Computational mesh of CFD modelling of RPB based CO2 absorption

The prepared geometry of the absorber was subjected to a discretisation process in order to generate a computational mesh. Due to disorderly air flow, it was decided to use a tetrahedral mesh. As gas flows through the porous layers, however, the wall effect on the flow pattern is significant. Thus, a boundary layer was generated in the rotating domain representing the porous body. It was necessary, however, to calculate the thickness of the first boundary layer element (yH) and the number of layers (N) that could describe the velocity gradient at the rotor walls (White 2009).

In the first step, the Reynolds number (Re) is calculated according to Eq. 1:


The characteristic geometric dimension l is represented by the width of the spacing of the rotor plates, ρ is the gas density, v is the gas velocity and μ is the gas dynamic viscosity. For the calculated Reynolds number, it is possible to determine the skin friction coefficient (cf) according to Eq. 2:


Having computed the skin friction coefficient, the wall shear stress (τw) is calculated following Eq. (3):


The friction velocity (uτ) can then be calculated from the wall shear stress (Eq. 4):


Finally, the distance of the first calculation point from the rotor wall (yp) can be determined:


As the boundary layer elements are prisms, the calculation point distance is half the thickness of the element (yp):


For the assumed value y+ = 1, the thickness of the first layer is equal to 7.22∙10-4 m.

In order to determine the number of elements of the boundary layer, it is necessary to calculate the thickness of the laminar sublayer (δ) using the Blasius corelation (White 2009):


where υ is the kinematic viscosity of gas. If each element of the boundary layer is 20% (G = 1.2) wider than the previous one, the total thickness of the laminar sublayer can be expressed as a geometric sequence:


where N is the number of boundary mesh layers. The above geometric sequence can be written in abbreviated form as follows:


By transforming the equation with respect to N, we obtained Eq. (10) for the number of layers:


Our calculations show that for the highest Reynolds numbers that can occur during gas flow, we need a boundary layer composed of seven sublayers.

Computational grid generation is a critical step that influences the convergence, stability and accuracy of the simulations. Therefore, a test of the independence of the result from the mesh density was performed. Figure 4 shows the results of CFD calculations of the gas pressure drop in the RPB device for different densities and mesh structures. At the beginning, a mesh was generated for a porous filling with cubic elements (cube). However, the lack of symmetry of the casing and quite a large jump in the size of the elements at the junction of the rotating and stationary domains resulted in the formation of elements with high skewness (the value of the average skewness of the elements is shown in parentheses in Fig. 4). Therefore, the shape of the element was changed to tetrahedrons, which allowed to improve the quality of the mesh cells. Five tetrahedral meshes with near wall boundary layers (wedge elements) of different element sizes were tested. Finally, a mesh with 1656K elements and 536K nodes with an average skewness of 0.33 was selected (Fig. 5). Further increasing the mesh density did not improve the result but only extended the computational time.

Fig. 4
figure 4

The result of the test of the independence of calculations from the mesh density. Cube, cubic mesh; Tet, tetrahedral mesh. The values in parentheses indicate the average skewness of the elements. The grid used in the calculations is marked in red

Fig. 5
figure 5

The final computational mesh used in RPB CFD simularions. Left- casing thetraedric mesh, Right – surface axisymmetric mesh of the rotor

The obtained average skewness classifies the quality of the generated mesh as good. In order to improve the quality of a grid adjacent to the rotating components and the gas outlet, the mesh in these locations is significantly concentrated.

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