NASA Technical Reports Server (NTRS) 20170001422: Validating a Monotonically-Integrated Large Eddy Simulation Code for Subsonic Jet Acoustics

17.8 MB·English

by  NASA Technical Reports Server (NTRS)

Validating a Monotonically-Integrated Large Eddy
Simulation Code for Subsonic Jet Acoustics
Daniel Ingraham∗ and James Bridges†
National Aeronautics and Space Administration, John H. Glenn Research Center, Cleveland, OH, 44135, USA
The results of subsonic jet validation cases for the Naval Research Lab’s Jet Engine
Noise REduction (JENRE) code are reported. Two set points from the Tanna matrix,
set point 3 (M = 0.5, unheated) and set point 7 (M = 0.9, unheated) are attempted
a a
on three different meshes. After a brief discussion of the JENRE code and the meshes
constructed for this work, the turbulent statistics for the axial velocity are presented and
compared to experimental data, with favorable results. Preliminary simulations for set
point 23 (M = 0.5, T /T = 1.764) on one of the meshes are also described. Finally, the
a j ∞
proposed configuration for the farfield noise prediction with JENRE’s Ffowcs-Williams
Hawking solver are detailed.
Nomenclature
x, y, z Cartesian coordinates, with origin at the nozzle exit and centerline,
x indicating the axial coordinate, increasing downstream
r Radial coordinate, r2 =y2+z2
∆ Approximate mesh spacing
L Length of the mesh region meant to resolve the turbulent nearfield
D Exit diameter of the nozzle
j
U Fully-expanded jet exit velocity
j
U, U(cid:48) Mean and root-mean square of axial velocity, respectively
T Fully-expanded jet exit temperature
j
T, T(cid:48) Mean and root-mean square of temperature, respectively
T , T Startup and statistics-gathering simulation times, respectively
0
θ Polar angle, with θ =0 pointing upstream (i.e. the negative-x direction)
y Estimate of viscous length scale in the nozzle boundary layer
τ
I. Introduction
Considerable effort has been invested by the computational aeroacoustic community in the prediction of
subsonic jet noise through large eddy simulation (LES)1–20 (see also the excellent review from Bodony21).
Most of this work has been focused on using codes that employ high-order finite difference or finite volume
schemes and structured grids in their discretization of the governing equations. A number examples of
the application of unstructured LES codes to the problem of supersonic jet noise can also be found in
the literature, e.g., the work done by researchers associated with Cascade Technologies22–26 and the Naval
Research Laboratory (NRL).27–33 Comparably little work has been done to validate the effectiveness of
unstructured LES codes at simulating the acoustics of subsonic jets. While not needed to capture the
geometry of the simple nozzles considered in this paper, the flexibility provided by unstructured meshes
allowsuserstousesmallcellsizesinlocalizedareasoftheflowwithoutaffectingthemeshdownstream,unlike
structured meshes. Also, simulating the subsonic regime of jet flows approximating the takeoff condition is
ofinteresttoNASA’sCommercialSupersonicTechnology(CST)project,withthegoalofprovidingacoustic
predictionsthroughtraditionalFfowcs-WilliamsHawkingtechniques34andmoresophisticatedmethods(e.g.,
∗AcousticsBranch,MS54-3,AIAAMember
†AcousticsBranch,MS54-3,AIAAAssociateFellow
1of22
AmericanInstituteofAeronauticsandAstronautics
the forthcoming Generalized Acoustic Analogy work of Leib et al.35). The combination of these needs has
motivated addressing this gap in the literature.
The Jet Engine Noise REduction (JENRE) application,36 developed by the NRL, is a computational
aeroacoustics code designed to provide farfield acoustic predictions of jets using the LES approach to the
simulation of turbulent flow. JENRE follows the Monotonically Integrated LES (MILES)37 philosophy of
sub-grid scale modeling, relying on the inherent numerical dissipation of the code’s schemes to capture the
effect of the unresolved turbulent scales will have on the resolved unsteady flow. Numerical dissipation
is provided by blending low- and high-order finite element schemes through the Flux-Corrected Transport
(FCT) approach. Proponents of this approach claim that the numerical dissipation effectively acts as an
implicit model for the turbulent sub-grid scales, citing as evidence modified equation analysis38 and the
results of applying such schemes to practical turbulent flows.39,40 Numerous finite element schemes are
available in the version of the JENRE code used in this work – here, the second-order Taylor-Galerkin
scheme41,42 has been chosen for spatial and temporal discretization, coupled with a lumped-mass Galerkin
scheme through the (FCT) method.43
II. Test Case Parameters
The flow parameters for the simulations described in this work are taken from the Tanna matrix,44 and
areshowninTable1. ThenozzlegeometrychosenforthisworkwasSMC000,thebaselineroundnozzlefrom
the Small Metal Chevron series developed at the NASA Glenn Research Center (GRC). Described in more
detail by Bridges and Wernet,46 SMC000 is an axisymmetric nozzle with a nominal two-inch exit diameter
that has been subjected to extensive experimental investigation at the GRC.45,46
Set Point 3 Set Point 7 Set Point 23
M 0.513 0.985 0.376
M =U /a 0.500 0.900 0.500
a j ∞
T /T 0.950 0.835 1.764
j ∞
p /p 1.197 1.860 1.102
0 j
Re = ρjUjD 5.99·105 1.36·106 2.06·105
j µj
Table 1. Set points used in this work.
Two mesh generation programs were used to create the meshes used in this work: Pointwise47 and
Gmsh.48 Thefirsttwomeshes,referredtohereasPW0andPW1,werecreatedwiththePointwiseprogram,
while the third mesh, GM0, was created with Gmsh. All meshes used the same SMC000 nozzle geometry.
The boundaries of the nearfield, sponge zone, and outer domain were also identical. Figure 1 shows a
diagram of the relative locations of the nozzle geometry, nearfield mesh region, and sponge zone and outer
mesh boundaries. Diagrams of PW0, PW1, and GM0’s mesh spacing distributions are shown in Figures 2,
3, and 4, respectively. Comparison of 2 and 3 shows that PW0 and PW1 differ in the element sizes in the
region just downstream of the nozzle exit to about 12.5D , with PW0’s spacing in the former axial location
j
being twice as large as PW1’s, and increasing to the 0.04D value more quickly. Figure 5 shows a crinkle
j
slice of PW0’s z = 0 surface, where the surface of the slice has been constructed from the mesh element
surfaces intersected by the z = 0 plane. Enlargements centered on the nearfield region for for this same
crinkle slice are shown for the PW0 and PW1 meshes, respectively, in Figures 9 and 10. The element edges
are colored in blue in these two figures to make the differences in mesh density more apparent.
InspectionofFigure4showstheGM0meshusedapproximatelythesamemeshspacingsizesasthePW1
mesh; however,themeshspacinggrowsmoregraduallyfromtheminimum0.005D tothemaximum0.04D
j j
value. GM0 also includes a refined region around the nearfield with target mesh spacing of about 0.05D ,
j
intended to propagate acoustic disturbances to a Ffowcs-Williams Hawking integration surface. The impact
of this change can be seen by comparing Figure 6 to Figure 11.
ThePW0andPW1meshescontainedapproximately15·106 and27·106 nodes,respectively,whileGM0,
with its FW-H refinement region, has about 55·106. The nearfield region consists of a conical frustum of
length L = 25D with a diameter of D at the nozzle exit and diverging at a rate of 4◦. The shape of the
j j
nearfieldwaschosentocapturethedevelopmentofthejet’sshearlayer,andwasinformedbytheshearlayer
2of22
AmericanInstituteofAeronauticsandAstronautics
y
5D
j
sponge zone
5D
D j
j
40D
j
4◦
x
Dj
25D
j
nearfield region
25D
j
Figure 1. Diagram of the extent of the domain boundaries, including the size of the nearfield region and
sponge zone.
y
∆≈D
j
∆(x=L)≈0.04D
j
∆(x=L/16)≈0.01D
j
x
∆(x=L/4)≈0.04D
j
∆(x=0)≈0.01Dj nearfield region
length L=25D
j
Figure 2. Approximate mesh spacing distribution for the PW0 mesh.
3of22
AmericanInstituteofAeronauticsandAstronautics
y
∆≈D
j
∆(x=L/2)≈0.04D
j
∆(x=L)≈0.04D
j
∆(x=L/16)≈0.01D
j
x
∆(x=L/4)≈0.02D
j
∆(x=0)≈0.005Dj nearfield region
length L=25D
j
Figure 3. Approximate mesh spacing distribution for the PW1 mesh.
y
∆≈D
j
∆≈0.05D all along FW-H region
j
FW-H region
∆(x=L )≈0.04D
nearfield j
φ3Dj 11◦
x
∆(x=0)≈0.005D
j
25D
j
Figure 4. Approximate mesh spacing distribution for the GM0 mesh.
4of22
AmericanInstituteofAeronauticsandAstronautics
Figure 5. z=0 slice of the PW0 mesh.
5of22
AmericanInstituteofAeronauticsandAstronautics
Figure 6. z=0 slice of the GM0 mesh, colored by instantaneous axial velocity.
Figure 7. x=2Dj slice of the PW1 mesh, colored by instantaneous axial velocity.
6of22
AmericanInstituteofAeronauticsandAstronautics
Figure 8. x=2Dj slice of the PW1 mesh, colored by instantaneous axial velocity, enlarged figure.
Figure 9. Enlargement of the nearfield region of the z =0 mesh slice shown in Figure 2 for the PW0 mesh,
with cell edges highlighted to make the mesh spacing distribution more clear.
7of22
AmericanInstituteofAeronauticsandAstronautics
Figure 10. Enlargement of the nearfield region of the z=0 mesh slice shown in Figure 3 for the PW1 mesh,
with cell edges highlighted to make the mesh spacing distribution more clear.
thickness growth rates reported by Bridges & Wernet.46 Figures 6 and 11 seem to show that this choice
was adequately large, as do Figures 7 and 8, x = 2D slices of the PW1 mesh. The nearfield length L is
j
comparableto15,16 orlongerthan4,5,7,17,19,20 thatusedbyotherresearchers, butthewidthof25D tan(4◦)
j
is considerably more narrow than similar simulations4,5,7,17,19,20 found in the literature (4D to 7.5D is
j j
typical).
For all meshes, anisotropic tetrahedra were extruded off the interior nozzle walls to partially resolve
the boundary layer, likely to be quasi-turbulent according to Bridges and Wernet.46 For PW0 and PW1,
this was done using Pointwise’s T-Rex tool, while Gmsh’s transfinite interpolation was used for GM0. The
spacing of these cells in the wall-normal direction is initially 5·10−4D , and grows at a rate of 1.2 until
j
the tetrahedra become isotropic. The length scale of the viscous sublayer for the flows studied here is
approximately y =4.1·10−5·D (estimated from smooth flat plate boundary layer theory as described by
τ j
Schlichting49), and thus the simulations will not meet the “wall-resolved” requirement of ∆≈2y .50
τ
The minimum mesh spacing in the nozzle nearfield region is 0.01D for the PW0 mesh, and 0.005D for
j j
the PW1 and GM0. Other subsonic jet LES examples in the literature use minimum mesh spacings ranging
from about 0.002D 5,20 to 0.003D ,15,16 and past supersonic jet calculations done by NRL researchers used
j j
spacings as small as 0.0035D in shear layer.29,31 The mesh spacing increases gradually downstream to
j
0.04D at the end of the nearfield region for both meshes.
j
Boundary conditions consisted of adiabatic no-slip for all nozzle walls, and the appropriate constant
stagnation pressure and temperature for the set point under investigation for the nozzle inflow. JENRE’s
characteristic-based farfield boundary condition was used for all other boundaries. As indicated in Figure 1,
a sponge zone was used to damp any spurious reflections from these farfield.
III. Results
A. Set point 3
Forsetpoint3andthetwoPointwisemeshes,aconstanttimestepwaschosensuchthatthelocalCFLnumber
would not exceed 0.65 anywhere during the calculation. This time step size was reevaluated periodically
during the run (about every 100 steps). The GM0 runs used a constant timestep of 5.13 · 10−5D /U ,
j j
correspondingtoaCFLofabout0.24. Eachsetpoint3runwasstartedfromauniformflowofzerovelocity
and ambient pressure and temperature. Table 2 shows the amount of time the simulation was run before
8of22
AmericanInstituteofAeronauticsandAstronautics
T ·U /D T ·U /D
0 j j j j
PW0 215.0 300.0
PW1 747.0 547.0
GM0 202.0 145.0
Table 2. Set point 3 startup (T0) and statistics (T) times.
gathering statistics (T ) and during the statistics-gathering process (T). The values for T ·U /D for the
0 j j
PW0 and PW1 meshes comparable to the periods of 87.5D /U ,20 500D /U ,17 and 833D /U 19 found in
j j j j j j
the literature. GM0, the largest and thus most computationally expensive mesh, may benefit from more
time.
Figure 11. Instantaneous axial velocity non-dimensionalized by Uj for set point 3 run on the PW1 mesh.
AfterperformingthesimulationswiththeJENREcodeasdescribedintheprevioussection,theresulting
data was post-processed to obtain mean and RMS statistics of axial velocity, and then compared to Bridges
andWernet’smeasurements.46 Figure11showstheinstantaneousaxialvelocityfromanarbitrarytimestep
forsetpoint3onthePW1mesh,andseemstoindicatethatthewidthofthemesh’snearfieldregionislarge
enough to capture the majority of the turbulent flow field.
Figure12and13showthemeanandRMSofaxialvelocityalongthecenterlineofthejetasafunctionof
the distance from the nozzle exit, and compare these values to the “consensus” dataset found in reference,46
which consists of a representation of an expected value for these quantities informed by experiments run by
many researchers performed at multiple labs over a considerable length of time, including to a significant
degree by Bridges and Wernet themselves.
Figure 12 shows that little difference is observed between the results for the mean axial velocity U
alongthecenterlineforthethreemeshes. Allsimulationspredictthelengthofthepotentialcore(theregion
downstreamofthenozzleexitthatisunaffectedbytheshearlayer)accurately,andconsistentlyunderpredict
U downstream slightly. More spread between the two simulations is seen in Figure 13’s root-mean square
axial velocity U(cid:48) results. Both simulations match the experimental data reasonably well for x<10D , and
j
show significant dissipation for the region beyond about x>15D . Interestingly, the simulation performed
j
on the coarser PW0 mesh agrees better than the the two finer meshes. GM0’s RMS results show a bit more
variation over x>10D , likely a result of the shorter statistics sampling time for this run.
j
9of22
AmericanInstituteofAeronauticsandAstronautics
1.0
0.8
0.6
Uj
/
U
0.4
0.2 RCA/BridgesConsensus
PW0,300TUj/Dj
PW1,547TUj/Dj
GM0,145TUj/Dj
0.0
0 5 10 15 20 25
x/D
j
Figure 12. Mean axial velocity U along centerline (r=0) for set point 3.
RCA/BridgesConsensus
PW0,300TUj/Dj
0.15 PW1,547TUj/Dj
GM0,145TUj/Dj
0.10
Uj
/
(cid:48)u
0.05
0.00
0 5 10 15 20 25
x/D
j
Figure 13. Root-mean square of axial velocity U(cid:48) along centerline (r=0) for set point 3.
10of22
AmericanInstituteofAeronauticsandAstronautics