The momentum flow exchange between the impeller and side channel produces highly turbulent flows in side channel pumps.The turbulent flows feature complex patterns of vortex structures that are partly responsible for ...The momentum flow exchange between the impeller and side channel produces highly turbulent flows in side channel pumps.The turbulent flows feature complex patterns of vortex structures that are partly responsible for the dissipation of energy losses and unsteady pressure pulsations.The concept of turbulent flows in side channel pumps requires a reliable vortex identification criterion to capture and predict the effects of the vortex structures on the performance.For this reason,the current study presents the application of the new Ω-criterion to a side channel pump model in comparison with other traditional methods such as Qand λ2 criteria.The 3D flow fields of the pump were obtained through unsteady Reynolds-averaged Navier-Stokes(RANS)simulations.Comparative studies showed that the Ω-criterion identifies the vortex of different intensities with a standard threshold,Ω=0.52.The Q and λ2 criteria required different thresholds to capture vortex of different intensities thus leads to subjective errors.Comparing theΩ-criterion intensity on different planes with the entropy losses and pressure pulsation,the longitudinal vortex plays an important role in the momentum exchange development which increases the head performance of the pump.However,the rate of exchange is impeded by the axial and radial vortices restricted in the impeller.Therefore,the impeller generates the highest entropy loss and pressure pulsation intensities which lower the output efficiency.Finally,the findings provide a fundamental background to the morphology of the vortex structures in the turbulent flows which can be dependent upon for efficiency improvement of side channel pumps.展开更多
The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tom′as et al., Phys. Rev. E 85(2012) 010104(R)]. The χ-criterion for Fe...The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tom′as et al., Phys. Rev. E 85(2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum χ is investigated.展开更多
The iteration maps of Euler family for finding zeros of an operator f in Banach spaces is defined as the partial sum of Taylor expansion of the local inverse fz-1 of f at z. The unified convergence theorem is establis...The iteration maps of Euler family for finding zeros of an operator f in Banach spaces is defined as the partial sum of Taylor expansion of the local inverse fz-1 of f at z. The unified convergence theorem is established for the iterations of Euler family under the assumption that α≤3 - 2 , while the strong condition that f is analytic in Smale’s criterion a is replaced by the weak condition that f is of finite order derivative.展开更多
This research utilizes theΩvortex identification method to address the turbulent flows in a single-stage side channel pump,to comprehensively characterize the three types of dynamic vortex structures classified based...This research utilizes theΩvortex identification method to address the turbulent flows in a single-stage side channel pump,to comprehensively characterize the three types of dynamic vortex structures classified based on directions.Premised on the Galilean invariance,the work employs coordinate rotation and transformation.Thus,the indistinguishable 3-D vortex can be simplified to 2-D vortex on typical research planes.When juxtaposing the overall performance,it was revealed that a diversity of areas with high values yielded enhanced reflection of the vortex intensity,as measured by velocity distribution.The axial vortex structure with high intensity exists at the outer radius under all conditions largely.While the longitudinal vortex usually shows high intensity between the middle and outer radius.Simultaneously,the radial vortex is more likely to be at the inner radius near the suction face.Finally,this paper introduces a specific valueξ,which represents the ratio of decomposition to the total of the manifestation of the fluid rotational pattern.From the fluctuation and mean value,it can be realized that the development of the specific vortex in three directions at different positions.For example,the specific valueξ2 refers to the typical longitudinal vortex as dynamic vortex are almost from 20%to 50%,which illustrates that the longitudinal vortex only occupies a minor percentage in the total vortex.This phenomenon is one of the main reasons for the low efficiency.The present work could provide some suggestions and references for in-depth studies in fluid engineering with intense swirling flows.展开更多
Supersaturated designs are common choice for screening experiments.This paper studies the properties of supersaturated designs.We give new lower bounds of E(s^(2))-criterion and E(f_(NOD))-criterion.Some linkages betw...Supersaturated designs are common choice for screening experiments.This paper studies the properties of supersaturated designs.We give new lower bounds of E(s^(2))-criterion and E(f_(NOD))-criterion.Some linkages between the combined/double design and its original design are firstly provided,and the lower bounds of E(s^(2)) and E(f_(NOD)) for the combined/double design are also given.Furthermore,the close relationship between the minimum Lee-moment aberration criterion and the criteria for optimal supersaturated designs is revealed.These theoretical results can be used to construct or search for optimal supersaturated designs in practice.Numerical results are also provided,which lend further support to our theoretical findings.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51809121,51879121)China Postdoctoral Science Foundation(Grant No.2021M701535).
文摘The momentum flow exchange between the impeller and side channel produces highly turbulent flows in side channel pumps.The turbulent flows feature complex patterns of vortex structures that are partly responsible for the dissipation of energy losses and unsteady pressure pulsations.The concept of turbulent flows in side channel pumps requires a reliable vortex identification criterion to capture and predict the effects of the vortex structures on the performance.For this reason,the current study presents the application of the new Ω-criterion to a side channel pump model in comparison with other traditional methods such as Qand λ2 criteria.The 3D flow fields of the pump were obtained through unsteady Reynolds-averaged Navier-Stokes(RANS)simulations.Comparative studies showed that the Ω-criterion identifies the vortex of different intensities with a standard threshold,Ω=0.52.The Q and λ2 criteria required different thresholds to capture vortex of different intensities thus leads to subjective errors.Comparing theΩ-criterion intensity on different planes with the entropy losses and pressure pulsation,the longitudinal vortex plays an important role in the momentum exchange development which increases the head performance of the pump.However,the rate of exchange is impeded by the axial and radial vortices restricted in the impeller.Therefore,the impeller generates the highest entropy loss and pressure pulsation intensities which lower the output efficiency.Finally,the findings provide a fundamental background to the morphology of the vortex structures in the turbulent flows which can be dependent upon for efficiency improvement of side channel pumps.
基金Supported by National Natural Science Foundation of China under Grant No.11322543
文摘The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tom′as et al., Phys. Rev. E 85(2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum χ is investigated.
文摘The iteration maps of Euler family for finding zeros of an operator f in Banach spaces is defined as the partial sum of Taylor expansion of the local inverse fz-1 of f at z. The unified convergence theorem is established for the iterations of Euler family under the assumption that α≤3 - 2 , while the strong condition that f is analytic in Smale’s criterion a is replaced by the weak condition that f is of finite order derivative.
基金supported by the Ranking the Top of the List for Science and Technology Projects of Yunnan Province(Grant No.202204BW050001)the Taizhou Science and Technology Project(Grant Nos.21gyb05,21gyb08)+2 种基金the Research Innovation Program for College Graduates of Jiangsu Province(Grant No.KYCX22_3641)gratefully acknowledge financial support from China Scholarship CouncilProject supported by the National Natural Science Foundation of China(Grant Nos.52279086,52150410397).
文摘This research utilizes theΩvortex identification method to address the turbulent flows in a single-stage side channel pump,to comprehensively characterize the three types of dynamic vortex structures classified based on directions.Premised on the Galilean invariance,the work employs coordinate rotation and transformation.Thus,the indistinguishable 3-D vortex can be simplified to 2-D vortex on typical research planes.When juxtaposing the overall performance,it was revealed that a diversity of areas with high values yielded enhanced reflection of the vortex intensity,as measured by velocity distribution.The axial vortex structure with high intensity exists at the outer radius under all conditions largely.While the longitudinal vortex usually shows high intensity between the middle and outer radius.Simultaneously,the radial vortex is more likely to be at the inner radius near the suction face.Finally,this paper introduces a specific valueξ,which represents the ratio of decomposition to the total of the manifestation of the fluid rotational pattern.From the fluctuation and mean value,it can be realized that the development of the specific vortex in three directions at different positions.For example,the specific valueξ2 refers to the typical longitudinal vortex as dynamic vortex are almost from 20%to 50%,which illustrates that the longitudinal vortex only occupies a minor percentage in the total vortex.This phenomenon is one of the main reasons for the low efficiency.The present work could provide some suggestions and references for in-depth studies in fluid engineering with intense swirling flows.
基金supported by the National Natural Science Foundation of China(No.11871237)the project of discipline overall planning construction of Zhongnan University of Economics and Law(No.XKHJ202125)。
文摘Supersaturated designs are common choice for screening experiments.This paper studies the properties of supersaturated designs.We give new lower bounds of E(s^(2))-criterion and E(f_(NOD))-criterion.Some linkages between the combined/double design and its original design are firstly provided,and the lower bounds of E(s^(2)) and E(f_(NOD)) for the combined/double design are also given.Furthermore,the close relationship between the minimum Lee-moment aberration criterion and the criteria for optimal supersaturated designs is revealed.These theoretical results can be used to construct or search for optimal supersaturated designs in practice.Numerical results are also provided,which lend further support to our theoretical findings.
