Sara Delport

Constrained optimization of turbulent mixing-layer evolution

Upstream flow conditions have a large impact on mixing in shear layers. Optimizing these flow conditions can significantly improve mixing effectiveness. We focus on the evolution of a mixing layer in a temporal framework using direct numerical simulations, and optimize the initial disturbances on the layer such that maximal mixing is achieved after a selected simulation time horizon. A gradient-based optimization strategy is used, which employs adjoint-based gradient calculations formulated in a continuous framework. This allows us to limit disk storage needed for the adjoint simulation. We further concentrate on algorithms which impose the necessary energy and continuity constraints on the initial perturbations. For the continuity constraints, parameter elimination is used. For the energy constraint two methods are compared: the gradient projection and the augmented Lagrangian. Optimization with the gradient projection method is shown to be the more robust methodology. We found that the augmented Lagrangian method is very sensitive to small gradient inconsistencies which originate from the adjoint-based gradient calculation. Finally, optimization results are presented for two different time windows T = 20 and 40, using five different cost functionals. These are based on momentum thickness, turbulent kinetic energy, mean-flow kinetic energy, total kinetic energy, and enstrophy. It is found that the first three cost functionals lead to large-scale mixing with 2D vortex structures and virtually no diffusion, while the last two promote small-scale structures in the flow.

Maximizing dissipation in a turbulent shear flow by optimal control of its initial state

Turbulent shear flows are known to evolve self-similar at sufficiently high Reynolds numbers. In this regime, flow properties remain constant when normalized with local large-scale reference values. Dissipation of turbulent energy occurs at small scales. Thus, controls which increase dissipation levels in a shear flow may lose their effectiveness once the shear flow attains self-similar behavior governed by large-scale motion. In the current work, we investigate the optimal control of kinetic-energy dissipation in a temporally evolving turbulent mixing layer, with controls acting on its initial condition. Gradient-based optimization is used, relying on direct numerical simulations, and adjoint formulations for the determination of the gradients. Focus is on long optimization time windows T up to 160 nondimensional time units. First we investigate the optimal controls which maximize the total energy dissipation over a simulation time window. For increasing T, optimal controls are found to become also optim...

Collector Pressure Losses in Micro Heat Exchangers

As collector losses are expected to play a crucial role in micro heat exchangers, an experimental method is developed to determine these losses. Experiments are performed on a micro heat exchanger consisting of 42 parallel microchannels positioned in a 6 by 7 matrix, with hydraulic diameters in the range of 260-280 mum. The proposed method is successfully applied. From the experimental results it can be concluded that the pressure drop of a small collector performs according to classical correlations. However, in a wider collector design the pressure drop clearly deviates from macro scale behaviour

Optimization of long-term mixing in a turbulent mixing layer

We focus on the enhancement of mixing in a mixing layer using a combination of adjointbased optimization and DNS. The mixing of momentum in a temporal mixing layer is considered, where small initial perturbations on the mean velocity field are optimized to reach a well-mixed turbulent state at the end of the simulation time window. Optimization cases are presented for 6 different optimization time horizons. Based on this, the sensitivity of the mixing-layer flow properties to the initial controls is investigated, including the behavior for long time windows, for which the optimized layer seems to converge to a selfsimilar state much faster than usually reported in literature.

The effect of noise on optimal perturbations for turbulent mixing

The evolution of a mixing layer is very sensitive to upstream flow conditions (Moser and Rogers, 1993). We optimize the initial flow conditions of a temporal mixing layer. We use this case as a substitute experiment to study how long flow control can affect the evolution of the mixing layer solution. In earlier work, we showed that optimization of the initial condition can be used to, e.g. increase the rate of kinetic energy dissipation at the end of a selected optimization time window significantly (Delport et al., 2009). The current paper focusses on longer time windows and addresses the robustness of the optima in presence of white noise.

Optimization of Turbulent Mixing Restricted by Linear and Nonlinear Constraints

The mixing in a temporal mixing layer after a selected simulation time horizon is maximized by optimizing the initial disturbances on the mean velocity field. We concentrate on algorithms which impose the necessary energy and continuity constraints on the initial disturbances. A constrained optimization method is selected and applied to five different cost functionals.