Analysis of the swept back planar wing

Hello, I am again back with a new CFD blog. In the previous blog, I wrote about the analysis of the airfoil, in this blog airfoil with sweep and finite span would be discussed. For this analysis of the wing, the wing was constructed with NACA 2411 profile. Different chords were chosen for the construction of the wing. Base airfoil was placed at the three different planes with different chords and they were joined. For the construction of the wing, it was constructed in 3DCAD the starccm+. The reason is that for different angles of attack and for the different airfoils, it would be quite easy to analyze; as it reduces the time for importing the geometry, then other procedures.

For the analysis of the steady,3D incompressible flow around the wing; bullet-shaped computational domain was constructed with 10 times the span of the wing, the domain is shown in fig.0.

fig. 0 Computational domain

Mesh 

For the meshing, surface re-mesher ,trimmer mesher with prismatic layer models were used. Surface remesher is generally used when the geometry is imported; the main usage is to improve the quality of the surface and prepare the geometry for the volume mesh. Along with that, it also helps in creating a subsurface generator while creating the prismatic layer.

Trimmer mesher was used for this analysis because it can be used for the simple as well as complex geometry, another advantage is that it can create hexahedral volume mesh with low numbers of skewness cell; along with that, it also gives the options for the template mesh, which means it is easy to control local mesh size. The prismatic layer was used to capture the boundary layer.

The base size for the mesh was kept 0.0625m,and other meshes on surfaces of the wing were controlled by the percentage of the base size(such as the leading edge and trailing edge of the wing). For the external aerodynamics to capture the pressure drop over the wake regions, it is necessary to refine the wake regions; these meshes can be controlled by creating the volume downstream and subsequently by refinement. For the boundary layer, prismatic layers were constructed with y+=1, for this analysis, there were 36 prismatic layers with a stretching of 1.1 with a prism layer thickness of 3.6e-03. A total number of cells was 3049400. For the quality of the mesh, all the cells have a face validity of 1.0 and volume change of 0.1, which is quite acceptable for CFD simulations. 

The following figures show the prismatic layers as well as meshes in the computational domain. 

i)

ii)

iii)

iv)

fig.1 i&i represent the domain mesh

iii) surface mesh over wing

iv)prismatic layers

                                        

Flow Condition

The simulation was carried out for the incompressible, three-dimensional, steady flow scenario with a velocity of 60 m/s, and zero incidence angle. The atmospheric conditions are as follows, rho=1.225 kg/m^3,mu=1.802e-05,Re=6.5e06.For the turbulence modeling RANS with Spalart-allmaras model was selected, as this model predicts good flow behavior for the attached boundary layer and flow with mild separation. Along with that this model solves only one transport equation to derive the turbulent eddy viscosity, it reduces the computational time. Moreover, standard Spalart-allmaras was used as this model resolves viscous sublayer accurately, unlike the high Reynold number Spalart-allmaras model. For this study segregated flow model was invoked, as it behaves well for constant density flow and it can handle the mildly compressible flow. Along with that 2^nd order upwind scheme was used for convection flux. There was no use of any wall function for this study, all y+ wall treatment was considered.

For the boundary conditions velocity inlet for upstream conditions, pressure outlet for downstream conditions, symmetry plane for the lateral conditions, and wall for wing with no-slip conditions. Reasons to choose such type of boundary conditions is simple as we know the velocity for the wing/aircraft then which can be applied at the inlet with 60 m/s, for downstream pressure outlet as an individual is aware of the atmospheric conditions. Here for 3 component of velocity, the velocity inlet is applied and for the pressure outlet pressure conditions is applied; as there are 4 equations to solve. For the initial condition, the flow domain was set at 60 m/s.

Convergence & Results

 Once all the flow conditions, respective boundary conditions, and mesh are created simulations was initialized and stopped until required convergence. The reference residual convergence and lift/drag convergence are shown in the below figure.

i) 

ii)

fig.2 i, ii represents representative residual

This study of the wing provided some rich information about how the flow variable and other relative parameters behave; which can affect the efficiency of the wing. If one talks about the efficiency of the wing, which is expressed in lift over drag ratio. For this study, this wing was selected arbitrarily, there are no data to validate it; however, the order of magnitude found in this study was the same as in practice. For this study lift/drag ratio was found around 12.4777 and the coefficient of the lift was around 0.221393 for the flow conditions given above. Since in this study, we aimed for y+=1, to calculate the first prism layer thickness; from below fig.. it is evident that the mean value for the y+=1, max for some regions around 4(below 5)

    fig.3  represents y+ value

As it is known that the upper surface of the wing and lower surface of the wing has pressure difference and this is the force that is responsible for the sustentation. Moreover, it is evident that flow on the upper surface moves inward toward the wing root, and flow under the wing surface moves toward the wing tip which can be seen from the below figures.

i)

ii)

    fig.4   i) represent the streamlines on the suction side

                          ii) represent the streamlines on the suction & pressure side

This pressure difference on the upper and the lower surfaces causes the vortex roll-up process. The positive gradient from the pressure side to suction side causes secondary flow generation, toward the wing tip separates it and forms a vortex, which is convected downstream. These generated vortex and vortex sheet can be shown in figure 5. 

If one does a close analysis then it can be found that how the vortex cores behave with the streamwise direction. As shown in figure 5 below, at the location around(x/c) 2.1, velocity deficit can be observed which is due to the shear effect and as it goes down further it vanishes. This study was not rigorously devoted to capturing the tip vortex,  this was just done for the basic flow analysis around the swept-back planar wing, so high-resolution activities of the vortex were not captured.

fig.5  vortex structure past wing

Moreover, some interesting images can be captured with a vector scene, which is shown below; in which u component of velocity is depicted.

    fig.6  vortex structure past wing II

Before finishing, some data are represented here. This study was conducted with limited available resources, so keeping all these things affects the result, for example, mesh refinement, and convergence time. With all these factors, the acquired L/D ratio was 12.4777, coefficient of the lift cl= 0.221393 & coefficient of the drag cd=0.017743. Moreover, individuals can extract the figures for the skin friction coefficient cf which is around 0.005893 which is shown in the following figure.if it skin friction coefficient is compared with the overall drag coefficient,then cf contributes to around 33.21 percent of the overall drag coefficient.

 fig.7  skin friction coefficient on the wing surface.

If an individual is interested in different angles of attack, then in the star ccm; it can be done just by doing a flow direction change or with a change in the geometry by setting at an angle.

Thank you.