The purpose of the post-processing is to help the user to organize the results of the CFD process in order to increase the data analysis speed. Another feature is to standardize and to improve the repeatability of the process. This makes possible to perform comparations between the same or different processes. The post-processing can be divided in two main targets, the quantitative and the qualitative one. The first is useful to monitor the data imposed during solving, these can be monitored in order to understand how the flow is being simulated. The qualitative data are generally used to describe the performance of the car. Hence these are very important aerodynamic parameters and can be used in form of images that illustrate the situation of the flow field.

Quantitative data

The main parameters that describes the aerodynamic performance is C_x∙S, C_z∙S, F_bal and ṁ, which are drag, lift, front balance and mass flow rate through any duct or heat exchanger, respectively. There are some simulations which the car model is symmetric, these are useful to evaluate the lateral performance of the car since the grip is different for each side. At the end of the simulation, the monitor of the generated data can be visualized in some files (Figure 1). In those, for each iteration or a group of ten iterations, if the monitor is used during the process, the iteration amount would be reduced. Hence, the lesser the monitor is used, the lower will be the iteration time.

For this reason, the iteration monitor is not opened during an experiment, or at least, only if it is really necessary. An example is when it is requested to monitor C_z∙S for the front and the rear wings. The same principle can be adopted for mass flow rate through the ducts. However, since these monitors exhibit raw data, this is not a proper approach for evaluation.

A possible solution is to plot these data together with the number of iterations to observe if the convergence occurs and when (Figure 2). After that it is possible to built a table that summarizes the values for C_x∙S, F_bal and ṁ (Figure 3). Another important table that can be built, is the one for temperatures.

This is useful for cases which particular batches are being analyzed, mainly the incompressible simulations, which it is interesting to evaluate temperature and pressure. The slope evaluates the convergence quality, thus if the results are reliable. Usually, when the downforce is increased by 1 point (0.01 C_Z∙S), the slope is increased by 2 points.

It means that the convergence is not well refined. The standard deviation evaluates the solution of different components of the car in order to evaluate the local forces on these ones.

The main components are the body work, front and rear assembling. Usually, rotating parts are taken out when evaluating the standard deviation of the solution.

Front balance

The Front Balance F_bal is a parameter that correlates the total balance proportion at the front axle. This feature is strongly sensitive to handling. The total downforce is decomposed between the front and the rear axles of the car. The portion at the front is F_bal. Actually, front and rear downforce are not real forces, these are partitioned force components which are derived from the total downforce. This is applied between the rear and the front wheel centerline (Figure 6).

This partitioning is calculated by putting the reference at the contact point of the wheel with the surface. The resultant moment in y, M_Y, makes able to balance the system of forces respective to the front wheel centerline. The formula for the front balance is written below:

F_bal = 1 + C_MY∙S∙L/(C_Z∙S∙L_ref)

The front balance is usually selected as the main target in the aerodynamic design, because it is important to know where to generate downforce. This depends on the kind of handling requirements of the car. The strongest part of the CFD analysis is that it is possible to obtain many solutions along the volume surface. Hence, it is possible to extract a huge number of information, not only in form of plots, but also as pictures of the volume surface. These plot the flow field around the car and with the option to use any of the calculated parameters.

Data reading

At the end of a CFD run, the output is huge file which contains the geometry, the variables for all elements and their solutions. There are two kinds of files as described below:

size data hour r007rc_001f01_b01_k01_g01_at5000.cas.gz → Fluent geometry file

size data hour r007rc_001f01_b01_k01_g01_at5000.dat.gz → Fluent solution file

The .CAS file contains only the geometry, which is comprised by the elements, nodes, boundaries and the interfaces. The .DAT files contains all the variables and calculations performed during the run. Since these contain a huge amount of information, it is impossible or, at least too time consuming, to analyze the entire file.

Strategies for data reading

There are some strategies to perform an efficient analysis. An interesting solution is to subgroup these data in order to reduce the amount of data exported and analyzed to only analyze what really matter for the customer or design requirements. Most of all CFD softwares allow to select the variables for post studying. The standard parameters usually exported are the pressure coefficient (C_p), the wall shear stress, the wall y⁺, the velocity and the total pressure coefficient (C_pt). The first is always considered due to the fast simulation of what is occurring. In addition, it is useful to perform fast comparisons. The wall shear stress is usually added because there is separation on the flow. y⁺ is a parameter that is useful to understand the non-turbulence and turbulence model in terms of quality. The velocity is a basic parameter that indicates the streamlines of the flow. Finally, C_pt is usually exported, because it is also a good indicator of the energy content in the flow field.

Data selection

There are some tricks to reduce the size of the data exported, which is to export smaller domains. The qualitative data usually analyzed are slices of the domain, or just boundaries, surfaces and for these there is no reason to export the full volume. For instance, if the hydro surfaces or the streamlines are requested, the velocity vector is the parameter to be exported. However, in case of just a slice of the boundary, the strategy is to export only the surfaces which are necessary for that slice. This reduce the time of the analysis, because once the simulation is finished, it is necessary to open the image generation software. Hence, as large the image is, longer will be to open the software. The image generation takes a lot of time, because there are many variables associated to these surfaces and planes. Hence, post-processing must be a standardized and repeatable procedure.

y⁺

The reason which y⁺ is calculated by the software is, because when considering the k-ξ model, this does not accept low Reynolds number (LRN). The boundary solution is not close to the solution for this model equation. For instance, the solution in some viscous region with y⁺ between 0 and 5 and under the logarithmic layer is a blend between y⁺ = 1 and the logarithmic layer. However, this solution is more an approximation, which is not advisable for the pressure side of the wings, for example. In this case, this assumption becomes critical, because the results are far from the real solution. For the pressure side of a front wing, y⁺ values between 5 and 30 are used, because this is critical due to the quick suction. The same case occurs when it is a set of too high height, over 500∙y⁺. For some areas like wing edges, it is observed that these are critical to discretize, because of their shape. These are small and the correct y⁺ at trailing and leading edges are difficult to get. For these cases, it is always a trade-off between how high y⁺ can be set and how low it is possible to go with the discretization.

Pressure coefficient

Usually in the racing car aerodynamic analysis, the first step that analysts and engineers use to do is the visualization of the boundaries of the car, its pressure coefficient C_p. The reason is, because it allows a complete view of the aerodynamic behavior. Just some views of the car is enough to understand the loading level of the car and the integral of the pressure at the surfaces of interest. In addition, the visualization of the C_p over the car body helps to check the stagnation points originated at the tires (Figure 8), if the maximum C_p is being obtained at the trailing edge of the wings and if the front floor is degrading C_p along the diffuser. Hence, the pressure coefficient along the car body put light on all aero devices of the car in order to proceed a fast visual check.

C_P 2 dimension plotting

Usually C_p is analyzed in slices, relative to the vehicle wheelbase, or even according to the pressure taps. However, there is also the possibility to analyze C_p in a 2 dimension plot. This is used for main plates, flaps, front and rear wing assemblies just to study the effect of different components on the aerodynamic pressure, suction and compression. It is mainly used with x-slice section to have a more clear visualization of what is a coherent structure and what is a wake. For instance, Figure 9 indicates a total pressure coefficient 2D plot. In this one everything will be wake, because all the structure will be merged inside the wake. For this cross-section it is not expected to see any particular structure, maybe a mirror wake due to the generation of this front wing wake. There is always some helicity for a better visualization and tracking of the air flow over the structure, specially in cases which the wing is near the floor. This accelerates the flow at the leading edge. Hence, it is possible to track the path of this structure. Vorticity is important once it is coherent. Actually, there are some kinds of vorticity that always rotate in the same structure (coherent), thus it is interesting that these could be controlled. Neither all types of vorticity are possible to be controlled, because these are just rotating around the wake of the car. The visualization seen in Figure 9 helps to identify which of the structures have coherent and non-coherent vorticity. In some cases the vorticity is tracked based on the boundary layer of the helicity value. For instance, in a particular region that has the maximum helicity, it is possible to visualize where the structure is going.

Oil flow

The oil flow visualization allows the shear vector visualization at the surface. The shear vector indicates the direction of the flow field close to the surface. This is particularly helpful when combined with C_p, because this already indicates the points of suction and compression, but together with the oil flow it is possible to understand the reason for a determined C_p value. For instance, a C_p indicating suction or compression while oil flow describes if this compression is due to a separation or a curvature on the surface. In addition, it allows to visualize if occurs some crossflow in diffusers (Figure 10). Therefore, oil flow visualization is a complementary tool for better understand of the aerodynamic behavior of the car.

Wall shear stress

The most valuable parameter to access separation is the wall shear stress τ. The main condition for separation is when the partial derivative of the velocity profile by the vertical component (∂u/∂y) is equal to zero.

τ_w = μ∙(∂u/∂y)

Since wall shear stress is the dynamic viscosity times the partial derivative of the velocity profile (∂u/∂y), the separation occurs when the wall shear stress is equal to zero. Hence, plotting this data over the vehicle data allows to spot the points which the air flow separates (Figure 11).

Total pressure coefficient C_PT

When visualizing the slices, it is exhibited the feature domain which is useful to understand the amount of energy that is present in that particular boundary. The total pressure coefficient C_pt is a variable that express the amount of energy going into the fluid. When C_pt goes below the reference values, which is 1 because it is normalized by the dynamic pressure q_∞, it represents that the flow is loosing energy. This is an unavoidable situation since there are points of the car that the flow lose some energy. For instance, the generation of the vorticity, always take some energy from the flow. From the analysis point of view, the objective is to ensure that the vehicle body loses the smallest energy quantity as possible. C_pt can be written as following:

C_pt = (p – ½ρV²)/q_∞ ; q_∞ = ½ρU_∞²

According to the Bernoulli’s principle, in an inviscid flow, C_pt is constant and uniform, thus each C_pt variation means a loss of energy caused by viscosity and/or turbulence. For race cars it is important to hold above the aerodynamic surface a C_pt = 1 flow, because this brings more energy which is able to generate stronger aerodynamic forces. Therefore, C_pt is a useful coefficient for the comprehension of energy content in the aerodynamic flow, which depends of vortex, viscous effects and turbulence.

C_PT analysis in the x direction

The front wing (Figure 12) is an example of component that exhibits a vorticity structure, which can be observed at the endplates. There is no solution for this situation to better reduce the vorticity and the energy loses. This is a very sensitive figure in terms of C_PT, since this parameter makes easy to spot where all the loses are from.

The effect of the wheels

An example of typical moving boundary condition are the wheels. This is motivated by the wake from the front wing. Since this one is a streamlined body, thus it does not have a big wake over the wheels. As can be seen on Figure 13, there is a very small loss of energy. However, it generates some coherent vorticity structure (green), which arises from the delta of pressure between the suction and the compression areas of the front wing element. This is a loss of energy, because this flow is ramping up.

The tire geometry exhibits a stagnation point at its top, that move backward towards the ground by both the rotation of the tire and the velocity relative to the ground (Figure 14). It is very important to handle this kind of loses in order to not have too much energy losses. The reason is that, this flow with such low energy goes inside the underbody, which is the main aero device of the car. Hence C_pt information delivers an overview of the pressure loses over the boundaries. The pressure for incompressible simulations is always expressed in respect to the reference value which is the free stream one.

Figure 15 illustrates that the C_pt visualization is 1 for the free stream value, but where the velocity increases relative to the free stream values, it goes to a negative C_pt. Actually, C_pt is an off-set between the free stream values normalized by the dynamic pressure. For this reason, it is possible to decompose C_pt between the sum of C_p and the quadratic ratio between the velocities. If C_p is negative, thus C_pt will be also negative. Figure 15 allows to understand the direction of the wake originated from the wheel and how much it goes below the underbody and if there are some possibility to steal the energy of the flow at this region, which is the most important one for the downforce generation.

C_pt analysis in the y section

The y slices are useful for the setup of the alignment of the streamlined bodies like front wings, suspension arms and wheel shields. For this reason, C_pt plot is overlapped by the oil flow and the streamlines, which are used to account the velocity and its alignment over the wing profiles, suspension arms and wheel shields. The plot of C_pt on the y section (Figure 16) is also useful to visualize if some profile is shielding or if there is some device to shield. For instance, some open wheels race cars have their rear tires shielded to avoid the effects caused by them. In this case, this method to visualize C_pt helps to shield them properly. In addition, it is interesting to visualize the extent of the brake separation, if it goes out of the flow and its alignment.

C_PT analysis in z direction

The z section slices are useful for the wake width visualization, this information is particularly important for the drag force (Figure 17). When the wake closes later than an optional aerodynamic configuration, this means that there is more drag than this option. Hence, this plot is a good approach to compare two options, because it illustrates in a very didactic and simple way if one option is more draggy than the others or if there is enough energy to close the wake. This makes able to test configurations in order to close sooner the wake, avoiding problems in the later stage of the development.

C_pt analysis through iso-surfaces

The C_pt iso-surfaces are a bit more complex to analyze. Around the boundary of the car, the iso-surface have a particular C_pt value. If this is different from the surface of the car, the colored surface (Figure 18) describes the energy level at that region of the car and how quickly the surface degrades the energy level around and along the car body, because if it goes towards a lower C_pt and closer to the car, the flow is losing energy. The iso-surfaces also can provide a 3 dimension overview of where all the wakes of the car are in terms of level of energy, type and direction.

Velocity

Another variable which is plotted in slices is the velocity. This is a good indicator for the extent of the wake, but it is less clear to analyze the vorticity formation. In cases which the vorticity structure is coherent, it does not merge in other wakes. However, when the vorticity is not coherent, the velocity plot is not a good method to distinguish what is a wake and what is vorticity factor.

Temperature

For compressible cases, it is interesting to analyze the temperature of the domain. For instance, the effect of the exhaust gases on the air flow through the rear wing (Figure 20).

Vorticity visualization

This analysis is based in two different method, both distinguish what are the wakes and what are the coherent vorticity structures. This is important, because wakes usually results in drag, while the vorticity structure increase the velocity, thus decreasing pressure in particular areas which is desirable to increase suction like in the flow entering, for instance. For this reason, it is interesting to have tools to distinguish wake and vorticity. Basically, there are two methods, the velocity gradient tensor and the vorticity. Their purpose is to highlight the zones of coherent vorticity.

Velocity gradient method

The method is based in the velocity gradient tensor is described by the characteristic equation:

λ³ + Pλ² + Qλ + R = 0

Where P, Q and R are the three invariants of the velocity gradient tensor. Usually, the criteria used is Q, which defines a vortex as a “connected fluid region with a positive second invariant of ∇U”, thus Q > 0. In addition, the Q-criterion is the one used to plot the graph illustrated by Figure 21, which is an iso-surface. This method requires more experience from the aero design team.

Vorticity method

The method based on vorticity is connected to the theory behind the vorticity, this is described the curl of the velocity:

ω = ∇×U

This is a measure of the rotation of the fluid. It can be used to visualize vortices when plotting the iso-surfaces of |ω|. As in the vortex axis the local velocity and vorticity vectors tends to be aligned in the vortex axis, the helicity can be used to visualize vortex cores, as described by the following formulae:

H = ω∙U

The helicity is also plotted in slices.

References

• This is article is based on the lecture notes taken by the author during the Industrial Aerodynamics lectures held by Muner at Dallara Accademy.