Bifurcation and stability analysis of stagnation points for an asymmetric peristaltic transport

2020 ◽  
Vol 98 (2) ◽  
pp. 172-182 ◽  
Author(s):  
Kaleem Ullah ◽  
Nasir Ali
Keyword(s):  
Flow Field ◽  
Amplitude Ratio ◽  
Nonlinear Differential Equations ◽  
Global Bifurcation ◽  
Flow Region ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Long Wavelength ◽  
Stagnation Points ◽  
The Stability

This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls.

Bifurcation Analysis for Peristaltic Transport of a Power-Law Fluid

2019 ◽  
Vol 74 (3) ◽  
pp. 213-225 ◽  
Author(s):  
Nasir Ali ◽  
Kaleem Ullah
Keyword(s):  
Power Law ◽  
Global Bifurcation ◽  
Shear Thickening ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Autonomous Differential Equations ◽  
Fluid Behaviour ◽  
Behaviour Index

AbstractIn this work, the streamline topologies and their bifurcations for peristaltic transport of shear-thinning and shear-thickening fluids characterised by power-law model are analysed. The flow is assumed in a two-dimensional symmetric channel. The analytical solution is obtained in a wave frame of reference under low Reynolds number and long wavelength approximations. To study the streamline topologies, a system of non-linear autonomous differential equations is formed and the method of dynamical system is employed to investigate the bifurcations and their changes. Three different types of flow situations occur: backward flow, trapping and augmented flow. The conversions of backward flow to trapping and then trapping to augmented flow correspond to bifurcations. The stability and nature of bifurcations and their topological changes are explained graphically. For this purpose, a global bifurcation diagram is constructed. The backward flow and trapping regions are significantly affected by fluid behaviour index. In fact, the trapping region expands and the backward region shrinks by increasing the fluid behaviour index. Theoretical results are verified by comparing them with the experimental data, which is available in the literature.

scholarly journals Peristaltic transport of a fractional Burgers’ fluid with variable viscosity through an inclined tube

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Hassan Rachid
Keyword(s):  
Reynolds Number ◽  
Radial Direction ◽  
Amplitude Ratio ◽  
Variable Viscosity ◽  
Pressure Rise ◽  
Mechanical Efficiency ◽  
Peristaltic Transport ◽  
Long Wavelength ◽  
Inclined Tube ◽  
Burgers Fluid

AbstractIn the present study,we investigate the unsteady peristaltic transport of a viscoelastic fluid with fractional Burgers’ model in an inclined tube. We suppose that the viscosity is variable in the radial direction. This analysis has been carried out under low Reynolds number and long-wavelength approximations. An analytical solution to the problem is obtained using a fractional calculus approach. Figures are plotted to show the effects of angle of inclination, Reynolds number, Froude number, material constants, fractional parameters, parameter of viscosity and amplitude ratio on the pressure gradient, pressure rise, friction force, axial velocity and on the mechanical efficiency.

scholarly journals The influence of density in population dynamics with strong and weak Allee effect

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kamrun Nahar Keya ◽  
Md. Kamrujjaman ◽  
Md. Shafiqul Islam
Keyword(s):  
Population Dynamics ◽  
Allee Effect ◽  
Global Bifurcation ◽  
Reaction Diffusion ◽  
Logistic Growth ◽  
Allee Effects ◽  
Reaction Diffusion Model ◽  
Positive Steady States ◽  
The Stability ◽  
The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

Peristaltic thrusting of a thermal-viscosity nanofluid through a resilient vertical pipe

2020 ◽  
Vol 75 (8) ◽  
pp. 727-738 ◽  
Author(s):  
Ramzy M. Abumandour ◽  
Islam M. Eldesoky ◽  
Mohamed H. Kamel ◽  
Mohamed M. Ahmed ◽  
Sara I. Abdelsalam
Keyword(s):  
Pressure Gradient ◽  
Hartmann Number ◽  
Amplitude Ratio ◽  
Variable Viscosity ◽  
Friction Forces ◽  
Long Wavelength ◽  
Viscosity Parameter ◽  
Long Wavelength Approximation ◽  
Wavelength Approximation ◽  
Theoretical Results

AbstractIn the article, the effects of the thermal viscosity and magnetohydrodynamic on the peristalsis of nanofluid are analyzed. The dominant neutralization is deduced through long wavelength approximation. The analytical solution of velocity and temperature is extracted by using steady perturbation. The pressure gradient and friction forces are obtained. Numerical results are calculated and contrasted with the debated theoretical results. These results are calculated for various values of Hartmann number, variable viscosity parameter and amplitude ratio. It is observed that the pressure gradient is reduced with an increase in the thermal viscosity parameter and that the Hartmann number enhances the pressure difference.

Effects of Heat Transfer During Peristaltic Transport in Nonuniform Channel With Permeable Walls

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Siddharth Shankar Bhatt ◽  
Amit Medhavi ◽  
R. S. Gupta ◽  
U. P. Singh
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Incompressible Fluid ◽  
Friction Force ◽  
Viscous Incompressible Fluid ◽  
Peristaltic Transport ◽  
Two Dimensional ◽  
Peristaltic Motion ◽  
Long Wavelength ◽  
Permeable Walls

In the present investigation, problem of heat transfer has been studied during peristaltic motion of a viscous incompressible fluid for two-dimensional nonuniform channel with permeable walls under long wavelength and low Reynolds number approximation. Expressions for pressure, friction force, and temperature are obtained. The effects of different parameters on pressure, friction force, and temperature have been discussed through graphs.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

Numerical Investigation of Effect of Inlet Distortion on Compressor Flow Field and Stability

2017 ◽  
Author(s):  
HaoGuang Zhang ◽  
Kang An ◽  
Feng Tan ◽  
YanHui Wu ◽  
WuLi Chu
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Total Pressure ◽  
Tip Clearance ◽  
Numerical Work ◽  
Stall Margin ◽  
Numerical Investigations ◽  
Inlet Distortion ◽  
Compressor Rotor ◽  
The Stability

The compressor aerodynamic design is conducted under the condition of clean inlet in general, but a compressor often operates under the condition of inlet distortion in the practical application. It has been proven by a lot of experimental and numerical investigations that inlet distortion can decrease the performance and stability of compressors. The circumferential or radial distorted inlet in mostly numerical investigations is made by changing the total pressure and total temperature in the inlet ring surface of the compressors. In most of inlet distortion experiments, distorted inlets are usually created by using wire net, flashboards, barriers or the generator of rotating distortion. The fashion of generating distorted inlet for experiment is different from that for numerical simulation. Consequently, the flow mechanism of affecting the flow field and stability of a compressor with distorted inlet for experiment is partly different than that for numerical simulation. In the numerical work reported here, the inlet distortion is generated by setting some barriers in the inlet ring surface of an axial subsonic compressor rotor. Two kinds of distorted inlet are investigated to exploring the effect of distorted range on the flow field and stability of the compressor with ten-passage unsteady numerical method. The numerical results show that the inlet distortions not only degrade the total pressure and efficiency of the compressor rotor, but also decrease the stability of the rotor. The larger the range of distorted inlet is, the stronger the adverse effect is. The comprehensive stall margin for the inlet distortion of 24 degrees and 48 degrees of ten-passages is reduced about 3.35% and 5.88% respectively. The detailed analysis of the flow field in the compressor indicates that the blockage resulted from tip clearance leakage vortex (TLV) and the flow separation near the suction surfaces of some blades tip for distorted inlet is more serious than that resulted from TLV for clean inlet. Moreover, the larger the range of distorted inlet is, the larger the range of the blockage is. The analysis of unsteady flow shows that during this process, which is that one rotor blade passes through the region affected by the distorted inlet, the range of the blockage in the rotor passage increases first, then reduces, and increases last.

Control of the Corner Separation in a Linear Cascade by Trailing Gaps

2017 ◽  
Author(s):  
Wenfeng Zhao ◽  
Bin Jiang ◽  
Qun Zheng
Keyword(s):  
Flow Field ◽  
Suction Surface ◽  
Optimal Length ◽  
Corner Separation ◽  
Linear Cascade ◽  
High Loss ◽  
Axial Compressors ◽  
Pressure Surface ◽  
Sst Turbulence Model ◽  
The Stability

Hub corner is the high-loss area in the blade passages of turbo machinery. It is well known that the flow separation and vortex development in this area affects directly not only the energy losses and efficiency, but also the stability of axial compressors. Linear compressor cascades with partial gaps and trailing gaps which can blow away the corner separation by the pressure difference between the suction surface and pressure surface are numerically simulated in this paper. A proposed linear cascade model with gaps has been built. The steady flow field in a linear cascade with different length gaps is studied by numerical simulation of RANS with SST turbulence model and γ-Reθ transition model focusing on the streamline structure between the corner separation vortex and the gap leakage vortex, especially the interaction of the two vertical vortex. When the length of trailing edge gaps is enough (in this paper, the optimal length of the gap is 30% chord), the corner vortex basically disappears completely. At the same time, the mode of flow field changes from the closed separation to the open separation.

scholarly journals Peristaltic transport of Johnson–Segalman fluid in a curved channel with compliant walls

2012 ◽  
Vol 17 (3) ◽  
pp. 297-311 ◽  
Author(s):  
Sadia Hina ◽  
Tasawar Hayat ◽  
Saleem Asghar
Keyword(s):  
Reynolds Number ◽  
Mathematical Analysis ◽  
Channel Wall ◽  
Peristaltic Flow ◽  
Weissenberg Number ◽  
Peristaltic Transport ◽  
Curved Channel ◽  
Long Wavelength ◽  
Channel Effects ◽  
Compliant Walls

The present investigation deals with the peristaltic flow of an incompressible Johnson–Segalman fluid in a curved channel. Effects of the channel wall properties are taken into account. The associated equations for peristaltic flow in a curved channel are modeled. Mathematical analysis is simplified under long wavelength and low Reynolds number assumptions. The solution expressions are established for small Weissenberg number. Effects of several embedded parameters on the flow quantities are discussed.

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