Second Computational Aeroacoustics (CAA) Workshop on ...

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simulation cannot be carried out at the Reynolds number requested with present computational capabilities, of particular interest is the success of the turbulent modeling employed and the dimensionality of the solution attempted. Exact solutions for all but the Category 4 problem are available for comparison and are contained in this volume. Christopher K.W. Tam, Florida State University Jay C. Hardin, NASA Langley Research Center iv i =i m _i E
ORGANIZING COMMITTEE This workshop was organized by a Scientific Committee which consisted of: Thomas Barber, United Technologies Research Center Leo Dadone, Boeing Helicopters Sanford Davis, NASA Ames Research Center Phillip Gliebe, GE Aircraft Engines Yueping Guo, McDonnell Douglas Aircraft Company Jay C. Hardin, NASA Langley Research Center Ray Hixon, ICOMP, NASA Lewis Research Center Fang Hu, Old Donfinion University Dennis Huff, NASA Lewis Research Center Sanjiva Lele, Stanford University Phillip Morris, Pennsylvania State University N.N. Reddy, Lockheed Martin Aeronautical Systems Lakshmi Sankar, Georgia Institute of Technology Rahul Sen, Boeing Commercial Airplane Company Steve Shih, ICOMP, NASA Lewis Research Center Gary Strumolo, Ford Motor Company Christopher Tam, Florida State University James L. Thomas, NASA Langley Research Center V
Page 1 and 2: NASA Conference Publication 3352 <s
Page 3 and 4: .Y NASA Conference Publication 3352
Page 5: PREFACE Thisvolumecontainstheprocee
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=
Page 54 and 55: n -3 -2 -1 0 +l 72 -6 -5 -4 -3 -2 -
Page 57 and 58:
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
Page 191 and 192:
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
Page 197 and 198:
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.
Page 222 and 223:
For the case w " _s_, there are thr
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where E is an (M + 1) x 5 matrix an
Page 226 and 227:
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
Page 239 and 240:
3e- 10 2.5e-10 ._ 2e-10 e-, • 1.5
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Future work involves the inclttsiot
Page 244 and 245:
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
Page 278 and 279:
the incoming wavesolution from the
Page 280 and 281:
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
Page 310 and 311:
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
Page 327 and 328:
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
Page 349 and 350:
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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