The Effect of Interpolation Errors on the Lagrangian Analysis of Simulated Turbulent Channel Flow

On the physical accuracy of scalar transport modeling in inhomogeneous turbulence

“…Figure 7 shows approximate curves for all four scales together with the data points used in determining them. Note that the magnitude of T12 is very large near the wall, as was mentioned previously in reference to the evaluation of (23 (29) where, as before, T = 2k/c. When S = 0 these equations become equivalent to (26) (l.nd (27) under the assumption that all of the scales are equal to T /Cv.…”

“…This also provides values of v 2 , k, f and T 22 appearing in (17) and (18 From the simulated velocity field the time scale T 22 was computed by first generating large ensembles of fluid particles arriving at fixed distances above the wall. To get highly accurate paths, velocities of the fluid particles at off nodal points were found by cubic hermite interpolation 29 . The estimates of T 22 are limited to the range 0 < y+ ~ 40, so that it was necessary to extrapolate T 22 to the centerline to get the complete curve for T22 needed in solving (16) using (17).…”

“…This appears to be a consequence of the fact that beyond the initial region, the model for vc-which according to (29) has no dependence on shear -is the dominant turbulent influence on the plume. It may be concluded that the success of gradient models in predicting the far field of homogeneous turbulence also extends · to the non-homogeneous case as well, so long as they include the basic dependence on Reynolds stress exhibited by (26) and (27) or (28) and (29). The use of physically accurate scales improves the predictions of the far field fluxes at the expense of greater errors in the near field, while the opposite happens if the modeled scales are used.…”

“…Figure 16 compares vc from the DNS with (27) and (29) the influence on C of the terms depending on S in (28) is relatively smalL In-fact, an / independent calculation of the plume using (28) and (29) in which S was set to zero, revealed a change in C of generally less than one percent. This appears to be a consequence of the fact that beyond the initial region, the model for vc-which according to (29) has no dependence on shear -is the dominant turbulent influence on the plume.…”

“…Figure 16 compares vc from the DNS with (27) and (29) the influence on C of the terms depending on S in (28) is relatively smalL In-fact, an / independent calculation of the plume using (28) and (29) in which S was set to zero, revealed a change in C of generally less than one percent. This appears to be a consequence of the fact that beyond the initial region, the model for vc-which according to (29) has no dependence on shear -is the dominant turbulent influence on the plume. It may be concluded that the success of gradient models in predicting the far field of homogeneous turbulence also extends · to the non-homogeneous case as well, so long as they include the basic dependence on Reynolds stress exhibited by (26) and (27) or (28) and (29).…”