Turbulent boundary layer prediction

In 1968 a conference was held at Stanford on turbulent boundary layer prediction-method calibration (S3), where for the first time a large number of methods, totaling 29, were compared on a systematic basis. This comparison established the viability of prediction methods based on various closure models for the partial differential equations describing turbulent boundary layer flows, and has stimulated considerable more recent work on this approach. 

The work leading up to the 1968 conference produced a volume of target boundary-layer data. A eommittee headed by D. Coles surveyed over 100 experiments and selected 33 flows for inclusion in this volume. The data of each experiment were carefully reanalyzed and recomputed for placement in a standard form critiques were solicited from the experimenters and all this was documented in a tidy manner by E. Hirst and D. Coles (S3). These data now stand as a classic base of comparison for turbulent boundary-layer prediction methods. Only the hydrodynamic aspects of these layers... 

For a turbulent boundary layer, the total drag may be roughly estimated using Eqs. (6-184) and (6-185) for finite cylinders. Measured forces by Kwon and Prevorsek ]. Eng. Jnd., 101, 73-79 [1979]) are greater than predicted this way. 

For a very thin liquid film, the value of 3 cannot be evaluated, and it should be replaced by a new parameter 3, using the generalized turbulent boundary-layer profile in an adiabatic flow as in Reference (Levy and Healzer, 1980). GF can be solved stepwise along the pipe until the G value goes to zero, where dryout occurs. This analysis was performed to compare the calculated g"rit with Wurtz data (Wurtz, 1978) and also to compare with the predictions by the well-known Biasi et al. correlation (1968), as shown in Figure 5.90. For the limited data points compared, the agreement was good. 

The present analysis therefore predicts that in turbulent boundary layer flow over a vertical surface ... 

Various analyses, similar to the one for the universal velocity profile above, have been performed to predict turbulent-boundary-layer heat transfer. The analyses have met with good success, but for our purposes the Colburn analogy between fluid friction and heat transfer is easier to apply and yields results which are in agreement with experiment and of simpler form. 

The prediction of turbulent boundary-layer separation by MVF methods has not been very successful. Indeed, it may be appropriate to identify turbulent separation in terms of the turbulence near the wall, and this will require use of a more sophisticated model (i ITE or MRS), quite possibly in their full (rather than boundary-layer) form. 

The i ITE methods include a calculation of the turbulence energy, and hence one may study the effects of variable free stream turbulence. Kearney et al. (K3) have compared such predictions with their data, and Fig. 22 shows a typical result for strongly accelerated turbulent boundary layer. 

Fully computational methods (FCM), using a variety of turbulence modelling methods, have been extensively applied to computing flows around single buildings in turbulent boundary layers. Using turbulence closure methods many models have predicted mean... 

Eddy Diffusivity Models. The mean velocity data described in the previous section provide the bases for evaluating the eddy diffusivity for momentum (eddy viscosity) in heat transfer analyses of turbulent boundary layers. These analyses also require values of the turbulent Prandtl number for use with the eddy viscosity to define the eddy diffusivity of heat. The turbulent Prandtl number is usually treated as a constant that is determined from comparisons of predicted results with experimental heat transfer data. 

Because the transition zone from a laminar to a turbulent boundary layer often covers a major portion of the exposed surface of a body, it is necessary to be able to predict the rapidly... 

S. A. Eide and J. P. Johnston, Prediction of the Effects of Longitudinal Wall Curvature and System Rotation on Turbulent Boundary Layers, Stanford Univ. Dept. Mech. Eng. Rep. PD-19, Stanford University, Stanford, CA, November 1974. 

Turbulence theories are not so far advanced that they allow us to extrapolate experimental data or to calculate flows around new shapes. Rather, turbulence specialists have concentrated on trying to reproduce the existing experimental data from some kind of comprehensive theory. This has not yet been accomplished. However, the partial results and partial understandings of turbulent flow have been useful in predicting the results of some experiments, e.g., turbulent boundary layers, as discussed in Sec. 11.5. 

Loss of energy in water due to frictional resistance at the static-bed surface arises within the (laminar or the turbulent) boundary layer. For nonbreaking waves, this is essentially the only mechanism that operates at the bed surface, and its magnitude depends on how rough the surface is. All other mechanisms are effective within the bed, and therefore require descriptions of dissipation that depend on the state (continuum or two-phased particle-water mixture, solid, or fluid) of the bottom. Several basic rheological models are available to predict ki (Table 27.1). 

Knight, D.D., Yan, H., Panaras, A.G., Zheltovodov, A.A. Advances in CFD prediction of shock wave turbulent boundary layer interactions. Progress in Aerospace Science 39, 121-184 (2003)... 

Chien, K. Y. Predictions of channel and boundary layer flows with a low-Reynolds-nuraber turbulence model. AIAA J., vol, 20, pp. 33-18, 1982. 

For reactors with free turbulent flow without dominant boundary layer flows or gas/hquid interfaces (due to rising gas bubbles) such as stirred reactors with bafQes, all used model particle systems and also many biological systems produce similar results, and it may therefore be assumed that these results are also applicable to other particle systems. For stirred tanks in particular, the stress produced by impellers of various types can be predicted with the aid of a geometrical function (Eq. (20)) derived from the results of the measurements. Impellers with a large blade area in relation to the tank dimensions produce less shear, because of their uniform power input, in contrast to small and especially axial-flow impellers, such as propellers, and all kinds of inclined-blade impellers. 

In turbulent flow, the edge effect due to the shape of the support rod is quite significant as shown in Fig. 6. The data obtained with a support rod of equal radius agree with the theoretical prediction of Eq. (52). The point of transition with this geometry occurs at Re = 40000. However, the use of a larger radius support rod arbitrarily introduces an outflowing radial stream at the equator. The radial stream reduces the stability of the boundary layer, and the transition from laminar to turbulent flow occurs earlier at Re = 15000. Thus, the turbulent mass transfer data with the larger radius support rod deviate considerably from the theoretical prediction of Eq. (52) a least square fit of the data results in a 0.092 Re0 67 dependence for... 

The approach described above is by no means complete or exclusive. For example, Lamb et al. (1975) have proposed an alternative route to assess the adequacy of the atmospheric diffusion equation. Their approach is based on the Lagrangian description of the statistical properties of nonreacting particles released in a turbulent atmosphere. By employing the boundary layer model of Deardorff (1970), the transition probability density p x, y, z, t x, y, z, t ) is determined from the statistics of particles released into the computed flow field. Once p has been obtained, Eq. (3.1) can then be used to derive an estimate of the mean concentration field. Finally, the validity of the atmospheric diffusion equation is assessed by determining the profile of vertical dififiisivity that produced the best fit of the predicted mean concentration field. 

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