A mathematical model is constructed to examine the characteristics of three layered blood flow through the oscillatory cylindrical tube （stenosed arteries）. The proposed model basically consists three layers of blo...A mathematical model is constructed to examine the characteristics of three layered blood flow through the oscillatory cylindrical tube （stenosed arteries）. The proposed model basically consists three layers of blood （viscous fluids with different viscosities） named as core layer （red blood cells）, intermediate layer （platelets/white blood cells） and peripheral layer （plasma）. The analysis was restricted to propagation of small-amplitude harmonic waves, generated due to blood flow whose wave length is larger compared to the radius of the arterial segment. The impacts of viscosity of fluid in peripheral layer and intermediate layer on the interfaces, average flow rate, mechanical efficiency, trapping and reflux are discussed with the help of numerical and computational results. This model is the generalized form of the preceding models. On the basis of present discussion, it is found that the size of intermediate and peripheral layers reduces in expanded region and enhances in contracted region with the increasing viscosity of fluid in peripheral layer, whereas, opposite effect is observed for viscosity of fluid in intermediate layer. Final conclusion is that the average flow rate and mechanical efficiency increase with the increasing viscosity of fluid in both layers, however, the effects of the viscosity of fluid in both layers on trapping and reflux are opposite to each other.展开更多
Nikuradse roughness(ks) is very important in the sediment transport prediction because it is related to the evaluations of the velocity distribution, shear stress and erosion depth. Dimensionless Nikuradse roughness(k...Nikuradse roughness(ks) is very important in the sediment transport prediction because it is related to the evaluations of the velocity distribution, shear stress and erosion depth. Dimensionless Nikuradse roughness(ks/D,where D is the sediment diameter) is usually given 1–2.5 on the immobile plan bed or at low shear stress. But it behaves differently on the mobile plan bed at high shear stress with much sediment picked up to movement when the Shields parameter(Θ) is larger than 0.8–1.0. The effective Nikuradse roughness on the mobile plan bed was derived indirectly from the erosion depth correlated to the mobile plan bed thickness considering the mass conservation in the present study. The proposed erosion depth confirmed the relation to the Shields parameters with an extra factor consisting of suspended sediment and its damping to turbulence. The decrement of the erosion depth caused by the increment of the sediment diameter at large shear stress was obtained, which was usually absent in classical empirical formulas based on the bedload theory. Good agreement with experiments was achieved by the present prediction of the Nikuradse roughness, erosion depth and sediment transport rate. Discussion was mainly focused on the prediction improvement caused by considering the impact of suspended sediment and its damping to turbulence.展开更多
文摘A mathematical model is constructed to examine the characteristics of three layered blood flow through the oscillatory cylindrical tube （stenosed arteries）. The proposed model basically consists three layers of blood （viscous fluids with different viscosities） named as core layer （red blood cells）, intermediate layer （platelets/white blood cells） and peripheral layer （plasma）. The analysis was restricted to propagation of small-amplitude harmonic waves, generated due to blood flow whose wave length is larger compared to the radius of the arterial segment. The impacts of viscosity of fluid in peripheral layer and intermediate layer on the interfaces, average flow rate, mechanical efficiency, trapping and reflux are discussed with the help of numerical and computational results. This model is the generalized form of the preceding models. On the basis of present discussion, it is found that the size of intermediate and peripheral layers reduces in expanded region and enhances in contracted region with the increasing viscosity of fluid in peripheral layer, whereas, opposite effect is observed for viscosity of fluid in intermediate layer. Final conclusion is that the average flow rate and mechanical efficiency increase with the increasing viscosity of fluid in both layers, however, the effects of the viscosity of fluid in both layers on trapping and reflux are opposite to each other.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51836010 and 51609244)the National Science-Technology Support Plan Projects(Grant No.2015BAD20B01)
文摘Nikuradse roughness(ks) is very important in the sediment transport prediction because it is related to the evaluations of the velocity distribution, shear stress and erosion depth. Dimensionless Nikuradse roughness(ks/D,where D is the sediment diameter) is usually given 1–2.5 on the immobile plan bed or at low shear stress. But it behaves differently on the mobile plan bed at high shear stress with much sediment picked up to movement when the Shields parameter(Θ) is larger than 0.8–1.0. The effective Nikuradse roughness on the mobile plan bed was derived indirectly from the erosion depth correlated to the mobile plan bed thickness considering the mass conservation in the present study. The proposed erosion depth confirmed the relation to the Shields parameters with an extra factor consisting of suspended sediment and its damping to turbulence. The decrement of the erosion depth caused by the increment of the sediment diameter at large shear stress was obtained, which was usually absent in classical empirical formulas based on the bedload theory. Good agreement with experiments was achieved by the present prediction of the Nikuradse roughness, erosion depth and sediment transport rate. Discussion was mainly focused on the prediction improvement caused by considering the impact of suspended sediment and its damping to turbulence.
