Real-time temperature measurement in stochastic rotation dynamics

Many physical and chemical processes involve energy change with rates that depend sensitively on local temperature. Important examples include heterogeneously catalyzed reactions and activated desorption. Because of the multiscale nature of such systems, it is desirable to connect the macroscopic world of continuous hydrodynamic and temperature fields to mesoscopic particle-based simulations with discrete particle events. In this work we show how to achieve real-time measurement of the local temperature in stochastic rotation dynamics (SRD), a mesoscale method particularly well suited for problems involving hydrodynamic flows with thermal fluctuations. We employ ensemble averaging to achieve local temperature measurement in dynamically changing environments. After validation by heat diffusion between two isothermal plates, heating of walls by a hot strip, and by temperature programed desorption, we apply the method to a case of a model flow reactor with temperature-sensitive heterogeneously catalyzed reactions on solid spherical catalysts. In this model, adsorption, chemical reactions, and desorption are explicitly tracked on the catalyst surface. This work opens the door for future projects where SRD is used to couple hydrodynamic flows and thermal fluctuations to solids with complex temperature-dependent surface mechanisms.

Figure 1

Flowchart of the OpenMPI algorithm for parallel averaging of local macroscopic variables in SRD. In this example we show $n_s=4$ instances (replicas).

Figure 2

Comparison of analytical and simulated velocity in Poiseuille flow. The walls are kept at a constant temperature.

Figure 3

Time evolution of the temperature distribution between two isothermal plates; the analytical solution is under the assumption of a constant thermal diffusivity evaluated at the temperature of the hot plate.

Figure 4

Comparison between the theoretical thermal diffusivity (Table 2) and the thermal diffusivity obtained from the measured heat flux [Eq. (15)].

Figure 5

Schematic of the heated wall. Blue represents the zone with variable temperature, yellow the heated zone and the red arrows denote the direction of heat flow. Domain boundaries in $x$ and $z$ coordinates are periodic.

Figure 6

Temperature evolution of the surface of the unheated (a) and heated (b) wall with time. Subsequent time steps are plotted above each other to illustrate the change in temperature profile with time.

Figure 7

Desorption rate versus temperature during a TPD virtual experiment where the sphere temperature is increased at a rate of $\beta =0.001$.

Figure 8

Time dependence of surface coverage of a catalytic sphere for isothermal adsorption-reaction-desorption.

Figure 9

Schematic overview of the simulation domain ($xy$ plane) for catalytic particles with heat effects.

Figure 10

Mean product number density distribution in a cross section of a domain. Panels (a), (b), and (c) shows results for one, two, and three spheres. Panel (d) compares the total number of B particles in each of the system with the results expected for multiple isolated spheres.

Figure 11

Steady-state temperature profiles for a cross section of the domain [(a)–(c)]. Panel (d) gives the transient change in local temperature midway between spheres 2 and 3 ($x=12$ and $y=14$).

Figure 12

Variation of local B number density (a) and temperature (b) in cross section of domain with time.