Tutorial:Modeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENTIntroductionThis tutorial demonstrates how to model2D turbulentflow across a circular cylinder using large eddy simulation(LES)and computeflow-induced(aeroacoustic)noise using FLUENT’s acoustics model.You will learn how to:•Perform a2D large eddy simulation.•Set parameters for an aeroacoustic calculation.•Save acoustic source data for an acoustic calculation.•Calculate acoustic pressure signals.•Postprocess aeroacoustic results.PrerequisitesThis tutorial assumes that you are familiar with the 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 the acoustics model.If you have not used this feature before,first read Chapter21,Predicting Aerodynamically Generated Noise,of the FLUENT6.2 User’s GuideModeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENTProblem DescriptionThe problem considers turbulent airflow over a2D circular cylinder at a free stream ve-locity(U)of69.2m/s.The cylinder diameter(D)is1.9cm.The Reynolds number based on the diameter is90,000.The computational domain(Figure1)extends5D upstream and 20D downstream of the cylinder.U = 69.2 m/s D = 1.9 cmFigure1:Computational DomainPreparation1.Copy thefile cylinder2d.msh to your working directory.2.Start the2D version of FLUENT.Approximately2.5hours of CPU time is required to complete this tutorial.If you are interested exclusively in learning how to set up the acoustics model,you can reduce the computing time requirements considerably by starting at Step7and using the provided case and datafiles.Modeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENT Step1:Grid1.Read the gridfile cylinder2d.msh.File−→Read−→Case...As FLUENT reads the gridfile,it will report its progress in the console window.Since the grid for this tutorial was created in meters,there is no need to rescale the grid.Check that the domain extends in the x-direction from-0.095m to0.38m.2.Check the grid.Grid−→CheckFLUENT will perform various checks on the mesh and will report the progress in the console window.Pay particular attention to the reported minimum volume.Make sure this is a positive number.3.Reorder the grid.Grid−→Reorder−→DomainTo speed up the solution procedure,the mesh should be reordered,which will substan-tially reduce the bandwidth and make the code run faster.FLUENT will report its progress in the console window:>>Reordering domain using Reverse Cuthill-McKee method:zones,cells,faces,done.Bandwidth reduction=32634/253=128.99Done.Modeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENT4.Display the grid.Display−→Grid...(a)Display the grid with the default settings(Figure2).Use the middle mouse button to zoom in on the image so you can see the meshnear the cylinder(Figure3).Figure2:Grid DisplayModeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENTFigure3:The Grid Around the CylinderQuadrilateral cells are used for this LES simulation because they generate less numerical diffusion than triangular cells.The cell size should be small enough to capture the relevant turbulence length scales,and to make the numerical diffusion smaller than the subgrid-scale turbulence viscosity.The mesh for this tutorial has been kept coarse in order to speed up the calculations.A high quality LES simulation will require afiner mesh near the cylinder wall.Modeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENT Step2:Models1.Select the segregated solver with second-order implicit unsteady formulation.Define−→Models−→Solver...(a)Retain the default selection of Segregated under Solver.(b)Under Time,select Unsteady.(c)Under Transient Controls,select Non-Iterative Time Advancement.(d)Under Unsteady Formulation,select2nd-Order Implicit.(e)Under Gradient Option,select Node-Based.(f)Click OK.Modeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENT2.Select the LES turbulence model.The LES turbulence model is not available by default for2D calculations.You can make it available in the GUI by typing the following command in the FLUENT console window:(rpsetvar’les-2d?#t)Define−→Models−→Viscous...(a)Under Model,select Large Eddy Simulation.(b)Retain the default option of Smagorinsky-Lilly under Subgrid-Scale Model.(c)Retain the default value of0.1for the model constant Cs.(d)Click OK.You will see a Warning dialog box,stating that Bounded Central-Differencing is default for momentum with LES/DES.Click OK.The LES turbulence model is recommended for aeroacoustic simulations because LES resolves all eddies with scales larger than the grid scale.Therefore,wide band aeroa-coustic noise can be predicted using LES simulations.Modeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENTStep3:MaterialsYou will use the default material,air,which is the workingfluid in this problem.The default properties will be used for this simulation.Define−→Materials...1.Retain the default value of1.225for Density.2.Retain the default value of1.7894e-05for Viscosity.You can modify thefluid properties for air or copy another material from the database if needed.For details,refer the chapter Physical Poperties in the FLUENT User’s Guide.Step4:Operating ConditionsDefine−→Operating Conditions...1.Retain the default value of101325Pa for the Operating Pressure.Step5:Boundary Conditions1.Retain the default conditions for thefluid.Define−→Boundary Conditions...(a)Under Zone,selectfluid.The Type will be reported asfluid.(b)Click Set...to open the Fluid panel.i.Retain the default selection of air as thefluid material in the Material Namedrop-down list.ii.Click OK.2.Set the boundary conditions at the inlet.(a)Under Zone,select inlet.The Type will be reported as velocity-inlet(b)Click Set...to open the Velocity Inlet panel.i.Set the Velocity Magnitude to69.2m/s.ii.Retain the default No Perturbations in the Fluctuating Velocity Algorithm drop-down list,and click OK..This tutorial does not make use of FLUENT’s ability to impose inlet pertur-bations at velocity inlets when using LES.It is assumed that all unsteadinessis due to the presence of the cylinder in theflow.Modeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENT3.Set the boundary conditions at the outlet.(a)Under Zone,select outlet.The Type will be reported as pressure-outlet(b)Click Set...to open the Pressure Outlet panel.i.Confirm that the Gauge Pressure is set to0.ii.Retain the default option of Normal to Boundary in the Backflow Direction Specification Method drop-down list,and click OK.The top and bottom boundaries are set to symmetry boundaries.No user input is required for this boundary type.Step6:Quasi-Stationary Flow Field SolutionBefore extracting the source data for the acoustic analysis,a quasi-stationaryflow needs to be established.The quasi-stationary state will be judged by monitoring the lift and drag forces.1.Set the solution controls.Solve−→Controls−→Solution...(a)Retain the default PISO scheme for Pressure-Velocity Coupling.(b)Under Discretization,select PRESTO!in the Pressure drop-down list.PRESTO!is a more accurate scheme for interpolating face pressure values fromcell pressures.Modeling Flow-Induced(Aeroacoustic)Noise Problems Using FLUENT(c)Retain the default Bounded Central Differencing for Momentum.For LES calculations on unstructured meshes,the Bounded Central Differencingscheme is recommended for Momentum.(d)Set the Relaxation Factor for Pressure to0.75.(e)Retain the default Relaxation Factor for Momentum.The pressurefield is relaxed only during the initial transient phase.The Relax-ation Factor for Pressure will be increased to1at a later stage.(f)Click OK.2.Initialize the solution.Solve−→Initialize−→Initialize...(a)Initialize theflow from the inlet conditions by selecting inlet in the Compute Fromdrop-down list.(b)Click Init to initialize the solution and click Close.3.Enable the plotting of residuals.Solve−→Monitors−→Residual...(a)Select Plot under Options.(b)Under Storage,enter10000Iterations.(c)Under Plotting,enter20Iterations.(d)Retain the default values for the other parameters and click OK.4.Set the time step parameters.Solve−→Iterate...(a)Set the Time Step Size(s)to5e-6.The time step size required in LES calculations is governed by the time scaleof the smallest resolved eddies.That requires the local Courant-Friedrichs-Lewy(CFL)number to be of an order of1.It is generally difficult to know the propertime step size at the beginning of a simulation.Therefore,an adjustment aftertheflow is established,is often necessary.For a given time step∆t,the highestfrequency that the acoustic analysis can produce is f=12∆t .For the time step sizeselected here,the maximum frequency is100kHz.Typically in most aeroacoustic calculations,the maximum frequency obtained from the analysis is higher than the audible range of interest.(b)Click Apply.5.Save the case and datafiles(cylinder2d t0.00.cas.gz and cylinder2d t0.00.dat.gz).File−→Write−→Case&Data...Save the case and datafiles before thefirst iteration.This will save you time in the event of user error or code divergence,where the casefile would have to be set up all over again.6.Run the case for a few time steps before activating the force monitors.Solve−→Iterate...(a)Set the Number of Time Steps to20.(b)Click Iterate.The residual history will be displayed as the calculation proceeds.When the non-iterative time advancement scheme is used,by default,two residuals are plotted per time step.7.Enable the monitoring of the lift and drag forces.Setting the force monitors after some initial transient state limits the range of the drag coefficient when starting from an impulse initial condition.Solve−→Monitors−→Force...(a)In the Coefficient drop-down list,select Drag.(b)In the Wall Zones list,select wall cylinder.(c)Verify that the X and Y values under Force Vector are1and0,respectively.(d)Under Options,select Plot to enable plotting of the drag coefficient.(e)Under Options,select Write to save the monitor history to afile,cd-history willbe the defaultfile name.If you do not select the Write option,the history information will be lost when you exit FLUENT.(f)Click Apply.(g)In the Coefficient drop-down list,select Lift.(h)Under Force Vector,specify X and Y to be0and1,respectively.(i)Under Options,select Plot to enable plotting of the lift coefficient.(j)Under Options,select Write to save the monitor history to afile.This time, cl-history will be the defaultfile name.(k)Close the panel.8.Set the reference values to be used in the lift and drag coefficient calculation.Report−→Reference Values...(a)Set the values as shown in the table:Parameter ValueArea0.019Velocity69.2Length0.019(b)Retain the default values for the other parameters and click OK.The reference area is calculated using the cylinder diameter,D,and the default depth of1m for2D problems.Adjust the reference area if a different depth (Depth)value is used.For the actual force coefficient calculation,only the reference area,density and velocity are needed.The reference length(Length)will be needed later for the Strouhal number calculation.9.Overwrite the previously saved initial conditions(cylinder2d t0.00.cas.gz andcylinder2d t0.00.dat.gz).File−→Write−→Case&Data...10.Advance theflow in time until a quasi-stationary state is reached.Solve−→Iterate...(a)Set the Number of Time Steps to4000.(b)Click Iterate.The4000time steps will advance theflow up to t=0.02s.At that time the bulkflow will have crossed the computational domain about three times.The residual history,lift and drag force histories will be displayed as the calculation proceeds.The lift and drag histories should be similar to Figure4and Figure5, respectively.Differences in the long-termflow evolution can occur due to operating system dependent round-offerrors.Once the lift and drag histories are sufficiently oscillatory and periodic in nature,you are ready to set up the acoustics model and perform the acoustic calculations.Figure4:Lift Coefficient History11.Verify that the selected time step size is reasonable for the given mesh andflowcondition.Plot−→Histogram...Figure5:Drag Coefficient History(a)Under Histogram of,select Velocity....(b)From the Velocity...category,select Cell Courant Number.(c)Set the value for Divisions to100.(d)Click Plot and verify that the peak CFL value is less than3.5.The histogram(Figure6)shows that most cells have a Cell Courant Number of less than1.12.Save the case and datafiles(cylinder2d t0.02.cas.gz and cylinder2d t0.02.dat.gz).File−→Write−→Case&Data...Figure6:A Histogram Displaying the Range of the CFL Number Step7:Aeroacoustics Calculation1.Define the acoustics model settings.Define−→Models−→Acoustics...(a)Under Model,select Ffowcs-Williams&Hawkings.(b)Under Options,select Export Acoustic Source Data.(c)Click the Sources...button.This will open the Acoustic Sources panel.i.Under Source Zones,select wall cylinder.All relevant acoustic source data(i.e.pressure in this case)will be extracted from the wall cylinder surface.ii.In the text-entry box for Source Data Root Filename,enter cylinder2d.This is thefilename root of the indexfile which will be created.The index file contains information about the source datafiles that are created when you run the case.The indexfile is automatically created with a.indexfile extension.iii.Under Write Frequency,enter2.Depending on the physical time step size and the important time scales in theflow,it is not necessary to write the acoustic source data at every time step.In this tutorial,the source data is coarsened(in time)by a factor of two.Thus,the highest possible frequency the acoustic analysis can generate is reduced to f=1=50kHz.2(2∆t)iv.Set the No.of Time Steps Per File to200.The source data can be conveniently segmented into multiple source data files.This makes it easier to process partial sequences when calculating the receiver signals.A value of200for No.of Time Steps Per File means that each source datafile covers a time span of200time steps.With a Write Frequency of2,there are100data sets written into each source datafile.v.Click Apply and Close.(d)Click OK to close the Acoustics Model panel.2.Modify the solution controls.Solve−→Controls−→Solution...(a)Increase the Relaxation Factor for Pressure to1.(b)Click OK.3.Resume the calculation.Solve−→Iterate...(a)Retain the Number of Time Steps at4000.(b)Click Iterate.The additional4000time steps will advance theflow up to t=0.04s.At every second time step,a message will be displayed in the FLUENT console window informing you that data is written to a source datafile(.asdfile extension).4.Save the case and datafiles(cylinder2d t0.04.cas.gz and cylinder2d t0.04.dat.gz).File−→Write−→Case&Data...5.Set the acoustics model constants.Define−→Models−→Acoustics...(a)Retain the Far-Field Density at1.225kg/m3.The far-field density is the density of thefluid outside the computational domain,i.e.the density of thefluid near the receivers.In most calculations it is the sameas the density within the computational domain.(b)Use the default value of340m/s for the Far-Field Sound Speed.(c)Leave the Reference Acoustic Pressure at2e-05Pa.The reference acoustic pressure is used to calculate decibel values during postpro-cessing.(d)Set the Source Correlation Length to0.095m.That is equal tofive cylinderdiameters.The source correlation length is very important when performing aeroacoustic cal-culations in2D.FLUENT assumes that the sound sources are perfectly correlatedover the specified correlation length,and zero outside.That is,FLUENT internallybuilds a source volume with a depth equal to the specified correlation length andneglects sources outside.In your practical2D application,you will have to esti-mate the source correlation length;your obtained sound pressure levels will de-pend on your input.That makes it difficult to rely on2D calculations to obtainabsolute sound pressure levels.Therefore,you should use aeroacoustic2D simu-lations primarily to observe trends.The source correlation length is not neededfor3D calculations.(e)Click OK to close the panel.6.Calculate the acoustic signals.Solve−→Acoustic Signals...(a)Click the Receivers...button.This will open the Acoustic Receivers panel.Note that you can open the Acoustic Receivers panel also from the Acoustics Model and Acoustic Sources panels.i.Increase the No.of Receivers to2.ii.For the receiver-1coordinates,enter0m for X-Coord.,-0.665m(35D)for Y-Coord.,and0for Z-Coord.iii.For the receiver-2coordinates,enter0m for X-Coord.,-2.432m(128D)for Y-Coord.,and0for Z-Coord.iv.Retain the defaults for Signal File Name(receiver-1.ard and receiver-2.ard).v.Click OK to close the Acoustic Receivers panel.(b)Under Active Source Zones,select wall cylinder.All source zones which were selected in the Acoustic Sources panel are now avail-able under the Active Source Zones.In this tutorial,the sound sources are ex-tracted from only one zone.It is important to select the source zones consistentlyif redundant source zones were selected in the Acoustic Sources panel.(c)Under Source Datafiles,select allfiles available.Selecting a subset of the available sourcefiles is a convenient way to analyzeshorter sequences.It is important to select a contiguous set of source datafiles.(d)Under Receivers,select the two available receivers.As soon as the source zones,source datafiles,and receivers are selected,theCompute/Write function becomes available.(e)Click Compute/Write.The FLUENT console window will confirm that the source datafiles are beingread and that the receiver signals are computed and written into receiverfiles.(f)Click Close to close the Acoustic Signals panel.Step8:Aeroacoustic Postprocessing1.Display the acoustic pressure signals at the two receiver locations.Plot−→File...(a)Click Add...in the File XY Plot panel.This will open the Select File panel where you can now select receiver-1.ardand receiver-2.ard from the Files list.(b)Click OK to close the Select File panel.(c)Click Plot to display the receiver signals(Figure7).Modify the line and markerstyles as necessary,using the Curves panel.You will notice a shift in time of approximately5e-3s for the signal at the second receiver.Receiver-2is farther away from the source surface and the sound will therefore arrive later.Also notice that the signal at receiver-2is weaker due to the increased distance and geometrical attenuation.Figure7:Acoustic Pressure Signals2.Perform a spectral analysis of the receiver signals.Plot−→FFT...(a)Under Process Options,select Process Receiver.This will activate the Receiverlist.If the Ffowcs Williams and Hawkings(FW-H)acoustics model is used and the receiver signals have been calculated,then the signals are directly available for postprocessing.As an alternative,the receiver data can be loaded manually from files by using the Process File Data option under Process Options.(b)Select receiver-1from the Receiver list.(c)Select Sound Pressure Level(dB)from the Y Axis Function drop-down list.(d)Select Frequency(Hz)from the X Axis Function drop-down list.(e)Click Plot FFT to plot the sound pressure spectrum for receiver-1(Figure8).The overall sound pressure level(OASPL)is printed to the FLUENT console window:>>Overall Sound Pressure Levelin dB(reference pressure=2.000000e-05)=1.156790e+02=50kHz,as expected.Note that the maximum frequency plotted is f=12(2∆t)Figure8:Spectral Analysis of Pressure Signal for receiver-1(f)Click Axes....This will open the Axes-Fourier Transform panel.i.Deselect Auto Range for the X Axis.ii.Manually set the Maximum for Range to5000.iii.Click Apply and Close the panel.(g)Replot the sound pressure spectrum for receiver-1.The spectrum peaks at about900Hz(Figure9).Note that the spectral resolution is only about50Hz,since the receiver signal was calculated for a short period only(approximately0.02s).For a sampled signal oflength T,the spectral resolution is1T .You may increase the spectral resolutionby running the simulation longer in time before recalculating the receiver signals.(h)Select the Strouhal Number from the X Axis Function drop-down list.i.Reset the Maximum for the x-axis Range to1,in the Axes-Fourier Transformpanel.(i)Replot the sound pressure spectrum as a function of the Strouhal Number.Thespectrum peaks at a Strouhal Number of about0.25(Figure10).If the Strouhal number calculation does not seem correct,verify that the correct values are specified in the Reference Values panel.(j)Repeat the spectral analysis for receiver-2by selecting receiver-2from the Receiver list.You should expect an OASPL of about104dB for receiver-2.3.Plot the power spectral density of the lift force history to see that the observed peaksin the receiver spectra match the dominant frequency in the lift force history.(a)Under Process Options,select Process File Data.(b)Click Load Input File...and select the lift monitorfile(cl-history).(c)Select Power Spectral Density from the Y Axis Function drop-down list.Figure9:Spectral Analysis of Pressure Signal for receiver-1at a Reduced Frequency RangeFigure10:Spectral Analysis of Pressure Signal for receiver-1as a Function of Strouhal Numbers(d)Under X Axis Function,select Strouhal Number.(e)Verify that the Maximum for the x-axis Range in the Axes-Fourier Transformpanel is1.(f)Click Plot/Modify Input Signal...to open the Plot/Modify Input Signal panel.Thispanel 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 to0.02.Without clipping the temporal range,the complete lift monitor history wouldbe analyzed including the initial transient state leading up to the quasi-stationary 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.(g)Click Plot FFT to plot the power spectral density for the lift monitor history(Figure11).The spectrum peaks at a Strouhal number of about0.25.As indicated in Step7,2D aeroacoustic predictions depend strongly on the selected source correlation length.As a consequence,the results can befine-tuned to be in better agreement with experimental data.4.You can repeat the calculation of the acoustic signals for the additional source corre-lation lengths of2.5D and10D,using Step7as a starting point.Table1compares the obtained OASPL values with experimental values reported by Revell et al.[1].Reasonable agreement is found for correlation lengths2.5D and5D.Figure11:Spectral Analysis of Lift Force HistoryTable1:Dependence of the Predicted OASPL on the Specified Source Correlation Lengths (L=2.5D,5D,10D)2.5D5D10D Experimental Resultsreceiver-1109.7115.7121.6117receiver-298.4104.4110.4100SummaryThis tutorial demonstrated the use of FLUENT’s acoustics model to calculate the far-field sound signals generated by theflow over a2D cylinder.You have learned how to set up the relevant parameters,save the acoustic source data,calculate,and postprocess the acoustic pressure signals.The main computational efforts are spent calculating the time dependent turbulentflow. It is therefore advisable to export the sound sources during theflow calculation.This allows you to recalculate the acoustic signals for different receivers or model parameters with minimal computational costs.The tutorial demonstrated the use of the Ffowcs Williams and Hawkings acoustics tool on a2D case.You have seen that it is difficult to obtain absolute SPL predictions in2D due to the need to estimate the correlation length of the turbulentflow structures in the spanwise direction.This difficulty does not exist when solving3D acoustics problems. References1.Revell,J.D.,Prydz,R.A.,and Hays,A.P.,“Experimental Study of Airframe Noise vs.Drag Relationship for Circular Cylinders,”Lockheed Report28074,Feb.1977.Final Report for NASA Contract NAS1-14403.。
