deliverable 2.4 global model: ground + tyre + fluent...

Project no. TST3-CT-2003-506437

ITARI

Integrated Tyre And Road Interaction Specific Targeted Research or Innovation Project Priority 6 Sustainable development, global change & ecosystems

DELIVERABLE 2.4

Global model: ground + tyre + Fluent + radiation

Due date of deliverable: 2006-08-01 (reported) Actual submission date: 2007-06-06

Start date of project: 2004-02-01 Duration: 40 months Lead contractor for this deliverable: Centre Scientifique et Technique du Bâtiment (CSTB)

Project co-funded by the European Commission within the Sixth Framework Programme (2002-2006) Dissemination Level

PU Public x PP Restricted to other programme participants (including the Commission Services) RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services)

ITARI Deliverable 2.4

Table of Contents Introduction ..................................................................................................................... 3

1 – CFD model of air pumping ...................................................................................... 4

1.1. Model description 4 1.2. Numerical considerations 6

2 – Study of simple cases ................................................................................................ 8

2.1. Study of the distance effect 8 2.2. Study of the distribution effect 9

3 – Simulation of air pumping for real 2D road texture profiles .............................. 11

3.1. Build up of a 2D road profile 11 3.2. Simulation of air pumping for a real road texture 14 3.3. Study of ISO and rough roads 16

4 – Global model ............................................................................................................ 19

4.1. Modelling of air pumping noise propagation 19 4.2. Comparison between different noise sources and road configurations 22 4.3. Full calculation 25

Conclusion ....................................................................................................................... 27 References ....................................................................................................................... 28

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Introduction In this project, work-package 2 is focused on noise radiation due to the interaction between the tyre and the road. The main noise sources are the vibrations of the tyre surface and aerodynamic mechanisms, called “air pumping”, in the contact region. The acoustic waves propagate in the surrounding air under the influence of the tyre geometry but also in the porous layers of the road. The purpose of this work-package is to model and to study the different stages of this process, in order to be able to treat the full process of noise radiation for real cases. The main task is the modelling of the air pumping phenomenon. In a first step, a CFD (Computational Fluid Dynamics) model has been set up [1, 2] in order to simulate air pumping mechanisms for the case of a single artificial road cavity. The acoustic propagation in the ground has been taken into account with the development of a multi-domain BEM (Boundary Element Method) formalism in 2D [3]. Moreover, a mixed approach called GRIM has been used in order to propagate with the BEM code, the noise due to the air pumping phenomenon, calculated with the CFD model [3]. The objective of this deliverable is to provide a model able to predict the noise due to the tyre/road interaction (vibrations and air pumping) considering the effects of the ground and the tyre. The noise sources are calculated by different models and the noise propagation is computed with the BEM method. Therefore, several noise sources have to be considered and some phenomenon like the horn effect or the absorption by a porous road are taken into account. These different stages are described in the previous deliverables (deliverables 2.2 and 2.3). The global model obtained has to be applied to real road texture in order to compare different roads or different noise sources. The approach consists in applying the CFD model set up for a single cavity to more realistic cases like cavities series and then to real road profiles. Parametric studies are carried out to evaluate the effect of different parameters for single cavities or successions of cavities. Several road textures are tested with the CFD model. This model is coupled with a BEM code in order to propagate air pumping noise. Finally, some comparisons are done between the air pumping noise and the vibration noise, different road textures or different porous layers.

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1 - CFD model of air pumping In this chapter, the modelling approach of the air pumping phenomenon chosen and the CFD model set up for a single cavity are briefly presented. In addition, numerical considerations for the model use, determined according to parametric studies, are described. 1.1 - Model description 1.1.1 - Approach Air pumping is an aerodynamic mechanism which generates noise mainly in medium and high frequency ranges (above 1 kHz) compared with tyre surface vibrations radiating in medium and low frequency ranges. This phenomenon is usually considered to be due to volume fluctuations related to the tyre deformation. It is generally associated to all air flow fluctuations and acoustic resonances near the contact patch. The main mechanism consists in the compression at the leading edge and the release at the trailing edge of the contact patch, of air trapped in cavities formed by the contact of the road and the tyre surfaces. Cavities can be due to the tyre tread profile or to the road texture profile. In this respect one would expect the cases of a smooth tyre rolling on a rough road and a commercial tyre on a smooth road to show similar physical mechanisms. Simple analytical models employing monopole theory have been found unsuitable [4] [5]. They cannot model properly the compression phase and the non-linearity of the mechanism. The use of numerical methods to model air pumping was suggested by Gagen [5] in 1999, where he employed CFD (Computational Fluid Dynamics) to study air compression in a tyre groove. The different stages of the use of a CFD model for the air pumping phenomenon in a single road cavity without volume change is presented in the deliverable 2.2 and its annex [1, 2, 6]. Only the problem of a smooth tyre rolling on road cavities is considered in this study. The phenomenon is basically composed of three phases (figure 1). At the leading edge, air in the cavities is compressed during closure. The overpressure is maintained along the contact for the closed cavities. Then, at the re-opening of the cavities at the trailing edge, the overpressure is released. This overpressure in the cavities of the road (or of the tyre tread) is created by several more or less important mechanisms. For the case of a road cavity, the tyre surface rolling and advancing on the road creates an overpressure in front of the tyre, fills the cavity with air during closure and so compresses it without volume change. The tyre tread deformation compresses also the cavity reducing its volume. Another smaller part of the released overpressure is due to air flow around the tyre generated by its displacement. The magnitude of these mechanisms depends on the case which is studied.

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In this study, only the first mechanism without volume change, corresponding to the passing of the tyre, is modelled for the case of cavities on a smooth road.

Air compression Air release

Overpressure

Figure 1: The three phases of the air pumping mechanism

Air pumping depends very much on the geometry and particularly for the compression phase. In order to take into account air flow near the contact patch, the numerical CFD method was chosen to model air pumping in road cavities. 1.1.2 - CFD model The FLUENT solver was used to simulate air pumping and the noise generated. This CFD code is based on the finite volume method and incorporates dynamic and moving meshing. A smooth tyre and a smooth road surface are considered. Some cavities are included in the road for each case. The static deformed shape of the tyre is taken into account to be able to model the effect of the sharp angle at the contact points. The displacement velocity is 80 km/h for all simulations. The reference frame is the centre of the wheel. The average radius of the tyre is 314 mm. Moving boundaries are considered: the tyre surface rotates and the road surface slides. The road cavities also slide under the tyre. The computational domain is composed of the road cavities and a domain around the tyre. It is meshed with hexahedral elements in 3D and quadrilateral elements in 2D. A finer mesh is needed in the horn region and in the road cavities in order to simulate the compression of air during the closure of the cavities (figure 3). The cavities in the road are meshed as a sliding zone with a displacement velocity advancing towards the contact patch (figure 2). 2D and 3D simulations have been carried out for the compression and the release phases, but all the parametric studies and the simulations of cavities series have been done in 2D.

Figure 2: Geometry of a rectangular cavity and a loaded tyre. The positions of the two receivers are represented by

crosses. Vectors represent displacements

The Navier-Stokes equations are solved on the discretized computational domain and in the time domain. Air flow due to the tyre displacement is not modelled in the simulations presented in this paper. This air flow causes less than 10% of the overpressure in the cavity, which can be seen in measurements [7]. It does not influence the main phenomenon which is the cavity compression. ________________________________________________________________________________

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This flow is not modelled in the presented results because in 2D, it is not representative. Indeed, it causes a big pressure difference between the two edges of the wheel, which is not the case in 3D since air flows on the sides. The influence of air flow on acoustic propagation is not studied here. The only air flow in these simulations is due to the moving walls. Indeed, the road surface is advancing with the cavity and the tyre is rotating; this is taken into account by modelling boundary layers. Air is considered as viscous and compressible. Its density is determined with the ideal gas law. The turbulence is modelled in a RANS (Reynolds-Averaged Navier-Stokes) simulation using a k-ω model. The input data and the used model are the same for all the simulations.

Figure 3: Examples of 2D mesh (compression phase - left) and 3D mesh (release phase - right)

1.1.3 - Validation This model has been validated qualitatively for the case of a cylindrical cavity [2] by comparing the results of the simulation with the measurements done at INRETS [7]. The phenomena and the trends of the computations are similar to the results of the experiments, but the magnitude of the overpressure inside the cavity is almost half smaller in the simulations because of the assumptions of the model (no tyre tread penetration, 2D... etc.). Nevertheless this model allows to carry out parametric studies and to study the phenomenon. 1.2 - Numerical considerations This model has been tested for different configurations in terms of geometry, meshing, physical models, boundary conditions, numerical parameters... etc. In this subpart, the effects of these parameters on the convergence of the simulation and on the results are presented. 1.2.1 - Effects on the convergence For the considered problem, some conditions have to be satisfied to get the convergence of the computation. These conditions are different for the compression phase and for the release phase. Two physical domains are considered: acoustics and fluid mechanics, and locally several phenomena are modelled. Fluid dynamics The computational domain is meshed with small cells. The cells size is chosen in order to get the

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convergence of the simulation. The segregated solver is used. Each equation is solved separately. Turbulent boundary layers are modelled at the wall boundaries (road and tyre surfaces). These boundary layers are meshed depending on the turbulence model with fine cells getting a small y+ (y+ =ρ*uτ*y/μ; ρ is the density, uτ is the friction velocity, y is the height, μ is the viscosity). With the k-ω turbulence model used, small cells are considered in order to get y+ lower than 5 in the contact region. Since the cavities are small and meshed with very small cells, the horn region, near the contact points, has to be meshed very finely in order to model properly the compression phase. A sliding mesh interface is used to model the displacement of the cavities. The difference of cell size between both sides of this interface, separating the cavities to the computational domain above the ground, has to be not too big in order to get the convergence. Several tests have been done, and a rate of two in the important zones and four in zones without interesting phenomena are acceptable. Several time-steps have been tested. It has to be small enough to model the dynamic of the mechanism since cells moves relatively to others. Therefore this time-step depends on the cells size. For most of the simulation, it is 2.5e-6 s. Acoustics The modelling of acoustic phenomena imposes other numerical conditions. A large frequency range has to be considered. Simulation needs to be run for long times with small time-steps. In order to model high frequencies, very fine mesh and time-steps are needed. The mesh size should be at least smaller than 1/10 of the wavelength, and the time-step smaller than 1/20 of a period. The modelling of low frequencies implies long calculation durations. In the frequency range, the domain studied for the air pumping phenomenon is around 1 kHz and between 1 kHz and 10 kHz. The mesh chosen respects these acoustic criteria in the region around the tyre where the receivers are located. 1.2.2 - Effects on the results Of course, each parameter in a numerical model has its effect on the results but some parameters have to be chosen carefully. In this paragraph, the effects of little changes on some parameters which have big effects are presented. The geometry discretization in the contact region is an important parameter. Indeed, the contact angle is cut to avoid a very fine triangular cell. The choice of this cut can change very locally the contact length and the tyre shape at the contact. The curvature of the tyre surface at the contact has a big effect in the compression phase. The choice of the turbulence model is also important. Indeed URANS simulations are carried out. Therefore, the turbulence is averaged and the choice between k-ε and k-ω models for example has a big effect during the compression phase. The k- ε model gives a bigger overpressure in the cavity. Actually, the difference comes from the modelling of the boundary layer. The k-ω model is finally chosen because the viscous sub-layer is meshed and more accurately described. The choice of the boundary conditions is important but there are not nonlinear effects. The tyre and road surfaces are considered as moving walls with a given wall velocity. The outlet condition is a pressure condition located as far as possible to avoid wave reflection in the calculation duration.

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2 – Study of simple cases Parametric studies have been done for single cavities. In real road textures, cavities are not isolated. Road profiles can be seen as successions of cavities. One of the objectives of these simulations is to find a way to model simply the air pumping phenomenon. Therefore, it would be interesting to compare cavities series with the results of several single cavities. In the annex of the deliverable 2.2 [2], the simulation of air pumping for a cavities series has shown that in reality the action of the road cavities is not isolated and there are interactions between close cavities. Therefore the behaviour of cavities series cannot be easily modelled from the behaviour of single cavities. In this part, successions of cavities were simulated to evaluate the interactions between the cavities. Different types of interaction have been shown during the compression phase or the release phase, however only the main phenomena due to the effects of the distance between the cavities and the distribution of the cavities are presented. 2.1 - Study of the distance effect Different cavities series were modelled varying the distance between the cavities. The interactions between the cavities should decrease when this distance increases. Five series, 8 cm long, of small triangular cavities (figure 4) were compared with a single triangular cavity (2 mm wide and 2 mm deep). Pressure signals were computed at the leading and the trailing edges.

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A B C D E F

Figure 4: Profiles of the 6 series of cavities (top graph) and example of the horn geometry (lower graph)

8 cm

C : 10 cavities

A : 40 cavities – d = 0 w = 0 mm

B : 20 cavities –

– d = 3 w = 6 mm

d = 1 w = 2 mm

D : 5 cavities d

– d = 7 w = 14 mm

E : 3 cavities – d = 15 w = 30 mm

2 mm

w = 2 mm

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-80

-60

-40

-20

0

20

40

60

80

7 7,5 8 8,5 9

Time (ms)

Pres

sure

(Pa)

40 cavities20 cavities5 cavities1 cavity

Figure 5: Pressure signals computed at the trailing edge for 4 series of cavities

In the case of the small single triangular cavity, a short pressure wave is generated at the trailing edge and another pressure wave much smaller is emitted at the leading edge. Simulations of cavities series show that when the cavities are close to each other, corresponding to a distance of less than three times their width in this case, the signal magnitude changes. There are interactions between cavities at both edges of the tyre. At the trailing edge, for very close cavities, the pressure signal generated by each cavity is damped by the previous one (figure 5). From a certain distance between cavities, there are no more interactions and the magnitude of the pressure wave is the same than for a single cavity. At the leading edge, the same phenomenon appears for close cavities. However, it seems that the interactions are different when the distance between the cavities increases; the magnitude of the pressure signal becomes higher than the magnitude of the single cavity signal and then it tends towards this single cavity magnitude and the interactions disappear. Interactions between cavities imply that it is not easy to model simply a cavities series. 2.2 - Study of the distribution effect A cavity succession with a regular distribution of cavities generates noise dominated by the frequency of the cavities occurrence and its harmonics. In real roads, the cavities distribution is often randomized. Two simulations of cavities series with the same number of cavities with and without a regular distribution were carried out to study the effect of the random distribution of cavities. Theoretically, the pressure spectrum for a succession of identical cavities is equal to the spectrum of the single cavity multiplied by the spectrum of occurrence of the cavities [8]. Consequently, if the cavities distribution is regular, the spectrum is discrete, and if it is randomized, the spectrum is proportional to the single cavity spectrum. The first cavities series contains 40 triangular cavities (2 mm wide and 2 mm deep) regularly separated by 6 mm. The second cavities series contains the same 40 cavities separated by a random distance in a range from 0 to 12 mm, with an average of 6 mm (figure 6). The lengths of both

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profiles are almost the same (respectively 31.4 cm and 32.8 cm).

Figure 6: Geometry of the random (green) and the regular (red) series

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Figure 7: Spectra of pressure signals at the rear (left) and front (right) sides (at 20 cm), for the cases of a single cavity,

a regular and an irregular series of cavities

The spectrum of the pressure signal generated at both edges by the first regular cavities series is composed of peaks at the frequency of cavity occurrence at 80 km/h (2777 Hz) and its multiple frequencies (figure 7). The height of these peaks is proportional to the magnitude spectrum of the single cavity. The simulation of the random cavities series provides spectra with many small peaks with an asymptote curve which is, without interactions, proportional to the spectrum of the single cavity. These spectra should tend towards this asymptote curve if the length of the profile was infinitely long. The coefficient between the spectra provided by the random cavities series is the density of cavity in the profile. If this density is high, it implies that there are more interactions than for a low density. Indeed, the random distribution means that some cavities can be very close to each other. In this case, the pressure signal generated by these cavities is weaker. Consequently, the magnitude of air pumping noise emitted by a random cavities series is not simply proportional to the noise of a single cavity.

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3 – Simulation of air pumping for real 2D road texture profiles In this part, the goal is to model the phenomenon of air pumping in the case of a real road in two dimensions. So, the numerical model set up in the case of artificial cavities is taken again and adapted to the problem considered. New assumptions are made. The principal difficulty lies in the representation of the profile of road texture for CFD calculation. The road texture profile given in entry of the model must have the form of a series of cavities. Various road texture and the effects of several parameters are studied. 3.1 - Build up of a 2D road profile 3.1.1 - Real road textures In order to model the phenomenon of air pumping in the case of a real road, the profile of road texture cannot be integrated in the CFD model such as it is measured. Indeed, in this model it is a matter of considering the road cavities formed at the time of the passage of the tyre. The real road comprises positive and negative indentations with variable size and density according to the road type. Contrary to the problem of the single cavity, the real road profiles deform particularly the tyre surface. The tread penetrates more or less in the road cavities. Moreover, the interface between the tyre and the cavities must be flat and cannot oscillate with the variations of the local average height of the road. Lastly, the model used is 2D and thus the profiles considered must be also in two dimensions. It is thus necessary to build an equivalent 2D road texture profile for the real problem studied. In order to do this, one must consider several assumptions and approximations. Several textures of roadways are studied in this chapter. The first road texture taken into account was measured on a German road [9] by Bundesanstalt für Strassenwesen (BASt). These measurements of 3D surface realized by a laser system were post-treated and provided by Müller-BBM. The resolution of measurements is 0,038 mm. Considering a 2D profile is an important approximation for the modelling of this 3D physical phenomenon. Indeed, in addition to the assumptions already formulated in the case of an isolated cavity, another major assumption must be made because of the geometry of the problem. The cavities created by the interaction between the tyre and the road are not often isolated in the contact zone and for the majority of roads, they are often connected to each other. Therefore, at the time of the compression phase, the cavities are not completely closed in general. One can imagine that ________________________________________________________________________________

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actually, overpressure in these open cavities will be less important or that flows between the cavities will change the phenomenon if the openings are sufficiently large. By considering a 2D profile, one supposes that the cavities are closed and infinitely long. The 2D model used underestimates overpressure in the cavities almost half [2, 6]. However, the phenomenon is also over-estimated in the 2D modelling since these cavities are regarded as closed.

Figure 8: 3D road texture profile [9]

To obtain a series of cavities usable in a CFD model, the envelope of the tyre must be modelled. The CFD model set-up does not take into account the dynamic deformation of the tyre [1]. Consequently, the geometry of the cavities of the road profile must be constant. Contrary to the problem of the single cavity for which the model was validated, the local deformation of the tire is not negligible. However compression and the release due to this penetration of gum are not modelled. This profile is cut (figure 9) to consider the tyre surface penetration. Two different average penetration depths are chosen approximately in these first simulations.

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Figure 9: 2D measured road texture profiles for 2 tracks of the road sample: the upper part of the profiles is cut (red)

and the lower part (blue and green) is kept. 4 studied cases are represented (cases 700-short, 700-2x, 70-2x-b, 300-full) – distances in mm.

Then several series of cavities are obtained (Figure 9). Several lengths of profiles are considered (of 8,5 cm to 43,8 cm). The computation time being related to the length of the road profile, it is important to know if there is a sufficient profile length in order to characterize the roadway.

Profile 300-full

Profile 700-2x

Profile 700-short

Profile 700-2x-b

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.1.2 - ISO and rough roads

wo other types of real roads were studied: an ISO pavement and a rough pavement. These road

3 Tprofiles were provided by Goodyear, during the previous European project RATIN (Road And Tyre Interaction Noise) [4]. These textures of roadway presented in the figure 10 are very different. The generating mechanisms of noise highlighted by these two profiles can be different. For a rough road for example, the contribution of the vibrations of the tyre is supposed to be important, whereas for a smoother road like the ISO profile, the phenomena of slip-stick and air pumping can dominate. Indeed, the small cavities of a smooth road are more easily isolated and communicate less between them, so the overpressure is bigger.

Figure 10: Roughness profile for the ISO road (left) and the rough road (right) [4].

s for the first road profiles presented, it is a matter of modelling the envelope of the tyre in order

centre of the contact, corresponding to the

Ato obtain cavities. In this case, one proposes to use the model of tyre/road contact of Chalmers [10]. This model calculates the dynamic deformation of the tyre in the contact region as well as the forces of contact from tyre model and a 3D road texture profile (figure 11). The penetration of the tyre in the road cavities is different according to whether one considers a 2D or 3D geometry. Although the modelling of the phenomenon of air pumping is done in 2D, the envelope of the tyre is calculated in 3D since the shape of the cavities is more realistic. The penetration of the tread is calculated at themaximum depth. The same equivalent road profile is used for each phase of the phenomenon.

Figure 11: Dynamic deformation shape of the tyre on an ISO road profile

he deformation of the tyre is then subtracted from the road profile in order to obtain a flat T

tyre/road interface. This operation allows to obtaining a flat interface needed for the simulation keeping at the same time the information of the shape of the cavities. The result of this calculation is presented in the figure 12. The static deformation shape of the tyre used in this case is the shape computed by KTH with a finite element model. The effects of the static deformation shape of the tyre are presented in the paragraph §3.3.

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Figure 12: Equivalent road profiles for one ck of the ISO (left) and the rough (right) surfaces

he CFD model is applied to the equivalent cavities series build up from the measured road

these simulations, only the effect of the passing of the tyre is considered in the modelling of the

Figure 13: Pressure fields at a certain time-step around the tyre (case “profil-300-full”)

s for the simulations of cavities series, the pressure signal generated at the trailing edge is much

tra

3.2 - Simulation of air pumping for a real road texture Tprofiles. In this paragraph, the results of the simulation of air pumping for the first road texture considered (road profile provided by Muller-BBM). Incompression phase.

Pressure (Pa) 60 40 20 0 -20 -40 -60

Amore important than at the leading edge (figure 13). The real road profile has the same behaviour than a random cavities series with a pressure signal at the rear which has varying magnitude and frequency. The figure 14 shows the chronology of the events. ________________________________________________________________________________

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Figure 14: Time pressure signals (left) at 20 cm at the rear and the front side of the tyre and their spectra (right) (case

he spectrum of the signal from the rear side is the most important between 1 and 4 kHz with a

Figure 15: Spectra of the pressure signal at the rear (left) and front (right) sides (at 20 cm) for the case of real road

Different re 9). All

tions due to their profile length and the average

also between “700-2x-b” and “300-full” which have different cavity sizes, show this phenomenon.

Opening of the first cavity at

the trailing edge

Closure of the first cavity at the

leading edge Closure of the lastcavity of the series at the leading edge

Contact time

“profil-700-2x-b”)

Tmaximum around 1.5 kHz (figure 14). The spectrum of the signal from the leading edge is much weaker under 4 kHz, and there are less differences between high and low frequencies. Qualitatively, it looks like what could be expected from air pumping noise sources for such road surfaces.

texture profiles (cases “profil-700-short” “profil-700-2x” “profil-700-2x-b” “profil-300-full”)

lengths of profiles have been tested from 8.5 cm to 43.8 cm (cases shown in figuthe cavities series have the same behaviour and the noise spectra have the same shape (figure 15). All the spectra at the rear side have their maximum between 1 kHz and 3 kHz, and the noise levels at the front side are lower. Nevertheless the results show that the length of the studied profile has a significant effect..

deed, some differences exist between these simulaInpenetration depth chosen. The longer the profile is, the higher the resolution of the spectrum is. With a long pressure signal, the spectrum is more chaotic with many peaks but it is of course more accurate. The short profile with just few cavities has not the same magnitude than the longer profile “700-2x”. For a profile length from 20 cm, the road profile is long enough to have the main trends. The average penetration depth has also an important effect since it changes the volume of thecavities. The bigger the volume of the cavity is, the smaller the overpressure inside is but also the stronger the noise emitted is. The comparisons between the profiles “700-2x” and “700-2x-b”, but

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3.3 - Study of an ISO and a rough road

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.3.1 – Simulation of the different tracks for the ISO and the rough roads

rough road are presented. he CFD model is applied to equivalent road profiles build up at 3 different tracks on the width of

Figure 16: Spectra of the pressure signals at 20 cm at the rear side (left) and front side (right) for 3 tracks of the ISO

surface The noise s6). It shows that the profile length is long enough to get the main trends of the air pumping

be considered because they are due to flow perturbations as

Figure 17: Spectra of the pressure signals at 20 cm at the rear side (left) and the front side (right) for 3 tracks of the

rough surface F

ynamic with a higher maximum between 1 and 2 kH the different tracks are

3 In this paragraph, the results of the simulations for the ISO road and the Tthe contact patch for each road texture. The length of the road profiles is approximately 20 cm long.

Rear Front

pectra for the three tracks are similar at the rear or at the front for the ISO road (figure 1phenomenon for this road type. There are some differences in the peaks position in the spectrum due to the limited resolution (Δf) linked to the profile length. However, by studying several tracks of the road, more information is obtained with less CPU time needed than for the simulation of a road profile three times longer. The spectra of all the tracks give a kind of envelope for the noise emitted by this type of road surface. The spectrum of the signal at the front side is more flat and lower than at the rear side. The strong levels at low frequencies must not explained in the paragraph §4.1.1. They do not represent acoustic waves and are not propagated. This spectrum looks like the spectrum of a white noise due to shockwave shape of the time signal at the front side.

FrontRear

or the case of the rough road (figure 17), the spectrum of the signal from the rear side is morez. The signals fromd

quite similar at low frequencies. However there are more differences between the tracks at high

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nce of the static deformation shape of the tyre

there are several tyre models. The static eformation shape of the tyre is calculated by KTH and Chalmers. The tyre diameter is 314 mm.

Figure 18: 3 different static deformation shapes of the tyre, and a zoom of the contact region (inside graph)

hese shapes are of course very similar. However they are different very locally close to the contact

frequencies. This could be due to the bigger volume of the cavities and the smaller distance between the cavities. 3.3.2 – Influe Several shapes of the tyre are available in this project since dThe tyre shape of Chalmers calculated in the project RATIN for a smooth road is cut at the contact when the distance between the tyre and the road is lower than 0.02 mm. The contact length is then 7.6 cm. For the tyre shape from KTH, there is no very flat zone in the contact region since this shape represents the mean penetration depth (for an ISO road in this case) of the tyre tread in this region. This shape is also more asymmetric. A first shape (KTH 1) is obtained by cutting the profile in order to have a contact length expected of 8.4 cm. A second shape (KTH 2) is chosen in order to have the contact points where there is an important inflection of the tyre surface like for the Chalmers shape. The contact length is then 6.5 cm. These different tyre shapes are represented in the figure 18.

Tpoints. It looks like a difference of load. As shown previously (§1.2.2, [2]), the shape of the contact region is very important during the compression phase in the air pumping mechanism. The sharper the contact angle is, bigger is the overpressure in the cavities. However this effect is important only

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he results of the simulations of these different static deformation shapes are shown in the figure 19

Figure 19: Spectra of the pressure signals at the rear side for the ISO road (left) and the rough road (right) for 3

he tyre shape from KTH is calculated with a finite element method for the tyre, accurate for the

for small cavities. Tfor the cases of the ISO and the rough roads. This shape has an important effect for the ISO road since there can be a difference of 10 or 15 db locally. Nevertheless the effect is much weaker in the case of the rough road. The difference is small in the maximum region of the spectrum. Indeed the sharpness of the contact angle has an important effect for the very small and flat cavities like for the ISO equivalent road profile considered.

different static deformation shapes of the tyre (track 8)

Tdisplacement modelling. Further more, this shape is calculated for the case of a real road (ISO road) and should have a less sharp angle at the contact points than for a smooth road. So the criterion of the contact length seems more realistic in the case of a real road. Even if it seems that the choice of the contact geometry is not really important for a rough road, it has a big influence for the ISO road. Therefore the tyre shape KTH1 was chosen to simulate air pumping for the ISO and rough roads.

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4 – Global model In this part, the different models are coupled, and the different phenomena are compared. The results of the CFD simulation of air pumping are used in the BEM model in order to simulate the acoustic radiation. The tyre vibrations are radiated on different roads with BEM. 4.1 – Modelling of air pumping noise propagation 4.1.1 – GRIM approach The CFD computations provide velocities V on a fictitious surface SV which closes the lower part of the tyre (two vertical lines in 2D as in figure 20). In a second stage these velocities are linked to an integral representation called GRIM [4, 11, 12]. Pressure are computed with the Rayleigh-like expression ∫−=

VS

QdSQVQRGjRP )().().,(...)( ωρ where the green function G is evaluated between points on SV and a receiver position R for a modified tyre geometry where the lower part of the tyre is closed by SV considered to be rigid. This expression is exact if solved in a coupled form. However we assume that the velocity obtained previously is little affected by spurious waves coming from unmodelled external boundaries so that the evaluation of P becomes straightforward. In practice several points are employed (between 3 and 10) along each vertical line of figure 20 at distances between 15 and 25 cm from the centre of the tyre. Alternatively computations can be done using the previous BEM code with imposed velocities on SV which leads to identical results. Velocities at the interface provided by Fluent are considered as acoustic velocities since there is no unsteady flow. The comparison pressure and velocity shows that it is true above 1 kHz. At low frequencies, there can be flow components near the ground for rough surfaces which are not propagated as acoustic waves. This phenomenon is more important at the front side below 2 kHz. It is acceptable since the maximum of the spectra is above 1 kHz. The set up of this interface between the CFD solver and the BEM code (Fluent and MICADO) is described in details in the deliverable 2.3 [3].

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Interface 1

Interface 2

BEM BEMCFD CFD

Figure 20: Location of the interfaces between the CFD domain and the BEM domain

Some validation cases have been carried out [3]. The figure 21 presents the results of 3 simulations with 3 different interface locations (15 cm, 20 cm, 25 cm). The results of the interface at 15 cm probably to close to the noise sources are different mainly at low frequencies. At the rear side, over 500 Hz the interfaces 20 and 25 cm fit quite well. However, at the front side, these two interfaces have roughly the same noise levels but they do not match. The interface at 20 cm (interface 2 on the figure 20) is used in the calculations.

Figure 21: Sound pressure levels at 1 m (top graph) and 7 m (lower graph) at the rear (left) and the front (right) sides

for the air pumping radiation for the case of the road profile rough track 6. Simulations with 3 different interface locations.

4.1.2 – Results for different roads The results of the simulation of air pumping noise propagation for different types of road are presented in this paragraph. The receivers are located at a distance of several meters from the tyre. The acoustic propagation is calculated for the four road profiles presented in the paragraph §3.1.1. The differences between the 4 profiles are analyzed in the §3.2. Figure 22 shows the noise levels averaged on the height (from 0.3 to 1.8 m) at two different distances. The decrease is not important because the horn shape of the geometry makes the noise source very directive with lobes oriented horizontally.

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Figure 22: Air pumping radiation in the case of 4 real roads. Sound pressure levels at 1 m and 7 m at the rear (left) and

front (right) sides The results of the simulations of the ISO road and the rough road are also propagated with the BEM code. Since several tracks are taken into account for both roads, an averaged result is calculated in order to compare these simulations to other results (figure 23).

Figure 23: Pressure spectra at the rear side for the 3 tracks of the ISO and rough roads compared with the averaged

result. The figure 24 shows the results of the simulations of the ISO and rough roads at two different distances. The sound pressure levels are much higher in the case of the rough surface because as explained before the cavities are bigger. However, one has to pay attention to the fact that in reality

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these cavities are more opened in the case of the rough road than for the ISO road. Therefore the levels of the rough roads should be much lower. The noise levels at the front side are lower. However, as explained before the strong levels below 2 kHz at the front side should not be considered (cf. §3.3.1 and §4.1.1).

Figure 24: Air pumping radiated pressure levels of the ISO and rough roads at the rear (left) and front (right) sides

4.2 – Comparisons between different noise sources and road configurations The main goal of the deliverable is to be able to compare different noise sources and different configurations in 2D for the noise generation due to tyre/road interaction. With the simulation of the acoustic radiation for the air pumping noise, the comparison between air pumping and the tyre vibrations for a same configuration is possible. Different configurations of road characteristics are compared as well. 4.2.1 – Comparison between the noise due to air pumping and vibrations in 2D The comparison and more particularly its analysis should be done carefully knowing the different assumptions done in the air pumping model and for the coupling. The comparison between air pumping and vibrations is done for the case of the ISO road and the rough road. The acoustic propagation is modelled with the BEM code MICADO. The air pumping noise is calculated with the CFD code Fluent, and the tyre vibrations are calculated with the W. Kropp’s model [13] by Chalmers and with a spectral finite element model by KTH [14, 15]. The provided velocities, which are 3D and vary both around and across the belt, are averaged across the tyre width to provide with an angular and frequency dependent description of the tyre behaviour. ISO road The air pumping noise and the vibration noise are compared in the case of the ISO road. Two ________________________________________________________________________________

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models are compared for the tyre vibrations in this case. Figure 25 presents the differences between the results of both models. One should keep in mind KTH model (spectral finite element) is more precise than Chalmers model.

Figure 25: Comparison of velocity levels on the tyre between the models of Chalmers and KTH

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Figure 26: Comparison of SPL of air pumping and vibrations for the ISO road for two models (Chalmers, KTH) at the rear (top graph) and front (lower graph) sides

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Figure 26 compares the sound pressure levels of the air pumping and the tyre vibrations for ISO road. In the case of the velocities from Chalmers, vibration levels are higher at low frequencies and have roughly the same value than air pumping until 1.5 kHz at the rear side. At the front side, the comparison is difficult since below 2 kHz, air pumping levels are over-estimated. About the comparison with the KTH vibrations, at the rear side, vibration levels are higher below 1 kHz. Around 1 kHz, vibrations and air pumping have the same levels, and air pumping is getting more important at higher frequencies. This result is close to what could be expected for such a situation. At the front side, vibrations are stronger. Rough road Figure 27 shows the comparison between air pumping and vibrations (only Chalmers vibrations available) in the case of the rough road. At the rear side, the vibration levels are higher below 500 Hz and then air pumping levels become much more important. Maximum levels for air pumping were expected between 1 and 2 kHz for this type of road, but the magnitude are over-estimated. At the front side, Air pumping levels are stronger but the analysis is the same than previously.

Figure 27: Comparison of SPL of air pumping and vibrations for the ISO road for Chalmers model at the rear (top

graph) and front (lower graph) sides The comparisons between air pumping and vibration have shown that in 2D, as expected, tyre vibrations are the main noise source at low frequencies, but above 1 kHz, air pumping becomes more important than tyre vibrations for ISO or rough surfaces.

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4.2.2 – Comparison of different configurations for the vibrations radiation An approach and a numerical model for the radiation of tyre vibrations into an asphalt layer have been developed [3]. This porous medium can be modelled by an equivalent fluid; this has already been proved in the literature. Consequently a multi domain BEM approach was found to be particularly well suited for this problem. Parametric studies have demonstrated that the introduction of the road into the model is very important [3]. In this paragraph, several configurations of road are compared in terms of vibration levels. Four configurations are actually considered: a rigid ground, an impedance condition for a porous layer 4 cm thick with Hamet impedance, a porous layer 4 cm thick with an equivalent fluid, and a porous layer 4 cm thick with an equivalent fluid with vibrations velocity considered in the contact patch.

Figure 28: Comparison of different configurations for the vibrations radiation for two roads (ISO and rough) and from

two models (Chalmers, KTH) Figure 28 presents the results of the different calculations. The levels due to a porous ground are higher around 300 Hz but are much lower at 1 kHz and at high frequencies than for a rigid ground. The modelling of the porous layer by the impedance of Hamet and by an equivalent fluid are quite similar. However, the second model allows to consider the tyre vibrations calculated at the contact which can be propagated in the porous layer. This contribution is important at low frequencies with the velocities of Chalmers and at high frequencies with the velocities of KTH. 4.3 – Full calculation Finally the sum of the different noise contribution is calculated for the case of the ISO road for which the air pumping model is better. The vibration velocities from KTH, which seems better as well, are considered. The acoustic radiation is calculated for a rigid ground. ________________________________________________________________________________

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Figure 29: SPL (in dB) of the rolling noise (tyre vibration and air pumping) for the ISO road at the rear (left) and front

(right) sides Figure 29 shows the noise levels of the rolling noise of a smooth tyre on an ISO road in 2D. The rolling noise is calculated from the contributions of the air pumping and the tyre vibrations. The domains of preponderance of each noise source are shown. Contrary to the 3D problem, in 2D, the maximum of the spectra is not situated at 1 kHz, because of the horn geometry of the tyre different in 2D.

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Conclusion The goal of this study was to provide a model able to predict the noise due to the tyre/road interaction considering the main noise sources (vibrations and air pumping) and the effects of the ground and the tyre. A CFD model set up for the study of a single cavity has been applied to cavities series to demonstrate the existence of interactions between cavities. The effects of the distribution of the cavities and the distance between cavities have been presented. These studies have shown that it cannot be simple to model the noise due to a cavities series directly from the noise emitted by single cavities. In order to simulate air pumping for real road textures, equivalent 2D road profiles have been built up for different road types with two different methods. The study of a first real road texture has shown the noise emitted at the trailing edge is much more important than at the leading edge with a maximum between 1 kHz and 2 kHz. Then equivalent profiles were built up using the dynamic tyre tread penetration for an ISO road and a rough road. The ISO surface has lower noise levels and its maximum is situated at higher frequencies. These simulations of air pumping noise generation are interfaced with a BEM code to model the acoustic propagation. This operation has allowed to compare air pumping noise with vibrations noise. The noise levels of tyre vibrations are higher at low frequencies and are lower above 1 kHz than noise levels of air pumping. This difference is more important for the rough road. Finally different road configurations were also compared, and a full simulation of tyre rolling noise has been presented. The CFD model of air pumping for a single cavity has been validated qualitatively but not quantitatively which has allowed to carry out parametric studies. Indeed, some strong assumptions of the model make the comparison between air pumping and vibration difficult. For the case of the rough road for example, the air pumping noise is overestimated knowing that cavities are not completely closed in reality. However, the results of the simulations of real road textures provide the correct trends and are similar to what was expected. As well, for the comparison with the tyre vibrations from KTH, the noise levels are roughly similar and the domains of preponderance of each noise source were expected. This model has allowed to study and to optimize the ITARI road textures in WP7. The perspectives of this work are the optimisation of road texture to get lower noise levels and to estimate their noise levels. In order to improve the air pumping model, 3D road geometry in the air compression simulation should be considered.

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References [1] ITARI project - Deliverable 2.2, “CFD model (FLUENT) for smooth surfaces”,

Sept.2005 [2] ITARI project - Annex of deliverable 2.2, “Improvement of the air pumping CFD

modelling” [3] ITARI project - Deliverable 2.3, “Porous model and description of interface with

FLUENT model”, August 2006 [4] RATIN project. “Final Technical report”. EEC contract GRD1-99-10583. January

2004 [5] M. J. Gagen: “Novel acoustic sources from squeezed cavities in car tires”, J. Acoust.

Soc. Am. 106(2), 794-801, 1999. [6] F. Conte, P. Jean: “CFD modelling of air compression and release in road cavities

during tyre road interaction”, in proceedings of Euronoise 2006. Tampere, Finland. [7] J. F. Hamet, C. Deffayet, and M. A. Pallas: “Air pumping phenomena in road

cavities”, in proceedings of the International Tire/Road Noise Conference, August 8-10 1990, Gothenburg, Sweden.

[8] M.A. Pallas: “Influence de la succession temporelle d’évènements dans différents

mécanismes de bruit de contact pneu/chaussée”, INRETS NNB 8904, April 1989 [9] ITARI project - Report Müller BBM N°M65 068/1 “Model texture and artificial

texture” [10] K. Larsson: “Modelling of Dynamic Contact – Exemplified on the tyre/road

interaction”, PhD Thesis, Chalmers University of Technology, Sweden 2002 [11] P. Jean, N. Noe, F. Gaudaire: “Calculation of tyre noise radiation with a mixed

approach”. Submitted to acta acustica. [12] P. Jean: “Coupling integral and geometrical representations for vibro-acoustical

problems”. Journal of Sound and Vibration 224, 475-487.1999. [13] W. Kropp: “Ein modell zur Beschreibung des Rollgeräusches eines unprofilierten

Gürtelreifens auf rauher Strassenoberfläche”. PhD Thesis, VDI-Fortschrittberichte Reihe 11, Vol. 166, VDI Verlag, Düsseldorf, Germany.1992.

[14] S. Finnveden: “Tyre vibration analysis with conical waveguide elements”, in

proceedings of Internoise 2002, Dearborn, US. [15] M. Fraggstedt and S. Finnveden: “A Waveguide Finite Element Model of a

Pneumatic Tyre”. Paper A in Power dissipation in car tyres, Licentiate Thesis, 2006.

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deliverable 2.4 global model: ground + tyre + fluent...

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