Stability Analysis Of Flow Research Articles

Numerical solutions and stability analysis of hybrid Casson nanofluid flow with MHD and heat transfer effects

AbstractThis research addresses the complex dynamics of hybrid Casson nanoliquids in flow and heat transfer applications, focusing on the interaction between fluid dynamics and thermal phenomena in the presence of magnetohydrodynamics (MHD), viscous dissipation, and Joule heating. The motivation behind this study stems from the need to enhance the efficiency of heat transfer processes in various engineering applications, such as cooling systems and electronic devices, where hybrid nanofluids can offer superior thermal performance compared to conventional fluids. The novelty of this work lies in its comprehensive numerical investigation of a hybrid Casson nanoliquid over a moving permeable surface, incorporating a detailed analysis of MHD effects, viscous dissipation, and Joule heating. Using the Tiwari and Das model to formulate the governing equations, the study employs similarity transformations to convert these equations into a system of ordinary differential equations (ODEs). MATLAB is then used to derive numerical solutions, with a stability analysis ensuring the physical dependability of these solutions. Key findings reveal that the temperature distribution of the hybrid nanoliquid shows a positive correlation with both Prandtl and Hartmann numbers. Additionally, a positive relationship between temperature and the Eckert number is observed. These insights offer valuable guidance for engineers aiming to optimize heat transfer processes using hybrid nanofluids, highlighting their potential for improved thermal management in practical applications.

On the asymptotic analysis of pulsating planar Poiseuille flow instabilities

The linear stability analysis of a pulsating flow between parallel plates at finite amplitudes and different frequencies demonstrates the presence of instability with a different nature to that initially reported in earlier studies at W o < 25 . The time-dependent stability problem is formulated using a Floquet expansion of the perturbation and solved in a matrix approach. At higher pulsation frequencies (i.e. W o > 30 ), pulsation amplitudes and sufficiently large Reynolds numbers, the time-dependent baseflow displays multiple inflexion points throughout the entire duration of the pulsation. A scaling analysis of the temporal growth rate reveals that the instability is of inviscid type and scales with R e − 1 . Freezing the time-dependent baseflow for a particular set of parameters, the growth rate is simultaneously controlled by viscosity solely acting on the perturbation, and the pulsating frequency coupling the harmonics. In the asymptotic limit ( R e → + ∞ ), we demonstrate that the temporal problem simplifies to a set of steady stability analyses dependent on the phase of the pulsation. In particular, we show that in this limit, Rayleigh and Fjørtoft’s criteria for instability become valid again, that sub-harmonic periodic orbits can be used to estimate the inviscid growth rate and match with the asymptotic values predicted from the viscous stability analysis.

New results on the motion of interfaces of multi-layer radial Hele-Shaw flows

We study the dynamical system arising from the linear stability analysis of multi-layer radial Hele-Shaw flows with time-dependent injection rates. An analysis of the system provides conditions under which the disturbances on all interfaces either monotonically decrease or monotonically increase. Additionally, we show that in any multi-layer radial Hele-Shaw flow, if all of the interfaces are circular initially except for one perturbed interface then there exists a time-dependent injection rate such that the circular interfaces remain circular as they propagate and the disturbance on the perturbed interface decays. The motion of the interfaces is also investigated numerically by integrating the dynamical system for the case of constant and time-independent injection rates. This reveals some very interesting dynamics of interfaces in multi-layer flows. It is found that: (i) A disturbance of one interface can be transferred to the other interface(s); (ii) The disturbances on the interfaces can develop either in phase or out of phase from any arbitrary initial disturbance; and (iii) The dynamics of the flow can change dramatically with the addition of more interfaces. With time-dependent injection rate, there are more possibilities. In particular it is shown that an appropriate injection rate can result in a stable configuration, which consists of all perfectly circular interfaces except for one that is perturbed with a monochromatic wave of infinitesimal amplitude. The prescribed injection rate results in the perturbation decaying even if the configuration (i.e., the setup consisting of all but one circular interface and one perturbed circular interface) itself is unstable to disturbances on any one or more of the circular interfaces. However, it may not be without a challenge to realize such a flow in practice.

Thermal transfer performance and flow instability analysis of direct steam generation for parabolic trough solar collectors

Parabolic trough solar direct-steam-generation (DSG) technology is the enabling technologies to achieve low carbon future. However, actual inlet boundary and flow boiling instabilities pose challenge to safe operation. In this paper, the coupled optical-thermal-flow pattern model for DSG loops is built utilizing conservation equations, separated flow model and Lagrangian method. The heat transfer performance, hydrodynamic characteristics and two-phase flow law of the loop are discussed under the coupled variation of direct radiation intensity (DNI), mass flow (m), inlet temperature (Tin) and inlet pressure (Pin). The correlation between multi-condition, thermodynamic characteristics and flow instability is analyzed. The results show that increasing Pin, Tin and DNI have almost no effect on the intermittent state. The percentage of annular flow only remained stable (about 84.8%) when the steam mass was 1. Increasing DNI and Tin did not effectively improve the flow heat transfer, while increasing Pin worsened the flow heat transfer and increased the probability that the annular flow would turn into stratified flow but could reduce the pressure drop and the fluid vapor-liquid density difference and stabilizes its hydrodynamic properties. The simultaneous increase in m not only weakens this effect and strengthens the heat transfer, but also permanently reduces the probability of stratified flow. The higher the Pin, Tin and DNI, the lower the flow instability of the DSG system. Manual operation is recommended to prevent the system having flow instability in the morning due to the lower solar radiation intensity and inlet temperature when the system is started in the morning.

Energy stability analysis of MHD flow in a rectangular duct

Energy stability analysis of MHD flow in a rectangular duct

Stability analysis for the anisotropic curve shortening flow of planar networks

In this article we consider the anisotropic curve shortening flow for a planar network of three curves which meet at a triple junction. We show that the anisotropic energy fulfills a Łojasiewicz–Simon gradient inequality from which we derive a stability result for the evolution. Precisely, we show that, for initial data which are close to the energy minimizer, the flow exists globally and converges to the minimizer.

Internal flow stability analysis of vertical mixed-flow pump device based on EGT and FFT

With the purpose of researching the internal flow stability of the vertical mixed-flow pump device (VMFPD), the entire flow field was solved through the very large-eddy simulation (VLES) k- ω model and the internal flow characteristics of the pump device were quantitatively analyzed with the use of the energy gradient theory (EGT) along with the physical parameters of the flow field. The research elucidates the variety rule of the pressure along the VMFPD and the energy gradient function K as well as the time-frequency features of the pressure pulsation (PP) in the impeller and guide vane. The results demonstrate that the solid wall restriction of the guide vane and the impeller rotation cause a significant shift in the velocity and direction of the water flow. This causes a significant pressure difference between the water bodies, which makes it easier to create an unstable flow. The suction surface of the impeller blade possesses the great concentration of the area with energy gradient function K > 107, which is the critical area influencing the internal flow stability of the pump device.

Linear stability analysis of a Couette-Poiseuille flow: A fluid layer overlying an anisotropic and inhomogeneous porous layer

We investigate the temporal stability analysis of a two-layer flow inside a channel that is driven by pressure. The channel consists of a fluid layer overlying an inhomogeneous and anisotropic porous layer. The flow contains a Couette component due to the movement of the horizontal impermeable upper and lower walls binding the two layers. These walls of the channel move at an identical speed but in opposite directions. The flow dynamics for the porous medium are modelled by the Darcy-Brinkman equations, and the Navier-Stokes equations are employed to describe the motion within the fluid layer. The hydrodynamic instability of infinitesimal disturbance is investigated using Orr-Sommerfeld analysis. The corresponding eigenvalue problem is derived and solved numerically using the Chebyshev polynomial-based spectral collocation method. Results reveal that stability features are strongly affected by the axial and spatial permeability variations of the porous medium. Further, the ratio of the depth of the fluid layer to the porous layer and the strength of the Couette component play a crucial role. The destabilization of the perturbed system is noticed by strengthening the Couette flow component. The combined impact of increasing the anisotropy parameter and depth ratio, decreasing Darcy number, and reducing the inhomogeneity factor stabilizes the system. This facilitates us to have greater control over the instability characteristics of such fluid-porous configuration by suitably adjusting various flow parameters. The outcome will be beneficial in relevant applications for enhancing or suppressing the instability of perturbation waves, as preferable.

Linstab2D: stability and resolvent analysis of compressible viscous flows in MATLAB

Linstab2D: stability and resolvent analysis of compressible viscous flows in MATLAB

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

Nonmodal linear stability analysis of hypersonic flow over an inclined cone

Nonmodal linear stability analysis results are presented for hypersonic flow over a cone at 6° angle of attack complementing earlier modal stability analysis. Based on the parallel flow assumption, singular value decomposition is applied to obtain the optimal linear combination of global crossflow modes. The optimal disturbance exhibits significant transient growth in the initial short distance and progressively follows the path of the most unstable mode downstream. The largest transient energy gain is observed for disturbances at around 40 kHz close to the most amplified modal frequency and tends to increase with the Reynolds number. The optimal disturbance initially exhibits two amplitude peaks in the azimuthal direction, one lying in the leeward region where the unstable crossflow modes reside and the other in the windward region where the adjoint modes exist. As the optimal disturbance travels downstream, the second amplitude peak rapidly shifts toward the leeward side and reaches the optimal energy gain when it eventually merges with the first amplitude peak. The evolution process of the optimal disturbance indicates that the optimal disturbance might have exploited the locally crossflow instability through traveling from the windward side to the leeward side.

Linear stability analysis of plane Poiseuille flow of a De-Kée–Turcotte fluid

Linear stability analysis of plane Poiseuille flow of a De-Kée–Turcotte fluid

Modeling reactive film flows down a heated fiber

We study the dynamics of an ultra-thin reactive liquid film flowing down a heated vertical fiber under the influence of gravity. A key focus is on the impact of the van der Waals attraction, which is proportional to h−3, where h denotes the film thickness. Linear stability analysis of the film flow reveals that the van der Waals attractions and the Marangoni effect enhance the instability. Furthermore, instability is reduced by exothermic chemical reactions, while it is strengthened in the case of endothermic chemical reactions. Moreover, the weakly nonlinear stability of the film flow is studied. The results indicate the possibility of both subcritical and supercritical stability in the system. Lastly, direct numerical simulations of the evolution equation are conducted for various flow parameters. These results enhance our understanding of the intricate interplay of chemical reactions, thermal effects, and intermolecular forces influencing the liquid film dynamics in complex systems.

Linear stability analysis of micropolar nanofluid flow across the accelerated surface with inclined magnetic field

PurposeThe purpose of this paper is to study the two-dimensional micropolar fluid flow with conjugate heat transfer and mass transpiration. The considered nanofluid has graphene nanoparticles.Design/methodology/approachGoverning nonlinear partial differential equations are converted to nonlinear ordinary differential equations by similarity transformation. Then, to analyze the flow, the authors derive the dual solutions to the flow problem. Biot number and radiation effect are included in the energy equation. The momentum equation was solved by using boundary conditions, and the temperature equation solved by using hypergeometric series solutions. Nusselt numbers and skin friction coefficients are calculated as functions of the Reynolds number. Further, the problem is governed by other parameters, namely, the magnetic parameter, radiation parameter, Prandtl number and mass transpiration. Graphene nanofluids have shown promising thermal conductivity enhancements due to the high thermal conductivity of graphene and have a wide range of applications affecting the thermal boundary layer and serve as coolants and thermal management systems in electronics or as heat transfer fluids in various industrial processes.FindingsResults show that increasing the magnetic field decreases the momentum and increases thermal radiation. The heat source/sink parameter increases the thermal boundary layer. Increasing the volume fraction decreases the velocity profile and increases the temperature. Increasing the Eringen parameter increases the momentum of the fluid flow. Applications are found in the extrusion of polymer sheets, films and sheets, the manufacturing of plastic wires, the fabrication of fibers and the growth of crystals, among others. Heat sources/sinks are commonly used in electronic devices to transfer the heat generated by high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light-emitting diodes to a fluid medium, thermal radiation on the fluid flow used in spectroscopy to study the properties of materials and also used in thermal imaging to capture and display the infrared radiation emitted by objects.Originality/valueMicropolar fluid flow across stretching/shrinking surfaces is examined. Biot number and radiation effects are included in the energy equation. An increase in the volume fraction decreases the momentum boundary layer thickness. Nusselt numbers and skin friction coefficients are presented versus Reynolds numbers. A dual solution is obtained for a shrinking surface.

Stability analysis of magnetohydrodynamic Casson fluid flow and heat transfer past an exponentially shrinking surface by spectral approach

The present analysis examines the magnetohydrodynamic (MHD) flow of non-Newtonian Casson fluid on an exponentially shrinking surface under constant and exponentially varying wall temperature with suction. The main objective is to investigate multiple solutions of self-similar coupled nonlinear ordinary differential equations derived semi-numerically via the shifted Chebyshev collocation approach. The occurrence of a dual solution is found and variations in the velocity and temperature profiles are analyzed under different physical flow governing factors. The stability analysis is performed and it confirms that the first solution is stable and the second solution is unstable. The obtained results are confirmed by comparing them with earlier published results and show good agreement. The skin friction coefficient and wall temperature gradient increase for the first solution and decline for the second solution with enhancement in Hartmann number and suction parameter in case of exponentially varying surface temperature. Whereas, for constant surface temperature, increasing the Hartmann number and suction parameter results in the intensification of the wall temperature gradient. The velocity and temperature profiles decrease with improving the Casson parameter. As the Prandtl number strengthens, the heat transfer rate in a constant surface temperature situation is comparatively higher than exponentially varying surface temperature situation.

Hybrid Nanofluid Flow over a Shrinking Darcy-Forchheimer Porous Medium with Shape Factor and Solar Radiation: A Stability Analysis

This research aimed to develop a numerical solution to analyze the effects of solar radiation and nanoparticle shape factors on the flow of a hybrid nanofluid past a shrinking Darcy-Forchheimer porous medium. The base fluid chosen for this study is water (H2O), and the hybrid nanofluid consists of nanoparticles of silver (Ag) and titanium dioxide (TiO2) in four different shapes: bricks, cylinders, platelets, and blades. To account for solar radiation, the energy model incorporated a radiative heat flux, while the momentum problem considers the influence of a magnetic field. The application of an appropriate similarity transformation method converts the partial differential equations (PDEs) model into a system of nonlinear ordinary differential equations (ODEs). The mathematical model is solved using the shooting technique method and the bvp4c solver. The obtained results, along with the effects of the nanoparticle shape factor, solar radiation parameter, shrinking parameter, Darcy-Forchheimer number, and nanofluid volume fraction, are visually presented through figures and tables. It is worth noting that, in our numerical results, we observed the presence of dual solutions when λ < 0. Our findings indicate that the thermal transmittance increases with an increase in the nanoparticle shape factor and solar radiative parameter. Additionally, we observed an escalation in the velocity distribution in relation to the shrinking parameter and nanofluid volume fraction. Before reaching the two solutions, a flow stability analysis revealed that the first branch appears to be the most stable. Overall, these findings provide valuable insights into the behaviour of hybrid nanofluid flow in the presence of solar radiation and porous media.

Flow stability analysis on low-speed compressor with swept rotor blades under radial inlet distortions

Flow stability enhancement for axial flow compressors under radially distorted inlet conditions through rotor sweep design is an important issue for designers. To investigate the couped effect of rotor swept and radial inlet distortion on flow stability, steady numerical simulations, theoretical model predictions, and experimental validations were conducted for a low-speed, single-stage axial compressor (TA36) under various intensities of tip total pressure distorted inlet conditions with different swept rotor configurations. The steady pressure rise significantly decreases as the intensity of the distortion increases, whereas the rotor sweep has little effect on the pressure rise characteristic. The maximum error via model prediction is 1.25 %, while for steady numerical calculation, it is 3.89 %. Higher intensities of distortion lead to worse flow stability. Under radially distorted inlet conditions, forward sweep enhances flow stability whereas backward sweep further worsens it. What's more, quantitative analysis shows that the stability enhancement of forward sweep cannot fully counteract the adverse impact of radial distortion on flow stability. Elevated rotor tip loading was identified as the primary cause of instability under tip total pressure distorted inlet conditions. Forward sweep can slightly reduce this loading, whereas backward sweep has the opposite effect. Furthermore, the impact of rotor sweep on rotor tip loading intensifies with increasing distortion intensity. Unsteady flow field analysis was conducted. Which shows that radial distortion and blade sweep both affect flow stability by altering the intensity of tip leakage flow.

Stability analysis of viscous multi-layer shear flows with interfacial slip

Abstract One of the most fundamental interfacial instabilities in ideal, immiscible, incompressible multifluid flows is the celebrated Kelvin–Helmholtz (KH) instability. It predicts short-wave instabilities that, in the absence of other mollifying physical mechanisms (e.g. surface tension, viscosity), render the nonlinear problem ill-posed and lead to finite-time singularities. The crucial driving mechanism is the jump in tangential velocity across the liquid–liquid interface, i.e. interfacial slip, that can occur since viscosity is absent. The purpose of the present work is to analyse analogous instabilities for viscous flows at small or moderate Reynolds numbers as opposed to the infinite Reynolds numbers that underpin KH instabilities. The problem is physically motivated by both experiments and simulations. The fundamental model considered consists of two superposed viscous, incompressible, immiscible fluid layers sheared in a plane Couette flow configuration, with slip present at the deforming liquid–liquid interface. The origin of slip in viscous flows has been observed in experiments and molecular dynamics simulations, and can be modelled by employing a Navier-slip boundary condition at the liquid–liquid interface. The emerging novel instabilities are studied in detail here. The linear stability of the system is addressed asymptotically for long- and short-waves, and for arbitrary wavenumbers using a combination of analytical and numerical calculations. Slip is found to be capable of destabilising perturbations of all wavelengths. In regimes where the flow is stable to perturbations of all wavelengths in the absence of slip, its presence can induce a Turing-type instability by destabilization of a small band of finite wavenumber perturbations. In the case where the underlying layer is asymptotically thin, the results are found to agree with the linear properties of a weakly non-linear asymptotic model that is also derived here. The weakly nonlinear model extends previous work by the authors that had a thin overlying layer that produces a different evolution equation.

Linear and non-linear stability analysis of double-diffusive Hadley-Prats flow through horizontal porous layer with non-uniform thermal and solutal gradients

A scientific model is devised to understand the onset of double-diffusion Hadley-Prats flow through an infinite parallel permeable channel with non-uniform thermal, solutal gradients, and concentration based internal heat generation under the influence of convection conditions is considered. Darcy’s model is implemented in the context of a porous medium, which is characterized as isotropic and homogeneous. A linear and nonlinear stability analysis is conducted with the help of energy functional method and longitudinal roll perturbations are examined. The emerged dimensionless eigenvalue problem in the linear and nonlinear stability analysis is solved numerically by utilizing fourth order Runge-Kutta method (RK-4) method and shooting scheme. The critical values of wave and vertical thermal Rayleigh numbers are examined. A comprehensive analysis of solutions concerning the onset of convection mechanism is conducted. The produced results are discussed for the various values of emerged physical parameters. It is evident that, the presence of non-uniform thermal and solutal gradients and the internal heat generation mechanism causes the significant variations in the critical values of vertical thermal Rayleigh number in the channel regime.

Onset of absolute instability on a pitching aerofoil

A global transient linear stability analysis of the three-dimensional time-dependent flow around an aerofoil undergoing small-amplitude pitching motion is performed using the optimally time-dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its spatial and temporal evolution, including the formation of a laminar separation bubble and its gradual spanwise modulation via primary global instability, leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of spanwise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted, which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself.