Investigations of the drying process of a water based paint film for automotive applications

Chemical Engineering and Processing 50 (2011) 495–502

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Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep

Investigations of the drying process of a water based paint film for automotive applications J. Domnick a,∗ , D. Gruseck a , K. Pulli b , A. Scheibe a , Q. Ye b,∗ , F. Brinckmann c,∗ a b c

University of Applied Sciences Esslingen, D-73728 Esslingen, Germany Institut für Industrielle Fertigung und Fabrikbetrieb, University Stuttgart, D-70569 Stuttgart, Germany Institute of Technical Thermodynamics, Technical University Darmstadt, D-64287 Darmstadt, Germany

a r t i c l e

i n f o

Article history: Received 23 February 2010 Received in revised form 8 August 2010 Accepted 26 August 2010 Available online 2 October 2010 Keywords: Modelling and numerical simulation Drying process Thin film Water based paint Automotive application Paint film defects

a b s t r a c t In a cooperative research project funded by the German BMBF the drying process in the automotive industry has been investigated. More precisely, it was the aim of the project to develop a simulation program that in its final stage allows the calculation of the heat-up process of a fully painted car body, including heat and mass transfer in the thin, water based paint film. The investigations focused on the joint base coat and clear coat drying process used in the automotive industry. A physical model was developed that treats mass and heat transfer of a ternary mixture applied as a thin film on a substrate. This model was added to the commercial CFD-Solver ANSYS-FLUENT and successfully compared with experimental data in practical conditions. The estimation of paint failures, i.e. pinholes that might occur due to unfavourable drying, which is based upon an empirical model applying a design-of-experiments scheme, was also added to the CFD-Solver. © 2010 Elsevier B.V. All rights reserved.

1. Introduction It is one of the key efforts in the automotive industry to realize the so-called virtual paint shop. This is basically a complete simulation of the automotive painting process, including the various steps of dip and spray coating as well as drying and curing. Using the virtual paint shop, the painting process of future car bodies may be verified long before extremely expensive full-scale prototypes are available. As part of the virtual paint shop activities, the drying process in the automotive industry has been investigated in a cooperative research project funded by the German BMBF. The project mainly focuses on the physical drying process of water borne base coats prior to curing, which is made together with the subsequent clear coat film. The quality of the final paint film is significantly depending on this base coat drying process, as film defects such as pinholes are related to the process operating parameters. A typical automotive paint system is shown in Fig. 1f. The water borne base coat is only physically dried (flash-off) before clear coat application. After clear coat application there is a joint final drying and cross linking of base and clear coat at 140 ◦ C. This baking pro-

∗ Corresponding authors. E-mail addresses: [email protected] (J. Domnick), [email protected] (Q. Ye), [email protected] (F. Brinckmann). 0255-2701/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2010.08.021

cess is important for the final film thickness quality, as various film defects may occur at unfavourable drying conditions, especially at a too fast drying process. Within this project different stages of experimental and numerical studies have been identified. In general, there are two parts of the investigation. One is the modelling of the unsteady turbulent heat transfer on complex 3D objects; another is the modelling of the evaporating process of a thin film of water born base coat on 3D objects. In previous stages of the research [1–3], investigations of the turbulent heat transfer in various laboratory and industrial dryers have been carried out. Assessments of the available turbulence models used in CFD-Solvers for turbulent heat transfer without paint film were performed, specifically aiming to identify models with low sensitivity of heat transfer prediction on the grid spacing. This is required since considering complex work pieces significant local variations of the grid quality and resolution are expected. The present contribution presents experimental and numerical results of investigations on the drying process of a thin film applying model water born paint. Drying experiments delivered comparative data for assessment of a paint film drying model that has been implemented into the commercial CFD-Solver FLUENT [6]. The calculated heating-up behaviours on the paint film and the film evaporation rate were compared with experimental results. Furthermore, a model for the occurrence of pinholes as a typical paint film failure related to the parameters of the base coat drying process is introduced.

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Fig. 1. Typical automotive paint system.

2. Experimental set-up and measuring techniques

3. Numerical simulation

The measurements have been performed in a specific oven (Hygrex drying system LBT2500) designed to deliver well controlled air velocity, temperature and humidity. Complying industrial operating conditions, typical water based paint with a solid content of 20% and water and butyl glycol as solvents has been applied on 500 mm × 200 mm large flat panels and further physically dried considering relevant process times. The geometry of the oven and the location of test panel are shown in Fig. 2. Defined horizontal air inlet conditions are produced by individual nozzles in the left wall of the dryer applied with specifically designed flow straightener. This is discussed further below. At the air outlet in the right wall a filter element avoided unwanted influences of subsequent components on the flow field in the dryer. Local paint film surface temperature using an infrared detector and evaporation rates through weighing were monitored on-line. Furthermore, the water content of the paint film before and after drying has been measured using thermogravimetry. Applying gas chromatography, the fractions of water and additional organic solvents after drying were also detected. Tests were performed at oven temperatures between 40 and 80 ◦ C, absolute humidities between 6 and 16 g/kg and nozzle inlet velocities between 6 and 20 m/s. These values correspond to conditions used in the automotive industry for forced flash-off of base coats prior to clear coat application. The test panels were painted using either a pneumatic spray gun or an electrostatically supported high-speed rotary bell atomizer with all important spraying parameters being equivalent to the practical application. Applied dry film thicknesses varied between 10 and 25 ␮m, corresponding to approximately 50 and 125 ␮m wet film thicknesses before drying.

The commercial state-of-the-art CFD-Solver FLUENT based on the finite-volume method was applied in the present numerical investigations. A 3D computational domain with typically one million cell elements was created for Hygrex dryer (Fig. 2). Around the substrate plate several boundary layers with prismatic cells were constructed, providing a good resolution of the near wall flow field. Physically, a sufficiently fine grid close to the wall should be employed. As a compromise, an appropriately fine grid with 1 mm as the first interior node distance was used to reduce large computer storage and runtime requirements, especially for later applications using industrial dryers with complete car bodies. The unsteady Reynolds-averaged Navier–Stokes equations with the sst-kω turbulence model that was found [2,3] to give a reasonably accurate prediction of heat transfer with lower grid sensitivity for complicated turbulent flow in drying processes were solved for the gas flow in the dryer. For the heat transfer calculation it was found that the radiation could not be neglected. Here, a discrete ordinates (DO) radiation model was used. The emission coefficient of the electro-coated plate (light grey) and the paint film was taken as 0.95. For the calculation of the film evaporation, it was found that the traditional approach, which uses Nusselt- and Sherwoodcorrelations to estimate the heat and mass transfer coefficients in the gas phase, is not suitable for the present drying process due to complicated turbulent flows and three-dimensional substrates. Therefore a novel film evaporation model especially adapted to drying processes in the automotive industry has been developed [4,5] and added as User Defined Function to the CFD-Solver FLUENT [6]. The drying model bases on the mass transport equation due to transient diffusion processes in the direction perpendicular to the

Fig. 2. Test oven arrangement.

J. Domnick et al. / Chemical Engineering and Processing 50 (2011) 495–502

Fig. 3. 1D model to predict drying process in the thin liquid film.

film surface. Transport processes parallel to the film surface are neglected. Due to the film shrinkage X(t) during the drying process, the transport equation is formulated non-dimensionally with respect to the length scale, simplifying the numerical solution of the transport equation given as: ∂(i )  ∂X ∂(i ) 1 ∂ − = 2 ∂ ∂ X ∂ X ∂



Di

∂i ∂



(1)

where  = z/X(t) and  = t. Fig. 3 shows the one-dimensional reference system in absolute and dimensionless coordinates in the paint film. At  = z = 0 the paint film is set on the substrate. The position z = X(t), i.e.  = 1, represents the gas-sided, free surface of the paint film. The transport equation (1) is solved by discretisation using the finite-difference method. The temperature of the substrate and the paint film changes in time due to heat transfer by convection, evaporation and radiation. According to [6], the temperature gradient in the paint film perpendicular to the film surface can be neglected. The heat transport equation can be then written as follows: ∂T ∂ c = ∂ ∂z



∂T  ∂z



+ q˙ Evaporation + q˙ Radiation

(2)

where z is the absolute coordinate in the substrate. The substrate is represented in FLUENT using the shell conduction model. Heat fluxes due to evaporation and radiation are represented by source terms which can be hooked to the relevant surfaces. A ternary water based dispersive mixture is used to represent the paint system. Beside water, the paint system consists of a second solvent, namely butyl glycol and the solid polyurethane. The initial composition of the paint on the panel at the beginning of the drying process is shown in Table 1. The composition depends on the paint formulation as well as on the application process. The initial paint mass is individually chosen due to the weight measured in the experiments using thermogravimetry. At the gas/liquid (paint) interface the pressure equilibrium can be calculated using following equation [9]: pi,s · ai (T, i,j ) = pi,ph

(3)

The saturation pressure pi,s of every component i is multiplied with it’s activity ai (T, i,j ) as a function of the temperature T and the concentration  i,j of the components i and j at the film surface. Some important physical properties of components and the equations for calculating activities are shown in Appendix A. The resulting gas-sided partial pressure pi,ph is converted to a mass fraction which can be applied as boundary condition to the gas phase. Using this approach, neither Nusselt- nor Sherwood-correlations are necessary to calculate the heat and mass transfer between the paint system and the gas phase. This is an important constraint for Table 1 Simulation parameters. Nozzle inlet velocity Temperature Air humidity Model paint system

6–20 m/s 50–80 ◦ C 6–10 g/kg Water: 46%, butyl glycol: 27%, polyurethanes (solid): 27%

497

the usage of the drying model on 3D surfaces. The drying model is set up to the CFD-domain using User Defined Functions in FLUENT. Basically, the one-dimensional continuity equations for the mass transfer of paint film components are solved in each surface cell on the substrate, where necessary information for mechanical equilibrium, for instance saturation pressure and species mass flow rate, is delivered to the 1D model calculation. After the evaporation calculation, the new equilibrium situation on the surface cell is updated and the corresponding information is delivered further to the solver for the calculation of gas flow field in the current time step. Fig. 4 shows such coupling calculation between the 1D-drying model and the gas flow field. The calculating procedure for the heating-up behaviour of paint film proceeds as follows: joint velocity and temperature fields are simulated using the steady solver in the presence of the substrate until the normalized maximum residuals of the mass, momentum and energy equations are below 1 × 10−4 . Afterwards, the substrate is patched to the initial temperature of 25 ◦ C and the paint film is initialized. The calculation of the heating-up behaviour was carried out by solving the complete set of conservation equations and 1D drying model using a time step size of 0.1 s. A more detailed assessment of the drying model has been carried out with experimental data [6,16] obtained in a geometrically simple dryer, i.e. a flat sheet located in a well defined channel flow. In the following section, comparisons between simulations and experimental results in a more complicated dryer (Fig. 2) will be presented.

4. Simulation results In Fig. 5, velocity contours in the centreline cross-section in the Hygrex-dryer are shown. The flow between nozzles and the plate is characterized by multiple jet impingements. The velocity distribution at wall-adjacent cells and the temperature distribution after 120 s, as well as the film thickness distribution on the plate are depicted in Fig. 6(a)–(c). Circular velocity patterns with a stagnation point inside that are typical for impinging jets can be observed. The maximum temperature difference on the plate is approximately 10 K. Higher temperatures are located on the edge of the plate and near the stagnation points where the local heat transfer coefficient are higher. After 120 s the film thickness on the edge of the plate was reduced to ca. 50% of initial wet paint film thickness (116 ␮m). Detailed heating-up curves at the pyrometer measuring point as indicated in Fig. 6(a) and the total mass decay of the paint film on the plate using different operating conditions are shown in Figs. 7–9 and compared with experimental results. A reasonably good agreement between experiment and calculation was obtained. The typical 2-stage drying process obtained especially at lower operating temperature and lower nozzle velocity was reproduced in the simulation (Fig. 7). In the first step, heat and mass transfer are controlled by convective fluxes at the film surface, the paint mass on the plate decreases linearly, corresponding to a constant evaporation rate, whereas in the second step diffusion inside the film begins to hinder the mass flux, leading to concentration gradients of water and solvents inside the film. As a consequence, a skinning effect may occur, diminishing the diffusion of water and solvent to the surface and leading to an increased residual water and solvent content in the base coat prior to clear coat application and final baking. These simulation results, especially the local air velocity at the film surface and the local maximum temperature gradients occurring in the paint film during the drying process, can be used to predict the paint film defects. This is further discussed below. In general, the simulations tend to underestimate the evaporation rate in the first stage of the drying process, which results in

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Fig. 4. Coupling calculation between 1D-drying Model and gas flow filed.

Fig. 5. Velocity contours (m/s) in a cross-section z = 0.

Fig. 6. (a) Velocity contours (m/s) in wall-adjacent cells, (b) temperature distribution (K) at the surface of the film and (c) film thickness distribution (m), both at t = 120 s.

J. Domnick et al. / Chemical Engineering and Processing 50 (2011) 495–502

14

Mass[g]

10 8 6 4 2 0

0

200

400

80 70 60 50 40 30 20 10 0

Temperature[ °C]

Exp_v8 Sim

12

600

800

me [s]

499

Exp_v8 Sim

0

100

200

300

400

500

me [s]

6

Exp_v208

5

Sim

Temperature [ °C]

Mass [g]

Fig. 7. Comparison between measured and calculated temperature (left) and mass decay (right) during base coat drying (v8: operating temperature 60 ◦ C, nozzle velocity 12.5 m/s, air humidity 10 g/kg).

4 3 2 1 0

0

100

200

300

400

80 70 60 50 40 30 20 10 0

500

Exp_v208 Sim

0

100

200

300

400

500

me [s]

me [s]

Fig. 8. Comparison between measured and calculated temperature (left) and mass decay (right) during base coat drying (v208: operating temperature 60 ◦ C, nozzle velocity 16.7 m/s, air humidity 10 g/kg).

5. Modelling of paint film defects From practical experience it is known that unfavourable drying conditions may lead to film defect that are subject to time consuming and expensive repair work. One class of defect is known as pinholes, i.e. very regular cones based directly on the dip coat layer underneath the base coat as shown in Fig. 10. The physical background for the appearance of pinholes is still unclear. In general, it is believed that a so-called skinning effect 7

Exp_v217 Sim

Mass [g]

6 5 4 3 2 1 0 0

100

200

300

me [s]

400

500

appears at high temperature gradients (temperature vs. time) of the paint film hindering the diffusion of residual water and solvents from the base coat through the clear coat to the surface during the final baking process [7]. In this case, the occurrence of pinholes should be a function of the residual water and solvent content in the basecoat after flash-off. However, this was not confirmed by the results in the present study. In an investigation performed directly by the automotive industry [8], an alternative mechanism is described: During the droplet formation process, air bubbles may be entrapped in the paint droplets, which survive the droplet impact and film build-up processes. Once the film is heated up during the drying process, these air bubbles expand and sometimes explode, leading to the described pinholes. This approach is partly supported by the present results, as variations of the application technique and parameters have in fact significant effects on the pinhole formation. Due to the absence of any stable physical models a series of drying experiments using a design-of-experiments (DOE) scheme were applied. As indicated by Table 2, temperature and absolute humidity of the air and the inlet nozzle air velocity were used as major influencing parameters. However, the DOE scheme was further refined by introducing the maximum temperature gradient derived from the measured temperature evolution during heat-up, and the local air velocity in the vicinity of the surface.

Temperature [°C]

over estimated film temperature in the first stage of drying. For instance in Fig. 7, the temperature is over estimated in the first stage (t < 80 s), but underestimated in the second stage of drying. The underestimation in the second stage can be explained by a higher solvent concentration in the film during the second stage of drying. Due to the evaporation, the film is cooled. The typical standard deviation of measured temperature is depicted also in Fig. 7. The discrepancy between the simulation and the measurement is lower using a higher operating temperature and nozzle velocity (see Figs. 8 and 9). Obviously the 1D-drying model should be further improved especially for the case with low operating temperature and low nozzle velocity. However, for current applications in the automotive industry with operating temperatures above 70 ◦ C in dryer, the 1D-model shows good results.

80 70 60 50 40 30 20 10 0

Exp_v217 Sim

0

100

200

300

400

500

me [s]

Fig. 9. Comparison between measured and calculated temperature (left) and mass decay (right) during base coat drying (v217: operating temperature 72 ◦ C, nozzle velocity 15 m/s, air humidity 6 g/kg).

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Fig. 10. Image and 3D measurement results of a typical pinhole (obtained after clear coat application and final baking).

The local air velocities given in Table 2 were taken from the results of numerical simulations of the oven flow. The maximum temperature gradient, occurring mostly in the second stage of the drying process, was chosen, since it is considered to be one of the most significant parameters influencing the occurrence of pinholes after final curing. The final equation is given as f (x) = 24.7132 + 29.1613 · −0.820482 · +5.98660 ·

 ϑ 

 ϑ 2 t

 ϑ t

t

− 545.089 · vloc + 29.6248 · x

+ 481.381 · vloc2 − 1.15395 · x2

· vloc



+ 0.949253 ·

 ϑ t

·x



−43.4554 · (vloc · x)

(4) Fig. 11. Comparison between measured and calculated pinhole densities.

Here f(x) is the so-called pinhole density (m−2 ) ϑ/ t the maximum temperature gradient occurring in the paint film during drying (K/s), vloc the local air velocity above the film (m/s) and x the global humidity (g/kg) of the dryer air. An indication of the quality of the developed model is given by Fig. 11, comparing measured and estimated pinhole densities as a function of the temperature gradient. The correlation factor of the model as given by the DOE-program is 0.72, the overall standard deviation between measurements and model values is 35 m−2 . These values suggest

an only fair model quality. Additional measurements are required to improve this situation. It is straightforward to integrate the above empirical model for the paint film failure estimation in the FLUENT CFD-Solver, provided that all necessary data including the maximum temperature gradient in each surface cell and the mean velocities in the cell layer above the paint film are stored. Finally, the pinhole density can be

Table 2 Chosen measurement matrix of the DOE with pinhole density as resulting parameter. Oven temperature (◦ C)

Velocity (m/s)

Absolute humidity (g/kg)

Temperature gradient (K/min)

Local velocity (m/s)

Pinhole density (m−2 )

40 48 48 72 48 48 60 60 60 60 48 60 60 80 60 72 60 72 60 72

12.5 15.0 15.0 15.0 10.0 15.0 12.5 16.7 8.3 12.5 10.0 12.5 12.5 12.5 12.5 10.0 12.5 15.0 12.5 10.0

10.0 6.0 6.0 14.0 6.0 14.0 10.0 10.0 10.0 10.0 14.0 10.0 10.0 10.0 3.3 6.0 10.0 6.0 16.7 14.0

12.7 13.4 16.1 16.8 19.9 20.2 22.6 22.9 22.9 23.3 23.3 23.6 23.6 24.3 26.0 27.4 30.5 32.9 34.2 37.0

0.7 0.9 0.9 0.9 0.5 0.9 0.7 0.9 0.4 0.7 0.5 0.7 0.7 0.7 0.7 0.5 0.7 0.9 0.7 0.5

148 162 175 337 256 404 242 310 350 323 296 323 296 256 310 417 202 202 283 242

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estimated locally in each region of the work piece with a resolution given by the surface mesh. Of course, this equation is only valid for the model paint used in the present investigations. Nevertheless, an interface in the numerical code has been realized that allows implementing other specific equations and models, including also other paint failure classes.

where the interaction-coefficients are chosen as proposed by [4], L1L2 = 1.19, L1P = − 0.113, L2P = − 1.9375 v¯ i are the molar volumes

6. Summary and outlook

and yi is the molar mass fraction.

In the present project, models for the evaporation of a thin paint film as well as the occurrence of paint film failures have been successfully implemented in the FLUENT CFD-Solver. The final code is, in principle, able to calculate the unsteady drying process of almost arbitrary three-dimensional work pieces. However, it should be noted that high computer speed and capacity is required. Considering a painted car body with a reasonable surface mesh resolution, requiring several millions of simulations cells, the simulation time is in the order of weeks even on a multiprocessor PC-type machine. So far, the realized models apply only to the model paint and conditions used in the present investigations. However, based on the chosen approaches models for varying materials and conditions may be easily implemented. Of course, the heaviest load is on the experimental side to determine all the necessary fluid properties, e.g. binary diffusion coefficients, heat conductivities etc.

A.3. Diffusion in the liquid phase (paint layer)

v¯ w = 0.018 m3 /kmol,

v¯ BG = 0.131758 m3 /kmol,

v¯ PUR = 3.478m3 /kmol

The diffusion coefficients for the ternary paint system consisting of water, butylglycol and polyurethane were determined by Sckuhr [12] for single droplets in a levitator. The following correlation was found: g

Di (PUR , T ) = (a · T b · c PUR + d · arctan(eT − f )(1 − PUR ) − h · PUR ) ×10−11 [m2 /2] where T is the temperature in Kelvin and a = 4.7606 × 10−10 b = 4.3258 c = 2.8155 × 10−2 d = 6.5535

e = 1.9404 f = 571 g = 3.3023 h = 0.9

A.4. Diffusion in the gas phase (air) Acknowledgements The support of the German Federal Ministry of Education and Research (BMBF), the German Aerospace Center (DLR) as project monitor and all partners within the project SILAT is gratefully acknowledged.

The diffusion coefficients in the gas phase are calculated using the approach of Fuller et al. [13] for an ideal mixture. The binary diffusion coefficient is ˆ ij = 10−7 D

¯ 1+M ¯ 2 )/M ¯ 1·M ¯ 2) T 1.75 ((M

 1/3

p

v

Appendix A.

i

+

1/2

2  1/3 2 · 1.013 [m /s]

v

j

The diffusion volumes are given by Sherwood et al. [14]:

A simplified water based paint system with polyurethane as solid and water and butylglycol as solvents has been applied in the present experimental and numerical investigations. Some important physical properties of both solvents used in the numerical simulation are described as follows. A.1. Saturation pressure



95.709−(9789.3/T )−10.205 log(T )+8.8492×10−18 T 6



A.2. Activities

v

w

= 12.7,

  v

BG

= 137.68

To provide the diffusion coefficients in FLUENT, the coefficients are fitted using a 3rd order polynomial in a range from 10 to 95 ◦ C where T is the temperature in Kelvin.

a = −2.67561 × 10−6 ˆ w,air D b = 3.90439 × 10−8 c = 1.82080 × 10−10

a = −7.59424 × 10−7 ˆ BG,air D b = 1.10819 × 10−8 c = 5.16800 × 10−11

ˆ w,BG a = −1.02423 × 10−6 D b = 1.49461 × 10−8 c = 6.97006 × 10−11

Di,mix =



1 − yi ˆ

y /Dij j,j = / i i

In the equation, yi is the molar fraction of the component i.

The activities are calculated using the following equations according to Favre et al. [11] applying the Flory–Huggins theory: ln aL1 = ln yL1 + (1 − yL1 ) −

 v¯  L1

v¯ L2

yL2 −

 v¯  L1

v¯ P

+(L1L2 yL2 + L1P yP )(yL2 + yP ) − L2P

ln aL2 = ln yL2 + (1 − yL2 ) −



air

 

= 20.1,

For a mixture, FLUENT internally uses the following equation e.g. given by Reid and Sherwood [15] to calculate the effective binary diffusion coefficients.

[Pa]

where T is the temperature in Kelvin. The correlation is valid in a range from 10 to 95 ◦ C.

+ L1L2 yL1

v

ˆ ij = a + b · T + c · T 2 D

The saturated vapour pressure at gas/liquid interface, for instance, for butylglycol (CAS: 111-76-2) was calculated using a correlation from the DIPPR material property database [10]: pBG,s = e

 

 v¯  L2

v¯ L1

 v¯  L2

v¯ L1

yL1 −

+L2P yP



 v¯ 

 v¯  L2

v¯ P

yP L1

v¯ L2

yL2 yP

yP

(yL1 +yP )−L1P

 v¯  L2

v¯ L1

yL1 yP

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