers and recuperators enhance the gas turbine cycle efficiency from a thermodynamic point of view. Wilfert et al. constructed an IR gas turbine components demonstrator that had thepotential to achieve a 17% reduction in fuel consumption compared with a baseline gas turbine. However, they noted that adapting recuperators, in particular, for a practical aviation gas turbineremained a future challenge [1]. Conventional IR gas turbines aretoo heavy for use as aviation gas turbines because they use a typeof tube matrix air-to-air heat exchanger [2] or a type of primarysurface air-to-air heat exchanger [3]. Although both types havehigh temperature effectiveness, they are heavy. Furthermore, hotand cold air must be collected at the heat exchanger. Therefore,long and heavy air connecting ducts are required.To overcome these problems, a heat exchange system using aheat transport liquid or supercritical refrigerant (abbreviated inthis paper to “refrigerant”) may be used, as shown in Fig. 1. Inthis system, the refrigerant transports heat from the hot section tothe cold section. Therefore, the hot and cold sections can be installed at separate sites. In the intercooling system, heat exchangerA works as an air cooler, and heat exchanger B works as a radiator. Conversely, in the recuperating system, heat exchanger Aworks as a heat absorber, and heat exchanger B works as an airheater. In addition, heat transport liquid and supercritical refrigerants have higher densities and greater specific heat values than air.Therefore, the refrigerant connecting tubes require a much smallerdiameter than air connecting ducts. Although an additional recirculation pump is needed, it must only drive the refrigerant againstthe pressure loss of the refrigerant loop. Ito proposed an IR aviation gas turbine that uses this heat exchange system in the form ofheat exchangers installed in already equipped components in abaseline aviation gas turbine, to reduce its weight [4]. In the intercooling system of this design, fixed stators and vanes in the compressor are used as the air cooler, and vanes in the bypass duct areused as the radiator. In the recuperating system, vanes in the combustor are used as the air heater, and vanes in the core nozzle areused as the heat absorber. Here, the working airflow path canremain in the same position as a baseline aviation gas turbine.Therefore, there is no additional pressure loss in the working airflow. Because vanes are used as heat exchangers, this type of heatexchanger is hereafter referred to as an “airfoil heat exchanger.”An airfoil heat exchanger is physically similar to the vanes of conventional air-cooled high-pressure turbines (HPTs) [5]. Thesewere in use prior to those of the current air-film-cooled HPTs,although the HPT vanes are not heat exchangers. In this paper, theheat transfer performance of an airfoil heat exchanger will be discussed compared with that of air-cooled HPT vanes.However, it is difficult to evaluate the heat transfer performanceof real heat exchanger components. Bejan developed the constructal theory of design for cooling fins [6], and Lorenzini and his colleague energetically applied this theory to optimize Y-shaped andI-shaped fins [7]. In addition, they conducted computer fluid dynamics calculations of the heat transfer for arrays of Y-shaped, Ishaped, and T-shaped fins, and optimized the results [8]. Moreover, the optimized results were compared with the constructaltheory’s results [9,10]. Similarly, modern compressor stators andguide vanes are three-dimensional airfoils optimized by computerfluid dynamics; however, a three-dimensional airfoil is too complex to use in experiments. Therefore, we chose a twodimensional NACA65-(12A2I8b)10 airfoil. An NACA65 seriesairfoil is a traditional two-dimensional airfoil for a compressorstator. The estimated heat transfer rates are more suitable thanthose of a simpler plane for realizing the airfoil heat exchanger.We prepared a cascade of three NACA65-(12A2I8b)10 airfoils,each of which had five inner refrigerant channels, as shown in Fig.2, as a test model of the airfoil heat exchanger. This cascade wasinstalled in a subsonic wind tunnel at Mach 0.55–0.62. On the airfoil surfaces, as described by Nishiyama [11], a developingboundary layer changes from a laminar boundary layer to a turbulent boundary layer across the minimum pressure point XSmax, i.e.,the maximum point of pressure coefficient S. This is because theboundary layer is stable in regions with favorable pressure gradients but unstable in those with adverse pressure gradients.To obtain the heat transfer coefficients on the outer and innersurfaces, Turner employed a heat conduction numerical analysisusing 31 discrete surface temperatures measured in experiments[12]. In contrast, we used an inverse heat transfer method. It wasconducted under conditions that included the pressure distributionaround an airfoil already reported by Dunavant et al. [13] and ourexperimentally measured temperatures at four points. This waseasier than Turner’s method because it is difficult to accurately
Fig. 1 Heat exchange system in which refrigerant transportsheat from hot section to cold sectionmeasure surface temperatures without disturbing a fast airflow.Furthermore, Turner used air as the inner cooling fluid, whereaswe used a refrigerant. Lorenzini and Moretti pointed out that a liquid always performs better than air if the focus is exclusively onheat removal maximization [14]. Their figure seemed that therewas a greater change in the temperature distribution in the finswhen using a liquid than when using air. This difference mayaffect the heat transfer performance of an airfoil heat exchanger.An additional contribution of our study involves the use of eithersupercritical carbon dioxide or compressed water as the inner cooling fluid for an airfoil heat exchanger, rather than the use of air.Liao and Zhao experimentally investigated the heat transfer coefficient of supercritical carbon dioxide in the range of 7.4–12 MPa[15]. Our study extended Liao and Zhao’s pressure range up to30 MPa for carbon dioxide, and we also considered compressed(but not supercritical) water at pressures up to 30 MPa.It is expected that this will help to clarify a more suitablemethod for estimating the heat transfer coefficients when designing airfoil heat exchangers.Experimental SetupTo experimentally estimate the heat transfer performance in ahigh-speed compressible flow, the Reynolds, Mach, and Prandtlnumbers should match those of the real gas and refrigerant flows.If scale-model experiments are conducted, all of the viscosity,thermal conductivity, specific heat, and sound speed ratios of thetested fluids should be the same as those of the real gas and refrigerant. However, rather than using such fluids in scale-modelexperiments, it is easier to prepare a real gas, real refrigerant, andreal-size airfoil heat exchanger under real conditions.Wind Tunnel. A closed-return wind tunnel at the Tokyo Institute of Technology was employed to produce a subsonic airflow. ABE-H125 Roots blower (made by ANLET Co. Ltd.) was used asthe continuous air source. The nozzle outlet size was 60 30 mm.Its Mach number capabilities ranged from 0 to 0.8, and Mach numbers of 0.55–0.62 were chosen for testing the airfoil heat exchangerin an aviation gas turbine. The inlet airflow was sufficiently turbulent because the inlet Reynolds number Reair,nozzle, whose representative length was the hydraulic diameter of the nozzle outlet,ranged from 3.92 105 to 4.52 105. In addition, the roots blowergenerated a turbulent airflow. Although this airflow conditioninvolved no wakes from the preceding airfoils, unlike in a practicalaxial gas turbine, it was sufficient for the time-averaged airflowcondition to be applied to the design of airfoil heat exchangers.Airfoil Heat Exchangers. NACA 65-(12A2I8b)10 airfoils withinner refrigerant channels were employed as test models, asshown in Fig. 2. The airfoils were made of SUS304 because itsthermal conductivity is 16 W/K m, which is almost the same asthe thermal conductivity of the materials used for practical compressors or vanes; for example, approximately 20 W/K m forFig. 2 NACA65-(12A2I8b)10 airfoil heat exchanger as testmodeltitanium alloy and 11–21 W/K m for nickel-based heat-resistantalloy. The chord length was 44 mm, and the width was 28 mm.These are average sizes for the stators or vanes in the compressorsection of middle or large class aviation gas turbines.Four type-K thermocouples with a diameter of 0.5 mm were installed in four taps with a 0.7 mm inner diameter and used to measure the temperature distribution of each airfoil heat exchanger.All were located at midspan. As seen in Fig. 2, the airfoil wasdeployed at an incidence n ¼ 0 (i.e., a flow direction angle fromthe airfoil camber line at its leading edge, corresponding to anangle-of-attack a ¼ 9.47 deg, i.e., an inlet flow direction anglefrom the airfoil chord). x and y axes were defined in the horizontaland vertical directions. Thermocouples Ti and Tii were located onthe camber line at x ¼ 3 and 41 mm, respectively. ThermocouplesTiii and Tiv were located 1.2 mm below and above the camber lineat x ¼ 22 mm, respectively. Here, to enhance the temperature measurement accuracy and detect temperature differences smallerthan 1 K among Ti–Tiv, the potential differences between themwere measured directly. This measurement method enhances theaccuracy when detecting small temperature differences. To calibrate all thermocouples, considering the digital voltage metererror, all of the thermocouples’ tips were placed in ice water at aconstant temperature of 273.15 K. We developed data acquisitionPC software to cancel out temperature drifts from 273.15 K.Therefore, an accuracy of 60.025 K was achieved for the temperature differences among all of the thermocouples.Test Section Configurations for Cascade of Airfoil HeatExchangers. Figure 3 shows the configurations of a cascade ofthree NACA65-(12A2I8b)10 airfoil heat exchangers. Three airfoilswere deployed at the same positions as some of those tested byFig. 3 Configurations of tested cascade of NACA65-(12A2I8b)10airfoils
Dunavant et al. [13]. The aerodynamic features of cascades ofNACA65-(12A2I8b)10 airfoils were previously investigated indetail by Erwin et al. [16] and Dunavant et al. [13]. In our study,the solidity r ¼ LC/LG was set at 1.5, where LC and LG are the airfoil chord and tangential spacing between the airfoils’ leadingedges, respectively. In addition, the flow direction angle from perpendicular to airfoil row b was varied from 45 deg to 70.5 deg,depending on a in the range of 0 deg–25.5 deg. To remove theboundary layer from the inlet flow, two inlet guide vanes wereused (with the distance between them being 58 mm or less), whichcould be moved to fit into the cascade position. Likewise, two slits(the distance between slits was 28 mm) mounted on the side wallswere used. The whole test section was deployed in a sufficientlylarge box with a width of 830 mm, depth of 825 mm, and height of1400 mm. This was to allow the outlet air from the cascade toleave in the appropriate direction, depending on the flow turningangle h.Recirculation System With Carbon Dioxide or Water as Refrigerant. The refrigerant flow loop is shown in Fig. 4. The recirculation pump was a magnetic-coupling-driven sealed pump head,GLHH21.PFS.E-N1CH50 (made by Micropump, Inc.), connectedto an inverter-controlled ac motor. The refrigerant cooler sectionwas submersed in a TRL-N11L cooling bath (made by ThomasKagaku Co. Ltd.). This was maintained at an arbitrary temperaturebetween 253 and 353 K ( 20 to 80 C), with an accuracy of 0.1 K.A pressure gauge, KDM30-35MPaG-E (made by Krone), was installed upstream of the airfoil heat exchangers. The refrigerantflowed inside the five serially connected stainless tubes in the airfoil heat exchanger with u-turn sections from the trailing toleading edges, as shown in Fig. 4, i.e., as a multipath heatexchanger. The five stainless tubes and airfoil heat exchangerwere bonded by DM4030LD/F890 thermally conductive adhesive(made by Diemat, Inc.) with a thermal conductivity of 15 W/K m.A structural analysis of the airfoil heat exchanger with the fivestainless tubes was conducted using ANSYS11. The maximum stresswas 32 MPa in the airfoil heat exchanger when the tubes’ innerpressure was 35 MPa. The 0.2% proof stress is 32 MPa at 1400 Kunder a strain rate of 1.0%/s for SUS304 [17]. Therefore, thestructural integrity of the airfoil heat exchanger could be maintained. Two thermocouples Tref,C and Tref,J were installedupstream and downstream of the center airfoil heat exchanger.The potential difference between Tref,C and Tref,J was also measured directly. The whole refrigerant flow loop was thermally insulated, and it could withstand a pressure of 34.4 MPa. Therefore,supercritical carbon dioxide or compressed liquid water could beused as the refrigerant. The refrigerant was pumped up into the refrigerant flow loop via an 8800 series plunger pump (made by L.TEX Corporation).Inverse Heat Transfer MethodThe experimentally obtained data alone were not sufficient toenable us to determine the air and refrigerant heat transfer coefficients hair and href. This was because the surface temperature distributions on the outer air-contact surfaces and inner refrigerantcontact surfaces should be known to accurately evaluate hair andhref. However, these were not measured. Therefore, in order tofind the best combination of hair and href, an inverse heat transfermethod and a least square method were used to explain the experimentally obtained data.Airfoil Heat Exchanger Temperature. There were only fourthermocouples in the airfoil heat exchanger, and these were notlocated on the surfaces. Therefore, the inverse heat transfer methodwas applied to estimate hair and href. Figure 5 shows the twodimensional control volumes of the airfoil heat exchanger used toperform the inverse heat transfer method by a numerical analysis ofthe heat conduction in the airfoil heat exchanger. For each controlvolume j, the finite control volume method was employed. Namely,the steady state basic equation in an integrated form isQconduction;j ¼ Qref;j þ Qair;j(1)Here, the left-hand term means the heat conduction rate of thesolid part of the airfoil heat exchanger. The right-hand termsFig. 4 Refrigerant recirculation loop (in case of carbon dioxideas refrigerant) and piping around airfoilsFig. 5 Control volumes for inverse heat transfer method basedon numerical analysis of heat conduction in airfoil heatexchanger and applied boundary conditions
indicate the heat transfer rates through the inner refrigerantcontact surfaces (along the five bigger circular regions in Fig. 5)and outer air-contact surfaces (along the peripheral region in Fig.5). As an example, we focus on control volume j whose neighborcontrol volumes are p, q, r, and s. The discretized heat conductionrate Qconduction,j isMass flow rate mref is found as follows:mref ¼uref;AB ¼ 3(2) qref;D Dref;DE 2uref;DE ;qref;A Dref;ABDPloss;AB ¼ 0:1582of course, the number of neighbor control volumes can be anynumber instead of four. For example, the heat conduction rateQconduction,j–p between control volume j and control volume p isQconduction;j p ¼ Aj p ksolidQref;j ¼ Aref;j href;j DTref;j ¼ Aref;j href;j ½Tref ðnÞ TðjÞ (4)where Aref,j is the contact surface area between control volume jand the refrigerant, href,j is the local heat transfer coefficient, andTref(n) is the refrigerant temperature of the nth section in contactwith control volume j. Here, n is any location from E to I inFig. 4. Similar procedures (5)Qair;j ¼ Aair;j hair;j DTair;j ¼ Aair;j hair;j Tair;adiabatic;j TðjÞshould be applied for control volume j in contact with air, whereTair,adiabatic,j is the adjacent local adiabatic air temperatures in contact with control volume j. It depends on the air boundary layercondition, namely, whether this is laminar or turbulent.Refrigerant Temperature. The refrigerant properties werecalculated using the procedures reported in Refs. [18,19] for carbon dioxide and [20] for water. The properties had accuracies of62% across the critical point. In the other regions, the accuracieswere better. Figure 4 shows the refrigerant tubes’ length Lref andinner diameter Dref. The refrigerant flow is usually turbulentthrough the airfoil heat exchanger in new IR aviation gas turbinesbecause a large heat flow rate per unit flow rate is preferable to asmall pressure loss. Here, as shown in Fig. 4, each position isnamed to facilitate the discussion as follows: A, inlet pressure sensor; B, cross fitting; C, inlet thermocouple; D, beginning point offlow rate meter by differential pressure; E, its ending point justupstream of the center airfoil heat exchanger; F, ending point ofthe first u-bend section; G, that of the second; H, that of the third;I, that of the fourth; and J, outlet thermocouple. Section DE wasthe flow rate meter, which was made of a smooth tube. The refrigerant pressure loss DPloss,DE was measured. The refrigerant velocity uref,DE was calculated using the Darcy–Weisbach equation andBlasius’ friction coefficient in a smooth tube for turbulent conditions as follows:"uref;DED1:25ref;DEDPloss;DE¼0:25 L0:1582q0:75lref;DEref;D ref;D1#1:75(6)0:251:75q0:75ref;A lref;A Lref;AB uref;AB(8)D1:25ref;ABIn section BC, the mass flow rate is mref , anddTsolidT ð pÞ T ð jÞ Aj p ksolid(3)dzdj pwhere ksolid is the thermal conductivity of the solid material of theairfoil heat exchanger, z is a local coordinate along the line thatgoes through the centers of control volumes j and p, dj–p is the distance between the centers of control volumes j and p, and Aj–p isthe projection area of the interfacial surface area on a plane normal to the z axis. In the case of the control volume next to a refrigerant or air boundary, the right-hand terms in Eq. (1) have values;otherwise they are 0. When control volume j contacts the refrigerant, for example, the discretized heat transfer rate is as follows:(7)However, in section AB, the mass flow rate is 3mref, andQconduction;j ¼ Qconduction;j p þ Qconduction;j q þ Qconduction;j rþ Qconduction;j spD2ref;DE qref;D uref;DE4uref;BC ¼ qref;D Dref;DE 2uref;DE ;qref;B Dref;BCDPloss;BC ¼ 0:15820:251:75q0:75ref;B lref;B Lref;BC uref;BC(9)D1:25ref;BCand similar considerations apply for sections CD, EF, FG, GH,HI, and IJ.Therefore, the total pressure at each point from A to J is asfollows:1Ptot;ref;A ¼ Pref;A þ qref;A u2ref;AB ;2Ptot;ref;B ¼ Ptot;ref;A DPloss;AB ; ; andPtot;ref;J ¼ Ptot;ref;I DPloss;IJ(10)Then, the measured Pref,A is known. Pref,B and Pref,J are found asfollows:1Pref;B ¼ Ptot;ref;B qref;B u2ref;AB ; and2(11)1Pref;J ¼ Ptot;ref;J qref;J u2ref;IJ2At point C, temperature Tref,C is measured and enthalpy Href,Cis defined as follows: Tref;C ¼ TC and Href;C ¼ Href Tref;C ; Pref;C(12)At each point from A to E, each refrigerant tube is adiabatic.Therefore, the total enthalpy Htot,ref at each point from A to E isthe same. Thus, the enthalpy Href at each point from A to E isfound as follows:Href;A þu2ref;ABu2ref;ABu2ref;BC¼ Href;B þ¼ Href;C þ222u2ref;CDu2ref;DE¼ Href;D þ¼ Href;E þ22(13)Therefore, temperature Tref at each point from A to E can be calculated by using Href and Pref.On the other hand, in each section from EF to IJ, heat inflowsfrom the airfoil heat exchangers. The steady state basic equationin an integrated form for section EF, for example, is as follows:Qconvection;EF ¼ Qref;EF(14)Based on the heat balance in section EF, the heat convectionrate Qconvection,EF is Qconvection;EF ¼ mref Htot;ref Tref ðFÞ; Pref;F ; uref;EF Htot;ref Tref;E ; Pref;E ; uref;DE(15)
and the refrigerant heat gain rate Qref,EF in section EF from theairfoil heat exchanger isEF EF Qref;EF ¼ R Qref;j ¼ R Aref;j href;j Tref;E TðjÞjj(16)where Qref,j was described in Eq. (4), and the summation of Qref,jat all of the control volumes j in contact with the refrigerant insection EF is used. Similar procedures can be applied for sectionsFG, GH, HI, and IJ.Adiabatic Air Temperature. Although the airfoil heatexchanger surfaces are rigorously nonadiabatic, the air temperature in a boundary layer of a high-speed compressible airflow on asolid surface is close to the adiabatic air temperature. Recently,Pinilla et al. investigated the effects of the adiabatic temperatureon the heat load of the blades of a gas turbine [21]. They mentioned that the adiabatic temperature plays a role in determiningthe heat flux through the air-contact surfaces.On the outer air-contact surfaces, the adjacent local static airpressure can be calculated using the adjacent local pressure coefficient Sj as follows:1Pair;j ¼ Ptot;air;in Sj qair;in u2air;in2(17)where Sj is obtained from Ref. [13] and interpolated. Note that adecrease in Sj implies an adverse pressure gradient, and vice versa.Thus, the adjacent local air Mach number and the adjacent localstatic air temperature are found as ffiffiffi( u c 1 )u 2Ptot;air;in cTtot;air;int 1 ; Tair;j ¼(18)Mair;j ¼2Pair;jc 11 þ c 12 Mair;jThe adjacent local adiabatic air temperatures Tair,adiabatic,j in theair’s laminar or turbulent boundary layer is formulated [22] as (19)Tair;adiabatic;j ¼ Tair;j þ Ttot;air;in Tair;j rjwhere rj is the adjacent local recovery coefficient. Each rj represents a laminar or turbulent boundary layer as follows:rj ¼Pr1 2Pr1 3for air laminar boundary layerfor air turbulent boundary layerHere, Tair,adiabatic,j was determined using only the airflow conditions, i.e., air Reynolds, Prandtl, and Mach numbers, and can besubstituted into Eq. (5).(20)If a pure air laminar flow enters the system, a transition to a turbulent boundary layer occurs across the maximum S pointXSmaxLC, i.e., Reair,transition XSmaxReair, in a cascade of airfoils.In the present test setup, there may be many main flow instabilities. Thus, the transition may occur slightly upstream of XSmaxLC.However, it probably occurs not far from XSmaxLC, as shown inFig. 6.Fig. 6 Schematic view of air boundary layers around airfoilheat exchangersCalculation Procedure of Inverse Heat Transfer Method.The following procedure was conducted for the assumed hair,j andhref,j to calculate the distribution of solid temperatures T(j) in theairfoil heat exchanger, as well as to calculate the refrigerant temperatures Tref(F)–Tref(J).First, we calculated the already determined values according tothe experimental conditions before using an inverse heat transfermethod. The already determined values were the distribution ofthe adiabatic air temperatures Tair,adiabatic,j around the airfoil heatexchanger, and the refrigerant temperatures Tref,A–Tref,E. The distribution of Tair,adiabatic,j around the airfoil heat exchanger wasgiven in the Adiabatic Air Temperature subsection when the airinlet conditions and cascade configuration were determined. Tref,A–Tref,E were given in the Refrigerant Temperature subsectionwhen the refrigerant inlet conditions were determined.Second, for the assumed values of hair,j and href,j, the solid temperatures T(j) and the refrigerant temperatures Tref(F)–Tref(J) werefound numerically by solving Eqs. (1) and (14). Here, Eqs. (2),(4), and (5) were substituted into Eq. (1) at all of the solid controlvolumes in the airfoil heat exchanger, and Eqs. (15) and (16) weresubstituted into Eq. (14) at all of the refrigerant sections. Thus, wecould generate simultaneous temperature equations for all the control volumes of the solid and refrigerant sections. To solve these,all of the T coefficients were arranged for control volume j asfollows:cj;j TðjÞ þ cp;j TðpÞ þ cq;j TðqÞ þ cr;j TðrÞ þ cs;j TðsÞ¼ cj;E Tref;E þ cj;n Tref ðnÞ þ cj;air Tair;adiabatic;j(21)where only Tref,E and Tair,adiabatic,j are known, and Tref(n), i.e.,Tref(F)–Tref(J), are unknown. Therefore, a large coefficient matrixfor all the airfoil temperatures for all the control volumes of thesolid and refrigerant sections was constructed. Then, this coefficient matrix was diagonalized. Finally, the distribution of the solidtemperatures T(j) in the airfoil heat exchanger and the refrigerantsections’ temperatures Tref(F)–Tref(J) were obtained for theassumed href,j and hair,j.Third, the heat removal rate from the hot air Qair,whole and theinput rate into the cold refrigerant Qref,whole were found asfollows:Qair;whole ¼wholeX Qair;j (22)j Qref;whole ¼ mref;DE Htot;ref Tref;J ; Pref;J ; uref;IJ Htot;ref Tref;E ; Pref;E ; uref;DE(23)Finding Heat Transfer Coefficients by Least SquareMethod. In the Calculation Procedure of Inverse Heat TransferMethod subsection, a procedure was described for using theassumed hair,j and href,j to calculate the solid temperatures T(j), refrigerant sections’ temperatures Tref(F)–Tref (J), and heat removalrate from the hot air Qair,whole. In the present subsection, we discuss how to find the best combination of hair,j and href,j. Here, thecalculation results for T(i), T(ii), T(iii), and T(iv) are expressed interms of the experimentally measured Ti, Tii, Tiii, and Tiv values tofacilitate the discussion. We divided the airfoil heat exchangerinto three parts: the front part forward of tube IJ, the rear partbehind tube EF, and the part between them, as shown in Fig. 6.Additionally, as shown in Fig. 6, the space-averaged heat transfercoefficients on the front part surface hair,front, rear part surface hair,rear, middle upper surface hair,middle,up, and middle lower surfacehair,middle,low were defined. href was locally determined based on
the local adjacent refrigerant Reynolds number. However, the difference in the local refrigerant Reynolds numbers between theinlet and outlet was negligible. Thus, the space-averaged href overall of the refrigerant-contact surfaces in the airfoil heat exchangerwas considered.In this study, the Levenberg–Marquardt algorithm [23] wasused. It is one of the least square methods. In this algorithm, fivefitting functions [f(1) ¼ {T(i) Ti}/Ti, f(2) ¼ {T(ii) Tii}/Tii,f(3) ¼ {T(iii) Tiii}/Tiii, f(4) ¼ {T(iv) Tiv}/Tiv, f(5) ¼ {Qair,whole Qref,whole}/Qref,whole] were set. The best combination of five independent variables [hair,front, hair,middle,up, hair,middle,low, hair,rear,href] was found to realize the minimum of [f(1)2 þ f(2)2 þ f(3)2þ f(4)2 þ f(5)2]. In other words, we numerically found the calculation results that were the closest to the experimental results. Thisnumerical analysis was performed by a VisualBasic2010 code thatwe developed using the Levenberg–Marquardt algorithm packageprovided by the ALGLIB Project [24].Nusselt Numbers and Modified Stanton Numbers. Based onthe calculation results, an average refrigerant Nusselt numberNuref and an average refrigerant modified Stanton number Stref areobtained as follows:Nuref ¼href pDref 5Wfringehref DrefNuref 20Wfringe; Stref ¼¼krefqref p4 D2ref uref CPref Reref Prref Dref(24)where pDref5Wfringe is the area of the refrigerant-contact surfaces.Here, Stref is a dimensionless number that measures the ratio ofthe heat transferred to the refrigerant to the total heat capacity ofthe refrigerant passing through the airfoil heat exchanger.The average hair over all the surfaces is calculated using theoverall energy balance as follows:Qair;wholehair ¼ Pair contact Aair;j DTair;jj(25)where DTair;j ¼ Tair;adiabatic;j T ð jÞ for control volume j on theouter air-contact surfaces. Then, an average air Nusselt numberNuair and an average air modified Stanton number Stair are calculated as follows:Nuair ¼hair LC;kairStair ¼hair LC WNuair¼qair LG sinðbÞWuair CPair Reair;channel Prair(26)where LGsin(b)W is the cross section of the air stream handled bya unit of the airfoil heat exchanger. Here, the representative lengthof Reair,channel is the height LGsin(b) of the air stream handled by aunit of the airfoil heat exchanger. Stair is a dimensionless numberthat measures the ratio of the heat transferred to the air stream tothe total heat capacity of the air stream handled by a unit of theairfoil heat exchanger.Results and DiscussionExperimental Conditions. The carbon dioxide critical pointswere TC,CO2 ¼ 304.2 K and PC,CO2 ¼ 7.38 MPa, whereas the watercritical points were TC,H2O ¼ 647.3 K and PC,H2O ¼ 22.12 MPa.The refrigerant
e-mail: tnagasak@es.titech.ac.jp Conjugate Heat Transfer in Air-to-Refrigerant Airfoil Heat Exchangers A light and compact heat exchange system was realized using two air-to-refrigerant air-foil heat exchangers and a recirculated heat transport refrigerant. Its heat transfer per-formance was experimentally investigated.
This standard applies to Liquid to Liquid Heat Exchangers as defined in Section 3, which includes the following types of heat exchangers: 2.1.1 Plate heat exchangers 2.1.2 Shell-and-tube heat exchangers 2.1.3 Shell-and-coil heat exchangers 2.1.4 Shell-and-U-Tube heat exchangers 2.2 Exclusions. This standa
The two basic types of heat exchangers are compact and conventional heat exchangers. The ratio of the heat transfer surface area of a heat exchanger to its volume is called the area density β. A heat exchanger with β 700 m2/m3 is classified as a Compact heat exchanger (CHEs) and if β 700 m2/m3 then they are the Conventional heat exchangers.
Relevance of heat transfer and heat exchangers for the development of sustainable energy systems B. Sundén1 & L. Wang2 1Division of Heat Transfer, Department of Energy Sciences, Lund University, Lund, Sweden. 2Siemens Industrial Turbines, Finspong, Sweden. Abstract There are many reasons why heat transfer and heat exchangers play a key role in the
API Heat Transfer (Suzhou) Co. Ltd. Air Cooled Aluminum Heat Exchangers Shell & Tube Heat Exchangers Plate Heat Exchangers 156 Qingqiu Street, 3rd District Suzhou Industrial Park Suzhou, Jiangsu 215126 China (86)512-88168000 Fax: (86)512-88168003 API Heat Transfer, Inc. 2777 Walden Avenue Buffalo, New York 14225 (716) 684-6700 www .
API Heat Transfer (Suzhou) Co. Ltd. Air Cooled Aluminum Heat Exchangers Shell & Tube Heat Exchangers Plate Heat Exchangers 156 Qingqiu Street, 3rd District Suzhou Industrial Park Suzhou, Jiangsu 215126 China (86)512-88168000 Fax: (86)512-88168003 API Heat Transfer, Inc. 2777 Walden Avenue Buffalo, New York 14225 (716) 684-6700 www .
OF HEAT EXCHANGERS Bureau of Energy Efficiency 55 4.1 Introduction Heat exchangers are equipment that transfer heat from one medium to another. The proper design, operation and maintenance of heat exchangers will make the process energy efficient and minimize energy losses. Heat exchanger performance can deteriorate with time, off
media involved in the heat exchange (standard). FUNKE is a leader in the development and production of quality heat exchangers with a heat transfer area of up to 2 400 m². The range of products comprises shell-and-tube heat exchangers, bolted and brazed plate heat exchangers as well as oil / air cooling units and electrical oil pre-heaters.
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