NASA Technical Reports Server (NTRS) 20010038419: Using Steady State CFD for Acoustic Predictions

8 Pages·0.1 MB·English

by  NASA Technical Reports Server (NTRS)

Using Steady State CFD for
Acoustic Predictions
Kader Frendi
University of Alabama in
Huntsville
Tom Nesman and T.-S. Wang
NASA Marshall
Background
_Pmblem_ * /
Empirical Model (1)
• Far-field Approximation to The Lighthill
Acoustic Analogy
_t)= __
4_c_
where
Tij = Pv iv j "3LT_ij"Jc(]'_--<P)4j
Empirical Model (2)
Steady State CFD EEE_ No Time History
_2- V -_2- tVp-
R,R;RkR, r t tpv, j) (pv k ,)d3 N
7(R'O'O)- _6_ t. lx JvJv O,'20t "2 Y"d_y
Which becomes
p 2(R,O,O)= P_Z-R_7iR_jXRk_Rgt ! ---3_-4_-v,vjv]v ,d3r
Empirical Model (3)
Using
so.=v..9_v,,=s..sj,+s.,sj,+s.A,
and assuming
S_j(r, r) = A_j(r)g('c)
with
, l ,rir,
Ao(r)= k f+--rf o--- '
2 2 r
Empirical Model (4)
where
g(r) - e-('/_°)_
and
f(r)
=e -'_2r2 / L2
Define
with
2
Empirical Model (5)
In addition
prk
k
ro,_=c:- and 2"O,Pr =C t
Pr
S
Define
--1/2
L=cfl¢ _'O,x
The spectrum is given by
1 )2
3 2 712 4 '-8 (f_r°-_
I(f2) =ct p k (f2Z'o,_) e
Empirical Model (6)
where
g2= 2_f4(1-M c cosO) 2 -t-(cclk 1/2 / C oo) 2
with
M c =-I + CcMjet
M
2
Empirical Model (7)
Finally
p2(R, 0,_2)= y(axx + zla.__:'+ 2ayy + 2ayz )kIJd3r
V
with
1 2R2 Ckp)kc) (I-McosO)-a(I-M_ cos0)-'
Results
4
CFD Solution
Hotfire Test
Mid-field locations
OASPL
Ill
---+_1 &
J
isa
2
SPL at 300' from the test stand and at 90 °
from the deflected plume
140
130 0 C:,:lq1="1il_i)lnlt_"l_ 1341i .... C_'l)-,dlbt.='r_,
12.1} _°°_o 1_
0 JO O0
"o
111} o I o ,_ 1111 0 0
o o
o%
IIo0o% 100
1 1
II %I o 9O ' !\ 0
I %
I %
iL,I,,,I10' ,/rlrl,,,I 111_ ,,1 iI,OIs L,tLl'_ 10° ' l'I'1'61"11 811 10' 10i 10' 1114 103
1/3-Om'l,_ Flecptncy, tk l_Ye F_quel_y, Ik
SPL on the test stand between the primary
and deflected plumes
160
I$o
150
140
llll
130
_ 120
i
_.3110
10g
11o
15.75 m
-- CFD 9O
.... 25.86 m
leO 13 Experiment 80 6.40 m
10] 10_ )_ 10_ l0I 7O 10_ 10' I(I_ 10" 10I
1/3-Octave Frequency, Hz 1/3-Octave Frequency, Hz
5
Axi-symmetric Jet Plume
140
.... CFD _ _,:_,_
130
[] E_per_ra
/N
12()
110
I(N)
90
80
II)l III J il)' |0_
l/3-Octave F_quency, Hz
Conclusions
°A semi-empirical model for acoustic
predictions has been presented.
°The predicted midfield directivity pattern
is in good agreement with the measurements
°The predicted midfield spectrum at 90 ° is
In good agreement with that measured.
°The results showed the importance of using
two time scales in the model.
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