Second Computational Aeroacoustics (CAA) Workshop on ...

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Cover photo (Contour plot of acoustic pressure field produced by source scattering from cylinder) Printed copies available from the following: NASA Center for AeroSpace Information 800 Elkridge Landing Road Linthicum Heights, MD 21090-2934 (301) 621-0390 National Technical Information Service (NTIS) 5285 Port Royal Road Springfield, VA 22161-2171 (703) 487-4650 ii E B L E !
PREFACE Thisvolumecontainstheproceedingsof the<strong>Second</strong><strong>Computational</strong><strong>Aeroacoustics</strong> (<strong>CAA</strong>) <strong>Workshop</strong>on BenchmarkProblemsco-sponsoredbyFloridaStateUniversityand NASA LangleyResearchCenter.<strong>Computational</strong><strong>Aeroacoustics</strong>embodiestheemployment of computational techniquesin thecalculationof all aspectsof soundgenerationand propagationin air directlyfrom thefundamentalgoverningequations.As such,it enjoys all thebenefitsof numericalapproaches includingremovalof therestrictionsto linearity, constantcoefficients,singlefrequencyandsimplegeometriestypicallyemployedin theoreticalacousticanalyses.In addition,mostimportantlyfrom theacousticviewpoint, soundsourcesproducedby fluid flows arisenaturallyfrom thefluid dynamicsanddo not requiremodeling. However,thesebenefitscomeat thecostof modificationof standard computationaltechniquesin orderto handlethehyperbolicnatureandsmallmagnitudeof thephenomenon. Thefirst <strong>Workshop</strong>in thisseries,whichwasheldin 1994,containedbenchmark problemsdesignedto demonstratethatthenumericalchallengesof <strong>CAA</strong> couldbe overcome.Thesuccessfulaccomplishment of thatgoalledto morerealisticbenchmark problemsbeingchosenfor this <strong>Second</strong><strong>Workshop</strong>in anattemptto convincetheU.S. Industrythat<strong>CAA</strong> waswell on its wayto comingof ageandwouldbecomeanimportant designtool asCFDistoday. Thebenchmarkproblemsare: Category1-AcousticScattering frgrn a Cylinder or a Sphere. Acoustic scattering from a cylinder is a model of the technologically important problem of propeller noise impinging on the fuselage of an aircraft. The sphere case was included to challenge the community to solve a computationally intensive, fully three-dimensional geometry in which the potential of parallel computations could be demonstrated. Category 2-Sound Propagation through and Radiation from a Finite Length Duct. Duct acoustics finds application in jet engine and shrouded propeller technology. Classically, such problems have been broken into three parts: source description, duct propagation, and radiation into free space. In these benchmark problems, although the source was specified, the contributor was challenged to solve the duct propagation and farfield radiation problems simultaneously. Category 3-Gust Interaction with a Cascade. Turbines, such as employed in jet aircraft engines, typically contain cascades of rotor and stator blades. The problems in this category were designed to demonstrate <strong>CAA</strong> technology, such as computing the sound generation due to the wake of an upstream cascade impinging on a downstream cascade and the ability to faithfully propagate waves through a sliding interface between a stationary and a moving grid, necessary to approach the industrial turbomachinery noise problem. Category 4-Sound Generation by a Cylinder in Uniform Flow. Aeolian tones which are generated by uniform flow into a cylinder are important in airframe and automobile noise. Further, this geometry is a model of the technologically critical class of high Reynolds number, massively separated flow noise generators. In this problem, the sound source is inherent in the fluid dynamics and would not exist if the flow were inviscid. Thus, the contributor is challenged to attack a fully turbulent flow. Since a direct numerical IIo Iil
Page 1 and 2: NASA Conference Publication 3352 <s
Page 3: .Y NASA Conference Publication 3352
Page 7 and 8: ORGANIZING COMMITTEE This workshop
Page 9 and 10: CONTENTS Preface ..................
Page 11 and 12: Large-Eddy Simulation of a High Rey
Page 13 and 14: Problem 1 Benchmark Problems Catego
Page 15 and 16: Problem 4 This is the same as Probl
Page 17 and 18: , / circilar duct I incoming sound
Page 19 and 20: Computational __ D
Page 21 and 22: where ANALYTICAL SOLUTIONS OF THE C
Page 23 and 24: The Greens function for (18)- (19)
Page 25 and 26: where b = In2/w 2. Boundary conditi
Page 27 and 28: SCATTERING OF SOUND BY A SPHERE: CA
Page 29 and 30: where h O) (z) is the spherical Han
Page 31 and 32: RADIATION OF SOUND FROM A POINT SOU
Page 33 and 34: ef. 6. Theincident pressureemitted
Page 35 and 36: 1 -g (Y3) lim .... - _ (X 3) - _ _
Page 37 and 38: 7. , , . Martinez, R., "Liner Dissi
Page 39 and 40: EXACT-SOLUTIONS FOR SOUND RADIATION
Page 41 and 42: n=l Here R,.m is the conversion coe
Page 43 and 44: where f_,(O) = (-i) ' J=(vm, )p24 (
Page 45 and 46: ,i Log e K(ot) da, with b_+< q_+< b
Page 47 and 48: As a approachesy, onereadilyobtains
Page 49 and 50: It follows thenthat, as7/(0)approac
Page 51: Ira(a) J . :::--::::::::_'.-.::, a=
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n -3 -2 -1 0 +l 72 -6 -5 -4 -3 -2 -
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Application of the Discontinuous Ga
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eference1. In addition, the allowed
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c_ = i. $/Igl, and fl = j-_/l_l. Ea
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(a). Pressurecontour at t = 10. P 0
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i 0.01 : " o.o - _;" .:y I -0.01 _
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...... r=5.5 --r=7.5 8e-06_ A /_ l
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COMPUTATION OF ACOUSTIC SCATTERING
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five-stage Runge-Kutta scheme (Hu e
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processing.Theunit processingtimewa
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lo ! 51- o' -1o 10 0 -10 I , •
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0 ] ' ' ' f i , , , -10 -5 0 5 10 1
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0. _5 i 5,0000E-6 O.O000EO -5.O000E
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o 13 soLvT ON Acoustic S ,ERIN PROB
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Gaussgrid, Xj+I/2 , mapped onto [0,
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The coefficients,a x and aY determi
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-4 -2 0 2 4 Figure 2: Subdomain dec
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four around the cylinder. The PML e
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Application of Dispersion-Relation-
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where damping factor v = eAr × A9
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O x 10-l° 4, , , , , .... i 3.5 1_
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DEVELOPMENT OF COMPACT WAVE SOLVERS
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supportedthat C3N is long-time stab
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Figure 2 shows intersectionsof hori
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0.08 0.06 0.04 0.02 -0.02 -0.04 0 C
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OV 10p --+---=0 0t 7- 00 Op 1 c)(rU
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parallel to the radial direction, s
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¢-_ 4e--10 3e--10 2e--10 le--10 0.
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[3L- 0.06 0.04 0.02 0.00 --0.02 ...
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over ahalf-plane.Theequationsusedar
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At the computational boundaries, fl
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esolution of the grid causing the s
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0.08 q'- I ' "'I ..... T--F --[ I I
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"o_ 0.05 0.04 0.03 0.02 0.01 -0.01
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Forbothproblems(1& 2 of Category1),
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0 -3 -6 -9 -12 -15 -18 -21 -24 -27
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0.07 0.06 0.05 0.04 0.03 0.02 0.01
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•sy" _'J ApplicationAbsorb,n..oun
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First, the grid pointswill be overc
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2.3.1 Results of Problem 1 2.3 Nume
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Ov Op 0--t-+ Or = 0 (7.2) Op Ou 0;,
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To absorbthe out-goingwavesat thefa
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4.2 Inflow condition At the inflow,
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and u-velocity contours. In the vel
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mtel r BPouMLary Condition Figure 1
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0°0005 0.0004 0.0003 0.0002 0.0001
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5 0 -5 Figure 7a. 0 -5 Figure 7b. i
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008 006 0,04 i 0.02 O,., 0.0 13, .0
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i / Figure 13. Pressure contours at
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100 i0 -I 10 -z i0"3 10 .4 lO-s Fig
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100 i0 "] i0 "_ e_ i0 "s 10 -4 10 -
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4.0 3,0 2.5 2.0 0.0 4.0 _-._-,_ 3.0
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5.e-07 4.5e-07 4.e-07 3.5e-07 ¢_¢
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5.e-07 | 4.5e-07 I 4.e-07 [ _ 2.5e-
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1 + 3 + (a) (b) Figure 1" Basic sec
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Unfortunately the resulting schemem
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Figure 3: A typical (but rather coa
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! -10.0 -3.3 3.3 10.0 Figure 5: Pre
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0.07 0.06 0.05 0.04 0,03 0.02 0.01
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CONCLUSIONS _Te have presented a pr
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The methodis basedon a least-square
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For the linear wave problem of Cate
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FIG.1 PROBLEM 2 OF CATEGORY 1 - ACO
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0 0 0 0 0 0 0 0 ! (e'£'],)d 172 -4
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"Z3 c_ E < Q "13 ii i {3. E < Fig.
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200 -100 FIG. 7 TIME HISTORY OF AN
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ABSTRACT ADEQUATE BOUNDARY CONDITIO
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}Ve note that each v (k) is determi
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FORMULATION OF THE PROBLEM AND THE
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where APPENDfX We considerthe follo
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0.06 0.01 -0.04 0.06 0.01 -0.04 m w
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i 0.05 - -0.00 - \ 0.05 - -0.00 - -
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ditions. The formulation and implem
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J ! s J 18D 4D 5D Figure 1. <strong
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10 -10 rm 3.0 2.5 2.0 1.5 1.0 0.5 .
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3. CATEGORY 2, PROBLEM 2 The axysim
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off the axis. Such a change often r
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In the space" below, we will concen
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3.5. Numerical Results 1 I 1 Three
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p(x) 2.0 1.5 1.0 0.5 0.0 2.0 1.5 1,
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p(x) 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0.
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For the case w " _s_, there are thr
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where E is an (M + 1) x 5 matrix an
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The v-velocity component in the out
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Figure 17 shows the calculated pres
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10-6 4.0 3.0 1.0 0.0 0.0 1.0 2.0 3.
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7'/ L/3
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w E W C w s S [.;sing this ceil-cen
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neighbors are involved. Both of the
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3e- 10 2.5e-10 ._ 2e-10 e-, • 1.5
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Future work involves the inclttsiot
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NONLINEAR, HYBRID CODE The hybrid d
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z agree better now although there a
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Figure 1: Snapshot of the acoustic
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-11 -12 -13 --% oT .9o -14 -15 Cat
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THREE-DIMENSIONAL CALCULATIONS OF A
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the IBM SP2. The computational doma
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intersects the center of the sphere
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ON COMPUTATIONS OF DUCT ACOUSTICS W
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It can be easily seen that duct aco
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the duct diameter D for problem 1 a
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To fix "this problem, a multi-domai
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60.0 , _ , , ,. _- f , 40.0 j 20.0
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0.004 [-- ' r .... , - , ," . ....
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w .................... 0..IJ'_l._ .
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{u} B= P 0 U M_v { M_p+w } ooP D= 0
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aseline case, as it employed a very
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the incoming wavesolution from the
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P(z) 1.0 Pressure Envelope ((o=7.2)
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v.rti_'al ¢li_tlllb;tl_('v. ;t11,1
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,l,>mairlOD. the,_4,_'r_ll_[ mt_'_L
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This is r,',',,g1_iz_',l a,,__zl ,q
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i ..J 2o i ¢.5 04 -2 0 fj,o_ DDD \
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2 8 ]or o 0,0 02 0.I 0.6 \ Circumfe
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Numerical Algorithm Equations (1) c
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The results are divided into differ
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0.012 0.01 0.008 0.006 0.004 0.002
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2 ... - -_ Patternrepeats I -- [ --
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-- o26 -7/ COMPUTATION OF SOUND GEN
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2.0 1.0i CI (Im.)o.o i ; -1.0 -2.0
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120 100 SPL, dB (re: 20 _Pa) 8O L
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REFERENCES 1. Lighthill, M. J., "On
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Perform numerical simulations to es
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[ RANS - Dirichlet B.C [ NNNNe , Pe
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.? _i, _ 80 .... 6O O0 02 04 0.6 0.
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A VISCOUS/ACOUSTIC SPLITTING TECHNI
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Ov' _" v o%' u'v' , OV v' OV Uv' Vu
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2 2 2 2 +L_ °_ _[_-_)J--T[_+d _) T
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corrector method was chosen. It is
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where # = p', u',v',p'. At the oute
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Finally, the latter portions of the
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p' o oo_ 9'3 t3 O3 75 7O 65 Nearfie
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LARGE-EDDY SIMULATION OF A HIGH REY
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In the implementation of the modeli
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to Cs = C 1/2 = 0.1. These LES gave
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a) c) ! • t r 2 i " i Figure 2. C
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t))
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A COMPARATIVE STUDY OF LOW DISPERSI
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Naturally, a left upwinded formula
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where F and G are flux vectors, and
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temporal integration of the semi-di
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vent reflected numerical waves from
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0.5 0.4 0.3 0.2 0.1 -0.1 0.6 0.4 0.
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13- Q- 0.2 0.15 0.1 0.050 [ -0.05 -
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1 e-06 9e-07 8e-07 7e-07 6e-07 5e-0
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133 cL cL 0.008 0.006 0.004 0.002 -
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0.0014 0.0012 0.001 0.0008 0.0006 P
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OVERVIEW OF COMPUTED RESULTS Christ
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10 -10 13.0 _i,i_ Illlllll, H _l,,l
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0.05 0.00 -0.05 0.05 0.00 -0.05 0.0
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0,05 0.00 -0.05 0.05 p(t) 0.00 -0.0
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SOLUTION COMPARISONS. CATEGORY 1: P
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_-12 8 Cat 2, Prob 1 " [_ Myers (BE
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p2=D(8) o.010 0.009 0.008 O.O07 0.0
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_:D(O) 0,12 0.11 0.10 0.09 0.08 0.0
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i° o. $ £ ,./ q 0.00 I i 1 1 0.20
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er .< o
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a- < (J O O ¢q o O O d J J o 0.00
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SOLUTION COMPARISONS: CATEGORY 4 Ja
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presenceof thewind tunnelwalls. The
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i == Slrul and Pylon Fan-OGV Pressu
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z >, O I.O O O O O (:3 O Some of no
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