Bettina Frohnapfel

Interpretation of the mechanism associated with turbulent drag reduction in terms of anisotropy invariants

A central goal of flow control is to minimize the energy consumption in turbulent flows and nowadays the best results in terms of drag reduction are obtained with the addition of long-chain polymers. This has been found to be associated with increased anisotropy of turbulence in the near-wall region. Other drag reduction mechanisms are analysed in this respect and it is shown that close to the wall highly anisotropic states of turbulence are commonly found. These findings are supported by results of direct numerical simulations which display high drag reduction effects of over 30% when only a few points inside the viscous sublayer are forced towards high anisotropy.

On the Mechanism Responsible for Turbulent Drag Reduction by Dilute Addition of High Polymers: Theory, Experiments, Simulations, and Predictions

Turbulent drag reduction by dilute addition of high polymers is studied by considering local stretching of the molecular structure of a polymer by small-scale turbulent motions in the region very close to the wall. The stretching process is assumed to restructure turbulence at small scales by forcing these to satisfy local axisymmetry with invariance under rotation about the axis aligned with the main flow. It can be shown analytically that kinematic constraints imposed by local axisymmetry force turbulence near the wall to tend towards the one-component state and when turbulence reaches this limiting state it must be entirely suppressed across the viscous sublayer. For the limiting state of wall turbulence, the statistical dynamics of the turbulent stresses, constructed by combining the two-point correlation technique and invariant theory, suggest that turbulent drag reduction by homogeneously distributed high polymers, cast into the functional space which emphasizes the anisotropy of turbulence, resembles the process of reverse transition from the turbulent state towards the laminar flow state. These findings are supported by results of direct numerical simulations of wall-bounded turbulent flows of Newtonian and non-Newtonian fluids and by experiments carried out, under well-controlled laboratory conditions, in a refractive index-matched pipe flow facility using state-of-the art laser-Doppler anemometry. Theoretical considerations based on the elastic behavior of a polymer and spatial intermittency of turbulence at small scales enabled quantitative estimates to be made for the relaxation time of a polymer and its concentration that ensure maximum drag reduction in turbulent pipe flows, and it is shown that predictions based on these are in very good agreement with available experimental data.

The dielectric breakdown limit of silicone dielectric elastomer actuators

Soft silicone elastomers are used in a generation of dielectric elastomer actuators (DEAs) with improved actuation speed and durability compared to the commonly used, highly viscoelastic polyacrylate 3M VHB™ films. The maximum voltage-induced stretch of DEAs is ultimately limited by their dielectric breakdown field strength. We measure the dependence of dielectric breakdown field strength on thickness and stretch for a silicone elastomer, when voltage-induced deformation is prevented. The experimental results are combined with an analytic model of equi-biaxial actuation to show that accounting for variable dielectric field strength results in different values of optimal pre-stretch and thickness that maximize the DEA actuation.

Experimental investigations of turbulent drag reduction by surface-embedded grooves

Consideration of near-wall turbulence in the functional space that emphasizes the level of anisotropy of the velocity fluctuations not only provides an understanding of the causative physics behind remarkable effects of turbulent drag reduction, but also leads to the logical design of a surface topology which is shown experimentally to be capable of producing a significant reduction of viscous drag which far exceeds what has been achieved so far.

Money versus Time: Evaluation of Flow Control in Terms of Energy Consumption and Convenience

Flow control with the goal of reducing the skin friction drag on the fluid-solid interface is an active fundamental research area, motivated by its potential for significant energy savings and reduced emissions in the transport sector. Customarily, the performance of drag reduction techniques in internal flows is evaluated under two alternative flow con- ditions, i.e. at constant mass flow rate or constant pressure gradient. Successful control leads to reduction of drag and pumping power within the former approach, whereas the latter leads to an increase of the mass flow rate and pumping power. In practical applications, however, money and time define the flow control challenge: a compromise between the energy expenditure (money) and the corresponding convenience (flow rate) achieved with that amount of energy has to be reached so as to accomplish a goal which in general depends on the specific application. Based on this idea, we derive two di- mensionless parameters which quantify the total energy consumption and the required time (convenience) for transporting a given volume of fluid through a given duct. Perfor- mances of existing drag reduction strategies as well as the influence of wall roughness are re-evaluated within the present framework; how to achieve the (application-dependent) optimum balance between energy consumption and convenience is addressed. It is also shown that these considerations can be extended to external flows.

A comparison of opposition control in turbulent boundary layer and turbulent channel flow

A comparison between classical opposition control applied in the configuration of a fully developed turbulent channel flow and applied locally in a spatially developing turbulent boundary layer is presented. It is found that the control scheme yields similar drag reduction rates if compared at the same friction Reynolds numbers. However, a detailed analysis of the dynamical contributions to the skin friction coefficient reveals significant differences in the mechanism behind the drag reduction. While drag reduction in turbulent channel flow is entirely based on the attenuation of the Reynolds shear stress, the modification of the spatial flow development is essential for the turbulent boundary layer in terms of achievable drag reduction. It is shown that drag reduction due to this spatial development contribution becomes more pronounced with increasing Reynolds number (up to Reτ = 660, based on friction velocity and boundary layer thickness) and even exceeds drag reduction due to attenuation of the Reynol...

Prediction of turbulence control for arbitrary periodic spanwise wall movement

In order to generalize the well-known spanwise-oscillating-wall technique for drag reduction, non-sinusoidal oscillations of a solid wall are considered as a means to alter the skin-friction drag in a turbulent channel flow. A series of direct numerical simulations is conducted to evaluate the control performance of nine different temporal waveforms, in addition to the usual sinusoid, systematically changing the wave amplitude and the period for each waveform. The turbulent average spanwise motion is found to coincide with the laminar Stokes solution that is constructed, for the generic waveform, through harmonic superposition. This allows us to define and compute, for each waveform, a new penetration depth of the Stokes layer which correlates with the amount of turbulent drag reduction, and eventually to predict both turbulent drag reduction and net energy saving rate for arbitrary waveforms. Among the waveforms considered, the maximum net energy saving rate is obtained by the sinusoidal wave at its optimal amplitude and period. However, the sinusoid is not the best waveform at every point in the parameter space. Our predictive tool offers simple guidelines to design waveforms that outperform the sinusoid for given (suboptimal) amplitude and period of oscillation. This is potentially interesting in view of applications, where physical limitations often preclude the actuator to reach its optimal operating conditions.

Does the choice of the forcing term affect flow statistics in DNS of turbulent channel flow

We seek possible statistical consequences of the way a forcing term is added to the Navier–Stokes equations in the Direct Numerical Simulation (DNS) of incompressible channel flow. Simulations driven by constant flow rate, constant pressure gradient and constant power input are used to build large databases, and in particular to store the complete temporal trace of the wall-shear stress for later analysis. As these approaches correspond to different dynamical systems, it can in principle be envisaged that these differences are reflect by certain statistics of the turbulent flow field. The instantaneous realizations of the flow in the various simulations are obviously different, but, as expected, the usual one-point, one-time statistics do not show any appreciable difference. However, the PDF for the fluctuations of the streamwise component of wall friction reveals that the simulation with constant flow rate presents lower probabilities for extreme events of large positive friction. The low probability value of such events explains their negligible contribution to the commonly computed statistics; however, the very existence of a difference in the PDF demonstrates that the forcing term is not entirely uninfluential. Other statistics for wall-based quantities (the two components of friction and pressure) are examined; in particular spatio-temporal autocorrelations show small differences at large temporal separations, where unfortunately the residual statistical uncertainty is still of the same order of the observed difference. Hence we suggest that the specific choice of the forcing term does not produce important statistical consequences, unless one is interested in the strongest events of high wall friction, that are underestimated by a simulation run at constant flow rate.

Secondary vortices over surfaces with spanwise varying drag

ABSTRACTA spanwise heterogeneity of streamwise drag is known to lead to the formation of large secondary motions of Prandtls second kind. Based on the data sets extracted from direct numerical simulations (DNS) of fully developed turbulent channel flow where streamwise stripes of free-slip surface with varying spanwise extension are introduced, we investigate the topological structure of the secondary motions. We find a complex restructuring of the secondary motion with increasing extent of free-slip/no-slip region where the width of the free-slip region in viscous units appears to be one important governing parameter for the vortex formation. The most striking feature of this restructuring is a change in the rotational direction of the major vortex pair such that the related high- and low-momentum pathways are found at different locations. The present results reveal that the spanwise inhomogeneity of the Reynolds stress distribution is strongly related to the observed change of rotational direction. In ...

Numerical simulation of the turbulent convective buoyant flow of sodium over a backward- facing step

A forced convective and a buoyancy-aided turbulent liquid sodium flow over a backward-facing step with a constant heat flux applied on the indented wall is simulated. Linear eddy viscosity models are used for the Reynolds stresses. Turbulent heat fluxes are modelled with a single gradient diffusion hypotheses with two different approaches to evaluate the turbulent Prandtl number. Moreover, the influence of turbulence on heat transfer to sodium is also assessed through simulations with zero turbulent thermal diffusivity. The results are compared with DNS data from literature. The velocity and turbulent kinetic energy profiles predicted by all models are in good agreement with the DNS data. The local Nusselt number trend is qualitatively well captured, however, its magnitude is underestimated by all models for the mixed convection case. For forced convection, the heat transfer is overestimated by all heat flux models. The simulation with neglected turbulent heat transfer shows the best overall agreement for the forced convection case. For the mixed convection best agreement is obtained using a correlation to locally evaluate the turbulent thermal diffusivity.