scholarly journals Effects of the computational domain size on direct numerical simulations of Taylor-Couette turbulence with stationary outer cylinder

2015 ◽  
Vol 27 (2) ◽  
pp. 025110 ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Numerical Simulations ◽  
Outer Cylinder ◽  
Domain Size ◽  
Direct Numerical Simulations ◽  
Computational Domain ◽  
Taylor Couette

scholarly journals Direct numerical simulations of local and global torque in Taylor–Couette flow up to Re = 30 000

2013 ◽  
Vol 718 ◽  
pp. 398-427 ◽  
Author(s):  
Hannes J. Brauckmann ◽  
Bruno Eckhardt
Keyword(s):  
Numerical Simulations ◽  
Outer Cylinder ◽  
Outer Region ◽  
Direct Numerical Simulations ◽  
Taylor Vortex ◽  
Scaling Exponent ◽  
Transverse Current ◽  
Counter Rotation ◽  
Turbulent Statistics ◽  
Taylor Couette

AbstractThe torque in turbulent Taylor–Couette flows for shear Reynolds numbers $R{e}_{S} $ up to $3\times 1{0}^{4} $ at various mean rotations is studied by means of direct numerical simulations for a radius ratio of $\eta = 0. 71$. Convergence of simulations is tested using three criteria of which the agreement of dissipation values estimated from the torque and from the volume dissipation rate turns out to be most demanding. We evaluate the influence of Taylor vortex heights on the torque for a stationary outer cylinder and select a value of the aspect ratio of $\Gamma = 2$, close to the torque maximum. The local transport resulting in the torque is investigated via the transverse current ${J}^{\omega } $ which measures the transport of angular momentum and can be computed from the velocity field. The typical spatial distribution of the individual convective and viscous contributions to the local torque is analysed for a turbulent flow case. To characterize the turbulent statistics of the transport, probability density functions (p.d.f.s) of local current fluctuations are compared with experimental wall shear stress measurements. P.d.f.s of instantaneous torques reveal a fluctuation enhancement in the outer region for strong counter-rotation. Moreover, we find for simulations realizing the same shear $R{e}_{S} \geq 2\times 1{0}^{4} $ the formation of a torque maximum for moderate counter-rotation with angular velocities ${\omega }_{o} \approx - 0. 4\hspace{0.167em} {\omega }_{i} $. In contrast, for $R{e}_{S} \leq 4\times 1{0}^{3} $ the torque features a maximum for a stationary outer cylinder. In addition, the effective torque scaling exponent is shown to also depend on the mean rotation state. Finally, we evaluate a close connection between boundary-layer thicknesses and the torque.

scholarly journals Taylor–Couette–Poiseuille flow with a weakly permeable inner cylinder: absolute instabilities and selection of global modes

2018 ◽  
Vol 849 ◽  
pp. 741-776
Author(s):  
Nils Tilton ◽  
Denis Martinand
Keyword(s):  
Numerical Simulations ◽  
Poiseuille Flow ◽  
Radial Flow ◽  
Temporal Frequency ◽  
Outer Cylinder ◽  
Global Mode ◽  
Permeable Membrane ◽  
Global Modes ◽  
Taylor Couette ◽  
Base Flows

Variations in the local stability of the flow in a Taylor–Couette cell can be imposed by adding an axial Poiseuille flow and a radial flow associated with one or both of the cylinders being permeable. At a given rotation rate of the inner cylinder, this results in adjacent regions of the flow that can be simultaneously stable, convectively unstable, and absolutely unstable, making this system fit for studying global modes of instability. To this end, building on the existing stability analysis in absolute modes developing over axially invariant base flows, we consider the case of axially varying base flows in systems for which the outer cylinder is impermeable, and the inner cylinder is a weakly permeable membrane through which the radial flow is governed by Darcy’s law. The frameworks of linear and nonlinear global modes are used to describe the instabilities and assess the results of direct numerical simulations using a dedicated pseudospectral method. Three different axially evolving set-ups are considered. In the first, fluid injection occurs along the full inner cylinder. In the second, fluid extraction occurs along the full inner cylinder. Besides its fundamental interest, this set-up is relevant to filtration devices. In the third, fluid flux through the inner cylinder evolves from extraction to injection as cross-flow reversal occurs. In agreement with the global mode analyses, the numerical simulations develop centrifugal instabilities above the predicted critical rotation rates and downstream of the predicted axial locations. The global mode analyses do not fully explain, however, that the instabilities observed in the numerical simulations take the form of axial stacks of wavepackets characterized by jumps of the temporal frequency.

scholarly journals Direct numerical simulations of spiral Taylor–Couette turbulence

2020 ◽  
Vol 887 ◽  
Author(s):  
Pieter Berghout ◽  
Rick J. Dingemans ◽  
Xiaojue Zhu ◽  
Roberto Verzicco ◽  
Richard J. A. M. Stevens ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Taylor Couette ◽  
Image Position

Feedback control of cavity flow oscillations using simple linear models

2012 ◽  
Vol 709 ◽  
pp. 223-248 ◽  
Author(s):  
Simon J. Illingworth ◽  
Aimee S. Morgans ◽  
Clarence W. Rowley
Keyword(s):  
Numerical Simulations ◽  
Linear Models ◽  
Controller Design ◽  
Cavity Flow ◽  
Direct Numerical Simulations ◽  
Feedback Controller ◽  
Computational Domain ◽  
Input Output ◽  
Cavity Flow Oscillations ◽  
The Time Domain

AbstractUsing data from direct numerical simulations, linear models of the compressible flow past a rectangular cavity are found. The emphasis is on forming simple models which capture the input–output behaviour of the system, and which are useful for feedback controller design. Two different approaches for finding a linear model are investigated. The first involves using input–output data of the linearized cavity flow to form a balanced, reduced-order model directly. The second approach is conceptual, and involves modelling each element of the flow physics separately using simple analytical expressions, the parameters of which are chosen based on simulation data at salient points in the cavity’s computational domain. Both models are validated: first in the time domain by comparing their impulse responses to that of the full system in direct numerical simulations; and second in the frequency domain by comparing their frequency responses. Finally, the validity of both linear models is shown most clearly by using them for feedback controller design, and then applying each controller in direct numerical simulations. Both controllers completely eliminate oscillations, and demonstrate the advantages of model-based feedback controllers, even when the models upon which they are based are very simple.

scholarly journals Direct numerical simulations of Taylor–Couette turbulence: the effects of sand grain roughness

2019 ◽  
Vol 873 ◽  
pp. 260-286 ◽  
Author(s):  
Pieter Berghout ◽  
Xiaojue Zhu ◽  
Daniel Chung ◽  
Roberto Verzicco ◽  
Richard J. A. M. Stevens ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Rough Surface ◽  
Open Systems ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Roughness Height ◽  
Taylor Couette ◽  
Logarithmic Layer ◽  
Grain Roughness

Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor–Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from $Ta=1.0\times 10^{7}$(corresponding to $Re_{\unicode[STIX]{x1D70F}}=82$) to $Ta=1.0\times 10^{9}$ ($Re_{\unicode[STIX]{x1D70F}}=635$). We focus on the influence of the roughness height $k_{s}^{+}$ in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from $k_{s}^{+}=5$ up to $k_{s}^{+}=92$. We analyse the global response of the system, expressed both by the dimensionless angular velocity transport $Nu_{\unicode[STIX]{x1D714}}$ and by the friction factor $C_{f}$. An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness $k_{s}^{+}$ is calculated to be $1.33k$, where $k$ is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (VDI-Forsch., vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer $h_{r}$ with $h_{r}=2.78k_{s}$.

scholarly journals Testing the Assumptions Underlying Ocean Mixing Methodologies Using Direct Numerical Simulations

2019 ◽  
Vol 49 (11) ◽  
pp. 2761-2779 ◽  
Author(s):  
J. R. Taylor ◽  
S. M. de Bruyn Kops ◽  
C. P. Caulfield ◽  
P. F. Linden
Keyword(s):  
Numerical Simulations ◽  
Field Measurements ◽  
Direct Numerical Simulations ◽  
Buoyancy Flux ◽  
Theoretical Development ◽  
Computational Domain ◽  
Vertical Profiles ◽  
Stratified Turbulence ◽  
Vertical Diffusivity ◽  
Thorpe Scale

AbstractDirect numerical simulations of stratified turbulence are used to test several fundamental assumptions involved in the Osborn, Osborn–Cox, and Thorpe methods commonly used to estimate the turbulent diffusivity from field measurements. The forced simulations in an idealized triply periodic computational domain exhibit characteristic features of stratified turbulence including intermittency and layer formation. When calculated using the volume-averaged dissipation rates from the simulations, the vertical diffusivities inferred from the Osborn and Osborn–Cox methods are within 40% of the value diagnosed using the volume-averaged buoyancy flux for all cases, while the Thorpe-scale method performs similarly well in the simulation with a relatively large buoyancy Reynolds number (Reb ≃ 240) but significantly overestimates the vertical diffusivity in simulations with Reb < 60. The methods are also tested using a limited number of vertical profiles randomly selected from the computational volume. The Osborn, Osborn–Cox, and Thorpe-scale methods converge to their respective estimates based on volume-averaged statistics faster than the vertical diffusivity calculated directly from the buoyancy flux, which is contaminated with reversible contributions from internal waves. When applied to a small number of vertical profiles, several assumptions underlying the Osborn and Osborn–Cox methods are not well supported by the simulation data. However, the vertical diffusivity inferred from these methods compares reasonably well to the exact value from the simulations and outperforms the assumptions underlying these methods in terms of the relative error. Motivated by a recent theoretical development, it is speculated that the Osborn method might provide a reasonable approximation to the diffusivity associated with the irreversible buoyancy flux.

Role of Klebanoff modes in active flow control of separation: direct numerical simulations

2018 ◽  
Vol 850 ◽  
pp. 954-983 ◽  
Author(s):  
Shirzad Hosseinverdi ◽  
Hermann F. Fasel
Keyword(s):  
Flow Control ◽  
Numerical Simulations ◽  
Active Flow Control ◽  
Low Frequency ◽  
Secondary Instability ◽  
Direct Numerical Simulations ◽  
Striking Difference ◽  
Computational Domain ◽  
Low Levels ◽  
Active Flow

Our previous research has shown that an active flow control strategy using two-dimensional (2-D) harmonic blowing and suction with properly chosen frequency and amplitude can significantly reduce the separation region, delay transition to turbulence and can even relaminarize the flow. How such effective flow control for transition delay and relaminarization is affected by free-stream turbulence (FST) remains an open question. In order to answer this question, highly resolved direct numerical simulations (DNS) are carried out where very low-amplitude isotropic FST fluctuations are introduced at the inflow boundary of the computational domain. With FST the effectiveness of the flow control is not diminished, and the extent of the separated flow region is reduced by the same amount as for the zero FST case. However, a striking difference observed in the DNS is the fact that in the presence of even very low levels of FST, the flow transitions shortly downstream of the reattachment location of the bubble, contrary to the case without FST. It appears that this different behaviour for even very small levels of FST is caused by an interaction between the high-amplitude 2-D disturbances introduced by the flow control forcing and 3-D Klebanoff modes (K-modes) that are generated by the FST. The streamwise elongated streaks due to the K-modes cause a spanwise-periodic modulation of the basic flow and subsequently of the primary 2-D wave. The disturbances associated with this modulation exhibit strong growth and initiate the breakdown process to turbulence. Linear secondary instability investigations with respect to low-frequency 3-D disturbances are carried out based on the linearized Navier–Stokes equations. The response of the forced flow to the low-frequency 3-D disturbances reveals that the time-periodic base flow is unstable with respect to a wide range of 3-D modes. In particular, the wavelength associated with the spanwise spacing of the K-mode falls into the range of, and is in fact very close to, the most unstable 3-D disturbances. Results from the secondary instability analysis and the comparison with DNS results, support the conjecture that the forcing amplitude has a major impact on the onset and amplification rate of the K-modes: lowering the forcing amplitude postpones the onset of the growth of the K-modes and reduces the growth rate of the K-modes for a given FST intensity. The net effect of these two events is a delay of the transition onset. Nevertheless, the instability mechanism that governs the transition process is the same as previously identified, i.e. interaction of the K-mode and 2-D primary wave. Furthermore, for low levels of FST, the amplitude of the low-frequency K-modes scales linearly with the FST intensity in the approach boundary layer up to the secondary instability regime.

scholarly journals The intermediate Rossby number range and two-dimensional–three-dimensional transfers in rotating decaying homogeneous turbulence

2007 ◽  
Vol 587 ◽  
pp. 139-161 ◽  
Author(s):  
LYDIA BOUROUIBA ◽  
PETER BARTELLO
Keyword(s):  
Numerical Simulations ◽  
Three Dimensional ◽  
Domain Size ◽  
Homogeneous Turbulence ◽  
Finite Domain ◽  
Rossby Number ◽  
Computational Domain ◽  
Two Dimensional ◽  
Number Range ◽  
Wide Range

Rotating homogeneous turbulence in a finite domain is studied using numerical simulations, with a particular emphasis on the interactions between the wave and zero-frequency modes. Numerical simulations of decaying homogeneous turbulence subject to a wide range ofbackground rotation rates are presented. The effect of rotation is examined in two finiteperiodic domains in order to test the effect of the size of the computational domain on the results obtained, thereby testing the accurate sampling of near-resonant interactions.We observe a non-monotonic tendency when Rossby number Ro is varied from large values to the small-Ro limit, which is robust to the change of domain size. Three rotation regimes are identified and discussed: the large-, the intermediate-, and the small-Ro regimes. The intermediate-Ro regime is characterized by a positive transfer of energy from wave modes to vortices. The three-dimensional to two-dimensional transfer reaches an initial maximum for Ro ≈ 0.2 and it is associated with a maximum skewness of vertical vorticity in favour of positive vortices. This maximum is also reached at Ro ≈ 0.2. In the intermediate range an overall reduction of vertical energy transfer is observed. Additional characteristic horizontal and vertical scales of this particular rotation regime are presented and discussed.

Sign in / Sign up

Export Citation Format

Share Document