modeling supersonic jet screech noise using direct...

© 2011 ANSYS, Inc. November 7, 2012 1

14.5 Release

Modeling Supersonic Jet Screech Noise Using Direct Computational Aeroacoustics (CAA)

Workshop

Advanced ANSYS FLUENT

Acoustics


Introduction

This tutorial demonstrates how to model screech tone noise radiated by an axisymmetric supersonic jet using direct computational aeroacoustics (CAA) in ANSYS FLUENT

This tutorial demonstrates how to do the following:

– Perform axisymmetric simulation of a steady-state supersonic jet flow using realizable k-e turbulence model with model constants modified for free jet flows

– Calculate unsteady flow and acoustic near field by direct CAA using unsteady realizable k-e turbulence model

– Save acoustic data at nearfield microphone location for further spectral analysis

– Postprocess flowfield and aeroacoustic results


Prerequisites

This tutorial assumes that you are familiar with the ANSYS FLUENT interface and that you have a good understanding of basic setup and solution procedures. Some steps will not be shown explicitly.

In this tutorial you will use direct CAA method. If you have not used this feature before, first read:

– Chapter 15, Aerodynamically Generated Noise, of the ANSYS FLUENT 14.5 Theory Guide, and

– Chapter 23, Predicting Aerodynamically Generated Noise, of the ANSYS FLUENT 14.5 User's Guide

Note: Approximately 27 hours of CPU time on a single 32-bit Windows machine is required to complete this tutorial. It will take only 2.5 hours on 8 parallel nodes! If you are interested exclusively in learning how to set up the steady-state and direct CAA models, you can reduce the computing time requirements considerably by skipping Steps 9 (converging steady-state run), and Steps 11 (time-marching unsteady simulation) and using the provided case and data files to postprocess results at Step 12


Problem Description

• Supersonic jet noise has three main components: 1. Broadband shock-associated noise 2. Turbulent mixing noise 3. Screech tones

• Screech tones radiate at discrete frequencies. They are generated by a feedback loop1,2 (Figure 1):

A quasi-periodic shock-cell structure is formed in the core of an imperfectly expanded jet. At the nozzle exist, jet shear layer is thin and receptive to external excitations. Acoustic disturbances impinge on the nozzle lip and excite instability waves, which then propagate downstream and grow as they extract energy from the meanflow. At the fourth or fifth shock cell, amplitude of the instability wave becomes large enough to interact with the shock-cell structure. This unsteady interaction generates acoustic waves which propagate, in part, upstream outside the jet, and excite another excitation of the jet mixing layer at the nozzle lip. This generates a new instability wave, and closes the feedback loop

Figure 1. Screech tone feedback loop

1Powell, A., “On the Mechanism of Choked Jet Noise,” Proceedings of the Physical Society, London, Vol. 66, 1953, pp. 1039-1056. 2Shen, H., and Tam, C. K. W., “Numerical Simulation of the Generation of Axisymmetric Mode Jet Screech Tones,” AIAA Journal, Vol. 36, No. 10, 1998, pp. 1801-1807

nozzle

shock cellsinstability waves

feedback acoustic waves


Problem Description

The problem considers turbulent air flow associated with Mach 1.2 cold jet emitted from 1” diameter round nozzle with 0.625” thick lip. Nozzle geometry and flow conditions are from experiments of Ponton and Seiner3

Figure 1. Nozzle geometry

1.0”

0.625”

Nozzle

lip

Jet flow

Microphone

locations

3Ponton, M. K., and Seiner, J. M., “The Effect of Nozzle Exit Lip Thickness on Plume resonance,” Journal of Sound and Vibration, Vol. 154, Issue 3, 1992, pp. 531-549


Preparation

1. Copy the file mesh-caa-jet-screech.msh.gz to your working directory

2. Start the 2D double-precision version of ANSYS FLUENT 14.5


Setup and Solution

1. Read the mesh file mesh-caa-jet-screech.msh.gz

File Read Mesh As FLUENT reads the mesh file, it will report its progress in the console window.

2. The mesh was created in inches, and it needs to be rescaled

Mesh Scale

Step 1: Mesh

(a) Select Convert Units under Scaling

(b) Select in under Mesh Was Created In

(c) Click Scale once

(d) Check Domain Extents:

Xmin (m) = -25.39998, Xmax (m) = 25.4

Ymin (m)= 0, Ymax (m) = 25.39451

(e) Click Close

3. Check the mesh

Mesh Check FLUENT will perform various checks on the mesh and report the progress in the console window. Pay particular attention to the reported minimum volume. Make sure this is a positive number


Setup and Solution – Steady-State Flow

4. Display the mesh

Results Graphic and Animation Mesh Set Up ...

Step 1: Mesh (continued)


Step 1: Mesh (continued)


(a) Display the grid with the default settings (Figure 3). Use the middle mouse button to zoom in on the image so you can see the mesh at the nozzle (Figure 4)

Figure 3. Mesh Display Figure 4. Mesh at the nozzle exit

Hybrid quad-tri mesh is used in this simulation. Structured quad cells are used to resolve the jet plume up to 20 nozzle diameters downstream. Tri cells are used in the far field. The cell size should be small enough to adequately resolve excitations of the jet shear layer at the nozzle lip, development of shear layer instability waves, shock cell structure in the nozzle core and nearfield propagation of screech acoustic waves.


Step 2: Models


1. Select the pressure-based steady-state axisymmetric solver

Problem Setup General

Note: pressure-based solver is used in this simulation to take advantage of higher order QUICK discretization scheme for the density, momentum, energy and turbulence equations on structured meshes


Step 2: Models (continued)


2. Select realizable k-e turbulence model

Problem Setup Models Viscous

(a) Select k-epsilon under Model

(b) Select Realizable under k-epsilon Model

(c) Retain Standard Wall Functions under Near

Wall Treatment

(d) Modify model constants as:

C2-Epsilon = 2.02

TKE Prandtl Number = 0.324

TDR Prandtl Number = 0.377

Energy Prandtl Number = 0.422

This modification follows Ref. [4] which proposed a set of new constants for the standard k-e model designed specifically for predicting turbulent jet flows

(e) Click OK

4Thies, A., and Tam, C. K. W., “Computation of Turbulent Axisymmetric and Nonaxisymmetric Jet Flows Using the K- model,” AIAA Journal, Vol. 34, No. 2, 1996, pp. 309-316.


Step 3: Materials


You will use the default material, air, which is the working fluid in this problem. Air is modeled as ideal compressible gas

Problem Setup Materials Fluid Air

1. Change the density formulation to ideal-gas

Energy equation will be turned on automatically. The message “Note: Enabling energy equation as required by material density method,” will be printed in the console window

2. Change the viscosity formulation to sutherland, and accept Three

Coefficient Method with default constants

3. Click Change/Create

You can modify the fluid properties for air or copy another material from the database if needed. For details, refer to the Chapter 8, Physical Properties, in the ANSYS FLUENT 14.5 User's Guide


Step 4: Cell Zone Conditions


Problem Setup Cell Zone Conditions

1. Select air i. Click Edit... to open the Fluid panel

ii. Retain the default selection of air as the fluid material in the Material Name drop-down list

iii. Click OK


Step 4: Cell Zone Conditions


Problem Setup Cell Zone Conditions

2. Select air-lam i. Click Edit... to open the Fluid panel, and check

Laminar Zone Small fluid region just at the nozzle exit is modeled as laminar (Figure 5). This is necessary to augment excitation of mixing layer instability waves. The rest of the fluid is modeled as turbulent air.

ii. Click OK

3. Click Operating Conditions... to open the Operating Conditions panel

Set Operating Pressure to 0

Laminar zone

Turbulent

zone

Figure 5. Mesh at the nozzle exit showing location of the laminar zone


Step 5: Boundary Conditions


Problem Setup Boundary Conditions

1. Set the boundary conditions at the inlet

a) Select inlet under Boundary Conditions

The Type will be reported as pressure-inlet

b) Click Edit... to open the Pressure Inlet panel, and select Momentum tab

i. Set the Gauge Total Pressure (pascal) to 242,496.5

ii. Set Supersonic/Initial Gauge Pressure (pascal) to 127,360

These settings are based on isentropic relationships, they correspond to fully expanded jet Mach number equal to 1.2

iii. Retain Normal to Boundary under Direction Specification Method

iv. Select Intensity and Hydraulic Diameter under Turbulence Specification Method, and set Turbulent Intensity (%) = 0.1, and Hydraulic Diameter = 0.0254

Low level of turbulence is assumed at the nozzle exit

c) Select Thermal tab in the Pressure Inlet panel

i. Set Total Temperature (K) to 300 K

For cold jets, total temperature is equal to the ambient static temperature


Step 5: Boundary Conditions (continued)



2. Set the boundary conditions at the pressure outlet

a) Select far-field under Boundary Conditions

The Type will be reported as pressure-outlet

b) Click Edit... to open the Pressure Outlet panel, and select Momentum tab

i. Set the Gauge Pressure (pascal) to 100,000

ii. Retain Normal to Boundary under Backflow Direction Specification Method

iii. Select Intensity and Viscosity Ratio under Turbulence Specification Method, and set Backflow Turbulent Intensity (%) = 1, and Viscosity Ratio = 2

c) Select Thermal tab in the Pressure Outlet panel

i. Set Backflow Total Temperature (K) to 300 K

Note: pressure-based coupled solver will be used in this simulation. Non-reflective outlet boundary condition option is not compatible with the pressure-based solver. To avoid spurious reflection of acoustic waves off the outlet boundary, the outlet is placed about 500 acoustic wavelengths away from the noise source, and a very coarse mesh with the mesh size Dx much larger than the acoustic wavelength L is applied in the far field (Dx / L = 25) to assure acoustic waves are fully dissipated by numerical viscosity before reaching the outlet boundary





3. Set the boundary conditions at walls

a) Select wall-back under Boundary

Conditions

The Type will be reported as wall

b) Click Edit... to open the Wall panel, and select Momentum tab

i. Select Specified Shear under Shear Condition, and set Shear Stress X- and Y- components to 0

Walls in this simulation are modeled as slip walls since the primary physics of screech noise generation is driven by free-stream jet flow structures, and wall turbulence does not contribute to the generation of screech noise

c) Select Thermal tab in the Wall panel, and retain default settings of zero heat flux





4. Copy setting for the wall-back to other walls

a) Click Copy... below Boundary Conditions to open the Copy Conditions panel i. Select wall-back under From Boundary Zone

ii. Select mic1, mic2, wall-lip and wall-lip-lam under To Boundary Zone, click Copy, and OK


Step 6: Solution Methods


Solution Solution Methods

1. Select Coupled under Pressure-Velocity Coupling

Scheme

This will activate pressure-based coupled solver

2. Select Green-Gauss Node Based under Gradient

3. Select Second Order under Pressure

4. Select QUICK for all other equations: Density, Momentum, Turbulent Kinetic Energy, Turbulent Dissipation Rate, and Energy


Step 7: Solution Controls


Solution Solution Controls

1. Set the Courant Number to 50

2. Set the Explicit Relaxation Factors for Momentum and Pressure to 0.25

3. Set Under-Relaxation Factor of 0.25 for Density

4. Retain default settings of Under-Relaxation Factors for other equations:

Body Forces = 1.0

Turbulent Kinetic Energy = 0.8

Turbulent Dissipation Rate = 0.8

Turbulent Viscosity = 1.0

Energy = 1.0


Step 8: Solution Initialization


1. Initialize the solution

Solution Solution Initialization

(a) Initialize the flow with values shown here Gauge Pressure (pascal) = 100,000 Axial Velocity (m/s) = 0 Radial Velocity (m/s) = 0 Turbulent Kinetic Energy (m2/s2) = 0.1 Turbulent Dissipation Rate (m2/s3) = 6 Temperature (K) = 300

(b) Click Initialize to initialize the solution


Step 8: Solution Initialization (continued)


2. Run Full Multigrid (FMG) initialization (a) In the console window, which is also called Text User Interface (TUI), type:

solve initialize set-fmg-initialization

(b) Hit Enter on the keyboard to move down trough FMG settings. Change only: set FMG courant-number = 0.15

enable FMG verbose? yes

(c) Run FMG initialization by typing in TUI: fmg-initialization yes

This will provide an initial approximate solution (Figure 6)

Figure 6. Contours of Mach number after FMG initialization

3. Enable the plotting of residuals

Solution Monitors Residuals Edit...

(a) Select Plot and Print to Console under Options

(b) Uncheck Check Convergence for all equations

(c) Keep other setting at defaults, and click OK

4. Write case and data files: run-screech-steady-fmg.cas.gz and run-screech-steady-fmg.dat.gz

File Write Case & Data...


Step 9: Steady-State Solution


1. Iterate the solution

Solution Run Calculations

(a) Set Number of Iterations to 200 and Calculate

After 200 iterations, residuals will drop three orders of magnitude (Figure 7). Contours of converged steady-state Mach number distribution are shown in Figure 8

Note: it will take about 16 minutes of CPU time to finish the steady-state run on a single Windows processor. You can reduce the computing time requirements by skipping to Step 10


Step 9: Steady-State Solution (continued)


Figure 7. Convergence of residuals Figure 8. Contours of Mach number

2. Write case and data files: run-screech-steady.cas.gz and run-screech-steady.dat.gz



Setup and Solution – Transient Flow

1. Read in converged steady-state results from the previous step:

run-screech-steady.cas.gz and run-screech-steady.dat.gz

File Read Case & Data...

2. Change Time formulation to Transient in

Problem Setup General

3. Change Transient Formulation to Second Order Implicit in Problem Setup Solution Methods

Step 10: Transient Case Setup



4. Modify solution controls

Solution Solution Controls (a) Set the Courant Number to 1e+15

(b) Set all other relaxation factors to 1.0 These are recommended Solution Controls settings when running transient pressure-based coupled solver

Note: in the pressure-based coupled solver, the value 1/CFL, where CFL stands for Courant number, acts as an implicit relaxation factor for coupled continuity and momentum system of equations. Setting CFL to a very large number equals to removing implicit relaxation from the coupled equations

Step 10: Transient Case Setup (continued)



5. Define Custom Field Function for pressure perturbations over its mean value:

Define Custom Field Functions...

(a) Select Pressure ... and Static Pressure under Field Functions, and click Select

(b) Click mouse pointer over keypad numbers to complete the function definition:

p - 100000

(c) Enter a new name pa under New Function Name, and click Define




6. Enable the monitoring of static pressure perturbations at two microphone locations on the nozzle lip:

Solution Monitors

(a) Click Create... Under Surface

Monitors

(b) Change Name to mic1

(c) Select Area-Weighted Average

under Report Type

(d) Select Custom Field Functions... and pa under Field Variable

(e) Select mic1 under Surface

(f) Uncheck Print to Console and check Plot under Options

(g) Check Write and specify File Name:

mic1.out

(h) Select Flow Time under X Axis

(i) Select Get Data Every 1 Time Step

(j) Click OK



(k) Repeat these steps to define the other monitor at mic2 surface:





7. Set the time step parameters

Solution Run Calculation

(a) Set the Time Step Size (s) to 5e-6

(b) Set Number of Time Steps to 2000

(c) Set Max Iterations/Time Step to 10

Based on experimental data, expected fundamental screech tone frequency, f, is about 7 kHz. Temporal discretization should provide 20 or more time steps per period of oscillation. This defines the maximum time step as Dtmax = 1/(20*f) = 7.14e-06 sec

8. Write case and data files:

run-screech-unsteady-0.00.cas.gz and run-screech-unsteady-0.00.dat.gz





1. Run the transient simulation

Solution Run Calculation

Click Calculate to time-march the solution to a time-periodic state

The solution will advance to t = 0.01 sec by the end of the run

2. Write case and data files: run-screech-unsteady-0.01.cas.gz and run-screech-unsteady-0.01.dat.gz


Note: it will take about 26 hours of CPU time to finish the run on a single 32-bit Windows processor. You can reduce the computing time requirements considerably by skipping to Step 12

Parallel run on 8 compute 64-bit processors will take only 2.3 hours!

Step 11: Transient Run


Setup and Solution

2. Display contours of Mach number:

Results Graphics and Animations Contours

(a) Select Contours of Velocity and Mach Number

(b) Check Filled, Node Values, Global Range and Auto Range under Options

(c) Click Display

Display Views

(a) Select axis and axis:001 under Mirror Planes

(b) Click Apply

(c) Zoom in to the region at the nozzle inlet (Figure 10b)

Step 12: Aeroacoustic Postprocessing

1. Read in transient results from the previous step:

run-screech-unsteady-0.01.cas.gz and

run-screech-unsteady-0.01.dat.gz

File Read Case & Data...


Setup and Solution Step 12: Aeroacoustic Postprocessing (continued)

Figure 10a. Contours of Mach number: steady-state simulation

Figure 10b. Contours of Mach number: transient simulation

Note the difference between steady-state (Figure 10a) and transient (Figure 10b) Mach number distribution. Steady-state solution significantly suppresses the shock cell structure in the jet plume


Setup and Solution

3. Display contours of static pressure perturbations:

Results Graphics and Animations Contours (a) Select Contours of Custom Field Functions... and pa

(b) Uncheck Global Range and set Min = -300 and Max = 300

(c) Uncheck Clip to Range and click Display

Sound waves of the screech tone propagate predominantly in the upstream direction

Figure 11. Contours of static pressure perturbations

Step 12: Aeroacoustic Postprocessing (continued)

sound waves


Setup and Solution

4. Display the acoustic pressure signals at the two receiver locations:

Results Plots File

(a) Click Add... in the File XY Plot panel This will open the Select File panel where you can now select mic1.out and mic2.out from the file list

(b) Click OK to close the Select File panel



Setup and Solution

(c) Click Plot to display the microphone signals (Figure 12). Modify the line and marker styles as necessary, using the Curves panel. Modify the X axis to show the signal over the time rage of 0.006 – 0.01 s. Modify legends using Change Legend Entry button in File XY Plot menu


Figure 12. Acoustic pressure signals at two microphone locations on the nozzle lip



5. Activate Ffowcs-Williams & Hawkings (FWH) acoustics model :

Problem Setup Models Acoustics Edit...

(a) Select Ffowcs-Williams & Hawkings under Model, retain default settings, and click OK

This step is required only to make Sound Pressure Level available for FTT spectral analysis. However, FWH model will not be used to predict noise propagation


Setup and Solution

6. Perform spectral analysis of the receiver signals:

Results Plots FFT (a) Click Load Input Files... , change Files of Type to All Files in Select File window

and select mic1.out

(b) Select Sound Pressure Level (dB) from the Y Axis Function drop-down list

(c) Select Frequency (Hz) from the X Axis Function drop-down list



Setup and Solution


(d) Click Plot FFT to plot the sound pressure spectrum for mic1 (Figure 13)

The overall sound pressure level (OASPL) is printed to the console window:

Overall Sound Pressure Level in dB (reference pressure = 2.000000e-005) = 1.453695e+002

Note: The maximum frequency plotted is f = 1/[2Dt] = 100 kHz, as expected.

Figure 13. Spectral analysis of pressure signal for mic1


Setup and Solution

i. Deselect Auto Range for the X Axis

ii. Manually set the Maximum for Range to 10000

iii.Set Precision to 0

iv. Click Apply and Close the panel

(e) Click Axes.... This will open the Axes - Fourier Transform panel




(f) Click Plot/Modify Input Signal... to open the Plot/Modify Input Signal panel. It

lets you modify and plot the signal before the Fourier Transform is applied

i. Select Clip to Range and set the Min value for X Axis Range to 0.006

Without clipping the temporal range, the complete pressure signal history would be analyzed including the initial transient state leading up to the quasiperiodic state

ii. Click Apply/Plot and Close to return to the Fourier Transform panel

Since the x-axis range was manually set for the spectral plot, you will not see the proper range when plotting the modified signal. You will need to temporarily reset the range if you want to plot the input signal


Setup and Solution

(g) Click Plot FFT to plot the sound pressure spectrum for mic1 (Figure 14a). The spectrum peaks at about 7000 Hz

(h) Repeat above steps to plot the sound pressure spectrum for mic2 (Figure 14b)

Figure 14. Spectral analysis of pressure signals at (a) mic1, and (b) mic2 microphone locations.

Note: only the fundamental frequency of screech tones is resolved in this simulation, higher order harmonics are not resolved


(a)

screech

tone (b) screech

tone


Comparison with Test Data

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

1 1.05 1.1 1.15 1.2 1.25

l/D

j

Mj

A1 - experiment

A2 - experiment

A1 - CFD

A1

125

130

135

140

145

150

155

160

1 1.05 1.1 1.15 1.2 1.25

SPL

(dB

)

Mj

A1 - experiment

A2 - experiment

A1 - CFD

microphone at r = 0.662"

Figure 15a. Wavelengths of fundamental screech modes

Figure 15b. Amplitudes of fundamental screech modes

Screech tones of low supersonic jets are characterized by two axisymmetric screech modes A1 and A2. Mach numbers at which transition from one mode to another takes place may vary from experiment to experiment because of sensitivity of jet screech mechanism to specifics of experimental set-up. Figure 15a shows comparison of calculated screech wavelengths with experimental measurements. Numerically predicted wavelengths follow very closely the experimentally measured A1 mode curve. Figure 15b shows favorable comparison between predicted and experimentally measured amplitudes of fundamental screech modes at two microphone locations at the nozzle lip.

Note: Data points at other Mach numbers were obtained by re-running the tutorial cases with different pressure inlet settings


Summary

This tutorial demonstrated the use of ANSY FLUENT's direct CAA capabilities to calculate near-field radiation of jet screech tones by an axisymmetric supersonic jet. You have learned how to set up the relevant parameters, record acoustic data at microphone locations, calculate, and postprocess the acoustic pressure signals.

Calculated sound pressure level and frequency are in favorable agreement with experimental data.

The main computational efforts are spent calculating the time dependent turbulent flow.

modeling supersonic jet screech noise using direct...

Documents