Academia.eduAcademia.edu

Figure 18 – uploaded by Jörn Sesterhenn

See full PDFdownloadDownload figure
Figure 18. Terms in the budget of pu'?/2 for incompressible (MM = 0, red curves) and compressible flows (M = 1.5, green curves).

Figure 18 Terms in the budget of pu'?/2 for incompressible (MM = 0, red curves) and compressible flows (M = 1.5, green curves).

Related Figures (23)

Journal of Turbulence 2 (2001) 001 (http://jot.iop.org/)
Journal of Turbulence 2 (2001) 001 (http://jot.iop.org/)
Turbulent supersonic channel flow
Turbulent supersonic channel flow
slow near-wall fluid to pass the channel (of length 47h) 2.86 times. One problem time, which corresponds to somewhat more than 8000 time steps, consumed 38.7 CPU hours.
slow near-wall fluid to pass the channel (of length 47h) 2.86 times. One problem time, which corresponds to somewhat more than 8000 time steps, consumed 38.7 CPU hours.
fluctuations of the buffer layer can certainly be removed by increased spanwise resolution. This is concluded from the high wavenumber behaviour of one-dimensional spanwise energy spectra. 4.2. On the nature of fluctuating variables Supersonic channel flow is achieved only if most of the heat generated by dissipation is removed through the walls, i.e. by wall cooling. Hence the walls are colder than the bulk of the flow. Since the mean flow is approximately isobaric (mean pressure variations normal to the wall reflect the behaviour of the wall-normal turbulence intensity), the mean density has its maximum at the wall and the normalized temperature and density gradients are practically equal in magnitude, but opposite in sign:
fluctuations of the buffer layer can certainly be removed by increased spanwise resolution. This is concluded from the high wavenumber behaviour of one-dimensional spanwise energy spectra. 4.2. On the nature of fluctuating variables Supersonic channel flow is achieved only if most of the heat generated by dissipation is removed through the walls, i.e. by wall cooling. Hence the walls are colder than the bulk of the flow. Since the mean flow is approximately isobaric (mean pressure variations normal to the wall reflect the behaviour of the wall-normal turbulence intensity), the mean density has its maximum at the wall and the normalized temperature and density gradients are practically equal in magnitude, but opposite in sign:
Turbulent supersonic channel flow The observed near-wall variations (figure 3) are rapid and qualitatively different to those found in adiabatic-wall boundary layers [13,14]. It can be shown that the steep mean density gradients are the cause for the surprisingly high level of density fluctuations in the buffer layer (see figure 5). The transport equation for p’? takes the following form in fully developed channel flow:
Turbulent supersonic channel flow The observed near-wall variations (figure 3) are rapid and qualitatively different to those found in adiabatic-wall boundary layers [13,14]. It can be shown that the steep mean density gradients are the cause for the surprisingly high level of density fluctuations in the buffer layer (see figure 5). The transport equation for p’? takes the following form in fully developed channel flow:
Figure 6. Rms temperature fluctuations: et al [3].
Figure 6. Rms temperature fluctuations: et al [3].
fe Figure 7. Total rms vorticity fluctuations, (Wijia1)ims: ——-— Coleman et al [3].
fe Figure 7. Total rms vorticity fluctuations, (Wijia1)ims: ——-— Coleman et al [3].
Figure 8. Scatter plots of temperature against density (top) and velocity fluctuations in planes parallel to the channel wall at z+ = 9 (left) and in the symmetry plane (right).
Figure 8. Scatter plots of temperature against density (top) and velocity fluctuations in planes parallel to the channel wall at z+ = 9 (left) and in the symmetry plane (right).
Figure 9. Close-up of temperature against density and total temperature fluctuations in a plane close to the wall at zt = 9.
Figure 9. Close-up of temperature against density and total temperature fluctuations in a plane close to the wall at zt = 9.
Let us now assume linear relations between thermodynamic fluctuations of the forr
Let us now assume linear relations between thermodynamic fluctuations of the forr
Turbulent supersonic channel flow Figure 11. Entropy fluctuations against density, temperature and pressure fluctuations in planes parallel to the channel walls at zt = 9 (left) and at the centreline (right).
Turbulent supersonic channel flow Figure 11. Entropy fluctuations against density, temperature and pressure fluctuations in planes parallel to the channel walls at zt = 9 (left) and at the centreline (right).
Figure 12. Rms total temperature fluctuations across the supersonic channel. Table 2. Mean flow quantities for the two channel positions. Turbulent supersonic channel flow From figure 12, which contains the profile of the rms total temperature fluctuations, we read peak values for To,rms/ To of 10% in the wall layer. The minimum value in the core is still 3%. fluc Figure 13 presents scatter plots of Tj,/ To against temperature, velocity and kinetic energy tuations (ui? — ul?) /(2u’) (cf also figure 9). From these we conclude, taking the data of table 2 into account, that in the wall layer the contributions from temperature, velocity and kinetic energy fluctuations to the total temperature fluctuations are of equal importance. Only in t he core region does a linear relation of the form
Figure 12. Rms total temperature fluctuations across the supersonic channel. Table 2. Mean flow quantities for the two channel positions. Turbulent supersonic channel flow From figure 12, which contains the profile of the rms total temperature fluctuations, we read peak values for To,rms/ To of 10% in the wall layer. The minimum value in the core is still 3%. fluc Figure 13 presents scatter plots of Tj,/ To against temperature, velocity and kinetic energy tuations (ui? — ul?) /(2u’) (cf also figure 9). From these we conclude, taking the data of table 2 into account, that in the wall layer the contributions from temperature, velocity and kinetic energy fluctuations to the total temperature fluctuations are of equal importance. Only in t he core region does a linear relation of the form
Figure 13. Total temperature fluctuations against temperature, velocity and kinetic energy fluctuations in planes parallel to the channel walls at zt = 9 (left) and at the centreline (right).
Figure 13. Total temperature fluctuations against temperature, velocity and kinetic energy fluctuations in planes parallel to the channel walls at zt = 9 (left) and at the centreline (right).
Turbulent supersonic channel flow Figure 14. Rms values of the normal components of the Reynolds stress tensor normalized with (7,)'/? and of the Reynolds shear stress —pulu{/tw: ——— M =0 [I] and M =1.5.
Turbulent supersonic channel flow Figure 14. Rms values of the normal components of the Reynolds stress tensor normalized with (7,)'/? and of the Reynolds shear stress —pulu{/tw: ——— M =0 [I] and M =1.5.
Turbulent supersonic channel flow Figure 15. Reynolds stress anisotropies for incompressible (IZ = 0 [1], red curves and compressible flows (M = 1.5, green curves).
Turbulent supersonic channel flow Figure 15. Reynolds stress anisotropies for incompressible (IZ = 0 [1], red curves and compressible flows (M = 1.5, green curves).
Turbulent supersonic channel flow Figure 17. Terms in the budget of pu{?/2 for incompressible (IM = 0, red curves) and compressible flows (M = 1.5, green curves).
Turbulent supersonic channel flow Figure 17. Terms in the budget of pu{?/2 for incompressible (IM = 0, red curves) and compressible flows (M = 1.5, green curves).
Turbulent supersonic channel flow Figure 19. Terms in the budget of pu4?/2 for incompressible (MM = 0, red curves and compressible flows (IM = 1.5, green curves).
Turbulent supersonic channel flow Figure 19. Terms in the budget of pu4?/2 for incompressible (MM = 0, red curves and compressible flows (IM = 1.5, green curves).
Figure 20. Terms in the shear stress budget, pu/u%, for incompressible (M = 0, red curves) and compressible flows (IM = 1.5, green curves).
Figure 20. Terms in the shear stress budget, pu/u%, for incompressible (M = 0, red curves) and compressible flows (IM = 1.5, green curves).
Turbulent supersonic channel flow Figure 21. Terms in the kinetic energy budget for incompressible (M = 0, red curves) and compressible flows (M = 1.5, green curves).
Turbulent supersonic channel flow Figure 21. Terms in the kinetic energy budget for incompressible (M = 0, red curves) and compressible flows (M = 1.5, green curves).
Figure 22. Velocity—pressure-gradient tensor, VPG;;._ Red curves denote incompressible flow (IM = 0) and green curves compressible flow (M = 1.5).
Figure 22. Velocity—pressure-gradient tensor, VPG;;._ Red curves denote incompressible flow (IM = 0) and green curves compressible flow (M = 1.5).
Figure 23. Contour lines of u!/um at 2* ~ 9 (green: u!/Um < 0, red: u!/um > 0) Turbulent supersonic channel flow
Figure 23. Contour lines of u!/um at 2* ~ 9 (green: u!/Um < 0, red: u!/um > 0) Turbulent supersonic channel flow
Figure 24. Top, contour lines of u//um and q at x = 11 (green, u’/um < 0; red, u'/Um > 0; white, g > 0). Bottom, isosurfaces of u//u, and q. (green, u!/Um = —0.15; red, u!/Um = 0.15; white, gh?/u?, = 1.0).
Figure 24. Top, contour lines of u//um and q at x = 11 (green, u’/um < 0; red, u'/Um > 0; white, g > 0). Bottom, isosurfaces of u//u, and q. (green, u!/Um = —0.15; red, u!/Um = 0.15; white, gh?/u?, = 1.0).
Related topics:
Compressible Fluid DynamicsSupersonic flowChannel Flow
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved