Tackling Boundary Layers and Near-Wall Regions in CFD

CFD is a crucial aspect to be considered in modern engineering practice, in order to minimise pressure drops, friction forces, and viscous phenomena that can hinder the system’s overall efficiency. While performing CFD simulations in systems like pumps, airfoils, compressors, turbines, wings, and other sort of aerodynamic devices that interact energetically with fluid, the above factors must be closely monitored in order to increase the accuracy of our results.

The first concern is how the flow interacts with the sturdy walls of the machinery we previously stated. When examining the physics, it is simple to note how a velocity gradient is developed in a region adjacent to a solid wall, as seen in the above figure. Different sizes and physical processes influence the inner portion of a flow that is restricted by a wall and the outer portion that is approaching the free stream. These streams are commonly called inner and outer layers. 

When considering the flow over a smooth, flat plate, two different types of boundary layers can be identified: laminar and turbulent. The calculation of the velocity gradient at the wall is crucial, and any error or inaccuracy here could lead to an inaccurate under- or overestimation of the friction forces. The zone where this velocity gradient must be precisely computed is therefore defined as the boundary layer.

Near wall region can be divided into 3 distinct layers.

i)  Viscous sublayer

ii)  Buffer layer

iii) Fully turbulent region(Log-region)

 

In fig 1a, The Reynolds number behavior as it approaches near to the wall falls into 3 categories with 24,000 then 43,000 and finally 61,000. Also the y+ estimation for various regions is limited between y+ =5 to y+ =30.

The y+ non dimensional distance from wall first cell thickness for various region is limited as below,

Y+ = 10-20 For Viscous sublayer

Y+ = 30-60 For Turbulent boundary layer

VISCOUS SUBLAYER:

Laminar (or viscous) sublayer refers to the thin layer immediately adjacent to the wall. Shear tension drops and turbulence activity increases as one moves farther away from the wall. While eddy transport predominates in turbulent zones, molecular methods are used in laminar sub-layer momentum transfer.

BUFFER LAYER:

The buffer layer, which cushions between the sublayer and the main flow when turbulence is fully active, is located between the viscous and boundary level layers. The existence of buffer layers is disregarded in streamlined analyses of flow within the turbulent boundary layer.

Although the flow is turbulent, the gradient of the time-averaged velocity is very large.

TURBULENT LAYER:

Only at higher Reynolds numbers does a turbulent boundary layer actually develop. Molecular viscosity alone cannot handle the scale of mixing. The term "turbulence viscosity" or "eddy viscosity," which lacks an expression, is used to calculate turbulent flow. For this, numerous models have been created.

Y+ APPROACH:

The y+ value is a non-dimensional distance (based on local cell fluid velocity) from the wall to the first mesh node, and is determining whether the influences in the wall adjacent cells are laminar or turbulent. CFD is often used to describe if a mesh is fine or coarse. 

There are three subdivisions of the near wall region in turbulent boundary layer (see figure 1a): 

Viscous sublayer region with y+ < 5 (velocity profiles assumed to be laminar and dominate the wall shear); 

Buffer region with 5 < y+ < 30 (dominates both viscous and turbulent shear); 

Fully turbulent portion or log-law region with 30 < y+ < 300 (turbulent shear dominates). 

The ideal values of y+ for wall function and y+ ≈ 1 for near wall modeling are those that are close to the lower bound of y+ ≈ 30. We may therefore conclude that y+ is an appropriate selection criterion for picking the best mesh layout and turbulence model.

Y+ is important during the pre-processing step, so knowing the appropriate size for the first layer of grid cells (the inflating layer) is important to ensure that the y+ is within the necessary range.

The real flow-field won't be known until the solution has been computed (and in some cases, it will be necessary to go back and remesh the model because of the computed y+ values).

u+= w/w

Here, w  and ware the shear stress and density of wall and by using this relation the non-dimensional velocity and the non-dimensional length, y+ are defined as below,

u+=  u+/u

y+ = u+. y/v

Where u, v, and y stand for the wall's parallel velocity, separation from the wall, and kinematic viscosity. Additionally, there are inner and outer layers in turbulent layers.

TURBULENCE MODELING:

The most important part of turbulence modeling is near wall modeling. Focusing on the turbulent boundary-layer is necessary when dealing with near wall models. Turbulence's primary source of vorticity is walls. Unless the wall creates turbulence, there won't be any. When walls are present, turbulent momentum boundary layers are created, and the innermost part of these layers has very steep gradients. How we choose to model this innermost region of the turbulent boundary-layer has a significant impact on the accuracy of our predictions of viscous drag in aerodynamic flows, pressure drop owing to separation, and heat transfer, to name just a few. Not only does the modeling option matter, but also the type of mesh resolution required in the boundary layer in order to produce reliable forecasts.The chosen model and the grid resolution are closely related in that a very good model for a particular application can only produce accurate predictions if the mesh resolution is chosen in a way that it corresponds to the model in question.

Near wall Modeling:

Given that walls are the primary source of mean vorticity and turbulence, the near-wall modeling has a substantial impact on the accuracy of numerical solutions. After all, the momentum and other scalar transports are most active at the region near the wall where the solution variables have significant gradients. Therefore, successful predictions of wall-bounded turbulent flows depend on precise description of the flow in the region near the wall.

For turbulent core flows, the k-models, RSM, and LES model are mostly applicable (i.e., regions somewhat far from walls). Therefore, it is important to think about how to adapt these models to work with wall-bounded flows. If the near-wall mesh resolution is enough, the Spalart-Allmaras and models can be used to analyze the entire boundary layer.The wall function technique significantly reduces processing resources in the majority of high-Reynolds-number flows because it avoids resolving the viscosity-affected near-wall area, where the solution variables change the quickest. Advantage of the wall function approach is a result of its affordability, dependability, and accuracy. 

K- and  K- :

The typical k-turbulence model, the most well-known and widely used turbulence model, has drawbacks that must be noted. In order to establish a boundary condition that is not closer to any solid boundaries, it is necessary to first consider the model as being fundamentally a high Reynolds model, which means that the wall effects (Law of Wall) should be indicated.

A mathematical, or "Low Reynolds'' technique, must be used to integrate the equations through the viscous/laminar sublayer. This is made possible because low-Reynolds formulations require additional highly nonlinear damping functions in order to integrate into the laminar sublayer (y+<10). Again, this results in numerical rigidity, which is difficult to manage in light of linear numerical techniques.

Furthermore, although many engineers utilize low Reynolds models to achieve a degree of transition from laminar to turbulence prediction, the low Reynolds technique shouldn't be mistaken with transitional Reynolds modeling. There is no reason to anticipate accurate transition predictions given that the low Reynolds methodology is designed to manage the near wall viscous/laminar sublayer, especially given that there are numerous pathways for transition initiation.From above discussion it is clear that the placement of the first node in our near-wall inflation mesh is very important.

As shown above, we must be keen to avoid getting our values so high that the first node is outside the boundary layer zone. If this occurs, our turbulence model's Wall functions, which are used to determine the flow parameters at this initial calculation point, may calculate them erroneously, which may add inaccuracies into our pressure drop and velocity outputs.This association may be very accurate when basic flows and simple geometry are taken into account. To ensure the intended value is reached, however, it could be necessary to refine the boundary layer when complex geometry is taken into account. In certain circumstances, re-meshing is necessary to get the desired value throughout the entire model, or mesh adaptation techniques must be applied.

The model's lack of sensitivity to negative pressure gradients is another significant flaw. It has been noted that in such circumstances, it overestimates the shear stress and delays separation as a result. This problem is resolved by Menter's k-SST using the Shear Stress Transport (SST) idea.This flaw, which connects the Reynolds stress to the mean flow strain in practically all eddy-viscosity models, actually marks the main distinction between this method of modeling and a comprehensive Reynolds-stress model (RSM).

The main turbulent shear-stress transfer has a significant impact on the RSM method. The objective is to include the finding that the shear stress in the boundary layer is proportional to the turbulent kinetic energy in the improved K-model (also known as the Baseline (BSL) model) in light of the implementation's encouraging results.

Summary:

As a result, we now understand that the near wall approach and value needed for a wall function and it depends on the flow characteristics as well as the turbulence model being applied. In general, we can apply a Wall Function technique when there is a connected flow, which results in a higher beginning value, a smaller overall mesh count, and faster run times. One would be encouraged to resolve the boundary layer to the wall with a finer mesh if they anticipate flow separation and realize that this will depend on their ability to estimate the separation point accurately. Hence, one needs to check the values as part of his normal post-processing to make sure to fall in the valid range for the flow physics and turbulence model selection.