Multi-scale modeling of aerosol formation in pipe flow

Many applied problems in fluid mechanics have a multiscale character due to physical processes evolving at many different time and/or length scales. Examples range from turbulent flows with different length scales to chemically reacting and multi-phase flows with various time scales. In most applied flow problems, resolving all scales in space and time present in a flow is not computationally feasible. For the non-resolved time-scales, e.g., time scales on which nucleation of over-saturated vapors is occuring, suitable models can be developed. In general, the nucleation time-scale can be some orders of magnitude smaller than the timestep of the fluid simulations. To demonstrate this, we focus on aerosol flows in a rather simple geometry, but with an abrupt phase change caused by an immediate cooling of hot vapors that triggers creation of the aerosol droplets. The flow cooling is introduced by a rapid change of wall temperature in the considered pipe geometry as seen in fig. 1(a). Consequently, an aerosol is formed from the hot vapors which are initially in the gas phase (fig. 1(b,c)). In our model, the aerosol is simulated in an Eulerian frame exploiting the computational efficiency of such approach. The formation of aerosol droplets is described by classical nucleation theory. Models for coagulation of, condensation to and evaporation from the droplets are included. In addition to the flow equations for mass, momentum and energy conservation, equations for the aerosol mass and number load are solved. In this method of moments approach, the diameter of average mass of the evolving aerosol can be easily determined. In order to account for the omitted time scales in the nucleation process, a sub-timestep model has been developed and included in our simulation to allow for computations at reduced computational effort. The accuracy of the obtained flow solution with this coarse-graining of the aerosol creation process is one of the key objectives for investigations presented in this work. Our aim is to provide a simple computational framework for testing and analyzing aerosol models. In the literature only a modest number of detailed numerical experiments are available for aerosol generation processes by nucleation in flows of condensable vapors. Here, we consider the generation of an aerosol by a rapid cooling of hot vapors in laminar flow (Nguyen et al., 1987). We use the setup and flow parameters described by Nguyen et al. (1987) and consider a pipe flow with prescribed axial wall temperature profile starting from the temperature of hot saturated vapors of Dibutyl phthalate and changing rapidly to room temperature within a short downstream distance (Nguyen et al., 1987; Pyykönen and Jokiniemi, 2000). The aerosol model is implemented as an extension to the open-source software OpenFOAMr, which provides sufficient flexibility for consideration of geometrically more complex flow domains. Our focus lies on two important aspects. First, the analysis of the time resolution at which the simulations need to be performed in order to obtain accurate results at minimal computational cost. For this, a set of simulations is carried out with different time-step sizes in order to investigate the accuracy and necessity of sub-time step modeling. Second, the validation of the method with experimental data available in the literature. The extension of this work to multi-component aerosol formation and turbulent flow is ongoing. Figure 1: snapshots from a laminar simulation of dibutyl phthalate: temperature field t[k] (a), species mass concentration in the gas phase yg[kg/kg] (b) and nucleation rate jn[m−3s−1] (c).