304 research outputs found
The role of non-uniqueness in the development of vortex breakdown in tubes
Numerical solutions of viscous, swirling flows through circular pipes of constant radius and circular pipes with throats have been obtained. Solutions were computed for several values of vortex circulation, Reynolds number and throat/inlet area ratio, under the assumptions of steady flow, rotational symmetry and frictionless flow at the pipe wall. When the Reynolds number is sufficiently large, vortex breakdown occurs abruptly with increased circulation as a result of the existence of non-unique solutions. Solution paths for Reynolds numbers exceeding approximately 1000 are characterized by an ensemble of three inviscid flow types: columnar (for pipes of constant radius), soliton and wavetrain. Flows that are quasi-cylindrical and which do not exhibit vortex breakdown exist below a critical circulation, dependent on the Reynolds number and the throat/inlet area ratio. Wavetrain solutions are observed over a small range of circulation below the critical circulation, while above the critical value, wave solutions with large regions of reversed flow are found that are primarily solitary in nature. The quasi-cylindrical (QC) equations first fail near the critical value, in support of Hall's theory of vortex breakdown (1967). However, the QC equations are not found to be effective in predicting the spatial position of the breakdown structure
Supercritical transition to turbulence in an inertially-driven von Karman closed flow
We study the transition from laminar flow to fully developed turbulence for
an inertially-driven von Karman flow between two counter-rotating large
impellers fitted with curved blades over a wide range of Reynolds number (100 -
1 000 000). The transition is driven by the destabilisation of the azimuthal
shear-layer, i.e., Kelvin-Helmholtz instability which exhibits
travelling/drifting waves, modulated travelling waves and chaos below the
emergence of a turbulent spectrum. A local quantity -the energy of the velocity
fluctuations at a given point- and a global quantity -the applied torque- are
used to monitor the dynamics. The local quantity defines a critical Reynolds
number Rec for the onset of time-dependence in the flow, and an upper
threshold/crossover Ret for the saturation of the energy cascade. The
dimensionless drag coefficient, i.e., the turbulent dissipation, reaches a
plateau above this finite Ret, as expected for a "Kolmogorov"-like turbulence
for Re -> infinity. Our observations suggest that the transition to turbulence
in this closed flow is globally supercritical: the energy of the velocity
fluctuations can be considered as an order parameter characterizing the
dynamics from the first laminar time-dependence up to the fully developed
turbulence. Spectral analysis in temporal domain moreover reveals that almost
all of the fluctuations energy is stored in time-scales one or two orders of
magnitude slower than the time-scale based on impeller frequency
Reduced order modeling of fluid flows: Machine learning, Kolmogorov barrier, closure modeling, and partitioning
In this paper, we put forth a long short-term memory (LSTM) nudging framework
for the enhancement of reduced order models (ROMs) of fluid flows utilizing
noisy measurements. We build on the fact that in a realistic application, there
are uncertainties in initial conditions, boundary conditions, model parameters,
and/or field measurements. Moreover, conventional nonlinear ROMs based on
Galerkin projection (GROMs) suffer from imperfection and solution instabilities
due to the modal truncation, especially for advection-dominated flows with slow
decay in the Kolmogorov width. In the presented LSTM-Nudge approach, we fuse
forecasts from a combination of imperfect GROM and uncertain state estimates,
with sparse Eulerian sensor measurements to provide more reliable predictions
in a dynamical data assimilation framework. We illustrate the idea with the
viscous Burgers problem, as a benchmark test bed with quadratic nonlinearity
and Laplacian dissipation. We investigate the effects of measurements noise and
state estimate uncertainty on the performance of the LSTM-Nudge behavior. We
also demonstrate that it can sufficiently handle different levels of temporal
and spatial measurement sparsity. This first step in our assessment of the
proposed model shows that the LSTM nudging could represent a viable realtime
predictive tool in emerging digital twin systems
A Near-Wall Reynolds-Stress Closure without Wall Normals
With the aid of near-wall asymptotic analysis and results of direct numerical simulation, a new near-wall Reynolds stress model (NNWRS) is formulated based on the SSG high-Reynolds-stress model with wall-independent near-wall corrections. Only one damping function is used for flows with a wide range of Reynolds numbers to ensure that the near-wall modifications diminish away from the walls. The model is able to reproduce complicated flow phenomena induced by complex geometry, such as flow recirculation, reattachment and boundary-layer redevelopment in backward-facing step flow and secondary flow in three-dimensional square duct flow. In simple flows, including fully developed channel/pipe flow, Couette flow and boundary-layer flow, the wall effects are dominant, and the NNWRS model predicts less degree of turbulent anisotropy in the near-wall region compared with a wall-dependent near-wall Reynolds Stress model (NWRS) developed by So and colleagues. The comparison of the predictions given by the two models rectifies the misconception that the overshooting of skin friction coefficient in backward-facing step flow prevalent in those near-wall, models with wall normal is caused by he use of wall normal
Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows
We find three types of steady solutions and remarkable flow pattern
transitions between them in a two-dimensional wavy-walled channel for low to
moderate Reynolds (Re) and Weissenberg (Wi) numbers using direct numerical
simulations with spectral element method. The solutions are called
"convective", "transition", and "elastic" in ascending order of Wi. In the
convective region in the Re-Wi parameter space, the convective effect and the
pressure gradient balance on average. As Wi increases, the elastic effect
becomes suddenly comparable and the first transition sets in. Through the
transition, a separation vortex disappears and a jet flow induced close to the
wall by the viscoelasticity moves into the bulk; The viscous drag significantly
drops and the elastic wall friction rises sharply. This transition is caused by
an elastic force in the streamwise direction due to the competition of the
convective and elastic effects. In the transition region, the convective and
elastic effects balance. When the elastic effect dominates the convective
effect, the second transition occurs but it is relatively moderate. The second
one seems to be governed by so-called Weissenberg effect. These transitions are
not sensitive to driving forces. By the scaling analysis, it is shown that the
stress component is proportional to the Reynolds number on the boundary of the
first transition in the Re-Wi space. This scaling coincides well with the
numerical result.Comment: 33pages, 23figures, submitted to Physical Review
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