Basic Steady State Research Articles

A data-driven approach to guide supersonic impinging jet control

A data-driven framework using snapshots of an uncontrolled flow is proposed to identify, and subsequently demonstrate, effective control strategies for different objectives in supersonic impinging jets. The open-loop, feed-forward control approach, based on a dynamic mode decomposition reduced-order model (DMD-ROM), computes forcing receptivity in an economical manner by projecting flow and actuator-specific forcing snapshots onto a reduced subspace and then evolving the dynamics forwards in time. Since it effectively determines a linear response around the unsteady flow in the time domain, the method differs materially from typical techniques that use steady basic states, such as stability or input–output approaches that employ linearized Navier–Stokes operators in the frequency domain. The method presented naturally accounts for factors inherent to the snapshot basis, including configuration complexity and flow parameters such as Reynolds number. Furthermore, gain metrics calculated in the reduced subspace facilitate rapid assessments of flow sensitivities to a wide range of forcing parameters, from which optimal actuator inputs may be selected and results confirmed in scale-resolved simulations or experiments. The DMD-ROM approach is demonstrated from two different perspectives. The first concerns asymptotic feedback resonance, where the effects of harmonic pressure forcing are estimated and verified with nonlinear simulations using a blowing–suction actuator. The second examines time-local behaviour within critical feedback events, where the phase of actuation becomes important. For this, a conditional space–time mode is used to identify the optimal forcing phase that minimizes convective instability growth within the resonance cycle.

A passive, neural correlate of verbal fluency in Mild Cognitive Impairment using Fastball neurocognitive assessment

AbstractBackgroundFastball provides a passive and objective measure of an individual’s ability to discriminate between different visual categories using Fast Periodic Visual Stimulation and EEG. Our previous work adapted this approach to assess recognition memory in Alzheimer’s disease (Stothart et al., Brain, 2021). This research builds on previous findings by expanding the range of cognitive functions assessed to include visuo‐perceptual performance, and working with patients in an earlier stage of dementia, i.e., Mild Cognitive Impairment (MCI). The aim was to determine whether Fastball responses are sensitive to visuo‐perceptual performance in the early stages of dementia (MCI).MethodAll EEG data were collected in patients' homes using low‐cost, portable systems. Healthy older adult controls (n = 56, ACE‐III = 96 +‐ 6) and MCI patients (n = 50, ACE‐III = 82 +‐ 21) completed a battery of Fastball and neuropsychological tasks (ACE‐III, Freiburg visual acuity) designed to assess visuo‐perceptual performance. We created a letter recognition Fastball task using diffeomorphically scrambled letters as standards and whole letters as oddballs, see Figure 1.ResultA one‐way (Group; Old vs MCI) ANCOVA, controlling for basic steady state magnitude, was conducted to test for differences in oddball responses. Controls had significantly increased oddball responses compared with MCI patients (F (1,103) = 9.61, p = .003, d = 0.48). Oddball responses did not correlate with any neuropsychological measure of vision, but correlated strongly with verbal fluency performance as measured by the ACE‐III, (MCI patients (r(48) = .46, p = .001), controls (r(54) = .34, p = .01)), see Figure 2. There were no correlations between oddball responses and any other neuropsychological measure.ConclusionThese results were not anticipated as we originally hypothesised that oddball responses would correlate with visual performance. Instead, the specific relationship with verbal fluency performance indicates that the Fastball letter recognition task may provide a novel, passive correlate of verbal fluency performance in early dementia. We propose that whole letter oddball stimuli are more salient to participants with greater verbal fluency, resulting in larger oddball responses. A passive measure of verbal fluency could potentially bypass educational and linguistic confounds that can affect traditional measures of verbal fluency performance.

A robust study on the listeriosis disease by adopting fractal-fractional operators

Listeriosis is one of the zoonotic diseases affecting most parts of the Sub-Saharan countries. The infection is often transmitted by eating and it can also pass by respiratory and direct contact. In this paper, a listeriosis mathematical model is formulated involving fractal-fractional orders in both Caputo and Atangana–Baleanu derivatives. Moreover, future behaviors of the disease are investigated by considering the fractal–fractional operators that are very effective in modeling the real-life phenomena by virtue of their memory effect. The basic properties and steady states are also obtained. The threshold parameter for determining the spread of the disease is computed. Numerical results are presented for each fractal-fractional-order operator. The results obtained in the paper show that the numerical schemes are effective for predicting and analyzing complex phenomena.

On three-dimensional flow structures and oscillatory instability due to free surface heat loss in half-floating zones under microgravity

Present work describes a numerical investigation concerning the response of oscillatory thermo-capillary convection to free surface heat loss in a cylindrical half floating zone of high Prandtl number liquid (Pr=67) under microgravity conditions. Unsteady and three-dimensional computations have been carried out in the liquid domain using the finite volume method (FVM) to reveal the oscillatory thermo-fluid dynamic regimes at the onset of instability. The influence of different free surface heat loss conditions on the bifurcation from the basic steady axisymmetric state has been discussed in terms of critical azimuthal wavenumber, m. The dynamic evolution of the temperature disturbances at supercritical conditions are characterized by ‘pulsating’ and ‘rotating’ modes of spatio-temporal convection. The development of counter-propagating hydrothermal waves in azimuthal direction is found to be followed by an even mode of convection characterised by m = 2. The liquid bridge system exhibiting the well-known transition from periodic (m=2) to quasi-periodic behaviour (m=1) with an increase in Biot number, Bi has been analysed from both spatial and temporal points of view. The existence of both symmetric and asymmetric modes of the supercritical state for different Bi are presented. The dominant fluid dynamic information of 3D oscillatory state are extracted from a specific set of disturbance temperature data by employing a data-driven computational technique ‘dynamic mode decomposition’ (DMD). Various neutral, stable and unstable dynamic modes responsible for bifurcation to the 3D supercritical state are depicted with the help of DMD spectrum and the frequency spectrum.

Unsteady double diffusive convection inside a partial porous building enclosure subjected to time-periodic temperature boundary condition

Unsteady double diffusive convection under the influence of time-periodic sidewall temperature inside a rectangular enclosure with a porous wall is performed using numerical simulation and analytical prediction. The ranges of investigated physical parameters are listed as Darcy number (10−10 ≤ Da ≤ 101), thickness of porous wall (0 ≤ d ≤ 1), thermal Rayleigh number (103 ≤ Ra ≤ 107), buoyancy ratio (−1 ≤ N ≤ 1) and oscillating frequency of time-periodic sidewall temperature (0.01 ≤ ω ≤ 10). Results indicate that rates of heat and moisture transfer are impacted by time-periodic temperature and have a sinusoidal variation with time. The heat and moisture resonance phenomenon occurs when the convection effect is sufficiently stronger. Scale analysis has been performed to obtain the correlations of overall heat and moisture transfer rates in basic steady state and the resonant frequency, where the fluctuations of heat and moisture transfer are increased. A good agreement is observed from the analytical and numerical results. Present work could be applied to determine the heat and moisture transfer rates and resonant frequency in a thermal storage system, where the sidewall temperature is varying periodically with time due to the weather condition (solar radiation) and ambient temperature during a typical day.

Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe

Abstract

Instabilities of a Time-Dependent Shear Flow

AbstractThis study offers a systematic stability analysis of unsteady shear flows representing large-scale, low-frequency internal waves in the ocean. The analysis is based on the unbounded time-dependent Couette model. This setup makes it possible to isolate the instabilities caused by uniform shear from those that can be attributed to resonant triad interactions or to the presence of inflection points in vertical velocity profiles. Linear analysis suggests that time-dependent spatially uniform shears are unstable regardless of the Richardson number (Ri). However, the growth rate of instability monotonically decreases with increasing Ri and increases with increasing frequency of oscillations. Therefore, models assuming a steady basic state—which are commonly used to conceptualize shear-induced instability and mixing—can be viewed as singular limits of the corresponding time-dependent systems. The present investigation is focused on the supercritical range of Richardson numbers (Ri > 1/4) where steady parallel flows are stable. An explicit relation is proposed for the growth rate of shear instability as a function of background parameters. For moderately supercritical Richardson numbers (Ri ~ 1), we find that the growth rates obtained are less than, but comparable to, those expected for Kelvin–Helmholtz instabilities of steady shears at Ri < 1/4. Hence, we conclude that the instability of time-dependent flows could represent a viable mixing mechanism in the ocean, particular in regions characterized by relatively weak wave activity and predominantly supercritical large-scale shears.

Linear Stability Analysis of Thermocapillary Flow in Rotating Shallow Pools Heated from Inner Wall

Thermocapillary flow of silicon melt (Pr=0.011) in shallow annular pool heated from inner wall was simulated at the dimensionless rotation rate ω ranging from 0~7000. The effect of pool rotation on the stability of the thermocapillary flow was investigated. The steady axisymmetric basic state was solved by using the spectral element method; the critical stability parameters were determined by linear stability analysis; the mechanism of the flow instability was explored by the analysis of energy balance. A stability diagram, exhibiting the variation of the critical Marangoni number versus the dimensionless rotation rate ω was presented. The results reveal that only one Hopf bifurcation point appeared in the intervals of ω 3965, and the corresponding instability was caused by the shear energy, which was provided by the thermocapillary force and pool rotation, respectively. In addition, the competition between thermocapillary force and pool rotation leads to three Hopf bifurcation points in the range of 3020<ω<3965 with the increase of Marangoni number.

Existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow

We study the existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow by time marching the three-dimensional incompressible Navier–Stokes equations numerically. Three wide-gap clearance ratios, $$\beta =\left( R_{2}-R_{1}\right) /R_{1}=0.33$$ , 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio $$\beta =0.18$$ at Reynolds number $${Re}=700$$ as the initial conditions and suddenly increasing $$\beta$$ to the target value, we can compute Taylor vortices for the three wide gaps. For $$\beta =0.33$$ , Taylor vortices exist in the range $$450\le {Re}\le 2050$$ . With increasing Re the steady symmetric 1-vortex flow becomes steady asymmetric at $${Re}=1850$$ , and then become periodic at $${Re}=2000$$ . When $${Re}>2050$$ the flow returns back to the steady basic flow state with no Taylor vortices. For $$\beta =0.38$$ , Taylor vortices can exist in the range $$500\le {Re}\le 1400$$ . With increasing Re, the steady symmetric 1-vortex flow become steady asymmetric at $${Re}=1200$$ , and then the flow evolves into the steady basic flow for $${Re}>1400$$ . For $$\beta =0.42$$ , Taylor vortices can exist in the range $$650\le {Re}\le 1300$$ . With increasing Re, steady asymmetric Taylor vortices occur at $${Re}=1150$$ , and then the flow evolves into the steady basic flow for $${Re}>1300$$ . The present numerical results are in good agreement with available numerical and experimental results. Furthermore, the existence regime of Taylor vortices in the $$(\beta ,{Re})$$ plane for $$\beta \ge 0.33$$ and the three-dimensional transition process from periodic asymmetric vortex flow to steady basic flow with increasing Re are presented for the first time.

Modeling and experimental research of hybrid PV-thermoelectric system for high concentrated solar energy conversion

Abstract An experimental research of a novel combination, within a photovoltaic-thermoelectric (PV-TE) system, for high concentrated solar energy (×300–1000) conversion to electricity is presented. Our hybrid system contains, at its core; a triple junction solar cell (TJSC); a thermoelectric cooler (TEC); a thermoelectric generator (TEG), all settled thermally in series respectively. The thermoelectric cooler enhances the solar cell efficiency by pumping its excess heat through the Peltier effect; the thermoelectric generator plays the role of a heat sink for the TEC, converting some of this waste-heat into electricity by means of the Seebeck effect. The basic steady state finite element modeling demonstrates the contribution of the TEC-TEG Module, inflating the overall efficiency of the hybrid system for high solar concentrated irradiation; the experimental and simulation results are matched. All of which evokes a new system that takes into consideration the PV electric power generation, without compromising the cooling potential and the immediate electric production of the thermoelectric devices.

Instabilities in electrically driven rotating MHD layers

Flows of electrically conducting fluids exposed to intense magnetic fields exhibit a common feature i.e. the formation of uniform cores in which electromagnetic forces are dominant. Cores are separated from each other by thin layers that extend along magnetic field lines. Across these parallel layers strong gradients of flow variables are present, which can lead to the onset of instabilities and non-linear flow transitions.In this work we investigate dynamics and stability issues of rotating parallel layers driven by electromagnetic forces caused by the interaction of injected electric currents with an applied magnetic field. The geometry considered consists of two coaxial circular electrodes used for current injection. They are placed in parallel electrically insulating planes perpendicular to a uniform magnetic field. The basic axisymmetric steady state flow, characterized by a rotating velocity jet confined in a parallel layer that connects the rims of the electrodes, is rather well understood. By increasing the driving current above a critical value the basic flow becomes unstable and undergoes a sequence of supercritical bifurcations.

On the onset of multi-wave patterns in laterally heated floating zones for slightly supercritical conditions

This analysis follows and integrates the line of inquiry started in past author’s works [M. Lappa, “Three-dimensional numerical simulation of Marangoni flow instabilities in floating zones laterally heated by an equatorial ring,” Phys. Fluids 15(3), 776–789 (2003) and “Combined effect of volume and gravity on the three-dimensional flow instability in non-cylindrical floating zones heated by an equatorial ring,” ibid. 16(2), 331–343 (2004)] about the typical instabilities of the Marangoni flow and associated hierarchy of bifurcations in laterally heated floating zones with various shapes and aspect ratios. The main motivation for re-examining this kind of problems, which have attracted so much attention over the last twenty years, is the recent discovery [M. Kudo et al., “Transition of thermocapillary convection in a full-zone liquid bridge,” Trans. JSME (in Japanese) 80(812), TEP0095 (2014)] of a chaotic state in the region of the space of parameters where on the basis of existing theories and earlier results for the classical liquid-bridge problem with organic fluids, the flow should be relatively regular in time and with a simple structure in space. Axisymmetric computations are used to obtain the steady basic state, and then the Navier Stokes equations are solved in their complete, three-dimensional, time-dependent, and non-linear formulation to investigate the evolution of azimuthal disturbances. It is shown that the “apparent” doubling or quadrupling of the azimuthal wavenumber in the equatorial plane, previously reported for the case of floating zones of liquid metals, is replaced for high-Prandtl-number liquids by the complex interaction of disturbances with distinct spatial and temporal scales. These disturbances become critical at relatively comparable values of the Marangoni number. The unexpected multiplicity of waveforms and competition of spatial modes are explained according to the increased complexity of the considered system in terms of flow topology and structure with respect to the classical half-zone configuration.

Nonhomogeneous Porosity and Thermal Diffusivity Effects on a Double-Diffusive Convection in Anisotropic Porous Media

Abstract A model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effects of variable permeability, thermal diffusivity and variable gravity with respect to the vertical direction, have been studied. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good predicts on the onset of instability in the basic steady state. It is known that as R c ${R_c}$ increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as R c $Rc$ increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.

Natural convection in a horizontal cylinder with axial rotation

We study the problem of thermal convection in a laterally heated horizontal cylinder rotating about its axis. A cylinder of aspect ratio Γ=H/2R=2 containing a small Prandtl number fluid (σ=0.01) representative of molten metals and molten semiconductors at high temperature is considered. We focus on a slow rotation regime (Ω<8), where the effects of rotation and buoyancy forces are comparable. The Navier-Stokes and energy equations with the Boussinesq approximation are solved numerically to calculate the basic states, analyze their linear stability, and compute several secondary flows originated from the instabilities. Due to the confined cylindrical geometry-the presence of lateral walls and lids-all the flows are completely three dimensional, even the basic steady states. Results characterizing the basic states as the rotation rate increases are presented. As it occurred in the nonrotating case for higher values of the Prandtl number, two curves of steady states with the same symmetric character coexist for moderate values of the Rayleigh number. In the range of Ω considered, rotation has a stabilizing effect only for very small values. As the value of the rotation rate approaches Ω=3.5 and Ω=4.5, the scenario of bifurcations becomes more complex due to the existence in both cases of very close bifurcations of codimension 2, which in the latter case involve both curves of symmetric solutions.

MODELING THE SPREAD OF HOOKWORM DISEASE AND ASSESSING CHEMOTHERAPY PROGRAMS: MATHEMATICAL ANALYSIS AND COMPARISON WITH SURVEILLANCE DATA

Soil-transmitted helminthes including hookworm infections result in a major disease burden worldwide. Periodic chemotherapy treatments with anthelminthic drugs remain major intervention strategy in highly endemic areas and currently there is no approved human vaccine. We developed a model to study the spread of the hookworm infection in the population level having a variety of parasite development stages. We investigated long-term effectiveness of selective and mass chemotherapy, scenarios in which the therapy becomes less effective, and is interrupted. We analyzed the mathematical model, which includes determining the basic reproductive number and steady states, defining model initial conditions, proving positiveness and boundedness of solutions, local and global stability of the disease-free and endemic steady states, and uniform persistence of the system. We fitted our model using field data from hookworm control programs in endemic areas in China and Zimbabwe. The model provided accurate predictions of disease prevalence for all considered locations for multiple years of utilizing deworming programs. We demonstrated that administration of the deworming therapy is an effective method in terms of controlling the hookworm infection. Nevertheless, the chemotherapy programs do not eradicate the disease in the villages and the infection occurrence promptly increases once the program is interrupted, thus ultimately leading to the pre-treatment levels. Our modeling results suggest that the deworming programs should be maintained at least once per year to control the infection.

A high-fidelity method to analyze perturbation evolution in turbulent flows

Small perturbation propagation in fluid flows is usually examined by linearizing the governing equations about a steady basic state. It is often useful, however, to study perturbation evolution in the unsteady evolving turbulent environment. Such analyses can elucidate the role of perturbations in the generation of coherent structures or the production of noise from jet turbulence. The appropriate equations are still the linearized Navier–Stokes equations, except that the linearization must be performed about the instantaneous evolving turbulent state, which forms the coefficients of the linearized equations. This is a far more difficult problem since in addition to the turbulent state, its rate of change and the perturbation field are all required at each instant. In this paper, we develop and use a novel technique for this problem by using a pair (denoted “baseline” and “twin”) of simultaneous synchronized Large-Eddy Simulations ( LES ). At each time-step, small disturbances whose propagation characteristics are to be studied, are introduced into the twin through a forcing term. At subsequent time steps, the difference between the two simulations is shown to be equivalent to solving the forced Navier–Stokes equations, linearized about the instantaneous turbulent state. The technique does not put constraints on the forcing, which could be arbitrary, e.g., white noise or other stochastic variants. We consider, however, “native” forcing having properties of disturbances that exist naturally in the turbulent environment. The method then isolates the effect of turbulence in a particular region on the rest of the field, which is useful in the study of noise source localization. The synchronized technique is relatively simple to implement into existing codes. In addition to minimizing the storage and retrieval of large time-varying datasets, it avoids the need to explicitly linearize the governing equations, which can be a very complicated task for viscous terms or turbulence closures. The method is illustrated by application to a well-validated Mach 1.3 jet. Specifically, the effects of turbulence on the jet lipline and core collapse regions on the near-acoustic field are isolated. The properties of the method, including linearity and effect of initial transients, are discussed. The results provide insight into how turbulence from different parts of the jet contribute to the observed dominance of low and high frequency content at shallow and sideline angles, respectively.

Stability of basic steady states of networks in bounded domains

In this article, we study the problem of a network of curves in a planar domain with the normal velocity proportional to each curvature and fixed angle conditions at the points at which the curves intersect. We introduce the evolution problem of networks, identify two cases of basic steady states in bounded and smooth domains and study their stability in terms of the geometry of the boundary.

Characters of basic steady state solutions for superfluid Fermi gas in Bessel optical lattices

We consider a dynamical model for superfluid Fermi gas, trapped in the central well of an axially symmetric Bessel optical lattice potential. The equation includes nonlinear power-law form of the chemical potential [Formula: see text], for [Formula: see text], which accounts for Fermi pressure. Reducing the equation to two-dimensional (2D) form, we obtain the basic steady state solutions of the system along the Bose–Einstein condensation (BEC) side to Bardeen–Cooper–Schrieffer (BCS) side by employing the energy balance condition, which are guided by the variational approximation. It is found that the strength [Formula: see text] and the radial scale [Formula: see text] of the Bessel optical lattice have an extreme effect on the characters of basic steady state solution. Analytically, we deduce the atomic density distribution, the average atom number and the average energy of basic steady state, where the atom distribution of the system presents on periodic change with [Formula: see text], and increases faster at unitarity than in the BEC limit. Furthermore, because of the Fermi pressure, the atomic density distribution at the unitarity is more extensive than that in the BEC limit. In particular, there exist very interesting changes, the average energy intends to collapse state with [Formula: see text], however it emerges as a stable state with varying [Formula: see text] both in the BEC limit and at unitarity.

Three dimensional simulations for convection induced by the selective absorption of radiation for the Brinkman model

Convection induced by the selective absorption of radiation in a porous medium is studied analytically and numerically using the Brinkman model. Both linear instability analysis and nonlinear stability analysis are employed. Then, the validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good predicts on the onset of instability in the basic steady state.

Three dimensional simulations and stability analysis for convection induced by absorption of radiation

Purpose – The purpose of this paper is to investigate a model for convection induced by the selective absorption of radiation in a fluid layer. The concentration based internal heat source is modelled quadratically. Both linear instability and global nonlinear energy stability analyses are tested using three dimensional simulations. The results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold. Design/methodology/approach – The author introduce the stability analysis of the problem of convection induced by absorption of radiation in fluid layer, then the author select a situations which have very big subcritical region. Then, the author develop a three dimensions simulation for the problem. To do this, first, the author transform the problem to velocity – vorticity formulation, then the author use a second order finite difference schemes. The author use implicit and explicit schemes to enforce the free divergence equation. The size of the Box is evaluated according to the normal modes representation. Moreover, the author adopt the periodic boundary conditions for velocity and temperature in the $x, y$ dimensions. Findings – This paper explores a model for convection induced by the selective absorption of radiation in a fluid layer. The results demonstrate that the linear instability thresholds accurately predict the onset of instability. A three-dimensional numerical approach is adopted. Originality/value – As the author believe, this paper is one of the first studies which deal with study of stability of convection using a three dimensional simulation. When the difference between the linear and nonlinear thresholds is very large, the comparison between these thresholds is very interesting and useful.