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Fig. 15 Resolved temperature field for N = 3 Fig. 14 Resolved temperature field for VN = 0 heat fluxes normalized by the friction velocity and tem- perature, for different rotation ratios N. Like the rms of fluctuating temperature, the streamwise turbulent heat flux

Figure 15 Resolved temperature field for N = 3 Fig. 14 Resolved temperature field for VN = 0 heat fluxes normalized by the friction velocity and tem- perature, for different rotation ratios N. Like the rms of fluctuating temperature, the streamwise turbulent heat flux

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Fig. 1 Schematic of the computational domain and grid structure where r and the velocity components are scaled by the pipe radius R and the centreline streamwise velocity of the laminar Poiseuille flow U, respectively. The Peclet number is defined as Pe = Re,Pr, where Re, = U,R/v. A mean pressure gradient in the equation of streamwise velocity component maintains the bulk velocity constant. The heating condition imposed on the wall implies a linear increase of the bulk temperature (T,) in the streamwise direction. For fully developed flows, the following equalities are satisfied: A /T\ A/m\ A/mm \ Ye
Fig. 1 Schematic of the computational domain and grid structure where r and the velocity components are scaled by the pipe radius R and the centreline streamwise velocity of the laminar Poiseuille flow U, respectively. The Peclet number is defined as Pe = Re,Pr, where Re, = U,R/v. A mean pressure gradient in the equation of streamwise velocity component maintains the bulk velocity constant. The heating condition imposed on the wall implies a linear increase of the bulk temperature (T,) in the streamwise direction. For fully developed flows, the following equalities are satisfied: A /T\ A/m\ A/mm \ Ye
Fig. 2. Mean streamwise velocity profile N varies from 0 to 2, and then decrease for N > 3, Fig. 4. Similar trends have been reported in literature for small N (Orlandi and Fatica [22], Feiz et al. [13], Redjem et al. [19]) for moderate rotation ratios. The present LES study extends the previous investigations, since the value of N has been increased up to 14.
Fig. 2. Mean streamwise velocity profile N varies from 0 to 2, and then decrease for N > 3, Fig. 4. Similar trends have been reported in literature for small N (Orlandi and Fatica [22], Feiz et al. [13], Redjem et al. [19]) for moderate rotation ratios. The present LES study extends the previous investigations, since the value of N has been increased up to 14.
Fig. 3 RMS of streamwise velocity fluctuation
Fig. 3 RMS of streamwise velocity fluctuation
Fig. 4 RMS of radial (a) and azimuthal (b) velocity fluctuations Far away from the wall, at yt ~ 100, the rotation induces slight changes on the jpdfs between streamwise and radial velocity components, Figs. 10a, lla and 12a. For the stationary pipe, Fig. 10a, sweeps and ejections mainly contribute to v;*v,+. With increasing N, contribu- tion of events from the four quadrants seems to be more and more equivalent, Figs. lla, 12a. The rotation induced changes are also weak on the correlation between vj), and vi, Figs. 10b, 11b and 12b (solid line), when WN varies, at yt ~ 100. On the contrary, the influence of the rotation on vy vet is significant (dashed line): the correlation viv Z ’ which was zero in the stationary case (symmetry around axis vb = 0), is modified when increasing N, with a reduction of ejection’s contributions and an enhancement of contributions from first quadrant.
Fig. 4 RMS of radial (a) and azimuthal (b) velocity fluctuations Far away from the wall, at yt ~ 100, the rotation induces slight changes on the jpdfs between streamwise and radial velocity components, Figs. 10a, lla and 12a. For the stationary pipe, Fig. 10a, sweeps and ejections mainly contribute to v;*v,+. With increasing N, contribu- tion of events from the four quadrants seems to be more and more equivalent, Figs. lla, 12a. The rotation induced changes are also weak on the correlation between vj), and vi, Figs. 10b, 11b and 12b (solid line), when WN varies, at yt ~ 100. On the contrary, the influence of the rotation on vy vet is significant (dashed line): the correlation viv Z ’ which was zero in the stationary case (symmetry around axis vb = 0), is modified when increasing N, with a reduction of ejection’s contributions and an enhancement of contributions from first quadrant.
Fig. 5 Turbulent shear stress v+v/+
Fig. 5 Turbulent shear stress v+v/+
Fig. 6 Turbulent shear stresses vity an 0
Fig. 6 Turbulent shear stresses vity an 0
Fig. 7 JPDF between velocity components, at yt ~ 5 and N= 0
Fig. 7 JPDF between velocity components, at yt ~ 5 and N= 0
Fig. 9 JPDF between velocity components, at yt ~ 5 and N= 14 Fig. 8 JPDF between velocity components, at yt ~ 5 and N = 3
Fig. 9 JPDF between velocity components, at yt ~ 5 and N= 14 Fig. 8 JPDF between velocity components, at yt ~ 5 and N = 3
Fig. 10 JPDF between velocity components, at yt ~ 100 and N = 0
Fig. 10 JPDF between velocity components, at yt ~ 100 and N = 0
Fig. 11 JPDF between velocity components, at yt ~ 100 and N = 3
Fig. 11 JPDF between velocity components, at yt ~ 100 and N = 3
Fig. 12 JPDF between velocity components, at yt ~ 100 anc N=14
Fig. 12 JPDF between velocity components, at yt ~ 100 anc N=14
Fig. 13. Mean temperature profile
Fig. 13. Mean temperature profile
Fig. 16 Resolved temperature field for N = 7
Fig. 16 Resolved temperature field for N = 7
Fig. 18 Thickness of conductive and dynamic sublayers vit ©'* decreases significantly with increasing N, Fig. 21a. Its decrease is more pronounced with increasing N than that in air flow. In addition, the streamwise turbulent heat flux is very large in water flow than in air flow and it remains arger for each N. Indeed, the conductive sublayer for air flows evident up to yt ~ 5. As Pr increases (for water flow), the thermal resistance is concentrated in the con- ductive sublayer which is immersed in the viscous sub- ayer. Thus, beyond the conductive sublayer, there is a more rapid transport of heat in water flow than in air flow, eading to larger axial and azimuthal turbulent heat fluxes. The dependence of the peak in the streamwise turbulent heat flux upon the rotation ratio N, Fig. 21a, is similar to that of the rms temperature fluctuations: the peak’s value is strongly reduced with increasing N, and shifts towards the wall (while that of in air flow moves towards the pipe centre [25]), Fig. 21b, denoting a conductive sublayer which is thinner and thinner, meaning that the correlation between streamwise velocity and temperature fluctuations becomes more rapidly poor in water flow than in air flow.
Fig. 18 Thickness of conductive and dynamic sublayers vit ©'* decreases significantly with increasing N, Fig. 21a. Its decrease is more pronounced with increasing N than that in air flow. In addition, the streamwise turbulent heat flux is very large in water flow than in air flow and it remains arger for each N. Indeed, the conductive sublayer for air flows evident up to yt ~ 5. As Pr increases (for water flow), the thermal resistance is concentrated in the con- ductive sublayer which is immersed in the viscous sub- ayer. Thus, beyond the conductive sublayer, there is a more rapid transport of heat in water flow than in air flow, eading to larger axial and azimuthal turbulent heat fluxes. The dependence of the peak in the streamwise turbulent heat flux upon the rotation ratio N, Fig. 21a, is similar to that of the rms temperature fluctuations: the peak’s value is strongly reduced with increasing N, and shifts towards the wall (while that of in air flow moves towards the pipe centre [25]), Fig. 21b, denoting a conductive sublayer which is thinner and thinner, meaning that the correlation between streamwise velocity and temperature fluctuations becomes more rapidly poor in water flow than in air flow.
Fig. 19 RMS of temperature fluctuation heat flux. The peak’s position of v,©'* follows the law 9.5 N°”? while that of vt @* andv,"©'* vary as 8 N~°”? and 24 N~°!5 respectively. Keeping in mind the estimation of the thickness of conductive and dynamic sublayers, Fig. 18, one can note that the maximum of all turbulent heat fluxes as well as that of the fluctuating temperature are reached in the buffer region of the scalar field, when N varies. Similarly, the peak’s position of turbulent Reynolds shear stresses decrease with increasing N, Fig. 25. The peak’s position of vi+v,* follows the law 31 N~°'® and that of v+ Vit evolves as 9.5 N~°-.
Fig. 19 RMS of temperature fluctuation heat flux. The peak’s position of v,©'* follows the law 9.5 N°”? while that of vt @* andv,"©'* vary as 8 N~°”? and 24 N~°!5 respectively. Keeping in mind the estimation of the thickness of conductive and dynamic sublayers, Fig. 18, one can note that the maximum of all turbulent heat fluxes as well as that of the fluctuating temperature are reached in the buffer region of the scalar field, when N varies. Similarly, the peak’s position of turbulent Reynolds shear stresses decrease with increasing N, Fig. 25. The peak’s position of vi+v,* follows the law 31 N~°'® and that of v+ Vit evolves as 9.5 N~°-.
Fig. 20 Peak’s position of rms
Fig. 20 Peak’s position of rms
Fig. 21 Streamwise turbulent heat flux
Fig. 21 Streamwise turbulent heat flux
Fig. 22, Azimuthal turbulent heat flux
Fig. 22, Azimuthal turbulent heat flux
Fig. 23, Wall-normal turbulent heat flux Fig. 24 Peak’s position of turbulent heat fluxes
Fig. 23, Wall-normal turbulent heat flux Fig. 24 Peak’s position of turbulent heat fluxes
Fig. 25 Peak’s position of turbulent shear stresses
Fig. 25 Peak’s position of turbulent shear stresses
Fig. 26 Skewness and Flatness of temperature fluctuations
Fig. 26 Skewness and Flatness of temperature fluctuations
Fig. 28 Contours: vi(—2.86; 1.98; A = 0.35) and ©'(—2.49; 16.46; A = 1.35), N=3 Fig. 27 Contours: vi(—1.97; 9.11; A = 1) and ©! (—1.78; 11.05; A= 1.16), N=0
Fig. 28 Contours: vi(—2.86; 1.98; A = 0.35) and ©'(—2.49; 16.46; A = 1.35), N=3 Fig. 27 Contours: vi(—1.97; 9.11; A = 1) and ©! (—1.78; 11.05; A= 1.16), N=0
Fig. 29 Contours: vi(—2.91,; 7.51; A = 0.74) and ©'(—1.97; 10.47; A = 0.89), N=7
Fig. 29 Contours: vi(—2.91,; 7.51; A = 0.74) and ©'(—1.97; 10.47; A = 0.89), N=7
Related topics:
Materials ScienceMechanicsTurbulent Heat TransferPipe FlowInterdisciplinary EngineeringLarge Eddy Simulation(LES)
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