AD-A242 628

NASA AVSCOM

Technical Memorandum 102079 Technical Report 89-C-013

A Generalized One Dimensional ComputerCode for Turbomachinery CoolingPassage Flow Calculations

Ganesh N. Kumar .

Sverdrup Technology, Inc.NASA Lewis Research Center GroupCleveland, Ohio

Richard J. RoelkeNational Aeronautics and Space AdministrationLewis Research CenterCleveland, Ohio

and

Peter L. MeitnerPropulsion DirectorateU.S. Arny Aviation Research and Technology Activity-A VSCOMLewis Research CenterCleveland, Ohio 91-14342

Prepared for the25th Joint Propulsion Conferencecosponsored by the AIAA, ASME, SAE, and ASEEMonterey, California, July 10-12, 1989

US ARMYAVIATIONSYSTEMS COMMAND

AVIATION R&T ACTIVITY

A GENERALIZED ONE DIMENSIONAL COMPUTER CODE FOR TURBOMACHINERYCOOLING PASSAGE FLOW CALCULATIONS

Ganesh N. Kumar* -.Sverdrup Technology, Inc.

NASA Lewis Research Center Group "Cleveland, Ohio 44135

Richard J. Roelke .National Aeronautics and Space Administration

Lewis Research CenterCleveland. Ohio 44135

and

Peter L. Meitner ' uePropulsion Directorate ,'

U.S. Army Aviation Research and Technology Activity-AVSCOM _ *

Lewis Research CenterCleveland. Ohio 44135

ABSTRACT IA generalized one dimensional computer code higher turbine inlet temperatures are desired. As the

for analyzing the flow and heat transfer in the tur- cooling scheme becomes more complex, a better un-bomachinery co.-ing passages has been developed. derstanding of the internal pressure and heat transferThis code is capable of handling rotating cooling coefficient distributions is necessary to be able to pre-passages with turbulators (inline, staggered, or in- dict the hot section metal temperatures accurately.dined), 180 degree turns (both sharp and gradual Typical cooling concepts of modern turbine bladingturns, with and without turbulators), pin fins, finned are shown in figure 1. Figure l(a) shows the coolingpassages, by-pass flows, tip cap impingement flows, scheme for an axial rotor, while figure l(b) shows aand flow branching. The code is an extension of a hypothetical cooled radial rotor. The shown coolingone-dimensional code developed by P. Meitner. In passages may have heat transfer enhancement devicesthe subject code, correlations for both heat transfer in the form of turbulators, pin fins, finned passages,coefficient and pressure loss computations have been leading edge tip cap impingement flows, etc. Thedeveloped to model each of the above-mentioned type main coolant flow may also be split into sub branchesof coolant passages. The code has the capability of as shown in figure l(a) and 1(c). It should be notedindependently computing the friction factor and heat that to obtain a 2-D distribution of heat transfer co-transfer coefficient on each side of a rectangular pas- efficient in the plane of the blade surface will reallysage. Either the mass flow at inlet to the channel or require a 3-D analysis. Because of the complex naturethe exit plane pressure can be specified. For a spec- of the flow field in cooling passages, it is extremely dif-ified inlet total temperature, inlet total pressure and ficult to develop a generalized 3-D flow analysis codeexit static pressure, the code computes the flow rates capable of modeling different cooling passage config-through the main branch and the sub branches (if urations and obtaining detailed distribution of heatany), flow through tip cap for impingement cooling transfer coefficients and pressure drops. Such infor-(if any), in addition to computing the coolant pres- mation is required in the detailed thermal and struc-sure, temperature and heat transfer coefficient distri- tural analysis of the rotor and blading J21. Hence itbution in each coolant flow branch. Predictions from was felt that development of a generalized 1-D codethe subject code for both non-rotating and rotating which can model various types of cooling passages in-passages agree well with experimental data. The code cluding flow branching should be useful in the designwas used to analyze the coolant passage of a research and analysis of cooled turbomachinery. Based on thecooled radial rotor. literature review, the authors conclude that such a

INTRODUCTION generalized 1-D code is not available in the open lit-erature.

Increasing the turbine inlet temperature is a The code reported in this paper is an extensionvery lucrative approach to improving the thermal ef- of the code developed by Meitner [31, and is appli-ficiency and specific thrust of gas turbine engines, cable to any combination of cooling passage config-However, this practice is limited by the availability urations mentioned above. Specifically, the reportedof materials which can withstand these high temper- code differs from the code of reference [31 in that itatures. Current materials cannot be exposed to tem- can calculate and balance flows in sub-branches, andperatures above 1250 K without a dramatic decrease can thus compute flows in passages shown in figurein life Il]. Blades must be cooled if significantly

l(a) and 1(c) whereas the code of reference (3] willnot be capable of handling these passages. Also,the code reported in this paper can make separatecalculations for the leading (suction) surface, trail-ing(pressure) surface, and side walls of a rotatingchannel of rectangular cross section. This is veryimportant for capturing the experimentally observedbehavior in rotating environnent. In addition, amore detailed modeling of each type of cooling pas-sage above has been incorporated in the present codecompared to the code of Meitner. The code can pre-dict the mass flow rates, internal pressure and temi-perature distribution, heat transfer coefficient andheat flux distribution at the walls along the passage.In a limited sense, it can predict the heat transfercoeflicient distribution along each side of rectangu-lar passage. It integrates the 1-D compressible noo- (a): Axial Turbine (91

xnentuni and energy equations along a defined flowpath and will account for area changes, mass ad-dition/subtraction, Coriolis acceleration, centrifugalforce effects, bouyancy force effects, friction and heataddition. Flow call be bled off for tip cap impinge-meit cooling and a flow 'bypass' can be specified in T / I,.-t 7 o

which the coolant flow is taken off at one point in - F.

the flow channel and re-introduced at a point fur- F.-

ther downstream in the same channel. As mentionedabove, other types of passages that can be modeled ....

include plain passages, rib-roughened passages (stag-gered and inline turbulators at various angles of at-tack), dilferent pin fin arrangements (with or withoutlateral flow ejection, as shown in figure 1(a)), finnedpassages, 180 degree turns (both sharp and gradual) Y

and flow branching.

BLsed on the most recent experimental data (b): Radial Turbine

available, correlations have been obtained to modelthe various types of rotating cooling passages. Theuspr has the option of specifying the temperature andpressure at inlet to the main branch and either the

main flow rate or the exit pressures from the subbraiches. T lhe present version of the code cannotaccomodate supersonic flow anywhere in the coolingpassage. The flow can at best be choked at exit fromminone or more of the branclies, Htowever, it is felt that -

this is not a serious restriction for modeling turbomia-chiinery cooling passages.

Comparisons have been made with a wide vari-

ety of non-rotating and rotating passage experimen-tal data representing various types and combinations (c): Radial tubine with Flow branching

of cooling pasages. It is shown that the predictionscompare well with the experimental data. Figure 1. Typical ('oliig Comcrpts of Modern Gas

Turbines

2

FLOW PATH MODELING ANDCOMPUTATION PROCEDURE

+r[lfmRT )21 dThe flow path is defined in cartesian co-ordinates + C A A dx

z,r and y as shown in figure 1(b). The flow path ge-ometry is described at nodes and the type of passage 2]/

between each set of nodes is specified using different r[1 (hRT dpparameters in the code input. + L pA J Jdx)

For specified entrance conditions and a specified(or guessed) flow rate, the flow solution is obtained 4hA(T - T..)by marching along the defined flow path from node + 4 C DT (4)to node. The pressure and temperature at each node rnis calculated from the values at the previous node by: where

Pa = Pn-I + (dp/dx). * dx,. (1) (drh/dx). = (h,. - th._ 1)/(l.) (5)

T. = T._ + (dT/dx)n. dx,. (2) (dA/dx). = (A,. - A. 1)/(1.) (6)

where (dp/dx)n and (dT/dx)n are given by the solu-tion of momentum and energy equations as [3]: (dr/dx). = (r. - ,. 1 )/(.) (7)

/ 2 The constants C1, C2 and CT are defined as fol-dp 1j1(C 3 m h RT T lows [3]:

C = (yh/A)2R (8)

- c.niti + 2 G))+ --7- [+ m2C

(r/CxR c 1 (rh/a)nT2] (9

2(iC/A)RT (dr1i ( (/A)2 RT C pP P(9)

pA -dx) + pA CA (rh/A) 2 R 2T(ST 1 +(10)

?TRT 2 dA 4fRT(mn/A) 2 Iteration takes place in each marching step untilpA ] ) 2pDh a convergence is acheived. After marching through all

d the nodes, the calculated branch or sub branch exit

pressures are compared with the given exit pressuresif specified). If necessary, a correction is made to the

N 2 rp dr _ 4hcACi(Tw - T, inlet flow rate and the marching procedure repeated+ RT dC -T.) (3) until the calculated and specified exit pressure values

Sdx mhCpDh Jagree within a prescribed tolerance.

For flows where the local coolant passage Machand number becomes high (> 0.9), pressure changes in the

flow direction become highly non-linear. A provisionhas been made in the code to automatically add ad-

dT) 1 3mn RT)2 T ditional nodes between the original nodes and repeat(-)= (-) + the iteration process mentioned above until the Machdx CT 2Cp number values at each of the original nodes do not

change between successive increases in the number ofnodes.

Cpijj+drri In the present paper, for the different types ofcooling passsages mentioned above, both friction fac-dx tor and heat transfer coefficients are modeled with

3

correlation3 developed from experimental data avail- on the work of Han, et al. [8,91 for in line rib ar-abic in the literature or using the correlations avail- rangement and Taslim and Spring [10] for staggeredable in the literature (with modifications). For val- arrangement. Correlations include the effects of nonidating the correlations developed, computations us- dimensional parameters like rib height to hydraulic di-ing these correlations have been compared with ex- ameter ratio (e/Dh), rib pitch-to-height ratio (P/e),perimental data from an entirely different source than channel aspect ratio (W/H) Reynolds number (Re).those used in the development of correlations. and rib angle of attack ratio In/90). Based on Boyle's

data 111], entrance effects have also been incorporatedr he correlation developed are generally of the in the correlations.form:

c) Pin Fins: Based on the work of Metzger, et al.[12,13,14,151, correlations are available to model pres-

Nu or f a(ND1)?'(ND2)c(ND3)d... (11) sure drop and heat transfer coeflicients (array aver-aged) for different staggered pin fin configurations.Nusselt number (Nu) correlations which include the

where Nu is the Nusselt number, f is the friction effects of streamwise pin spacing are given by Metzgerfactor, NDI, ND2, etc are relevant non-dimensional [121. The local row resolved heat transfer coefficientquantities like Reynolds number (Re), Rotational correction has been correlated based on the data ofRayleigh number (Ra), Rossby number (R, Prandtl Metzger [12] as well as the corrections to Nu to in-number (Pr), rib height (or roughness height) to hy- clude effects of channel convergence. Nusselt numberdraulic diameter ratio (e/Dh), the rib pitch-ta-height correlations are also available based on the work ofratio (P/e), channel aspect ratio (W/H), pin-fin span- VanFossen [16]. It should be noted that in VanFos-wise spacing to diameter ratio (S/d), pin-fin stream- sen correlations, the Nuiselt numbers are based onwise spacing to diameter ratio(X/d), pin height to hydraulic diamete DV which depends on the openpin diameter ratio (14/d), etc. The correlations were volume in the pin fin bank an(l the total heat trans-obtained from the experimental data using the SAS fer surface area whereas the Metzger correlations are[4] multiple correlation and regression analysis pro- based on pin diameter. In a recent review paper oncedure. The correlation equations are not shown in staggered array pin fin heat tansfer, Armstrong andthe paper due to space limitations. Additional de- Winstanley [17] recommend the use of Metzger ortails of the correlation equations and the code will be VanFossen correlations for short pin fins (I/d <= 3)presented in a future NASA report. and the correlation of Faulkner [18] for i- rg pin fins

(Ht/d > 3). Friction factor correlations fc:r both shortIn the present version of the 1-D code, correla- and long pin fins are based on the work of Metzger

tions have been included to model any combination [13].of the followbig types of passages: The effect of channel convergence on friction fac-a Ptor is incorporated based on the work of Brown [10].the magnitude of relative roughness parameter For pin fin channels with lateral ejection, the correla-(e/D,), the passages are classified as smooth or rough tions developed by Lau et al [2 are used.

and! the corresponding correlation equations are used. d) 180D. ree Turns: Based on the experimental dataof Metzger, et al. [21,22,23,241, correlations were de-

IFriction Factor: For laminar flow in circular, rectan- veloped for heat transfer coefficient and pressure lossgular or square dicts, based on the data available in in smooth and turbulated sharp 180 degree timrs. ForKays and Crawford [5] in the form of tables and fig- gradual 180 degree turns, the pressure loss coefficientsuscorre.lations have been obtained to model both gaul10dge untlepesr oscefcetures, c lwere based on the equations from reference [251 andsmooth ad rough non-rotating passages and for both the correlations for the heat transfer coefficient vari-fully developed and entrance regions of flow. For tur- ation was based on the experimental data of Baughn,bulent flow and in the transition region in ducts, cor- et al. [26].relations listed in Welty, Wicks and Wilson [61 havebeen us-ed for both smooth and rough passages e) k trLcLP_t "g : For cooling passage channels

S sf with fins parallel to the flow direction (usually nearheat Transfer Coefficient: For laminar flow, correla- the trailing edges of blades, figure 1(b)),an effectivetions are developed based on the data of Kays and heat transfer coefficient is obtained [3] which can beCrawford [5] for the fully developed as well as the apidt h or.pnigpanasg ufc

entrance regions of flows in both circular and non- applied to the corresponding plain passage surfacecircular ducts. For fully developed turbulent flows, area without fins.

correlations given by Kreith and Bohn [7] and/or f) Flow Lrainching: Pressure loss due to flow branch-those in reference [5] have been included. Entrance ing has been modeled based on reference 125].effects are modeled bamed on Kays and Crawford [5]. g) LeadingE Tp_CapImiiny np _Cooljg:

b) Turbilated Passages: Correlations have been in- Modeling of the tip cap impingement cooling is basedcorporated to model the heat transfer coefficient and on the development by Meitner [31 who utilized thepressure drop di7tributions for rectangular or circular data of Chupp et al. [27]. It include0 the effects ofpassages with transverse rib rougheners (both inline rotation on pressure chianges across the tip cap inr-and staggered arrangements and at any given angle pingement chamber and the temperature increase dueof attack). Correlations have been included for both to impingement in the chamber. The model also coin-the turbulated walls and the smooth side walls based putes the mass flow through the impingement holes.

4

Corrections have been applied to the Meitner model transfer coefficient and friction factor (pressurebased on the work of Epstein et al. [28] which include drop) distribution due to enhancement devices andthe effects of rotation on heat transfer in a impinge- then computing the effects of rotation as a ra-ment cooled turbine blade. Modeling of by-pass flows tio of a) Nu (rotating)/Nu(non-rotating) and b)

(see figure 1 (b)) is also based on Meitner's develop- f(rotating)/f(non-rotating) based on the experimen-ment [3]. tal correlations mentioned above. The validity of the

h) Rotational Effects of Plain Passages: Effects on correlations used is shown in the following section.

both pressure drop and heat transfer coefficient due It should be noted that the user always has theto Coriolis forces, centrifugal forces, and centripetal option of providing the pressure loss coefficient, fric-buoyancy have been included for ducts (circular, tion factor, and/or heat transfer coefficient for anysquare or rectangular) rotating in orthogonal and/or given interval in the form of data to be curve fitted,parallel modes (with respect to the axis of rotation) equations, or a set of given values.and for both laminar and turbulent flows. COMPARISON WITH

For laminar flow in plain passages with smooth EXPERIMENTAL DATAor rough walls, and with their axes normal to the axis In the following paragraphs, the predictons fromof rotation, the pressure loss correlations are based on the code are compared with a wide variety of exper-the work of Mori and Nakayama [29] and heat trans- t al dat a for vari et of e-fer correlations are based on the work of Morris [301 imental data for various types of heat transfer en-and for moderate temperature differences on the an- hancement devices. As mentioned earlier, the predic-alytical work of [29]. For turbulent flows, the heat tions from the code are compared with the data fromtransfer correlations are based on the work of Clifford the sources which are different from those used in the[31] or Morris and Ayhan [32,33] with corrections for correlation. Both non-rotating and rotating passagethe leading and trailing surfaces based on Harsagama data with and without various heat transfer enhance-and Morris [34]. The user also has the choice of bas- ment devices are compared to give a clear picture ofing it on the theoretical work of Mori, Fukada and the range of application of the code.

Nakayama [35]. The pressure loss correlations are ob- a) Non-Rotating Passage Data:tained from the work of Ito and Nanbu [36] or fromreference [35]. For a straight duct with 90 degree turbulators,

the code predictions are compared with the experi-For laminar flow in plain passages rotating about mental data of Taslim and Spring [46,471 in figures

a parallel axis, the pressure drop correlations are 2 and 3. Figure 2 compares the mean Nusselt num-baLcd on the rotating friction factor given by ber variation with Reynolds number (Re) for a fixed

rib height to channel hydraulic diameter ratio (e/Dh,fl t = fLt + f, (12) also known as blockage factor), rib pitch to height ra-

tio (P/e) and channel aspect ratio (W/H). The defini-tion of these terms are clarified in the inserts in figures

= 0.503 Roin (13) 2 and 3. Figure 3 compares the Nusselt number en-hancement, expressed as (Nu/Nu,t), with a variation

where f , is "the excess friction factor" suggested by in the blockage factor e/Dh for fixed values of P/e,Morris [36]. The heat transfer correlations are based W/H, and Re. Predictions are in excellent agreementon the work of Morris and Dias [38] and for moder- with the experimental data.ate temperature differences on the theoretical work In figures 4 and 5, the code predictions for a two-of Mori and Nakayama [39]. For turbulent flows, the pass serpentine passage with a 180 degree turn, forheat transfer correlations are based on the work of both smooth and turbulated walls, are compared withMorris and Dias [40] and Woods and Morris [41] and experimental measurements. The calculated Nusseltfor nioderate temperature differences on the theoret- number variation along the passage is compared withical work of Nakayama 142]. The pressure drop corre- the data of Chandra [48] in figure 4 and with thelatioris are based on [43. For the entrance region, the data of Boyle [11] in figure 5. Agreement with dataheat transfer correlations are based on work of Morris of [48] is very good for both smooth and turbulatedand Woods [43]. passages. The reason for the reduction in the Nusselt

It has been shown from the experimental data number in the 180 degree turn region (X/Dh = 12of Hajek et al. [441, and Guidez [45] that the heat to 14) for the turbulated case is that there are notransfer characteristics due to rotation are radically turbulators in the turn region. In the case of Boyle'sdifferent for the leading and trailing surfaces and also data, the 180 degree turn region (X/Dh = 14 to 16)for the centrifugal (radially outward) and centripetal has turbulators.(radially inward) passages. These features have been Predictions agree very well with Boyle's data [1lcaptured in the correlations used in the present code. at higher values of Re where as at low values of Re (<

i) Rotating Channels with Heat Transfer = 20000), the agreement is good except in the regionEnhancement Devices:

The combined effects of rotation and heattransfer enhancement devices (like ribs, pin finsetc.) are obtained by first computing the heat

Z 4001 P Li -

z -

n 30 6 L00 5 1 5 2 5 3

Rey-uds nmber Re/0000Non-dimensiona0l distance olcag flow path, X/D I

Figure 2. Coiiiparistoi of Niisselt iiiiiber variatioil Figure 4. Comparison of vaiiation of Nusselt numberwith Reynolds number with the turlbulated passage with XII, with the two-pass rib roughened passagedata of TJaslu and Spring [46,471 (at 90'~ with a sharp 180 (leg. turn) data of Chandra

481.

0 EP 0 20. 0CC. -5 - COMPUTATION ~

[717zz

C~~ ~~~~ 050t .5 0002

1"iiir 3. (7o ip ris n o Nu sel n inh r v riaionim ned ateyNote d ieoo 180sden re Wlong fl wohere t ecom

sae ato of rai hilt hdaicg diameter) e/Dh datae. Toeiparisoun erf o vaito of Nhel ndr ber t

In% in this region. T1hue reason for this behavior isniot known at present.

For passages with p~in fuis, thle code predlictionsare comipared with the experimental data of Lani etal. [49[ and hPeng [,50] ini 6gure-t 6 and 7. Figure 6comllpares the pm edictedl Nui variatioii w ithi row wni uherwith thle dat~a of laul mm 491 and~ figmre 7 comipares thepredicted variation of friction factor (f) and Colbut nfactor (j) wit h Reynolds niumber with the (hita of Peng501. Both time figures show that the predictions are

in excellent agreemnetit with1 the experimiental data.

6

*Gjo 1 2,V (l14 33. 000)

2 YP ....... ..,.00

...............

L, X/d - 2. 0 2 0 0

75 I -- CO dr fp# - 91, QU) H/d - 1 0 ROW'' ' -

cl EXP (RA- , OoO) P

3 4 Figure 8. Schematic of the rotating serpentine pas-Row number sage of llajek 144 showing the four zones compared

with the code predictions,

Figu e u. Coiparison of variation of Nusselt number Figure 9(a)-(d) compare the Nusselt numberwith row numnber with tle pin fin data of Lau 149J. variation with Rossby number (Rb) for'the abovementioned four zones along the passage. As seen in

figures 9(a) and 9(b), the predictions clearly show theexperimentally observed trend for the centrifugal sec-

X/d-2 3.01tions zones 1 and 2, that as the ltossby numiber in-creases, due to increasing rotational speed Nusselt

(CO- number increases on the trailing (presaurec surface

0 f - m I l/ - 3 and decreases on the leading (suction) surface. This, Rxo It f trend is observed for both smooth and turbulated pas-o oo..... ............................... .. sages. This is due to the increased secondary floweffects at higher values of Rb. Figures 9(c) and 0(d)compare Nusselt number variation with Ro for thecentripetal channel. These figures also show that the

0.00 - trend of Nu variation with Ro is in general opposite toS (COPI that of the centrifugal section. Comparison of pres-sure variations along the passage with the data ofIlajek 1441 is made in figure 10 for the turbulated pas-

0' 00 1 sages. All the above figures clearly show that the codeWOOo 100oo predictions agree well with the data of Hlajek [44).

Roynolds number, Re

["ig,, 7 Comparison of variation of friction factor 0 LLOa 3GlipmlAJLffA;d

and Coi, u.. , jum walh Reynolds uumber with the .pin fin data of Peng [501, 4 W &=P I'.M.OT..

b EXP I0UR41,}

h) Roatwgj~ (~yExtensive comparison has 3 1. .......... .. ..... . . Me - {S O

beeni madc with the rotating passage data (bothsmuootlh and turbulated serpentine passages) of Hlajek, . .et al. 144{. A schematic of the serpentine passage of tibu'llajek is a own in figure 8. As shown in figure 8, four .........typical zounes have been chosen for comparison with .code predictions to illustrate the validity of the corre- o_lations developed for rotating channels. Zones 1 and 04 0 0 P '

2 are in the radally outward (centrifugal) section and Rocuby Number, Rozones 3 and 4 are in the radially inward (centripetal)section of the passage. As explained earlier, separatecorrelations are used to predict the effects of rotation (a): Zone 1.on the leading surface (suction surface), trailing stur. Figure 9. Comparison of Nusselt number variation

face (pressure surface) and the two side walls of the wihe Rossby Number for the smooth and 45 deg.coolant pasilage, Thl enables the code to compute turbulated serpentine rotating passage data of ]lajekthe rotational effects more accurately. j44J.

7

PC 25000 L

I'ML

0.4 0.2 0.0 0,2 0.4 ~ ,t,

Roosby Number, Ro 0 to a0 so 40

Non-dimenslonal dietonce along flow path, X/Dh

(bi): Zone 2. F~igurie 10. Co3IaJarkNou of presitie distribuiiii almigthe Pasenge with the turbilated rotatig serpenltinepameage data of Ilajek 144).

0 ~~ ~ ~ ~ ~ CPl lr7~00inniir~rpo U7A of Niisnelt ,wiiber vitriatirn wi'lh theceltriilg) lassge ataof 011lidcz 1461il illade ill fig-

cU r 1ill with thec data of Iskakov awl Th1,ishliij (5ijA figure 12, These figiirces srhow that the code lrcdic-

.. ~tioiis are ini good agreemenoit with lie exper mencitalA- :5 I-.-- (SW:: " data in both cases withi a minimil error of about

* ~~ 20%, Th.Je trcwido showna in these figilres are the saineC3,,.~.. 0*a ecerifugal jmssage data of Jlajek 144).

O.4 O,8 0.00.0.

Rossby Number, Ro

(c): Zone 3,

tflADMU4 rJA'CU1 20P1!A

COMP (SM4OOTH)0,

4 0 1 P (SMOO) /l-I

C Tto TUOJ -

As 25000

0,0 0 Q 99

Rosaby Nubr o00,4

RoayNumber, Ro

Yig ore I I. Conipn, in of Niimpelt, ii ber variAtion

(d): zone" 4, wiiJ ItoPshy Niumnlber with tipe lntta of' Oitdes [461J.Figure P. Coinclucled at X/VD,- 7.4.

I .EACONG SURFACE TRAILING SURFACE MAI PS5h U

COW

Ft 32000 CLE

z -1

1.0' -

3 2 Flow path location

Gr/(Resl 00)

Figure 12. Coi p arisot of Nusselt niumber with Figure 13. Pressure distribution along the coolantthe parameter Gr/ R e with the data of Iskakov and passage of a NASA research radial turbine.Trushiii [51 1 atX/D,, = 7.

CONCLUDING REMARKS

COOLED) RADIAL TURBINE ROTOR ANALYSIS A generalized one dimensional flow code appii-The coolant flow of a cooled NASA research ra- cable to comupressible flow throughk complex rotat-

dial turbine rotor, which will be tested at tile Lewis ing turbine cooling passages with various heat trans-Research Center, has been analyzed using the code. fer enhancement devices hias been developed. EvenThe cooling passage consists of a main passage split- though this is a 1-i) code, the effects of rotation oiitiiig into three braiiches and includes pin fins and] heat transfer is takeni into account iii a quasi 2-D3 fash-finned passagos. Thle scheiiiatic of the cooling pas- ion, i.e. a separate correlation is available for eachsage is shown inl figure 1(c). For a given inlet total side of a rectangular passage. The code ha" been val-temiperature aiid pressure and exit pressures fromn tile idated using a wide variety of both non rotatiiig andbranches, the piesent code was used to predict the di q- rotating passage data. The authors feel that the code'; ibution of presslire along the eiitire passage and also will be useful to the tuirbine designer in evaluating

the mass flow through the mnain and sub braiiclies. the effects of various cooliiig passage designs oii the

T1hie results are shown in figure 13 and table 1 respec- overall performance of the turbine. For miore accuratetively. These predictions will be compared with the computations, it may be necessary to include a local-

experimental results as they become available. ized 3-D3 analysis where flow reversals aind flow stag-nation may cause the 1-1) code predictions at theselocations to be in error by a wide miargini.

''able 1. mass flow comiputationms for the coolant pas- NOMENCLATUREsage of a NASA research radial turbine

A areaC,, specific heat at coiistant pressureD) diamieter

m/ h, 4 Dh hydraulic diameter defined byD,, = A/P

code d pin fill diameterBranch Comnputation e surface rouighnieqq; or rill heighlt

f faniiing friction factor definied by

Mlain 6.734 f - 6Pjh ( 2LV 2p)

BI 2.399 Gr rotational Crashiof numiber definied by

132 1.632 Gr N,.r(73f, -

B3 2.703 11 flow chiaiinel heighthi enthialpy

Y =,, 0.001kg/s h0 coolant heat traiisfer coefficient

j Colhorii factor (If'fiuied by

k tltermial conirductivity

S iiitei val length,m conlatt, as~us flow rate aIt iiilet to

thle ch'an med

N rotational speed REFERENCESNu Nusselt number; Nu = h,/(Dhk)Nu, -Nusselt number for a stationary plain [11 Rodi, W. and Scheuerer, G. "Calculation of

passage Heat Transfer to Convection Cooled Gas TurbineP perimeter; or pitch of turbulators Blades," Transactions of the ASME, Vol. 107,Pr Prandtl number; Pr = Cpj/k July 1985, pp 620-627,p pressurePr4 reference pressure [2] Kumar, G.N. and DeAnna, R.G. "DevelopmentRa gas constant of a Thermal and Structural Analysis ProcedureRa Rotational Rayleigh number; defined by for Cooled Radial Turbines," ASME paper no.

Ra GrPr 88-GT.18, presented at the 33rd InternationalrNen l(T , - Tn b )Dea Pr/(nnep)2 Gas Turbine and Aeroengine Congress, Amster-

Re Reynolds number; defined by dam, The Netherlands, June 6-0, 1988.Re = pVDhU//

Ro Rossby number; defined by Ro = NDh/Vr radius; co-ordinate direction used in 13] Meitner, P.L. "Computer Code for Predicting

the code Coolant Flow and Heat Transfer in Turboma-S pin fin spacing in spanwise (transverse) chinery," to be published as AVSCOM TR No.

direction 80-C-008, 1089T temperatureT1, bulk temperature of the fluid [41 SAS User's Guide, Version 5.16, 1987, SAS In-TW wall temperature stitue Inc., Box 8000, Cary, NC 27512.TLW adiabatic wall temperatureV fluid velocity [5] Kays, W.M., and Crawford, M.E., "ConvectiveW flow channel width; Heat and Mass Transfer," McGraw-Hill BookW/H channel aspect ratio (ribs (if any) on Company, New York, Second Edition, 1980.

side, W)x distance along the flow path J.R., Wicks, C.E., and Wilson, R.E,X pin fin spacing in streamwise direction or [6] WVelty, JRWcs .. n isn ..

streamwise distance o "Fundamentals of Momentum, Heat, and Massa efrom entrance to Transfer," Second Edition, John Wiley & Sons,

chian nel17.y co-ordinate direction used in the code 1979.z co-ordinate direction used in the codefi volumeexpansion coefficient 17] Kreith, F., and Bohn, M.S., "Principles of Hat'y ratio of specific heats Transfer," Fourth Edition, Harper & Row Pub-6 a change in a quantitiy lishers, New York; 1986.

S /P absolute viscosityp density [81 Han, J.C., and Park, J.S., "Developing Heat

SUBSCRIPTS Transfer in Rectangular Channels with Rib Tur-aw adiabatic wall bulators," International Journal of Heat andex excess factor due to rotation Mass Transfer, Vol. 31, No. 1, pp 183-195, 1988.inj injectionni interval number 19] Ilan, J.C., Park, J.S., and lbralim, M.Y., "Mea-t stationary cise surement of Heat Transfer and Pressure Drop in

ref reference value Rectangular Channels with Turbulence Promot-rot rotating case ers," NASA Contractor Report 4015 (or AVS-x component in the direction of main COM Technical Report 86-C-25), pp 1-197, 1986.

stream flow[10] Taslim, M.E., and Spring, S.D., "Experimentalt conditions Heat Transfer and Friction Factors in Turbu-

)' total conditions lated Cooling Passages of Different Aspect Ra-tios, Where Turbulators are Staggered," PaperNo. AIAA-88-3014, AIAA/ASME/SAE/ASEE24th Joint Propulsion Conference, July 11-13,Boton, Massachsetts.

[11 Boyle, R.J. "Ieat Transfer in Serpentine Pas-sages with furbulence Promoters," ASME Paper84-HT-24, presented at the 22nd National HeatTransfer Conference, Niagara Falls, NY , August5-8, 1984.

[12] Metzger, D.E., Shepard, W.B., and Haley, S.W.,"Row Resolved Heat Trasnfcr Variations in Pin

10

Fin Arrays Including Effects of Non-Uniform Ar- Transfer and Pressure Losses in Rectangularrays and Flow Convergence," ASME Paper No. Ducts with Sharp 180-Degree Turns," Paper86-GT-132, presented at the 31st International No. AIAA-88-0166, presented at the AIAA 26thGas Turbine Conference and Exhibit, Dusseldorf, Aerospace Sciences Meeting, Reno, Nevada, Jan-West Germany, June 8-12, 1986. uary 11-14, 1988.

[131 Metzger, D.E., Fan, Z.X., and Shepard, W.B., [24] ran, C.S., and Metzger, D.E., "Effects of Chan-"Pressure Loss and Heat Transfer Through Rows nel Aspect Ratio on Heat Transfer in Rectan-of Short Pin Fins," Heat Transfer 1982, Vol. 3, gular Passage Sharp 180-Degree Turns," ASMEU. Grigull et al. eds., Hemisphere Publishing Paper No. 87-GT-113, presented at the ASMECompany, Washington, 1982, pp 137-142. 32nd International Gas Turbine Confererce and

Exhibition, May 31-June 3, 1987, Anaheim, CA.[14] Metzger, D.E., and Haley, S.W., "Heat Transfer

Experiments and Flow Visualization for Arrays [25] Belvins, R.D., "Advance d Fluid Dynamicsof Short Pin Fins," ASME Paper No. 82-GT-138, Handbook," Mcmillan Publishing Co, 1986, ppApril 1982. 56-70.

[15] Metzger, D.E., Berry, R.A., and Bronson, J.P., [26] Baughn, J.W., Iacovides, H., Jackson, D.C., and"Developing Heat Transfer in Rectangular Ducts Launder, B.E., "Local Heat Transfer Measure-with Staggered Arrays of Short Pin Fins," Trans. ments in Turbulent Flow Around a 180-deg Pipeof ASME, Journal of Heat transfer, Vol. 104, Bend," Trans. of ASME, Journal of Heat Trans-Nov. 1982, pp 700-706. fer, Vol. 109, February 1987, pp 43-48.

[16] VanFossen, G.J., "Heat Transfer Coefficients for [27] Chupp, R.E., Helms, H.E., McFadden, P.W,Staggered Arrays of Short Pin Fins," ASME and Brown, T.R., "Evaluation of Internal HeatJournal of Engineering for Power, Vol. 104, pp Transfer Coefficients for Impingement Cooled268-274, 1982. Turbine Airfoils," Journal of Aircraft, Vol. 6,

1969, pp 203-208.[17] Armstrong, J., and Winstanley, D., "A Review of

Staggered Array Pin Fin Heat Transfer for Tur- [28] Epstein, A.H., Kerrebrock, J.L., Koo, J.J., andbine Cooling Applications," Trans. of ASME, Preiser, U.Z., "Rotational Effects on Impinge-Journal of Turbomachinery, Vol. 110, Journal of ment Cooling," Heat Transfer and Fluid FlowTurbomach;nery, January 1988, pp 94-103. in Rotating Machinery, Wen-Jei Yang, Editor,

Hemisphere Publishing Company, 1987, pp 86-[18] Faulkner, F.E., "Analytical Investigation of 101.

Chord Size and Cooling Methods on TurbineBlade Requirements," NASA CR-120882, 1971, [29] Mori, y., and Nakayama, W., "Convective Heatpp-18 9 -1 9 4 . Transfer in Rotating Radial Circular Pipes (1st

Report, Laminar Region," Int. Journal of Heat[19] Brown, A., Mandjicas, B., and Burgraf, F., and Mass Transfer, Vol. 11, 1968, pp 1027-1040.

"Blade Trailing Edge Heat Transfer," ASME Pa-per No. 80-GT-45. [30] Morris, W., "Heat Transfer and Fluid Flow in

Rotating Coolant Channels," Research Studies[20[ Lau, S.C., Han, J.C., aqnd Kim, Y.S., "Tur- Press-Wiley, 1981.

bulent Heat Transfer and Friction in Pin FinChannels With Lateral Flow Ejection," Trans. [31] Clifford, R.J. "Rotating Heat Transfer Investiga-of ASME, Journal of Heat Transfer, Vol 111, No. tions on a Multi-Pass Cooling Geometry", paper1, February 1989, pp 51-58. presented at the Conference on Heat Transfer

and Cooling in Gas Turbines, Bergen, Norway,[21] Metzger, D.E., and Sahm, M.K., "Heat Trans- May 6-10, 1985; AGARD-CP-390.

fer around Sharp 180-Degree Turns in SmoothRectangular Channels," Trans. of ASME, Jour- [32] Morris, W.D., and Ayhan, T. "Observations onnal of Heat Transfer, Vol. 108, August 1986, pp the Influence of Rotation on Heat Transfer in the500-506. Coolant Channels of Gas Turbine Rotor Blades",

Proc. I. Mech Engrs., Vol 193., 1979, pp 303-311.[22] Metzger, D.E., Plevich, C.W., and Fan, C.S.,

"Pressure Loss through Sharp 180-Degree Turns [33] Morris, W.D., and Ayhan, T. "An Experi-in Smooth Rectangular Channels," Trans. of mental Study of Turbulent Heat Transfer inASME, Journal of Gas Turbines and Power, Vol. a Tube which Rotates about an Orthogoanal106, July 1984, pp 677-681. Axis", Proc. XIV ICHMT Symposium on

Heat and Mass Transfer in Rotating Machinery,[23] Metzger, D.E., Fan, C.S., and Plevich, C.W., Dubrovnik, Yugoslovia, August 30- September 3,

"Effects of Transverse Rib Roughness on Heat 1982.

11

[34] Harsagama, S.P. and Morris, W.D. "The In- [46] Taslim, M.E., and Spring, S.D., "Friction Fac-fluence and Rotation on the Heat Transfer tors and Heat Transfer Coefficients in Tur-Charecteristics of Circular, Triangular, and bulated Cooling Passages of Different AspectSquare Sectioned Coolant Passages oof Gas Tur- Rations, Part I: Experimental Results," Pa-bine Rotor Baldes" Trans. of ASME, Journal of per No. AIAA-87-2009, presented at theTurbomachinery, Vol 110, January 1988, pp 44- AIAA/ASME/SAE/ASEE 23rd Joint Propul-49. sion Conference, June 29 - July 2, 1987, San

Diego, California.

[35] Mori, Y., Fukuda, T., and Nakayama, W., "Con-vective Heat Transfer in a Rotating Radial Circu- [47] Taslim, M.E., and Spring, S.D., "An Experimen-lar Pipe (2nd Report)," International Journal of tal Investigation of Heat Transfer CoefficientsHeat and Mass Transfer, Vol. 14, pp 1807-1824, and Friction factors in Passages of Different As-197!. pect Ratios Roughened with 450 Turbulators,"

Proceedings of the 1988 ASME National hteat[361 Ito, H., and Nanbu, K., "Flow in Rotating Transfer Conference, Houston, Texas, July 24-

Straight Pipes of Circular Cross Section," ASME 27, 1988, Vol. 1, pp 661-668.Trans., Journal of Basic Eng., Vol. 93, No. 3,1971, pp 383-397. 148] Chandra, P.R., Han, J.C., and Lau, S.C., "Effect

of Rib Angle ol Local Heat/Mass Transfer Dis-[37] Morris, W.D., "A Pressure Transmission System tribution in a Two-Pass Rib-Roughened Chan-

for Flow Resistance Measurements in a Rotating nel," ASME paper no. 87-GT-94 presented atTube," Journal of Phys. E: Sci. Instrum., vol the 32nd International Gas Turbine Conference14., pp 208-214., 1981. and Exhibition, May 31 - June 4, 1987, Anaheim,

California.[38] Morris, W.D., and Dias, F.M., "Laminar Heat

Transfer in Square Sectioned Ducts which Rotate [49] Lau, S.C., Kim, Y.S., and Hlan, J.C., "Effects ofin Parallel Mode," Power Ind. Res., Vol. 1, 1981. Fin Configuration and Entrance Length on Local

Endwall Heat/Mass Transfer in a Pin Fin Chan-[391 Mori, y., and Nakayama, W., "Forced Convec- nel," ASME paper No. 85-WA/HT-62, presented

tive Heat Transfer in a Straight Pipe Rotating at the ASME Winter Annual Meeting, Nov 17-Around a Parallel Axis (1st Report, Laminar Re- 21, 1985, Miami Beach, Florida.gion)," Int. Journal of tteat and Mass Transfer,Vol. 10, 1967, pp 1179-1194. [50] Peng, Y., "Heat Transfer and Friction Loss

Charecteristics of Pin Fin Cooling Arrange-140] Morris, W.D., and Dias, F.M., "Turbulent Heat ments," Trans. of ASME, Journal of Engineering

Transfer in a Square Sectioned Tube", Journal of for Gas Turbines and Power, Vol. 246, JanuaryMechanical Engineering Science, Vol. 22, no. 2, 1984, pp 246-25!.1980, pp 95-101.

[511 Iskakov, K.M., and Trushin, V.A., "The Effect of[41] WoodsJ.L., and Morris, W.D., "A Study of Heat Rotation on Heat Transfer in the Radial Cooling

Transfer in a Rotating Tube", ASME Journal of Channels of Turbine Blades," Thermal Engineer-Heat Transfer, Vol 102, Nov. 1980 pp 612-616. ing, Vol. 32, No. 2, 1985, pp 93-96.

[42] Nakayama, W., "Forced Convective IHeat Trans-fer in a Straight Pipe Rotating Around a Paral-lel Axis (2nd Report, Turbulent Region)," Int.Journal of Heat and Mass Transfer, Vol. 11,1968, pp 1185-1201.

[43] Morris, W.D., and Woods, J.L., "Heat Trans-fer in the Entrance Region of Tubes that Rotateabout a Parallel Axis", journal of Mech EngrScience, Vol. 20, No. 6, 1978, pp 319-325.

[441 Hajek, T.J., Wagner, J.H., and Johnson, B.V.,"Coolant Passage Heat Transfer with Rotation,""lurbine Engine Hot Section Technology 1987,NASA CP-2444, October 1987, pp 211-223.

[45] Guidez, J. "Study of the Convective Heat Trans-fer in Rotating Coolant Channel," ASME pa-per no. 88-GT-35, presented at the 33rd Inter-national Gas Turbine and Aeroengine Congress,Amsterdam, The Netherlands, June 6-9, 1988.

12

lAReport Documentation PageSoace Administration

1. Report No. NASA TM-102079 2. Government Accession No. 3. Recipient's Catalog No.

AVSCOM TR 89-C-013

4. Title and Subtitle 5. Report Date

A Generalized One Dimensional Computer Code for TurbomachineryCooling Passage Flow Calculations

6. Performing Organization Code

7. Author(s) 8. Performing Organization Report No.

Ganesh N. Kumar, Richard J. Roelke, and Peter L. Meitner E-4839

10. Work Unit No.9. Performing Organization Name and Address 535-05-10

NASA Lewis Research Center 1L161102AH45Cleveland, Ohio 44135-3191and11. Contract or Grant No.

Propulsion DirectorateU.S. Army Aviation Research and Technology Activity-AVSCOMCleveland, Ohio 44135-3127 13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address Technical MemorandumNational Aeronautics and Space AdministrationWashington, D.C. 20546-0001 14. Sponsoring Agency CodeandU.S. Army Aviation Systems CommandSt. Louis, Mo. 63120-1798

15. Supplementary Notes

Prepared for the 25th Joint Propulsion Conference cosponsored by the AIAA, ASME, SAE, and ASEE, Monterey,California, July 10-12, 1989. Ganesh N. Kumar, Sverdrup Technology, Inc., NASA Lewis Research CenterGroup, Cleveland, Ohio 44135; Richard J. Roelke, NASA Lewis Research Center; Peter L. Meitner, PropulsionDirectorate, U.S. Army Aviation Research and Technology Activity-AVSCOM

16. Abstract

A generalized one-dimensional computer code for analyzing the flow and heat transfer in(the turbomachinerycooling passages has been developed. This code is capable of handling rotating cooling passages with turbulators(inline, staggered, or inclined), 180 degteeturns (both sharp and gradual turns, with and without turbulators), pinfins, finned passages, by-pass flows, tip cap impingement flows, and flow branching. The code is an extension ofa one-dimensional code developed by P. Meitner. In the subject code, correlations for both Jleat transfer coefficientand pressure loss computations have been developed to model each of the above mientioned type,of coolant pas-sages. The code has-te capability of independently computing the friction factor and heat transtfer coefficient oneach side of a rectangular passage. Either the mass flow at inlet to the channel or the exit plane pressure can bespecified. For'a specified inlet total, temperature, inlet total pressure and exit static pressure, the code computestheflow rates through the main branch and the subbranches (if any), flow through tip cap for impingemeitcooling (if any), in addition to computing the coolant pressure, temperature and heat transfer coefficientdistribution in each coolant flow branch. Predictions from the subject code for both nonrotating and rotatingpassages agree well with experimental data. The code was used to analyze the coolant passage of a researchcooled radial rotor.

17. Key Words (Suggested by Author(s)) 18. Distribution Statement

Turbine cooling Unclassified - UnlimitedCooling passage flows Subject Category 34Heat transfer

19. Security C/asslt, (of this report) 20. Security Clasilf. (of this page) 21 No of pages 22 Price'Unclassified Unclassified 14 A03

NASA FORM 1626 OCT W *For sale by the National Technical Information Servie, Springfield, Virginia 22161