Proceedings of NHTC’00 34th National Heat Transfer Conference August 20-22, 2000, Pittsburgh, Pennsylvania, USA NHTC2000-12268 THE EFFECT OF WORKING FLUID INVENTORY ON THE PERFORMANCE OF REVOLVING HELICALLY-GROOVED HEAT PIPES R. Michael Castle Scott K. Thomas Department of Mechanical and Materials Engineering Wright State University Dayton, Ohio 45435 Kirk L. Yerkes Air Force Research Laboratory (PRPG) Wright–Patterson AFB, Dayton, Ohio 45433–7251 ABSTRACT The results of a recently completed experimental and analyt- ical study showed that the capillary limit of a helically–grooved heat pipe (HGHP) was increased significantly when the trans- verse body force field was increased. This was due to the ge- ometry of the helical groove wick structure. The objective of the present research was to experimentally determine the perfor- mance of revolving helically–grooved heat pipes when the work- ing fluid inventory was varied. This report describes the mea- surement of the geometry of the heat pipe wick structure and the construction and testing of a heat pipe filling station. In addition, an extensive analysis of the uncertainty involved in the filling procedure and working fluid inventory has been outlined. Ex- perimental measurements include the maximum heat transport, thermal resistance and evaporative heat transfer coefficient of the revolving helically–grooved heat pipe for radial accelerations of a r = 0.0, 2.0, 4.0, 6.0, 8.0, and 10.0-g and working fluid fills of G = 0.5, 1.0 and 1.5. An existing capillary limit model was updated and comparisons were made to the present experimental data. NOMENCLATURE a adiabatic length near the evaporator end cap, m α radial acceleration, m/s 2 A e surface area in the evaporator section, πr 2 v L e ,m 2 A gr cross–sectional area of a groove, m 2 Author to whom correspondence should be directed. b adiabatic length near the condenser end cap, m C p specific heat at constant pressure, J/(kg-K) D o tube outside diameter, m D vs diameter of the heat pipe vapor space, m G Ratio of liquid volume to total groove volume, V l V gr h groove height, m h e local heat transfer coefficient in the evaporator section, Q t A e T w T a , W/m 2 -K I heater current, A L a adiabatic length, m L c condenser length, m L e evaporator length, m L gr helical groove length, m L t total heat pipe length, m m d mass of working fluid dispensed by the filling station, kg m l mass of liquid, kg m t total mass of working fluid inventory, kg m v mass of vapor, kg ˙ m c coolant mass flow rate, kg/s N gr number of grooves p helical pitch, m Q cap capillary limit, W Q in heat input at the evaporator, W Q t heat transported, ˙ m c C p T out T in ,W r h radius of the helix, m r v radius of the heat pipe vapor space, m R radius of curvature, m R th thermal resistance, T eec T cec Q t , K/W 1 Copyright 2000 by ASME
Transcript
Proceedings of NHTC’0034th National Heat Transfer Conference
August 20-22, 2000, Pittsburgh, Pennsylvania, USA
NHTC2000-12268
THE EFFECT OF WORKING FLUID INVENTORY ON THE PERFORMANCE OFREVOLVING HELICALLY-GROOVED HEAT PIPES
R. Michael CastleScott K. Thomas �
Department of Mechanical and Materials EngineeringWright State University
Dayton, Ohio 45435
Kirk L. YerkesAir Force Research Laboratory (PRPG)
Wright–Patterson AFB,Dayton, Ohio 45433–7251
ABSTRACTThe results of a recently completed experimental and analyt-
ical study showed that the capillary limit of a helically–groovedheat pipe (HGHP) was increased significantly when the trans-verse body force field was increased. This was due to the ge-ometry of the helical groove wick structure. The objective ofthe present research was to experimentally determine the perfor-mance of revolving helically–grooved heat pipes when the work-ing fluid inventory was varied. This report describes the mea-surement of the geometry of the heat pipe wick structure and theconstruction and testing of a heat pipe filling station. In addition,an extensive analysis of the uncertainty involved in the fillingprocedure and working fluid inventory has been outlined. Ex-perimental measurements include the maximum heat transport,thermal resistance and evaporative heat transfer coefficient of therevolving helically–grooved heat pipe for radial accelerations ofj~ar j = 0.0, 2.0, 4.0, 6.0, 8.0, and 10.0-g and working fluid fillsof G = 0.5, 1.0 and 1.5. An existing capillary limit model wasupdated and comparisons were made to the present experimentaldata.
NOMENCLATUREa adiabatic length near the evaporator end cap, mα radial acceleration, m/s2
Ae surface area in the evaporator section,πr2vLe, m2
Agr cross–sectional area of a groove, m2
�Author to whom correspondence should be directed.
b adiabatic length near the condenser end cap, mCp specific heat at constant pressure, J/(kg-K)Do tube outside diameter, mDvs diameter of the heat pipe vapor space, mG Ratio of liquid volume to total groove volume,Vl=Vgr
h groove height, mhe local heat transfer coefficient in the evaporator section,
Qt=Ae(Tw�Ta), W/m2-KI heater current, ALa adiabatic length, mLc condenser length, mLe evaporator length, mLgr helical groove length, mLt total heat pipe length, mmd mass of working fluid dispensed by the filling station, kgml mass of liquid, kgmt total mass of working fluid inventory, kgmv mass of vapor, kgmc coolant mass flow rate, kg/sNgr number of groovesp helical pitch, mQcap capillary limit, WQin heat input at the evaporator, WQt heat transported, ˙mcCp(Tout�Tin), Wrh radius of the helix, mrv radius of the heat pipe vapor space, mR radius of curvature, mRth thermal resistance,(Teec�Tcec)=Qt , K/W
1 Copyright 2000 by ASME
s coordinate along the centerline of the heat pipe, mtw tube wall thickness, mTa adiabatic temperature, KTcec condenser end cap temperature, KTeec evaporator end cap temperature, KTin calorimeter inlet temperature, KTout calorimeter outlet temperature, KTsat saturation temperature, KTw outer wall temperature, Kvl , vv specific volume of liquid and vapor, m3/kgV heater voltageVgr volume of the grooves, m3
Vvs vapor space volume, m3
w width along the bottom of the groove, mx distance from the evaporator end cap, m∆ uncertaintyθ1, θ2 angles from the sides of the groove to vertical, radφ helix angle, rad
INTRODUCTIONHelically–grooved heat pipes (HGHPs) have potential appli-
cations in the thermal management of rotating equipment suchas aircraft alternators, large–scale industrial electric motors, andspinning satellites. In two recent studies (Klasing et al., 1999;Thomas et al., 1998), the performance of revolving HGHPs wasinvestigated. It was found that the capillary limit increased withthe strength of the acceleration field perpendicular to the heatpipe axis. In order to move HGHPs closer to application, knowl-edge must be gained concerning the sensitivity of the capillarylimit to working fluid fill amount, since variations in the fillamount are inevitable during the manufacture of these devices.Very few studies were available concerning the effect of workingfluid fill on the performance of axially–grooved heat pipes, butthose found have been outlined below. In addition, synopses ofthe two aforementioned studies on revolving HGHPs have alsobeen provided.
Brennan et al. (1977) developed a mathematical modelto determine the performance of an axially–grooved heat pipewhich accounts for liquid recession, liquid–vapor shear inter-action and puddle flow in a 1-g acceleration environment. Themodel considered three distinct flow zones: the grooves unaf-fected by the puddle, the grooves that emerge from the puddle,and the grooves that are submerged by the puddle. The model forthe puddle consisted of satisfying the equation of motion for thepuddle and the continuity equation at the puddle–groove inter-face, and was solved by a fourth–order Runge–Kutta integrationmethod with self–adjusting step sizes. The assumptions made bythe model for the puddle were uniform heat addition and removalwith a single evaporator and a single condenser section, and one–dimensional laminar flow in the puddle. The transport capabil-
ity of the grooves unaffected by the puddle and the grooves ex-tending beyond the puddle were approximated by a closed–formsolution with laminar liquid and vapor flow. The working flu-ids used for the experiment were methane, ethane and ammonia.Brennan et al. (1977) stated that the mathematical model agreedwell with the experimental data for ideally filled and overfilledheat pipes, but some differences were noted for underfilled heatpipes. In general, it was found for ideally filled heat pipes thepredicted transported heat was higher than that measured. Also,this discrepancy was more significant for lower operating tem-peratures. In addition, it was found during the experiments thatthe maximum transported heat increased with fill volume.
Vasiliev et al. (1981) performed a series of experiments onan aluminum axially–grooved heat pipe which was overfilled andideally filled. The width and height of the grooves werew =0.123 mm andh = 0.7 mm, respectively, with an overall heatpipe length ofLt = 80.0 cm. The working fluids were acetoneand ammonia. Vasiliev et al. showed that the temperature differ-ence from the evaporator to the adiabatic regions increased at amuch slower rate with increasing overfills. This was attributedto a thin film of liquid emerging from the overfill pool wettingthe upper grooves. Vasiliev et al. stated that this thin film waslifted over the grooves by capillary forces due to microroughnesson the groove surface. A mathematical model was developedfor low temperature axially–grooved heat pipes to estimate heatpipe performance for 0-g and 1-g applications. The mathemati-cal model was a set of boundary–value problems applied to eachgroove and was solved by a numerical iteration method. Themodel was based on pressure balance equations and mass conti-nuity written for a single groove. The temperature of the vaporin the adiabatic region was an input parameter, and the vaporpressure gradient was assumed to be one–dimensional. In addi-tion, the liquid–vapor shear stress was assumed to be constant,and the starting liquid film thickness was of the same order ofmagnitude as the groove microroughness. Very good agreementwas reported between the mathematical model and experimentaltransported heat results for ideally filled and overfilled heat pipesunder gravity.
Thomas et al. (1998) presented experimental data obtainedfrom a helically–grooved copper heat pipe which was tested ona centrifuge table. The heat pipe was bent to match the radius ofcurvature of the table so that uniform transverse (perpendicular tothe axis of the heat pipe) body forces field could be applied alongthe entire length of the pipe. The steady–state performance of thecurved heat pipe was determined by varying the heat input (Qin
= 25 to 250 W) and centrifuge table velocity (radial accelerationj~ar j = 0.01 to 10-g). It was found that the capillary limit increasedby a factor of five when the radial acceleration increased fromj~ar j = 0.01 to 6-g due to the geometry of the helical grooves.A model was developed to calculate the capillary limit of eachgroove in terms of centrifuge table angular velocity, the geometryof the heat pipe and the grooves, and the temperature–dependent
2 Copyright 2000 by ASME
working fluid properties. The agreement between the model andthe experimental data was satisfactory.
Klasing et al. (1999) developed a mathematical model todetermine the operating limits of a revolving helically–groovedstraight heat pipe. The capillary limit calculation required ananalysis of the total body force imposed by rotation and gravityon the liquid along the length of the helical grooves. The boilingand entrainment limits were calculated using methods describedby Faghri (1995). It was found that the capillary limit increasedsignificantly with rotational speed due to the helical geometryof the heat pipe wick structure. The maximum heat transportwas found to be a function of angular velocity and tilt angle fromhorizontal. In addition, a minimum value of angular velocity wasrequired to obtain the benefits of the helical groove geometry.
The first objective of the present study was to determine thesensitivity of the performance of revolving HGHPs to the work-ing fluid fill amount. This required a precise knowledge of thegeometry of the heat pipe and helical grooves. In addition, a pre-cision filling station was constructed and calibrated to determinethe uncertainties involved in the filling procedure. The copper–ethanol heat pipe was tested on a centrifuge table at Wright–Patterson AFB (AFRL/PRPG) to determine the capillary limit,thermal resistance and evaporative heat transfer coefficient forfill ratios of G = 0.5, 1.0 and 1.5, and radial accelerations ofj~ar j = 0.01, 2.0, 4.0, 6.0, 8.0 and 10.0-g. The second objec-tive of the present study was to improve the existing analyticalcapillary limit model developed by Thomas et al. (1998) usingthe above–mentioned geometric measurements and by using im-proved equations for the working fluid properties.
Determination of Heat Pipe Working Fluid InventoryThe objective of this analysis was to determine the working
fluid inventory of a HGHP, which consists of the mass of liquidin the grooves and the mass of vapor in the vapor space. Sincethe heat pipe is a closed container under saturation conditions,the total mass of working fluid in the heat pipe is given by
mt = mv+ml =Vvs
vv+
GVgr
vl(1)
whereG = Vl=Vgr is the ratio of the volume of liquid to totalgroove volume. The volume of the vapor space is
Vvs=π4
D2vsLt +Vgr(1�G) (2)
The second term in eqn. (2) accounts for the increase or decreasein the vapor space volume when the parameterG is varied. Thetotal volume of the grooves is
Vgr = LgrNgrAgr (3)
Figure 1. Photomicrograph of the helical groove geometry.
A cross–sectional view of a typical helical groove in the ex-perimental test article is shown in Fig. 1. The cross–sectionalarea of the trapezoidal groove accounts for the differing side an-gles.
Agr = wh+12
h2(tanθ1+ tanθ2) (4)
The total length of each groove is
Lgr = Lt
"�2πrh
p
�2
+1
# 12
(5)
The radius of the helix is given by
rh =12(Dvs+h) (6)
The helical pitch is the distance through which the helix makesone revolution around its radius.
p=2π(s�s1)
(φ�φ1)(7)
The helix angleφ corresponds tos, which is the distance traveledalong the centerline of the heat pipe.
In order to calculate the working fluid inventory for theHGHP, measurements of the appropriate geometric parameterswere made. In addition, an extensive uncertainty analysis wasperformed to determine the uncertainties of both the measuredand calculated variables used in finding the working fluid inven-tory.
The physical variables given in eqn. (4) for the cross–sectional area of the grooves have been measured. A sampleof the HGHP container was set in an epoxy resin mold, pol-ished, and examined under a microscope with 50� magnifica-tion. Computer software was used to make bitmap pictures of
3 Copyright 2000 by ASME
ten different grooves and a microscopic calibration scale. Thesepictures were then analyzed to determine the geometric valuesshown in Fig. 1. Since the corners at the top of the land be-tween grooves were not well defined, a special procedure wasestablished to determine the geometry of the grooves. First, lineswere drawn along the bottom and sides of each groove. Then, aline was drawn across the bottom of the land between grooves,as shown in Fig. 1. This line was then transposed to the top ofthe land. The intersections between this line and the lines alongthe sides of the groove were defined as the upper corners of thegroove. Note that the two lines along the land tops are at differentangles due to the radius of curvature of the heat pipe container.The anglesθ1 andθ2, and the height and width of the grooveh andw were found using a bitmap picture of the microscopiccalibration scale as described by Castle (1999).
An optical comparator was used to determine the vaporspace diameter of the heat pipe container sample. The cross hairsof the optical comparator were carefully aligned with the top ofthe land between grooves on the left edge of the pipe. The com-parator table was then moved until the land tops on the right edgeof the pipe were aligned with the cross hairs. The diameter of theheat pipe vapor space was the distance of the table movement.
The helical groove pitch was found using a vertical millingmachine and an angular displacement transducer. The heat pipecontainer material was originally 1 m long. Approximately one-half was used to form the heat pipe, and the other half was usedto determine the pitch. The rotation angle(φ� φ1) and the cor-responding distance along the centerline of the heat pipe(s�s1)has been found as shown in Fig. 2(a). A heat pipe holding devicewas constructed from two angle aluminum uprights mountedto the table of a vertical milling machine. Precision alignmentblocks were attached to the undersides of the uprights to engageone of the grooves in the milling machine table for improvedalignment. Nylon bushings were placed in the uprights to centerboth the heat pipe container and the shaft, which was concentricwith the heat pipe container. A small pin was made from a 1.58mm (0.0625 in) dowel pin, where one end was ground to 0.26mm to fit in the base of the helical groove. This sprung pin wasset in a hole in the shaft where it engaged one of the grooves,as shown in Fig. 2(b). An angular displacement transducer wasmounted onto another piece of angle aluminum. A vertical 6.35mm (0.25 in) dowel pin was placed in the angle aluminum toalign with the angular displacement transducer shaft. The dowelpin was held by a collet installed in the milling machine spindlein order to fix the location of the displacement transducer. Theshaft of the transducer was linked to the shaft within the heatpipe by three set screws. As the milling machine table moved thepipe over the stationary shaft, the pin followed the helical groove,causing the shaft to rotate. The angular displacement transducermeasured this rotation. A multimeter was used to measure theoutput voltage of the angular displacement transducer. The dis-tance of the table movement was(s� s1), which was read from
Figure 2. Schematic of the helical pitch measurement technique: (a)
Major components; (b) Cross-sectional view of sprung pin engaging a
helical groove.
the milling machine display unit. The transducer output voltagewas measured over 10 cm lengths for ten different groups. Back-lash errors were avoided by not reversing the table movementwhile taking data. The pitch was calculated using eqn. (7) at apoint in the center of each 10 cm length. An average of 88 valueswere used to calculate the helical pitch.
Using the analysis given by Miller (1989), the root–sum–square uncertainties for the groove cross–sectional area, helicalpitch, helix radius, groove length, groove volume, vapor spacevolume, and total mass of the working fluid inventory have beencalculated. The measured and calculated uncertainties for all ge-ometric variables presented are shown in Table 1.
A literature survey was completed to determine the specificvolumes of ethanol vapor and liquid at various saturation tem-peratures, as shown in Fig. 3. This information was needed todetermine the total mass and uncertainty of the working fluid in-ventorymt �∆mt . While existing texts report these properties(Faghri, 1995; Peterson, 1994, Lide and Kehiaian, 1994; Carey,
4 Copyright 2000 by ASME
Table 1. The geometric variable values associated with the working fluidinventory.
Figure 3. Specific volume of ethanol versus temperature: (a) Saturated
liquid; (b) Saturated vapor.
1992; Schlunder, 1983; Ivanovskii et al., 1982), it was foundthat most simply referred to previous sources. Therefore, thedata shown in Fig. 3 represent information gathered from pri-mary sources that cannot readily be traced further. In Fig. 3(a),the available data for the specific volume of liquid in the rangeof Tsat = 0 to 100�C are relatively scattered. Vargaftik (1975)stated that the ethanol used was 96% pure by volume, with watermaking up most of the other 4%. Ethanol is agressively hygro-scopic, so special procedures are required for further purifica-tion as outlined by Timmermans (1950) concerning anhydrousethanol. Since the data by Timmermans (1950) and TRC (1983)are nearly coincident, it is believed that the data reported by TRC(1983) are also for anhydrous ethanol. Dunn and Reay (1978) donot provide information concerning purity. Therefore, the Var-gaftik (1975) data and the Dunn and Reay (1978) data have beendiscarded in Fig. 3(a). In Fig. 3(b), the deviation of the Dunn andReay (1978) data for the specific volume of vapor is significant.Therefore, the Dunn and Reay (1978) data has been discarded inFig. 3(b). Polynomial curve fits from 0�Tsat� 100�C have beenobtained for the data shown in Figs. 3(a) and 3(b) for the specificvolumes of liquid and vapor ethanol. These curve fits have beenevaluated at room temperature to determine the proper values tobe used in the uncertainty analysis, since the heat pipe was filledat room temperature. Information concerning the uncertainty ofthe original data was not available. Therefore, the uncertaintiesof these properties have been estimated to be the maximum vari-ance of the data from the curve fits (∆vl = 3:5� 10�8 m3/kg,∆vv = 0:39 m3/kg). The specific volumes of liquid and vaporethanol (m3/kg) as functions of saturation temperature (�C) areshown below for the range 0� Tsat� 100�C
Figure 4. Schematic of the heat pipe filling station.
methanol) into a heat pipe without also introducing ambient air(Fig. 4). The station consisted of a manifold of valves and in-terconnecting stainless steel tubing, a working fluid reservoir,a dispensing burette, a vacuum pump, and a container of com-pressed dry nitrogen gas. Previous experience with filling sta-tions showed that long runs of horizontal tubing could cause sig-nificant filling errors due to vapor bubbles within the tubing. Toaddress this problem, the manifold was constructed such that theinterconnecting tubing runs were very short (on the order of 2
cm). In addition, the tubes which intersect the main vertical tubebetween valves 2 and 5 (Fig. 4) were offset from each other andran at a diagonal from the main tube. Again, the purpose of thisdesign was to reduce the possibility of vapor bubbles adheringto the tubing walls, thus causing errors in the fill amount. How-ever, it is likely that some vapor still does adhere to the tubing,so certain procedures were carried out during filling to eject asmuch vapor as possible. For instance, the 1 psig relief valveover valve 1 was cycled on and off several times. In addition,valves 2 and 5 were cycled on and off while noting the menis-cus displacement within the dispensing burette. If the meniscuswas displaced more than 0.06 cm3, vapor was probably trappedwithin the valve. The valve in question was then cycled until thebubble was ejected.
To fill the heat pipe, the container was first evacuated to apressure of 10�6 Torr using a turbomolecular vacuum pump. Thesealed pipe was then connected to the filling station at valve 5.The working fluid was frozen and thawed repeatedly to reducethe amount of dissolved air within the fluid. The entire filling sta-tion was then evacuated by a roughing pump, except the workingfluid reservoir. After evacuation, the liquid working fluid wasdrawn up into the dispensing burette and into all interconnect-ing tubing. After noting the height of the meniscus, the desiredamount of working fluid was metered into the heat pipe by care-fully opening the heat pipe fill valve 8. The difference in heightof the liquid column was related to the dispensed mass of work-ing fluid.
During initial testing of the filling station, it was found thatthe mass of working fluid dispensed into the heat pipe containerwas different than what was indicated by the dispensing burette.Therefore, a rigorous calibration of the filling station was under-taken to determine a correlation between the change in volumeread by the dispensing burette and the change in mass of a re-ceiving burette attached at valve 5, which was measured usinga precision scale. The total uncertainty of the working fluid in-ventory dispensed by the heat pipe filling station∆md is given inTable 2.
Experimental SetupThe purpose of the experiment was to examine the steady–
state performance of a helically–grooved copper–ethanol heatpipe under various heat inputs and transverse body forcefields using a centrifuge table located at Wright–Patterson AFB(AFRL/PRPG). Specifically, the amount of working fluid wasvaried (G = 0.5, 1.0 and 1.5) to determine the effects of un-der/overfilling on the capillary limit, thermal resistance and evap-orative heat transfer coefficient of the HGHP. To ensure uniformradial acceleration fields over the length of the heat pipe, the pipewas bent to match the radius of curvature of the centrifuge table(R = 1.22 m). Physical information concerning the heat pipe isgiven in Table 3. It should be noted that the total helix angle
Working fluid EthanolWorking fluid charge mt = 1.47, 2.92 and 4.38 gEvaporator length Le = 15.2� 0.16 cmAdiabatic length La = 8.2� 0.16 cmCondenser length Lc = 15.2� 0.16 cmTube outside diameter Do = 1.588� 0.005 cmTube wall thickness tw = 0.0757 cmRadius of curvature R = 1.22 mWall/wick materials CopperWick structure Helical groovesNumber of Grooves Ngr = 50Heater element Nichrome heater tapeFill valve Nupro B-4HW bellows valveCalorimeter 1/8 in. OD coiled copper tubing
was very small: Each groove rotated through an angle of approx-imately 2.03 rad (116 arc degrees) over the length of the pipe.The heat pipe was mounted to a platform overhanging the edgeof the horizontal centrifuge table. This allowed the heat pipe tobe positioned such that the radius of curvature was equivalent tothe outermost radius of the centrifuge table. Insulative mountingblocks were used to ensure that the heat pipe matched the pre-scribed radius as closely as possible. The horizontal centrifugetable was driven by a 20-hp dc motor. The acceleration fieldnear the heat pipe was measured by a triaxial accelerometer. Theacceleration field at the centerline of the heat pipe radius was cal-culated from these readings using a coordinate transformation.
A pressure–sensitive nichrome heater tape with an alu-minized backing was uniformly wound around the circumferenceof the evaporator section for heat input. Power was supplied tothe heat pipe evaporator section by a power supply through powerslip rings to the table. While the current reading could be madedirectly using a precision ammeter, the voltage across the elec-tric heater had to be measured on the rotating table because of thevoltage drop between the control room and the table. Therefore,the voltage at the heater was obtained through the instrumenta-tion slip ring assembly and read by a precision multimeter.
The calorimeter consisted of a length of 1/8 in. OD cop-per tubing wound tightly around the condenser section. The sizeof the tubing was chosen to be small to minimize the effectsof acceleration on the performance of the calorimeter. Thermalgrease was used between the heat pipe and the calorimeter to de-crease contact resistance. Type T thermocouples were insertedthrough brass T–branch connectors into the coolant inlet and exitstreams, and a high-resolution digital flow meter was used tomeasure the mass flow rate of the coolant (50% by mass ethyleneglycol/water mixture). The mass flow rate was controlled us-ing a high–pressure booster pump, which aided the low–pressurepump in the recirculating chiller. The percentage of ethylene gly-
Figure 5. Thermocouple locations and relevant lengths.
col was measured periodically during testing using a precisionhydrometer to ensure that the mixture did not change. The tem-perature of the coolant was maintained at a constant setting bythe recirculating chiller. Coolant was delivered to the centrifugetable via a double–pass hydraulic rotary coupling. The mass flowrate was constant for all experiments. Values of the specific heatof ethylene glycol/water mixtures were obtained from ASHRAE(1977), which were in terms of percent ethylene glycol by weightand temperature. The average temperature between the calorime-ter inlet and outlet was used to evaluate the specific heat. Thespecific heat did not vary appreciably during testing since it is aweak function of temperature.
Heat pipe temperatures were measured by Type T surface–mount thermocouples, which were held in place using Kaptontape. Mounting locations for the thermocouples are shown in Fig.5. A short unheated length next to the evaporator end cap wasinstrumented with thermocouples specifically for accurate ther-mal resistance measurements. In addition, groups of four ther-mocouples were arranged around the circumference of the heatpipe at stations in the evaporator section for local heat transfercoefficient information. Temperature signals were conditionedand amplified on the centrifuge table. These signals were trans-ferred off the table through the instrumentation slip ring assem-bly, which was completely separate from the power slip ring as-sembly to reduce electronic noise. Conditioning the temperaturesignals prior to leaving the centrifuge table eliminated difficultiesassociated with creating additional junctions within the slip ringassembly. Temperature and acceleration signals were collectedusing a personal computer with data logging software. Since ashortage of thermocouple channels existed on the centrifuge ta-ble, a series of three electrical relays were engaged to read oneset of thermocouples, and disengaged to read the other set.
Since the heat pipe assembly was subjected to air velocitiesdue to the rotation of the table (up to 11 m/s = 25 mi/hr), effortswere made to reduce convective heat losses from the exterior ofthe heat pipe. A thin–walled aluminum box was fabricated to fit
7 Copyright 2000 by ASME
Table 4. Maximum uncertainties of measured and calculated values.
Measured ValuesCoolant mass flow rate ∆mc =� 0.05 g/s
Heater voltage ∆V =� 0.5 VHeater current ∆I =� 0.1 A
Radial acceleration ∆ar =� 0.1-gCalorimeter inlet temperature ∆Tin =� 0.07 KCalorimeter outlet temperature ∆Tout=� 0.08 KEvaporator end cap temperature∆Teec=� 0.09 KCondenser end cap temperature∆Tcec=� 0.11 K
Calculated ValuesHeat input See Fig. 6
Heat transported ∆Qt =� 3.2 WThermal resistance See Fig. 7
Heat transfer coefficient See Figs. 12 and 13
around the heat pipe. Ceramic wool insulation was placed insidethe box and around the heat pipe through three small doors onthe top of the box. This insulation/box arrangement provided aneffective barrier to convective losses from the heat pipe to theambient.
The helically-grooved copper-ethanol heat pipe was testedin the following manner. The recirculating chiller was turned onand allowed to reach the setpoint temperature, which was mea-sured at the calorimeter inlet. The centrifuge table was startedfrom the remote control room at a slow constant rotational speedto prevent damage to the power and instrumentation slip rings. Inthis case, the radial acceleration was less thanj~ar j < 0:01-g. Inall cases, the centrifuge table rotated in a clockwise direction asseen from above. Power to the heater was applied (Qin = 10 W)and the heat pipe was allowed to reach a steady-state condition.The power to the heater was then increased toQin = 20 W andagain the heat pipe was allowed to reach a steady–state condition.This was repeated until the maximum allowable evaporator tem-perature was reached (Tw;max= 100�C). After all data had beenrecorded the power to the heater was turned off, and the heat pipewas allowed to cool before shutting down the centrifuge table.
Using the analysis given by Miller (1989), the uncertaintiesfor all of the measured and calculated values for the experimentaldata are presented in Table 4.
Results and DiscussionThe objective of this experiment was to determine the
steady–state performance of a revolving helically–grooved heatpipe as a function of the working fluid inventory. The heat input,radial acceleration and working fluid fill were varied as follows:Qin = 10 to 180 W,j~ar j = 0.01 to 10-g, andG = 0.5, 1.0 and 1.5.Thermocouples on the inboard, outboard, top, and bottom sidesof the heat pipe (Fig. 5) were used to determine the axial and
circumferential temperature distributions. Typical steady–statetemperature distributions for the heat pipe forG = 1.0 atj~ar j =0.01-g are shown in Fig. 6. For low power input levels, the tem-perature distribution was uniform. As the power input increased,the temperatures within the evaporator and the short unheatedsection adjacent to the evaporator increased significantly, indi-cating a partial dryout situation. Since the coolant temperature
Figure 7. Thermal resistance versus heat transport: (a) G = 0.5; (b) G= 1.0; (c) G = 1.5.
and flow rate were constant for all tests, the adiabatic and con-denser temperatures increased slightly with input power. Figure7 shows the thermal resistance versus transported heat over theentire range of radial acceleration for each fill level. In Fig. 7(a)the thermal resistance was quite high, which indicates that theheat pipe was partially dried out forG = 0.5, even at the lowestpower input levels. However, the thermal resistance decreased
Ta = 80�C PresentTa = 60�C PresentTa = 40�C PresentTa = 80�C ThomasTa = 60�C ThomasTa = 40�C Thomas
j~arj (g)
Qcap
(W)
1086420
500
450
400
350
300
250
200
150
100
50
0
Figure 8. Capillary limit versus radial acceleration comparison of present
model and Thomas et al. (1998).
significantly as the radial acceleration increased, showing thatthe capillary pumping ability of the helical grooves increased.For G = 1.0 and 1.5, the thermal resistance decreased and thenincreased with transported heat when dryout commenced. TheG= 1.5 fill tests showed dryout occurring only forj~ar j = 0.01 and2.0-g. Dryout was not reached forG = 1.5 with j~ar j = 4.0, 6.0,8.0 and 10.0-g due to reaching the maximum allowable heatertemperature. The capillary limit was considered to be reachedwhen the thermal resistance began to increase.
Thomas et al. (1998) presented a mathematical model whichpredicted the capillary limit of a helically–grooved heat pipe sub-jected to a transverse body force. This model accounted for thegeometry of the heat pipe and the grooves (including helix pitch),body force field strength, and temperature–dependent workingfluid properties. This model was updated to include the im-proved measurements of the wick geometry and working fluidproperties. The capillary limit versus radial acceleration is givenin Fig. 8 for various working temperatures with the Thomas etal. (1998) model and the present model. The capillary limit in-creased steadily with radial acceleration and working temper-ature. The present model shows a significantly lower predic-tion for the capillary limit when compared to the Thomas modeldue to the improved geometric measurements and working fluidproperty equations.
Figure 9 shows a comparison of the experimental data andpresent analytical model for the capillary limit of a revolvinghelically–grooved heat pipe. No attempt was made to maintaina constant adiabatic temperature during the experiments. There-fore, the working fluid temperature in the model was set to theadiabatic temperature found experimentally. ForG = 0.5, theheat pipe operated successfully only forj~ar j � 8.0-g. In Fig.9(b) (G = 1.0), the capillary limit increased significantly with
Figure 9. Comparison of present model and experimental capillary limit
data versus radial acceleration: (a) G= 0.5; (b) G = 1.0; (c) G = 1.5.
radial acceleration. With the heat pipe overfilled by 50% (G =1.5), the capillary limit increased dramatically, showing the ef-fect that overfilling has on performance. The agreement of theanalytical model was very good forG = 1.0 as expected. ForG = 0.5, the model overpredicted the experimental data becauseit was assumed that the grooves were completely filled. ForG= 1.5, the model underpredicted the data due to the assumptionthat no liquid communication occurred between the grooves.
Temperatures within the evaporator section are shown inFigs. 10 and 11 forj~ar j = 0:01-g and 10.0-g, respectively. Ingeneral, the temperatures within the evaporator increased withtransported heat. In addition, the wall temperatures decreasedwith G for a given heat transport due to the fact that more grooveswere active. The temperatures along the length of the evaporatorsection can be tracked by examining the case forG = 1.0. Nearthe evaporator end cap, the temperatures departed those forG =1.5 at approximatelyQt = 15 W (Fig. 10(a)). At x = 92.1 mm
InboardTop
OutboardBottom
(a)
G = 1.5
G = 1.0
G = 0.5
T(�C)
100806040200
12011010090807060504030
(b)
G = 1.5
G = 1.0
G = 0.5
T(�C)
100806040200
12011010090807060504030
(c)
G = 1.5G = 1.0
G = 0.5
T(�C)
100806040200
12011010090807060504030
(d)G = 1.5G = 1.0
G = 0.5
Qt (W)
T(�C)
100806040200
12011010090807060504030
Figure 10. Temperatures within the evaporator section versus trans-
ported heat for j~ar j = 0:01-g: (a) x = 54.0 mm; (b) x = 92.1 mm; (c)
x = 130 mm; (d) x = 168 mm.
(Fig. 10(b)), this departure was delayed until approximatelyQt
= 25 W, and atx = 168 mm (Fig. 10(d)), the data forG = 1.0 and1.5 were nearly coincident. This behavior shows that the grooveswere essentially full near the adiabatic section, and proceeded todry out closer to the evaporator end cap, as expected. Dryout fortheG = 1.5 case can be seen in Fig. 10(a) where the temperaturesconverged to nearly the same value around the circumference. Itshould be noted that the temperatures around the circumferencewere relatively uniform forj~ar j = 0:01-g. Evaporator temper-atures forj~ar j = 10:0-g are shown in Fig. 11. In comparison toj~ar j= 0:01-g, the evaporator temperatures were in general lowerdue to the improved pumping ability of the helical grooves un-
10 Copyright 2000 by ASME
InboardTop
OutboardBottom
G = 1.5
G = 1.0
G = 0.5
(a)
T(�C)
140120100806040200
12011010090807060504030
G = 1.5
G = 1.0
G = 0.5
(b)
T(�C)
140120100806040200
12011010090807060504030
G = 1.5
G = 1.0
G = 0.5
(c)
T(�C)
140120100806040200
12011010090807060504030
G = 1.5
G = 1.0
G = 0.5
(d)
Qt (W)
T(�C)
140120100806040200
12011010090807060504030
Figure 11. Temperatures within the evaporator section versus trans-
ported heat for j~ar j = 10:0-g: (a) x = 54.0 mm; (b) x = 92.1 mm; (c)
x = 130 mm; (d) x = 168 mm.
der increased radial acceleration. In addition, the temperaturestended to overlap over a greater range of heat transport values.In contrast toj~ar j= 0:01-g, the evaporator temperature variationwas greater around the circumference at higherQt , but no patternwas distinguishable in the data.
Local heat transfer coefficient data versus heat transport isshown in Figs. 12 and 13 forj~ar j = 0:01-g and 10.0-g. Overall,the values forhe were very low forG = 0.5 due to the fact thatmost of the grooves were dried out. As the percent fill increasedfrom G = 0.5 toG = 1.0, the heat transfer coefficient increasedsignificantly. Forj~ar j = 0:01-g (Fig. 12),he increased and thendecreased with transported heat. This trend was also reported
by Vasiliev et al. (1981) for an aluminum axially–grooved heatpipe with acetone as the working fluid. ForG = 1.0 and 1.5, theheat transfer coefficient near the evaporator end cap (Fig. 12(a))decreased until all of the values around the circumference con-verged. Closer to the adiabatic section, the heat transfer coef-ficient values around the circumference had not yet converged,showing these portions to still be active. Forj~ar j = 10.0-g (Fig.13), the values ofhe were significantly more uniform around thecircumference and along the axial direction, even during a dry-out event (G = 1.0, Fig. 13(a)). In addition, the heat transfercoefficient seems to be more constant with respect to the trans-ported heat compared toj~ar j= 0:01-g. During the experiments,the heat pipe working temperature was not constant, which re-sulted in changes in the specific volume of the liquid and vaporof the working fluid. Since the heat pipe was filled at room tem-perature, it was important to quantify the potential effects of thechange in volume of liquid in the grooves with temperature. Fig-ure 14 shows the variation of the percentage of groove volumeoccupied by liquidG with saturation temperature for the threefill amounts over the range of working temperatures seen in theexperiments. The maximum percent difference was 2.7%, whichwas not deemed to be significant.
ConclusionsThe effect of fluid inventory on the steady–state performance
of a helically–grooved copper–ethanol heat pipe has been ex-amined both experimentally and analytically. It was found thatthe capillary limit increased and the thermal resistance decreasedsignificantly as the amount of working fluid within the heat pipeincreased. In addition, the evaporative heat transfer coefficientwas found to be a strong function of the fill amount. The updatedanalytical model was in very good agreement with the experi-mental capillary limit results forG = 1.0. However, the analyti-cal model overpredicted the capillary limit data forG = 0.5 andunderpredicted the data forG = 1.5.
AcknowledgementsFunding for this project was provided by the Air Force Re-
search Laboratory (PRPG) under Grant F33615-98-1-2844, andby the Ohio Board of Regents. The authors would also like toacknowledge the technical assistance of Mr. Don Reinmuller.
ReferencesASHRAE, 1977,Handbook of Fundamentals, American So-
ciety of Heating, Refrigerating and Air–Conditioning Engineers,Inc., Atlanta, GA.
Brennan, P., Kroliczek, E., Jen H., and McIntosh R., 1977,“Axially Grooved Heat Pipes,”AIAA 12th Thermophsics Conf.,Paper No. 77-747.
Castle, R., 1999, “The Effect of Working Fluid Inventory onthe Performance of Revolving Helically–Grooved Heat Pipes,”Masters Thesis, Wright State University, Dayton, Ohio.
Dunn, P., and Reay, D., 1978,Heat Pipes, Pergamon, Ox-ford.
Faghri, A., 1995,Heat Pipe Science and Technology, Taylorand Francis, Washington, D.C.
Ivanovskii, M., Sorokin, V., and Yagodkin, I., 1982,ThePhysical Principles of Heat Pipes,Clarendon, Oxford.
Klasing, K., Thomas, S., and Yerkes, K., 1999, “Predictionof the Operating Limits of Revolving Helically–Grooved HeatPipes,”ASME Journal of Heat Transfer, Vol. 121, pp. 213–217.
Lide, D., and Kehiaian, H., 1994,CRC Handbook of Ther-mophysical and Thermochemical Data, CRC Press, Boca Raton,FL.
Miller, R., 1989, Flow Measurement Engineering Hand-book,2nd Edn., McGraw-Hill.
Peterson, G., 1994,An Introduction to Heat Pipes: Model-ing, Testing, and Applications, Wiley, New York.
Schlunder, E., 1983,Heat Exchanger Design Handbook,Hemisphere, Washington, D.C.
Thomas, S., Klasing, K., and Yerkes, K., 1998, “The Effectsof Transverse Acceleration Induced Body Forces on the Capil-lary Limit of Helically–Grooved Heat Pipes,”ASME Journal ofHeat Transfer, Vol. 120, pp. 441–451.
Timmermans, J., 1950,Physico-Chemical Constants of PureOrganic Compounds, Elsevier, New York.
TRC, 1983, TRC Thermodynamic Tables—Non-hydrocarbons,Thermodynamic Research Center: The Texas A& M University System, College Station, TX (Loose-leaf datasheets).
Vargaftik, N., 1975,Handbook of Physical Properties ofLiquids and Gases, Hemisphere, Washington, D.C.
Vasiliev, L., Grakovich L., and Khrustalev D., 1981, “Low–Temperature Axially Grooved Heat Pipes,”Proc. 4th Int. HeatPipe Conf., London, pp. 337–348.
j
jj
(a)
G = 1.5G = 1.0G = 0.5
he
(W/m
2K)
100806040200
2500
2000
1500
1000
500
0
InboardTop
OutboardBottom
(b)
he
(W/m
2K)
100806040200
2500
2000
1500
1000
500
0
(c)
he
(W/m
2K)
100806040200
2500
2000
1500
1000
500
0
(d)
Qt (W)
he
(W/m
2K)
100806040200
2500
2000
1500
1000
500
0
Figure 12. Heat transfer coefficients within the evaporator section versus
transported heat for j~ar j = 0:01-g: (a) x = 54.0 mm; (b) x = 92.1 mm;
(c) x = 130 mm; (d) x = 168 mm.
12 Copyright 2000 by ASME
j
jj
(a)
G = 1.5G = 1.0
G = 0.5
he
(W/m
2K)
140120100806040200
2500
2000
1500
1000
500
0
InboardTop
OutboardBottom
(b)
he
(W/m
2K)
140120100806040200
2500
2000
1500
1000
500
0
(c)
he
(W/m
2K)
140120100806040200
2500
2000
1500
1000
500
0
(d)
Qt (W)
he
(W/m
2K)
140120100806040200
2500
2000
1500
1000
500
0
Figure 13. Heat transfer coefficients within the evaporator section versus
transported heat for j~ar j = 10:0-g: (a) x = 54.0 mm; (b) x = 92.1 mm;
(c) x = 130 mm; (d) x = 168 mm.
mt = 0.00438 kgmt = 0.00292 kgmt = 0.00147 kg
Tsat (�C)
G
6560555045403530
1.8
1.6
1.4
1.2
1
0.8
0.6
Figure 14. Ratio of liquid volume to total groove volume versus satura-
