Modeling of Continuous Physical Vapor Deposition: From Continuum to Free Molecular Flow

Physical Vapor Deposition (PVD) is the resublimation of a substance on a cold surface coating it with a thin solid layer. PVD coatings are utilized in industry to modify surface properties and appearance. Since the industrial process requires vacuum conditions, it has been mainly conducted in a batch process. Recently, PVD is considered a promising alternative coating technology to the hot-dip galvanization in order to apply a corrosion protective coating on steel. However, a continuous process is missing to manufacture protective coatings for strip steel on an industrial scale using PVD. First approaches suggest the following process: The steel strip is pulled into a vacuum chamber through air-tight seals to ensure a non-reactive coating atmosphere and avoid impurities; then its surface is treated to obtain high adhesion during the coating process; afterwards it passes a Vapor Distribution Box (VDB) from which vapor jets (or plumes) emerge and coat the steel surface; eventually the strip leaves the vacuum chamber again via air-tight seals, is coiled and shipped. To make this process usable on a large scale - or even superior to galvanization - multiple challenges need to be overcome: ensuring the tightness of the seals, cleaning the strip, preventing stray coating of the vacuum chamber, guaranteeing a uniform coating thickness, and providing a uniform high vapor mass flow to maintain a high speed of the production line. This thesis tackles the last challenge by modeling the vapor transport both inside the VDB and inside the vacuum chamber.First the flow inside the VDB is modeled using a SIMPLE-/PISO-based algorithm for transsonic flows. To account for the evaporation at the melt surface, a boundary condition for the inlet pressure is implemented based on the Hertz-Knudsen equation. The total mass flow rate for different melt temperatures is compared to experimental values as well as an analytical, isentropic estimation. Furthermore, the sensitivity of the model to material properties and process conditions is studied.The total mass flow rate of the system is found to depend on evaporation and choking. With higher melt temperatures the total mass flow rate increases. The trend found in the simulations resembles the one from the experiment. Both yield only 33%-54% of the mass flow rate estimated by the analytical isentropic relation. This low efficiency improves with higher melt temperature. A comparison of the pressure loss across the VDB reveals that the main losses appear due to the viscous boundary layer in the nozzles connecting the VDB with the vacuum chamber. The simulation overpredicts the experimental result by a factor of 1.3. This may be due to the used assumption of an idealized value of unity for the evaporation coefficient; a value of approximately 0.3 would produce a better match between simulations and experiments. Impurities found in the experiment may cause this reduction of the evaporation coefficient.When expanding from the nozzles into the vacuum chamber, the flow accelerates to supersonic speeds and rarefies. We study the interaction of two planar sonic plumes that causes a shock next to the interaction plane. This in turn produces peaks in deposition rate and thus in the coating. Direct Simulation Monte Carlo (DSMC) method is applied for the flow which ranges from continuum at the nozzles to rarefied and free molecular flow downstream. The results are compared to the analytical effusion solution and the inviscid continuum solution from a Riemann solver. The expansion and shock regions of the DSMC simulation are visualized by the Method of Characteristics (MOC). The mass flow distribution as a function of the degree of rarefaction, the nozzle-separation-distance and the inclination of the nozzles is studied. The DSMC result of plume interaction outside the VDB closely resembles the inviscid continuum solution at low degrees of rarefaction. The flow structure with expansions and shocks coincides, deviations are apparent in the actual number density, velocity and temperature especially in the shock region. With higher rarefaction, the shock structure diminishes and the flow field approaches the free molecular flow field. However, the rarefied flow field is not within the limits of the inviscid continuum and the free molecular flow field, but may exceed them in both deposition peaks and temperature peak in the shock region. Using the MOC for visualization reveals that with higher rarefaction the shock bends away from the interaction plane which can be explained by the increased temperature in the secondary expansion. While the shock location shifts with the nozzle-separation distance, it merges to one location when scaling it with the nozzle-separation distance. Bending the nozzle outlets towards each other produces a stronger shock starting further upstream, which in turn causes a stronger secondary expansion and thus smoother deposition.In addition to studying the impact of geometry changes in the PVD setup, the effect of adding a light, inert carrier gas on the plume interaction and the resulting deposition uniformity is investigated. To this end, the carrier-gas mole fraction is varied at a given Knudsen number. Species separation focuses the heavy species along the primary axes, whereas the light inert carrier gas is scattered towards the periphery. Due to the higher mean molecular weight, the speed of sound decreases and consequently the interaction shock occurs farther downstream, is less bent and weaker producing a more uniform deposition profile. Desirable side effects of the carrier-gas are less stray deposition and a higher conductance of the coating material from the inlet nozzle. The last part of the thesis focuses on the numerical method, since DSMC is accurate but computationally costly. The substitution of the collision step in DSMC with a kinetic relaxation using the Bhatnagar-Gross-Krook (BGK) operator is implemented in order to speed up the algorithm. The choice of the target distribution for the relaxation is crucial. The Maxwellian velocity distribution produces an incorrect Prandtl number; the Ellipsoidal-Stochastical BGK (ES-BGK) corrects for the Prandtl number by taking the stress into account; the Shakov model (S-BGK) corrects by considering the heat flux vector. The implemented models are verified against literature data and evaluated for their accuracy in simulating the interacting plumes case. In addition, we evaluated a hybrid coupling of the various kinetic relaxation models in dense, near-continuum regions with DSMC for rarefied and non-continuum regions. The switching criterion for the hybrid coupling was the gradient-length local Knudsen number. The implemented kinetic models compare well to literature data for rarefied Poiseuille flow. The lower resolution criteria lower the computational cost to approximately 30% of the one of DSMC. For the planar jet interaction, the BGK model (using the Maxwellian target distribution) overestimates the shock strength, the S-BGK model overpredicts the diffusion of the shock, whereas the ES-BGK models results are in good agreement with the DSMC results. This indicates that the velocity sorting and breakdown of temperature isotropy in the expansions have a more significant influence on the flow field than the shock, which skews the velocity distribution. Coupling the kinetic models with DSMC in the highly rarefied regions improves the flow field for the BGK and S-BGK model, but not significantly.In short, this thesis examines the influence of process conditions, geometry and carrier-gas use on the mass flow rate and deposition uniformity in continuous PVD for coating steel strips with anti-corrosive coatings. It provides modeling tools for the mass transport both inside and outside the VDB which can be used for further investigation and optimization.ChemE/Transport Phenomen

Diffusive separation in rarefied plume interaction

In the present study, we propose the use of a light, inert carrier gas to support deposition uniformity and rate in continuous physical vapor deposition, in which closely spaced slots or nozzles are required to achieve a sufficiently high deposition rate. Interaction shocks between the emerging rarefied plumes cause undesired nonuniformities in the deposited coating. The present work evaluates the effect of adding a carrier gas on the interaction shock. We study the interaction between two sonic plumes consisting of a binary mixture, i.e., silver as coating material and helium as a light inert carrier gas, by direct simulation Monte Carlo. While the inlet Mach and Knudsen numbers were kept constant, the fraction of carrier gas was varied to single out the effect of species separation. The influence of rarefaction on species separation was also studied. Species separation produces a high carrier-gas fraction in the periphery and an accumulation of the heavier species in the jet core. The resulting change in the speed of sound alters the local expansion characteristics and, thus, shifts the shock location and weakens the shock. These phenomena intensify with the degree of rarefaction. It is shown that adding a light carrier gas increases deposition rate may enhance uniformity and reduce stray deposition.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.ChemE/Transport Phenomen

Numerical analysis of effects of fins and conductive walls on heat transfer in side heated cavities — Onset of three-Dimensional phenomena in natural convection

In the present study, we analyse individual and combined effects of conductive horizontal walls and conductive fins on the natural convection of air in side heated cavities (SHC). The flow and heat transfer are studied for Rayleigh numbers in the range of 104−−109: Direct Numerical Simulation (DNS) is conducted for the lower and Large Eddy Simulation (LES) for the higher Rayleigh numbers (>108). Thermally conductive walls destabilize the flow yielding an earlier transition to turbulence and expedite the decay in boundary layer thickness with increase in Rayleigh number. The preheating/precooling along the conductive walls reduces the actual heat transfer at the vertical walls. Above the fin, instabilities are only marginally enhanced for adiabatic horizontal walls, whereas for conductive horizontal walls, plumes erupt from the fin. This localized Rayleigh-Bénard-like effect triggers 3D instabilities in the entire flow field and yields a steeper slope in Nusselt-Rayleigh diagram. The presence of a fin increases the integral heat transfer by 18% for adiabatic and 21% for conductive horizontal walls. We show that 2D and 3D simulations are similar for the smooth cases (i.e., without fin), but differ by 4% and 13% for the adiabatic and conductive fin cases respectively. The local heat transfer characteristics even deviates up to 50%, therefore a 2D simplification should be avoided.ChemE/Transport PhenomenaJ.M. Burgers Center for Fluid Mechanic

Combined Large-Eddy and Direct Numerical Simulations of a Planar Jet with Heated Co-Flow with Medium and Low Prandtl Fluids

In the present work, we have applied a combined dynamic large-eddy simulation (LES) and direct numerical simulation (DNS) approach for a three-dimensional planar jet in a turbulent forced convection regime (Re = 18000) with a heated co-flow. Results from LES are compared with Reynolds Averaged Navier-Stokes (RANS) simulations and experimental data. We have analyzed flow and heat transfer features for four values of the characteristic Prandtl numbers (Pr = 0.71, 0.2, 0.025, and 0.006), which are representatives of air, He-Xe gas mixture, Lead-Bismuth Eutectic (LBE), and sodium, respectively. The latter two low-Prandtl fluids have been considered because of their role as primary coolants in advanced fast pool-type reactor prototypes (such as the Multi-purpose Hybrid Research Reactor for High-tech Applications (MYRRHA) at SCK•CEN, Belgium). We have provided detailed insights into instantaneous and long-term time-averaged behavior of the velocity and temperature fields (the first- and second-order moments). Furthermore, we have analyzed profiles of characteristic velocity and temperature time scales and dissipation rates, as well as the power spectra of the streamwise velocity component and temperature at several characteristic locations. The mean temperature profiles demonstrated rather low sensitivity for various values of the Prandtl number. In contrast, profiles of the temperature standard deviation exhibited larger variations, decreasing in magnitude with lower Prandtl values. Here presented results of the high fidelity numerical simulations (dynamic LES/DNS) for the low-Prandtl working fluids can be used for further development, testing, and validation of the advanced RANS-type turbulence models.ChemE/Transport Phenomen

The interaction of parallel and inclined planar rarefied sonic plumes—From free molecular to continuum regime

The interaction between rarefied vapor plumes can cause shocks and consequently distinct peaks in mass flux which produce undesirable non-uniformities. To evaluate the impact of shock formation, we study pairs of interacting planar plumes, varying the degree of rarefaction and general geometric parameters, namely, the nozzle-separation-distance and the mutual plume inclination. To consider the extremes of rarefaction, we give the analytic solution for free molecular flow and simulate the inviscid continuum solution using an approximate Riemann solver. In the transitional flow regime, direct simulation Monte Carlo is applied. To detect the shock location, we make use of the Method of Characteristics. We conclude that, although the rarefied flow regime physically lies in between the free molecular and the inviscid continuum flow regimes, the peak value of mass flux in the transitional flow regime exceeds both the one of free molecular flows and the one of inviscid continuum flows (the latter by Rarefied flow exhibits a broader, but weaker secondary expansion after the shock than continuum flow. For planar jet interaction, the occurrence of the shock is rather insensitive to nozzle separation distance. Despite the intuitive expectation that inclining the plumes away from each other would lead to shock reduction and thus give a more uniform mass flux, the opposite is the case: Inclining the plumes toward each other leads to a stronger shock, but also to a stronger expansion, thus producing a more uniform mass flux with less stray mass fluxes.ChemE/Transport PhenomenaJ.M. Burgers Center for Fluid Mechanic

Modeling of a continuous physical vapor deposition process: Mass transfer limitations by evaporation rate and sonic choking

In recent years, Physical Vapor Deposition has been advanced to a continuous process which makes it amenable for in-line, high-quality and energy-efficient galvanization. To achieve the high and uniform mass flow required for in-line production, a Vapor Distribution Box is used, in which the zinc is evaporated. The zinc fills the Vapor Distribution Box at a relatively high pressure and leaves into the coating chamber via nozzles. A reliable modeling approach that can be used in the design and optimization of Vapor Distribution Boxes is as yet not available in the literature. The present paper analyses which phenomena play a major role and therefore have to be included in a simulation model of continuous Physical Vapor Deposition processes, and identifies process parameters which have a significant impact on deposition rate and uniformity. To this end, a model for the flow and heat transfer is developed based on the numerical solution of the compressible Navier–Stokes-Fourier equations in combination with the Launder and Sharma low-Reynolds k-∊ turbulence model, using the open-source CFD-library OpenFOAM. To account for the vapor mass flow to be limited by both evaporation and sonic choking, a novel inlet boundary condition is proposed based on the Hertz-Knudsen condition. Results from the CFD model are compared to those of analytical models based on isentropic flow, the influence of various modeling parameters is evaluated against experiments, and sensitivity of the process to various process parameters studied. The proposed numerical model predicts mass flow rates with a much better accuracy than analytical models previously proposed in the literature. The latter overpredict the mass flow rate by a factor of 2.1–2.5, whereas the proposed numerical model overpredicts only by a factor of 1.3. Next to the novel Hertz-Knudsen boundary condition, the inclusion of viscous effects is found to be crucial to achieve this improvement, since viscous effects – especially in the boundary layer inside the nozzles – severely reduce the mass flow. The numerical model is shown to be only weakly sensitive to uncertainties in the evaporation coefficients and metal vapor viscosity. For the device studied, the mass flow discharge efficiency was found to be relatively low (≈40%). To increase this efficiency, viscous losses in the nozzle boundary layers have to be reduced, for instance by employing shorter or a bigger radius nozzles (possibly impairing nozzle-to-nozzle uniformity) or by employing a higher melt temperature and vapor pressure.ChemE/Transport Phenomen