Pub Date : 2024-10-09DOI: 10.1016/j.jnnfm.2024.105331
Panagiotis Sialmas, Kostas D. Housiadas
An exact analytical solution of the lubrication equations for the steady, isothermal, incompressible flow of a viscoelastic Oldroyd-B fluid in a hyperbolic cylindrical contracting pipe is derived. The solution is valid for values of the Deborah number, De, up to order unity (De is defined as the ratio of the longest relaxation time of the polymer to the characteristic residence time of the fluid in the pipe), all values of the ratio of the polymer viscosity to the total viscosity of the fluid, η, and typical values of the contraction ratio, Λ, encountered in experiments and practical applications. It is provided in terms of the streamfunction only and is used in the momentum balance to derive a strongly non-linear ordinary differential equation of second order with unknown a function which corresponds to a modified fluid velocity along the main flow direction. The final equation is solved semi-numerically using a fully spectral (Legendre)-Galerkin approach to resolve the unknown function almost down to machine accuracy. The exact solution for the polymer extra-stresses, which is emphasized is not the full solution of the complete lubrication equations, allows for the derivation of a variety of theoretical expressions for the average pressure-drop along the pipe. In all cases, a decrease in the pressure drop compared to the Newtonian value with increasing De, η and/or Λ is predicted. The differences between the corresponding analytical solution for the planar geometrical configuration are also identified and discussed.
{"title":"An exact solution of the lubrication equations for the Oldroyd-B model in a hyperbolic pipe","authors":"Panagiotis Sialmas, Kostas D. Housiadas","doi":"10.1016/j.jnnfm.2024.105331","DOIUrl":"10.1016/j.jnnfm.2024.105331","url":null,"abstract":"<div><div>An exact analytical solution of the lubrication equations for the steady, isothermal, incompressible flow of a viscoelastic Oldroyd-B fluid in a hyperbolic cylindrical contracting pipe is derived. The solution is valid for values of the Deborah number, De, up to order unity (De is defined as the ratio of the longest relaxation time of the polymer to the characteristic residence time of the fluid in the pipe), all values of the ratio of the polymer viscosity to the total viscosity of the fluid, η, and typical values of the contraction ratio, Λ, encountered in experiments and practical applications. It is provided in terms of the streamfunction only and is used in the momentum balance to derive a strongly non-linear ordinary differential equation of second order with unknown a function which corresponds to a modified fluid velocity along the main flow direction. The final equation is solved semi-numerically using a fully spectral (Legendre)-Galerkin approach to resolve the unknown function almost down to machine accuracy. The exact solution for the polymer extra-stresses, which is emphasized is not the full solution of the complete lubrication equations, allows for the derivation of a variety of theoretical expressions for the average pressure-drop along the pipe. In all cases, a decrease in the pressure drop compared to the Newtonian value with increasing De, η and/or Λ is predicted. The differences between the corresponding analytical solution for the planar geometrical configuration are also identified and discussed.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"335 ","pages":"Article 105331"},"PeriodicalIF":2.7,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-05DOI: 10.1016/j.jnnfm.2024.105332
P.S.D. Surya Phani Tej , Pratyush Kumar Mohanty , V. Shankar
We demonstrate that velocity profiles for steady, unidirectional shear flows of the FENE-P (Finitely-Extensible Nonlinear Elastic, with Peterlin closure) fluid, undergoing canonical rectilinear (pressure-driven flow in a rectangular channel or a circular pipe) or curvilinear (in Taylor–Couette or Dean configurations) flows, obey universal master curves that are a function only of the ratio , for a fixed solvent to solution viscosity parameter . Here, is the Weissenberg number defined as the product of the dumbbell relaxation time and an appropriate shear rate, while is the ratio of the maximum extension of the polymer to its equilibrium root-mean-square end-to-end distance. The data collapse and the resulting master curves for the velocity profile is a generalization of the recent demonstration of master curves for polymer viscosity and first normal stress coefficient for a FENE-P fluid under steady simple shear flow (Yamani and McKinley, 2023). For pressure-driven channel and pipe flows, we derive simple analytical expressions for the velocity profiles, in the high shear-rate regime of , that readily elucidate the role of finite extensibility of the polymer on the velocity profiles. In the regime, for all the flows considered, the limit of zero solvent () is shown to be singular, owing to the absence of a high-shear plateau in the total solution viscosity, resulting in very different velocity profiles for and .
{"title":"Master curves for unidirectional flows of FENE-P fluids in rectilinear and curvilinear geometries","authors":"P.S.D. Surya Phani Tej , Pratyush Kumar Mohanty , V. Shankar","doi":"10.1016/j.jnnfm.2024.105332","DOIUrl":"10.1016/j.jnnfm.2024.105332","url":null,"abstract":"<div><div>We demonstrate that velocity profiles for steady, unidirectional shear flows of the FENE-P (Finitely-Extensible Nonlinear Elastic, with Peterlin closure) fluid, undergoing canonical rectilinear (pressure-driven flow in a rectangular channel or a circular pipe) or curvilinear (in Taylor–Couette or Dean configurations) flows, obey universal master curves that are a function only of the ratio <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi></mrow></math></span> , for a fixed solvent to solution viscosity parameter <span><math><mi>β</mi></math></span>. Here, <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi></mrow></math></span> is the Weissenberg number defined as the product of the dumbbell relaxation time and an appropriate shear rate, while <span><math><mi>L</mi></math></span> is the ratio of the maximum extension of the polymer to its equilibrium root-mean-square end-to-end distance. The data collapse and the resulting master curves for the velocity profile is a generalization of the recent demonstration of master curves for polymer viscosity and first normal stress coefficient for a FENE-P fluid under steady simple shear flow (Yamani and McKinley, 2023). For pressure-driven channel and pipe flows, we derive simple analytical expressions for the velocity profiles, in the high shear-rate regime of <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi><mo>≫</mo><mn>1</mn></mrow></math></span>, that readily elucidate the role of finite extensibility of the polymer on the velocity profiles. In the <span><math><mrow><mi>W</mi><mspace></mspace><mi>i</mi><mo>/</mo><mi>L</mi><mo>≫</mo><mn>1</mn></mrow></math></span> regime, for all the flows considered, the limit of zero solvent (<span><math><mrow><mi>β</mi><mo>=</mo><mn>0</mn></mrow></math></span>) is shown to be singular, owing to the absence of a high-shear plateau in the total solution viscosity, resulting in very different velocity profiles for <span><math><mrow><mi>β</mi><mo>=</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>β</mi><mo>→</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105332"},"PeriodicalIF":2.7,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-03DOI: 10.1016/j.jnnfm.2024.105328
D.R. Hewitt , N.J. Balmforth
Stokes’s second problem is reconsidered for three models of complex fluids: an elasto-viscoplastic fluid, a thixotropic viscoplastic fluid and a discontinuously shear-thickening fluid. In each case, the Stokes-layer dynamics is interrogated with a view to examining the signatures of the detailed rheology. Significant deformations are possible below the yield stress for elasto-viscoplastic fluids as a result of the excitation of elastic waves, particularly near resonances. Thixotropic fluids with viscosity bifurcations layer internally, but surface-speed signatures mostly appear similar to those for simple yield-stress fluids. Stokes-layer oscillations of discontinuous shear thickening fluids can prompt abrupt increases in viscosity, introducing sudden jumps in surface speed. Pre-existing experimental results for layers of kaolin slurries in a motorized, oscillating tray are reconsidered and compared with the results for elasto-viscoplastic and thixotropic fluids.
{"title":"Stokes layers in complex fluids","authors":"D.R. Hewitt , N.J. Balmforth","doi":"10.1016/j.jnnfm.2024.105328","DOIUrl":"10.1016/j.jnnfm.2024.105328","url":null,"abstract":"<div><div>Stokes’s second problem is reconsidered for three models of complex fluids: an elasto-viscoplastic fluid, a thixotropic viscoplastic fluid and a discontinuously shear-thickening fluid. In each case, the Stokes-layer dynamics is interrogated with a view to examining the signatures of the detailed rheology. Significant deformations are possible below the yield stress for elasto-viscoplastic fluids as a result of the excitation of elastic waves, particularly near resonances. Thixotropic fluids with viscosity bifurcations layer internally, but surface-speed signatures mostly appear similar to those for simple yield-stress fluids. Stokes-layer oscillations of discontinuous shear thickening fluids can prompt abrupt increases in viscosity, introducing sudden jumps in surface speed. Pre-existing experimental results for layers of kaolin slurries in a motorized, oscillating tray are reconsidered and compared with the results for elasto-viscoplastic and thixotropic fluids.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105328"},"PeriodicalIF":2.7,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.jnnfm.2024.105329
Maksim A. Pakhomov , Uzak K. Zhapbasbayev
A transition of Newtonian turbulent fluid to viscoplastic non-Newtonian fluid by cooling in a pipe with a sudden expansion is numerically studied. A recirculation region with negative velocities appears for fluid velocity profiles corresponding to the zone of flow recirculation. A small corner eddy disappears for a non-Newtonian fluid. Significant anisotropy between axial and radial components of Reynolds stresses is numerically shown. The heat transfer distributions along the pipe surface for turbulent non- and Newtonian fluids are qualitatively similar. The peak of heat transfer is shifted upstream in the Schwedoff-Bingham fluid in comparison with the Newtonian one. Authors’ numerical predictions are compared with numerical simulations by other authors for turbulent Schwedoff-Bingham fluids.
{"title":"RANS predictions of turbulent non-isothermal viscoplastic fluid in pipe with sudden expansion","authors":"Maksim A. Pakhomov , Uzak K. Zhapbasbayev","doi":"10.1016/j.jnnfm.2024.105329","DOIUrl":"10.1016/j.jnnfm.2024.105329","url":null,"abstract":"<div><div>A transition of Newtonian turbulent fluid to viscoplastic non-Newtonian fluid by cooling in a pipe with a sudden expansion is numerically studied. A recirculation region with negative velocities appears for fluid velocity profiles corresponding to the zone of flow recirculation. A small corner eddy disappears for a non-Newtonian fluid. Significant anisotropy between axial and radial components of Reynolds stresses is numerically shown. The heat transfer distributions along the pipe surface for turbulent non- and Newtonian fluids are qualitatively similar. The peak of heat transfer is shifted upstream in the Schwedoff-Bingham fluid in comparison with the Newtonian one. Authors’ numerical predictions are compared with numerical simulations by other authors for turbulent Schwedoff-Bingham fluids.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"334 ","pages":"Article 105329"},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142417120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-23DOI: 10.1016/j.jnnfm.2024.105327
Zhen Liu , Shuai Dong , He Yang , Wenzhi Yang , Muyao Zhu
Coal seam water injection technology is adopted by many mines as an effective means of dust reduction in coal mines. There is a threshold pressure gradient phenomenon in the process of water injection in low permeability coal seam, which makes the flow of pressure water in the fracture structure of coal body present nonlinear seepage characteristics. To reveal the theoretical relationship between the structural parameters of coal and the nonlinear seepage characteristics, firstly, the Bingham fluid constitutive equation is used to describe the non-Newtonian behavior in low-permeability coal. Combined with the fractal tree-like bifurcation fracture network model, a mathematical analytical model of threshold pressure gradient is established. Secondly, the model was verified by high-pressure water invasion and radial seepage experiments, and the sensitivity of the model was analyzed. The results show that the error between the theoretical calculation value and the experimental measurement value is between 8.65 % and 42.4 %, which verifies the validity of the model. The above research results can provide a theoretical basis for improving the water injection effect of low permeability coal seam.
{"title":"Theoretical study on nonlinear seepage mechanism in fractal dendritic fracture network of low permeability coal with water injection","authors":"Zhen Liu , Shuai Dong , He Yang , Wenzhi Yang , Muyao Zhu","doi":"10.1016/j.jnnfm.2024.105327","DOIUrl":"10.1016/j.jnnfm.2024.105327","url":null,"abstract":"<div><div>Coal seam water injection technology is adopted by many mines as an effective means of dust reduction in coal mines. There is a threshold pressure gradient phenomenon in the process of water injection in low permeability coal seam, which makes the flow of pressure water in the fracture structure of coal body present nonlinear seepage characteristics. To reveal the theoretical relationship between the structural parameters of coal and the nonlinear seepage characteristics, firstly, the Bingham fluid constitutive equation is used to describe the non-Newtonian behavior in low-permeability coal. Combined with the fractal tree-like bifurcation fracture network model, a mathematical analytical model of threshold pressure gradient is established. Secondly, the model was verified by high-pressure water invasion and radial seepage experiments, and the sensitivity of the model was analyzed. The results show that the error between the theoretical calculation value and the experimental measurement value is between 8.65 % and 42.4 %, which verifies the validity of the model. The above research results can provide a theoretical basis for improving the water injection effect of low permeability coal seam.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105327"},"PeriodicalIF":2.7,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.jnnfm.2024.105326
A. Gharagozlou , M. Pourjafar-Chelikdani , K. Sadeghy
The classic Richards equation is a good model for predicting imbibition of viscous fluids in porous materials such as dry soils or filter papers. It cannot, in principle, be used for physiological fluids such as blood simply because such fluids often exhibit a variety of non-Newtonian behavior such as a yield stress. In the present work, we have theoretically extended the classic Richards equation to viscoplastic fluids obeying the Bingham model using the concept of the effective viscosity together with the bundle-of-tube model. The new imbibition model could partly resolve the discrepancy reported in the literature between the predictions of the classic Richards equation for the stain growth of sessile blood droplets in a typical filter paper. A better fit, however, requires considering other non-Newtonian effects of the blood such as its viscoelasticity. Using the Bingham-modified Richards equation, it is demonstrated that yield stress in a test fluid has a retarding effect on the imbibition phenomenon, so that such fluids may not necessarily reach the test line of a paper-based diagnostic kit. But yield stress is predicted to extend the duration of the quasi-steady regime on the test line of diagnostic kits, which is a desirable effect. The results suggest that inducing (or elevating) the level of yield stress in a test liquid such as blood can be used as a passive means to control imbibition characteristics in paper-based systems.
{"title":"Yield-stress effects on spontaneous imbibition in paper-based kits","authors":"A. Gharagozlou , M. Pourjafar-Chelikdani , K. Sadeghy","doi":"10.1016/j.jnnfm.2024.105326","DOIUrl":"10.1016/j.jnnfm.2024.105326","url":null,"abstract":"<div><div>The classic Richards equation is a good model for predicting imbibition of viscous fluids in porous materials such as dry soils or filter papers. It cannot, in principle, be used for physiological fluids such as blood simply because such fluids often exhibit a variety of non-Newtonian behavior such as a yield stress. In the present work, we have theoretically extended the classic Richards equation to viscoplastic fluids obeying the Bingham model using the concept of the effective viscosity together with the bundle-of-tube model. The new imbibition model could partly resolve the discrepancy reported in the literature between the predictions of the classic Richards equation for the stain growth of sessile blood droplets in a typical filter paper. A better fit, however, requires considering other non-Newtonian effects of the blood such as its viscoelasticity. Using the Bingham-modified Richards equation, it is demonstrated that yield stress in a test fluid has a retarding effect on the imbibition phenomenon, so that such fluids may not necessarily reach the test line of a paper-based diagnostic kit. But yield stress is predicted to extend the duration of the quasi-steady regime on the test line of diagnostic kits, which is a desirable effect. The results suggest that inducing (or elevating) the level of yield stress in a test liquid such as blood can be used as a passive means to control imbibition characteristics in paper-based systems.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105326"},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.jnnfm.2024.105324
Kai Tian , Chundong Xue , Jifeng Cui , Kai-Rong Qin , Zhaodong Ding
This study conducts a comprehensive exploration of the elasticity and Marangoni instability exhibited by a non-Newtonian polymer film flow down an inclined plane within the context of an upper-convected Maxwell (UCM) model. The asymptotic solutions are derived utilizing the stream function and perturbation method based on the long-wave assumption. The numerical solutions are effectively solved at arbitrary wavelengths through the implementation of the Chebyshev spectral collocation technique. The results show that the presence of elastic stress renders the film more susceptible to destabilization. The underlying mechanisms that instigate the instability are examined from an energy balance perspective. It is determined that the instability of the film is predominantly governed by shear stress (SHE) and elastic stress (DIP) effects. Shear stress increases the perturbation kinetic energy to promote instability, while elastic stress decreases the perturbation kinetic energy to enhance stability. However, for the Weissenberg number , the shear stress changes from an unstable to a stabilizing factor, and the elastic stress changes from stable to unstable when the wave number . This intriguing inversion is attributed to the dual nature of elasticity, possessing both stabilizing and destabilizing tendencies. Despite the work of Marangoni stress (MAT) magnitude remaining within the order of , the Marangoni effect indirectly contributes to instability enhancement.
{"title":"Instabilities of Marangoni and elasticity in a molten polymer film","authors":"Kai Tian , Chundong Xue , Jifeng Cui , Kai-Rong Qin , Zhaodong Ding","doi":"10.1016/j.jnnfm.2024.105324","DOIUrl":"10.1016/j.jnnfm.2024.105324","url":null,"abstract":"<div><div>This study conducts a comprehensive exploration of the elasticity and Marangoni instability exhibited by a non-Newtonian polymer film flow down an inclined plane within the context of an upper-convected Maxwell (UCM) model. The asymptotic solutions are derived utilizing the stream function and perturbation method based on the long-wave assumption. The numerical solutions are effectively solved at arbitrary wavelengths through the implementation of the Chebyshev spectral collocation technique. The results show that the presence of elastic stress renders the film more susceptible to destabilization. The underlying mechanisms that instigate the instability are examined from an energy balance perspective. It is determined that the instability of the film is predominantly governed by shear stress (SHE) and elastic stress (DIP) effects. Shear stress increases the perturbation kinetic energy to promote instability, while elastic stress decreases the perturbation kinetic energy to enhance stability. However, for the Weissenberg number <span><math><mrow><mi>W</mi><mi>i</mi><mo>=</mo><mn>1</mn></mrow></math></span>, the shear stress changes from an unstable to a stabilizing factor, and the elastic stress changes from stable to unstable when the wave number <span><math><mrow><mi>k</mi><mo>></mo><mn>1</mn></mrow></math></span>. This intriguing inversion is attributed to the dual nature of elasticity, possessing both stabilizing and destabilizing tendencies. Despite the work of Marangoni stress (MAT) magnitude remaining within the order of <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math></span>, the Marangoni effect indirectly contributes to instability enhancement.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105324"},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-19DOI: 10.1016/j.jnnfm.2024.105323
Xiang Qiu , Xu Ding , Yizhou Tao , Junwang Qu , Jiahua Li , Yulu Liu
In this study, direct numerical simulations (DNS) was used to investigate the flow behavior of power-law fluids flow around a circular cylinder near a wall at the Reynolds number of 200. The power-law index represents the typical situation of shear-thinning fluids ( to 1.0), whereas the gap ratio ranges from 0.2 to 1.0 (where represents the gap between the cylinder and the plane wall and represents the diameter of the cylinder). This study aimed to analyze the influence of the power-law index and gap ratio on the time-averaged flow, vortex dynamics, and the force exerted on the cylinder. The results indicate that for and , two secondary vortex structures form behind the cylinder because of the induction of the primary vortices, and they are in reverse rotation. An analysis of the signed enstrophy revealed a positive correlation between the strengths of the primary and secondary vortices, both of which diminished as the gap ratio decreased and increased as the power-law index decreased. Notably, vortex shedding was observed at when , which is absent in Newtonian fluids. Through the analysis of vorticity transport equation, the development of vorticity is attributed to changes in the convection term, viscosity diffusion term and viscosity gradient term. By examining the key points, the formation of secondary vortex structure and the reason of vortex shedding at in power-law fluids are explained. Furthermore, the time-averaged drag coefficient initially decreases and then increases with decreasing , and decreases with decreasing . The time-averaged lift coefficient exhibits a typical L-type curve with increasing gap ratios, where initially decreases and then increases.
本研究采用直接数值模拟（DNS）方法研究了雷诺数为 200 时，幂律流体在靠近壁面的圆柱体周围的流动行为。幂律指数 n 代表剪切稀化流体的典型情况（n=0.2 至 1.0），而间隙比 G/D 的范围为 0.2 至 1.0（其中 G 代表圆柱体与平面壁之间的间隙，D 代表圆柱体的直径）。本研究旨在分析幂律指数和间隙比对时均流动、涡旋动力学和气缸受力的影响。结果表明，当 G/D≥0.5 和 n≤0.5 时，由于主涡旋的诱导，在圆柱体后方形成了两个次级涡旋结构，它们处于反向旋转状态。对符号漩涡的分析表明，主漩涡和副漩涡的强度呈正相关，两者都随着间隙比的减小而减小，随着幂律指数的减小而增大。值得注意的是，当 n≤0.3 时，在 G/D=0.3 处观察到涡流脱落，而这在牛顿流体中是不存在的。通过对涡度传输方程的分析，涡度的发展归因于对流项、粘度扩散项和粘度梯度项的变化。通过对关键点的研究，解释了幂律流体在 G/D=0.3 时次级涡旋结构的形成和涡旋脱落的原因。此外，时均阻力系数 C¯D 随 n 的减小先减小后增大，并随 G/D 的减小而减小。时均升力系数 C¯L 随着间隙比的增大呈现典型的 L 型曲线，即 C¯L 先减小后增大。
{"title":"Research on the flow around a circular cylinder near a wall for shear-thinning power-law fluids","authors":"Xiang Qiu , Xu Ding , Yizhou Tao , Junwang Qu , Jiahua Li , Yulu Liu","doi":"10.1016/j.jnnfm.2024.105323","DOIUrl":"10.1016/j.jnnfm.2024.105323","url":null,"abstract":"<div><div>In this study, direct numerical simulations (DNS) was used to investigate the flow behavior of power-law fluids flow around a circular cylinder near a wall at the Reynolds number of 200. The power-law index <span><math><mi>n</mi></math></span> represents the typical situation of shear-thinning fluids (<span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn></mrow></math></span> to 1.0), whereas the gap ratio <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi></mrow></math></span> ranges from 0.2 to 1.0 (where <span><math><mi>G</mi></math></span> represents the gap between the cylinder and the plane wall and <span><math><mi>D</mi></math></span> represents the diameter of the cylinder). This study aimed to analyze the influence of the power-law index and gap ratio on the time-averaged flow, vortex dynamics, and the force exerted on the cylinder. The results indicate that for <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi><mo>≥</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span> and <span><math><mrow><mi>n</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span>, two secondary vortex structures form behind the cylinder because of the induction of the primary vortices, and they are in reverse rotation. An analysis of the signed enstrophy revealed a positive correlation between the strengths of the primary and secondary vortices, both of which diminished as the gap ratio decreased and increased as the power-law index decreased. Notably, vortex shedding was observed at <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></mrow></math></span> when <span><math><mrow><mi>n</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>3</mn></mrow></math></span>, which is absent in Newtonian fluids. Through the analysis of vorticity transport equation, the development of vorticity is attributed to changes in the convection term, viscosity diffusion term and viscosity gradient term. By examining the key points, the formation of secondary vortex structure and the reason of vortex shedding at <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn></mrow></math></span> in power-law fluids are explained. Furthermore, the time-averaged drag coefficient <span><math><msub><mrow><mover><mrow><mi>C</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>D</mi></mrow></msub></math></span> initially decreases and then increases with decreasing <span><math><mi>n</mi></math></span>, and decreases with decreasing <span><math><mrow><mi>G</mi><mo>/</mo><mi>D</mi></mrow></math></span>. The time-averaged lift coefficient <span><math><msub><mrow><mover><mrow><mi>C</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>L</mi></mrow></msub></math></span> exhibits a typical L-type curve with increasing gap ratios, where <span><math><msub><mrow><mover><mrow><mi>C</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>L</mi></mrow></msub></math></span> initially decreases and then increases.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105323"},"PeriodicalIF":2.7,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-18DOI: 10.1016/j.jnnfm.2024.105321
Ann Aisling, Renee Saraka, Nicolas J. Alvarez
This work focuses on inferring the molecular state of the polymer chain required to induce stress relaxation and the accurate measure of the polymer’s longest relaxation time in uniaxial stretching of dilute polymer solutions. This work is facilitated by the discovery that constant velocity applied at early times leads to initial constant extension rate before reaching the Rayleigh–Plateau instability. Such constant rate experiments are used to correlate initial stretching kinematics with the thinning dynamics in the final thinning regime. We show that there is a minimum initial strain-rate required to induce rate independent elastic effects, and measure the longest relaxation time of the material. Below the minimum extension rate, insufficient stretching of the chain is observed before capillary instability, such that the polymer stress is comparable to the capillary stress at long times and stress relaxation is not achieved. Above the minimum strain-rate, the chain reaches a critical stretch before instability, such that during the unstable filament thinning the polymer stress is significantly larger than the capillary stress and rate-independent stress relaxation is observed. Using a single relaxation mode FENE model, we show that the minimum strain rate leads to a required initial stretch of the chain before reaching the Rayleigh–Plateau limit. These results indicate that the chain conformation before entering the Rayleigh Instability Regime, and the stretching induced during the instability, determines the elastic behavior of the filament. Lastly, this work introduces a characteristic dimensionless group, called the stretchability factor, that can be used to quantitatively compare different materials based on the overall material deformation/kinematic behavior, not just the relaxation time. Overall, these results demonstrate a useful methodology to study the stretching of dilute solutions using a constant velocity stretching scheme.
{"title":"The importance of initial extension rate on elasto-capillary thinning of dilute polymer solutions","authors":"Ann Aisling, Renee Saraka, Nicolas J. Alvarez","doi":"10.1016/j.jnnfm.2024.105321","DOIUrl":"10.1016/j.jnnfm.2024.105321","url":null,"abstract":"<div><div>This work focuses on inferring the molecular state of the polymer chain required to induce stress relaxation and the accurate measure of the polymer’s longest relaxation time in uniaxial stretching of dilute polymer solutions. This work is facilitated by the discovery that constant velocity applied at early times leads to initial constant extension rate before reaching the Rayleigh–Plateau instability. Such constant rate experiments are used to correlate initial stretching kinematics with the thinning dynamics in the final thinning regime. We show that there is a minimum initial strain-rate required to induce rate independent elastic effects, and measure the longest relaxation time of the material. Below the minimum extension rate, insufficient stretching of the chain is observed before capillary instability, such that the polymer stress is comparable to the capillary stress at long times and stress relaxation is not achieved. Above the minimum strain-rate, the chain reaches a critical stretch before instability, such that during the unstable filament thinning the polymer stress is significantly larger than the capillary stress and rate-independent stress relaxation is observed. Using a single relaxation mode FENE model, we show that the minimum strain rate leads to a required initial stretch of the chain before reaching the Rayleigh–Plateau limit. These results indicate that the chain conformation before entering the Rayleigh Instability Regime, and the stretching induced during the instability, determines the elastic behavior of the filament. Lastly, this work introduces a characteristic dimensionless group, called the stretchability factor, that can be used to quantitatively compare different materials based on the overall material deformation/kinematic behavior, not just the relaxation time. Overall, these results demonstrate a useful methodology to study the stretching of dilute solutions using a constant velocity stretching scheme.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105321"},"PeriodicalIF":2.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S037702572400137X/pdfft?md5=d1f32f9cee619f02d115117fa2418228&pid=1-s2.0-S037702572400137X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-18DOI: 10.1016/j.jnnfm.2024.105325
Banashree Samanta , Manish Kaushal , Gargi Das , Subhabrata Ray
Laminar planar hydraulic jump during viscoplastic liquid flow in a horizontal channel is investigated through experiments and numerical simulation using Herschel-Bulkley (HB) model. The simulations are performed using the phase-field method with Papanastasiou regularization parameter and validated against experimental results. Both experiments and simulations show the free surface height to gradually increase upstream of jump and recede after the jump with a remarkable increase in free surface height and surface waviness at the jump. The model further reveals that an increase in any of the rheological parameters [yield stress () flow behaviour index (n) and flow consistency index (k)] keeping the other properties constant increases film thickness. This increases jump strength and shifts jump towards the entry. However, each parameter influences free surface profile and jump characteristics in a different way. While a higher τo suppresses the development of the shear zone and results in a thicker plug zone, a higher n increases shear zone thickness and decreases the plug zone thickness. On the other hand, a higher k increases both shear and plug zone thickness. The steady state fully developed self-similar velocity profile is independent of k and depends on and n. Different jump types, obtained from simulations, are presented as phase diagrams in non-dimensional coordinates for a generalised approach.
{"title":"A numerical investigation of laminar planar hydraulic jump in Herschel-Bulkley fluid","authors":"Banashree Samanta , Manish Kaushal , Gargi Das , Subhabrata Ray","doi":"10.1016/j.jnnfm.2024.105325","DOIUrl":"10.1016/j.jnnfm.2024.105325","url":null,"abstract":"<div><div>Laminar planar hydraulic jump during viscoplastic liquid flow in a horizontal channel is investigated through experiments and numerical simulation using Herschel-Bulkley (HB) model. The simulations are performed using the phase-field method with Papanastasiou regularization parameter and validated against experimental results. Both experiments and simulations show the free surface height to gradually increase upstream of jump and recede after the jump with a remarkable increase in free surface height and surface waviness at the jump. The model further reveals that an increase in any of the rheological parameters [yield stress (<span><math><msub><mi>τ</mi><mi>o</mi></msub></math></span>) flow behaviour index (<em>n</em>) and flow consistency index (<em>k</em>)] keeping the other properties constant increases film thickness. This increases jump strength and shifts jump towards the entry. However, each parameter influences free surface profile and jump characteristics in a different way. While a higher τ<em><sub>o</sub></em> suppresses the development of the shear zone and results in a thicker plug zone, a higher <em>n</em> increases shear zone thickness and decreases the plug zone thickness. On the other hand, a higher <em>k</em> increases both shear and plug zone thickness. The steady state fully developed self-similar velocity profile is independent of <em>k</em> and depends on <span><math><msub><mi>τ</mi><mi>o</mi></msub></math></span> and <em>n</em>. Different jump types, obtained from simulations, are presented as phase diagrams in non-dimensional coordinates for a generalised approach.</div></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105325"},"PeriodicalIF":2.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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