case studies in thermal engineering...2017/06/27 · y. taamneh case studies in thermal engineering...

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Case Studies in Thermal Engineering

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Thermal analysis of gas turbine disk integrated with rotating heatpipes

Yazan TaamnehDepartment of Aeronautical Engineering, Jordan University of Science and Technology, P. O. Box 3030, 22110 Irbid, Jordan

A R T I C L E I N F O

Keywords:Heat pipesTurbine diskTransient analysisFinite element

A B S T R A C T

The combination of the rotating heat pipe with conventional air cooling technique can be con-sidered as an emerging and effective cooling technique for gas turbine disk. Accordingly, thethermal steady and transient analysis of a simplified turbine disk integrated with heat pipes havebeen numerically investigated. The steady and transient temperature variations in the presenceand absence of heat pipes were investigated for various parameter, such as the thermal con-ductivity of the disk, the convective heat transfer coefficient for both the air and heat pipes, thedimension of the disk, and the number of heat pipes. The thermal analysis were performed byusing finite element (FE) modeling software ANSYS-17.2. The extensive numerical simulationsshowed that when the number of heat pipes equal to 32, the maximum temperatures at the diskedge can be decreased by more than 100 degree. Additionally, increasing the convective heattransfer coefficient of the working fluid inside the heat pipes up to 10,000 W/m2.°C, the max-imum temperature at the disk rim can further be reduced by more than 280 degree. It has alsobeen observed that the time required to achieve the minimum steady-state temperature was moresensitive to the air convective heat transfer coefficient.

1. Introduction

Temperature is one of the most significant factors affecting the gas turbine cycle efficiency. Increasing the turbine inlet tem-perature improves both thrust to weight ratio and decreases the specific air consumption [1,2]. However, the desirability of highturbine inlet temperature is often overlapping with the capacity of the material to resist this rise of heat. Moreover, the outer diskedge in a modern gas turbine engine (i.e rim) is always close to a high temperature working fluid, and may approach 1300 K. Thus,these critical locations require higher material performance than others which improved the creep resistance of disk structure.Therefore, turbine blades, vanes and disk cooling technique are crucial for a safe operation and heat flow improvement. In the pastdecades, many researches associated with turbine disk cooling have confirmed that the local heat-transfer coefficient at the disk edgeis relatively low. Impinging liquid jet onto rotating turbine disk is often used to supply high local heat transfer coefficient, but thehigh cost of implementation and utilization is an important limiting factor [3–7]. In more advanced aero-engines and gas turbines, asmall percentage of high pressurized air is extracted from various locations in the compressor for sealing and cooling purposes. Someof the air is employed for cooling the turbine blades, nozzle guide vanes, and the turbine disks. Steam has been used as alternativecoolant for the gas turbine blade cooling. Steam cooling as applied to gas turbine blades has many advantages over traditional aircooling such as high cooling efficiency, fast cooling speed, and simple structure. However, it is not adequate for operation and is notpractical for an aircraft gas-turbine engine. It is well known that higher gas turbine power density can be achieved as a result ofengine size reduction. Thus, the area available for the cooling process at the disk edges will be minimized, and the upper temperature

http://dx.doi.org/10.1016/j.csite.2017.09.002Received 27 June 2017; Received in revised form 7 September 2017; Accepted 8 September 2017

E-mail address: [email protected].

Case Studies in Thermal Engineering 10 (2017) 335–342

Available online 09 September 20172214-157X/ © 2017 The Author. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

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limits incorporated the aircraft engine will be more significant. Furthermore, what makes the temperature along the disk rim veryhigh is the fact that disk material is poor in thermal conductivity. In addition, the traditional methods of cooling are woefullyinefficient. The needed heat transfer surface area for the cooling purpose is limited. Such extraordinary gas turbine working con-ditions and size constraints require a new and more efficient cooling technique. Based on this understanding, the most features of thecommon practice methods for the enhancement of cooling is to employ the radially rotating heat pipes [8–14].

Generally, heat pipe is passive heat transfer-device that merges the principles of both thermal conductance and phase mutation toconvey the heat between two materials. The working fluid inside the heat pipe comes into contact with the hot interface and convertit into a vapor by soaking up heat from that surface. The heated working fluid then moves over the heat pipe to the cold region andsubsequently condensing the vapor by releasing the heat there. The working fluid then comes back to the hot region to repeat thecycle by many mechanisms such as centrifugal force or capillary motion. A heat pipes are extremely high effective thermal conductorsbecause of their high boiling and condensation heat transfer coefficients. The advantage of heat pipes over many other conventionalmechanisms is in their great efficiency in conveying heat. Moreover, simplicity in design, manufacturing, and the ability to dominatethe amount of heat at high temperature scales make them distinctive and unlike any other methods [15–18].

The impact of the low-temperature heat pipes on the temperature decrease on the periphery of the disk was numerically estimatedby Ling et al. [19]. The numerical analysis was based on the comparison between disks in the presence and absence of the heat pipes.The analysis of their results showed that heat pipes are highly efficient in the cooling process, which can decrease the temperature ofthe disk edge to over 100 °C under similar working conditions. This analyses was only performed on the disk, while the effect of theheat pipes cooling on the blades were neglected. They found that the use of miniature heat pipes with a liquid metal as an idealcoolant in disk cooling are effective, because they have a high heat transfer capacity compared to heat pipes working on water as anideal coolant. Based on the results of Cao (1997), the effective thermal conductance of heat pipe working on liquid metal wereevaluated to be about 500–1000 times that of copper. This in turn means that thermal conductivity is more than 5000 times higherthan the common materials used in manufacturing the disk itself.

In this paper, the transient and steady state thermal analysis were performed for a typical turbine disk integrated with andwithout heat pipes by exploiting the numerical model of Ling et al. (2004). Moreover, the numerical analysis is based on three-dimensional model to improve the accuracy of the analysis. Various factors that affect the cooling effectiveness of heat pipes on thegas turbine disk such as the thermal conductivity, the heat transfer coefficient of the disk and heat pipes, the dimension of the disk,and the number of heat pipes required have been analyzed and evaluated.

2. Governing equations and numerical procedure

The equation governing the rotating disk exposed to a heat input at the disk edge and cooled at the disk lateral surface throughconvection are the heat conduction equation in cylindrical coordinates (see Fig. 1). Fig. 1 shows the schematic diagram of a simplifiedturbine disk model integrated with heat pipe and subjected thermal boundary conditions. As a result of high disk rotation speed, thetwo lateral surfaces of the disk are subjected to heavy thermal convection and so the two surfaces dissipate the heat. It is noted thatthe two sides surface of the disk are assumed to expose to the same cooling conditions, so due to the presence of symmetry one half of

Fig. 1. Schematic of a turbine disk (a) without heat pipes (b) with heat pipes.

Y. Taamneh Case Studies in Thermal Engineering 10 (2017) 335–342

336

the disk is considered. Therefore, the bottom surface of the half-disk shown in Fig. 1 can be considered as an adiabatic boundarycondition due to the symmetry. Because the temperature gradient is very small at the inner surface of the disk (r = ri), it has beentreated as an adiabatic surface. To simplify the form of the partial differential equation of heat conduction and the boundary con-ditions, the dependent variable (T) is transformed by defining an excess temperature, θ = T - T∞, where, T∞ is the ambient tem-perature. Accordingly, the partial differentia equation of heat conduction and the boundary conditions in cylindrical coordinates canbe expressed as follows:

Table 1Parameter of the gas turbine disk [14].

Inner disk diameter, ri 200 mmOuter disk diameter, ro 1000 mmHalf disk thickness, H 17 mmHeat pipe length, Lhp 200 mmHeat pipe diameter, rhp 7 mmSpace between the disk edge and heat pipe top end, s 20 mmHeat flux input, ″q 3 × 105 W/ m2

Cooling air temperature, ∞T 525 °CAir heat transfer coefficient, h 150–350 W/m2.°CThermal conductivity of the disk, k 24–105 W/m.°CHeat transfer coefficient of the heat pipes, hhp 250– 10,000 kW/m2.°C

Fig. 2. Temperature distribution for (a) different thermal conductivity (b) different heat transfer coefficients (t = 2000 s, ″ = ×q W m3 10 /5 2, z = 0, T∞ = 525 °C).


337

∂

∂+

∂

∂+

∂

∂+

∂

∂=

∂

∂≤ ≤ ≤ ≤ >

θr r

θr r

θϕ

θz α

θt

r r r z H t1 1 1 , and 0 0i o2

2 2

2

2

2

2 (1)

∂

∂= =

θr

r r0 at i (1.a)

∂

∂=

″=

θr

qk

r rat i (1.b)

∂

∂= =

θz

z0 at 0(1.c)

∂

∂= − =

θz

hk

θ z Hat(1.d)

Separation of variables is one of the mathematical techniques that may be employed to obtain exact solutions to two dimension (r,z) and steady-state conduction problem for infinite disk. An exact solution to this problem is of the form Arpaci [20].

∑=″ +

−=

∞

θ r zqk

η HN η η

K η r I η r I η r K η rK η r I η r I η r K η r

η z( , )sin( )

( ).

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

cos( )m

m

m m

m i m m i m

m i m o m i m om

12

1 0 1 0

2 1 1 1 (2)

Where I and K are the 1st and 2nd kinds of modified Bessel functions, respectively, ηm is the eigenvalues, ″q is the heat flux input, k isthe disk thermal conductivity, H is the disk thickness. It is important to note that the temperature distribution in disk depends on heat

Fig. 3. Variation of the maximum and the minimum temperature over the time for (a) different heat transfer coefficient (b) different thermal conductivity( ″ = ×q W m3 10 /5 2, z = 0, T∞ = 525 °C).


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transfer coefficient, heat flux, dimensions of the disk, and thermal conductivity. The same problem was solved using the commercialsoftware ANSYS 17.2 and the results were compared to the analytical results under the same geometry and boundary conditions.Firstly, the steady state temperature distribution were tracked along the disk and validated with the exact analytical solution. Theresearch presented in this work is mainly concerned with the transient thermal analysis of a turbine disk integrated with rotating heatpipes utilizing ANSYS model, a finite element software. The turbine disk integrated with various amount of radially rotating min-iature heat pipes model was developed in SpaceClaim/ANSYS, 3-D design modeling software. Meshing can be defined as the processof discretization of a geometric domain into small shape called elements. Fine tetrahedral elements were generated according to thequality specifications for both the disk and heat pipes. The half disk integrated with heat pipes model shown in Fig. 1.b is generatedusing total of 29,000 nodes and 13,500 elements, while the time step used during the numerical computation was 0.1 s. For thethermal transient analysis, the initial temperature is assumed to be 22 °C. At time t = 0, heat will start to flux from disk rim to inwardwhere some of the heat is stored and some of it is dissipated through the lateral surfaces of the disk. After a considerable length oftime (about 2000 s), the temperature contours along the disk will become uniform. The steady state solutions supposed that thesystem of equations defining the model must be solved once, while transient solutions require reevaluation at each time step. Solutionaccuracy is fully dependent on the time steps magnitude as well as the quality of the mesh. In order to simplify the analysis, theworking fluid inside the heat pipe was considered as liquid metals with high heat transfer capacity. This hypothesis was adopted byCao et al. [9] in a previous study in order to avoid solving the problem based on a two phase flow for the heat pipe. The dimensionsand the parameters of gas turbine disk used in the transient thermal analysis are summarized in Table 1 [14].

3. Result and discussion

Steady state thermal analysis for turbine disk with and without heat pipe is carried out before conducting transient analysis for theeffect of heat pipes on the disk cooling process. A good agreement has been obtained between the exact solution and the numerical

Fig. 4. Variation of the maximum and the minimum temperature over the time for different number of heat pipes (h = 250 W/m2, ″ = ×q W m3 10 /5 2, z = 0, k =60 W/m °C, T∞ = 525 °C).


339

calculation for steady-state thermal analysis under the same geometry and boundary conditions (see Fig. 2). The belief behind the riseof temperature at the disk edge is due to the low thermal conductivity of the material used in turbine disk manufacturing (k = 24 W/m.°C). It is noticeable form Fig. 2a that the temperature level gradually decreases by increasing the thermal conductivity from 24 to105 W/m.°C under the same geometry and boundary conditions. It should be noted from Fig. 2a that increasing the thermal con-ductivity of the disk from 24 to 105 W/m.°C, the temperature at the disk edge is reduced by about 250 °C and at the inner surface ofthe disk increased by about 50 °C.

In addition to the comparison between the exact and numerical solution, the steady-state thermal model is firstly utilized toinvestigate the effect of several factors on the temperature distribution in the disk. The heat transfer coefficient showed a significantimpact on the temperature level of the lateral surfaces of the turbine disk. Fig. 2b shows the temperature distribution according todifferent heat transfer coefficient on the disk surface. It can be noted form Fig. 2b that the temperature level gradually decreases byincreasing the heat transfer coefficient from 150 to 350 W/m2.°C. Moreover, the disk rim temperature remains very high despite therelative augmentation in the heat transfer coefficient. In addition, the increase in the heat transfer coefficient requires an additionalincrease of cold air associated with the compressor capacity and the fuel consumption of the power plant.

Transient thermal analysis of the turbine disk models without heat pipe have also been carried out using ANSYS 17.2. To displaythe results of the transient simulation, temperatures are calculated along fixed path goes from the inner to the outer radius of the diskat z = 0. Fig. 3a shows the evolutions of inner (minimum) and outer (maximum) disk surface temperature over the time for variousheat transfer coefficient under the same conditions. The time required to achieve the maximum steady-state disk rim temperaturevaried according to heat transfer coefficient. The steady-state conditions can be nearly reached at t = 1000, 1400 and 2000 s whenthe heat transfer coefficient decreases from 350 to 150 W/m2.°C, respectively. In contrast, there is no significant change on the

Fig. 5. Comparison of the temperature distribution (a) with different number of heat pipes (b) with different heat transfer coefficient of heat pipes (h = 250 W/m2,″ = ×q W m3 10 /5 2, z = 0, k = 60 W/m °C, T∞ = 525 °C, t = 2000 s).


340

minimum temperature at the disk bore when the steady-state condition is reached. After 2000 s the inner surface disk temperaturegets almost constant. Fig. 3b displays the maximum and minimum temperature evolutions on the disk edge over the time when thethermal conductivity of the turbine disk is varied. It can be noted that the maximum temperature at the disk edge reduces when thedisk thermal conductivity increase. Moreover, the steady-state maximum temperature is reached after 1600 s regardless of thethermal conductivity values. It is clearly noticeable that the thermal conductivity of the disk does not have a considerable effect onthe minimum temperature evolutions.

Fig. 4 displays the minimum and maximum temperature evolutions on the disk rim and the bore over the time when the heat

Fig. 6. Contours of the temperature distribution for the full disk and different number of heat pipes (h = 250 W/m2, ″ = ×q W m3 10 /5 2, z = 0, k = 60 W/m °C, T∞ =525 °C, t = 2000 s).


341

pipes are integrated. It can be noted that the minimum and maximum temperature values at the disk edge and the inner bore surfacereduces when the heat pipes number increase. This is because the amount of heat absorbed by the heat pipes (effective heat transferarea increased) will be increased when the heat pipes number are increased.

The transient thermal model is also utilized to study the effect of the number of heat pipes on the temperature distribution in thedisk. To present the results of the transient simulations for disk integrated with heat pipes, temperatures are evaluated along fixedpath located in the middle of any two heat pipes and extend from the bore to the edge of the disk at z = 0. The comparison betweendisks in the presence and absence of heat pipes for temperature reduction at disk rim and the bore with various number of heat pipesare shown in Fig. 5. It can be noted that the maximum temperature values are reduced at the disk edge whereas the minimumtemperature values at the bore are increased with an increase in heat pipes number. It can be noted from Fig. 5a that increasing thenumber of heat pipes up to n= 32, the temperature at the disk edge reduces about 100 °C compared to disk without heat pipes underthe same conditions.

The present numerical results indicate that the temperature level on the disk will not be reduced significantly when the number ofheat pipes increases from 4 to 8. (See Fig. 5a). The increase in the number of heat pipes would be significantly affect the coolingeffectiveness on the turbine disk. Turbine disk having more heat pipes would have a larger heat transfer surface and thus higher heattransfer capacity. As a result, heat can be conveyed from the perimeter of the disk, which in turn reduces temperatures in those areasfor a particular heat input. However, the amount of excess heat pipes must be constrained by the structural and functional of theturbine disk material. But the number of pipes should not be large because it can be one of the fundamental determinants of thestructure and discrete disk.

Fig. 5b shows the temperature distribution and the decrease of the minimum and maximum temperature at the disk edge and thebore surface for different heat transfer coefficient of the heat pipes. It can be noted from Fig. 5b that the local temperature level isrelatively low when the heat transfer coefficient of the heat pipes is below 1000 W/m.°C. As a result, cooling effectiveness can beimproved dramatically by increasing the heat transfer coefficient of the heat pipes. When the heat transfer coefficient of the heatpipes is reached 10,000 W/m.°C, the decreases in the maximum and minimum temperature values at the disk edge and the inner boresurface reached 280 °C and 40 °C, respectively.

To get a better idea about the temperature contours over the turbine disk and the heat pipe, Fig. 6 displays the temperaturecontours plots of three-dimensional disk at steady state (t = 2000 s). In general, it is clear that the minimum and maximum tem-perature decreases by increasing the number of heat pipes. Due to the high heat transfer coefficient of the working fluid of the heatpipe, heat can be conveyed effectively from the disk edge to the disk bore. Such a high rate of heat flux causes a decrease in disk rimtemperature.

4. Conclusion

Transient and steady-state thermal analysis of a simplified gas turbine disk integrated with heat pipes was numerically in-vestigated. In general, the numerical results confirmed that the temperature distribution in the disk is influenced by various para-meters such as the thermal conductivity of the turbine disk, the heat transfer coefficient of the air, dimension of the disk, the numberof heat pipes, and the heat transfer coefficient of the working fluid of the heat pipes. The numerical results showed that the maximumtemperature of the disk can be reduced by 100 °C when using 32 heat pipes distributed radially inside the turbine disk compared tothe disk without heat pipes. Moreover, it was found that the temperature at disk edge can be further reduced when a large value ofheat transfer coefficient for the working fluid used in the heat pipes. When the heat transfer coefficient of the heat pipes was10,000 W/m.°C, the maximum temperature value at the disk edge was reduced by 280 °C. It was observed that the time required toachieve the minimum steady-state temperature was sensitive to the external convective heat transfer coefficient.

References

[1] J.C. Han, S. Dutta, S.V. Ekkad, Gas Turbine Heat Transfer and Cooling Technology, Taylor & Francis, New York, 2000.[2] W.W. Bathie, Fundamentals of Gas Turbines, Wiley, New York, 1996.[3] X. Liu, J.H. Lienhard, Extremely high heat fluxes beneath impinging jets, J. Heat Transf. 115 (1993) 472–476.[4] J.H. Lienhard, J. Hadeler, High heat flux cooling by liquid jet-array modules, Chem. Eng. Technol. 22 (1999) 967–970.[5] D.E. Metzger, W.J. Mathis, L.D. Grochowsky, Jet cooling at the rim of a rotating disk, J. Eng. Power 101 (1979) 68–72.[6] D.E. Metzger, L.D. Grochowsky, Heat transfer between an impinging jet and a rotating disk, ASME J. Heat Transf. 99 (1977) 663–667.[7] D.E. Metzger, Heat transfer and pumping on a rotating disk with freely induced and forced cooling, J. Eng. Power (1970) 342–348.[8] J.M. Owen, Air-cooled gas-turbine discs: a review of recent research, Int. J. Heat Fluid Flow 9 (1988) 354–365.[9] Y. Cao, L. Jian, Performance simulations of a gas turbine disk-blade assembly employing miniature rotating heat pipes, ASME, in: Proceedings of the Second International

conference on Micro/Nanoscale Heat and Mass Transfer Volume 3, 2009.[10] Y. Cao, Rotating Micro/Miniature heat pipes for turbine blade cooling applications, AFOSR contractor and grantee meeting on turbulence and Internal Flows, Atlanta, GA,

1996.[11] Y. Cao, J. Ling, An experimental study of micro radially rotating heat pipes with water as the working fluid, ASME Paper No. MNHT2008-52115 981-984, 2008.[12] Y. Cao, B. Reding, J. Ling, Experimental study of miniature radially rotating heat pipes with water as the working fluid, Heat Transf. Res. 45 (2014) 137–144.[13] Y. Cao, B. Reding, M. Gao, Rotating miniature and sector heat pipes for cooling gas turbine rotor blades and disks, Heat Transf. Res. (2013) 101–114.[14] J. Ling, Y. Cao, W.S. Chang, Analyses of radially rotating high temperature heat pipes for turbomachinery applications, J. Eng. Gas Turbines Power 121 (1997) 306–312.[15] P.D. Dunn, D.A. Reay, Heat Pipes, Pergamon Press, Oxford, UK, 1982.[16] S.W. Chi, Heat Pipe Theory and Practice, A Sourcebook, Hemisphere, Washington, DC., 1976.[17] A. Faghri, Heat Pipe Science and Technology, Taylor & Francis, Washington, DC, 1995.[18] A. Faghri, S. Gogineni, S. Thomas, Vapor flow analysis in an axially rotating heat pipe, Int. J. Heat Mass Transf. 36 (1993) 2293–2303.[19] J. Ling, Y. Cao, R. Rivir, C. MacArthur, Analytical investigations of rotating disks with and without incorporating rotating heat pipes, ASME J. Eng. Gas Turbines Power 126

(2004) 680–683.[20] V.S. Arpaci, Conduction Heat Transfer, Addison-Wesley Publishing Company, Menlo, California, 1966.


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Thermal analysis of gas turbine disk integrated with rotating heat pipesIntroductionGoverning equations and numerical procedureResult and discussionConclusionReferences

case studies in thermal engineering...2017/06/27 · y. taamneh case studies in thermal engineering...

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