Numerical Prediction of Mean Flow and
Acoustic Field of a Supersonic Impinging Jet
Konstantin A. Kurbatskii, Saravana Kumar
and Hossam El-Asrag
1
© 2011 ANSYS, Inc.
December 6, 2016
ANSYS, Inc.
Outline
1. Objectives
2. Problem description
3. Numerical model
–
–
–
–
Pressure-based coupled solver
Physical models and boundary conditions
Computational meshes
Turbulence models
4. Numerical results and comparison with test data
– Steady-state results
– Transient results – impingement tone radiation
– Evaluation of structural resonant effects
5. Summary
2
© 2011 ANSYS, Inc.
December 6, 2016
Objectives
• Steady-state simulation of hover lift loss due to impinging cold
and hot jets
• Unsteady simulation of generation and near-field propagation
of acoustic tones of a hot impinging jet
• Evaluation of a potential resonant response of the structure to
impinging acoustic tones
3
© 2011 ANSYS, Inc.
December 6, 2016
Problem Description
• Convergent-divergent nozzle
–
•
•
•
•
design Mach = 1.5
D = 2.54 cm – nozzle throat diameter
De = 2.75 cm – nozzle exit diameter
2.0 ≤ h/D ≤ 8.0 – steady-state
h/D = 4.0 – transient
• Nozzle pressure ratio NPR = 3.7
–
perfectly expanded jet
• Two temperature ratios
TR = 1.0 – cold jet
– TR = 1.4 – hot jet
–
Ref: Krothapalli, A., Rajkuperan, E., Alvi, F., and
Lourenco, L., “Flow Field and noise characteristics
of a supersonic impingement jet,” Journal of Fluid
Mechanics, Vol. 392, 1999, pp. 155-181.
Kumar, R., Lazic, S., and Alvi, F. S., “Control of
High-Temperature Supersonic Impingement Jets
Using Microjets,” AIAA Journal, Vol. 47, No. 12,
2009, pp. 2800-2811
4
© 2011 ANSYS, Inc.
December 6, 2016
Pressure-Based Coupled Solver
•
•
•
•
Unsteady numerical simulation using CFD code ANSYS Fluent 15.0
Pressure-based coupled double-precision solver
Control-volume-based technique
QUICK-type scheme for interpolation of face values from cell centers in the
momentum and energy equations (steady-state)
– a weighted average of 2nd order upwind and 2nd order central differencing
– uses a variable, solution-dependent value of the weight factor to avoid introducing
new solution extrema
• Bounded 2nd-order central differencing (BCD) for momentum and energy
equations (transient)
– BCD is a composite normalized variable diagram (NVD)-scheme that consists of:
pure central differencing,
,
= (
+
)+ (
·
+
·
)
blended scheme of the central differencing and the second-order upwind scheme, and
1st order upwind scheme (used only when the convection boundedness criterion violated)
5
© 2011 ANSYS, Inc.
December 6, 2016
Pressure-Based Coupled Solver (continued)
• 2nd-order scheme for reconstructing face values of pressure
• Least-squares cell-based calculation of gradients
– preserves 2nd-order spatial accuracy
• Non-differentiable Minmod gradient limiters
• Fully implicit coupling between momentum and continuity equations
– implicit discretization of pressure gradient terms in momentum equations
– implicit discretization of face mass flux and pressure dissipation terms
• System of discretized algebraic equations solved using coupled algebraic
multigrid (AMG) scheme
• Incomplete Lower Upper (ILU) decomposition to smooth residuals between
levels of AMG
– ILU has better smoothing properties than Gauss-Seidel for block-coupled systems
– allows for more aggressive coarsening of AMG levels
6
© 2011 ANSYS, Inc.
December 6, 2016
Time-Marching Scheme
• Second-order fully implicit time marching algorithm
– implicit equations solved iteratively at each time level before moving to the next
time step
– unconditionally stable with respect to the time step size
– time step size chosen to resolve impingement tone frequencies up to 20 kHz
∆t = 0.004 D / Vj
7
© 2011 ANSYS, Inc.
December 6, 2016
Physical Models and Boundary Conditions
• Air modeled as a single-species calorically perfect gas
• Molecular viscosity as a function of temperature by Sutherland's law
• Pressure inlet condition at the nozzle inlet
– total pressure and total temperature
• Far-field boundary
– Stead-state:
pressure outlet
specifies static pressure, all other variable extrapolated from interior
– Transient:
acoustically non-reflective pressure boundary
based on characteristic wave relations derived from the Euler equations
• Adiabatic no-slip walls
8
© 2011 ANSYS, Inc.
December 6, 2016
Computational Mesh
• 3D conformal hexahedral meshes using ANSYS Meshing
• h parameterized for automatic regeneration of the solid model and mesh
Cell size at nozzle exit
in radial direction
Cell size at nozzle
exit along jet axis
Cell size
far-field
Total cell count
h/D = 4.0, ¼ model
Coarse
0.016D
0.06D
0.08D
1.4 million
Medium
0.008D
0.03D
0.06D
5.5 million
Fine
0.0047D
0.03D
0.03D
24.7 million
DDES
Medium mesh
9
© 2011 ANSYS, Inc.
December 6, 2016
Turbulence Models
• SST k-ω (steady-state)
• Wall-modeled Large Eddy Simulation (WMLES) model (transient)
– WMLES with the S-omega formulation
– covers the inner portion of the boundary layer by RANS and the outer portion by LES
– avoids the very high resolution requirements of LES in the inner wall layer along the
impingement plate
10
© 2011 ANSYS, Inc.
December 6, 2016
Numerical Results
• Numerical runs carried out in parallel on two 48-core nodes (total of 96
compute processors)
• Converged steady-state jet flow RANS solution is used as an initial flowfield
for transient simulations
• The solution is then time-marched until it locks into a self-sustained
impingement tone feedback loop
• No synthetic turbulence is generated at the nozzle inlet, all the turbulence is
produced by jet flow instabilities
11
© 2011 ANSYS, Inc.
December 6, 2016
Numerical Results – Steady-State
Hover Lift Loss
Normalized static pressure
Velocity vectors
12
© 2011 ANSYS, Inc.
December 6, 2016
Numerical Results – Steady-State
Hover Lift Loss
0.7
0.9
CFD - medium mesh
CFD - coarse mesh
Test
-Lift / Thrust
0.7
0.6
0.5
0.4
0.3
TR = 1.4
0.2
0.5
0.4
0.3
0.2
0.1
0.1
0
0
0
1
2
3
4
5
6
h/D
7
8
9
CFD - medium mesh
CFD - coarse mesh
Test
0.6
-Lift / Thrust
0.8
10
TR = 1.0
0
1
2
3
4
5
6
7
8
h/D
Comparison of calculated hover lift loss as a function of h/D with experimental data
13
© 2011 ANSYS, Inc.
December 6, 2016
9
10
Numerical Results – Steady-State
1.2
1.2
1.0
Test
z/D = 0.5
CFD
1.0
0.8
0.6
V / Vj
V / Vj
0.8
TR = 1.0
0.4
0.0
0.0
-0.2
-0.2
0
1
z/D = 0.5
CFD
0.4
0.2
-1
Test
0.6
0.2
-2
TR = 1.4
-2
2
-1
1
1.2
1.2
1.0
0.8
TR = 1.0
Test
z/D = 4.0
CFD
1.0
0.8
V / Vj
0.6
0.4
TR = 1.4
Test
z/D = 4.0
CFD
0.6
0.4
0.2
0.2
0.0
0.0
-0.2
-0.2
-2
-1
0
x/D
1
2
-2
-1
0
1
x/D
Normalized mean velocity distribution across the jet, h/D = 5.0
14
2
x/D
x/D
V / Vj
0
© 2011 ANSYS, Inc.
December 6, 2016
2
Impingement Tone Generation Mechanism
Impingement tone feedback loop
15
© 2011 ANSYS, Inc.
December 6, 2016
Numerical Results – Transient
Instantaneous contours of Mach number showing development of large-scale
structures in the shear layer (medium mesh).
16
© 2011 ANSYS, Inc.
December 6, 2016
Numerical Results – Transient
Instantaneous turbulence structures by Q-criterion, colored by the ratio of eddyviscosity to molecular viscosity
17
© 2011 ANSYS, Inc.
December 6, 2016
Numerical Results – Transient
Instantaneous pressure field plotted on a log scale (medium mesh)
18
© 2011 ANSYS, Inc.
December 6, 2016
Numerical Results – Transient
Comparison of calculated and experimentally measured noise spectrum.
x/D = 2.0 location on the lift plate (left), and microphone location at x/D = 15 (right).
TR = 1.4
19
© 2011 ANSYS, Inc.
December 6, 2016
Analysis of Spectral Data
• Favorable prediction of the dominant peak frequency at 7 kHz
• SPL of the dominant peak is under-predicted
• The fine mesh did not improve SPL prediction of the dominant peak
– mesh resolution may not necessarily be the primary factor
– under-prediction of the dominant peak SPL was observed even in a very large-scale
simulation of the same problem* using higher-order numerics
• Other factors not included in the CFD simulations may contribute to SPL levels
– structural resonant response
*Uzun,
A., Kumar, R., Hussaini, M. Y., and Alvi, F. S., “Simulation of Tonal Noise Generation by
Supersonic Impinging Jets,” AIAA Journal, Vol. 51, No. 7, 2013, pp. 1593-1611.
20
© 2011 ANSYS, Inc.
December 6, 2016
Structural Modal Analysis
• Modal analysis of 20 mm thick aluminum lift plate
using ANSYS Mechanical to predict its natural
frequencies
• Fixed support at the inner ring surface where the
plate is attached to the nozzle
21
© 2011 ANSYS, Inc.
December 6, 2016
Structural Modal Analysis of the Lift Plate
Natural frequencies of the lift plate
f, Hz
923.01
923.19
1115.1
1242.9
1597.2
1597.2
3509.6
3509.7
4959
4959.1
Mode
11
12
13
14
15
16
17
18
19
20
f, Hz
5942.3
5942.3
6415.1
7051.6
7052.1
8760.6
8760.6
9396.2
9396.3
9563.8
Mode
21
22
23
24
25
26
27
28
29
30
f, Hz
9563.9
11879
11879
12855
12855
13328
13328
14034
14034
14167
Lift plate
h/D = 4.0, x/D = 2.0
170
160
SPL, dB/17 Hz
Mode
1
2
3
4
5
6
7
8
9
10
180
150
140
130
120
110
100
Test
90
80
1
f, kHz
10
• Natural frequencies of the plate at 7 kHz coincide with the dominant
impingement tone frequency
• Two other plate natural frequencies at 3.5 kHz and 14 kHz are also nearly
coincidental with two other impingement tone peaks
• Fluid-structure resonant response may amplify impingement tone SPLs
– will be confirmed by a fluid-structure interaction simulation in a future investigation
22
© 2011 ANSYS, Inc.
December 6, 2016
Summary
• Pressure-based coupled solver (PBCS) proves to be a robust and effective
method for predicting flow and acoustic field of impinging jets
– PBCS is less memory and CPU intensive than a traditional density-based approach
– PBCS is an attractive alternative to density-based algorithms for obtaining transient
solutions to supersonic jet noise problems
• Steady-state predictions of hover lift loss and mean jet velocity distributions
are in favorable agreement with experimental data
• Predicted frequency of the dominant impingement tone matches with the
experimental data
– this frequency coincides with predicted natural frequency of the lift plate structure
– a potential for fluid-structure resonance which can significantly amplify SPL at this
frequency
23
© 2011 ANSYS, Inc.
December 6, 2016
Questions?
24
© 2011 ANSYS, Inc.
December 6, 2016
Nozzle Parameters
Static discharge coefficient, Cd
& m
& i
Cd = m
& Mass flow Rate from CFD at
m
nozzle exit,
Isentropic
Mass Flow
Rate
& i = PA t
m
γ  2 


RT  γ + 1 
γ +1
γ −1
P Total Pressure at Nozzle Inlet
T Total temperature at Nozzle Inlet
p∞ Ambient pressure
At Throat Area
Nozzle thrust performance, Cfg
Cfg = Fj / Fi
Isentropic
Thrust
25
© 2011 ANSYS, Inc.
&i
Fi = m
December 6, 2016

2γ
p 
RT 1 −  ∞ 
  P 
γ −1

Fj Thrust from CFD
γ −1
γ




& Ve + (p e − p ∞ )A e
Fj = m
pe Area-averaged pressure at Exit
Ae Exit Area
Ve Mass-Averaged velocity at Exit