Highly turbulent Taylor-Couette flow: direct numerical simulations

Turbulence is all around us. Even if we are familiar with every day instances of turbulence, like the smoke coming out of a chimney, it remains a not-well-understood phenomenum. As it is impossible to fully simulate turbulence to precisely take into account its effect, models must be used. These rely on a series of assumptions about the characteristics of turbulence, which have been checked in diverse canonical flows.\ud \ud One of the flows which remains relatively unexplored is Taylor-Couette (TC) flow. TC flow is the flow in a fluid layer between two coaxial and independently rotating cylinders. In this thesis, we numerically simulate TC flow to explore the behaviour of TC flow at high Reynolds numbers (high turbulence).\ud \ud The thesis starts with the development of a highly parallel computer code, which is demonstrated to have adequate performance up to sixty-four thousand cores. Other new numerical strategies to deal with the effect of temperature, or salinity on the flow are also detailed in the thesis.\ud \ud After this, the thesis focuses on the physics of TC flow. Three things are explored: First, the behaviour of highly turbulent TC flow, and how it transitions to this “ultimate" regime, which is expected to be similar to that found in astro- and geo-physical flows is studied. The nature of turbulence in accretion disks is also explored in this context.\ud \ud Second, the existence of an optimal transport, i.e. a maxima in the torque required to rotate the cylinders for a given shear rate as a function of the ratio between the rotation rates of both cylinders is also analysed. This phenomena was earlier observed in experiments, but remained unexplained. Simulations have allowed us to unravel the physics behind this process in more detail.\ud \ud Last, the universality of turbulence was explored. Earlier experiments provided indication that the turbulence in TC flow appeared to be of a slightly different nature to that seen in pipes and channels. In the thesis, this is further explored, and the reasons behind these discrepancies are elucidated

The effect of modulated driving on non-rotating and rotating turbulent plane Couette flow

Direct numerical simulations of turbulent non-rotating and rotating plane Couette flow with a periodically modulated plate velocity are conducted to study the effect of modulated forcing on turbulent shear flows. The time-averaged shear Reynolds number is fixed at Re-s = 3 x 10(4), which results in a frictional Reynolds number of approximately Re-tau approximate to 400. The modulating frequency is varied in the range Wo is an element of (20, 200), while the modulating amplitude is kept fixed at 10 % of the shear velocity except to demonstrate that varying this parameter has minimal effect. The resulting shear at the plates is found to be independent of the forcing frequency, and equal to the non-modulated baseline. For the non-rotating simulations, two clear flow regions can be seen: a near-wall region that follows Stokes' theoretical solution, and a bulk region that behaves similar to Stokes' solutions but with an increased effective viscosity. For high driving frequencies, the amplitude response follows the scaling laws for modulated turbulence of von der Heydt et al. (Phys. Rev. E, vol. 67, 2003, 046308). Cyclonic rotation is not found to modify the system's behaviour in a substantial way, but anti-cyclonic rotation changes significantly the system's response to periodic forcing. We find that the persistent axial inhomogeneities introduced by mild anti-cyclonic rotation make it impossible to measure the propagation of the modulation adequately, while stronger anti-cyclonic rotation creates regions where the modulation travels instantaneously

Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow

Direct numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of {Re_i=10^5} for a radius ratio of {\eta=r_i/r_o=0.714} between the inner and outer cylinder. With increasing {Re_i}, the flow undergoes transitions between three different regimes: (i) a flow dominated by large coherent structures, (ii) an intermediate transitional regime, and (iii) a flow with developed turbulence. In the first regime the large--scale rolls completely drive the meridional flow while in the second one the coherent structures recover only on average. The presence of a mean flow allows for the coexistence of laminar and turbulent boundary layer dynamics. In the third regime the mean flow effects fade away and the flow becomes dominated by plumes. The effect of the local driving on the azimuthal and angular velocity profiles is quantified, in particular we show when and where those profiles develop.Comment: 22 pages, submitted to Po

A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with ad- hoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors

Visual Analysis of Spatia-temporal Relations of Pairwise Attributes in Unsteady Flow

Despite significant advances in the analysis and visualization of unsteady flow, the interpretation of it’s behavior still remains a challenge.In this work, we focus on the linear correlation and non-linear dependency of different physical attributes of unsteady flows to aid theirstudy from a new perspective. Specifically, we extend the existing spatial correlation quantification, i.e. the Local Correlation Coefficient(LCC), to the spatio-temporal domain to study the correlation of attribute-pairs from both the Eulerian and Lagrangian views. To studythe dependency among attributes, which need not be linear, we extend and compute the mutual information (MI) among attributes overtime. To help visualize and interpret the derived correlation and dependency among attributes associated with a particle, we encodethe correlation and dependency values on individual pathlines. Finally, to utilize the correlation and MI computation results to identifyregions with interesting flow behavior, we propose a segmentation strategy of the flow domain based on the ranking of the strengthof the attributes relations. We have applied our correlation and dependency metrics to a number of 2D and 3D unsteady flows withvarying spatio-temporal kernel sizes to demonstrate and assess their effectiveness

Optimal Taylor-Couette flow: Radius ratio dependence

Taylor-Couette flow with independently rotating inner (i) and outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio {\eta} on the system response. Numerical simulations reach Reynolds numbers of up to Re_i=9.5 x 10^3 and Re_o=5x10^3, corresponding to Taylor numbers of up to Ta=10^8 for four different radius ratios {\eta}=r_i/r_o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T^3C) setup, reach Reynolds numbers of up to Re_i=2x10^6$ and Re_o=1.5x10^6, corresponding to Ta=5x10^{12} for {\eta}=0.714-0.909. Effective scaling laws for the torque J^{\omega}(Ta) are found, which for sufficiently large driving Ta are independent of the radius ratio {\eta}. As previously reported for {\eta}=0.714, optimum transport at a non-zero Rossby number Ro=r_i|{\omega}_i-{\omega}_o|/[2(r_o-r_i){\omega}_o] is found in both experiments and numerics. Ro_opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between {Ta\sim3\cdot10^8} and {Ta\sim10^{10}}, Ro_opt saturates to an asymptotic {\eta}-dependent value. Theoretical predictions for the asymptotic value of Ro_{opt} are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.Comment: Submitted to JFM, 28 pages, 17 figure

Effects of the computational domain size on DNS of Taylor-Couette turbulence with stationary outer cylinder

In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the computational domain (“box”) size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to η = ri/ro = 0.909. The outer cylinder was kept stationary, while the inner rotated at a Reynolds number Rei = 105. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is found to play a minor role in the simulations, as the boxes are large enough. For all boxes studied, the spectra do not reach a box independent maximum

Prácticas Mecánica de Fluidos II GIA Curso 2022-3

Colección de las seis prácticas propuestas a los estudiantes de Mecánica de Fluidos II del Grado de Ingenería Aeronáutica en el curso 2022-23. Estan hechas para cubrir un temario básico que les lleve desde la solución de ecuaciones diferenciales ordinarias, a familiarizarse con limitadores de flujo, métodos iterativos y otras herramientas avanzadas.PDF de seis página