Stability Analysis Of Flow Research Articles

Multifractal analysis of flow instability of centrifugal compressor with dynamic pressure

In order to identify the surge, multifractal spectrums are investigated in the analysis of dynamic pressure at the outlet of centrifugal compressor with 800 kW. At first, the time series of dynamic pressure, including stable and unstable states, are obtained. Then, the relationships between characteristics of multifractal spectrums and dynamic pressure series are studied and explained in detail. The results show that the multifractal spectrum parameter Δf(α) is narrow as the centrifugal compressor is working in stable state. However, Δf(α) becomes wide, as it is working in unstable states. Finally, probability analysis of multifractal variation tendency is used to describe the predictability of the variation. The studies indicated that the associated probability between the data of adjacent periods is highest and the predictability is the strongest in transition period. Thus, the method can be used to predict and avoid surge for centrifugal compressor in early time.

Stability analysis of holographic RG flows in 3d supergravity

Stability analysis of holographic RG flows in 3d supergravity

Dual solutions and linear temporal stability analysis of mixed convection flow of non-Newtonian special third grade fluid with thermal radiation

The present study aims to investigate the steady mixed convection stagnation-point flow of a special third grade fluid over a vertical stretching/shrinking sheet with the inclusion of suction and thermal radiation effects. The governing momentum and energy equations are transformed into a system of ordinary differential equations (ODEs) using the Lie scaling group of transformations. The resulting system of highly nonlinear boundary value problems (BVPs) is solved numerically with the help of Matlab solver ‘bvp4c’. Dual similarity solutions are found for the opposing flow case within the range λc≤λ<0, where λ is the buoyancy parameter. Emphasis has been given to conducting a temporal stability analysis to determine the practically reliable solution. The analysis reveals that the primary (upper) solution branch is stable while the other solution branch is unstable. It has been observed that the range of dual solutions and the magnitude of the critical point increase with the increasing value of the suction parameter. The increment of the thermal radiation parameter enhances fluid temperature in the upper solution branch, whereas temperature diminishes far away from the sheet in the lower solution branch.

Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper: part 2.

In 1923, the Philosophical Transactions published G. I. Taylor's seminal paper on the stability of what we now call Taylor-Couette flow. In the century since the paper was published, Taylor's ground-breaking linear stability analysis of fluid flow between two rotating cylinders has had an enormous impact on the field of fluid mechanics. The paper's influence has extended to general rotating flows, geophysical flows and astrophysical flows, not to mention its significance in firmly establishing several foundational concepts in fluid mechanics that are now broadly accepted. This two-part issue includes review articles and research articles spanning a broad range of contemporary research areas, all rooted in Taylor's landmark paper. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Noise induced effects in the axisymmetric spherical Couette flow.

We study the axisymmetric, wide gap, spherical Couette flow in the presence of noise in numerical simulations and experiments. Such studies are important because most of the flows in nature are subjected to random fluctuations. Noise is introduced into the flow by adding fluctuations to the inner sphere rotation which are random in time with zero mean. Flows of a viscous incompressible fluid are induced either by rotation of the inner sphere only or by the co-rotation of the spheres. Mean flow generation was found to occur under the action of additive noise. A higher relative amplification of meridional kinetic energy compared to the azimuthal component was also observed under certain conditions. Calculated flow velocities were validated by laser Doppler anemometer measurements. A model is proposed to elucidate the rapid growth of meridional kinetic energy for flows induced by varying the co-rotation of the spheres. Our linear stability analysis for flows induced by the rotation of the inner sphere revealed a decrease in the critical Reynolds number, corresponding to the onset of the first instability. Also, in this case, a local minimum of the mean flow generation on approaching the critical Reynolds number was observed, which is consistent with the available theoretical predictions. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (Part 2)'.

Experimental investigation on flow boiling characteristics in offset strip fin channels under different sloshing conditions

In order to reveal the effects of sloshing movement on the performance of the plate-fin heat exchangers applied in floating liquefied natural gas platforms and environment control system of aircrafts, the flow boiling characteristics in offset strip fin channels of plate-fin heat exchangers under different sloshing conditions were investigated experimentally, covering rolling, pitching and swaying movements. The results show that, the rotational type movements enhance the transient heat transfer coefficient by a maximum of 21.1% at low vapor quality condition and weaken the transient heat transfer coefficient by a maximum of 27.7% at high vapor quality condition, while the transitional type movements enhance the heat transfer at high vapor quality. Fast Fourier transform method was used in the spectrum analysis of flow instabilities, and there are two peak frequencies caused by the inlet fluctuations, the distribution of the liquid phase and the enhanced turbulence. The time-average factors were proposed to evaluate the average heat transfer performance during the sloshing period. The ranges of sloshing time-average factors for rolling, pitching, and swaying conditions are 0.861 ∼ 1.079, 0.923 ∼ 1.061, 0.834 ∼ 1.064 and 0.994 ∼ 1.090, respectively. As the mass flux and sloshing period increase, the time-average factors trend to 1.0, and increase at the transitional sloshing movement. With the increasing amplitude, the time-average factors increase from 1 to a maximal value of 1.093. The correlations to predict the time-average two-phase heat transfer coefficients under rolling, pitching, swaying, and heaving conditions for offset strip fins have been developed, and the deviations are within ± 10 %.

Experimental research and theoretical analysis of flow instability in advanced secondary passive residual heat removal system

To cope with station blackout (SBO) accident in the pressurized water reactor (PWR) nuclear power plant (NPP), the advanced secondary passive residual heat removal system (ASP) was developed. A newly advanced secondary passive heat removal system test facility (ASPTF) for generation III NPP was designed and constructed to obtain the thermal hydraulic characteristics of ASP. The flow instability in ASP was observed in ASPTF, which was more likely occurred under low heating power and system pressure conditions. The effects of different influencing factors on flow instability in ASP were obtained. Then, the theoretical analysis of flow instability in ASP was conducted. Based on the experimental and theoretical analysis results, the optimization and improvement measures of ASP were summarized.

Stability analysis of radiative-magnetic hybrid nanofluid slip flow due to an exponentially stretching/shrinking permeable sheet with heat generation

The present article aims to find the duality of solutions and investigate the magneto-radiative hybrid nanofluid flow over an exponentially stretching/shrinking permeable sheet with heat generation and multiple slip boundary conditions. The governing nonlinear partial differential equations are transformed into dimensionless nonlinear ordinary differential equations which are computed by bvp4c in Matlab platform. The hybridisation of alumina and copper nanoparticles enhances the system's heat transfer performance. The dual nature solution is obtained only if the suction is applied to the stretching/shrinking surface. From stability analysis, we can conclude that the first solution is stable, but the other is unstable. It is realistic to have the solution stable with the smallest positive eigenvalues, while the lower solution branch is unstable with the smallest negative eigenvalues. It is found that the upsurges of solid volume fraction of the copper nanoparticle enhanced the skin friction coefficient and the local Nusselt number.

Multiple Solutions and Stability Analysis of Magnetic Hybrid Nanofluid Flow Over a Rotating Disk with Heat Generation

This study highlights the hybrid Fe3O4-CoFe2O4/H2O ferrofluid flow and heat transfer with the effects of linear heat generation, magnetic field and suction on a rotating disk. Using the similarity transformation, the mathematical model is simplified and reduced to a similarity set of equations. The bvp4c solver is used for computational analysis as well as the stability analysis procedure. The present model is successfully validated with previous results, and also verified with the fulfillment of the asymptote profiles. Triple solutions are observed within a limited range of testing parameters. The flow progress of Fe3O4-CoFe2O4/H2O is reduced when some changes made by varying the magnetic and suction parameters while a reverse result is obtained for the third solution. Only the suction parameter boosts the thermal progress of Fe3O4-CoFe2O4/H2O. The stability analysis surprisingly shows that two of the solutions have positive smallest eigenvalues and align with the physical results.

Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper: part 1.

In 1923, the Philosophical Transactions published G. I. Taylor's seminal paper on the stability of what we now call Taylor-Couette flow. In the century since the paper was published, Taylor's ground-breaking linear stability analysis of fluid flow between two rotating cylinders has had an enormous impact on the field of fluid mechanics. The paper's influence has extended to general rotating flows, geophysical flows and astrophysical flows, not to mention its significance in firmly establishing several foundational concepts in fluid mechanics that are now broadly accepted. This two-part issue includes review articles and research articles spanning a broad range of contemporary research areas, all rooted in Taylor's landmark paper. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Numerical solutions and stability analysis of unsteady hybrid nanofluid flow over a shrinking sheet with heat generation

The study focuses on the generation of multiple numerical solutions and stability analysis for the case of an unsteady copper-alumina/water hybrid nanofluid subjected to a shrinking sheet. Heat generation as the potential contributing factor in the heat transfer progress is considered as well as the suction effect. The governing model (partial differential equations) is developed based on the boundary layer assumptions, which then are transformed into a set of ordinary (similarity) differential equations. The bvp4c solver is used to search all possible solutions and conduct the stability analysis for the generating solutions. Suction induces the movement of heated fluid particles towards the wall, resulting in increased velocity and heat transfer and a decrease in temperature. The first solution is proved to be the stable real solution as compared to the other solution.

Stability analysis for heat transfer flow in micropolar hybrid nanofluids.

Objective: hybrid nanofluids have superior thermal efficiency and physical durability in contrast to regular nanofluids. The stagnation point flow of MHD micropolar hybrid nanofluids over a deformable sheet with viscous dissipation is investigated. Methodology: the controlling partial differential equations are converted to nonlinear ordinary differential equations using the transmuted similarity, and are subsequently solved using the bvp4c solver in MATLAB. The hybrid nanofluids consist of aluminum and copper nanoparticles, dispersed in a base fluid of water. Results: multiple solutions are obtained in the given problem for the case of shrinking as well as for the stretching sheet due to the variation in several influential parameters. Non-unique solutions, generally, exist for the case of shrinking sheets. In addition, the first branch solution is physically stable and acceptable according to the stability analysis. The friction factor is higher for the branch of the first solution and lower in the second branch due to the higher magnetic parameters, while the opposite behavior is seen in the case of the local heat transfer rate. Originality: the novelty of this model is that it finds multiple solutions in the presence of Cu and Al2O3 nanoparticles and also performs the stability analysis. In general, non-unique solutions exist for the phenomenon of shrinking sheets.

Buoyancy-Induced Instability of a Power-Law Fluid Saturating a Vertical Porous Slab

Abstract Many engineering applications involve porous media and rely on non-Newtonian working fluids. In this paper, the seepage flow of a non-Newtonian fluid saturating a vertical porous layer is studied. The buoyant flow is thermally driven by the boundaries of the porous layer, which are permeable surfaces kept at different temperatures. In order to model the seepage flow of both shear-thinning (pseudoplastic) and shear-thickening (dilatant) fluids, reference is made to the Ostwald-de Waele rheological model implemented via the power-law extended form of Darcy's law. The basic stationary flow is parallel to the vertical axis and shows a single-cell pattern, where the cell has infinite height and can display a core-region of enhanced/inhibited flow according to the fluid's rheological behavior. By applying small perturbations, a linear stability analysis of the basic flow is performed to determine the onset conditions for a multicellular pattern. This analysis is carried out numerically by employing the shooting method. The neutral stability curves and the values of the critical Rayleigh number are computed for different pseudoplastic and dilatant fluids. The behavior of a Newtonian fluid is also obtained as a limiting case.

Stability Analysis of Buoyancy Magneto Flow of Hybrid Nanofluid through a Stretchable/Shrinkable Vertical Sheet Induced by a Micropolar Fluid Subject to Nonlinear Heat Sink/Source

The utilization of hybrid nanofluids (HNs) to boost heat transfer is a promising area of study, and thus, numerous scientists, researchers, and academics have voiced their admiration and interest in this area. One of the main functions of nanofluids is their dynamic role in cooling small electrical devices such as microchips and associated gadgets. The major goal of this study is to perform an analysis of the buoyancy flow of a shrinking/stretching sheet, whilst considering the fascinating and practical uses of hybrid nanofluids. The influence of a nonlinear heat source/sink induced by a micropolar fluid is also inspected. Water-based alumina and copper nanoparticles are utilized to calculate the fine points of the fluid flow and the features of heat transfer. The governing equations are framed with acceptable assumptions and the required similarity transformations are used to turn the set of partial differential equations into ordinary differential equations. The bvp4c technique is used to solve the simplified equations. Dual solutions are presented for certain values of stretching/shrinking parameters as well as the mixed convective parameter. In addition, the shear stress coefficient in the first-branch solution (FBS) escalates and decelerates for the second-branch solution (SBS) with the superior impact of the magnetic parameter, the mass transpiration parameter, and the solid nanoparticles volume fraction, while the contrary behavior is seen in both (FB and SB) solutions for the larger values of the material parameter.

Stability analysis of thermo-bioconvection flow of Jeffrey fluid containing gravitactic microorganism into an anisotropic porous medium

This paper presents a novel study on the stability of thermo-bioconvection due to gravitactic microorganisms into an anisotropic porous fluid layer saturated with Jeffrey liquid. A Jeffrey-Darcy model along with Boussinesq approximations is utilized. The field equations are treated with non-dimensionalization, linear stability analysis, and the normal mode technique to formulate a set of ordinary differential equations. These equations along with Robin boundary conditions are then analytically solved by employing the weighted residual Galerkin method utilizing the trigonometric trial functions. The traditional thermal Rayleigh-Darcy number Ra,c is obtained as a well-compiled function of the mechanical anisotropy parameter ξ, Jeffrey parameter γ, the thermal anisotropy parameter η, bioconvection Rayleigh-Darcy number Rb, and Péclet number Q, while it is independent from bioconvection Lewis number Lb. It is observed that mounting ξ and γ in between 0 to 1 hasten the formulation of bioconvection patterns and also enlarges the size of convective cells. The results demonstrate that increasing bioconvection Péclet number and microorganism concentration constitute an unstable system. η ranged between 0 to 1 has shown dual effect which is dominated by the concentration of gravitactic microorganism. For small microorganism concentration, augmenting thermal anisotropy strength stabilizes the system and increases the size of the convective cells. Mathematically, the stabilizing nature of η is bounded by the feasibility of the inequality (π2+δc2ξ)(1+γ)ξ>2Rbδc2(eQ−1)π2Q2(π2+δc2)(π2+Q2)(4π2+Q2). This study may find relevance in applications related to pharmaceutical, bio-mechanics, and in microbial enhanced oil recovery (MEOR). The experimental Ra,c value of measure 4π2 at critical wave number value δc=π is also regained as a limiting case from this study.

Comparison analysis of density wave oscillation type two-phase flow instability of superheated and saturated boiling tubes

Most of previous conclusions about two-phase flow instability come from saturated two-phase flow boiling tubes (SatTFB). Superheated two-phase flow boiling tubes (SupTFB) can generate superheated steam, which will make the thermodynamic cycle efficiency higher and the steam generator or system simpler. However, there is no systematic mathematical analysis about the difference between the two-phase flow instabilities of SatTFB and SupTFB. Algebraic criteria composed of dimensionless numbers are deduced to easily determine their flow instability boundary. Different from six dimensionless numbers used in SatTFB, SupTFB have one more dimensionless number. It is superheated number or two-phase number. The verified model is applied to investigate the parameters’ effects and the transient characteristics of density wave oscillation (DWO) type two-phase flow instability. The effects of Froude number and friction number for SupTFB are the same as that for SatTFB. When system pressure is low, only the case with high inlet resistance coefficients can be stable in SupTFB. Thus for SupTFB at low system pressures, they become stable when increasing the inverse of Froude number (or inclination angle) or decreasing friction number, which do not have the nonmonotonic phenomenon as the SatTFB. For the added superheated steam region, increasing its friction number makes SupTFB unstable. The reasonable application range of the figure expressed by subcooling number and phase change number is the same for both SatTFB and SupTFB when analyzing parameters’ effects. Different from increasing continually for SatTFB, the ratio between oscillation period and transit time for the SupTFB first increases with subcooling numbers and then keeps unchanged at high subcooling numbers.

Flow behavior analysis and prediction of flow instability of a lamellar TA10 titanium alloy

The flow behavior analysis and prediction of flow instability of TA10 titanium alloy were investigated during isothermal compression. TA10 titanium alloy was prepared by an electron beam cold hearth, and the TA10 titanium alloy ingot had a lamellar structure. The ingots were subjected to isothermal compression by a Gleeble-1500 thermomechanical simulator at 800–1050 °C, the strain rate range was 0.01–1 s −1 and the height reduction was 60%. An analysis of the flow stress-strain curves showed that discontinuous yielding behaviors occurred when the deformation temperature exceeded the β-transus temperature, and flow softening occurred at all deformation temperatures except 900 °C. The sample microstructure was studied, and the microstructural evolution was summarized. When the deformation temperature was 950 °C and the strain rate was 1 s −1 , an adiabatic shear band appeared in the microstructure, and the element distribution in the adiabatic shear band was analyzed. Based on the dynamic material model, processing maps under Prasad's and Murty's instability criterion were established. Combined with the microstructure and instability situation, the applicability of Prasad's instability criterion in lamellar TA10 titanium alloy was clarified. The suitable processing parameters were 1020–1050 °C and 0.1–1 s −1 or 875–950 °C and 0.01–0.05 s −1 . Combined with electron back-scattered diffraction, the flow-softening mechanism was analyzed, and the results revealed that the lamellar kinking, deformation heat and dynamic recovery were the flow-softening mechanisms when the deformation temperature was lower than the β-transus temperature, and when the deformation temperature exceeded the β-transus temperature, the dynamic recovery was only the flow-softening mechanism. • The microstructural evolution, flow stress-strain curves and flow-softening extent were analyzed in detail. Only one flow instability was found and the type of flow instability was the adiabatic shear band. • The flow instability was predicted by establishing Prasad's and Murty's processing maps and the accuracy of the process maps was compared. • Combined with the flow-softening extent, the flow-softening mechanism was analyzed by EBSD in detail. The flow-softening mechanism changed with deformation temperatures and strain rates.

A novel optimization algorithm for the selective frequency damping parameters

Flow stability analysis is of great importance in flow physics and control. The solution of base flow, achieved as the steady state of the unsteady Navier–Stokes equation (UNSE), counts among keystones in the field of flow stability analysis. To obtain the numerical solution of base flow, the selective frequency damping (SFD) method has been widely used, with the numerical effectivity and computational efficiency being closely related to the selection of a pair of parameters (χ,Δ), where χ represents the control coefficient and Δ denotes the filter width. In the present work, a novel method for calculating the base flow of the unsteady Navier–Stokes equation (UNSE) has been established, by combining the SFD method with the immersed boundary method. Detailed analysis of the influences of the SFD parameters is presented, attempting to establish the relationships between the parameters and eigenvalues for the Jacobian matrix of UNSE. The dynamic mode decomposition method is introduced to calculate the eigenvalues for the velocity field, and several techniques and strategies are applied for improving the solving accuracy. Further, an optimization method of the parameter pair is developed to accelerate the convergence to the steady state, trying to minimize the spectral radius of the Jacobian matrix in the parameter space of (χ,Δ). Two test simulations, that is, flow past a cylinder and flow past two side-by-side cylinders at Re=100, are conducted by applying the optimization method. A faster convergence rate and higher efficiency are demonstrated compared to the results using the previous methods.

Global linear stability analysis of flow inside an axial swirl generator with a rotating vortex rope

In hydraulic turbines, either Francis or axial turbines, a high swirling flow is generated at PL conditions at the inlet of the draft tube resulting in the formation of a rotating vortex rope (RVR). This leads to pressure fluctuations which limit the operating range of single regulated turbines. In the present study, an axial hydraulic turbine has been numerically simulated by the k−ϵ and SST-based Scale-Adaptive Simulation model (SST SAS) turbulent models to capture helical RVR. Considering the formation of the RVR as the result of a global instability, linear global stability analysis of the time-averaged turbulent flow field has been conducted. For the first time in axial hydraulic turbines, how boundary conditions affect the unstable mode and which frequency, plunging or rotating, is related to the vortex rope instability have been studied. It is found that the flow inside the draft tube is sensitive to the asymmetrical disturbances with a frequency close to the rotational component.

Optimal computational parameters for maximum accuracy and minimum cost of Arnoldi-based time-stepping methods for flow global stability analysis

Global instability analysis of flows is often performed via time-stepping methods, based on the Arnoldi algorithm. When setting up these methods, several computational parameters must be chosen, which affect intrinsic errors of the procedure, such as the truncation errors, the discretization error of the flow solver, the error associated with the nonlinear terms of the Navier-Stokes equations and the error associated with the limited size of the approximation of the Jacobian matrix. This paper develops theoretical equations for the estimation of optimal balance between accuracy and cost for each case. The 2D open cavity flow is used both for explaining the effect of the parameters on the accuracy and the cost of the solution, and for verifying the quality of the predictions. The equations demonstrate the impact of each parameter on the quality of the solution. For example, if higher order methods are used for approaching a Fr\'echet derivative in the procedure, it is shown that the solution deteriorates more rapidly for larger grids or less accurate flow solvers. On the other hand, lower order approximations are more sensitive to the initial disturbance magnitude. Nevertheless, for accurate flow solvers and moderate grid dimensions, first order Fr\'echet derivative approximation with optimal computational parameters can provide 5 decimal place accurate eigenvalues. It is further shown that optimal parameters based on accuracy tend to also lead to the most cost-effective solution. The predictive equations, guidelines and conclusions are general, and, in principle, applicable to any flow, including 3D ones.