Microstructured reactors are characterized by rapid mixing processes and excellent temperature control of chemical reactions. These properties allow the safe operation of hazardous chemistry in intensified processes. Problems occur during scale-up of these processes, where heat transfer becomes the limiting effect. With high flow rates and transitional or even turbulent flow regimes in small channels, rapid mixing and excellent heat transfer can be maintained up to high production rates. For exothermic reactions, limits for parametric sensitivity and safe operation are shown from literature and combined with convective heat transfer for consistent scale-up. Good knowledge of reaction kinetics, thermodynamics and heat transfer is essential to determine runaway regions for exothermic reactions. From these correlations, consistent channel design and continuous-flow reactor setup is shown.

Scale-up concept for modular microstructured reactors based on mixing, heat transfer, and reactor safety

Heat transfer to supercritical CO2 in a horizontal pipe is investigated using direct numerical simulation (DNS). A well resolved DNS eliminates the uncertainty brought by turbulence modeling. The small pipe diameter (D = 1 mm, 2 mm) with a moderately low inlet Reynolds number (Re0 = 5400) can be compared to the channel flow in a compact heat exchanger, e.g. a printed circuit heat exchanger (PCHE). In our simulation, the inflow temperature T0 is set to be lower than the pseudo-critical temperature Tpc. The thermo-physical properties change rapidly when the fluid temperature rises across Tpc under heating conditions. In the present DNS, the wall temperature T w is found to be variable in the circumferential direction. The magnitude of T w is higher at top than at the bottom surface. As a result of buoyancy, flow stratification with low density in the upper region of pipe is developed. The streamwise velocity field U ˜ z is also modified by the flow stratification. Low-velocity flow near the circumferential wall is heated firstly and transported to the top region by the secondary flow. High-velocity bulk fluid is concentrated at the bottom as a result of high density. It is also observed that the turbulent kinetic energy and the radial turbulent heat flux are strongly suppressed near the top surface. The attenuated momentum transport and heat transfer enhance the flow stratification. A further analysis shows a significantly decreased turbulence production in this position.

Flow stratification of supercritical CO2 in a heated horizontal pipe

When a turbulent flow in a porous medium is determined numerically, the crucial question is whether turbulence models should account only for turbulent structures restricted in size to the pore scale or whether the size of turbulent structures could exceed the pore scale. The latter would mean the existence of macroscopic turbulence in porous media, when turbulent eddies exceed the pore size. In order to determine the real size of turbulent structures in a porous medium, we simulated the turbulent flow by direct numerical simulation (DNS) calculations, thus avoiding turbulence modelling of any kind. With this study, which for the first time uses DNS calculations, we provide benchmark data for turbulent flow in porous media. Since perfect DNS calculations require the resolution of scales down to the Kolmogorov scale, often only approximate DNS solutions can be obtained, especially for high Reynolds numbers. This is accounted for by using and comparing two different DNS approaches, a finite volume method (FVM) with grid refinement towards the wall and a lattice Boltzmann method (LBM) with equal grid distribution. The solid matrix was simulated by a large number of rectangular bars arranged periodically. The number of bars in the solution domain with periodic boundary conditions was reduced systematically until a minimum size was found that does not suppress any large-scale turbulent structures. Two-point correlations, integral length scales and energy spectra were determined in order to answer the question of whether or not macroscopic turbulence can be found in porous media.

Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study

To investigate which component of the anisotropic permeability tensor of porous media influences turbulence over porous walls, direct numerical simulation of anisotropic porous-walled channel flows is performed by the D3Q27 multiple-relaxation-time lattice Boltzmann method. The presently considered anisotropic permeable walls have square pore arrays aligned with the Cartesian axes. Vertical, streamwise and spanwise pore arrays are systematically introduced to the walls to impose anisotropic permeability. Simulations are carried out at a friction Reynolds number of 111 and 230, which is based on the averaged friction velocity of the porous bottom and the smooth top walls. It is found that streamwise and spanwise permeabilities enhance turbulence whilst vertical permeability itself does not. In particular, the enhancement of turbulence is remarkable over porous walls with streamwise permeability. Over streamwise permeable walls, development of high- and low-speed streaks is prevented whilst large-scale intermittent patched patterns of ejection motions are induced. It is revealed by two-point correlation analysis that streamwise permeability allows the development of streamwise large-scale perturbations induced by Kelvin–Helmholtz instability. Spectral analysis reveals that this perturbation contributes to the enhancement of the Reynolds shear stress, leading to significant skin friction of the porous interface. Through the comparison between the two different Reynolds-number cases, it is found that, as the Reynolds number increases, the streamwise perturbation becomes larger and more organized. Consequently, owing to the enhancement of the large-scale perturbation, a significant Reynolds-number dependence of the skin friction of the porous interface can be observed over the streamwise permeable wall. It is also implied that the wavelength of the perturbation can be reasonably scaled by the outer-layer length scale.

Direct numerical simulation of turbulence over anisotropic porous media

The lattice Boltzmann method for nearly incompressible flows

In this study, we address the question of whether turbulent structures in a porous medium are restricted in size by the pore scale or whether the size of eddies may exceed the pore scale, leading to the formation of macroscopic coherent structures. Based on direct numerical simulations in porous media, we conclude that the size of turbulent eddies is restricted by the pore size, leading to the pore scale prevalence hypothesis (PSPH). We prove this hypothesis by considering four different porous matrices. In particular, we simulated turbulent flow in a two-dimensional matrix, a three-dimensional unbounded matrix, a three-dimensional matrix bounded by two parallel solid walls, and a three-dimensional matrix with two characteristic pore scales. The obtained results for the four simulated porous matrices support the PSPH. However, there is a partly open question of whether turbulent structures can reach the size of the largest pore scale if the solid matrix is characterized by more than one length scale.

A direct numerical simulation study on the possibility of macroscopic turbulence in porous media: Effects of different solid matrix geometries, solid boundaries, and two porosity scales

Structure of a turbulent flow through plane channels with smooth and rough walls: An analysis based on high resolution DNS results

The concept of head loss coefficients K for the determination of losses in conduit components is discussed in detail. While so far it has mainly been applied to fully turbulent flows it is extended here to also cover the laminar flow regime. Specific numbers of K can be determined by integration of the entropy generation field (second law analysis) obtained from a numerical simulation. This general approach is discussed and illustrated for various conduit components.Copyright © 2010 by ASME

Loss Coefficients in Laminar Flows: Indispensable for the Design of Micro Flow Systems

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall It can be implemented very easily for a Navier-Stokes (NS) SolverInstead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis It models the streaming and interaction of particles statistically The pressure and the velocity can be calculated at every time step from the current particle distribution functions The resulting fields are solutions of the Navier-Stokes equations Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver An additional problem is the structure of the grid Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implementIn this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis The other one is based on the Navier-Slip model We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid We will also show what limits the slip rate and give an outlook of how this can be avoidedCopyright © 2013 by ASME

Marc-Florian Uth

Papers

Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study

A direct numerical simulation study on the possibility of macroscopic turbulence in porous media: Effects of different solid matrix geometries, solid boundaries, and two porosity scales

Structure of a turbulent flow through plane channels with smooth and rough walls: An analysis based on high resolution DNS results

Loss Coefficients in Laminar Flows: Indispensable for the Design of Micro Flow Systems

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method