**3. Results from various CFD model calculations**

Now that the main CFD models have been presented, we turn attention to comparisons of the results from different models. There are comparisons available in [7, 8, 34, 35, 37, 39–46] and a very small subset of those comparisons will be provided here. We have selected the classic problem of flow over a square blockage. This canonical problem has the features that elucidate the strengths and weaknesses of the particular models. For instance, some important parameters relate to the time-averaged interactions between the fluid and the solid structure (drag force). Also, there are significant unsteady phenomena, particularly in the wake region that provide a challenging test for the models. In addition, this is a problem with extensive experimental work that will serve as the basis for evaluating the results. To begin we refer to **Figure 4** which shows the solution domain (similar to [35]).

**Figure 4.** *Geometry for flow over a square cylinder.*

#### **Figure 5.**

*Computational mesh used for square cylinder simulation.*

#### **Figure 6.**

*Drag coefficients for flow over a square cylinder and comparison with experiments. Reynolds numbers range from 1 to 10,000,000.*

**Figure 7.**

*Drag coefficients for flow over a square cylinder and comparison with experiments, Reynolds numbers ranging between 10 and 10,000.*

A number of computational meshes were used and an example mesh is shown in **Figure 5**. The images are provided in a series of increasing magnification. Image (a) is the most global view, part (b) is focused on the square obstruction, and image (c) reveals details of the elements in the near-wall region, near a corner of the cylinder.

With this mesh, we present results for a large number of computational methods. We note here that in reality appropriate meshes may differ depending on the turbulence model that is used. For instance, a mesh that is suitable for a k-w simulation may not be appropriate for SST, and vice versa. We recommend that mesh independent studies be carried out for each turbulence mode that is employed. The results, set forth in **Figures 6** and **7**, provide the drag coefficient on the square cylinder (large aspect ratio). Each model has its own color. Literaturebased values from experiments are also included (shown as gray x symbols).

In the above calculations, which were first set forth in [35], the SST and transitional-SST models were most accurate (when compared with existing experiments) for calculating the drag coefficient. On the other hand, since these approaches were RANS, they lose some local detail and flow structure. For example, in **Figure 8** which is provided below, we show velocity vectors, overlaid atop a velocity contour image. It is evident from the upper part of the figure that there are the expected stagnation locations at the leading edge, and in the wake region. There is also a slow-moving recirculation zone above and below the cylinder that are a result of flow separation at the leading corners. However, the lower images show a focus on the flow patterns at the leading edge. It is seen that with the SST RANS model, there are no small-scale eddies at this location. But for the LES model, there are two LES results that are obtained at two different instances in time. These sequential images show the time-varying flow field. While a RANS model like the SST is excellent for full-body drag, it does not capture some small flow structures. Researchers thus need to consider their computational needs before selecting a CFD model.

#### **Figure 8.**

*(upper image) velocity contour and vectors for SST model and (lower image) side-by-side comparison of leading-edge flow for SST and WALE LES models.*

The last result to be presented is shown in **Figure 9**. There, instantaneous results are displayed for the SST model. There, clearly, the unsteady nature of flow in the downstream wake region are evident. If the simulation of **Figure 9** was carried out with a steady state SST solver, there would still be timewise changes in the flow field but they would have a different frequency than the unsteady calculations.

In order to elucidate the iteration-by-iteration fluctuations in drag that result from a steady state solver (compared to an unsteady simulation), **Figure 10** is prepared. This figure shows the timewise (iteration wise) fluctuations in drag force on the square cylinder first with a steady state SST solution and then with a truly unsteady solution. The steady state results are calculated using a "false transient" approach wherein the algorithm steps forward to new iterations using a nonphysical time. The figure has two call outs that provide focus on different parts of the graph. The important conclusion is that the average value of unsteady fluctuations of drag obtained by the steady state algorithm are an excellent match that that *Turbulence Models Commonly Used in CFD DOI: http://dx.doi.org/10.5772/intechopen.99784*

**Figure 9.**

*Streamline patterns and velocity contours for Re = 100,000 flow over a square cylinder. Images at a sequence of time instances, using SST model.*

attained from the unsteady calculations. On the other hand, the period is very different between the two.

### **4. Concluding remarks**

This chapter has presented a brief overview of a large number of turbulence models. While there is no "correct" turbulence model, there are models that are better suited for particular situations.

For flows that are truly laminar with no regions of intermittency or turbulence, a laminar solver can be used. However, if there is a potential for any turbulent flow, caution is warranted. For flows that are fully turbulent, particularly wall bounded flows, the SST model is recommended. In our experience it is more able to capture flow phenomena compared to other RANS models. It also has excellent performance for a wide range of thermal-transport situations.

If regions of mixed flows (laminar/transitional/turbulent) are expected, of if the flows might change in time (pulsatile flows for example), the SST transitional
