Aeroacoustic Analysis of a NACA Duct

Nicolas J. Pignier, Ciarán J. O'Reilly, Susann BoijThe Centre for ECO2 Vehicle Design at KTH, Teknikringen 8, 100 44 Stockholm, Sweden.

KTH Royal Institute of Technology, Department of Aeronautical and Vehicle Engineering, Teknikrin-

gen 8, 100 44 Stockholm, Sweden.

Jeremy A. DahanLinné Flow Centre at KTH, KTH Royal Institute of Technology, Department of Aeronautical and

Vehicle Engineering, Teknikringen 8, 100 44 Stockholm, Sweden.

Summary

An initial aeroacoustic study of a typical NACA inlet is presented. In this paper, the shape of the

NACA inlet is based on the experimental work of the National Advisory Committee for Aeronautics.

The study is performed at low Mach numbers. A time-averaged solution is obtained through a RANS

simulation and validated against experimental results. The results show good agreement both in

terms of overall performance of the inlet and in terms of local surface pressures. From the steady

simulations, a broadband noise source model is applied to get an estimate of the location of the noise

source regions on the surface of the inlet. This model of the NACA inlet will be used for a future

acoustic analysis based on unsteady detached eddy simulation (DES) of the �ow and on the Ffwocs

Williams-Hawkings integral.

PACS no. 43.28.+h, 47.85.Gj

1. Introduction

NACA inlets, also called NACA ducts, are a com-monly used type of submerged air inlet that has foundapplication on many types of air and ground vehicles.Developed by the National Advisory Committee forAeronautics (NACA) in the 1940s [1, 2], they weredesigned to e�ciently draw air from the outside tothe inside of a vehicle, providing fresh air that canbe used, for instance, in heating, ventilating, and airconditioning systems. Their submerged shape has theadvantage of adding only a little additional drag to thevehicle, while providing a design-friendly way to getair into the vehicle compartments. Nowadays, NACAducts can be found on many types of vehicles, bothon ground and air vehicles. Their standard design fol-lows the guidelines provided by the previously men-tioned NACA reports. Despite their extensive use inthe transport industry, few research papers have beenpublished since the mid-twentieth century. Recently,a couple of numerical studies have investigated thephysics of the �ow [3, 4], with the aim of designingaerodynamically optimized inlets [5, 6]. These studiesprovide some insight into the �ow that complementthe early experimental work by NACA. Recent obser-

(c) European Acoustics Association

vations have indicated that NACA inlets could be aconsiderable source of noise when placed on a vehicleat speci�c operating conditions. However, the litera-ture on the subject is very scarce. Airbus developed amodel of silent NACA inlets aimed at reducing noisein stationary operation [7], when external air is ac-tively sucked into the duct. Here, we focus our studyon a NACA inlet �xed on a moving vehicle. The over-all goal of the project is to develop a NACA inletwhich is both aerodynamically and aeroacousticallyoptimized. In this paper, an initial study is presented,which aims at validating the model for steady �owusing Reynolds-averaged Navier-Stokes (RANS) sim-ulations. First acoustic estimations are shown, result-ing from the application of a broadband noise sourcemodel on the RANS simulations. Later on, unsteadydetached eddy simulations (DES) of the �ow will beperformed on the same NACA inlet, and coupled to aFfowcs Williams-Hawkings (FW-H) integral [8] to getthe far-�eld noise.This paper is organized as follows. In the �rst section,the geometry of the NACA inlet and the methods forthe �ow and the broadband noise are presented. In thesecond section, results from the RANS simulations areshown and compared to experimental measurements;results for the broadband noise model are also given.Conclusions and next steps for the project are pre-sented in the last section.

Copyright© (2015) by EAA-NAG-ABAV, ISSN 2226-5147All rights reserved

1997

Figure 1. Model of NACA inlet used in the computations.

2. Method

2.1. Model description

The NACA inlet studied in this paper is shown inFigure 1. Its design is based on one of the submergedinlets studied by Mossman et al. [2] in wind tunneltests. The measurements were made on a test inlet forwhich the shape could be changed according to fourmain design characteristics: the ramp angle, the cur-vature of the ramp walls, the lip shape and the widthto depth ratio. In the conditions of the experiment, aset of design parameters was identi�ed as being op-timal. This optimal inlet had curved diverging rampwalls, a 5◦ to 7◦ ramp angle and a width-to-depth ra-tio of 3 to 5. The submerged inlet that we simulated isa reproduction of this optimal inlet. The external di-mensions of the simulated inlet match the ones of theexperimental inlet; the only noticeable di�erence canbe found in the duct section downstream of the in-let entrance plane. The experimental duct transitionsfrom a constant rectangular section duct to a circu-lar section di�user as can be seen in Figure 2. Ourmodel uses only the rectangular duct. Nevertheless,the absence of di�user in the simulated model is notexpected to be a source of error as the experimentalresults used for validation were measured upstream ofthe di�user.

2.2. Fluid dynamic model

The RANS simulations were run on the commercialsoftware STAR-CCM+ [9] in its release 9.06. Twoturbulence models were tested: the Spalart-Allmarasmodel [10] and the SST k−ω model [11]. The Spalart-Allmaras model is well-known for its simplicity of for-mulation and its fast and robust convergence. TheSST k − ω model was chosen for its ability to have

Figure 2. Experimental model and apparatus used byNACA [2].

the accuracy of the k − ω model in boundary layerswhile avoiding its sensitivity to free stream bound-ary conditions by switching to a k− ε model far fromthe walls. The simulations were run in compressiblemode. No signi�cant increase of the computationaltime was observed between incompressible and com-pressible simulations. The Reynolds number based onthe entrance depth of the duct is around 105.

2.3. Broadband noise source model

To perform an early analysis of the acoustic �eldgenerated by the inlet from the RANS simulations,a broadband noise model was used. The model thatwas used is the one implemented in Star-CCM+ thatestimates the broadband acoustic power of Curle'ssources, on the surface of the inlet. This model isbased on a semi-empirical formula to estimate thepressure �uctuations derivative from the wall-shearstress, the free-stream density, the turbulent kineticenergy, the turbulent time scale and the turbulentlength scale. For more details about this method,the reader is referred to the documentation of Star-CCM+ [9] and to Hinze's book [12].

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Figure 3. Domain and boundary conditions.

2.4. Computational domain, grid and bound-

ary conditions

The NACA inlet described in Figure 1 is placed in awind tunnel-type con�guration as shown in Figure 3.

Boundary conditions and initial conditions Atthe inlet, a constant velocity of 60 m/s in the x-direction is imposed. A pressure outlet boundary con-dition is used at the outlet, the pressure being set to101325 Pa. The �oor of the domain, the surface of theNACA inlet as well as the surface of the duct are mod-elled as no-slip walls, whereas the walls of the wind-tunnel are modelled as slip walls. At the duct outlet,the pressure is prescribed, through a targeted mass-�ow. On this boundary, the solver essentially adjuststhe prescribed value of pressure to reach the targetedmass �ow during the simulation. Regarding the tur-bulence models, the turbulent viscosity ratio is set to200. The length of the domain upstream of the NACAinlet could be adjusted to get the correct boundarylayer thickness at the position of the NACA inlet en-trance.

Mesh The mesh was generated in Star-CCM+, us-ing trimmed cells on top of a prism layer. The prismlayer covers all the no-slip walls and was adjusted toensure a y+ value slightly below 1 on these walls.Volumetric controls were used in the vicinity of theNACA inlet to re�ne the mesh locally. These controlsare shown in Figure 4 and their corresponding meshsize in Table I.A mesh of 55M cells was also tested, and no signif-

icant di�erence was observed; the results are thereforepresented for the 13.2M cells mesh.

3. Results

3.1. Analysis of steady RANS simulations

Boundary layer It was shown by Mossman thatthe boundary layer thickness - more speci�cally itsratio with the entrance depth - can have a signi�cantimpact on the e�ciency of the inlet [2]. In order tovalidate our simulations against the experiments, it isthus important to ensure that the boundary layer cor-rectly matches the experimental one. The boundarylayer velocity pro�le at the location of the duct en-trance is shown in Figure 6. This pro�le is extractedfrom a simulation in the same domain as presented inFigure 3, but without the NACA inlet.

Figure 5. Mesh.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

0.2

0.4

0.6

0.8

1

z

V/V

0

Experimental (NACA)

Simulated (Spalart−Allmaras)

Simulated (SST k−ω)

Figure 6. Boundary layer pro�le at the location of the ductentrance.

Ram recovery ratio NACA introduced the ramrecovery ratio as a mean to estimate the performanceof a given submerged inlet, and de�ned it as the ratioof dynamic pressure between the duct entrance andthe free stream. The ram recovery ratio is given by

ram recovery ratio =PT,1 − p0PT,0 − p0

, (1)

where PT,0 and PT,1 are the total pressure measuredrespectively in the free stream and at the entranceplane (averaged over the section for the latter), andwhere p0 is the static pressure of the free stream. Theram recovery ratio is represented on Figure 7 as afunction of the inlet velocity ratio, de�ned by theratio between the averaged velocity at the entranceplane and the free stream velocity V1/V0. NACA data

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Figure 4. Volumetric controls.

Table I. Volumetric controls and associated cell size.

Volume Cl Cc D C L Lc, R T Ld Total number of cells

Cell size (mm) 10 5 25 2 1 0.5 2 1 13.2M

were measured for a free stream speed V0 between55 m/s and 80 m/s, our results were obtained forV0 = 60 m/s. The results are in good agreement, witha maximum error of around 5%. For decreasing veloc-ity ratios from 1 down to 0.4, the ram recovery ratioincreases, a trend that is well reproduced by the simu-lations. The overall over-prediction of the ram recov-ery ratio could be explained by the imperfect match inboundary layer thickness between the simulated andexperimental cases. Mossman showed that a thickenedboundary layer can trigger a loss of ram recovery ratioof 0.12 [2]. A closer match of the ram recovery ratiocould certainly be obtained by further adjustment ofthe boundary layer. Another explanation could be thedi�erence in shape of the duct downstream of the ductentrance. Convergence was not obtained for velocityratios below 0.4, therefore we cannot draw conclusionsfor this regime at this stage.

Flow An example of the surface pressure andstreamlines of the �ow is shown in Figure 8 for aninlet velocity ratio of V1/V0 = 0.6. As it is well-knownfor this type of inlets, the �ow is characterized by thecounter rotating vortices that are created at the sharpedges between the ramp walls and the external sur-face. These vortices impinge on the sides of the lip, re-sulting in part of the �ow being drown inside the ductand part of it being dragged with the external �ow,the proportion of which depends on the inlet velocityratio: the lower the inlet velocity ratio, the higher thepressure inside the duct and the less air coming in. Inview of this complex �ow around the lip, it seems rea-sonable to think that the main noise sources shouldbe located in this area. A characteristic frequency ofaround 1000 Hz can be associated with the vortices,based on their length and velocity scales. Assuming

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60.7

0.75

0.8

0.85

0.9

0.95

1

Inlet velocity ratio

ram

recovery

ratio

Experimental (NACA)

Simulated (Spalart−Allmaras)

Simulated (SST k−ω)

Figure 7. Ram recovery ratio vs inlet velocity ratio.

that the vortices are the phenomenon from which thenoise originates, i.e. that they are causing directly orindirectly the pressure �uctuations on the surface, wemay expect this frequency to play a particular role inthe noise generated.

Pressure coe�cient on the inlet surface As thenoise emitted by the inlet is our point of focus, it isimportant to predict the values of surface pressureaccurately. In terms of acoustics, the pressure �uctu-ations matter more than the mean pressure values,but a �rst step is to verify that the latter are wellpredicted in the RANS simulation. The pressure coef-�cient along the ramp and on the lip are representedfor various inlet velocity ratio respectively in Figures9 and 10. The results are shown for both the Spalart-Allmaras and the SST k − ω turbulence models. The

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Figure 8. Surface pressure and streamlines for V1/V0 = 0.6

−20 −10 0 10 20 30 40 50 60 70 80 90 100−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

PercentageVofVrampVlengthV(m)

Pre

ssur

eVco

effic

ient

V1/V

00.60.81.00.60.81.0

Figure 9. Pressure coe�cient distribution along the rampfor various velocity ratio, for the Spalart-Allmaras and theSST k − ω turbulence models. The lines represent simu-lated data, the points experimental values [2].

values are extracted in the y = 0 plane, that is thesymmetry plane of the inlet.The pressure over the lip is very well predicted for

the three velocity ratios. The pressure along the rampis overall correctly predicted: it is approximately con-stant in the �rst half of the ramp and increases in thesecond half. The slope of this increase gets lower witha higher inlet velocity ratio and this trend is well pre-dicted. A local drop in pressure can be observed atthe starting point of the ramp in the simulated data.This is probably due to the sharp transition betweenthe 0◦ external wall and the 7◦ ramp on the simu-lated model, which must have been rounded on theexperimental inlet.

3.2. Broadband noise sources results

The broadband noise sources on the surface of the in-let are represented in Figure 11. These results wereobtained based on the RANS solutions of the �owwith the SST k − ω turbulence model. According to

0 0.02 0.04 0.06 0.08 0.1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Distance from leading edge of lip (m)

Pre

ssur

e co

effic

ient

V1/V

00.60.810.60.81.0

Figure 10. Pressure distribution over the lip for variousvelocity ratio, for the Spalart-Allmaras and the SST k−ωturbulence models. NACA for speeds between 55 and 80m/s, simulated for speed 44.4 m/s. The lines representsimulated data, the points experimental values [2].

these results, the main noise sources would be locatedon the lip, with strong disturbances at the positionof impact of the vortices. The strength of the sourceseems to increase with decreasing velocity ratio, cor-responding to situations where the vortices impact inlarger extent on the lip.

4. Conclusion

An initial aeroacoustic analysis of a NACA inlet hasbeen led. RANS simulations of the �ow were per-formed and assessed against experimental data, show-ing good agreement. The model and the simulationprocess have thus been validated, and can be usedwith con�dence to predict the �ow over various shapesof NACA inlet.First acoustic estimations could be drawn from a

broadband noise source model. From these results itseems that the sources are potentially mainly localizedon the lip of the inlet, with maximal values at thelocation where the vortices created at the ramp walledges impinge on the lip.This preliminary study has built a solid foundation

for a more thorough acoustic analysis based on un-steady simulations.

Acknowledgement

The work presented here is part of the project: "NoisePropagation from Sustainable Vehicle Concepts" ledat the Centre for ECO2 Vehicle Design, a VinnEx-cellence Centre performing multi-vehicular multidis-ciplinary research to support a sustainable vehicle de-sign development.

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Figure 11. Broadband noise sources on the surface of the inlet.

References

[1] C. W. Frick, W. F. Davis, L. Randall, E. A. Mossman:An experimental investigation of NACA submerged-duct entrances. National Advisory Committee forAeronautics Collection (1945).

[2] E. A. Mossman, L. M. Randall: An experimental in-vestigation of the design variables for NACA sub-merged duct entrances. National Advisory Committeefor Aeronautics Collection (1948).

[3] E. S. Taskinoglu, D. Knight: Numerical analysis of sub-merged inlets. AIAA Paper, Vol. 3147 (2002).

[4] S. Sun, R.-W. Guo: Numerical analysis and experi-mental validation of a submerged inlet on the planesurface. Chin. J. Aeronaut., Vol. 18, No. 3 (2005) 199-205.

[5] E. S. Taskinoglu, V. Jovanovic, D. Knight, G. Elliott:Design optimization for submerged inlets-Part II. 21stAIAA Appl. Aerodyn. Conf., Orlando, Florida, 2003,23-26.

[6] E. S. Taskinoglu, V. Jovanovic, D. Knight, G. Elliott:Multi-objective design optimization and experimen-tal measurements for a submerged inlet. 42nd AIAAAerosp. Sci. Meet. Exhib, Reno, Nevada, 2004, 2004-2025.

[7] M. Siercke, U. Heise, J. Holmgren, A. Gommet: Airinlet for a vehicle. U.S. Patent No. 8,393,566, issuedMarch 12, 2013.

[8] J. E. Ffowcs Williams, D. L. Hawkings: Sound gener-ation by turbulence and surfaces in arbitrary motion.Philos. Trans. R. Soc., Ser. A, Math. Phys. Sci., Vol.264, No. 1151 (1969) 321-342.

[9] STAR-CCM+, http://www.cd-adapco.com/products/star-ccm [Accessed: 2015-01-21]

[10] P. R. Spalart, S. R. Allmaras: A one-equation turbu-lence model for aerodynamic �ows. Rech. Aérosp., 1(1994) 5-21.

[11] F. R. Menter: Two-equation eddy-viscosity turbu-lence modeling for engineering applications. AIAA J.,32(8) (1994) 1598-1605.

[12] J. O. Hinze: Turbulence. McGraw-Hill, 1975, 672-673.

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