Table Of ContentAIAA 2001-0664
Predicting the Rotor-Stator Interaction
Acoustics of a Ducted Fan Engine
Robert T. Biedron
Christopher L. Rumsey
NASA Langley l_esearch Cent el. Hampton, \'irginia
Gary G. Podboy
NASA Glenn Research C_nter, Cleveland, OH
T 4•
M. H. Dunn
Old Donfinion University. Norfolk, \'irginia
39th AIAA Aerospace Sciences
Meeting & Exhibit
8-11 January 2001/Reno, NV
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344
AIAA-2001-0664
PREDICTING THE ROTOR-STATOR INTERACTION ACOUSTICS OF A
DUCTED FAN ENGINE
Rol)erl T. Biedron* and (hrislo)he" 1,. tlumseyt
NASA Langley I_seai'('h (!ellt.er
Iiaml)ton, Virginia
(,ary (i. Podboy 1
NASA Glenn l:lesearch (Tenter
('lev,'land. OH
M. lt. Dram _'
Old l)ominion I:niversity
Norfolk, Virginia
Abstract slat.or inleraction modes have exisled for quite some
time (see, e.g., Tyler and ,qofrin 1), bul mosl COml)U-
A Navier-Stokes computation is performed for a
tational t.echniques to date rely exl ensively on exl)er-
ducted-fan configuration with the goal of predicting
imenla] measuren/ents and analytical sealing tech-
rotor-stator noise generation without having to re-
niques. Although such het, risl.ic melhods can pro-
tort to heuristic modeling. The calculated pressure
vide reasonable I)rediclions of engine lone noise ill
field in the inlet region is decom])osed into classical
many eases, they are fat' from perfect and il is ditfi-
infinite-duet modes, which are then used ill either
cuh to know where to turn when they are ill error.
a hybrid finite-eDment/Kirchhofl" surface met hod or
On the olher hand, l)redictions from firsl I)rin('il)les,
boundary integral equation method to calculate the
although more expensive, hold the promise of otf;'r-
far field noise. Conq)arisons with exl)erimenta] data
ing greater insight into and control of tile physical
are presenled, including rotor wake surveys and far
mechanisms behind tile noise gelleralion and l)ropa -
field sound pressure levels for 2 blade passage fre-
gallon processes. As eomt)ulers eonlinue to become
qllelley (BPF) t,olleS.
more powerful and inexpensive, tim grealer expense
1 Introduction of the first-principles al)proach it I)ecoming h'ss of
an impediment.
Tone noise in dueled fan engines, resultiug from
Humsey el. al.'-' first explored tile use of lhe firsl-
the interaction and response of the moving rotor-
blade wakes with the stationary staler vanes, prop- principles approach for predicting the one blade
passage frequency (1 BPF) modes in an advanced
agates both forward and aft through the duel and
ducted propeller (ADP) model. Only tile forwaM-
radiates to the far field. This noise impacts t)oth
l)ropagating modes were considered. The Navier-
(ommunilies as well as passengers and crew flying
Stokes equations were solved time-accurately on a
in aircraft. Theoretical models for predicting rotor-
moving grid will, sliding pal elwd inlerfaces between
*Research Scientist, Computational Modeling and Simula- the rotor and st.at.or grids. Turbulent flow was
lion Bl'aneh.
achieved lhrough the use of a one-equation lurlm-
tSenior Hesearch Scientist, (%mputational Modeling and
Simulation Branch. Associate Fellow AIAA. lenee model with a wall functioll al)l)roaeh. "fhe
;Aer_space Engineer, Acoustics Branch, Senior Member acoustic modes inside the engine were bolh geuer-
AIAA. ated and propagaled using this numerical lnelllod,
*_Assislalll Professor. Departmenl t)f Malhenlatics and and a particular mode of int.eresl was shown to prop-
Statistics. Member AIAA.
C(q)yrighl @2001 I)ythe American Instilute of Aeronau- agate well upstream of the rotor inside the engine
tics and Astronautics, Inc. No copyright is asserted in the with minimal attenuation. Separale acoustic codes
llnited States under Title 17, 17.S. ('ode. The l!.S. Govern- were used to propagate lhese internal results ()Ill l.o
ment has a royalty-free license to exercise all rights under the the far field.
c_,pyrigh( claimed herein for government purposes. All olher
rights are reserved by the copyright owner. The study of t{ulnsey el. al. demonstrated the
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feasibilityof usinga Navier-Stokes
CFD code to tially first-order accurate, which results in block-
both generate and propagate tile tone noise within a tridiagonal inversions for each sweep. However, for
dueled fan engine, tlowever, the initial study was for solutions that use FDS the block-tridiagonal inver-
1 BPF modes, which are often stronger and hence sions are further simplified with a diagonal algo-
easier' to predict than higher harnlonic modes. Also, rithm. Turbulence equations are solved uncoupled
most engines are designed with blade counts such from the mean equations.
l.]Jal all I BPF modes are cut off (do not propagate), Tile turbulence model used is the one-equation
so ill this sense the earlier ADP case was unrealistic. Spalart-Alhnaras (SA) model, 4 in combination with
The current study applies the same methodology a wall flmction al_proa.ch. The wall funct.ion ap-
as Ref. 2 to a lnore realistic case for which the 1 BPF proach obtains a "pseudo'-wall viscosity l]lal forces
nlodes do not propagate but tile 2 BPF modes do. the law-of-the wall to hold. Details can be found
Furthermore, more extensive experimental data is in Re['. 3. The advantage of using the wall time-
available for this new case, including rotor wake ve- lion form is thai the grid spacing does not need to
locity profiles between the rotor and sta.tor rows, al- be as tight near the solid walls (,q+ _ 80 as op-
lowing for a better assessment of tile first-principles posed to g+ _ 1), so the stretching into the field is
method. This reporl details the progress and lessons less severe. This is particularly iml_ortant for acous-
learned to date, with the purpose of guiding fllture tic computations, tbr which good grid resolution is
COlllplll ational efforts ill t.his area. Specifically, rotor needed throughout the field to resolve the acoustic
wake profiles belween the rotor and staler rows are perturbal ions.
compared with measured data, and forward-moving A sliding patched interface colulect,s tile rotor
acoustic mode amplitudes within the duct are ana- and slat,or rows. At this interface, non-conservative
lyzed. These in-duct acoustic results are then used interpolations are used, as described in Rumsey. '5
to conlput.e the far field noise in comparison with In this reDreuce, an engineering rule-of-thunlb was
experinmntally measured levels, using both a wave developed for determining the maximum computa-
envelope/Kirchhoff method and a boundary integral tional time step allowable so that the acoustic waves
equal ion method. that pass through the interface are not distorted. We
adhere to this rule-of-thumb ill the current work.
2 Numerical Methods
For all the computations performed in this study,
2.1 the (:FL3D code was run time-accurately with three
Navier-Stokes method in interaction region r-TS subiterations per time step performed in com-
The (TD code used in the current investigation bination with mult, igrid, as described in Refi_. :2and
is ('FL3D, a a widely-used structured-grid upwind 3.
finite-volume method. It, neglects viscous cross-
2.2 PropaKation technique to the far field
derivative ternls, which results in lhe thin-layer
Navier-Stokes equations in specified coordinate di- In principle, the CFD code could be used to di
rections. Third-order upwind-biased spatial differ- rectly calculat.e tile far field noise. However, because
of the code is only second-order accurate, such all ap-
encing on the convective and pressure terms, and
second-order differencing on the viscous terms are proach would require a prohibitive number of grid
used; it is globally second-order spatially accurate. points. To make the problem tractable, a hybrid
The CFLaD code can solve flow over multiple-zone methodology is used that combines the modal data
extracted from the CFD solution with more efficient
grids that, are connected in a one-to-one, patched,
or overset lnanner, and call elnploy grid sequencing, means of computing tile far field noise.
multi-grid, and local time stepping when accelerat- Two approaches are considered. In the first, the
ing convergence to steady state. Upwind-biased spa- modal data is input to Eversman's Finite Element
tial differencing is used for tile inviscid terms, and Model (FEM) duct radiatiou codefl This velocity-
flux limiting is used to obtain smooth solutions in potential based FEM code is then used to propagate
the vicinity of shock waves, when present. No lira- the acoustic waves away from tile inlet region; no at-
tier was employed for this study. Viscous terms are tempt is made to include acoustic propagation from
centrally differenced. Tile flux differem'e-st)litting the exhaust flow. While the FEM code has beetl
(FDS) method of Roe is employed t,o obtain fluxes found to be accurate in the near field, pha,,_e infor-
at the cell faces. mation is not welt represented in the far field. To
The CFLaD code is advanced in time with overcome this ditficulty, a Kirchhoff surface is con-
an implicit three-factor approximate factorization structed using the near field FEM solution, and a
method. The implicit derivatives are written as spa- Kirchhoff integral fornmlation is employed to corn-
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Anlerican Institute of Aeronautics and Astronautics
putethenoiseat,allypointin thefartield. This harnionic./7 is the nunlber of rotor blades, 1" is the
apl)roachis<lescribeinddetailill Ref.7. Thiswas
liillllber ofstator vanes, and /,' is zero or ;-ill)' positive
alsotileapproacuhsedill tileprevioursoior-stator
or negative integer.
noisestudy.'-'
In tile cllrrent study we are focusing Oll lit("
The second approach uses the dueled fan noise Ul)slreani-nloving 2 BPI" m = -6 lnodes (h = :2
t)rediction code TBIEM)D. s,<'' l ising boundary in- and k = -1). All I BPF modes are cut-off for lifts
tegral equaiiou techniques for solving the lilne har- configuration, il The m = -6 niodes are periodic
nionic convective wave equation, TBIEM3D calcu- over 1/61h of the engine eireuinference (60°). and
lates the SOulld scattered by an illfnitely thin, con- rol,_tl.e in the direct,ion opllo.sHf to thai of the rotor.
st,ant radius cylindrical duel. ill a Ullifornl axial flow These are the lowest-order circnnffereniial nlodes.
feld. Fan noise generation is approxinlated by silu- and hence have the least slringent grid-spacing re-
pie spinning illonopole or dipole point and/or line quirenienls for tile (II;'D code; the higher the order
sources, hi the present siinulation, spinning line the mode, the lnore points are required to accuralely
sources were used i.o generate the circuniferential represent it. Given an average ill-duel Math iiUlllber
modes of interest. The lille source strengtiis were of JI = 0.26F) between the rotor alld staler rows and
adjusted to match as closely as possil)le the radial M = 0.2.5 ill froul of the rotor, the only m = -6
mode decomposition front the (TI). nlodes that propagate upstrealn without decay ac-
cordiug to the infinite-duel theory are lhe first three
3 Results
radial nlodes. The axial wavelengths associated with
3.1 Description of the test ease each of these modes are: A(_,;.l) = 0.087 -- 0.089 m,
An advanced high bypass subsonic fan was de- A(_,;,_,) = 0.104--0.106 nl, and At_,;.3 ) = 0.151-0.157
signed and built by the Allison Engine Company m. The first, number ill the range represents tile
under contract to NASA Glenn Research Center, as wavelength a.ssocialed with the higher Mach nun>
described by Woodward et al. 1° The fan has 18 ro- ber. Note that these wavelengths are theoretical val-
tor blades with a diameter of :22 in. {0.5,59 m), and ues for a constant Mach-nunlber infinite duct: there-
4:2 stator vanes. In the acoustic tests performed at fore they represent approximate levels expected in
NASA Glenn, various configurations of st,ator vanes the engine, where the Mach nuniber varies.
were used: forward radial, aft, radial, swept only,
and swept plus leaned. For the present computa- 3.2 Grid size and spacing
tions, only the radial stators in the forward posi- For this case, it is necessary to have a grid that
t.ion are considered. (In the forward position, the covers a full 600 of the inside of the engine. Thus, 3
staler leading edge is al)proximately 3.95 in. (0.10 rotor passages and 7 sial.or passages nlust be mod-
m) behind the rotor trailing edge.) Tile COlnpuia- eled for the engine with 18 blades and 42 vanes. The
lions use a fail speed of 5210 RPM, whMl is 50% grid for tile current Sltldv iS lnade up of these 10
of the nontinal design speed (approach setting), and ZOIles. plus 3 additional ZOlleS nlodeliug the exlerior
ouly forwar(l-proi)agating acoustic lllodes are con- of tile engine, out t,o a far field approxinlalely 117
sidered. The current computations are run using in. (O..qF)lit) in from, 62 in. (1.;57 lit) above, and .rig
a free stream Math number of M = 0.:2. This is in. (1.:15 iii) t)ehind the engin(' cow] (the eligille cowl
higher than the 3I = 0.1 used in Ret'. 10. However, is approxinlately 34.5 in. (0.88 hi) long). All overall
the higher free slreanl Math nlnnber primarily all view of the far field grid is showll ill Fig. 1. The
feels the flow external t.o tile engine, including the grid size of each rotor passage is 321 x 5T x 41 (these
stagnation point on the cowl. Tile flow inside the en- numbers represent axial, radial, and circumferential
gine itself is priniarily deternlined by the rotor RPM spacing, respectively). Tile grid size of each staler
and is not expected to differ signifcantly for the two passage is 129 x 57 x 33. There are approximately
conditions. The Reynolds number is taken to be 4.12 x 10'; total grid poiuts in the 13 zones.
4.882 x l(l'; per hi. To do a reasonable job in an engine acoustic COlll-
With 18 rotors and 42 st,at,ors, Tyler-Sofrhi inli- lmiation, the CFD code has to adequately re,,,oive
nile dnci linear theory I ('all be used to deternline two iniportant aspects of tile flow: the "'creation"
tile R)rward-lnoving modes that l)rol)agat.e. Duet phase and tile "'propagalion" phase. The "creation"
acoustic niodes are generally characterized as (tn, n) phase is lhe phase that. occurs near tile stat.or lead-
nlodes by their circumDrent, ial and radial mode ing edge, where the int,eraction of the rotor wakes
numbers m aud l_. As discussed in fief. I, the niode witli the vanes ('reales tile duct acouslic iliodes in
number in for a rotor-staler interaction can be ob- tile firsl place. The "'prot)agaiion'" phase is life ad-
tained from nl = lib + ,4"I', where h is the BPF vection of these modes through the flow fiek[. The
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ideabehindafirst-principleaspproacihstousethe
diffuses potential spurious reflections from the exte-
Navier-Stokeesquat.iontosresolvbeoththecreation rior boundaries of the grid. (If one were t.o attempt
andpropagatiopnhasewsithintilehighlynonlinear this type of computation with only an unstretched
regimeof theenginew, heresimplerlinearacous- internal-engine grid, the acoustic tield woukt be con-
ticmethodasrenotexpectetd.obevalid.Oncethe laminated by reflections from the boundary unless
acoustimc odehsavebeenpropagateadwayfrom
the special non-reflective acoustic boundary conditions
nonlinear regions, linear acoustic methods can then were employed.)
take over and be used to determine the noise in the I/easonably accurate resolution of the rotor wakes
far field. is necessary, because it is their interaction with the
The grid size and spacing is a very crucial as- stator vanes that causes the tonal acoustic modes.
pect of an engine acoustic computation. This point To achieve high resolution, the rotor grids nmst be
calmot be stressed enough. To apply the current ch, stered near the approximate location of the wakes
first-principles approach to compute acoustic fea- as they convect aft,. A view of the j = aa planes
lures, it is necessary to sufficiently resolve the acous- of one rotor and one st.ator passage are showu in
tic waves of interest as they propagate and the re- Fig. 4. The "wake cut,s" of the rotor grid are ap-
gion where the acoustic modes are initially gener- proximately aligned with the local rotor direction,
ated must be fine enough to adequately resolve their so the grid lines follow the approximate paths of the
creation. Several close-ups of the grid are shown in wakes themselves. Additionally, the rotor grids ex-
Figs. 2 - 6. The grid was generated using TIGEIR. r-' tend downstream to be within 0.877 in. (0.022 m) of
In the following paragraphs, we will point out. some the stator leading edge. As a result., the rotor wakes
important elements of the grid and their relatiouship are in a "clustered-grid'" region for a long distance
to the acoustic asl)ects of the computation. before the wake passes through the rotor-stator in-
The grid is ch,stered near all solid walls, and terface, where clustering is ndmlnized to improve
stretches as it moves into the interior. As mentioned inter-grid interpolations.
earlier, to avoid cells that are too large (because of Initial computations with what was originally con-
too-large stretching factors), we utilize a turbulence sidered "reasonable" axial spacing near the stator
model with a wall function and use a mininmm spac- leading edge led t.o results in which the (-6, 1) mode
ing near walls such that the y+ level at. the first, grid was not captured at. all in the "'creation" phase. It.
point, from the wall averages approximately 80. The was subsequently determined that considerably finer
current grid maintains fine axial spacing within the spacing is required near the staler leading edge. A
engine from the front of the inlet to past the leading close-up of the sial, or leading edge region in the cur-
edge on the stator. This axial spacing is fine enough rent grid is shown in Fig. 5. It. is still an open
so that there are at least 25 - 30 points per axial question whether even finer grid spacing in the re-
wavelength tbr each acoustic mode of interest.. The gions surrounding the leading edge would signifi-
results for the model problem studied in [/ef. 5 indi- cantly benefit the prediction of the acoustic modes.
cate that this is an adequate resolution, at least, for 1 In all of the COmlmtations done for this study,
BPF modes. A view of the k = 1 planes of one rotor the rotor tip gap is crudely modeled by collapsing
and one stator passage is given in Fig. 2. (Note that ("zipping") the rotor grid zones for the upper 5 grid
the figure distorts the inner cowl apparent shape, be- points. This zipping results in an average tip gap
cause the grid lines sweep circumferentially to align spacing of approximately 0.03 in. (7.6 × 10-4 m).
with the rotor angled direction.) The axial spac- which is similar t.o the actual tip gap measured in the
ing is necessarily clustered in the regions near the experiment near the leading edge, but. is over three
leading and trailing edges, but the average spacing times larger than the tip gap lneasured at the trail-
elsewhere ranges from roughly 0.05 in. (0.0013 m) to ing edge. A view of the rotor tip is shown in Fig. 6.
0.12 in. (0.0031 m). Typical circunfferential spacing looking aft. We originally attempted to model the
in the rotor and stator zones between the two rows actual tip gap spacings, but the finer grid spacing
of blades is showl| in Fig. 3. ('lustering in the cir- required near the trailing edge made grid generation
cumt_rentiat direction is necessary both for the wake lnore difficult and also caused excessive local stretch-
region (see below) as well as near the blades. ing factors that we decided were best to aw)id.
In front of the engine inlet and behind the starers.
the Navier-Stokes code is no longer nsed to track the 3.3 Computations
acoustic modes, so the grid is allowed to stretch ax- Computations were performed at, a nondimen-
ially in these regions. This stretching accomplishes sional time step of Al' = 0.05 (nondimensional-
two objectives: it reduces the total grid size, and it. ized by characteristic length divided by free stream
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American Institute of Aeronautics and Astronautics
speedofsound).Tilecharacteristilcengthinthe
The first station corresl)onds l,o the LDV location
(!FDsolutionis 1ill. (0.02,5m4) andtile speed closest to the rotor while the second station corre-
ofsoundis takenas(% = :HOA45m/s.
I)imen- sponds to tile" I,I)V location closesl to the stator.
sionally, this time step corresponds with a time The second station is located within the stator zones
step of ,._kl = 3.73 × 10-e; s. The frequency of all of the computational grid. Note that the LDV data
2 BPF modes is given I)3' A = 2B_2/c = ,57.69 was taken with the slat.or vanes in the aft position.
m -t, so the time corresponding to one period is whereas the CFD is perfornled with the stators in
Ir = 2rr/(c,,,, K) = 3.2 x l0 -4 s. (A given rotor blade tim forward i)osition. However, the I)osilion of the
rotates through 1 blade passage = 20° iu 6.4 x 10-4 sialors is not exl)e('te(t to significanlly impact the
s.) Thus, tile current time step yields approxintately rotor wakes at the positions measured. Axial veloe-
b6 time steps per period for tile 2 BPF modes. This ily contours at constant axial positions are shown in
lmmber exceeds the 60 recommended in Ref. 5. Figs. 9- 1"2, with colnl)uted co,ltottrs corresponding
As a first phase of tile COml)utation for this case, to the fine grid. (;enerally speaking, the COml)uted
we investigate the ability of the CFD code to propa- wakes are nmch narrower and exhil)it more curva-
gate a specified duct acoustic mode forward through lure than the LDV measurements. Axial velocity
the duct. V_'e do this by removing the stator defect i)rofiles at. a radius of al)proxintately 8.5 in.
grid zones and specifying time-varying duct acoustic (0.216 m) are, shown in Figs. 13 and 14, correspond-
pressures at the exit face of the rotor grids, accord- ing l,o tile (lashed lines in Figs. !I- 12. Although
ing to the formula: tile computed width arm general shape are different
from the experiment. (:1"1) does a reasonable job
p(r, 0, x) = A J,,, (l\,.r)expi[c-,. l'(t - me - IC,,x]. (1)
capturing the depth of the rotor wake as well as the
overall trend of its evolution downstream. The axial
.-t is the magnitude of the perturbation. J,,, is the
Bessel function of the firsl kind and order n), /(,. is velocity defects on the fine grid are not nmch differ-
the radial wave number, and 1\,_ is the axial wave ent fro,n the medium grid at the first slalion, t)t,l at
the second station the wake depth of the fine grid is
nunlber, lit essence, this computation is a check (.o
larger and in better agreement with exl)eriment..
test whether the grid resolution is stlfficient.ly fine for
the propa.qalion part of the conlputal.io,i. In other \¥e now turn to an analysis of the duct acoustic
words, given a duct acoustic mode of given strength, modes generated 1)3' lhe Navier-Stokes code. This is
is the given grid fine enough to prol)agate it forward do]le in a 1)ost-processing step by decoml)osing tile
without significant attenuation to the rotor blades htstantaneous pressures output by (TL3D within
(where seine of the nlo(le is scattered into different the duct into its colnpone,/t duct lnodo strengths.
fl'equencies'3); and, for the part of the tootle that The strength .4 of the (-6, 1) mode is shown between
survives the passage through the rotor, is the given the rotor and stator rows in Fig. 15 and in front of
grid in front of the rotor fine enough to propagate it. the rotor row in Fig. 16. Axial distances in these fig-
forward without signifieam all.enuation to the duct ures are given in ternts of the distance forward of the
mlet? rotor st acking axis. The nlode strength approaches a
As shown in Figs. 7 and 8, when an initial (-6, 1) quasi-constant level as it. prol)agat.es forward toward
mode acoustic amplitude of apl)roximately _4 = 40 the rotor t.rai[ing edge, altd is roughly coztsta,tl after
Pa is iml)osed at the rear of the rotor grid. it, propa- it passes through tile rotor row and travels forward
gates forward to the trailing edge of the rotor blades through the duct. The wave-like structure is evident
with very little attenuation on either the fine or in both figures, and is close to the theoretical value
me(lium-level grid. Then. roughly a third of the of A(-,;,1)_ 0.09 m.
wave strength makes it through the rotors. The Note in Fig. 15 that there is no distortion in the
wave is t)ropagated forward on the fine grid all tile acoustic signal evident near tile rotor-staler sliding-
way t,o tile inlet wit.h no attenuation, whereas on the zone interface at .r = -0.]2'56 nl. This lack of dis-
medium-level grid it, loses a small l)ereentage of its tortion indicates sm-cessful transfer of acoustic infer-
strength. Therefore, the current fine grid appears ]nation across the 1)arched interface. 5 Between the
to be fine enough for the propagation of the (-6, 1) rotor and stator rows. the (-6, 1) strength front the
mode of interest. fine grid averages roughly 20 Pa, and in fl'ont of the
Next, we run the full l)rol)lem, including the sta- rotor row. it averages roughly .5 Pa. This 7'5_7cper-
rers, and determine the ability of the (TD code to cent reduction in mode strenglh is similar to that
successfully .q_n_r(tle the 2 BI)F modes. As a first. seeu in tile earlier preseril)ed-mode ease. There is a
step, we compare the (-Oml)uled rotor wakes with modest increase in magnitude oftit,' mode strength
LDV data taken at. NASA (;lenn Research Center. between tile nlediunl and title level grids ill front
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Anterican Institute of Aeronautics and Astronautics
oftilerotor,indicatingthatfurtherrefinemenbte-
dicted far field noise levels increase by nearly 10 dB
yondthefinegridmaystillyieldincreaseadcoustic and are much closer to the experilnental measure-
strength.Resultsforthe (-6, 2) and (-6, 3) modes ments. Other noise-prediction methodologies ignore
in front of the rotor are shown in Figs. 17 and 18. tile t,ransmission losses entirely.ll
The (-6, 2) mode from tile fine grid is yery weak,
Why tile inlet inodal strengths are underpredicted
with an average strength of only about 3 Pa. The
remains an open question. It may be thai the inter-
(-6,3) mode has a higher amplitude of about 10
action of the rotor wakes with the stators is not pre-
Pa. Tile wavelengths of both the (-6, 2) and (-6, 3)
modes are close to the theoretical levels. Note that, dicted adequately because the predicted rotor wakes
are much narrower than the measured wakes. This
among the three modes, the (-6, 3) mode shows the
underprediction of wake width is possibly due to ei-
most significant change in magnitude between the
ther inadequate physics in the turbulence model or
medium and title level grids.
under-resolution of the rotor wake vortical structure
Although not shown, as a further check on tile
and its inherent unsteadiness.
acoustic computations, we studied the mode behav-
ior at a given station in front of the rotor as a func-
Thinking ill t.erms of a Fourier transform of the
tion of time. Given that the mode behavior is kin(- rotor wakes in the circmnferential direction, liar-
matt(ally determined, we know theoretically ,how rower wakes have a higher frequency contenl than
much it should rotate in a given number of itera- wider wakes. Perhaps, then, the eolnput.ed noise
tions. 1Result,s confirm that the (-6, 1) and (-6,3)
sources are biased towards harnmlfiCS higher than
modes rotate at approximately the correct rate and 2 BPF. Alternatively, the losses that occur as the
in the correct direction. The (-6,2) mode is too
sonnd propagates forward through the rotors may
weak t.o yield meaningful analysis.
be exacerbated by tile numerical scheme. However,
solutions obtained for two grid resolutions did not
4 Far Field Noise
show a significant variation of the modal amplitudes
The final step in the current study was to use the with mesh size.
extracted m = -6 modal strengths in the inlet duct
forward of the fan {at x = 0.1269 m) t,o predict the
far field noise. The predicted far feld directivity is 5 Sunnnary
shown in Fig. 19. Note that past approximately 60
(leg., the measured levels in the experiment are ele- Performing acoustic computations on full rotor-
vat,ed due to aft-end noise, which was not included staler ducted fan configurations using the Navier-
ill the CFD computation. As can be seen, the com- Stokes equations is by no means a simple push-
puted sound pressure levels forward of 60 (leg. are button task. The work presented here is the sec-
significantly lower than the experilnentally measured ond of a series of COml)utations performed to as-
levels, using both the FEM/Kirchhoff approach and sess whether Navier-Stokes solvers can be used to
tile TB1EM3D approach. (Note that TBIEMaD uses directly capture the sound generation mechanisms
all idealized duct, whereas FEM/Kirchhoff uses tlle of rotor-stator interaction, without resorting to more
actual duct geometry. Thus, results are not expected heuristic modeling techniques. The earlier study, for
to agree: ['or example, TB1EM3D yields higher SPLs a configuration exhibiting 1 BPF tones, had a fair
al higher emission angles because of diffraction from degree of success in predicting the far field noise. In
the idealized duct's sharp leading edge.) Tile cause the current study, for which the lowest order propa-
of the discrepancy between CFD and experiment is gating modes are 2 BPF, the predicted far field noise
therefore almost certainly related to the extracted levels are about 10 12 dB low. It was determined
modal data from the (:FD solution - the computed that tile propagation within the duct, of the 2 BPF
source strengths in the inlet region are too low by modes was not as ditficu]t as their treat*on via the
about a factor of 3---6. first-principles approach. The wake widths obtained
As discussed previously, there is a 6,5%-75(7_, reduc- from the computation were considerably narrower
tion in the modal amplitudes as the waves generated than those measured in the exl)eriment. This may
by rotor-stator interaction travel forward through be be the primary cause of the discrepancy in the
the rotor and into the inlet. Although not shown. computed and measured far field noise levels. Addi-
if the transmission losses through the rotor are ig- tional research is needed to explore ill greater depth
nored, i.e.. if the modal strengths between the stator the grid and turbulence model requirements ill the
and the rolor (e.g., Fig. 15) are used instead of those interaction region where the rotor wakes convect and
in front of the rotor (e.g. Fig. 16), then the pre- the acoustic modes are created.
6
American Institute of Aeronautics and Astronautics
Acknowletlgments 11. Envia. E., and Nallasamy. N.. "'Design Selection
and Analysis of a Swept and Leaned Staler ('on-
Tile authors would like to thank F. Farassat of
('el)t ,'" NASA 'I'M- 1.998-2D86(i2, I)ecemher 1.q.q_.
NASA Langley t/esearch Center for malG fruitfiil
discussions during the course of this work. The au- 12. Shill \1. It.. Soni, B. K.. and Janus, J.
thors also thank R. \\'oodward of NASA Glenn He-
M.. "TIGEH: Turbomachinery Interactive (;rid
search Center for providing measured sound data, (hmel'atioll / l:low Silnulatiol_ System Iser's
and L. Heidelberg and D. tluff of NASA (,lenn Fie- Mamlal,'" Mississippi Stale ITniversil.y Pul)lica-
search Center for their advice and experlise. lion, 1994.
R,eferences la. ltanson, D. B., "Coupled Two-l)inwnsional (:ar-
I. Tyler. J. M. and Sofrin. T. G., -Axial Flow cade Theory for Noise and Insteady Aerody-
namics of Blade Bow Interact ions in Turbofans,"
(!omt)l'essor Noise Studies," SAE Transactions.
NASA CR-4506, 1994.
Vol. 70, 1962, Pl). 3()9 332.
_. ]{tllllSey, (!. L., Biech'on, R. T., Farassat. F..
and SI)enee, P. L., "[)ucted-Fan Engine Acoustic
Predictions Ising a Navier-Stokes (%de,'" Jour-
nal of 5ound and libralton, Vol. 213, No. 4,
l.().(}_,pp. 643 66t.
3. Krist. S. L., Biedl'on, H. T., and flumsey, ('. L.,
"'('FLaD l!ser's Mmmal (Version 5.0)". NASA
TM- 19,qS-2()8444, June 1998.
4. Spalart, P. H.. and Alhnaras. S. t:1,, "A One-
Equatiotl Turbulence Model for Aerodynamic
Flows," La Roche rH_, Atrospatlal(, No. 1. 1994,
I)1). 5 21, M=0.2
5. t_Imnsey, (I. L., "(?Oml)Utalion of Acouslic
'i
\¥aves Through Sliding-Zone lnlerfa('es,'" AL4A
stator zones
Journal. \%1. :;5, No. 2, 1.q97,Pl). :26:; :2(i8. rotor zones
6. Floy, I. D., Eversman. W., and Meyer, tl. D..
"lmprovetl Finite Element Modeling of the Tur-
Figure 1. Far tield view of grid (/,'= 11)lane).
t)ofan Engine Inlet Fladiatioll Problem," Report
Prepared for NASA Lewis Research (_enler [Tn-
der (:ontract NASa-25952, Task 10, April 1993.
7. Spenee, P., "Dueled Fall Noise Pre(liction [:s-
ing Wave Envelope Analysis and the Kirchhoff
Formula," AIAA Paper .(t7-1651, May 1997.
8. Dunn. M. H., "'TBIEM31) - A Computer Pro-
gram for Predicting I)ueted Fan Engine Noise,
Version I. 1,'" NASA/('[IA)7-206232, September
1.q97.
9. l)unn. M. I1.. Tweed..J., and Farassat, F., "'The
Apt)lication of a Boundary Inl.egral Equation
Method to tilt, Prediction of Ducted Fan En-
gine Noise," Jottrnal of ,",'ound and libration,
Vol. 227, No. 5, 1999, I)I). 1019 1l)48.
l(I. Woodward. R. P.. Elliot, D. M., Hughes, (I E.,
and Berlon..1..I., "'Benefits of Swept and Leaned
Slat ors for Fan Noise t{eduction,'" AIAA Paper
9.()-047(.), .]anuary 1999.
7
Anlerican Institut,e of Aeronautics and Astronautics
rotor-stator interface
stator T.E.
stator LE. , Y_x
rotor T.E. z
rotor T.E.
rotor LE.
stator L.E. stator T.E.
rotor L.E.
inflow
from
zone 1
hub L.E.
Figure 2. View of rotor and st,ator grid zones (k = 1 Figure 4. View of rotor and stator grid zones (j = 35
plane). plane).
rotor zones stator L.E.
stator zones
¥
i
Figure :{. View of rotor and slat, or grid zones (i =
l:igure 5. Close-up view near stat, or leading edge
250 plane in rot, or zones and i = 19 plane in slat or
(j -- 35 plane).
ZOllOS).
8
American Inst,itute of Aeronaut, ics and Ast,ronaut, ics
