Rotating Moving Boundary Analysis Using ANSYS 5.7

Transcription

1 Abstract Rotating Moving Boundary Analysis Using ANSYS 5.7 Qin Yin Fan CYBERNET SYSTEMS CO., LTD. Rich Lange ANSYS Inc. As subroutines in commercial software, APDL (ANSYS Parametric Design Language) provides a strong tool for software development. APDL is not only merely a language, but a language based on the applications of ANSYS. In such an environment the software development can be done based not only a language and library, but also on some applications. With ANSYS/FLOTRAN 5.7 enhanced with ALE and Interpolation, a rotating moving boundary calculation is designed with APDL. The APDL flow chart will be listed for general reference of rotating moving boundary analysis. The new approach is validated in 2 models: the flow around a rotating square and the flow around a rotating fan. Introduction Some examples show that interpolation of ANSYS version 5.7 can be used for data transformation of steady state compressible flow simulation to saving CPU time. In this case, the coarse mesh is used to get a result that is late transferred to a finer new mesh as initial condition for further analysis [1]. In another way, during the transient simulation of flow with moving boundary, the computational mesh may undergo considerably distortion using ALE (Arbitrary Lagrangian Eulerian) [2] Method. A distorted mesh with large aspect ratio, small mesh angel, etc. provides poor reference system and becomes unsuitable for further analysis. When this occurs, a more suitable mesh is desirable to be generated and all solution variables from the old distorted mesh are desirable to be transferred to the new one. This is known as interpolation or rezoning. In ANSYS version 5.7, there are some examples of ALE such as torsion oscillation and squeeze film [1]. All the rotating movement of boundary is less than 45 degree. In this paper, with ALE and Interpolation, a rotating moving boundary calculation approach is designed with APDL and the approach is validated in 2 models: the flow around a rotating square and the flow around a rotating fan. As subroutines in commercial software, APDL (ANSYS Parametric Design Language) provides a strong tool for software development. APDL is not only merely a language, but a language based on the applications of ANSYS. In such an environment the software development can be done based not only a language and library, but also on some applications. Rotating movement calculations are a kind of development using APDL based on applications of ALE and interpolation of ANSYS5.7. At last, the improvement requirements about interpolation accuracy, result file arrangement, tabular boundary conditions are listed. Models And Boundary Conditions Fan model and boundary conditions For ALE rotating boundary simulation, at least two mesh patterns must be prepared for interpolation. According to the model shape, three, four or more patterns are necessary. In figure 1, the simplest example of rotating fan is shown. The length of the domain is 20 mm, the breadth of inlet is 8 mm. The center of fan is mm away from the inlet and is at the centerline of the domain in y direction. The radius of circle area is 2 mm. There are all 8563 nodes and 8140 elements for the whole domain. There are 6286 nodes and 5869 elements in

2 circle areas. In the circle area, the movement of nodes is considered in ALE calculation. Out of the circle area, the nodes are fixed. Figure 1 - the domain of calculation. Detail of blades is shown in figure 2. In the model, there are 32 rotating blades in the circle area and they rotate around the center of the circle area. The length of blades is 0.4 mm and the breadth of blades is 0.04 mm. The outside of blades is 1.8 mm to the circle center and the inner side of blades is 1.4 mm to the circle center. The inlet of flow is at left side of the domain and the inlet velocity is 20 mm/s. Outlet is on the right side defined as zero pressure. The above and bottom of the domain are fixed wall with zero velocity in both x and y directions. In figure 3, the starting mesh is shown. With defined moving boundary conditions and method of ALE, the rotating blades move to the position in figure 4. Forty time steps are calculated from the position in figure 3 to the position in figure 4. The size of time step is s. Namely, 0.08 s elapses when blades rotate degree. Blades rotate at an angular velocity about RPM and the outside of blades moves at a tangent velocity about mm/s. In this case, fluid is uncompressible, Reynolds Number is 11.3 and laminar flow is defined. Figure 2 - Left: the detail of domain. Right: the detail of some blades.

3 Figure 3 - Left: the first mesh pattern for starting. Right: the blade position. Figure 4 - Left: the first mesh pattern before interpolation. Right: the blade position. When blades move to the position in figure 4, the mesh cannot be distorted anymore. Especially the aspect ration and angle of meshes in the forward direction become very bad. That means a more suitable mesh is desirable to be generated and all solution variables from the old distorted mesh are desirable to be transformed to the new one. As the reason of above, for interpolation, a new domain is made as in Fig. 5. The blades in figure 5 are all in the same position as in figure 4, but the domain is divided with different meshes compared with figure 4. The result is interpolated (or transferred) from the old mesh in figure 4 to the new mesh in figure 5. The old mesh in figure 4 is named as the first mesh pattern before interpolation. The new mesh in figure 5 is named the second mesh pattern for continuing. After the same time steps, blades move from the position in figure 5 to the position in figure 6. Figure 5 - Left: the second mesh pattern for continuing. Right: the blade position.

4 At last, the second mesh pattern in figure 6 constructs the same domain as the pattern in figure 3, but in a different mesh pattern. So, the above process can be repeated between figure 6 and figure times of interpolation are necessary for one rotation of fan. And the process is repeated again and again until the end time of calculation is arrived. Figure 6 - Left: the 2nd mesh pattern before interpolation. Right: the blade position The moving velocity of nodes on lines around every blade is defined to keep the good shape of the meshes during the calculation. There are all together 128 lines for all 32 blades. Rotating square cylinder model and boundary conditions For a rotating square cylinder, the 2D domain is shown in figure 7. The domain length in x direction is 20 m. The inlet breadth in y direction is 8 m. The center of rotating square is m away from the inlet and at the centerline of the domain in y direction. The radius of circle area is 2 m and the size of the square is 1.2 m. There are all 1771 nodes and 1669 elements for the whole domain. There are 576 nodes and 512 elements in areas between square and circle. The movement of nodes in the area between square and circle is considered in ALE calculation. There are 16 areas between square and circle. That let the 16 times interpolations be possible for one rotation of the square. Figure 7 - Domain of rotating square cylinder Inlet is at left side of the domain and is defined as 1.0 m/s. Outlet is at right side of the domain and is defined as zero pressure. The upper and lower boundaries are defined as no-slip wall. The fluid is uncompressible air and the density and viscosity are constant at 293 K. and one atmosphere pressure. So the Reynolds Number is and turbulent model of standard k-ε is used.

5 Four mesh patterns are necessary in this calculation as shown in figure 8. When the square rotates from the position of figure 8(1-1) to 8(1-2), e.g degrees, 200 time steps, the result of figure 8(1-2) is interpolated to the new mesh in figure 8(2-1) and the calculation then continues. These are repeated from pattern 2 to 3 and then from pattern 3 to 4. At last, when the square rotates 90 degree, the next necessary pattern becomes pattern one. With these four patterns, the calculation can go to the end time of the calculation. Time step size is s and there are 200 time steps between one interpolation such as that between figure 8(1-1) and 8(1-2). The four edges of square are defined as moving boundaries that are rotating at a rotational magnitude of 37.5 RPM. (1-1) (1-2) (2-1) (2-2) (3-1) (3-2) (4-1) (4-2) Figure 8 - (a) Left: (n-1) original shape of the nth mesh patterns. Right: (n-2) the shape of the nth mesh pattern after 10 time steps. (n=1,2,3,4). The moving velocity of some nodes is defined to keep the good shape of the meshes during the calculation. These nodes position radiation lines around the square of sections of blades. There are four radiation lines around every the square in Fig. 3. Analysis Results & Discussion The results of fan model The results of rotating fan are plotted in Fig. 9 and 10. The wall time of every picture is noted at the above-left corner respectively. As the rotating velocity is much slower than the inlet velocity, the rotation less affects the flow. No complex flow pattern in the area near the fan or after the fan blades can be observed. In another way, because the incompressible flow becomes steady state at once after the calculation, little change can be seen after 0.08 s too.

6 Figure 9 - Pressure variation of domain to time of 0.08 s intervals

7 Figure 10 - The velocity distribution of the domain at different time The results of rotating square cylinder The results of rotating square cylinder are shown in figure 11 and 12. In Fig.11, the velocity vectors at time 0.4 s, 0.5, 0.6, 0.7, , 1.0, 1.5, 2.0 and 2.5 s are plotted. The time is noted at the above-left corner of the every figure respectively. As the rotating velocity is faster than the inlet velocity, the rotation of square affects the flow strongly. A very complex flow pattern in the area near the square is observed.

8 Figure 11 - Velocity vectors of flow around the square cylinder at time 04 to 2.5 s.

9 Figure 12 - Stream functions of flow around the square cylinder at time 04 to 2.5 s.

10 The stream functions of flow are shown in figure 12. They are at the same time as velocity vectors shown in figure 11. When the time increases the affected area become bigger and bigger. The corner nodes of the rotating square have the biggest radius to the rotating center. The tangent velocity of the four nodes should be the biggest velocity in the four moving edges of the square. The value can be estimated using the rotating angle velocity and it is about m/s. But near the square, the maximum velocity about 10 m/s is observed and increases to passing time. This can be considered as 1) an accumulation of error of a coarse mesh, 2) or the affection of an unsuitable turbulent model, 3) or the accumulation of error of many times interpolation. Until 2.5 s, 25 times of interpolation have been executed. After investigation about interpolation, the movement energy may become smaller than before interpolation. In figure 13, the above is the result before interpolation and the bottom is the result after interpolation. After interpolation the maximum velocity always become smaller than before as at the time 0.9 s in figure 13. So, the third reason can be put out of here. The previous two reasons are planned to investigate in detail. Figure 13 - Comparison of velocity vector distributions before and after interpolation at 0.8s Although, the above two models are validated, very complex manipulation must prepared for every calculation. At first several pattern of mashes must be made. Second, the interpolation time is not very easy to determine. Third, the accumulated error can not be avoided and the CPU time is wasted during many times of interpolations. Especially for 3D calculations, the above listed problems will become more rigid. Even, they may be difficulties that could not be solved for many models. Quite the contrary, the Shear-Slip Mesh Update Method [3] can be used in ANSYS very easily. If the Deformable-Spatial-Domain/Stabilized Space Time (DSD/SST) formulation [3] can be introduced into ANSYS. ANSYS can become a strong tool for moving boundary condition calculations.

11 Conclusion Rotating movement calculation has been verified to show the development possibility using APDL basing on applications of ALE and interpolation of ANSYS5.7. The models of rotating square and 32 blade rotating fan validate the method. In this paper, the authors have only enough time to time to put the method in order. Further investigations are scheduled about the result verification of flow around one rotating cylinder and the calculation of flow around two counter-rotating square cylinders. Although both examples are 2D models, the method can be considered as a general useful method for 3D rotating calculation too. Surely the following several matters should be improved to let the method can be much easily to use. 1) The pre processor should be improved to make the mesh patterns easily that can be interpolated to each other. 2) The accuracy of interpolating should be improved for transient ALE application. 3) The post processor should be improved to show the continuous result such as rotating calculation. 4) Other method such as the shear-slip mesh update method and the Deformable-Spatial-Domain/Stabilized Space Time (DSD/SST) formulation (3) should be introduced into ANSYS. References 1) New Features 5.7 Training Manual, ANSYS.inc August 15, ) C.W. Hirt, A.A. Amsden, and H.K. Cook, An arbitrary Lagrangian Eulerian computing method for all flow speeds. J. Comput. Phys. 14(1974) ) M. Behr and T. Tezduyar, The Shear-Slip Mesh Update Method, Comput. Methods Appl. Mech. Engrg. 174(1999)