EFFECT OF MESH SIZE ON CFD ANALYSIS OF EROSION IN ELBOW GEOMETRY Preshit Tambey and Michael Lengyel, Jr. Faculty Co-Author and Sponsor: Quamrul H. Mazumder Department of Computer Science, Engineering and Physics, University of Michigan-Flint Abstract Erosion due to solid particle laden flow is a major problem in piping, valves, pumps, pneumatic conveyors and other similar equipment. With changing direction of the particulate flow in geometry such as an elbow, smaller solid particles impinge on the wall resulting material loss from the surface. Computational Fluid Dynamic (CFD) analysis of erosive wear behavior can provide information about the magnitude and location of maximum damage in the wall of the fluid handling components. Factors such as mesh size used in the computational analysis can affect the CFD results due to differences in the number of elements and nodes. The effect of mesh size and density on erosion in a 1.27 mm diameter elbow was evaluated using commercially available CFD code FLUENT. Air with sand particles of 50-350 microns was used in the analysis. The results showed that the increased mesh density with a larger number of elements affects the magnitude of erosion in a component. Introduction Most CFD codes and commercial packages utilize unstructured mesh to map its complex domains because unstructured mesh systems don t require transformation of physical domains into computational ones. The unstructured meshes are formed by connecting arbitrary distributed points which are also called vertices. These results in the formation of polygonal elements called cells. Four different 90 degree elbows were created with different mesh and 4300, 12826, 18492, 25926 nodes. Longest and Vinchurkar defined the term structured mesh as having continuous grid lines on all faces, which require the domain to be subdivided into structured blocks [1]. Unstructured meshes are defined as having at least one face on which the grid lines do not remain continuous. The mesh styles considered include a block structured hexahedral mesh, an unstructured tetrahedral mesh, a tetrahedral mesh that is adapted to the steady flow field to better
resolve regions of significant velocity gradients and a hybrid mesh consisting of internal tetrahedral elements surrounded by a layer of higher order five-sided pyramid elements. CFD analysis was performed using commercial code FLUENT to determine erosion with air and sand particles of 50-350 microns diameter with velocities 15.24 m/s, 30.48 m/s and 45.72 m/s respectively. Kabir [2] defined erosion as erosion is the process of metal removed by the impact of a solid particle. In the selection of the most appropriate mesh style for specific tasks depends on the available time for grid construction and the accuracy required for the results. This is governed by the number of cells in the grid, which has the larger the number of cells, and finally which yields better solution accuracy. Background There has been numerous experimental and numerical researches on prediction of erosion in elbows. The most accepted approach is a three-step approach; the prediction of erosion from the data gathered, calculations of particle motion, and prediction of the flow field. In 1975, two approaches were used to predict two-phase flows, the Eulerian and Lagarangian approach. The Lagrangian approach treats the fluid phase as a continuum and predicts the trajectory of a single particle in the fluid flow as a result of various forces acting on the particle. The Eulerian approach treats the solid as some kind of continuum and appropriate continuum equations for the fluid and particle phases are solved. In the Lagrangian approach, the particle impact velocities and angles could be determined at solid surfaces [3]. Recently, Longest and Vinchurkar considered the effects of different common mesh styles on grid convergence, velocity fields and particle deposition profiles in a bifurcating respiratory model. The meshes considered included a structured multiblock hexahedral style, an unstructured tetrahedral mesh, a flow-adaptive tetrahedral design, and a hybrid style consisting of tetrahedral and prism elements. Erosion modeling made it possible to extract a greater wealth of information from erosion testing techniques than would be given otherwise. Clark [4] considered a range of factors involved in slurry erosion in the light of various studies where the fluid flow field and particle trajectories were calculated. The conclusion drawn was that actual particle impact properties (velocity, angle, quantity etc) across a surface could vary widely from the mean free stream properties generally reported in experimental studies. Quantitative analysis of results could only
be made if particle trajectories were known. Hamad and Takaboff [5] mentioned that turbo machinery erosion is affected by many factors such as the ingested particle characteristics, gas, flow path, blade geometry, operating conditions, and blade materials. Experimental and numerical studies were conducted to determine the pattern and intensity of compressor and turbine-blade erosion. They also determine that blade chord reduction and material removal from the pressure surface increased with particle size. The prediction of erosion requires that individual particle speeds and trajectories be known. For this, a Lagrangian formulation of the particle equation of motion is necessary. In order to neglect particle-particle interactions in such a formulation, the particle volume fraction of a solid-gas suspension must be less than approximately 0.001 as reported by Schuh [6]. Habib observed and reported that the rate of erosion depends exponentially on the velocity [7]. Computational Fluid Dynamics (CFD) Analysis The CFD Code FLUENT [8] was utilized to analyze the effect of different mesh sizes on erosion in a 90 deg elbow. The elbow geometry with four different mesh densities was analyzed at 3 different velocities with 7 different particle sizes accounting for a total of 84 cases. The turbulence used was k-epsilon and the default values were retained and the discrete phase model (DPM) allowed interaction with continuous phase. The injection type was set to surface with z-velocity defined as -15.24, -30.48, and -45.72 depending on the velocity being tested, the diameter varied also depending on the size being tested these values were 50e-06, 100e-06, 150e- 06, 200e-06, 250e-06, 300e-06, and 350e-06, the mass flow rate remained constant at 1 kg per sec. The turbulent dispersion discrete random walk model was used with inert-particle was set to sand at a density of 1500. Erosion model was defined as a piecewise-linear function at 5 points; point 1 angle 0 value 0, point 2 angle 20 value.8, point 3 angle 30 value 1, point 4 angle 45 value.5, point 5 angle 90 value.4. The velocity exponent function is also defined at a constant at 2.6. The solution was initialized and computed from all-zones with the turbulent dissipation rate changed to 1e+5. It was then iterated and converged at n iterations. CFD Results
CFD analysis results for different particle sizes at different velocities with 5394, 12826, 18492 and 25926 nodes are presented in this section to evaluate the optimum node size. As the number of nodes increased, erosion results were compared to see if significant changes are occurring in the results. For certain node values, further mesh refinement does not provide significantly different output. The node value at which CFD results becomes consistent is assumed to be the optimum node value or optimum mesh. 1.4E 02 1.3E 02 50 micron 100 micron 150 micron 200 micron 250 micron 300 micron 350 micron Erosion (Kg/m^2 sec) 1.2E 02 1.1E 02 1.0E 02 9.0E 03 8.0E 03 5394 12826 18492 25926 No of nodes Figure 1: Comparison of Erosion Results at 15.24 m/sec Velocity Figure 1 shows the CFD output at 15.24 m/sec. It can be observed that, erosion values increased significantly from 5394 to 12826 nodes with no significant change with higher nodes or further mesh refinement.. It must be noted that higher number of nodes requires more time for convergence and more computational resources that should be avoided if there is no advantage with such refinement.
8.00E 02 Erosion (Kg/m^2 sec) 7.50E 02 7.00E 02 6.50E 02 6.00E 02 5.50E 02 5.00E 02 50 Micron 100 Micron 150 Micron 200 Micron 250 Micron 300 Micron 350 Micron 5394 12826 18492 25926 No of Nodes Figure 2: Comparison of CFD erosion results at 30.48 m/sec 2.4E 01 2.3E 01 Erosion (Kg/m^2 sec) 2.2E 01 2.1E 01 2.0E 01 1.9E 01 1.8E 01 1.7E 01 1.6E 01 50 micron 100 micron 150 micron 200 micron 250 micron 300 micron 350 micron 5394 12826 18492 25926 No of Nodes Figure 3: Comparison of Erosion results at 45.72 m/sec.
Figure 2 and 3 shows the CFD outputs at 30.48 and 45.72 m/sec. similar observations of increased erosion values were observed between 5394 and 12826 nodes with no significant change with higher nodes or further mesh refinement.. Consistent CFD results were observed for all thirty different CFD analysis performed during this study for different particle sizes and different velocities.. Summary and Conclusion In conclusion, a study of mesh size and mesh density was conducted to determine the optimum mesh for accurate CFD results. It is important to perform CFD analysis with appropriate number of node and mesh size for accurate results. Mesh sizes and the number of nodes appears to have an affect on computational results. Mesh refinement should be continued until consistent CFD results were obtained. Consistent CFD out put were obtained for mesh with 12826 nodes and higher, the optimum number of node for this analysis is approximately 12826. Further refinement of mesh with higher node value did not provide results different than 12826 nodes. Acknowledgement We would like to thank the Office of Research, at the University of Michigan- Flint for financial support through the Undergraduate Research Opportunity Program (UROP). Thanks also to Mechanical Engineering Program for providing funding for the FLUENT software. References [1] P.Worth Longest, Samir Vinchurkar, Effects of mesh style and grid convergence on particle deposition inbifurcating airway models with comparisons to experimental data.(2006) 353 [2] Muhammad Ehsanul Kabir, Numerical Investigation of Erosion of a Pipe Protruded in a Sudden Contraction, (2005) 29-31 [3] Samir Vinchurkar a, P. Worth Longest Evaluation of hexahedral, prismatic and hybrid mesh styles for simulating respiratory aerosol dynamics [4] H.McI. Clark, The influence of the flow field in slurry erosion, Wear152 (1992) 233 240.
[5] A. Hamed and W. Tabakoff, Erosion and Deposition in Turbomachinery, (2006) [6] M.J. Schuh, C.A. Schuler, J.A.C. Humphrey, Numerical calculation of particle-laden gas flows past tubes, AIChE J. 35 (3) (1989) 466 480 [7] Solid-particle erosion in the tube end of the tube sheet of a shell-and-tube heat exchanger M. A. Habib, H. M. Badr, S. A. M. Said, R. Ben-Mansourand S. S. Al-Anizi [8] FLUENT User Manual, FLUENT Inc, Lebanon, New Hampshire 03766, U.S.A