Near Wall Computation

If the user wants higher accuracy in the predictions, and if he/she is willing to pay for the increase in accuracy in terms of increased computing cost, more grid nodes should be used. In general, more grid nodes should be located where the flow is complex. For an empty room without furniture or persons, this normally means that more grid nodes should be placed near walls and in... 

The preferred range for the thickness of the near-wall cell layer is y+ >30. However, this is difficult to achieve in packed tubes. The cells sizes are constrained by the need to fit in between the gaps and/or narrow spaces between particles, so they cannot be too large. This can result in the y+ values being too small for proper application of wall functions. The alternative to use small enough cells to resolve the boundary layer (y+ < 1) increases the computational... 

With increased computer power, our next step was to construct full beds of particles N —2 for validation studies as described above in Section II.D.2, and N = 4 for further investigation of the temperature fields and near-wall transport processes as described above in Section II.B.2. Some early flow maps and path... 

At this stage it seemed clear that to improve near-wall heat transfer modeling would require better representation of the near-wall flow field, and how it was connected to bed structure and wall heat transfer rates. Our early models of full beds of spheres at N — 4 were too large for our computational capacity when meshed at the refinement that we anticipated to be necessary for the detailed flow fields that we wanted. We therefore developed the WS approach described above in Section II.B.3. 

In most high Reynolds number flows, the wall function approach gives reasonable results without excessive demands on computational resources. It is especially useful for modeling turbulent flows in complex industrial reactors. This approach is, however, inadequate in situations where low Reynolds number effects are pervasive and the hypotheses underlying the wall functions are not valid. Such situations require the application of a low Reynolds number model to resolve near-wall flows. For the low Reynolds number version of k-s models, the following boundary conditions are used at the walls ... 

For quite a few flow situations this relation provides results being in better agreement with experimental data, compared to the corresponding predictions obtained using the equilibrium formulation. Versteeg and Malalasekera [175] state that this approach represents the optimum near wall relationships from extensive computing trails. 

CFD-simulations of the measurement apparatus were carried out using a computational mesh with a near-wall refinement on the surface of the rotating cylinder. The simulations reported here were done without the additional baffle at the bottom of the tank (see Fig. 1). Computations with different /rvalues were first conducted in order to find out the dependence of the drag reduction on k. Drag reduction was calculated from the torque on the rotating cylinder due to wall shear forces. 

The chapter by Beris and Housiadas ( Computational Viscoelastic Fluid Mechanics and Numerical Studies of Turbulent Flows of Dilute Polymer Solutions ) aims at resolving the famous long-standing problems of turbulent drag reduction. This contribution describes recent efforts and achievements in direct computations of near-wall turbulent flows of dilute polymer solutions and comparisons with experimental data. 

Through the use of lab tests implemented by the pulp and paper companies in the United States and Canada it was determined that all but one manual technique were both unrepeatable and inaccurate. During some years ago the operators of black liquor recovery boilers have been able to take advantage of the latest teehnology to inspect the wall thickness of the near drum generator tubes. The technology utilises immersion ultrasound and automated computer... 

Sillinian, W. J. and Scriven, L. E., 1980. Separating flow near a static contact line slip at a wall and shape of a free surface.. /. Comput. Phys. 34, 287-313. 

When a coarse grid is used, wall functions are used for imposing boundary conditions near the walls (Section 11.2.3.3). The nondimensional wall distance should be 30 < y < ]Q0, where y = u,y/p. We cannot compute the friction velocity u. before doing the CFD simulation, because the friction velocity is dependent on the flow. However, we would like to have an estimation of y" to be able to locate the first grid node near the wall at 30 < y < 100. If we can estimate the maximum velocity in the boundary layer, the friction velocity can be estimated as n, — 0.04rj, . . After the computation has been carried out, we can verify that 30 nodes adjacent to the walls. 

However, the assumption of molecule orientation normal to the surface is not convincing enough for this author, and it does not consist well with the results of the molecular d5mamics simulations for the alkane confined between solid walls. An example in Fig. 3 shows that the chain molecules near the wall are found mostly lying parallel, instead of normal, to the wall [6]. This means that the attractions between lubricant molecules and solid wall may readily exceed the inter-molecule forces that are supposed to hold the molecules in the normal direction. Results in Fig. 3 were obtained from simulations for liquid alkane with nonpolar molecules, but similar phenomenon was observed in computer simulations for the functional lubricant PFPE (per-fluoropolyether) adsorbed on a solid substrate [7], confirming that molecules near a solid wall lie parallel to the surface. 

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