Heiko Schmidt

A generalized level-set/in-cell-reconstruction approach for accelerating turbulent premixed flames

An extended numerical technique for the simulation of accelerating turbulent premixed flames in large scale geometries is presented. It is based on a hybrid capturing tracking technique. It resembles a tracking scheme in that the front geometry is explicitly computed using a level-set method. The basic flow properties are provided by solving the compressible flow equations. The flame-flow-coupling is achieved by an in-cell-reconstruction technique. In cells cut by the flame, the discontinuous solution is reconstructed from given cell averages by invoking explicitly some Rankine–Hugoniot type jump conditions. Then the reconstructed states and again the front geometry are used to define accurate effective numerical fluxes across grid cell interfaces intersected by the front during the time step considered. Hence, the scheme also resembles a capturing scheme in that only cell averages of conserved quantities are computed. To be able to model inherently unsteady effects, like quenching, reignition, etc, during flame acceleration, we modified the standard Rankine–Hugoniot jump conditions. A source term appearing in the modified jump conditions is computed by evaluating a suitable functional on the basis of a one-dimensional flame structure module, that is attached in the normal direction to the flame front. This module additionally yields quantities such as the net mass burning rate, necessary for the propagation of the level set, and the specific heat release important for the energy release due to the consumption of fuel. Generally, the flame structure calculation takes into account internal physical effects which are not active in the outer flow but essential for the front motion and its feedback on the surrounding fluid. If a suitable set of different (turbulent) combustion models to compute the flame structure is provided, the new numerical technique allows us to consistently represent laminar deflagrations, fast turbulent deflagrations as well as detonation waves. Supplemented with suitable criteria that capture the essence of a deflagration-to-detonation-transition (DDT), the complete evolution of such an event can be implemented in principle.

Wind shear and buoyancy reversal at the stratocumulus top

AbstractA numerical experiment is designed to study the interaction at the stratocumulus top between a mean vertical shear and the buoyancy reversal due to evaporative cooling, without radiative cooling. Direct numerical simulation is used to eliminate the uncertainty introduced by turbulence models. It is found that the enhancement by shear-induced mixing of the turbulence caused by buoyancy reversal can render buoyancy reversal comparable to other forcing mechanisms. However, it is also found that (i) the velocity jump across the capping inversion Δu needs to be relatively large and values of about 1 m s−1 that are typically associated with the convective motions inside the boundary layer are generally too small and (ii) there is no indication of cloud-top entrainment instability. To obtain these results, parameterizations of the mean entrainment velocity and the relevant time scales are derived from the study of the cloud-top vertical structure. Two overlapping layers can be identified: a background sh...

Probability density functions in the cloud-top mixing layer

The cloud-top mixing layer is an idealized configuration often employed in the literature to study local aspects (over length scales of the order of 10 m) of the top of stratocumulus-topped mixed layers. Latent heat effects are further investigated here by means of direct numerical simulations, discussing the probability density functions of the horizontal and vertical velocities, as well as the mixture fraction (equal to a normalized enthalpy and total water-specific humidity). The focus is on the turbulent convection layer that develops from the buoyancy reversal instability as a consequence of the evaporative cooling at the upper cloud boundary. An approximately self-similar behavior is found, where the convection scales based on the molecular buoyancy flux at the cloud top characterize the distributions at different times, at least to leading order and within the statistical convergence achieved in the simulations. However, a very strong vertical variation in the density functions across the turbulent convection layer is found, which is of relevance to possible models. Non-Gaussian behavior is often observed, even in the horizontal component of the velocity vector. In particular, large values of skewness and flatness are measured at the lower end of the turbulent zone, where external intermittency is very strong.

Towards a Compressible Reactive Multiscale Approach Based on One-Dimensional Turbulence

Due to its huge complexity, progress in understanding and prediction of turbulent combustion is extremely challenging. In principle, progress is possible without improved understanding through direct numerical solution (DNS) of the exact governing equations, but the wide range of spatial and temporal scales often renders it unaffordable, so coarse-grained 3D numerical simulations with subgrid parameterization of the unresolved scales are often used. This is especially problematic for multi-physics regimes such as reacting flows because much of the complexity is thus relegated to the unresolved small scales. One-Dimensional Turbulence (ODT) is an alternative stochastic model for turbulent flow simulation. It operates on a 1D spatial domain via time advancing individual flow realizations rather than ensemble-averaged quantities. The lack of spatial and temporal filtering on this 1D domain enables a physically sound multiscale treatment which is especially useful for combustion applications where, e.g., sharp interfaces or small chemical time scales have to be resolved. Lignell et al. recently introduced an efficient ODT implementation using an adaptive mesh. As all existing ODT versions it operates in the incompressible regime and thus cannot handle compressibility effects and their interactions with turbulence and chemistry which complicate the physical picture even further. In this paper we make a first step toward an extension of the ODT methodology towards an efficient compressible implementation. The necessary algorithmic changes are highlighted and preliminary results for a standard non-reactive shock tube problem as well as for a turbulent reactive case illustrate the potential of the extended approach.

Flexible flame structure modelling in a Flame Front Tracking Scheme

A numerical technique for the simulation of accelerating turbulent premixed flames in large scale geometries is presented. It is based on a hybrid capturing/tracking method. It resembles a tracking scheme in that the front geometry is explicitly computed and propagated using a level set method. The basic flow properties are provided by solving the reactive Euler equations. The flame-flow-coupling is achieved by an in-cell-reconstruction technique, i.e., in cells cut by the flame the discontinuous solution is reconstructed from given cell-averages by applying Rankine-Hugoniot type jump conditions. Then the reconstructed states and again the front geometry are used to define accurate effective numerical fluxes across grid cell interfaces intersected by the front during the time step considered. Hence the scheme also resembles a capturing scheme in that only cell averages of conserved quantities are updated. To enable the modelling of inherently unsteady effects, like quenching, reignition, etc., during flame acceleration, the new key idea is to provide a local, quasi-onedimensional flame structure model and to extend the Rankine-Hugoniot conditions so as to allow for inherently unsteady flame structure evolution. A source term appearing in the modified jump conditions is computed by evaluating a suitable functional on the basis of a onedimensional flame structure module, that is attached in normal direction to the flame front. This module additionally yields quantities like the net mass burning rate, necessary for the propagation of the level set, and the specific heat release important for the energy release due to the consumption of fuel. Generally the local flame structure calculation takes into account internal (small scale) physical effects which are not active in the (large scale) outer flow but essential for the front motion and its feedback on the surrounding fluid. If a suitable set of different (turbulent) combustion models to compute the flame structure is provided, the new numerical technique allows us to consistently represent laminar deflagrations, fast turbulent deflagrations as well as detonation waves. Supplemented with suitable criteria that capture the essence of a Deflagration-to-Detonation-Transition (DDT), the complete evolution of such an event can be implemented in principle.

Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model

ABSTRACT The turbulent asymptotic suction boundary layer is studied using a one-dimensional turbulence (ODT) model. ODT is a fully resolved, unsteady stochastic simulation technique. While flow properties reside on a one-dimensional domain, turbulent advection is represented using mapping events whose occurrences are governed by a random process. Due to its reduced spatial dimensionality, ODT achieves major cost reductions compared to three-dimensional (3D) simulations. A comparison to recent direct numerical simulation (DNS) data at moderate Reynolds number (Re = u∞ / v0 = 333, where u∞ and v0 are the free stream and suction velocity, respectively) suggests that the ODT model is capable of reproducing several velocity statistics, i.e. mean velocity and turbulent kinetic energy budgets, while peak turbulent stresses are under-estimated by ODT. Variation of the Reynolds number in the range Re ∈ [333,400,500,1000] shows that ODT can reproduce various trends observed as a result of increased suction in turbulent asymptotic suction boundary layers, i.e. the reduction of Reynolds stresses and enhanced skin friction. While up to Re = 500 our results can be directly compared to recent LES data, the simulation at Re = 1000 is currently not feasible through full 3D simulations, hence ODT may assist the design of future DNS or LES simulations at larger Reynolds numbers.

Numerical study of radiatively induced entrainment.

Numerical simulations using the one-dimensional turbulence (ODT) model are compared to water-tank measurements emulating convection and entrainment in stratiform clouds driven by cloud-top cooling. Measured dependences of the entrainment rate on Richardson number are reproduced. An additional parameter variation suggests more complicated dependences of the entrainment rate than previously anticipated. Uncertainties in the modeling assumptions and in the experimental results are discussed.

DNS of the turbulent cloud-top mixing layer

The turbulent cloud-top mixing layer is studied using direct numerical simulation (DNS). This configuration models the top of stratocumulus clouds and is employed to investigate the role of latent heat effects. A partial description of the turbulent flow that develops when the cloud and the cloud-free air mix under buoyancy reversal conditions is presented in this paper.