The relationship between entropy production and vortex evolution affects the efficiency and stability of rotating machinery.This study investigated the energy characteristics of a rocket turbopump and revealed the cor...The relationship between entropy production and vortex evolution affects the efficiency and stability of rotating machinery.This study investigated the energy characteristics of a rocket turbopump and revealed the correlated mechanisms of the entropy production rate using the dissipation effects and characteristic vortex evolution.For the first time,direct and turbulent dissipation and rigid and shear vorticity decomposition methods were utilized to analyze the correlation between flow loss and characteristic vorticities in rotating machinery.With an increase in the flow rate,the hydraulic losses of the dissipation effects and wall decreased by 60%and 38.3%,respectively,and the proportions of the input energy decreased(from 13%to 8%)and remained stable(8%),respectively.The local direct dissipative entropy production(DDEP)in the inducer-impeller is strongly related to shear entropy,and the correlated effect of total enstrophy on DDEP is weaker than that of shear vorticity,indicating that rigid enstrophy suppresses direct dissipation.The correlation between turbulent dissipation and rigid enstrophy was significantly weaker in the static flow passage of the turbopump owing to the weak rigid rotational effect.The correlation between the rigid entropy and local turbulent dissipative entropy production(TDEP)gradually increased with increasing flow rate,reaching a medium correlation(the maximal correlated degree in the turbopump)and exhibiting rigid rotation effects on the hydraulic loss.Moreover,the flow rate significantly affected the correlation(except for the diffuser),and the two characteristic vorticities reached a maximum at the designed flow rate owing to optimal efficiency and minimum hydraulic loss.展开更多
The newly developed vortex-identification method,Liutex,has provided a new systematic description of the local fluid rotation,which includes scalar,vector,and tensor forms.However,the advantages of Liutex over the oth...The newly developed vortex-identification method,Liutex,has provided a new systematic description of the local fluid rotation,which includes scalar,vector,and tensor forms.However,the advantages of Liutex over the other widely used vortexidentification methods such as Q,Δ,λ2,andλci have not been realized.These traditional methods count on shearing and stretching as a part of vortex strength.But,in the real flow,shearing and stretching do not contribute to fluid rotation.In this paper,the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness.Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations.The results show that the Liutex method is the only method that is not affected by either stretching or shear,as it represents only the local fluid rigid rotation.These results provide supporting evidence that Liutex is the superior method over others.展开更多
This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natura...This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.展开更多
In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field wit...In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (2c.) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector.展开更多
Atmospheric variables(temperature, velocity, etc.) are often decomposed into balanced and unbalanced components that represent low-frequency and high-frequency waves, respectively. Such decompositions can be defined, ...Atmospheric variables(temperature, velocity, etc.) are often decomposed into balanced and unbalanced components that represent low-frequency and high-frequency waves, respectively. Such decompositions can be defined, for instance, in terms of eigenmodes of a linear operator. Traditionally these decompositions ignore phase changes of water since phase changes create a piecewise-linear operator that differs in different phases(cloudy versus non-cloudy). Here we investigate the following question: How can a balanced–unbalanced decomposition be performed in the presence of phase changes? A method is described here motivated by the case of small Froude and Rossby numbers,in which case the asymptotic limit yields precipitating quasi-geostrophic equations with phase changes. Facilitated by its zero-frequency eigenvalue, the balanced component can be found by potential vorticity(PV) inversion, by solving an elliptic partial differential equation(PDE), which includes Heaviside discontinuities due to phase changes. The method is also compared with two simpler methods: one which neglects phase changes, and one which simply treats the raw pressure data as a streamfunction. Tests are shown for both synthetic, idealized data and data from Weather Research and Forecasting(WRF) model simulations. In comparisons, the phase-change method and no-phase-change method produce substantial differences within cloudy regions, of approximately 5K in potential temperature, due to the presence of clouds and phase changes in the data. A theoretical justification is also derived in the form of a elliptic PDE for the differences in the two streamfunctions.展开更多
基金supported by the Heilongjiang Postdoctoral Fund(Grant Nos.LBH-Z18071,LBH-TZ2015)the Fundamental Research Funds for the Central Universities(Grant No.HIT.NSRIF.2019063).
文摘The relationship between entropy production and vortex evolution affects the efficiency and stability of rotating machinery.This study investigated the energy characteristics of a rocket turbopump and revealed the correlated mechanisms of the entropy production rate using the dissipation effects and characteristic vortex evolution.For the first time,direct and turbulent dissipation and rigid and shear vorticity decomposition methods were utilized to analyze the correlation between flow loss and characteristic vorticities in rotating machinery.With an increase in the flow rate,the hydraulic losses of the dissipation effects and wall decreased by 60%and 38.3%,respectively,and the proportions of the input energy decreased(from 13%to 8%)and remained stable(8%),respectively.The local direct dissipative entropy production(DDEP)in the inducer-impeller is strongly related to shear entropy,and the correlated effect of total enstrophy on DDEP is weaker than that of shear vorticity,indicating that rigid enstrophy suppresses direct dissipation.The correlation between turbulent dissipation and rigid enstrophy was significantly weaker in the static flow passage of the turbopump owing to the weak rigid rotational effect.The correlation between the rigid entropy and local turbulent dissipative entropy production(TDEP)gradually increased with increasing flow rate,reaching a medium correlation(the maximal correlated degree in the turbopump)and exhibiting rigid rotation effects on the hydraulic loss.Moreover,the flow rate significantly affected the correlation(except for the diffuser),and the two characteristic vorticities reached a maximum at the designed flow rate owing to optimal efficiency and minimum hydraulic loss.
文摘The newly developed vortex-identification method,Liutex,has provided a new systematic description of the local fluid rotation,which includes scalar,vector,and tensor forms.However,the advantages of Liutex over the other widely used vortexidentification methods such as Q,Δ,λ2,andλci have not been realized.These traditional methods count on shearing and stretching as a part of vortex strength.But,in the real flow,shearing and stretching do not contribute to fluid rotation.In this paper,the decomposition of the velocity gradient tensor is conducted in the Principal Coordinate for uniqueness.Then the contamination effects of stretching and shearing of the traditional methods are investigated and compared with the Liutex method in terms of mathematical analysis and numerical calculations.The results show that the Liutex method is the only method that is not affected by either stretching or shear,as it represents only the local fluid rigid rotation.These results provide supporting evidence that Liutex is the superior method over others.
文摘This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.
基金supported by the National Nature Science Foundation of China (Grant Nos. 11702159, 91530325).
文摘In the present study, the physical meaning of vorticity is revisited based on the Liutex-Shear (RS) decomposition proposed by Liu et al. in the framework of Liutex (previously called Rortex), a vortex vector field with information of both rotation axis and swirling strength (Liu et al. 2018). It is demonstrated that the vorticity in the direction of rotational axis is twice the spatial mean angular velocity in the small neighborhood around the considered point while the imaginary part of the complex eigenvalue (2c.) of the velocity gradient tensor (if exist) is the pseudo-time average angular velocity of a trajectory moving circularly or spirally around the axis. In addition, an explicit expression of the Liutex vector in terms of the eigenvalues and eigenvectors of velocity gradient is obtained for the first time from above understanding, which can further, though mildly, accelerate the calculation and give more physical comprehension of the Liutex vector.
基金supported by the National Science Foundation through grant AGS–1443325 and DMS-1907667the University of Wisconsin–Madison Office of the Vice Chancellor for Research and Graduate Education with funding from the Wisconsin Alumni Research Foundation
文摘Atmospheric variables(temperature, velocity, etc.) are often decomposed into balanced and unbalanced components that represent low-frequency and high-frequency waves, respectively. Such decompositions can be defined, for instance, in terms of eigenmodes of a linear operator. Traditionally these decompositions ignore phase changes of water since phase changes create a piecewise-linear operator that differs in different phases(cloudy versus non-cloudy). Here we investigate the following question: How can a balanced–unbalanced decomposition be performed in the presence of phase changes? A method is described here motivated by the case of small Froude and Rossby numbers,in which case the asymptotic limit yields precipitating quasi-geostrophic equations with phase changes. Facilitated by its zero-frequency eigenvalue, the balanced component can be found by potential vorticity(PV) inversion, by solving an elliptic partial differential equation(PDE), which includes Heaviside discontinuities due to phase changes. The method is also compared with two simpler methods: one which neglects phase changes, and one which simply treats the raw pressure data as a streamfunction. Tests are shown for both synthetic, idealized data and data from Weather Research and Forecasting(WRF) model simulations. In comparisons, the phase-change method and no-phase-change method produce substantial differences within cloudy regions, of approximately 5K in potential temperature, due to the presence of clouds and phase changes in the data. A theoretical justification is also derived in the form of a elliptic PDE for the differences in the two streamfunctions.
