scholarly journals Optimal energy growth in pulsatile channel and pipe flows

2021 ◽  
Vol 926 ◽  
Author(s):  
Benoît Pier ◽  
Peter J. Schmid
Keyword(s):  
Base Flow ◽  
Parameter Study ◽  
Flow Profile ◽  
Transient Growth ◽  
Pipe Flows ◽  
Pulsation Amplitude ◽  
Flow Features ◽  
Slow Part ◽  
Parabolic Flow ◽  
Pulsation Cycle

Pulsatile channel and pipe flows constitute a fundamental flow configuration with significant bearing on many applications in the engineering and medical sciences. Rotating machinery, hydraulic pumps or cardiovascular systems are dominated by time-periodic flows, and their stability characteristics play an important role in their efficient and proper operation. While previous work has mainly concentrated on the modal, harmonic response to an oscillatory or pulsatile base flow, this study employs a direct–adjoint optimisation technique to assess short-term instabilities, identify transient energy-amplification mechanisms and determine their prevalence within a wide parameter space. At low pulsation amplitudes, the transient dynamics is found to be similar to that resulting from the equivalent steady parabolic flow profile, and the oscillating flow component appears to have only a weak effect. After a critical pulsation amplitude is surpassed, linear transient growth is shown to increase exponentially with the pulsation amplitude and to occur mainly during the slow part of the pulsation cycle. In this latter regime, a detailed analysis of the energy transfer mechanisms demonstrates that the huge linear transient growth factors are the result of an optimal combination of Orr mechanism and intracyclic normal-mode growth during half a pulsation cycle. Two-dimensional sinuous perturbations are favoured in channel flow, while pipe flow is dominated by helical perturbations. An extensive parameter study is presented that tracks these flow features across variations in the pulsation amplitude, Reynolds and Womersley numbers, perturbation wavenumbers and imposed time horizon.

Study of Single Pixel Evaluation for Experimental Measurements in a Microchannel

2006 ◽  
Author(s):  
Han-Sheng Chuang ◽  
Steve T. Wereley ◽  
Lichuan Gui
Keyword(s):  
Image Quality ◽  
Cross Correlation ◽  
Particle Image ◽  
Signal To Noise Ratio ◽  
Experimental Measurements ◽  
Flow Profile ◽  
Particle Image Diameter ◽  
Micro Piv ◽  
Parabolic Flow ◽  
Single Pixel

A newly proposed algorithm named single pixel evaluation (SPE) has been developed to increase the resolution of micro-PIV to its physical limit of one pixel. Despite the SPE is able to improve the resolution significantly in comparison with conventional cross-correlation, some phenomenon are still unknown due to its infancy, resulting in discrepancies between the analytic predictions and the experimental measurements. To provide reliable rules as applying the SPE, an overall inspection of the algorithm's behaviors is essential. This paper investigated five general factors, determining their performances via synthetic particle images subjected to a parabolic flow profile. The factors include particle image quality, particle image density, search radius (SR), particle image displacement, and particle image diameter. The results indicate that the particle image quality behaves the most significantly among the factors. Moreover, the SPE was also compared with the fast Fourier transform based cross-correlation (FFT-CC) under the equivalent signal-to-noise ratio (SNR). The tendencies of optimal values with respect to different factors are revealed in the following text. To complete the study, experiments on a straight microchannel were implemented to verify the observations from the simulations. The measured images which followed the suggested rules show better results than the other ones.

Limits of Parabolic Flow Theory in Microfluidic Particle Separation: A Computational Study

2013 ◽  
Author(s):  
Ryan S. Pawell ◽  
Tracie J. Barber ◽  
David W. Inglis ◽  
Robert A. Taylor
Keyword(s):  
Computational Study ◽  
Lateral Displacement ◽  
Particle Separation ◽  
Flow Profile ◽  
Flow Rates ◽  
Deterministic Lateral Displacement ◽  
Flow Development ◽  
Separation Threshold ◽  
Parabolic Flow ◽  
Size Based Separation

Microfluidic particle separation technologies are useful for enriching rare cell populations for academic and clinical purposes. In order to separate particles based on size, deterministic lateral displacement (DLD) arrays are designed assuming that the flow profile between posts is parabolic or shifted parabolic (depending on post geometry). The design process also assumes the shape of the normalized flow profile is speed-invariant. The work presented here shows flow profile shapes vary, in arrays with circular and triangular posts, from this assumption at practical flow rates (10 < Re < 100). The root-mean-square error (RMSE) of this assumption in the circular post arrays peaked at 0.144. The RMSE in the triangular post array peaked at 0.136. Flow development occurred more rapidly in circular post arrays when compared to triangular post arrays. Additionally, the changes in critical bumping diameter (DCB) the DLD design metric used to calculate the size-based separation threshold were examined for 10 different row shift fractions (FRS). These errors correspond to a DCB that varies as much as 11.7% in the circular post arrays and 15.1% in the triangular post arrays.

Spatial stability analysis of subsonic corrugated jets

2019 ◽  
Vol 876 ◽  
pp. 766-791 ◽  
Author(s):  
F. C. Lajús ◽  
A. Sinha ◽  
A. V. G. Cavalieri ◽  
C. J. Deschamps ◽  
T. Colonius
Keyword(s):  
High Reynolds Number ◽  
Base Flow ◽  
Flow Profile ◽  
Azimuthal Direction ◽  
Instability Mechanism ◽  
Helmholtz Instability ◽  
Circular Jets ◽  
Unstable Solutions ◽  
High Reynolds ◽  
Axis Switching

The linear stability of high-Reynolds-number corrugated jets is investigated by solving the compressible Rayleigh equation linearized about the time-averaged flow field. A Floquet ansatz is used to account for periodicity of this base flow in the azimuthal direction. The origin of multiple unstable solutions, which are known to appear in these non-circular configurations, is traced through gradual perturbations of a parametrized base-flow profile. It is shown that all unstable modes are corrugated jet continuations of the classical Kelvin–Helmholtz modes of circular jets, highlighting that the same instability mechanism, modified by corrugations, leads to the growth of disturbances in such flows. It is found that under certain conditions the eigenvalues may form saddles in the complex plane and display axis switching in their eigenfunctions. A parametric study is also conducted to understand how penetration and number of corrugations impact stability. The effect of these geometric properties on growth rates and phase speeds of the multiple unstable modes is explored, and the results provide guidelines for the development of nozzle configurations that more effectively modify the Kelvin–Helmholtz instability.

Some features of steady separated flow from low speed to hypersonic

2008 ◽  
Vol 112 (1128) ◽  
pp. 109-113
Author(s):  
S. L. Gai
Keyword(s):  
Shear Layer ◽  
Bluff Body ◽  
Separated Flow ◽  
Base Flow ◽  
The Body ◽  
Wake Flow ◽  
Recirculating Flow ◽  
Flow Features ◽  
Hypersonic Speeds ◽  
Low Speeds

Steady non-vortex shedding base flow behind a bluff body is considered. Such a flow is characterised by the flow separation at the trailing edge of the body with an emerging shear layer which reattaches on the axis with strong recompression and recirculating flow bounded by the base, the shear layer, and the axis. Steady wake flows behind a bluff body at low speeds have been studied for more than a century (for example, Kirchhoff; Riabouchinsky). Recently, research on steady bluff body wake flow at low speeds has been reviewed and reinterpreted by Roshko. Roshko has also commented on some basic aspects of steady supersonic base flow following on from Chapman and Korst analyses. In the present paper, we examine the steady base flow features both at low speeds and supersonic speeds in the light of Roshko’s model and expand on some further aspects of base flows at supersonic and hypersonic speeds, not covered by Roshko.

Eigenvalue Sensitivity to Base Flow Variations in Hagen-Poiseuille Flow

2002 ◽  
Author(s):  
Isabella M. Gavarini ◽  
Alessandro Bottaro ◽  
Frans T. M. Nieuwstadt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Transient Growth ◽  
Cylindrical Pipe ◽  
Low Reynolds Numbers ◽  
Parabolic Profile ◽  
Eigenvalue Sensitivity ◽  
The Ideal

Transition in a cylindrical pipe flow still eludes thorough understanding. Most recent advances are based on the concept of transient growth of disturbances, but even this scenario is not fully confirmed by DNS and/or experiments. Based on the fact that even the most carefully conducted experiment is biased by uncertainties, we explore the spatial growth of disturbances developing on top of an almost ideal, axially invariant Poiseuille flow. The optimal deviation of the base flow from the ideal parabolic profile is computed by a variational tecnique, and unstable modes, driven by an inviscid mechanism, are found to exist for very small values of the norm of the deviation, at low Reynolds numbers.

Transient Growth of Three-Dimensional Vortex Perturbations During Near-Parallel Collision With a Circular Cylinder

2006 ◽  
Author(s):  
X. Liu ◽  
J. S. Marshall
Keyword(s):  
Circular Cylinder ◽  
Vortex Core ◽  
Computational Study ◽  
Three Dimensional ◽  
The Body ◽  
Transient Growth ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Features

A computational study is reported that examines the transient growth of three-dimensional flow features for nominally parallel vortex-cylinder interaction problems. We consider a helical vortex with small-amplitude perturbations that is advected onto a circular cylinder whose axis is parallel to the nominal vortex axis. The study assesses the applicability of the two-dimensional flow assumption for parallel vortex-body interaction problems in which the body impinges on the vortex core. The computations are performed using an unstructured finite-volume method for an incompressible flow, with periodic boundary conditions along the cylinder axis. Growth of three-dimensional flow features is quantified by use of a proper-orthogonal decomposition of the Fourier-transformed velocity and vorticity fields in the cylinder azimuthal and axial directions. The interaction is examined for different axial wavelengths and amplitudes of the initial helical waves on the vortex core, and the results for cylinder force are compared to the two-dimensional results. The degree of perturbation amplification as the vortex approaches the cylinder is quantified and shown to be mostly dependent on the dominant axial wavenumber of the perturbation. The perturbation amplification is observed to be greatest for perturbations with axial wavelength of about 1.5 times the cylinder diameter.

scholarly journals Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows

2020 ◽  
Vol 907 ◽  
Author(s):  
Duo Xu ◽  
Baofang Song ◽  
Marc Avila
Keyword(s):  
Transient Growth ◽  
Pipe Flows

Abstract

The transverse force on a drop in an unbounded parabolic flow

1974 ◽  
Vol 62 (1) ◽  
pp. 185-207 ◽  
Author(s):  
Philip R. Wohl ◽  
S. I. Rubinow
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Weber Number ◽  
Lift Force ◽  
Body Force ◽  
The Body ◽  
Flow Profile ◽  
External Fluid ◽  
Parabolic Flow ◽  
Undisturbed Flow

The steady flow in and around a deformable liquid sphere moving in an unbounded viscous parabolic flow and subject to an external body force is calculated for small values of the ratio of the Weber number to the Reynolds number in the creeping-flow regime. It is found that, in addition to the drag force, the drop experiences a force orthogonal to the undisturbed flow direction. When the body force is absent (neutrally buoyant drop), this lift force tends to drive the drop inwards to the axis, where the undisturbed flow velocity is maximum, i.e., towards a position of lower velocity gradient. In the case for which the parabolic flow profile is a Poiseuille flow profile, the lift force is given by the expression. \[ {\bf F}_1 =-6\pi\mu\epsilon U_0\frac{\alpha +\frac{2}{3}}{\alpha + 1}\bigg(\frac{a}{R_0}\bigg)^4{\bf b}F[1+o(\epsilon)]. \] Here a is the radius of the undeformed sphere, R0 is the radial distance from the position of maximum undisturbed flow U0 at the profile axis to the position of zero flow, ε is the ratio of the Weber number to the Reynolds number, given by ε=μU0T−1, where μ is the external fluid viscosity and T is the surface tension of the drop, α is the ratio of the drop and external fluid viscosities, b is the radial vector from the flow axis to the centre of mass of the drop, and F is a function of α and a dimensionless parameter dependent on the body force that is determined in the analysis. Reasonable agreement is found between the observations by Goldsmith & Mason (1962) of the axial drift of liquid drops in Poiseuille flow and the predictions of the theory herein.

Perturbation dynamics in unsteady pipe flows

2007 ◽  
Vol 570 ◽  
pp. 129-154 ◽  
Author(s):  
M. ZHAO ◽  
M. S. GHIDAOUI ◽  
A. A. KOLYSHKIN
Keyword(s):  
Growth Mechanism ◽  
Flow Instability ◽  
Initial Conditions ◽  
Laminar Flows ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Transient Growth ◽  
Energy Growth ◽  
Long Time ◽  
Short Time

This paper deals with perturbed unsteady laminar flows in a pipe. Three types of flows are considered: a flow accelerated from rest; a flow in a pipe generated by the controlled motion of a piston; and a water hammer flow where the transient is generated by the instantaneous closure of a valve. Methods of linear stability theory are used to analyse the behaviour of small perturbations in the flow. Since the base flow is unsteady, the linearized problem is formulated as an initial-value problem. This allows us to consider arbitrary initial conditions and describe both short-time and long-time evolution of the flow. The role of initial conditions on short-time transients is investigated. It is shown that the phenomenon of transient growth is not associated with a certain type of initial conditions. Perturbation dynamics is also studied for long times. In addition, optimal perturbations, i.e. initial perturbations that maximize the energy growth, are determined for all three types of flow discussed. Despite the fact that these optimal perturbations, most probably, will not occur in practice, they do provide an upper bound for energy growth and can be used as a point of reference. Results of numerical simulation are compared with previous experimental data. The comparison with data for accelerated flows shows that the instability cannot be explained by long-time asymptotics. In particular, the method of normal modes applied with the quasi-steady assumption will fail to predict the flow instability. In contrast, the transient growth mechanism may be used to explain transition since experimental transition time is found to be in the interval where the energy of perturbation experiences substantial growth. Instability of rapidly decelerated flows is found to be associated with asymptotic growth mechanism. Energy growth of perturbations is used in an attempt to explain previous experimental results. Numerical results show satisfactory agreement with the experimental features such as the wavelength of the most unstable mode and the structure of the most unstable disturbance. The validity of the quasi-steady assumption for stability studies of unsteady non-periodic laminar flows is discussed.

scholarly journals Second-order sensitivity of parallel shear flows and optimal spanwise-periodic flow modifications

2015 ◽  
Vol 782 ◽  
pp. 491-514 ◽  
Author(s):  
E. Boujo ◽  
A. Fani ◽  
F. Gallaire
Keyword(s):  
Temporal Stability ◽  
Mixing Layer ◽  
Plane Channel ◽  
Second Order ◽  
Base Flow ◽  
Periodic Flow ◽  
Transient Growth ◽  
Flow Modification ◽  
Beta 2 ◽  
Sensitivity Operator

The question of optimal spanwise-periodic modification for the stabilisation of spanwise-invariant flows is addressed. A second-order sensitivity analysis is conducted for the linear temporal stability of parallel flows $U_{0}$ subject to small-amplitude spanwise-periodic modification ${\it\epsilon}U_{1},{\it\epsilon}\ll 1$. It is known that spanwise-periodic flow modifications have a quadratic effect on stability properties, i.e. the first-order eigenvalue variation is zero, hence the need for a second-order analysis. A second-order sensitivity operator is computed from a one-dimensional calculation, which allows one to predict how eigenvalues are affected by any flow modification $U_{1}$, without actually solving for modified eigenvalues and eigenmodes. Comparisons with full two-dimensional stability calculations in a plane channel flow and in a mixing layer show excellent agreement. Next, optimisation is performed on the second-order sensitivity operator: for each eigenmode streamwise wavenumber ${\it\alpha}_{0}$ and base flow modification spanwise wavenumber ${\it\beta}$, the most stabilising/destabilising profiles $U_{1}$ are computed, together with lower/upper bounds for the variation in leading eigenvalue. These bounds increase like ${\it\beta}^{-2}$ as ${\it\beta}$ goes to zero, thus yielding a large stabilising potential. However, three-dimensional modes with wavenumbers ${\it\beta}_{0}=\pm {\it\beta}$, $\pm {\it\beta}/2$ are destabilised, and therefore larger control wavenumbers should be preferred. The most stabilising $U_{1}$ optimised for the most unstable streamwise wavenumber ${\it\alpha}_{0,max}$ has a stabilising effect on modes with other ${\it\alpha}_{0}$ values too. Finally, the potential of transient growth to amplify perturbations and stabilise the flow is assessed with a combined optimisation. Assuming a separation of time scales between the fast unstable mode and the slow transient evolution of the optimal perturbations, combined optimal perturbations that achieve the best balance between transient linear amplification and stabilisation of the nominal shear flow are determined. In the mixing layer with ${\it\beta}\leqslant 1.5$, these combined optimal perturbations appear similar to transient growth-only optimal perturbations, and achieve a more efficient overall stabilisation than optimal spanwise-periodic and spanwise-invariant modifications computed for stabilisation only. These results are consistent with the efficiency of streak-based control strategies.

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