Control of Wall-Bounded Turbulence Through Closed-Loop Wall Transpiration

Many wall-bounded flows of practical relevance are turbulent, including the flows past airplanes and ships. The turbulent motions enhance momentum mixing and, as a result, the drag force on the engineering surface increases, for transportation vessels typically by at least a factor of two compared to laminar flow. Turbulent flow control aimed at drag reduction therefore has the potential to deliver enormous energetic and economic savings, but many challenges remain despite active research for well over a century. The present thesis aims to contribute towards two open questions of the field: first, what are suitable controller design tools for high Reynolds number flows? And second, how does actuation through closed-loop wall transpiration change the flow physics? We investigate aspects of these questions through direct numerical simulation (DNS) and modal analyses of an example control scheme, which is applied to a low Reynolds number turbulent channel flow. The controller is a generalization of the opposition control scheme, and introduces a phase shift between the Fourier transformed sensor measurement and actuator response. The first part of the thesis demonstrates that a low-order model based on the resolvent framework is able to approximate the drag reduction results of DNS over the entire parameter space considered. The model is about two orders of magnitude cheaper to evaluate than DNS at low Reynolds numbers, and we present a strategy based on subsampling of the wave number space and analytical scaling laws that enables model-based flow control design at technologically relevant Reynolds numbers. The second part of the thesis shows that the physics of the controlled flow can be understood from two distinct families of spatial scales, termed streamwise-elongated and spanwise-elongated scales, respectively. Wall transpiration with streamwise-elongated scales attenuates or amplifies the near-wall cycle and therefore leads to drag reduction or increase, depending on the phase shift. In contrast, wall transpiration with spanwise-elongated scales only leads to drag increase, which occurs at positive phase shifts and is due to the appearance of spanwise rollers which largely enhance momentum mixing. Both patterns are robust features of flows with closed-loop wall transpiration, and the present study offers a simple explanation of their origin in terms of phase relations at distinct spatial scales. The findings of this study may set the stage for a unifying framework for various forms of wall transpiration, and implications for future flow control design are discussed.</p

Predicting the response of turbulent channel flow to varying-phase opposition control: Resolvent analysis as a tool for flow control design

The present study evaluates the capabilities of a low-order flow model based on the resolvent analysis of McKeon and Sharma [B. J. McKeon and A. S. Sharma, J. Fluid Mech. 658, 336 (2010)] for the purpose of controller design for drag reduction in wall-bounded turbulent flows. To this end, we first show that the model is able to approximate the change in mean wall shear stress, which is commonly used as measure for drag reduction. We also derive an analytical expression that decomposes the drag reduction in internal flows into terms that can be predicted directly by the model and terms that allow for quantification of model error if high-fidelity data are available. We then show by example of varying-phase opposition control in a low-Reynolds-number turbulent channel flow that the drag reduction predicted by the resolvent model captures the trend observed in direct numerical simulation (DNS) over a wide range of controller parameters. The DNS results confirm the resolvent model prediction that the attainable drag reduction strongly depends on the relative phase between sensor measurement and actuator response, which raises interesting flow physics questions for future studies. The good agreement between the resolvent model and DNS further reveals that resolvent analysis, which at its heart is a linear technique, is able to approximate the response of the full nonlinear system to control. We also show that in order to make accurate predictions the model only needs to resolve a small subset of the DNS wave numbers and that the controlled resolvent modes obey the Reynolds-number scaling laws of the uncontrolled resolvent operator derived by Moarref et al. [R. Moarref et al., J. Fluid Mech. 734, 275 (2013)]. As a consequence, our results suggest that resolvent analysis can provide a suitable flow model to design feedback flow control schemes for the purpose of drag reduction in incompressible wall-bounded turbulent flows even at technologically relevant Reynolds numbers

Nine-Propagator Master Integrals for Massless Three-Loop Form Factors

We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold Mellin-Barnes representation which we use to compute the coefficients of the Laurent expansion in epsilon. Using Riemann zeta functions of up to weight six, we give fully analytic results for one integral; for a second, analytic results for all but the finite term; for the third, analytic results for all but the last two coefficients in the Laurent expansion. The remaining coefficients are given numerically to sufficiently high accuracy for phenomenological applications.Comment: 15 pages, 2 figures. Minor modifications and reference added. Matches published versio

Acute Effects of Psilocybin After Escitalopram or Placebo Pretreatment in a Randomized, Double-Blind, Placebo-Controlled, Crossover Study in Healthy Subjects

The psychedelic psilocybin is being investigated for the treatment of depression and anxiety. Unclear is whether antidepressant treatments interact with psilocybin. The present study used a double-blind, placebo-controlled, crossover design with two experimental test sessions to investigate the response to psilocybin (25 mg) in healthy subjects after pretreatment with escitalopram or placebo. The treatment order was random and counterbalanced. Pretreatment consisted of 10 mg escitalopram daily for 7 days, followed by 20 mg daily for 7 days, including the day of psilocybin administration, or 14 days of placebo pretreatment before psilocybin administration. Psilocybin treatments were separated by at least 16 days. The outcome measures included self-rating scales that evaluated subjective effects, autonomic effects, adverse effects, plasma brain-derived neurotrophic factor (BDNF) levels, electrocardiogram QTc time, whole-blood HTR2A and SCL6A4 gene expression, and pharmacokinetics. Escitalopram pretreatment had no relevant effect on positive mood effects of psilocybin but significantly reduced bad drug effects, anxiety, adverse cardiovascular effects, and other adverse effects of psilocybin compared with placebo pretreatment. Escitalopram did not alter the pharmacokinetics of psilocin. The half-life of psychoactive free (unconjugated) psilocin was 1.8 hours (range 1.1-2.2 hours), consistent with the short duration of action of psilocybin. Escitalopram did not alter HTR2A or SCL6A4 gene expression before psilocybin administration, QTc intervals, or circulating BDNF levels before or after psilocybin administration. Further studies are needed with a longer antidepressant pretreatment time and patients with psychiatric disorders to further define interactions between antidepressants and psilocybin