The stone chip resistance performance of automotive coatings has attracted increasing attention in academic and industrial communities. Even though traditional gravelometer tests can be used to evaluate stone chip resistance of automotive coatings, such experiment-based methods suffer from poor repeatability and high cost. The main purpose of this work is to develop a CFD-DEM-wear coupling method to accurately and efficiently simulate stone chip behavior of automotive coatings in a gravelometer test. To achieve this end, an approach coupling an unresolved computational fluid dynamics (CFD) method and a discrete element method (DEM) are employed to account for interactions between fluids and large particles. In order to accurately describe large particles, a rigid connection particle method is proposed. In doing so, each actual non-spherical particle can be approximately described by rigidly connecting a group of non-overlapping spheres, and particle-fluid interactions are simulated based on each component sphere. An erosion wear model is used to calculate the impact damage of coatings based on particle-coating interactions. Single spherical particle tests are performed to demonstrate the feasibility of the proposed rigid connection particle method under various air pressure conditions. Then, the developed CFD-DEM-wear model is applied to reproduce the stone chip behavior of two standard tests, i.e., DIN 55996-1 and SAE-J400-2002 tests. Numerical results are found to be in good agreement with experimental data, which demonstrates the capacity of our developed method in stone chip resistance evaluation. Finally, parametric studies are conducted to numerically investigate the influences of initial velocity and test panel orientation on impact damage of automotive coatings.

Automotive coating plays an important role in providing resistance to corrosion, rusting, stone impact and aging for vehicle surface. However, the possible damage of coating caused by flying debris during high-speed driving could do harm to a vehicle in terms of appearance and safety. Since the anti-impact capability of automotive coating has always been highly concerned by vehicle companies and users, it is of great significance to find an effective and accurate method to evaluate the stone chip resistance of the surface coating. At present, automobile companies usually adopt tests according to standards, e.g., DIN 55996-1 and SAE J400-2002, to evaluate the stone chipping resistance of the coating. Although test evaluation has the advantages of intuition and reliability, it is of high cost, low efficiency and poor repeatability. Evaluation by computer simulation can parameterize the research and overcome the deficiency of experiment. Besides, the simulation results can also serve to guide the test, which significantly shortens the development cycle.

The standardized tests are often performed on a gravel projecting test apparatus, which is named gravelometer in standard SAE J400-2002. In order to accurately and efficiently reproduce the movement of particles in the experiment and obtain reliable impact velocity and impact position for wear model by simulation, the widely accepted coupled CFD-DEM method (unresolved CFD-DEM) is employed in this study. Attributed to its excellent computational efficiency and the capability to trace the particle motion, the unresolved CFD-DEM method is widely used in particulate flow simulations such as pneumatic conveying, fluidized bed and blast furnace [

Nevertheless, the conventional unresolved CFD-DEM method has its limitations. The first limitation is the difficulty of non-spherical particle representation, which is of great necessity in this study as is demanded in the corresponding standardized tests. However, the models implemented in the conventional unresolved CFD-DEM method are mostly developed for spherical particles, which means both DEM approaches and CFD-DEM coupling strategies need to be further redeveloped for non-spherical particles [

The most popular approach to define non-spherical particle is the composite particle method, in which several component spheres are bonded together for shape approximation. The composite spheres method is excellent in its simplicity and unrestricted shape representation [

The composite particle model with component spheres overlapping is broadly used to form non-spherical particles in granular flows. Li et al. [

The second limitation is the mesh-particle size ratio. For the unresolved CFD-DEM method, by solving the locally averaged Navier-Stokes equation, the flow around each particle is volume-averaged in the local domain [

The other method is to improve the void fraction model on the basis of the unresolved CFD-DEM method. At present, the most broadly used void fraction models in the unresolved CFD-DEM method are the particle centroid method (PCM) and the divided particle volume method (DVPM) [

Taking the aforementioned limitations into account, Xiong et al. [

In this work, the rigid connection particle method is proposed to address the issues of the bonded particle method mentioned above. While the unresolved CFD-DEM method is still adopted to describe the gas-particle two-phase flow field, the adhesive bond connections between particles in the bonded particle method is replaced by rigid connections to form composite particles. This method uses hundreds of and possibly thousands of non-overlapping spheres to approximately represent the shape of the original particle. The sphere cluster is treated as a rigid body. According to the resultant external force and position of each component sphere, the resultant force and moment of the rigid composite particle is computed, which is then used to solve the motion of the rigid composite particle. The proposed method combines the composite sphere method with the idea of the porous sphere method. It replaces the original particles with non-overlapping composite particles to realize the porous structure. On the one hand, particles of any shape can be represented using the composite particle method. On the other hand, the local extremes of void fraction around particle centroid can also be avoided, attributed to the porous structure. Moreover, by controlling the diameter of component spheres, the requirement of mesh-particle size ratio can be met to keep the numerical results accurate and convergent. As a consequence, it can cope well with the simulations of DIN and SAE tests. Moreover, as an optimization of the BPM, the proposed method has better performance in reproducing the particle rotation and is free from the concerns of bond breakage.

This paper is organized as follows. In

The unresolved CFD-DEM method employed in this study is founded on the Euler-Lagrangian framework [

In this study, a novel method called rigid connection particle method is proposed to handle large particles in a narrow channel. A group of spheres are rigidly connected to form a rigid composite particle of arbitrary shape, and some instances are shown in

A rigid composite particle usually consists of hundreds of component spheres which do not overlap and fit tightly. It was pointed out in previous studies that the size of the mesh should at least be 3 times as large as the size of particles to ensure the accuracy and astringency of the computation [

Although the appearance of the rigid composite particle is similar to that of the bonded composite particle proposed by Xiong et al. [

In comparison, the rigid connection particle method fixes the relative position of the two spheres and treats them as a whole, transforming the forces on sphere to the forces and moments on the center of mass of the composite particle, which has better performance in describing particle movement. As shown in

The fluid phase is assumed to be incompressible in order to simplify the simulation model. It is governed by the corresponding locally averaged Navier-Stokes equations [

The particle-wall contact and particle-particle contact are computed based on the Hertz-Mindlin no-slip contact model [

Further, the normal and tangential elastic constant as well as viscoelastic damping constant are computed as [

The equivalent Young's Modulus, equivalent shear modulus, equivalent radius, equivalent mass are defined as:

In the unresolved CFD-DEM method, the interaction force between the fluid and particle is generally calculated by an empirical formula determined via experiments. In this study, the drag force

Moreover, Kodam et al. [

Subsequently, a parameter _{p}_{s}

The coating damage is predicted by using the erosion wear model proposed by Finnie [

The eroded mass (EM) during contact time can be computed as:

In this paper, the proposed method and the unresolved CFD-DEM method are implemented in CFDEM®coupling framework [

Currently, most researches on large particles focus on low Reynolds number conditions. In order to verify the feasibility of the proposed method under the situations of high Reynolds number, single particle motion tests were carried out on the stone chip resistance gravelometer, and the corresponding simulation is performed in our study. The structure of the gravelometer used in this research is shown schematically in

Five single particle tests S1 to S5, with air pressures setting ranging from 0.05 MPa to 0.25 MPa, were used to verify the applicability of the proposed approach in a variety of high Reynolds number conditions. Simulations are conducted in both the rigid connection particle method and the bonded particle method according to the experimental conditions to compare their computational efficiency and accuracy. The simulations focus on the motion of particle inside the DIN accelerating pipe, and the computational domain is set to be a horizontal circular pipe with a length of 290 mm and an inner diameter of 30 mm. Its schematic diagram and related dimensions and parameters are shown in

Case | Air pressure setting (MPa) | Stable gas velocity (m/s) |
---|---|---|

S1 | 0.05 | 26.1 |

S2 | 0.1 | 31.3 |

S3 | 0.15 | 37.3 |

S4 | 0.2 | 42.0 |

S5 | 0.25 | 46.1 |

Simulation parameters are set according to experimental conditions, with the stable gas velocity

The outlet is set as a pressure outlet, with the fixed pressure value set as 0. No-slip boundary condition is applied on the wall of the pipe. The 5 mm diameter spherical composite particle is made up of 615 component spheres with a diameter of 0.5 mm, and is placed in the corresponding position of the steel ball in the experiment. The composite particle used in the rigid connection particle method and the bonded particle method are identical except for the way the component spheres are connected. Other parameters for fluid and particles are displayed in

Parameters | Values |
---|---|

Fluid phase: | |

Gas density (kg/m^{3}) |
1.225 |

Gas viscosity (Pa⋅s) | 1.79 × 10^{−5} |

CFD time step (s) | 1 × 10^{−5} |

Solid phase: | |

Particle density (kg/m^{3}) |
7890 |

Young's modulus (GPa) | 208 |

Poisson ratio (--) | 0.3 |

Restitution coefficient (–) | 0.8 |

Friction coefficient (–) | 0.3 |

DEM time step (s) | 1 × 10^{−6} |

In the vertical direction, it is hard to capture the particle movement accurately since the movement amplitude is not large enough for the high-speed camera and corresponding post-processing software. Given the above, the results are described with the maximum height the particle reaches and the number of particle collisions against the pipe wall. The data is displayed in

Parameters | Values | |||||
---|---|---|---|---|---|---|

Air pressure set (MPa) | 0.05 | 0.1 | 0.15 | 0.2 | 0.25 | |

The max height (mm) | Experiment | 1.24 | 2.27 | 4.06 | 4.87 | 5.11 |

Simulation (R) | 1.19 | 2.57 | 4.15 | 5.49 | 6.5 | |

Simulation (B) | 0.63 | 2.00 | 3.58 | 4.56 | 5.48 | |

The number of collisions | Experiment | 2 | 2 | 1 | 1 | 0 |

Simulation (R) | 2 | 1 | 1 | 0 | 0 | |

Simulation (B) | 3 | 1 | 1 | 0 | 0 |

Therefore, for the several conditions involved in the standardized multi-particle experiment in this study, it can be considered that the proposed rigid connection particle method shows higher accuracy and greater applicability in describing large particle motion.

Simulations presented in this paper can be divided into three parts: in

This simulation is established according to the DIN55996-1 standard experiment. Its schematic diagram and some relevant parameters are shown in

In the experiment, flow conditions at the three-way pipe which connects the nozzle, the accelerating pipe, and the feeding tube are complicated. For the purpose of minimizing the computational cost, the model is simplified. The horizontal particle velocity at the inlet of accelerating pipe is measured through experiment, and it is set to be the initial velocity of particles once they generate in simulation. It can be concluded from experiments that the horizontal initial velocity is approximately proportional to the nozzle flow velocity, and negatively related to the equivalent diameter and density of the particles. It can be simply estimated by an empirical formula:

Simulation is then performed by using the simplified model, with the inlet of accelerating pipe being velocity-inlet, outlet of the protection box being pressure-outlet, and the wall being no slip boundary condition. A one-third sphere-shaped composite particle made up of 809 component spheres is used to approximately represent the chilled cast iron particle in experiment, and its shape is shown in

The evaluation of the simulation results will be carried out from two aspects: particle impact velocity and particle impact damage distribution. For the assess of particle impact velocity, 30 particles in a continuous period are selected from experiment and simulation respectively, whose impact velocities as well as impact angles are compared in

Parameter | Method | Average value | Standard deviation | Maximum value | Minimum value |
---|---|---|---|---|---|

Impact velocity | Experiment | 5.763886 | 0.90782 | 7.38567 | 3.72422 |

Simulation | 5.638991 | 0.549886 | 6.57404 | 4.53922 | |

Impact angle | Experiment | 129.3204 | 6.288138 | 140.9314 | 118.875 |

Simulation | 129.6234 | 5.282901 | 139.6818 | 114.2849 |

In terms of impact damage distribution, the picture of the coating panel after DIN standard test and the simulated coating damage presented by wear model are displayed in

The simulation established according to the SAE J400-2002 standard experiment is shown in

Parameters | Values |
---|---|

Fluid phase: | |

Air pressure (MPa) | 0.48 |

Gas density (kg/m^{3}) |
1.225 |

Gas viscosity (Pa⋅s) | 1.79 × 10^{−5} |

Fluid time step (s) | 1 × 10^{−5} |

Solid phase: | |

Component sphere diameter (mm) | 1.0 |

Particle density (kg/m^{3}) |
2660 |

Young's modulus (GPa) | 60 |

Poisson ratio (--) | 0.25 |

Restitution coefficient (–) | 0.8 |

Friction coefficient (–) | 0.3 |

Initial velocity (m/s) | (8.5, 0, −1.0) |

Solid time step (s) | 1 × 10^{−6} |

By sorting and categorizing the pebbles used in the experiment, two ellipsoidal composite particles of different sizes, two rounded quadrangular pyramid composite particles of different sizes, i.e., a total of four kinds of composite particles are used to approximate the shape of the pebbles during the experiment. The shapes of the composite particles as well as the pebbles are shown in

In the experiment and simulation respectively, 30 particles are selected in succession with their trajectories recorded. The results are compared through a scatter diagram with the particle impact velocity v being the x coordinate and the impact angle α being the y coordinate, as shown in

Parameter | Method | Average value | Standard deviation | Maximum value | Minimum value |
---|---|---|---|---|---|

Impact velocity | Experiment | 8.424316 | 1.375961 | 11.51017 | 5.76509 |

Simulation | 8.243987 | 0.759827 | 9.77719 | 6.76235 | |

Impact angle | Experiment | 93.16781 | 5.967271 | 104.5742 | 78.31063 |

Simulation | 92.66519 | 6.600232 | 106.439 | 78.9241 |

The picture of the coating panel after test and the coating damage presented by wear model in simulation is displayed in

Also, compared with the DIN simulation in

To further study the influence of impact velocity as well as impact angle on the impact damage, simulations with different test panel orientations and initial particle velocity are carried out. The parameter differences in each case are shown in

Case | Initial velocity (m/s) | Test panel orientation (°) |
---|---|---|

M0 | 8.5 | 90 |

M1 | 8.5 | 72 |

M2 | 8.5 | 54 |

M3 | 7.0 | 90 |

M4 | 10.0 | 90 |

Likewise, the sample is divided into six parts for analysis. The eroded mass and the impact damage distribution among different cases are showed in

The comparison of the simulated eroded mass between the simulations of different panel orientations is presented in

The above simulation results indicate that the simulation implemented with the rigid connection particle method and the Finnie wear model is able to reproduce the influence of particle velocity and impact angle on the impact damage of the test panel, further demonstrating the reliability of this method in predicting the impact damage on the test panel.

This work develops a CFD-DEM-wear model for stone chip resistance analysis of automotive coatings in a gravelometer test. Such complex physical phenomena normally involve fluid-particle interactions and impact wear of automotive coatings. In the developed method, the unresolved CFD-DEM method is employed to account for interactions between fluids and large particles, and a rigid connection particle method is proposed to facilitate the description of large particles using a number of non-overlapping rigidly connected spheres. The fluid-particle forces are initially calculated on each component sphere, and then converted to the resultant force and moment of larger particles based on the rigid connection. The proposed rigid connection particle method neatly avoids the local extreme of void fraction around particle centroid by making large particles physically porous, and the translation and rotation of non-spherical particles can be better represented. A Finnie wear model is used to calculate the impact damage of automotive coatings subjected to non-spherical particles.

Single- and multi-particle tests are performed to demonstrate the accuracy of the CFD-DEM coupling method in simulating spherical and non-spherical large particle movement in terms of motion trajectory. The developed CFD-DEM-wear coupling method is applied to evaluate stone chip resistance performance of automotive coatings in two standard gravelometer tests, i.e., DIN 55996-1 and SAE-J400-2002 tests. Numerical results are found in consistent with experimental data in terms of impact velocity and damage distribution, which validates the capacity of our developed method in stone chip resistance evaluation of automotive coatings. Finally, parametric studies are conducted to numerically investigate the effects of initial particle velocity and test panel orientation. Results show that when the initial velocity increases, the eroded mass increases as well, and the impacted area appears to be located in a lower position. In addition, from 90° to 54°, the increase of the angle between the test panel and the vertical plane will lead to the increase in the eroded mass and expansion of the area being impacted.

In the current study, the movement of particles near the high-pressure air nozzle is circumvented, so as to dramatically improve computational efficiency. Instead, an initial velocity obtained from the preliminary experiment is set for each particle to replace the acceleration effect. However, this numerical treatment will lead to mismatch of inlet boundary conditions for the stone chip resistance analysis, which contributes to the large differences between some experimental and numerical results. Our future works have scheduled to develop numerical methods to better describe the inlet boundary conditions for stone chip simulations.

Particle impact angle

Volume fraction occupied by the fluid

Position vector from the particle's center to the contact point

Drag force coefficient

Diameter of the component sphere

Volume-equivalent diameter of the original particle

Overlap distance of two particles in contact

Tangential displacement vector between the two particles in contact

Coefficient of restitution

Eroded mass

Particle-wall contact force

Particle-particle and particle-wall contact forces

Particle-wall contact forces

Fluid-particle interaction force

Bonding force

Resultant force of rigid composite particle

Resultant force of component sphere

Normal contact force between particle i and particle j

Tangential contact force between particle i and particle j

Drag force

Buoyancy force

Resultant force after bonded

Acceleration of gravity

Equivalent shear modulus

Moment of inertia of the composite particle

Normal elastic constant

Tangential elastic constant

Equivalent mass

Mass of the component sphere

Mass of the composite particle

Resultant moment on the mass center of rigid composite particle

Number of component sphere in the composite particle

Fluid density

Particle density

Air flow rate

Position vector from the center of mass of the composite particle to the component sphere

Particle Reynolds number

Momentum exchange with the particulate phase

Radius of particle i

Equivalent radius

Impingement angle

Normal viscoelastic damping constant

Tangential viscoelastic damping constant

Normal stiffness

Tangential stiffness

Contact time

Stress tensor for the fluid phase

Fluid velocity

Particle velocity

Fluid dynamic viscosity

Poisson's ratio of particle i

Initial velocity of particles

Relative velocity of the particle

Particle impact velocity

Stable gas velocity

Inlet velocity

Fluid kinematic viscosity

Young's Modulus of particle i

Equivalent Young's Modulus