UNIVERSITY OF WISCONSIN SYSTEM SOLID WASTE RESEARCH PROGRAM

Transcription

1 UNIERSITY OF WISCONSIN SYSTEM SOLID WASTE RESEARCH PROGRAM A Feasibility Study on Solid Waste Elimination fo Envionmentally Benign Machining Pocesses 6 Final Repot Tien-Chien Jen Depatment of Mechanical Engineeing Univesity of Wisconsin-Milwaukee

2 Final Repot on A Feasibility Study on Solid Waste Elimination fo Envionmentally Benign Machining Pocesses Statement of Objectives In many machining pocesses, a metalwoking fluid seves many system functions such as lubication, themal sink, coosion inhibito, chip contol and washing. These fluids can advesely affect the health of pesonnel in the machine oom. Metal chips contained used cutting fluid ae a souce of pollution and must be disposed of in an appopiate manne. Contaminants etained in the swaf (shavings and chippings of metal) usually means the scap cannot be ecycled fo a use simila to the oiginal application. The cost of ecovey fo these contaminated mateials can account fo nealy 3% of the total opeational cost of the machining pocesses. In Japan, Toyota geneated moe than 3,5 tons of waste (excluding the amount that could be ecycled) in 3. Appoximately 5% the waste was geneated fom machining pocesses. In the US, the Janesville Geneal Motos Assembly Plant alone geneated about 3, tons of waste duing. About 4, tons of this waste was fom machining opeations. The main objective of this poject is to demonstate the feasibility of unning a completely dy machining opeation, which would not only eliminate the use of metalwoking fluid, but also eliminate the contaminated swaf. The swaf can then be fully ecycled. Howeve, in any mateials emoval pocess, most of the input enegy is conveted into heat in the cutting zone. The geneated heat is then tansfeed to the tool and wokpiece, and caied away by the machining fluid and the chips. The absence of the metalwoking fluid educes the amount of heat caied away, esulting in an incease in tool and wokpiece tempeatues. Elevated tempeatue can significantly shoten the tool life. Excessive heat accumulated in the tool and wokpiece can contibute to themal distotion and poo dimensional contol of the wokpiece. The concept behind this eseach is to demonstate that an intenally-cooled machining tool can pefom at the same level as a conventional extenally cooled machining tool and thus eliminate the use of metalwoking fluids Poject Desciption Manufactuing in the US eleases moe toxic emissions than all othe industies except fo metal mining with waste teatment and disposal estimated to cost $7 billion pe yea. Addessing the dilemma of achieving economic gowth while potecting the envionment is a seious societal issue. In machining opeations (metal cutting) metalwoking fluids ae used fo thei lubication and heat dissipation qualities. These metalwoking fluid popeties enable inceased cutting speeds (poductivity) and longe tool life (lowe costs). Besides positively influencing the immediate economics of mateial emoval they also affect plant waste teatment and disposal, ai quality, mist contol, machine maintenance, and electical powe consumption. Metalwoking fluids, on aveage, account fo less than 5% of total plant expenditues, howeve, these fluids can impact moe than 4% of the plant s opeational budget. The National Institute fo Occupational Safety and Health estimates that. million wokes in the US ae exposed to metalwoking fluids by beathing aeosols o though skin contact. These fluids can contain a vaiety of oils and chemical additives while wate-based fluids can suppot micobial gowth such as bacteial and fungal cells and thei bypoducts (endotoxins, exotoxins, and mycotoxins). In many machining pocesses, a cutting fluid seves many system functions including lubication, themal sink, coosion inhibito, chip contol and washing. These fluids can advesely affect the health of the pesonnel in the machine oom. Metal chips in used cutting

3 fluid ae a souce of pollution and must be disposed of in an appopiate manne. Contaminants etained in the scap usually means that the scap cannot be ecycled fo an application simila to the oiginal application. Thee types of cutting fluids ae commonly used: oil with additives such as sulfu, chloine, and phosphous; emulsions, and synthetics containing inoganic and othe chemicals. Thee has been some wok done to eplace these fluids with cyogenic fluids such as liquid nitogen o cabon dioxide. Although this method shows some pomise in inceasing tool life and obviates the need fo cutting fluid emoval and disposal, many technical issues, including safety, emain unesolved. The most common method of applying cutting fluids is flooding. This exposes the woking envionment to fluids that may cause significant contamination to the envionment and health hazads fo the wokes. Disposal of the used cutting fluids ae subject to fedeal, state, and local laws and egulations. It has been documented that the cost of complying with egulations, which can include lage capital investments in coolant equipment and annual opeational costs to maintain cutting fluid systems and dispose of used fluids and swaf in a typical poduction plant can total millions of dollas. In Gemany, the estimated opeating cost due to coolant usage is between 5-5% of total opeating cost. If moe stingent egulations in envionmental pollution ae employed in the futue, we can expect the cost associated with coolants to continue to ise. Recently, thee has been a stong global tend towads the minimization of cutting fluids because they have been demonstated to be pimay souces of industial pollution. The NSF Envionmentally Conscious Manufactuing initiative guidelines have put a majo emphasis on eseach topics that addess the elimination of metalwoking fluids. In ode fo machining pocess to un dy, an altenative method to emove the heat accumulated in the tool-wokpiece egion must be developed. In the mateials emoval pocess, most of the input enegy is conveted into heat in the cutting zone. The geneated heat is then tansfeed to the tool and wokpiece, and caied away by the machining fluid and the chips. The absence of the fluid educes the amount of heat caied away, esulting in an incease in tool and wokpiece tempeatues. Elevated tempeatue can significantly shoten the tool life. Excessive heat accumulated in the tool and wokpiece can contibute to themal distotion and poo dimensional contol of the wokpiece. In this poposal, we shall apply heat pipe technology as a method of emoving heat fom the cutting zone in two majo machining pocesses, namely dilling and milling pocesses to demonstate its feasibility. A thee-dimensional model fo a heat pipe unde otation will be developed, and a solution will be obtained eithe analytically o numeically. These esults will then be coupled with the tansient tempeatue model to pedict the tool tempeatue in the vicinity of the cutting tip. Expeiments will be pefomed unde actual dilling and milling conditions. The esults of the expeiments will be used to (a) quantify the efficiency of the heat pipe cooling effect, and (b) povide the data needed as input to, and validation of, the model. A bette undestanding of intenal cooling of end mills will help advance geene manufactuing pactices enabling Wisconsin companies to become moe competitive paticulaly with inceasing envionmental emediation costs. DESCRIPTION OF RESEARCH DESIGN / PROCEDURE In any machining pocess, mechanical wok is conveted to heat though the plastic defomation involved in chip fomation and though fiction between the tool and the wokpiece. Some of this heat conducts into the cutting tool, esulting in high tool tempeatues nea the cutting edge. Elevated tool tempeatues have a negative impact on tool life. Tools become softe and wea moe apidly by abasion at inceased tempeatue. In many cases, constituents of the 3

4 tool may diffuse into the chip o eact chemically with the wokpiece o cutting fluid. In addition, high tool tempeatues pomote the fomation of Built Up Edge (BUE) on the tool tip. Because of the impact on tool life and BUE, cutting tool tempeatues have been widely studied fo many yeas. Most eseach, howeve, has centeed on the taditional cutting pocesses such as cutting, tuning and milling. Reseach on end mill tool tempeatue is elatively ae. In the end milling pocess, tool tempeatues ae paticulaly impotant because the chips, which absob much of the cutting enegy, ae geneated in a confined space and emain in contact with the tool fo a elatively long time in compaison to the taditional cutting pocesses. As a esult, end mill tool tempeatues ae highe than in othe pocesses unde simila conditions. Theefoe, an effective cooling method is desiable to decease the end mill tool tempeatue. The heat pipe is one of the most effective modes of tanspoting heat without any additional powe input to the system. Since lage quantities of heat can be tanspoted though a small coss-sectional aea ove a consideable distance, heat pipes have been widely used in heat exchanges, themal contol of sola and heat geneation systems, electonic cooling systems, and in othe manufactuing industy applications such as die casting and injection molding, etc. Figue : Physical Configuation of Heat Pipe The physical configuation of a heat pipe is illustated in Figue. The components of a heat pipe ae a sealed containe (pipe wall and end caps), a wick stuctue, and a small amount of woking fluid in equilibium with its own vapo. Typically, the heat pipe can be divided into thee sections: evapoato section, adiabatic (tanspot) section and condense section. The extenal heat load on the evapoato section causes the woking fluid to vapoize. The esulting vapo pessue dives the vapo though the adiabatic section to the condense section, whee the vapo condenses, eleasing its latent heat of vapoization to the povided heat sink. The condensed woking fluid is then pumped back by capillay pessue geneated by the meniscus in the wick stuctue. Tanspot of heat can be continuous as long as thee is enough heat input to the evapoato section such that sufficient capillay pessue is geneated to dive the condensed liquid back to the evapoato. In some cases, such as a themosyphon, gavity is used to etun the condensed liquid to the evapoato, instead of the wick stuctue. This eseach consisted of two majo pats; modeling & simulation, and expeimentation. A compehensive 3-D numeical model fo the heat pipe pefomance was developed and simulated unde simulated heat input conditions simila to the actual cutting conditions. Subsequently, a FEM (finite element model) was developed to couple the esults fom the heat pipe analysis to include the actual dill/end mill tool geomety with ealistic themal bounday conditions imposed at the cutting zone. The constaints of the mateials fo the tool wee also simulated and detemined. Based on the simulated esults, optimized cutting tools wee developed and designed. Base on the numeical esults, six ¾-inch dills and ½-inch dills and 4

5 end mills wee designed with hollow shanks fo incopoation of heat pipes (GE Healthcae). CPC povided the same end mill and dill with a solid shank fo expeimental compaison. Close collaboation of CPC, GE Healthcae and the PI esulted in a tool design that maintains sufficient igidity fo effecting stable cutting while placing the evapoato as close to the cutting edges as possible. A tool holde that can eject the heat eleased fom the condense of the themosyphon was designed as an integal pat of the tool/tool holde system. CPC built the tool while UWM installed the themosyphon. Modeling & Simulation In this study, a numeical model of the vapo flow in an axially otating heat pipe is developed. Suction and blowing velocities at the inne wall of the heat pipe wee assumed. Note that in actual dilling opeations, the suction and blowing velocities at the inne wall of the heat pipe ae elated to a local heat flux input in the evapoato section, and local heat output in the condense section, espectively. A paametic study is conducted fo diffeent otating speeds and diffeent satuation tempeatues of the woking liquid of the heat pipe. These paametes significantly affect the hydodynamics of the vapo flow. It is obseved that the maximum velocity moves to the wall when otating speed is inceased, with the eventual appeaance of flow evesal. The esult of this study will be beneficial fo futhe and moe complete analysis on the inteaction between the vapo flow and the liquid flow. The vapo flows in a heat pipe is in opposite diection to the liquid flow. At high vapo velocity, the shea stess at the vapoliquid inteface could be sufficient to disupt the liquid flow, poducing an entainment limit of the heat pipe. The shea stess at the inteface is popotional to the velocity gadient of the vapo. These paametes ae a vey stong function of the satuation tempeatue of the vapo and the otating speed of the pipe. In this study, the hydodynamics of the vapo flow is investigated in detail fo diffeent satuation conditions. It is woth noting that this effect has been ovelooked fom the liteatue. THE PHYSICAL MODEL The idea of using a heat pipe in a dill/end mill is illustated in Figue. In dilling/end milling opeations, most of the heat is geneated nea the dill/end mill tip. This heat accumulated nea the dilling tip can cause vaious themal damages to the dill as well as the wokpiece, such as tool wea, lage themal esidual stesses, themal expansion and eduction of Figue - Location of heat pipe inside dill and end mill the geometic accuacy. With the heat pipe implemented into the dill/end mill, the heat that penetates into the dill/end mill can be absobed quickly by the heat pipe. With latent heat evapoation in the evapoation section (i.e., nea the dill/end mill tip), this heat can be tanspoted apidly to the condense section (dill shank). Note that dill/end mill shank is usually attached to the tool holde, which has a lage mass and can be viewed as a heat sink. Theefoe, the dill/end mill tip tempeatue can be geatly educed. The latest expeimental esults show that the tempeatue eduction in a heat pipe dill compaed to a solid dill can each moe than 5%. 5

6 Refeing to Figue, it can be seen fom the figue that thee is vapo flow flowing fom evapoato section towad the condense section in the coe egion, with the condensed liquid flowing back to the evapoato section along the pipe inne wall. In this eseach, attention is focused on the vapo flow in the coe egion of the heat pipe. To uncouple the conjugated heat tansfe poblem with the pipe wall, an assumption is needed about the heat flux input at the evapoato section and the heat flux output at the condense section, both heat fluxes being elated to blowing and suction flow conditions at these sections. It is assumed that a tiangula heat flux distibution is pesent at the evapoato and a unifom heat flux distibution is pesent at the condense. This tiangula heat flux distibution is a easonable assumption because highe heat flux is geneated at the tip of the dill/end mill. Note that, unde steady state condition, the amount of heat enteing the pipe though evapoato section must be equal to the total heat leaving the condense section. Thus, the heat flux emoved fom the condense section can be easily estimated. In this study, wate is selected as the woking fluid; vapo is assumed to be a satuated ideal gas and the flow is assumed to be lamina and incompessible. Mathematical Fomulation Evapoation and condensation ae consideed unifom aound the cicumfeential diection. Based on this assumption, the poblem becomes axis-symmetic and all the deivatives with espect to the cicumfeential diection ae zeo. Thus, the poblem becomes two-dimensional in cylindical coodinates. Howeve, in axis-symmetic swiling flow the momentum equation in the cicumfeential diection has to be solved as well. The consevation equations fo the vapo flow with the axis-symmetic condition become: Consevation of mass ) ( = + z z () Momentum equation in the adial diection θ θ ρ ρ µ ρ ρ z p z z Ω = + ) ( ˆ ) ( ) ( () Momentum equation in the cicumfeential diection z z z Ω + = + ρ ρ µ ρ ρ θ θ θ θ θ θ ) ( ) ( ) ( (3) Momentum equation in the axial diection + + = + ) ( ˆ ) ( ) ( z z p z z z z z z µ ρ ρ (4) whee is the educed pessue pˆ ˆ p p Ω = ρ (5) and, and ae the adial, cicumfeential and axial velocities espectively. Note that the coodinate system is assumed fixed to the otating pipe (non-inetial fame); then, the Coiolis acceleation appeas explicitly in the momentum equations. The centifugal acceleation is combined with the pessue and it does not appea explicitly (see equation (5)) θ z It is woth noting the momentum equation in the adial and cicumfeential diection have additional coupling though the tems θ ρ and θ ρ Ω in the diection and ρ θ and 6

7 ρ Ω in the θ diection. Special teatment of these tems is equied, and is discussed in the next section. If the coodinate system is assumed to be an inetial fame (not-fixed to the otating pipe) the tems ρ Ωθ and ρ Ω do not appea explicitly in equations () and (3) espectively. Bounday Conditions At the cente line of the pipe (fom symmety) = θ = z = (6) Since the coodinate system is fixed to the otating pipe, at the end caps of the pipe (z= and z=l), the adial and axial velocities ae zeo (no-slip condition). At the inne wall of the heat pipe (R = D/), the cicumfeential and adial velocities ae assumed zeo (no-slip condition, no intefacial stesses ae consideed). Fo the inetial fame, the non-slip condition at the walls fo the cicumfeential velocity is θ = Ω instead of zeo as it is fo the non-inetial fame. Fom the theoetical point of view, the choice of the efeence fame is ielevant but fom the numeical point of view, using the otating fame (i.e., non-inetial fame) esults in bette numeical stability. Evapoation and condensation at the inne wall of the evapoation egion and the condensation egion of the heat pipe ae modeled as blowing and suction velocities and ae elated to the local heat ate as: q( z) w = ± (7) π D ρ h fg whee q(z) is the local ate of heat tansfe pe unit length, D is the diamete of the heat pipe, ρ is the density of the vapo and is the latent heat of vapoization. The positive sign coesponds to suction action in the condense and the negative sign coesponds to the blowing action in the evapoato. The satuation tempeatue is elated to the satuation pessue at the liquid-vapo inteface fo an ideal gas, though the Clausius-Clapeyon equation: h fg R P T sat sat = v ln (8) T h fg P hee T and P ae efeence tempeatue and pessue at satuation condition (i.e.. 5 Pa and 373 K) and R v is the gas constant fo the vapo. The density of the vapo is linked to the satuation tempeatue and satuation pessue though the equation of state fo an ideal gas: P sat = ρ R v T sat (9) 7

8 At the adiabatic egion the adial velocity is assumed to be zeo (impemeable wall) as well as the cicumfeential and axial velocities (no-slip condition). Figue 3 shows the physical domain and the coodinate system of a otating heat pipe. The development of the fiction coefficient along the pipe in the plane -z, can be defined as: * z z µ * τ n n f o = ρ w w * z f Re * = w ρ w w = Re w = () n * n * Hee, z and ae the dimensionless axial velocity and the dimensionless diection nomal to the wall. Fo all the cases pesented in this study the Reynolds numbe is the same, so the fiction coefficient f is a measue of the axial velocity gadients at the wall. Numeical Modeling Fo the puposes of the numeical analysis, it is useful to have a geneic consevation equation, fom which the equations of consevation of mass and momentum ae obtained. This geneic () θ z θ z D Ω Le La Lc w w Figue 3 Physical domain and coodinate consevation equation in cylindical coodinates can be witten as: ( ρ φ) ( ρ zφ) φ φ + = Γ Sφ z ( ) + z + whee φ is a geneic popety, Γ is the diffusivity fo the geneic popety φ, and () is the souce tem. It can be seen fom Table that one can epoduce the govening equations fom this geneic equation. The advantage of the geneic consevation equation is in development of the numeical code because one needs to deal with only a single equation of that fom. Note that, fo convenience, the pessue gadient tem is included in the souce tem in equation (). In the numeical scheme, this tem is teated sepaately since the pessue field has to be obtained as pat of the solution. A pessue coection (o pessue equation) is deived fom the momentum equation to enfoce mass consevation. This is the basis of the SIMPLE-like algoithms. S φ 8

9 The discetization in cylindical coodinates geneates additional coupling between the momentum equations as shown in Table. These tems ae teated as exta body foces including the Coiolis foce tems (i.e., ρ Ωθ and ρ Ω ). The tems θ ρ and µ θ in the θ- momentum equation ae teated implicitly when the contibution of these tems to the cental coefficient in the discetized equations is positive, in ode to avoid instabilities of the iteative solution scheme that can occu when diagonal dominance of the matix is not maintained. Othewise, these tems ae teated explicitly. A contol volume appoach is used to discetize the govening equations. The geneic equation is discetized using the powe law scheme. The pessue velocity coupling is solved using the SIMPLEC algoithm. Table - Tems in the Geneic Consevation Equation φ Γ S φ Equation - continuity pˆ θ µ + ρ + ρ Ωθ -momentum θ θ µ ρ µ θ ρ Ω θ-momentum z µ Numeical pocedue pˆ z-momentum z. Solve the, θ and z momentum equations simultaneously using the cuent values fo pessue and velocities (in the fist iteation a zeo velocity and pessue field is assumed, except at the boundaies whee the bounday conditions ae applied).. Since the velocities obtained in Step may not satisfy the continuity equation locally, the pessue coection equation is solved to obtain the necessay coections fo the velocity field (using the SIMPLEC algoithm the pessue does not need a coection). 3. Coect the velocity field until continuity is achieved. 4. Repeat Steps to 3 until the esidual of the momentum equations and pessue equation ae less than a pe-assigned convegence citeion. The convegence citeion used is the esidual of each equation less than -6. Gid independence was checked by systematically vaying the numbe of contol volumes in the and z diections until the solution was adequately gid independent. Table summaizes the gid efinement test. Fo this test, the case with a otational speed ω = pm and opeating tempeatue T sat = ºC was selected. The test is pefomed fo thee diffeent gid sizes and the maximum dimensionless axial velocities at the middle of the evapoato, adiabatic and condense section ae compaed. The maximum change is less than.5 % when the gid size change fom 4 to 5 6. A gid size of 4 was selected fo all the calculations. The computational domain was divided in thee sub-domains: evapoato, adiabatic egion, and condense. A numbe of contol volumes wee used fo the evapoato and condense espectively and 6 contol volumes fo the adiabatic egion. In the adial diection 4 contol volumes wee used. 9

10 Maximum Dimensionless axial velocity Table Gid Independence Test Section at the Gid size middle of: Evapoato Adiabatic Condense RESULTS AND DISCUSSION In the discussion that follows, the axial, adial and cicumfeential velocity pofiles at diffeent otating speeds and axial locations will be examined closely. The effect of diffeent satuation conditions on the velocity pofiles will be demonstated. Note that this effect has neve been investigated in any pevious studies. A benchmak compaison with numeical esults is also pesented. Fo compaison pupose, the esults fom Faghi, et al. (993) ae epoduced in Figue 4. The velocity pofiles in Figues 4 and 5 ae nondimensionalized using the aveage axial velocity at the adiabatic egion, z = 4 w Lc / D, as the efeence velocity. Hee, the axial velocity pofiles fo a unifom heat flux (unifom blowing and suction velocities) fo diffeent otating speeds and a Reynolds numbe of Re=. ae used. Fo this test the following paametes ae applied: Le=. m, La=.6 m, Lc=. m, D=. m with satuation tempeatue at ºC. The pesent numeical simulation has successfully epoduced Faghi, et al. (993) esults with essentially no eos. elocity pofiles fo othe Reynolds numbes wee also benchmaked with excellent ageement. To demonstate the effect of diffeent heat flux input conditions, Figue 5 shows the axial velocity pofiles fo a tiangula heat flux input in the evapoato section instead of the unifom heat flux input as shown in Figue 4. All othe conditions and geometic dimensions ae the same as in Figue 4. It can be seen fom Figue 5a that the axial velocities at the evapoato ae vey diffeent than the case fo unifom heat flux inputs as shown in Figue 4. Thee is no supise that the maximum axial velocity is lage fo the case of tiangula heat flux input since moe heat entes the fist half of the evapoato section. This causes moe vapos to be geneated, thus leading to highe maximum axial velocity. Note that the blowing velocity is diectly popotional to the heat flux input (see equation (7)). When the heat pipe is stationay (i.e., pm), the axial velocity pofile is paabolic. As the otating speed inceases, a significant change is seen in Figues 4 and 5. Nea the heat pipe wall, the vapo axial velocity inceases as the otating speed inceases. This is because the Coiolis and centifugal foce ae both acting in the adial diection (see Table ). The Coiolis foce, ρω θ depends on two components, θ and Ω. Lage otating speed Ω and/o lage cicumfeential velocity θ, causes lage axial velocity gadient nea the wall because these foces ae squeezing the flow fom the cente to the wall. It is woth pointing out that the othe Coiolis foce tem, ρω (see Table ), also plays a significant ole in detemining the cicumfeential velocity, θ, which in tun affects the Coiolis foce in the adial diection. Due to the stonge heat flux input in the fist half of the evapoato section, the adial velocity (i.e., blowing velocity) is lage, thus inceasing the stength of the cicumfeential velocity, and the Coiolis foce in the adial diection. This lage axial velocity

11 .5 dimensionless axial velocity /R a pm 7 pm 4 pm 8 pm dimensionless axial velocity /R a pm 7 pm 4 pm 8 pm.5.5 dimensionless axial velocity /R dimensionless axial velocity /R b pm 7 pm 4 pm 8 pm pm 7 pm 4 pm 8 pm dimensionless axial velocity /R c pm 7 pm 4 pm 8 pm dimensionless axial velocity /R c pm 7 pm 4 pm 8 pm Figue 4 Axial velocity pofiles (fo a unifom heat flux, Faghi et. al. (993)) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. Figue 5 Axial velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense.

12 gadient can be seen in Figue 4a. As the otating speed inceases futhe, it can be seen that the axial velocity gadient inceases significantly. Howeve, in the coe egion, the axial velocity deceased significantly with inceasing otating speed. This is because the incease in mass flow ate nea the wall egion must be balanced by the decease in the mass flow ate nea the coe egion to conseve mass. As the otating speed inceases to pm, coe egion flow evesal is obseved. Figues 5b and c demonstate the effect of diffeent otating speeds on the axial velocity distibutions at adiabatic section and at the condense section, espectively. It is noted that, in compaison to Figues 4b and c, the velocity pofiles at the cente of the adiabatic egion and of the condense ae almost the same. This indicates that the changes in the input condition (i.e., fom unifom to tiangula heat flux distibution) at the evapoato do not have a stong effect of the velocity distibution at the adiabatic and the condense sections. It can be seen that the axial vapo flow has achieved a fully developed condition in the adiabatic egion. The movement of the egion of maximum velocity to the heat pipe wall with inceasing otational speed is efeed to as the Ekmann suction in otating flow. It is impotant to note that even fo small Reynolds numbe, such as Re=., sepaation can occu fo inceasing otating speed. This tuns the poblem into a fully elliptic one. In the case of a tiangula heat flux distibution, sepaation at the evapoato occus fo lowe otating speed as it can be seen fom compaison between Figue 4a and Figue 5a. In the pesent study, we ae aiming at a fundamental study of vapo flow on an application of heat pipe dill fo dilling opeation conditions. The dimension of the heat pipe and paametes fo the cuent study ae summaized in Table 3: Table 3: Heat Pipe Geomety and Paametes Le.5 m Q total 85 W La.5 m µ -5 kg/(m s) Lc.5 m h fg 3 KJ/kg D.5 R v.465 KJ/(kg K) This type of heat pipe, which has been inseted ion the dill, is significantly diffeent fom the one used in Faghi, et al. (993). The heat pipe used in this study has much shote evapoato section and condense section. This is because the heat is concentated only in the dill tip aea, thus a smalle heat input aea ae equied. Note that this may cause highe heat flux input due the lage intensity of the heat geneation in the dill tip aea. The density is calculated fom the equation of state (9) fo diffeent satuation conditions. Fou diffeent satuation conditions wee studied (Note that the woking condition depends on satuated tempeatue o woking tempeatue): Table 4: Satuation Conditions and Blowing elocities Psat (Pa) Tsat (ºC) ρ (kg/m 3 ) w (m/s) Re

13 Fo each of these cases, fou diffeent otational speeds wee assumed:, 4, 8 and pm (, 4.89, and 5.66 ad/s). The heat flux distibutions at the evapoato and the condense wee calculated fom the condition that the amount of heat enteing and leaving the pipe has to be the same. Figues 6, 7, 8 and 9 show dimensionless axial velocity pofiles fo fou diffeent satuation tempeatues: ºC, 9 ºC, 75.8 ºC and 53.4 ºC espectively, as a function of the dimensionless adial coodinate /R. In these figues, dimensionless axial velocities ae nomalized with the suction velocity, w, at the condense egion. In all the cases the heat flux input and the Reynolds numbe ae kept the same. In the wok by Faghi et al. (993), a fixed satuation tempeatue (i.e., o C) was assumed in thei study, while the Reynolds numbe and the otating speed ae vaied. Howeve, it is woth pointing out that fo diffeent satuation tempeatues, the density, the blowing velocity as well as the hydodynamics of the flow change. It is not enough to specify only the Reynolds numbe and the otational speed to completely define the poblem. It will be demonstated that the satuation tempeatue plays an impotant ole in the vapo flow velocity distibution. If we compae the esults depicted in Figues 6, 7, 8, and 9, it can be seen clealy that the satuation tempeatue has a stong effect on the axial velocity distibution. It can be seen fom these fou figues (Figues 6, 7, 8, and 9) that when the satuation tempeatue deceases, the effect of the Coiolis foce diminishes. This is because the lowe the satuation tempeatue esults in smalle vapo density (see Table 4). Note that the Coiolis foces depend on the magnitude of the density (see Table ). When the satuation tempeatue deceases fom o C to 53.4 o C, the density changes by a facto of appoximately 6 (i.e., fom.586 kg/m 3 to. kg/m 3 ), implying a eduction in Coiolis foce by the same facto. By deceasing the satuation tempeatue, the velocity pofiles appoaches to the cases without otation as shown in Figue 9. Note that in the typical stationay blowing/suction heat pipe condition, the blowing bounday condition tends to stabilize the flow, and the suction bounday condition tends to destabilize the flow, and thus the flow evesal can be seen in the condense section. It is also inteesting to note that the otating effect in the condense section tends to stabilize the flow due to the cicumfeential Coiolis foce. Figues and show the dimensionless adial velocity pofiles nomalized with the suction velocity at the condense w as a function of the adial coodinate /R, fo the case with satuation tempeatue at o C and 53.4 o C, espectively. Note that at the evapoato, the input velocity at the wall (/R=.) is negative (blowing) and positive (suction) at the condense. Fo T sat = ºC in Figue a, a negative adial velocity at the evapoato fo otating speed up to 4 pm was obseved. It can be seen that at 4 pm, the adial velocity nea the cente becomes vey small. With futhe incease in otational velocity, the slope of the adial velocity becomes nealy zeo. This implies that the axial velocity is negative, a sign of flow evesal. The eason that this happens is because the otating effect causes the axial velocity gadient to incease, and thus in ode to satisfy mass consevation, axial flow evesal occus nea the coe egion of the heat pipe. Theefoe, the adial velocity becomes positive to satisfy continuity. Simila eason can be applied to the condense section (Figue c), whee the wall bounday condition now changes to suction condition (i.e., positive adial velocity). Thus, a negative axial velocity implies the adial flow becomes negative (i.e., flow evesal). Fo the case with T sat = 53.4 o C, the otating induced Coiolis foces have diminished geatly as explained above, thus the vaiation of adial velocity due to Coiolis foce effect is also insignificant as shown in Figue. 3

14 8 8 Dimensionless axial velocity /R a pm 4 pm 8 pm pm Dimensionless axial velocity /R a pm 4 pm 8 pm pm 4 4 Dimensionless axial velocity pm /R 4 pm 8 pm pm b Dimensionless axial velocity pm /R 4 pm 8 pm pm b 8 8 Dimensionless axial velocity /R c pm 4 pm 8 pm pm Dimensionless axial velocity /R c pm 4 pm 8 pm pm Figue 6 Axial velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. T sat = ºC Figue 7 Axial velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. T sat = 9 ºC 4

15 Dimensionless axial velocity /R a pm 4 pm 8 pm pm Dimensionless axial velocity /R a pm 4 pm 8 pm pm 4 4 Dimensionless axial velocity pm /R 4 pm 8 pm pm b Dimensionless axial velocity pm /R 4 pm 8 pm pm b 8 8 Dimensionless axial velocity /R c pm 4 pm 8 pm pm Dimensionless axial velocity /R c pm 4 pm 8 pm pm Figue 8 Axial velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. T sat = 75.8 ºC Figue 9 Axial velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. T sat = 53.4 ºC 5

16 Dimensionless adial velocity pm 4 pm 8 pm /R pm Dimensionless adial velocity /R pm 4 pm 8 pm pm - - a a Dimensionless adial velocity /R pm 4 pm 8 pm pm Dimensionless adial velocity /R pm 4 pm 8 pm pm -. b -. b.5.5 Dimensionless adial velocity /R c pm 4 pm 8 pm pm Dimensionless adial velocity /R c pm 4 pm 8 pm pm Figue Radial velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. T sat = ºC Figue Radial velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. T sat = 53.4 ºC 6

17 Cicumfeential velocity θ (m/s) /R pm 4 pm 8 pm pm Cicumfeential velocity θ (m/s) /R pm 4 pm 8 pm pm - a - a Cicumfeential velocity θ (m/s) /R pm 4 pm 8 pm pm Cicumfeential velocity θ (m/s) /R pm 4 pm 8 pm pm - b - b Cicumfeential velocity θ (m/s) /R pm 4 pm 8 pm pm Figue Cicumfeential velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. T sat = ºC c Cicumfeential velocity θ (m/s) /R pm 4 pm 8 pm pm -.5 Figue 3 Cicumfeential velocity pofiles (fo a tiangula heat flux distibution) at the middle of a) Evapoato, b) Adiabatic egion, c) Condense. T sat = 53.4 ºC c 7

18 Figues and 3 show cicumfeential velocity pofiles as a function of the adial coodinate /R fo the cases with T sat = ºC and T sat = 53.4 ºC, espectively. Fo solid otation, the cicumfeential velocity is a linea function of, θ =Ω. Howeve, with the effect of Coiolis foce, the cicumfeential velocities ae no longe linea as shown in Figues and 3. In the evapoato section, Figues a and 3a, it can be seen that the cicumfeential velocity inceases significantly due to the Coiolis foce, ρω, which is aiding the flow in the same diection of the solid otation. Due to the no-slip bounday condition, the cicumfeential velocity at the wall equals the solid otation velocity. The cicumfeential velocities ae lage fo the case of low satuation tempeatue (i.e., T sat = 53.4 ºC) because the adial velocity is lage as shown in Figue a. In the adiabatic section, since the adial velocities ae small, the distotions of the velocity pofiles due to the Coiolis foces ae not significant. In the evapoato section, howeve, the tends ae evese. In Figues c and 3c, the cicumfeential velocities nea the heat pipe wall have been suppessed significantly. This effect is stonge fo the case with highe satuation tempeatue case, T sat = ºC, since the Coiolis foce is stonge in the θ diection at this tempeatue. Figue 4 shows the development of the fiction coefficient along the pipe in the -z plane. Fo all the cases pesented in this study the Reynolds numbe is the same, so the fiction coefficient f is a measue of the axial velocity gadient at the wall (see equation ()). It can be seen that the fiction coefficient inceases monotonically in the evapoato egion due to the development of the axial velocity pofiles. At the middle of the adiabatic section the fiction coefficient is essentially constant showing that the flow has eached a fully developed condition. Figue 4a also shows that the fiction facto inceases as the otating speed is inceased. Howeve, the otating effect on fiction coefficient is negligible due to the diminishing effect of Coiolis foces due to low satuation tempeatue as shown in Figue 4b. It is woth noting that in Figue 4a, the fiction coefficient becomes negative fo the stationay case (i.e., pm), this Opeating tempeatue T sat = C 3 Opeating tempeatue T sat =53.4 C 9 8 Fiction coefficient axial diection z/l pm 4 pm 8 pm pm a Fiction coefficient axial diection z/l pm 4 pm 8 pm pm b Figue 4 Fiction facto along the pipe fo diffeent otating speeds indicates that flow evesal occus at the condense section. This is because the suction bounday condition at the condense section causes the flow evesal. Fo inceasing otating speeds, the fiction coefficient stats to incease and becomes positive at the condense section. This eveals that the Coiolis foces tend to stabilize the flow as descibed ealie. Fo lowe satuation tempeatue as shown in Figue 4b, howeve, thoughout the otating speed ange studied (i.e., - pm), the flow evesal exists. Again, this is due to the diminishing Coiolis foce effect. 8

19 It can be seen that the effect of the suction velocity in the condense popagates fathe upsteam fo inceasing otating speeds at lage satuation tempeatue as in Figue 4a. In Figue 4b, howeve, the effect of the suction bounday condition in the condense is not felt upsteam, except in a vey shot distance. It is impotant to point out that the magnitude of the velocity gadient in the condense, fo an opeating tempeatue of ºC, is about fou times highe than the one fo T sat = 53.4 ºC fo the case of pm. This demonstates the stong local effect of L Opeating Tempeatue ºC and ω = pm R o Opeating Tempeatue 53.4 ºC and ω = pm Opeating Tempeatue ºC and ω = pm Opeating Tempeatue 53.4 ºC and ω = pm Figue 5 ecto plot in the z- plane the Coiolis foce. Figue 5 shows a vecto plot in the plane -z fo a otating speed of pm and pm at opeating tempeatues of ºC and 53.4 ºC. It can be seen clealy that fo T sat = 53.4 ºC the velocity field is not vey much influenced by the otating speed and in the adiabatic section is almost a paabolic pofile. Also, the evesal flow at the cente of the pipe is clealy seen fo the case of T sat = ºC and ω = pm. This is consistent with esults shown in Figues 6 and 9. CONCLUSIONS A numeical study was caied out to analyze the effect of otating speeds and diffeent satuation conditions on the hydodynamics of the vapo flow of a otating heat pipe fo dilling applications. The following conclusions can be made:. Fo the same amount of total heat input and geometic configuation, flow patten is stongly influenced by the satuation tempeatues as well as the otating speed.. Fo inceasing otating speeds the axial velocity inceases nea the wall due to the stong adial Coiolis foce acting towad the wall. Meanwhile, the axial velocity nea the centeline deceases due to mass consevation and flow evesal can occu at lage otating speed. 9

20 3. The Coiolis foce is educed fo smalle satuation tempeatues whee inetial effects dominate. This indicates that fo lowe satuation tempeatues the otating effect is less impotant. 4. Flow evesal can occu even fo small Reynolds numbes and the poblem become fully elliptic. A fully developed condition is eached at the adiabatic section of the heat pipe. Suction bounday condition in the condense section influences the upsteam velocity distibution futhe as the satuation tempeatue and the otating speed ae inceased. 5. The cicumfeential velocity deviates vey significantly fom solid body otational velocity Ω. This effect is stonge fo deceasing opeating tempeatues. 6. Fo numeical analyses, using the coodinate system fixed to the otating fame (i.e., noninetial) is ecommended since this system shows bette numeical stability, especially fo high otating speeds. The esults of this study will be used fo a moe complete analysis when the liquid flow and heat conduction on the wall as well as the effect of the contact esistance between the heat pipe and the dilling tool ae consideed. Themal Management of a Heat-Pipe Dill/End Mill - A FEM Analysis A peliminay analysis was caied out fo the pupose of veifying the concept of heat pipe cooling. Fom the heat tansfe point of view, one of the pimay assumptions made in the analysis was that a dill/end mill could be appoximated by a cylinde. This assumption was made based on vey caeful mathematical and physical consideations. In the cente of the cylinde a heat pipe was modeled as a small hollow cylinde with the pipe wall maintained at a fixed tempeatue (i.e. isothemal). This was justified by the fact that the lage latent heat of the woking fluid in the heat pipe causes small vaiations in the heat pipe tempeatue. Due to the symmety in the angula diection (i.e. cicumfeential diection), the tempeatue dependence in this diection was neglected. Thus, the enegy equation educed to a two-dimensional conduction equation in cylindical coodinate system with constant themal popeties, which can be witten as: T T T T = + + (3) α τ z T whee T is the tempeatue and α T is the tool themal diffusivity. The esults obtained fom expeiments and peliminay FEA ae shown in Figue 6. Detailed analysis has been caied out to show the appopiateness of this assumption. A FEM themal analysis involving the actual dill and cylinde with simila physical configuation is used fo the pupose. Since the main pupose of the analysis is to show the compatibility between the dill and cylinde, hence the bounday conditions that would appoximately epesent the actual conditions expeienced by the dill in dilling opeation have been used.

21 Model Development 3 5 Tempeatue ( C) 5 5 S o lid D ill (e xp e im e n ts) Solid Dill(FEM) Heat pipe, no heat sink (expeiments) Heat pipe, no heat sink (FEM ) Heat pipe, heat sink (expeiments) Convection B.C. (FEM ) Time (sec) Figue 6: Dilling Tempeatues in the Tip It is intended to compae two geometies, an actual dill and a cylinde, which is consideed as an appoximation to the actual tool fo the pesent peliminay analysis. To pefom the analysis, ANSYS was used. Fist an actual dill is consideed. This dill geomety has been ceated using Po-E taking into consideation the actual tool pofile and hence it epesents the actual dill used in industy. The specifications of the dill ae descibed in Figue 7. The specifications ae as follows:. ¾ inch, two-flute dill H.S.S.,.5 inch long.. 38º RHH-RHC Heavy duty Milled web, blend thinned to.6 chisel point. 4. Finished Shank to.75/.7495 inch. To analyze the effect of the heat pipe a cylindical cavity epesenting heat pipe has been made in the geomety. Figue 8 shows the dill that was used fo analysis. Figue 7 Typical twist dill/end mill design A gid convegence test was caied out on the model to test the gid size that was used in the analysis.

22 Figue 8 Model of Dill Used in Analysis. Themal Analysis: The element type used fo this analysis is Solid 87. It is a 3-D node tetahedal themal solid element. This element type has a quadatic tempeatue function. The tetahedal shape allows meshing the iegula geometies moe compehensively. Since the element is defined by nodes it can epesent cuved edges and sufaces moe accuately than linea elements. It is ecommended to use this type of element if accuacy of esults is highly impotant. As well, bette esults ae obtained as compaed to linea elements and in many cases with fewe elements. Figue 9 shows the element used. Figue shows the mesh distibution in the twist dill consideed in this study. The gid convegence test showed that a gid size of 983 elements yielded the most stable esults. Any futhe incease in the numbe of elements Figue 9 Solid-87 Element didn t affect the tempeatue distibution significantly (less than.%). Hence a mesh of 983 elements was selected fo the futhe analysis. The mateial fo dill is consideed to be high speed steel. The diffeent themal and physical popeties consideed fo the dill ae: Conductivity, K = 4 W/m o C; Specific heat, Cp = 46 J/kg o C; Density, ρ = 785 kg/m 3

23 A B Figue Meshed Dill Geomety The ambient tempeatue is consideed on the suface A, which is taken as 5 o C, the tempeatue in the heat pipe (the intenal hole) is consideed to be constant at o C. A heat input of 85 W is applied at the tip of the dill. The aea of the tip is.99 x -3 m and hence a unifom heat flux of kw/m is applied on the tip. Eveywhee else, that is on all othe sufaces an insulate bounday condition is applied. The esults ae pesented in Figue. As seen fom Figue, the peak tempeatue occus at the tip of the dill. The maximum tempeatue is o C. This can be expected since the maximum heat flux is applied at the tip of the dill. Only the maximum tempeatue will be used in the compaison since Figue Tempeatue Distibution in the Dill this is the tempeatue causes the tool failue. The othe sides of the dill ae insulated except fo the fa end of the dill, which is maintained at ambient tempeatue. Thus all the heat flows though the dill tip into the dill. Now, to compae the actual maximum dill tempeatue with that of a cylinde, which is consideed as an appoximation to the actual dill, a simila FEM themal analysis is pefomed on the cylinde. 3

24 Figue Cylinde Geomety Figue shows the cylinde, which is the appoximation that was consideed by the PI. The majo dimensions of the cylinde ae exactly simila to the dill used in the ealie analysis. The diamete of the cylinde is equal to the flank diamete of the dill. The heat pipe used in this cylinde is of exactly the same dimensions as that used in the dill analysis. Figue 9 shows the meshed geomety of the cylinde. The type of element used fo the analysis is solid 87, the 3-D themal element used in the analysis of dill. A B Figue 3 Meshed Cylinde The bounday conditions ae applied to the cylinde ae as follows: The tempeatue on suface A is maintained at 5 o C, the tempeatue in the heat pipe is maintained at o C. Heat input of 85 W is consideed though the tip of the cylinde, the aea of the tip is.8 m, and hence a unifom heat flux of kw/m is applied on the tip. The esults of the analysis ae pesented in Figue 3. As seen fom Figue 4, the maximum tempeatue occus at the tip of the cylinde. The maximum tempeatue that is expeienced in the dill is o C. The distibution of the tempeatue emains simila to the one obtained in the analysis on dill. 4

25 Figue 4 Tempeatue Distibutions in Cylinde. Compaing the maximum tempeatues obtained in the actual dill and a cylinde, we can ealize an eo of 4.% in pedicting the maximum tempeatue in actual dill using an equivalent cylindical geomety. Exploatoy uns fo inceasing the total heat inputs have been pefomed and the pecentage diffeence in tempeatues emains the same. Thus it can be infeed that the appoximation would not lead to any significantly eoneous esults in pedicting the maximum tempeatue. This analysis has been caied out to pove the fact that while pefoming numeical simulation of the dill with heat pipe using a customized numeical code, the dill can be assumed to be a cylinde and the esults hence obtained would be within ange of acceptance. This would be helpful especially in continuing effots of the authos to model the actual physics of the heat pipe close to eality. Optimization Analysis: One of the pimay objectives of this pape is to come up with technical details of the heat pipe that can lead to least effect on the stength of the dill and at the same time being themally vey effective as a heat sink. Thus, a paametic study was pefomed to wok out citical details of the heat pipe that wee identified as the length of the heat pipe and the diamete of the heat pipe fo both highe stuctual stability and themal efficiency. The manufactuing constaints ae also consideed in the design paametes of the heat pipe. Model Set-up To make the analysis close to actual dilling application, geomety of a commecially available dill was used in the analysis. The technical specifications of the dill emain the same as in the ealie analysis. Diffeent heat pipe diametes anging fom.5 in. to.3 inches wee used fo the analysis. The lengths of the heat pipe anged fom 8 in. to 9.75 ae used in the analysis. The geomety was meshed vey finely with 7, elements fo bette accuacy. Stuctual Analysis Stuctual analysis was caied out with the dill fo vaying diametes of heat pipe and diffeent lengths of heat pipe to investigate the effect of that on the stesses induced in the dill in the cutting opeation. The type of element used in the analysis is solid-9 element. This element is a 3-D node tetahedal stuctual element. It has a quadatic displacement function. Thus it 5