L Bergamasco

D Fuster

Oscillation regimes of gas/vapor bubbles

Keywords: Phase change, Bubble oscillation, Evaporation

In this work we investigate the effect of heat and mass transfer on the dynamics of gas-vapor bubbles. We present phase diagrams for the bubble oscillation regimes, which are built by comparison of various models with different level of simplification for an air-water system. These diagrams show the range of validity of the simplifying assumptions on the Peclet-number/vapor-content plane, providing an insight on the physical process which regulates the bubble response with respect to external pressure perturbations. The analysis is presented for both the linear and weakly nonlinear regime. In the former case we use linearized solutions of the full system; in the latter, numerical simulations validated against the analytical solutions in the linear limit. We show that even at very low frequencies, there exist regimes where transient diffusion effects arise and restrict the applicability of the commonly-adopted assumption of full-equilibrium conditions inside the bubble. Non-linearity is found to restrict even further the range of applicability of this hypothesis, due to the variation of the vapor content beyond a critical value.

INTRODUCTION

The response of liquids containing bubbles to external pressure changes has important implications in engineering, geophysical and biomedical applications [START_REF] Brujan | Cavitation in Non-Newtonian Fluids: With Biomedical and Bioengineering Applications[END_REF][START_REF] Lauterborn | Experimental and theoretical bubble dynamics[END_REF]. Dilute systems in which bubbles contain a negligible amount of vapor have been extensively investigated, both theoretically and experimentally (see [START_REF] Commander | Linear pressure waves in bubbly liquids: Comparison between theory and experiments[END_REF] for a review). However, the consequences of phase transition in liquids containing bubbles with an appreciable amount of vapor are not completely understood. Although theoretical and experimental studies show that heat-and mass-transfer effects have a non-negligible influence on the bubble response [START_REF] Brennen | Cavitation and bubble dynamics[END_REF] and thus, on the overall fluid properties [START_REF] Coste | Sound propagation in a liquid with vapour bubbles[END_REF][START_REF] Brennen | Fundamentals of Multiphase Flows[END_REF][START_REF] Saurel | A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation[END_REF], it is also possible to find conditions where mass-transfer effects are not evident and/or more difficult to capture [START_REF] Shamsborhan | Experimental determination of the speed of sound in cavitating flows[END_REF]. Available works in the literature propose different quantities to determine whether mass-transfer effects are relevant or not [START_REF] Brennen | The dynamic behavior and compliance of a stream of cavitating bubbles[END_REF][START_REF] Watanabe | Steady analysis of the thermodynamic effect of partial cavitation using the singularity method[END_REF] but the problem is that a solid base for modeling still lacks [START_REF] Prosperetti | The speed of sound in a gas-vapour bubbly liquid[END_REF]. Systematic approaches for dilute mixtures with bubbles containing vapor in addition to a permanent gas have been proposed only recently [START_REF] Prosperetti | The speed of sound in a gas-vapour bubbly liquid[END_REF][START_REF] Fuster | Mass transfer effects on linear wave propagation in diluted bubbly liquids[END_REF][START_REF] Prosperetti | Vapor bubbles[END_REF]. In these latter works, the authors firstly address the response of a single bubble to a varying pressure field considering heatand mass-transfer effects, and then discuss the implica-tions on the speed of sound in the mixture.

The development of numerical codes able to correctly predict the response of bubbles undergoing phase change is challenging. One possibility for fast bubble oscillations is to assume that the influence of both the heat and the mass flux across the interface on the bubble's pressure are negligible compared to the pressure changes imposed by the gas volume change. In this case the bubble response is adiabatic and one can relate volume and pressure changes through a polytropic transformation. At the other extreme, for very slow pressure/temperature variations, it can be assumed that the bubble reaches a thermodynamic equilibrium with its surroundings so that the vapor pressure is uniform and solely given by the system's temperature. Within these two limiting solutions, the mass flux across the interface is influenced by the diffusion of mass and heat both in the liquid surrounding the bubble and inside the bubble playing an important role on how the bubble's pressure change as a function of volume. Unfortunately, the definition of the relevant dimensionless parameters that determine the relevance of various mechanisms on the bubble's response and the total mass flux is not straightforward and it is difficult to find in the literature quantitative studies about the range of validity of various assumptions. In this view, the spherically symmetric assumption provides a simple yet interesting situation to clarify important phenomena about the dynamic response of a single bubble with respect to external pressure/temperature perturbations. Using this framework, several phenomena have already been investigated using simplified models based on the Rayleigh-Plesset equation and an effective equation of state that relates the bubble's pressure and volume changes. For instance, it is possible to derive analytical expressions for the resonance frequency and damping factor for pure-gas bubbles oscillating in the linear limit (reviewed in [START_REF] Ainslie | Review of scattering and extinction cross-sections, damping factors, and resonance frequencies of a spherical gas bubble[END_REF]); heat-transfer, rectified diffusion and secondary resonance frequency for pure-vapor bubbles [START_REF] Legendre | Thermal and dynamic evolution of a spherical bubble moving steadily in a superheated or subcooled liquid[END_REF][START_REF] Scriven | On the dynamics of phase growth[END_REF][START_REF] Ruckenstein | The effects of bubble translation on vapor bubble growth in a superheated liquid[END_REF][START_REF] Gumerov | Dynamics of vapor bubbles with nonequilibrium phase transitions in isotropic acoustic fields[END_REF][START_REF] Hao | The dynamics of vapor bubbles in acous-tic pressure fields[END_REF] and the effect of soluble or insoluble gas on the dynamics of vapor bubbles [START_REF] Nigmatulin | Dynamics, heat and mass transfer of vapour-gas bubbles in a liquid[END_REF][START_REF] Fuster | The importance of liquid evaporation on rectified diffusion processes[END_REF][START_REF] Gumerov | Weakly linear oscillations of the radius of a vapour bubble in an acoustic field[END_REF]. Fuster & Montel [START_REF] Fuster | Mass transfer effects on linear wave propagation in diluted bubbly liquids[END_REF] have recently proposed an analytical derivation of the resonance frequency and damping factor for gas-vapor bubbles. This manuscript presents an analysis of heat-and mass-transfer effects on the dynamic response of gasvapor bubbles. The manuscript is structured as follows. Firstly, we address the problem of linear oscillations and propose phase diagrams for the bubble oscillation regimes, which are built by the comparison between different simplified models and the full analytical solution for gas-vapor bubbles. These diagrams show the range of applicability of the various simplifying modeling assumptions, providing new insight into the transport phenomena which control the physical response of the bubble with respect to the vapor content and the external pressure perturbation. Firstly, we discuss the regimes on the Peclet-number/vapor-quantity plane for the transfer function (which relates the bubble radius oscillation with the external perturbation) and show that, even for very low frequencies, transient effects can prevent the commonly-adopted assumption of full-equilibrium conditions inside the bubble. Secondly, we explore the regimes beyond the linear limit using numerical solutions. The code, which is validated against the analytical solution in the linear limit, allows us to analyze the response of the bubble for various pressure amplitudes and to show the orbits described by the local quantities on the phase diagrams. Non-linearity is found to restrict the range of applicability of the full-equilibrium assumption when local orbits span into other regimes.

PHYSICAL MODEL

Governing equations

We consider a spherically-symmetric, non-reacting, gas-vapor bubble standing in a pure liquid. The model relies on the mass, momentum, energy and species conservation equations [START_REF] Hauke | Dynamics of a single cavitating and reacting bubble[END_REF]. Integrating the mass and momentum equations in the liquid yields the well-known Rayleigh-Plesset equation, which, neglecting the compressibility of the liquid while considering mass transfer effects reads as [START_REF] Prosperetti | A generalization of the Rayleigh-Plesset equation of bubble dynamics[END_REF]:

R R = - 3 2 Ṙ - J ρ l 2 + R J ρ l + 2 J ρ l Ṙ - J ρ l (1)
+ p b -p ∞ ρ l - 2σ ρ l R - 4µ l ρ l Ṙ R .
In the above equation, R is the radius of the bubble, J the vapor-mass flux across the interface, ρ l the liquid density, p b the bubble pressure (assumed to be uniform), p ∞ the far-field liquid pressure, σ the surface tension and µ l the viscosity of the liquid. The internal pressure is assumed to obey the ideal gas law p b = ρ b R b T b , being ρ b the density inside the bubble and R b the average specific gas constant for the gas/vapor mixture. The energy and species conservation equations in the radial coordinate are:

DT Dt = 1 ρc p Dp Dt + Γ t ∇ 2 r T ; (2)
ρ DY Dt = Γ m ∇ r • (ρ∇ r Y); (3)
where c p is the specific heat, Y the vapor molar fraction, Γ t and Γ m are the thermal and mass diffusivities respectively and r is the radial coordinate. The properties of the gas/vapor mixture are computed from those of the pure substances using an arithmetic average. The total derivative for a generic (scalar or vector) quantity φ is defined as Dφ = ∂ t φ+v r ∂ r φ, being v r the radial velocity.

The energy equation ( 2) is solved both inside the bubble and in the surrounding liquid, while the species conservation equation ( 3) is solved only for the vapor content inside the bubble, as in this work we neglect the gas solubility in the liquid. We remark as this latter approximation implies to neglect the rectified diffusion due to the gas intake inside the bubble [START_REF] Hsieh | Theory of rectified diffusion of mass into gas bubbles[END_REF][START_REF] Eller | Rectified diffusion during nonlinear pulsations of cavitation bubbles[END_REF]; this effect arises in second order and becomes relevant only for very large time scales [START_REF] Crum | Generalized equations for rectified diffusion[END_REF]. In this work we focus on time scales much shorter than those where rectified diffusion effects play a role, which allows us to assume this effect to be negligible.

The radial velocity profile inside the bubble is obtained from the continuity equation, which can be rewritten using the energy equation as [START_REF] Commander | Linear pressure waves in bubbly liquids: Comparison between theory and experiments[END_REF]:

v b (r) = 1 γp b (γ -1)λ b ∂T b ∂r r=R - 1 3 ṗb r ; (4)
with γ being the polytropic index (ratio of specific heats) and λ b the averaged thermal conductivity of the species inside the bubble.

In order to close the problem, an additional equation is required. One possibility is to impose that the interface of the bubble is in equilibrium with the surrounding liquid at every instant. In this case, the vapor concentration is given by the Clausius-Clapeyron equation. Another possibility is to account for kinetic mass transfer effects using the Hertz-Knudsen-Langmuir (HKL) equation, which imposes the mass transfer flux as a function of the difference between the instantaneous vapor pressure and the equilibrium pressure at the interface's conditions. It can be shown that the model accounting for kinetic mass transfer effects converges to the model assuming equilibrium conditions when either vapor diffusion or heat transfer controls the overall mass transfer rate [START_REF] Fuster | Mass transfer effects on linear wave propagation in diluted bubbly liquids[END_REF]. In this work we focus on these latter conditions, where the kinetics of the phase change does not have important contribution; however, for practical purposes, we retain the HKL model in the implementation of the equations in the numerical code with an accommodation coefficient equal to 0.35 (see [START_REF] Hauke | Dynamics of a single cavitating and reacting bubble[END_REF] for further details).

Boundary conditions

At the bubble center, the boundary conditions for the energy equation ( 2) and the species equation (3) are imposed by spherical symmetry as a zero-flux condition:

∂T b ∂r r=0
= 0 and ∂Y ∂r r=0

= 0.

(

) 5
At the bubble interface, the temperature profile is assumed to be continuous, so T b (r = R) = T l (r = R). The energy balance yields:

λ l ∂T l ∂r r=R = λ b ∂T b ∂r r=R + JH v ; (6)
with H v being the enthalpy of vaporization/condensation at the interface's temperature. We remark that the mass and momentum conservation at the interface have been directly applied in the derivation of Eq. ( 1), where the pressure far from the bubble is known. For species, the boundary condition at the interface is given by the continuity of the vapor mass:

ρ b | r=R Γ m,b ∂Y ∂r r=R = J (1 -Y| r=R ) . (7)
Finally, in the far field, the liquid temperature is imposed to be equal to the bulk reference temperature T ∞ .

NUMERICAL METHOD

Implementation

The physical model described in Section 2 is numerically solved using the code Bubbles. The code is a Fortran 90 library for the numerical solution of ordinary and partial differential equations, which we developed and tailored for our applications on the basis of a previous code [START_REF] Fuster | Influence of accommodation coefficient on nonlinear bubble oscillations[END_REF]. Spatial integration relies on a stabilized Finite Element Method (FEM) and uses an Arbitrary-Lagrangian-Eulerian (ALE) framework. The code now disposes of several explicit and implicit time-integration schemes. In this work we adopt an explicit Runge-Kutta method (4-th order) with predictor-corrector algorithms.

Validation

In order to validate the code, we run simulations covering a wide range of forcing frequencies and various vapor contents. The bubble is forced with a sinusoidal pressure wave p

∞ (t) = p ∞ (1 -∆ p ∞ sin(ωt)), with ∆ p ∞ 1.
In this situation there exists an analytical solution of the physical model [START_REF] Fuster | Mass transfer effects on linear wave propagation in diluted bubbly liquids[END_REF] that is summarized next. In the frequency domain, the dimensionless radius oscillation is a function of the external pressure perturbation as:

∆ R = - 1 ω 2 0 -ω 2 + 2i δ ω ∆ p ∞ ; (8)
being the variables in the form y = y 0 (1 + ∆ ye iωt ), with ∆ y 1 for the linear solution to be valid. The parameters are made dimensionless with the characteristic angular frequency ω 2 c = p ∞ /(ρ l R 2 0 ) so that the resonance angular frequency and damping factor are:

ω 2 0 = p b,0 p ∞ (Φ) - 2σ p ∞ R 0 + ρ b ω 2 R 2 0 p ∞ ( J 0 ); (9) 2 δ ω = p b,0 p ∞ (Φ) + 4 ωµ l p ∞ - ρ b ω 2 R 2 0 p ∞ ( J 0 ). ( 10
)
In the above parameters, Φ is the transfer function

NAME SYMBOL BUBBLE LIQUID

Peclet number Pe

ωR 2 0 /Γ t,b ωR 2 0 /Γ t,l Sherwood number Sh ωR 2 0 /Γ m,b - Enthalpy of vaporization H H v /(c p,b T ∞ ) - Conductivity ratio λ λ b /λ l - Vapor mass fraction Y 0 Y 0 -
which relates the bubble radius oscillation with the internal pressure as ∆ p b = -Φ∆ R and J 0 = J 0 /(ρ b,0 ωR 0 ) is the total dimensionless mass-transfer flux accross the bubble interface such that J(t) = J 0 ∆Re iωt . The operators (•) and (•) indicate respectively the real and imaginary parts of the complex numbers.

The linearized analytical solution of the full model described in Section 2 yields the following expressions for the transfer function and the total, dimensionless mass-transfer flux:

Φ = 3γ 1 -3i(γ -1) f Pe (1 -ζ) + 3γi J c ( H v ζ -1) ; (11)
J 0 = J c (1 -H v ζ)Φ, (12)
with:

ζ = λ f Pe + J c Pe b H v γ (γ -1) -1 1 + √ iPe l + λ f Pe + J c Pe b H 2 v γ (γ -1) -1 ; (13)
f Pe = Pe -1 b iPe b coth( iPe b ) -1 . (14)
In these forms, Pe b and Pe l are the bubble and liquid Peclet numbers, H v is the dimensionless enthalpy of evaporation/condensation and λ is the thermal conductivity ratio (see definitions in Tab. 1); ζ is a complex function that is proportional to the temperature variations at the bubble interface given by

T l ( r = 1) = 1 + γ -1 γ ζ( p b (t) -1), (15)
and J c is a characteristic mass flux across the bubble interface (the function f Pe has been defined only for compactness).

In this work we focus on regimes where equilibrium conditions prevail at the interface at every instant, so that the kinetics of the phase change process is neglected and the characteristic mass flux used in Eq. 12 is [START_REF] Fuster | Mass transfer effects on linear wave propagation in diluted bubbly liquids[END_REF]:

J c = Sh b √ iSh b coth( √ iSh b ) -1 1 -Y 0 Y 0 , (16)
which is a function of the bubble Sherwood number Sh b (see definition in Table 1) and of the initial vapor content Y 0 . This flux accounts only for the diffusion of the vapor through the interface, neglecting kinetic contributions due to the phase change process itself. This approximation holds when kinetic vaporization effects are much faster than the diffusive ones, such as for the size of the bubbles and the characteristic forcing frequencies considered here. It is important to remark that the total mass transfer flux J 0 of Eq. ( 12) depends both on mass diffusion and thermal effects through its dependence on the dimensionless enthalpy of vaporization, the conductivity ratio appearing in ζ and the transfer function Φ.

Numerically, it is possible to obtain the value of the transfer function running the simulation until steady state is reached. The number of oscillation cycles required to reach the steady state depend on the forcing frequency (bubble's Peclet number). The higher the Peclet number, the larger the number of cycles to reach steady state is. In the numerical simulations we obtained values ranging from 2 cycles for Pe b = 10 -3 to 10 4 cycles for Pe b = 10 5 in the linear regime (where rectified diffusion effects can be disregarded as they arise in second order). Once the steady state is reached, the radius and pressure oscillation data is made dimensionless and fitted with a complex variable in the form ae iωt , which gives the solution in the frequency domain for the comparison. The convergence of the numerical solution with the number of nodes and the time step has been studied over the full range of the bubble Peclet number. The comparison between the analytical solution and the numerical values obtained for the real and imaginary parts of the transfer function Φ for an air- water system is shown in Fig. 1. The real part of this function is of particular concern, as it can be physically interpreted as an effective polytropic index, which, for air-water systems, varies between 1 and γ g for pure gas bubbles and between 0 and γ v for pure vapor bubbles (in the isothermal and adiabatic limits respectively). We obtain excellent agreement of the numerical data with the analytical solution in the full parameter range tested in this work. The dimensionless flux across the interface numerically obtained is also compared in Figure 2 showing excellent agreement with the theoretical predictions.

LINEAR OSCILLATION REGIMES

In this section we discriminate between the various physical effects influencing the response of the bubble and the mass transfer flux by comparing the solution obtained with the full model with those obtained with various simplified models.

The full-equilibrium model: slow bubble oscillations

The range of applicability of the full-equilibrium model is interesting given its widespread utilization in various situations involving phase change. This model is obtained assuming that: (a) the characteristic oscillation velocity is smaller than the characteristic heatdiffusion velocity inside the bubble (Pe b 1), which guarantees uniform temperature inside the bubble; (b) the characteristic oscillation velocity is smaller than the characteristic mass diffusion velocity inside the bubble (Sh b 1), which guarantees that the vapor concentration inside the bubble is uniform; (c) that the interface's temperature is constant, that is, the characteristic velocity of phase change is sufficiently slow to avoid any significant change on the temperature of the interface. This last condition imposes that Pe b has to be smaller than a critical Peclet number Pe cr b , below which temperature variations at the interface are negligible. The exact expression for the critical Peclet number is derived in [START_REF] Fuster | Mass transfer effects on linear wave propagation in diluted bubbly liquids[END_REF] and is shown to depend on the ratio between the bubble/liquid thermal conductivities and on the enthalpy of vaporization:

Pe cr b = 3 λ H 2 v 1 -Y 0 Y 0 γ -1 γ . ( 17
)
Under these conditions, the bubble's pressure is given by

p b = p g,0 R 0 R 3 + p v (T ∞ ), (18)
and the transfer function becomes Φ(ω → 0) = 3(1 -Y 0 ). The general expression for the total mass transfer flux across the interface (Eq. 12) is simplified using the limiting expression of Eq. 16 for Sh b 1 and ζ ≈ 0, so that J c ≈ 1 3 i Y 0 1-Y 0 . In these circumstances, Eq. 12 simplifies to

J 0 = Y 0 i. ( 19
)
Figure 3 represents the isolines of the relative error of the modulus of the transfer function for the full- equilibrium model compared with the full expression,

= |Φ(ω → 0) -Φ full | Φ full ( 20
)
where Φ full corresponds to the expression of Eq. 11.

As expected, the diagram shows that the fullequilibrium model correctly captures the bubble radial evolution with an error below 10% with respect to the full model in the low-frequency range. We also emphasize that as predicted by Eq. 17, the characteristic Peclet below which the full-equilibrium model is applicable is smaller when the vapor content is large.

The adiabatic model: fast bubble oscillations

In the adiabatic gas model neither heat or mass are exchanged across the interface and the equation of state relating bubble's pressure and volume changes is

p b = p b,0 R 0 R 3γ , (21)
and thefore, Φ ad = 3γ. Figure 3 represents the range of validity of this approximation using the iso-error lines obtained by comparing Φ ad with the full-model expresion given in Eq. 11. As expected, at high frequencies the adiabatic model provides a good representation of the bubble response as heat-and mass-transfer effects across the interface can be neglected in order to correctly predict the bubble's pressure evolution. In this regime, the water vapor is trapped inside the bubble given that it has no time to diffuse. This effect, identified in simulations of strong non-linear collapses [START_REF] Storey | Water vapour, sonoluminescence and sonochemistry[END_REF][START_REF] Fujikawa | Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid[END_REF], has been found to have important implications on the sonochemical activity [START_REF] Moss | Computed optical emissions from a sonoluminescing bubble[END_REF][START_REF] Moss | Calculated pulse widths and spectra of a single sonoluminescing bubble[END_REF], being an important ingredient in models able to reproduce experimental data for violent collapse of gas-vapor bubbles [START_REF] Matula | Radial response of individual bubbles subjected to shock wave lithotripsy pulses in vitro[END_REF]. The amount of vapor trapped in the linear regime is quantified here defining a vapor trapping parameter η trap as the relative difference between the total mass transfer flux across the bubble interface, J 0 , and the mass transfer flux across the interface assuming equilibrium conditions (Eq. [START_REF] Hao | The dynamics of vapor bubbles in acous-tic pressure fields[END_REF],

η trap = | J 0 -J 0,eq | | J 0,eq | . ( 22
)
Figure 4 shows this parameter as a function of the bubble Sherwood number and of the vapor content. As expected, the amount of vapor trapped increases at large frequencies (high Sherwood numbers). Remarkably, the dimensionless amount of the trapped vapor only depends slightly on the vapor content for Sherwood numbers between 10 -2 to 10 2 .

Liquid-heat diffusion regime

It is well known that the heat diffusion in the liquid surrounding the bubble can control the total flux across the interface and therefore the dynamic response of the bubble. These effects can be captured using the full expression for ζ still imposing the limiting expression of J c ≈ 1 3 i Y 0 1-Y 0 in order to neglect any effect of vapor diffusion on the solution. Thus we find

Φ LHD = 3γ 1 -3i(γ -1) f Pe (1 -ζ) -γ Y 0 1-Y 0 ( H v ζ -1) ; ( 23
)
J 0,LHD = 1 3 i Y 0 1 -Y 0 (1 -H v ζ)Φ LHD ( 24
)
where the subindex LHD denotes liquid-heat diffusion model.

Figure 5 depicts the iso-error lines of the approximated expression for the modulus of the transfer function compared to the exact expression (Eq. 11). As we can see this model works remakably well for a wide range of situations in the Peclet-number/vapor-content plane. The model includes the full equilibrium model and the adiabatic model as particular solutions for the case of a pure gas bubble. Note that although the limiting expression used for the mass transfer flux assumes that Sh b 1, the impact of the flux on the dynamic response of the system at high frequencies is not relevant as the characteristic dimensionless mass-transfer velocity is small compared to the expansion velocity, J 0 1 (see Figure 2). In other words, the dynamics of the bubble at high frequencies is controlled by the expansion/compression of the bubble rather than the phase change process. Only at intermediate frequencies and conditions where the content of water vapor and immiscible gas are similar, the model is not able to correctly capture the response of the bubble. As we will show next, in these conditions the vapor diffusion plays an important role on the dynamic response of the bubbles.

The dimensionless interface's temperature variations ζ and the thickness of the thermal boundary layer in the liquid δ l are relevant parameters when liquid's heat diffusion controls the response of the bubble. We can ob- tain the fluctuation of the liquid's temperature with respect to the interface's temperature variation as

T l ( r) -1 T l ( r = 1) -1 = e √ iPe l (1-r) r . ( 25
)
Figure 6 shows the dependence of the thickness of the thermal boundary layer in the liquid, taken as the distance at which T l (δ l /R 0 ) -1 = 0.01( T l ( r = 1) -1).

For completeness, this figure also includes the dimensionless temperature variation ζ as a function of the Peclet's number. The boundary layer thickness takes its largest values at low frequencies, reaching an asymptotic value of 100 times the bubble radius for Peclet's number below 10 -8 . This parameter does not depend on the amount of vapor because of the normalization chosen in Eq. ( 25). The influence of the vapor content can be clearly seen in the parameter ζ. The larger interface's temperature fluctuations are found for pure vapor bubbles in the low frequency limit which can be analytically shown to be ζ(Pe b → 0) = H -1 v . This value corresponds to the limiting case where the interface follows the saturation curve. As the relative amount of vapor decreases, the interface's temperature fluctuations are significantly attenuated. In addition, for a constant gas/vapor content we observe the appearance of a peak value for intermediate values of the Peclet number. This peak shifts towards larger frequencies when decreasing the vapor content.

Vapor-mass diffusion regime

In order to complete the analysis of the range of validity of simplified approaches we consider here the vapor mass diffusion regime proposed by Preston et al [START_REF] Preston | A reduced-order model of diffusive effects on the dynamics of bubbles[END_REF] where the total mass transfer flux across the interface is given by the diffusion of the vapor inside the bubble. This model neglects any influence of heat diffusion in the thermal boundary layer surrounding the bubble and therefore, it assumes the interface to be at constant temperature (ζ ≈ 0). In this case, the simplified expressions for the transfer function and the total flux are

Φ MD = 3γ 1 -3i(γ -1) f Pe (1 -ζ) -3γi J c ; (26)
J 0,MD = J c Φ MD (27)
The range of applicability of this approach in the Peclet-number/vapor-content plane is represented in Figure 7. As we can see this model also includes the full-equilibrium model and the adiabatic model as particular solutions for pure gas bubbles. For sufficiently small vapor contents, the model predicts well the transition between the two models for the full range of frequencies. Only for large vapor contents, liquid-heat diffusion takes control of the flux and this model is unable to correctly predict the bubble radius evolution. Within the range of applicability of this regime, the gas exerts a strong resistance to the process of vapor diffusion and controls the total mass flux irrespective of the heat transport process in the liquid boundary layer. These observations become clear in Fig. 8, where we compare the predictions of the simplified models with the exact solution for Φ. The high frequency limit corresponds to the limit of an adiabatic transformation, while the low frequency limit corresponds to the isothermal limit of a liquid/vapor mixture where the transfer function becomes Φ(ω → 0) = 3(1 -Y 0 ). While the liquid-heat diffusion model predicts better the transition between the isothermal and adiabatic limit for large vapor contents (Y 0 = 0.8) the vapor-mass diffusion model performs better for small vapor concentrations (Y 0 = 0.2). It also becomes clear that the Peclet number required to reach the low-frequency limit (where all the models converge to the full-equilibrium model) decreases when increasing the vapor content from 0.2 to 0.8. This is consistent with the fact that the critical Peclet number of Eq. ( 17) is 16 times smaller in the case of Y 0 = 0.8 than in the case of Y 0 = 0.2.

Summary of linear oscillation regimes

Using the simplified models described above we propose in Figure 9 full oscillation diagrams for a 10 µm and 1 mm bubble taking the isolines for 10% error. In the case of a coexistence of models we priviledge the simplest one. As previously discussed, the results are especially interesting in the intermediate-to-low frequency range, when transient effects related to heat and mass diffusion arise and play an important role on the bubble oscillation. On the one hand, for high vapor contents, the bubble oscillation is controlled by heat-diffusion effects in the liquid, that is, the mass flux across the interface is limited by the energy required to vaporize the liquid, which is controlled in turn by the heat transport in the liquid boundary layer. On the other hand, for low vapor contents, there exists a regime where the dynamic response of the bubble is controlled by vapor-mass diffusion effects inside the bubble (red region) rather than by heat diffusion effects in the liquid. Note that we also identify regions where a concurrency between heat and mass diffusion occurs and no approximation applies (FULL model region). At high frequencies, Pe b > 10, the dynamic response of the bubble is no longer influenced by mass transfer and the adiabatic model applies.

LINEAR TO NON-LINEAR TRANSITION

Based on the theoretical diagrams obtained for the linear regime and on the validation of the numerical code presented in Section 3.2, in this section we investigate the influence of the vapor content on the non-linear response of bubbles. To this purpose, we show and discuss the evolution of the bubble radius obtained numerically and the local orbits described by the volumeaveraged vapor content inside the bubble Y and an instantaneous Peclet number. This latter quantity is defined as the ratio between the oscillation velocity and the characteristic heat transfer rate Γ t,b /R(t):

Pe b,i := 3 4π c p,b λ b Ṙ(t) R 2 (t) m(t); (28)
being m(t) the instantaneous (total) mass of the bubble.

For reference, we will include in the analysis the solution provided by the full-equilibrium model given that it is widely-used and all transient effects related to heat diffusion in the surrounding liquid and the vapor-mass diffusion inside the bubble are neglected.

In Fig. 10a and 10b we show the results obtained for Pe b = 0.01, Y 0 = 0.8, R 0 = 10 µm, corresponding to point A in the diagram of Fig. 9a. For reference, we show the critical vapor fraction, Y cr , defined as the value beyond which, for a given Peclet number, the error is equal to 10% in the linear regime (obtained from Fig. 9a). The dimensionless pressure amplitudes ∆ p ∞ tested range from 0.1 to 0.16. In these conditions, while pressure amplitudes are well below previously reported values for non-linear oscillation of pure gas bubbles [START_REF] Lauterborn | Physics of bubble oscillations[END_REF], non-linear effects become apparent while the oscillation is not chaotic yet. When the perturbation is smaller than a critical threshold (e.g. ∆ p ∞ = 0.10) the local orbit is completely within the full-equilibrium regime in the phase diagram and the full-equilibrium model provides a good approximation of the exact solution. For ∆ p ∞ = 0.13, the orbit gets closer to the critical vapor content, transient heat-diffusion effects in the liquid become non-negligible and the error becomes important. Finally, the error blows up for ∆ p ∞ = 0.16, where the vapor content oscillates outside the regime of validity of the full-equilibrium model and the solution provided by this model diverges from that obtained from the full model. Figure 10b reveals that transient diffusion in the liquid boundary layer around the bubble has a strong damping influence on the bubble response when increasing the pressure amplitude, which stresses the importance of modeling the liquid-heat diffusion in situations where the vapor content reaches large values.

A similar response is observed in Fig. 11a full-equilibrium model the dynamic response of the bubble is well predicted. As soon as the critical pressure amplitude is exceeded, the errors on the oscillation orbits become significant and unphysical oscillations are predicted by the full-equilibrium model.

In order to provide a general overview about the importance of transient heat-and mass-transfer effects on the (weakly) non-linear response of the bubble, we represent the difference between the full-equilibrium and the full model by the L1-norm error:

|| R|| 1 = 1 t e |R FE -R F | R 0 dt, (29)
where t e is the final simulation time, R FE and R F are the radius given by the full-equilibrium model and the full model respectively.

As shown in Fig. 12a, for high Peclet numbers (Pe b = 100) the error does not depend significantly on the vapor content because the mass transfer flux does not have a strong influence neither on the bubble interface evolution nor in the change of the bubble's mass. At low Peclet numbers, mass transfer effects become relevant and the bubble dynamic evolution strongly depends on the vapor content. Fig. 12b shows the evolution of the dimensionless quantity || R|| 1 /∆ p as a function of the amplitude of the pressure disturbance and of the vapor content for a low Peclet number (Pe b = 0.01). We can see that the dimensionless error given by the full-equilibrium model reaches an asymptotic value for low-amplitude disturbances. This asymptote depends on the vapor content and on the bubble Peclet number. This analysis shows that the dynamic response for pure gas bubbles is well reproduced by an isothermal model even for ∆ p ≈ 1, while for bubbles containing a large amount of vapor it becomes critical to model transient heat-transport effects in the surrounding liquid when ∆ p is below a certain critical dimensionless pressure amplitude ∆ p cr ∞ . The critical amplitude below which the error reaches an asymptotic value is numerically obtained and shown in Fig. 12b. As clearly seen, it becomes smaller as the vapor content is increased. For instance, for the largest vapor fraction tested here, Y 0 = 0.8, the critical dimensionless pressure amplitude beyond which the error blows up is 0.1.

CONCLUSIONS

In this work we have presented an analysis of heatand mass-diffusion effects on the oscillating dynamics of gas-vapor bubbles. Based on analytical solutions, we have proposed phase diagrams for the oscillation regimes of air/water systems in the linear limit. Using the diagrams we have shown that, even at very low frequencies, transient heat diffusion in the liquid and mass diffusion inside the bubble can play an important role on the dynamic response of the bubble. The accuracy of the proposed regimes has been assessed beyond the linear limit by means of numerical solutions. The code, validated against the theoretical solutions in the linear limit, has been used to obtain the orbits described by the instantaneous bubble properties. We have discussed the importance of accurate modeling of transient effects in various regimes predicted by the linear theory and shown that non-linearity severely restricts the validity of the full-equilibrium assumption. In particular we have observed that, as soon as the bubble is filled with vapor, it becomes critical to model transient heat-diffusion effects in the bubble surroundings, which act as a strong damping mechanism.

Figure 1 :

 1 Figure 1: Validation of the numerical solution (points) against the analytical solution (lines) of the transfer function Φ for the full model: (a) real and (b) imaginary part.

Figure 2 :Figure 3 :

 23 Figure 2: Validation of the numerical solution (points) against the analytical solution (lines) of the dimensionless total flux across the interface for the full model: (a) real and (b) imaginary part.

Figure 4 :

 4 Figure 4: Measurement of the trapped vapor content as a function of the bubble Sherwood number for Y 0 = 0.1, 0.5, 0.9. The bubble radius is R 0 = 10 µm.

Figure 5 :

 5 Figure 5: Range of applicability of the liquid-heat diffusion model. The lines represent iso-error lines obtained by the comparison of the simplified and full expressions of the modulus of the transfer function (Eqs. 23 and 11 respectively).

Figure 6 :Figure 7 :

 67 Figure 6: Black line: Thickness of the thermal boundary layer in the liquid δ l /R 0 as a function of the Peclet's number. Color lines: Dimensionless interface's temperature fluctuations ζH * v as a function of the liquid's Peclet number and vapor content.

Figure 8 :

 8 Figure 8: Modulus of the transfer function obtained with the full model (black), the liquid-heat diffusion model (green) and the mass-diffusion model (red) for vapor content Y 0 = 0.2 (solid lines) and Y 0 = 0.8 (dashed lines).

Figure 9 :

 9 Figure 9: Linear oscillation regimes according to the error (10% with respect to the full model) on the magnitude of the transfer function |Φ| for two different bubble radii: (a) R 0 = 10 µm and (b) R 0 = 1 mm. Numerical simulations for the time evolution of the bubble radius at points A and B in (a) are shown in Fig. 10 and 11.

Figure 10 :Figure 11 :

 1011 Figure 10: Analysis of the bubble response to external pressure pulses for the point A in the diagram of Fig. 9a. (a) Orbits described by the average vapor content and the instantaneous Peclet number. For reference, the critical vapor fraction given by the boundary between the full-equilibrium and the liquid-heat diffusion model in Fig. 9a is included; (b) dimensionless radius R = R/R 0 as a function of the dimensionless time t = tω/(2π) (first oscillation period). Solid and dashed lines represent respectively the solution given by the full model and the full-equilibrium model.

Figure 12 :

 12 Figure 12: Analysis of the L1-norm error of Eq. (29) given by the full-equilibrium with respect to the full model: (a) as a function of the vapor content and of the Peclet number in the low-amplitude oscillation limit (∆ p ∞ = 10 -3 ); (b) as a function of the pressure amplitude and vapor content for Pe b = 0.01 (linear to non-linear transition). The grey dashed line represents the critical pressure amplitude, numerically fitted, beyond which the error of the full-equilibrium model blows up.

Table 1 :

 1 Summary of the dimensionless variables used in this work and their definition.

This work is meant to clarify in a systematic way the range of applicability of the most commonly-adopted models in bubble dynamics. Given the relevance of the dynamics of gas-vapor bubbles in cavitating flows, we expect this work to motivate further efforts in the development of simplified and/or reduced-order models (such as those proposed by Preston et al [34]) accounting for the influence of liquid-heat diffusion on the dynamic response of the bubbles.

Acknoweledgements

This work has been financially supported by the PERSU program (Sorbonne Universités) and the ANR CachMap project (ANR-15-ASTR-0026-02).


Patrick Müller
email: patrick.mueller@ipk.fraunhofer.de

Florian Pasch
email: florian.pasch@ipk.fraunhofer.de

Roland Drewinski

Heinz Bedenbender
email: bedenbender@vdi.de

Haygazun Hayka
email: haygazun.hayka@ipk.fraunhofer.de

Rainer Stark
email: rainer.stark@ipk.fraunhofer.de

Study on Collaborative Product Development and Digital Engineering Tools

Keywords: Collaborative Engineering, Product Data and Lifecycle Management (PDM/PLM), Digital Engineering Tools, Virtual Product Creation, Process Standards, Engineering Efficiency, new Media in Engineering 1 Capability Maturity Model Integration 2 Standards and Architectures for eGovernment Applications CAM -Computer-aided Manufacturing CIM -Computer Integrated Manufacturing ERP -Enterprise Resource Planning

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Product creation is facing the next level of fundamental changes and severe challenges in terms of collaboration and information management. Global demands are growing substantially to achieve energy efficient and sustainable value creation networks for production, products, and services without compromising traditional success factors such as time to market, cost, and quality.

In order to stay competitive under such conditions, collaboration partners in industry and public sectors will require new interplay solutions for engineering design execution, domain knowledge representation, expert competence utilization, and digital assistance systems; for further details see [START_REF] Stark | Competing in Engineering Design-the Role of Virtual Product Creation[END_REF]. Product development is characterized by cross-company collaboration and an intensive exchange of product data. Engineers typically apply a multitude of digital engineering tools and act in diverse engineering processes. Finally, efficient collaboration amongst companies and disciplines is a key for successful engineering of complex systems, variant-rich systems, and customized products and needs for efficient application of digital engineering tools. Process standards on the one hand and tools for virtual product creation on the other hand play a major role in engineering practice. Product Data and Lifecycle Management (PDM/PLM) and process standards are central means to enable and control information exchange amongst (internal and external) collaboration partners. Anyhow, the supply chain and engineering competencies are distributed in terms of location, discipline, etc.

Finally, the product development process cannot be carried out by individual product developers [START_REF] Ehrlenspiel | Integrierte Produktentwicklung: Denkabläufe, Methodeneinsatz, Zusammenarbeit[END_REF][START_REF] Eigner | Product Lifecycle Management: Ein Leitfaden für Product Development und Life Cycle Management[END_REF][START_REF] Gausemeier | Vernetzte Produktentwicklung: Der erfolgreiche Weg zum Global Engineering Networking[END_REF][START_REF] Kern | Verteilte Produktentwicklung -Rahmenkonzept und Vorgehensweise zur organisatorischen Gestaltung[END_REF][START_REF] Lu | A scientific Foundation of Collaborative Engineering[END_REF]. There is a growing need for a collaborative product development process. This allows collaboration across domains, organizational boundaries and product development phases including a consistent consideration of customer requirements and restrictions from the entire product life cycle [START_REF] Ehrlenspiel | Integrierte Produktentwicklung: Denkabläufe, Methodeneinsatz, Zusammenarbeit[END_REF][START_REF] Lu | A scientific Foundation of Collaborative Engineering[END_REF][START_REF] Willaert | Collaborative engineering: A case study of concurrent engineering in a wider context[END_REF]. Collaboration capability across individuals, teams, and organizations becomes a key engineering work skill in both directions: horizontally along the phases of the PDP (Product Development Process); vertically along the supply chain and between disciplines. Figure 1 is summarizing such aspects. This scenario is challenging for engineers performing their daily tasks and for vendors of virtual product creation tools at the same time. To analyze this setup from a neutral and scientific perspective a -Study on collaborative product development and digital engineering tools‖ has been carried out in German industry by three partners: Firstly, the Division Virtual Product Creation of the Fraunhofer Institute for Production Systems and Design Technology IPK (Berlin, Germany), a research institution. Secondly, CONTACT Software (Bremen, Germany), a PLM solution vendor. Thirdly, the VDI (Verein Deutscher Ingenieure, Düsseldorf, Germany), an important engineers' association.

Within the study, the -culture‖ of today's collaborative product development is investigated in detail. The target of this study is to gain deep insight into dependencies of collaboration influencing factors, to develop a model to assess collaboration in industrial product creation processes and to derive indication for improvement of digital engineering and collaboration tools. Capabilities and Strategies in Industry

Product Creation and Collaboration Capability in Industry

From a business perspective, collaboration capability is an issue of competitiveness, as explained above. Nevertheless, so far, there is hardly any model to assess collaboration capability as such, assessing internal and external collaboration processes and tool usage. Similar is the situation for product creation in particular. There is no standard certificate for product development process (PDP) capability, which is suitable to assess reliability, repeatability, innovation strength, and compatibility with standard processes as known form quality management assessments. Particular models for process maturity assessment do existfor instance CMMI 1 or SAGA 2 but these just apply to a subset of aspects of PDP capability and IT use.

From an engineer's perspective, the feeling is dominating that there is a lack of time to concentrate on the main development task, which is to design and validate new systems or system components. Standard processes, tools, techniques etc. request much concentration / attention and -consume‖ huge amounts of working time.

The coordination of modern development projects is increasingly repressing technically sound design work. Digital engineering tools and PLM solutions for most users are technically and functionally too complex. This dilemma is becoming a serious risk, which just few top managers consider to the necessary extent. Virtual product creation needs stepwise extendable PLM solutions, in order to support the daily work of various disciplines.

PLM Vision and Strategies in Industry

Valuable studies on PDM/PLM have recently been carried out, for instance by Abramovici et al. [START_REF] Abramovici | Delphi Studie PLM 2020, Experteneinschätzungen zur zukünftigen Entwicklung des Lifecycle Managements[END_REF] or the RAAD Research unit of Hoppenstedt [START_REF]RAAD Research: Product Lifecycle Management Deutschland 2012, PLM-Markt 2012, Integrierte Lösungen vs. offene Systeme (Study)[END_REF]: Abramovici et al. [START_REF] Abramovici | Delphi Studie PLM 2020, Experteneinschätzungen zur zukünftigen Entwicklung des Lifecycle Managements[END_REF] for instance investigated the trends of lifecycle management solutions until 2020 in a study involving 47 PLM experts. The focus is on PLM solutions, but not on the subtleties of collaboration. Anyhow, according to their data 71% of the experts agreed that PLM will establish as the central integration platform for engineering data, processes, and applications until 2020. Approximately two third of the experts suggested that PLM solutions will be independent solutions while one third thinks that PLM will be integrated element of corporate (company-spanning) ERP and Supply Chain solutions. Almost all experts (96%) expected that PLM solutions in 2020 will increasingly support cross-domain and cross-company engineering cooperation. Parameter-driven optimization of engineering-processes, PLM supported planning of engineering processes, and information analysis and visualization for top managers are expected becoming core functionality of PLM solutions (all awaited by more than two thirds of the experts). Finally, the amount of PDM functionality and use will rise not just for the management of virtual product data but also for data of installed systems over their entire lifecycle. RAAD [START_REF]RAAD Research: Product Lifecycle Management Deutschland 2012, PLM-Markt 2012, Integrierte Lösungen vs. offene Systeme (Study)[END_REF] investigated the situation in 227 companies with more than 500 employees with an inquiry under managing engineers in engineering, production, and IT departments. The majority of companies were related to mechanical engineering and metal machining. RAAD found out that 66% (of n=193) had no dedicated PLM strategy, which was committed with the company management. Just 22% have a strategy, which involves all units. 37% (of n=213) said that PLM has a high or very high relevance in their companies. Both studies show that PLM is a future-oriented topic. Nevertheless, consolidated PLM strategies still are lacking in most even large companies. Anyhow, both studies do not address engineering practice in detail.

Study on collaborative Product Development and digital Engineering Tools

To understand the very nature and culture of collaboration in industry, to update facts and figures on engineers' daily schedules and finally to calibrate ideas on process and collaboration improvement, a study has been carried out in Germany at the end of 2011. This study is complementary to those mentioned above. The premise of this study was an explicit scientific orientation, which was required by all three partners. Firstly, a comparably high number of answered questionnaires was required in order to have a resilient set of up-to-date data. Secondly, there was explicitly no focus on IT systems or solutions of selected vendors. Thirdly, end users have been asked without any channel through company mailing lists or filters.

Study Design and Execution

The study was executed in two major phases: One phase for a -pre-study‖ based on telephone interviews, one phase for the -core study‖ applying web-based questionnaires. The following paragraphs provide insight into the major research questions and details of the two phases. Figure 2 briefly summarizes facts of the study design.

Research Questions

The core research questions of the study are the following:

 How do engineers work today?  Which tasks play a major role in their daily business?  How much time is remaining for core engineering tasks like design, calculation and design validation?  How do engineers assess their workplace (environment)?  What are promising future technologies to enhance collaboration in industry?

Questions Blocks

These questions have been broken down into the following question blocks, which contained different sub-questions and response items: 1. Questions on the company (branch, size, competencies, supply chain position) 2. Questions on the tasks of the respondent (education, discipline, position, main engineering tasks) 3. Questions on development activities (PDM and ERP usage, workplace location and time spent in each location, amount of time spent on creative work, formal tasks etc.) 4. Questions on collaboration (time spent on internal and external product data exchange; technical environments used for data exchange; assessment of work environment such as tool and facility availability, assessment of coordination, communication, knowledge integration and information logistics) 5. Question on -future-oriented‖ ideas and permanent issues Findings are related to collaborative engineering and engineering design, Product Data and Lifecycle Management (PDM/PLM), virtual product creation, information and process management, and new media in engineering design.

Pre-Study: Interview Study

In order to -calibrate‖ the questionnaire study, an interview study with eight companies from German industry (automotive, plant construction, chemical industries, energy systems, engineering service provider) was undertaken in advance. Each interview was carried out via telephone and took between one and one and a half hour. The participants have been engineers (development experts, (technical) project leaders, managing IT engineers (responsible for PDM/PLM, CAx, ERP)). This pre-study was vital to calibrate the own terminology and to understand, if own suggestions were going into the right direction. Interesting is that the small number of cases brought results drawing a parallel to the results of the large questionnaire study (see section 4).

Core Study: Web-based Questionnaire (Online Inquiry)

The link to a web-based questionnaire was mailed to 22,000 engineers in Germany being members of a large German engineers association, namely the VDI. All receivers were personally asked -addressing their engineering background and work in gen-eral‖ and not their work affiliated to a particular employer. This was necessary to lower confidentiality obstacles. The response rate was higher than 6%, which enabled a total sum of 1,401engineers having participated. The elicitation was carried out from end of October to the mid of November (3 weeks) in 2011.

Three Steps of Data Analysis and Collaboration Modeling

The data analysis is separated in three steps: In step 1 (finished), all data was investigated towards response rates of the various answer items and values. This step was performed for the data with segmentation after branches, company size, roles, and engineering disciplines, cp. Figure 3. In step 2 (finished), correlations and dependencies amongst key factors have been analysed. In step 3 (started), a further data use to design a collaboration assessment model is scheduled to support further studies and process investigations in industry. Especially results from analysis step 1and some of step 2 are presented in this paper.

Fig. 3. Areas of further Investigation and Analyses

Demographic Analysis of returned Questionnaires

Amongst the 1,401 respondents, approximately 23% development engineers and 27% project leaders contributed with their practical experience. Managing directors (7%), team leaders (22%), department leaders (13%) and engineering practitioners from IT and process development departments (8%) participated as well. Some represented more than one job role. More than 50% of all returning questionnaires came to almost equal proportion from the branches automotive engineering and mechanical and plant engineering. Throughout the branches aviation and aerospace, energy technologies, electrical engineering and industry, chemical and process engineering, plastics engineering, medical engineering, IT services in engineering, and engineering services there was a satisfying distribution.

Engineering Today -Tasks, Time, and Turbulences

A big portion of time is spent at the typical office workplace or in meeting rooms -67% of the respondents work more than 40% of working time in their office and labs. Only 6% work more than 20% of their time at home. Only 5% work more than 20% of their working time during travelling. Even working at customer/supplier sites is more likely an exception (just 14% spend there more than 20% of their working time) nevertheless many engineers wish to have a better support of mobile working: approx. 82% of all respondents view the possibility of to have all necessary data offline or via access through mobile devices available as a useful or very useful future vision.

Currently, the collaboration is manly happening inside the companiesbetween 70 and 80% answered that their internal collaboration is (very) intensive. Collaboration with partners and suppliers is less intensively performedbetween 50 and 70% said that their external collaboration happens betimes or almost never. Nevertheless, almost all liked to work with partners, suppliers and customers on the same database (86% positive answers). According to 58% still much product data is predominantly exchanged with customers via e-mail. This is interesting, because security concerns in opposite dominate IT policies in many companies. The possibility to digitally define and execute (engineering) workflows, which include customers, partners and suppliers, is ranked as (very) helpful by 76% of all respondents. This finding is correlating with the interview results of the pre-study: The process-oriented thinking of engineers seems to be much stronger than typically expected.

Asking for the most pressing issues, the statements from the introduction are validated: As especially wearing most engineers selected the acquisition of needed information (71%), and the capturing of data and other routine tasks (48%), although such tasks do not consume a large proportion of time (approx. 63% said that this is less than 20% working time). Independent of available management solutions, just round about the haft of all participants estimated that the data necessary for their work is available in time (57%) and in an adequate form (48%). Especially in case of belated changes, 51% of all participants feel informed not early enough.

The majority, 87%, finally thinks that Google-like tools to search in all enterprise data would be (very) helpful. A use of social networks for an exchange of engineering process and product information is still regarded skeptically. Social networks within the company are regarded as (less) useless by 60% and solutions within enterprise networks are regarded as (less) useless by 63%. This is also a fact correlating with the pre-study. High potential for improvement is seen in the area of information logistics: Still almost all (97%) miss a project management, which brings more transparency to responsibilities, work amount and project progression. This in turn not just applies to running projects. Many (49%) criticize that results and experiences of earlier projects a comparably difficult to find and access. This is not astonishing, because there is hardly any time available or taken for systematic knowledge management. 58% say that knowledge management (project reflection, lessens learnt) is done in less than 10% of working time.

PDM and ERP

Interesting is the question how far engineers personally feel supported by PDM (Product Data Management) and ERP (Enterprise Resource Planning) systems: In the automotive segment, most feel personally well supported by PDM systems. Most also regard PDM systems as well supporting the company targets. In all other branches there is no big difference between the assessment of PDM and ERP. Figure 5

Summary

This study has a comparably high number of participants and is one of the largest undertaken in this area in the last decade. The distribution among branches, engineer roles, and disciplines is representing a relevant set from German industry. The findings fit to principle -feelings‖ about engineering practice today. Furthermore, the findings fit to other studies, for instance the study of Abramovici et al. [START_REF] Abramovici | Delphi Studie PLM 2020, Experteneinschätzungen zur zukünftigen Entwicklung des Lifecycle Managements[END_REF]. One fact clearly corresponding is that process support (esp. for change processes) and project management support will play a major role of PDM/PLM in 2020. This has been found out in the expert study of Abramovici. In our study, this was formulated by the respondents as a kind of need and improvement potential.

-Trend technologies‖ such as social networks are seen skeptically. One reason, which was elicited in the pre-study, might be security concerns. Another might be missing engineering applications. Instead, typical improvement issues such as database integration and transparent process control are of major interest.

Finally, alarming is the small amount of working time, which is available for core engineering tasks, cp. Figure 4. This is clearly an issue which needs to be addressed by better process control and software support. The system supports me personally very well.

Automotive (n = 351)

The system supports the needs of our company overall very well.

Automotive (n = 351)

Other Industries (n = 1050)

Other Industries (n = 1050) 5 Prospects

Collaboration Capability Model

To realize a collaborative product development process, there are primarily aspects of communication, coordination, integration of knowledge and information logistics necessary [START_REF] Eigner | Product Lifecycle Management: Ein Leitfaden für Product Development und Life Cycle Management[END_REF][START_REF] Kern | Verteilte Produktentwicklung -Rahmenkonzept und Vorgehensweise zur organisatorischen Gestaltung[END_REF][START_REF] Seiffert | Virtuelle Produktentstehung für Fahrzeug und Antrieb im Kfz: Prozesse Komponenten Beispiele aus der Praxis[END_REF][START_REF] Steinheider | Supporting the co-operation of R&D-teams in the product development process[END_REF]. Communication is the exchange of data, information and knowledge and also includes cultural factors. Coordination includes the traditional project management tasks and determines the allocation of tasks to actors with view to the super-ordinate objective. Knowledge integration enables the collaboration of actors with different professional backgrounds by using shared mental models, metaphors and analogies [START_REF] Steinheider | Supporting the co-operation of R&D-teams in the product development process[END_REF]. Finally, information logistics is about delivering the required and understood information for the actors. The information must be available in the right quality, in the right quantity, at the right time, and at the right place [START_REF] Kern | Verteilte Produktentwicklung -Rahmenkonzept und Vorgehensweise zur organisatorischen Gestaltung[END_REF].

The study delivered valuable information to understand the four dimensions cooperation, coordination, knowledge integration (engineering process knowledge, project knowledge, product knowledge), and information logistics in more detail. One further target is now to integrate this finding in a model to assess Collaboration Capability (cp. section 2 and analysis step 3 of the study design). A first draft of this model has already been defined and will be detailed and evaluated in further research.

Compilation of the Study Report

A conference paper is much too short for a comprehensive presentation of the study results. Anyhow, the data analysis is about to be finished. All findings and relevant illustrations are currently being compiled in a study report, which can be ordered via the partners of the study.

Continuation of the Study

The study probably will be repeated on a national level in Germany in the next years. New partners are currently motivated to join the study on an international level. The challenging task is to scale up the study and to synchronize cross-country work.

Fig. 1 .

 1 Fig. 1. Complexity in Product Development Processes and Engineering Collaboration

2

 2

Fig. 2 .

 2 Fig. 2. Phases of the Study and Study Design



  Time allocated to tasks  Assessment of workplace / environment  Creativity, formalism, fun,

Figure 4 Fig. 4 .

 44 Figure4finally is summarizing some facts mentioned. Astonishing high is the amount of communication and coordination, which is information verifying the statements in the introduction (section 1.)

Fig. 5 .

 5 Fig. 5. Comparison of PDM and ERP Value


Monica Rossi
email: monica.rossi@polimi.it

Endris Kerga
email: endris.kerga@mail.polimi.it

Marco Taisch
email: marco.taisch@polimi.it

Sergio Terzi
email: sergio.terzi@unibg.it

Learning Methodologies to Diffuse Lean Product Development to Industries

Keywords: Lean Product Development, Product Development Wastes, Set-Based Concurrent Engineering, Learning and Serious Games

Every company strives to come-up with innovative products that satisfy customer requests efficiently and effectively. The principles and working methods of Lean thinking have been suggested in literature for companies to optimize stakeholders' interests throughout their product development (PD) process. However, the application of the Lean PD remains unclear from practitioner's perspective. As a consequence, there is a low level of awareness about it and its associated elements. This paper first identifies and presents key challenges and gaps that exist to implement Lean PD in practice, using some of the results of a field study done in Italy. Then, learning methodologies that are developed to fill practical gaps will be presented along with the results achieved in terms of increasing awareness about lean product development.

Introduction to Lean Product Development (Lean PD)

The complexity of a PD process makes it difficult to be monitored, streamlined, and standardized. The ever growing business dynamics pose challenges to effectively organize innovation process in such a way that the right customer value can be captured and delivered efficiently [START_REF] Chesbrough | The era of open innovation[END_REF], [START_REF] Chesbrough | Open Innovation: Researching a New Paradigm[END_REF]. Therefore, companies require equipping themselves with the right methodology to pace with the shift in the paradigm of managing product innovation process and keep ahead with the intense competition. Toyota consistently developed higher quality vehicles faster than its competitors, for less costs and at a greater profit [START_REF] Womak | Lean thinking: Banish waste and create wealth in your corporation[END_REF], [START_REF] Womack | Lean Thinking-Banish Waste and Create Wealth in Your Corporation[END_REF]. It also launches more new vehicles annually than most of its competitors, creating a steady flow of high quality new products to meet consumer demand. This has fuelled industry leading profits, reaching a Japanese record of 10.9 billion dollars by 2005, a market capitalization greater than that of GM and Ford combined and a continuing growth in market share. Toyota has also achieved the lowest in the ratio of R&D cost to sales compared with its competitors [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF].

Toyota's remarkable achievement can be attributed to a leaner and systematic approach it follows to manage PD [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF], [START_REF] Ward | Lean Product and Process Development[END_REF] and [START_REF] Balle | Lean Development[END_REF]. Figure 1 shows some of the elements of lean product development that are suggested in literature and are the interests of this paper. Each element will be briefly discussed below:

 Chief Engineer (CE) System: customer value research traditionally is a marketing activity based on surveys. The drawbacks of this approach are two. First, customers might not be explicit or might not be aware of what can potentially be offered to them. Second, customer value research and design process are disconnected in traditional PD. In contrast, in Lean PD it is the Chief Engineer who is responsible for investigating and defining customer values. CEs represent the customer throughout the development process, and ensure that program objectives and the goals among the cross-functional team are well aligned [START_REF] Haque | Applying Lean Thinking to New Product Introduction[END_REF]. The classical project managers spent most of their time on administrative activities. In contrast, CEs at Toyota involve heavily in technical decisions and ideally are the most knowledgeable engineers. Therefore, such a strong project leader enables Toyota to understand the right customer values early and lead the development process effectively and efficiently [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF], [START_REF] Ward | Lean Product and Process Development[END_REF] and [START_REF] Balle | Lean Development[END_REF].  Cross Functional Knowledge Capturing, Using and Reusing: effective management of knowledge in PD is critical. Since PD is a knowledge creation factory, organization should have in place the proper competencies and procedures to capture, use, document and reuse previous knowledge and lesson learned gained in a design process [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF], [START_REF] Ward | Lean Product and Process Development[END_REF]. Traditionally, PD projects are taken as independent, unrelated entities, and the knowledge gained in one project hardly be used in another. Toyota uses extensively the so called tradeoff and limit curves [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF], [START_REF] Ward | Lean Product and Process Development[END_REF]. The use of trade-off and limit curves allow to generalize and visualize knowledge to be effectively be reused. And, strongly facilitate the integration of different functional domains throughout a project [START_REF] Ward | The Second Toyota Paradox: How Delaying Decisions Can Make Better Cars Faster[END_REF], [START_REF] Sobek | Toyota's Principles of Set-Based Concurrent Engineering[END_REF].  Simultaneous Engineering (SE): SE concerns with paralleling interdependent activities to reduce developed lead time and improve product quality. To improve the concurrency in PD, Toyota uses two mechanisms; Module Development Team (MDT) and Obeya room [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF]. Once a concept paper with set of alternative solutions developed by CE the MDT break down the concept into technical details. Each MDT consists of one or more manufacturing engineering to investigate the manufacturability of the concepts developed [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF]. The MDT team along with the manufacturing engineer/s investigates the alternative cost of manufacturing and assembly solutions to avoid late changes, as a consequence, cross functional knowledge sharing become a norm. In addition, Toyota has set up special rooms, called Obeya, which is used to hold regular meetings between designers, CEs and manufacturing engineers. This room facilitates the sharing of up-to-date or real time information and status about projects [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF].  Standardization and Reusing (Product Variety Management): a large variety of products, components or parts bring more complexity, inefficiencies and lower the possibility to use economies of scale and scope [START_REF] Ward | The Second Toyota Paradox: How Delaying Decisions Can Make Better Cars Faster[END_REF]. To deal with such tradeoffs, standardization and reusing previous modules have been suggested as Lean PD elements [START_REF] Ward | The Second Toyota Paradox: How Delaying Decisions Can Make Better Cars Faster[END_REF]. Toyota, for example, has a carry-over rate, i.e. percent reuse of components from a previous model to the successor, of about two third. Toyota is very cautious about introducing new technologies and tries to leverage their proven solutions from existing products as much as possible [START_REF] Oppenheim | Lean Product Development Flow[END_REF]. The strategy significantly reduce the time and cost of development.  Supplier Involvement in PD: in automotive industry, about 70-80% of all the parts are purchased from suppliers. Efforts made to improve PD efficiency and effectiveness should involve suppliers [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF]. Traditionally, supplier selection is based on pure cost advantage. Suppliers fear to share details information to win bidding. This makes inevitable design rework once problems reveled late in a PD process. Japanese manufacturer use different strategy with their partner suppliers. They integrate their partners early in a design process to anticipate risks and capabilities [START_REF] Morgan | The Toyota Product Development System: Integrating People, Process, and Technology[END_REF]. This relationship brings cost reduction and improves other performance targets in a long term partnership agreements.  Set-Based Concurrent Engineering(SBCE): the most central element of Lean PD is set based engineering [START_REF] Ward | Lean Product and Process Development[END_REF], [START_REF] Ward | The Second Toyota Paradox: How Delaying Decisions Can Make Better Cars Faster[END_REF], and [START_REF] Sobek | Toyota's Principles of Set-Based Concurrent Engineering[END_REF]. SBCE is a design paradigm that revolutionizes PD process from structural and task based development to knowledge based development. Traditionally, designers decide to choose a single design concept to develop, among many potential concepts, as early as possible without having sufficient knowledge that the selected concept will be feasible and optimal [START_REF] Ward | Lean Product and Process Development[END_REF].

In SBCE paradigm, multiple alternative conceptual solutions for a component/module/full-product will be explored and developed early based on proven data and knowledge. Concepts are progressively eliminated once more knowledge about product, process and customers are known. In this way, SBCE creates a planned flexibility in a PD for expected and unexpected uncertainties. Moreover, it enables Toyota to reduce design iterations and foster innovation [START_REF] Ward | Lean Product and Process Development[END_REF], [START_REF] Ward | The Second Toyota Paradox: How Delaying Decisions Can Make Better Cars Faster[END_REF], and [START_REF] Sobek | Toyota's Principles of Set-Based Concurrent Engineering[END_REF].

The Lean PD elements mentioned above are enablers for industries to reduce wastes and focus on value creating activities. Researches show that product developers spend only 12% of the time creating value, 11% on necessary but non value adding activities, and 77% of the time is wasted on activities that add no value [START_REF] Oehmen | Waste in Lean Product Development[END_REF]. The central problems are not designers or project managers but it is the way PD is structured and managed [START_REF] Ward | Lean Product and Process Development[END_REF].

Although the detail discussion of each lean element is beyond the scope of the paper, the introductions make a foundation for the discussions that follow in this paper. In section 2, the gaps in adopting the elements across Italian Industries will be discussed. Section 3 presents the rationale behind developing learning methodologies to increase the awareness and the adoption level of Lean PD. In section 4, the two learning instruments/methodologies that are developed will be presented as cases. Finally, in section 5 conclusions and future plans will be discussed.

Gaps between in Application

Are companies aware about Lean PD concepts? Are they applying Lean PD elements within their development processes? In order to answer these questions and investigate the gap between theory and application, a field study was undertaken [START_REF] Rossi | Lean Product Development: Fact Finding Research in Italy[END_REF]. Fourteen Italian companies were asked to share the knowledge and maturity level of implementation of the Lean PD. The results of the investigation are discussed as follows:

 Chief Engineer (CE) System: more than half of the interviewed companies (59%) has a non-technical leader to manage projects. On the contrary, the rest 41% recognizes the importance of having a technical leader. However, cost and performance target definitions based on a deep customer value analysis is still up to nontechnical leaders across the industries.  Cross Functional Knowledge Capturing, Using and Reusing: the importance to have proven knowledge for decision making in PD process is considered very important among the 62% of the companies. However, the ways in which knowledge are documented and reused is far from being lean. In fact, knowledge is captured in 94% of the cases using verbal communication. In order to share and reuse knowledge most company use extensive reports (46% of cases) and experts' personal judgment (47% of cases). Only in 19% of the cases, lesson learned documents are reused for future projects. None of the companies interviewed use limit and trade-off curves.  Simultaneous Engineering (SE): the concept of Module Development Team is not so diffused in Italian companies. In fact only in 31% of cases, manufacturing engineers provide design constraints to design engineers before design solutions are prepared. In most of cases (50%) manufacturing engineers are involved after concept selection. The sharing of up-to-date or real time information and status about projects using Obeya rooms is only followed by one company. Toyota, is not diffused in Italian companies. In very few cases (11%), multiple solutions for each product/component are designed and ruled out as more information becomes available (due to prototyping, testing, integration etc.). In most cases (89%), even if concurrent engineering is in some way considered, only one solution is quickly frozen and designed. The SBCE paradigm is still unknown by the majority of designers. The same is true for front loading process. Companies are still following the norm of "firefighting" at the end of a project than investing resources early to explore the feasibilities and risks of alternative conceptual designs.

Learning Methodologies towards Lean PD Application

As discussed in Section 2, the adoption level of the Lean PD elements is at a fledgling stage. Although several reasons can be attributed to the causes, the level of awareness about the elements can be taken as a significant inhibitor. The level of awareness means that: i) the meaning of each Lean PD element is new to companies, ii) how to implement those elements might be unclear, and iii) the advantages of each Lean PD elements are not well understood. To fill the awareness gaps, developing learning methodologies1 sought to be important. According to Knight [START_REF] Knight | Trade in Higher Education Services: The Implications the General Agreement on Trade in Services (GATS). The Observatory on borderless higher education[END_REF], innovation potential of an organization depends on the learning approaches exerted to introduce a new working method. In our case, Lean PD has a great potential to improve PD performances. However, companies are not yet aware how to adopt Lean PD systematically. Serious games are one way of facilitating learning. Serious game is defined as "Entertaining games with non-entertainment goals" [START_REF] Raybourn | Adaptive Thinking & Leadership Simulation Game Training for Special Forces Officers[END_REF]. The aim of developing a serious game is to create a hand-on experience to participants to learn a certain issue. The engaging power of serious games brings participants' attention on the learning, and facilitates discussion among participants as a consequence. In this paper, two serious games, developed by the authors, will be presented. The first one is called "MyWaste". This game is used to identify and prioritize PD wastes, and further create opportunities to brainstorm possible continuous improvement activities in a bottomup fashion. The second one is called "Lean PD Game". This computer-based serious game aims at introducing the Lean PD elements in an engaging manner. Both serious games have been validated across industries in Italy and Spain. The details about the games and the validation are presented in the following sections.

4

Cases (MyWaste and Lean PD Game)

MyWaste

MyWaste is a learning tool developed to support practitioners on how to deal with wastes in PD [START_REF] Rossi | Proposal of a method to systematically identify wastes in New Product Development Process[END_REF]. It can be used by designers, engineers and project managers. Players will be able to: (i) understand what are wastes in PD, (ii) measure the impact of each waste on PD performances (cost, time and quality), and (iii) identify focus areas for improvements.

MyWaste is structured in a check-list form, contains a library of 33 possible wastes designers might face in during their daily activities. For example, time spent on reworks and revisions due to changing priorities, information, data, requirements; reworks and revisions derived by poor-quality products; and inability to reuse previous knowledge etc. Players has to understand the meaning of each waste by, i) trying to translate the waste in real cases, ii) analyzing the possible effects of each waste, iii) brainstorming on the causes/sources of each waste, and iv) evaluating possible way to detect the waste inside a PD process. Then, for each waste, four indicators will be estimated (1-4 scale), see Table 1 as an example:

 Probability (P): How frequently a waste occurs in PD? Never/Rarely (1), Sometimes (2), Often (3) and Always (4).  Severity (S): How much a waste represents a problem for the company? Unimportant (1), A Little (2), Enough (3) and Very Much (4).  Detectability (D): How easy it is to detect a waste in a process? Very Easy (1), Easy Enough (2), Hard Enough (3) and Impossible (4).  Avoidability (A): Is it possible to avoid the waste? Not Avoidable Waste (1), Difficult to Avoid Waste (2), Quite Avoidable Waste (3), and Avoidable Waste (4).

By multiplying these four indicators, a Priority Index of Intervention (PII) can be determined for each waste. Using PII, it is possible to measure and rank wastes, identifying those that have significant impacts on performances, and to create opportunities to reduce and/or eliminate wastes at the source. Playing MyWaste allows designers to be aware of the activities that do not generate value. Moreover, by playing MyWaste continuously, management will be able to identify priority areas for continuous improvement actions. Not only the literature analysis has showed lacks about waste measurement methods, but also the field study introduced in section 2 resulted in an explicit need for a tool able to teach practitioners what are wastes and how they can affect the PD per-formances. MyWaste was built with the goal to fill this gap and to validate it across industries.

Table 1. Check-list example

The game has been validated in 10 Italian companies, by more than 40 participants from different industrial sectors with the result shown in Figure 2. Simplicity and intuitiveness are Mywaste's main advantages. Industries can also use it as a benchmark mechanism to compare themselves with other industries. MyWaste should be used as a team exercise. Different functional teams can use it to communicate inefficiencies in a product development process.

Lean PD Game

MyWaste can be used to diagnose a process, but it doesn't give a hand-on experience on how to make a PD process better. The Lean PD game is a computer based serious game designed to create a learning environment for applying Lean PD elements systematically while developing a simplified airplane structure. Given a set of customer requirements, players should design an airplane on a given design table. Each player will act as a company who wants to satisfy the customer. The airplane should have four sub-systems; body, wing, tail and cockpit. Players should use supplier catalogues to build the subsystems of the airplane.

The game is divided into two stages; first and second. In the first stage, players will use their primarily knowledge to build an airplane needed. This stage simulates the traditional PD environment where players will not have any supporting Lean PD element to make their design decisions. Once players completed a prototype design, they should submit to "testing department" to check for stability, flying conditions and dimensional configurations. If it fails, the prototype should be redesigned. Redesigning has penalty costs. If the prototype passes the testing constraints, players will be given the breakdown of their performances in terms of quality, time and cost. The comparison between customer requirements and a player's performance will be given as an aggregate value called "Lean score".

In the second stage, players supported systematically by the Lean PD elements. This stage is divided into phases to lead players in a Lean PD environment and arrive to optimal airplane at a lower cost and time than the first stage. As shown in Figure 3, each phase is supported by different lean technique/s to create the Lean PD environment. Below, each phases of the game is briefly explained: tions. This equips players to have the right previous knowledge before designing an airplane. Moreover, the CE guides players to understand better the customer requirements.  Front loading process: at this phase, player will be provided with airplane models which are already in a knowledge library. These help players to compare what have already been designed by other designers before, so as not to waste time creating from scratch.  Explore alternative set of solutions: at this phase, players will be supported by "tradeoff-curves" to explore alternative sub-system solutions and able to ingrate customer requirements into an airplane design parameters. This phase is the beginning of a SBCE process in the game.  Elimination of weak solutions: players at this phase can eliminate airplane's subsystem solutions that are proved to be infeasible. Here, players supported by the so called "limit-curves" that show the feasibilities of the design alternatives early in the PD process.  Explore alternative solutions: the above phases help players to come up with feasible bodies and wings. For each alternative body and wing solutions players can use standard cockpits and tails to prototype alternative airplanes. In a way, they are introduced with one of the Lean PD element (Product variety management through reusing and standardization).  Eliminate weak alternative airplane solutions: at this phase, player has alternative airplane solutions which should be evaluated against pre-prepared knowledge from "testing department" in the form of checklist. This checklist uses to classify full airplane design solutions as "safe" and "risky".  Convergence to optimal solution: once alternative feasible airplanes are found, cross functional information from manufacturing, assembly, and supplier will be visible in a real time basis to estimate the cost and development time of each airplane solutions. Moreover, visual charts are provided to show a rough estimation of the aggregate "Lean score" values of each designs to support decision making.

Finally, the detail performance comparison of the two stages will appear for discussion among participants in the game.

Lean PD Game has been validated among industries and engineering classes in Italy and Spain. In total, about 80 participants have participated in the validation. To evaluate the success of the Lean PD elements in the second stage of the game, an average percentage improvement of playing time, development time and cost are taken. The comparison is between first and second stages of the game or non-Lean PD with Lean PD. According to the results, in average, players improve playing time by 55%, development time by 45% and development cost by 43%. This shows that, Lean elements enable players to quickly converge into an optimal airplane that satisfies a given set of customer requirements.

Garris model has been used to evaluate the improved level of awareness about Lean PD using the game [START_REF] Garris | Games, Motivation, and Learning: A Research and Practice Model[END_REF]. Garris et.al. describe three aspects to measure the effectiveness of a serious game in attaining a predefined objectives. Declarative knowledge, targeted at measuring if the game increases the domain understanding of players; Procedural knowledge, aims at learning of procedures, and also to the understanding of patterns of processes and behavior; Strategic knowledge, finally this aspect refers to if players get knowledge to translate concepts from game to real application problem. Based on the above framework, a structured questionnaires based on the Liker five scale model is developed. Players form different industry have been asked immediately after playing it. Figure 4 shows the result of the survey concerning the declarative knowledge of the Lean PD game.

Fig. 4. Assessment of the declarative knowledge

As shown in the figure above, the game has been effective in translating the theory to practitioners. Most of the players agreed that playing the game give them a good level of understanding on how to explore alternative solutions and communicate among the teams using the provided Lean PD elements. Similarly, players been asked to relate the Lean PD elements and their possible impacts on PD performance improvements.

Figure 5 shows the procedural knowledge assessment in terms of players' perceived improvements of the Lean PD elements embedded in the game. The theoretical advantages of Lean PD seems to be confirmed by the practitioners. Most of the designers played the game agreed that the most significant perceived advantages are 'facilitate learning about design solutions' and 'avoid design risks'. Using knowledge from past designs and exploration of alternative designs enable the PD teams to brainstorm about set of solutions rather than one alternative. Moreover, frontloading the PD process minimize the probability of 'false positive feasibility' to occur. False positive feasibility is a major problem in industry, and it refers to a phenomena where project teams assume a concept is feasible, but will learn later in the development process that it is not.

Conclusion and Future work

As clearly showed in section 1, traditional PD results in a series of inefficiencies, for example long development time, high design cost, unnecessary reworks and iterations. The application of Lean principles and techniques to PD allows encompassing these problems by fostering knowledge sharing and re-using, customer value capturing, concurrent product development, SBCE process, and so on. Toyota is very well aware about how to implement the elements in order to gain competitive advantage. But the level of maturity and awareness of applying these elements is in other companies (at least in Italy) are not well developed or systematized.

Learning approaches are crucial in creating awareness on the importance of applying Lean PD elements in order to obtain improved performances. The two serious games proposed by the authors are to facilitate learning and improvement, creating a hand-on experience to participants to learn the Lean PD benefits.

The games have been tested and validated in both Italian and some European companies. The level of awareness about the elements has been improved, and the feedback obtained from the validation is encouraging.

The research will continue to validate the methodologies across other industries and countries to build more robust learning methodologies for adopting Lean PD elements in industries.

Fig. 1 .

 1 Fig. 1. Elements of Lean PD with the goal to minimize waste and maximize value

Fig. 2 .

 2 Fig. 2. Waste prioritization example (Note: W indicate a waste sub-category)

Fig. 3 .

 3 Fig. 3. Lean PD game phases (Stage 2) and supporting lean elements

Fig. 5 .

 5 Fig. 5. Assessment of the 'perceived performance improvement' of applying lean in PD

  Supplier Involvement: a proactive involvement of suppliers during PD process is low within the interviewed companies. Only 11.8% of companies is informed by their suppliers on what they can provide. In 64.7% of the cases, suppliers are not involved at all in concept development and are requested to provide one concept solution, based on already pre-defined specifications. Communication between companies and suppliers is not frequent and continuous.  Set-Based Concurrent Engineering: the concept of SBCE, as described and used by

	platforms are re-used in most of cases (72%). But, often re-using causes poor
	product differentiation and low level of innovation. Only one company implements
	optimized Product Variety Management approaches.
	
	 Standardization and Reusing (Product Variety Management): standardization and
	reusing parts are used by 1/3 of the cases. In designing new products, previous

In this paper, the terms learning methodology and serious game are used interchangeably to refer MyWaste and Lean PD game. However, in stricter sense MyWaste should not be taken as a serious game as the Lean PD game.

Acknowledgments

This work was partly funded by the European Commission through the project Lean Product and Process Development -LeanPPD (NMP-2008-214090, www.leanppd.eu) and the network of excellence Games and Learning Alliance GALA (ICT-2009-258169, www.galanoe.eu). The authors wish to acknowledge their gratitude and appreciation to the rest of the project partners for their contributions during the development of various ideas and concepts presented in this paper.