Investigation of pitchfork bifurcation phenomena effects on heat transfer of viscoelastic flow inside a symmetric sudden expansion

Shahbani-Zahiri, A.; Shahmardan, Mohammad Mohsen; Norouzi, M.

doi:10.1063/1.5009434

Cited by 12 publications

(5 citation statements)

References 40 publications

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“…Their results showed that the heat transfer rate and average Nu are increased and decreased respectively for the high velocities of flowing fluid at the channel inlet. Also, Shahbani-Zahiri et al [28] examined the pitchfork bifurcation phenomena for the inertial and non-isothermal flow of viscoelastic fluid in the channel with a sudden expansion by employing the exponential form of PTT model. They investigated the streamlines, length of vortices, streamlines, first and second normal stress differences and local and mean Nu for different Re (Reynolds number), El (elasticity number) and Br.…”

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confidence: 99%

Effects of fluid inertia and elasticity and expansion angles on recirculation and thermal regions of viscoelastic flow in the symmetric planar gradual expansions

Shahbani-Zahiri

Shahmardan

Norouzi

2018

J Braz. Soc. Mech. Sci. Eng.

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The formation and growth of symmetric and asymmetric recirculation regions play an important role in the viscous dissipations, temperature distribution, and heat transfer rate. In this study, the inertial and non-isothermal flow of viscoelastic fluid has been simulated in the planar channel with a 1:3 symmetric gradual expansion for different Reynolds and elasticity numbers at three expansion angles of 30°, 45°, and 60°. Also, the thermal boundary condition of constant temperature has been used on the walls, and the constitutive equation of exponential Phan Thien-Tanner has been employed for modeling the polymeric stresses of the viscoelastic fluid. Due to the significant effect of temperature on the properties of the viscoelastic fluid, and the role of viscous dissipation in heat generation, the fluid properties are considered temperature dependent, and the terms of viscous dissipation are considered in the energy equation. The main purpose of current study is to investigate the effects of fluid inertia and elasticity and the expansion angles on the flow pattern, heat transfer characteristics, and viscous dissipation of inertial viscoelastic flow in the planar channel with gradual expansions. Therefore, the streamlines, length of vortices, isothermal lines, total viscous dissipations, and local and mean Nusselt numbers (Nu) have been examined inside the channel expansion for different Reynolds and elasticity numbers in the range of 10 ≤ Re ≤ 100 and 0.01 ≤ El ≤ 2. The results show that the maximum values of local Nusselt numbers are enhanced by increasing the Reynolds and elasticity numbers and the expansion angle for the hydrodynamically and thermally developing conditions.

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confidence: 99%

Effects of fluid inertia and elasticity and expansion angles on recirculation and thermal regions of viscoelastic flow in the symmetric planar gradual expansions

Shahbani-Zahiri

Shahmardan

Norouzi

2018

J Braz. Soc. Mech. Sci. Eng.

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“…In addition, the timeliness of this interesting rheological topic can be demonstrated by following selected works published in the last five years. In 2017, Shahbani-Zahiri et al published theoretical work [17] focused on the effects of recirculation regions and vortex lengths on temperature distribution, Nusselt numbers and first/second normal stress differences in flows of non-isothermal viscoelastic fluids within a 1:3 sudden planar symmetric expansion channel. In the same year, López-Aguilar et al [18] theoretically studied pressure drops in vortex contraction flows for Boger fluids described by continuous-spectrum and discrete-mode differential models.…”

Section: Introductionmentioning

confidence: 99%

“…However, the online version of record will be different from this version once it has been copyedited and typeset. bonding [20] and molecular structure [21,27,28,31], development and testing of constitutive equations [18,23,25,26], parametric analysis [22,24,30], numerical algorithms [17,19] or experimental visualization methodology [29].…”

Section: Introductionmentioning

confidence: 99%

Flow-induced birefringence study of secondary flow in entrance region of rectangular slit channel for long-chain-branched polyethylene melt

Musil

Zatloukal

2022

Physics of Fluids

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This work presents an analysis of the inner boundary of the secondary flow (i.e. corner vortex flow) in entrance region of rectangular slit channel for long-chain-branched polyethylene melt evaluated using particle tracking and stress-induced birefringence measurements. Further, the flow-induced birefringence technique was used to investigate the effects of temperature and shear rate on the size of the secondary entry flow. Obtained results and trends were compared with the laser-Doppler velocimetry data taken from the open literature for the same polymer melt and comparable flow conditions. Interestingly, the results of both methods were very similar. This suggests that the stress-induced birefringence measurements may be a useful tool for investigating secondary entry flows of polymer melts.

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“…Flow stability analysis 10 predicts how small flow perturbations grow or decay with respect to an equilibrium flow solution (the base flow), providing information about the onset of asymmetries or unsteadiness, the physical mechanism associated to the perturbation responsible for the bifurcation, and can help to determine means by which to control it. This technique has been used to analyse similar geometries: sudden expansions [11][12][13][14] , sudden contractions 7,15 , geometries with both an expansion and a contraction 16 , X-junctions 17 , or more recently T-junctions [18][19][20] . The physical mechanism behind the onset of asymmetry, in these cases, is a stationary unstable global mode.…”

Section: Introductionmentioning

confidence: 99%

Enhanced stability of flows through contraction channels: Combining shape optimization and linear stability analysis

et al. 2019

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The first flow bifurcation, in channels with a sudden geometry contraction, is controlled through shape optimisation to delay the onset of asymmetry. First, we confirm the existence of a pitchfork type bifurcation instability, already reported in similar geometries. The global mode responsible for this bifurcation leads to asymmetric flow for Reynolds numbers beyond a critical value. Second, we propose a global shape optimisation methodology to introduce small modifications in the channel geometry that lead to flows with enhanced stability. Our results include three contraction ratios C = 2, 4 and 8, where C is the ratio of upstream to downstream channel widths.The shape optimisation aims at minimising the growth rate of the unstable mode responsible for asymmetry. Sensitivity analysis is used to find an appropriate geometry parametrisation, which is defined through super-elliptic curves, and limited to small deformations. Additionally, a dynamically updated surrogate model (based on Radial Basis Functions) is developed to drive the optimisation. This substitutes expensive function evaluations, each requiring the solution of a steady Navier-Stokes base flow computation and a solution of an eigenvalue problem (linear stability analysis). Finally, a mode tracking algorithm identifies the eigenmode responsible for the onset of asymmetry during the optimisation.The optimised geometries show rounded corners and are stable for Reynolds numbers well beyond the original values. For all contraction ratios, the critical Reynolds number increases by at least 7.9 times with respect to the original values. three-dimensional simulations confirm that the optimised geometry is more stable than the original when periodic boundaries are used on the side walls. When comparing the drag of the optimised geometry to the original, we obtain a reduction of at least 64%.

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Investigation of pitchfork bifurcation phenomena effects on heat transfer of viscoelastic flow inside a symmetric sudden expansion

Cited by 12 publications

References 40 publications

Effects of fluid inertia and elasticity and expansion angles on recirculation and thermal regions of viscoelastic flow in the symmetric planar gradual expansions

Effects of fluid inertia and elasticity and expansion angles on recirculation and thermal regions of viscoelastic flow in the symmetric planar gradual expansions

Flow-induced birefringence study of secondary flow in entrance region of rectangular slit channel for long-chain-branched polyethylene melt

Enhanced stability of flows through contraction channels: Combining shape optimization and linear stability analysis

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