Validation
Validation of the LUMA solver, including its FSI capabilities has been performed for a number of cases and compared to available data in the literature. Available validation results are summarised below.
The flow past a circular cylinder at is simulated using LUMA v1.4.0. Drag and lift values over the cylinder are computed by LUMA with coefficients,
and
as well as the pressure coefficient over the cylinder surface calculated in post-processing. Results are compared to the set of experiments presented by Park and Kwon [1].
Consider a two dimensional cylinder of diameter located at the centre of a square (
) computational domain. Freestream velocity boundary conditions are used on all domain edges with a value set to
. The cylinder boundary uses the bounce-back boundary condition. The computational domain is shown in Figure 1.
INSERT FIGURES 1
The table below presents the primary setup configuration in non-dimensional units as used in the definitions file.
| Parameter | Value |
|---|---|
| L_DIMS | 2 |
| L_RESOLUTION | 8 |
| L_TIMESTEP | 0.0125 |
| L_BX | 50 |
| L_BY | 50 |
| L_RE | 2-160 |
| L_GEOMETRY_FILE | defined |
| L_INLET_ON | defined |
| L_FREESTREAM_TUNNEL | defined |
| L_NUM_LEVELS | 4 |
The validation of pressure coefficient around a cylinder is based on [1] who present pressure coefficient for . We also compare to the results of Dennis and Chang [2] for
and Norberg [3] at
. Surface pressure coefficient is calculated at cylinder surface between 0 and 180 degrees as
Figure 2a and 2b present the surface pressure coefficient computed with LUMA compared with Park [1]. Figure 2a considers
while Figure 2b shows
. At low
it is possible to see good qualitative results, but as soon as
increase quantitative results improve considerably obtaining identical values to the reference.
INSERT FIGURES 2a and 2b
The pressure coefficient at the base and stagnation
points. Results were compare with Park[1], Dennis [2], Williamson and Roshko [3], Norberg [4] and Henderson[5]. In all cases LUMA achieves excellent results as indicated in Figure 3.
INSERT FIGURE 3
Figure 4 shows a comparison of drag coefficient for and Strouhal number. In both cases, good agreement with the literature is obtained.
INSERT figure 4
Figure 5 compares the length of time average separation bubble. Again, the results from LUMA are in excellent agreement with the reference results.
INSERT FIGURE 5
[1] J. PARK, K. KWON, AND H. CHOI, Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160, KSME International Journal, 12 (1998), pp. 1200–1205. [2] S. C. R. DENNIS AND G.-Z. CHANG, Numerical solutions for steady flow past a circular Cylinder at Reynolds numbers up to 100, Journal of Fluid Mechanics, 42 (2006), p. 471. [3] WILLIAMSON AND ROSHKO, Vortex formation in the wake of an oscillating cylinder, Journal of Fluids and Structures, 2 (1988), pp. 355–381. [4] C. NORBERG, An experimental investigation of the flow around a circular cylinder: influence of aspect ratio, Journal of Fluid Mechanics, 258 (1994), pp. 287–316. [5] R. D. HENDERSON, Details of the drag curve near the onset of vortex shedding, Physics of Fluids, 7 (1995), pp. 2102–2104.
A similar investigation to the previous case can be conducted for an inclined flat plate in 2D. The problem presented by Tiara and Colonius [1] is simulated using LUMA v1.4.0.
We consider a computational domain with the same boundary conditions as the previous case. This time the freestream velocity is set to
. The flat plate is also treated as bounce back boundary condition and angles of incident of
. The computational domain is shown in Figure 1.
INSERT FIGURE 1
The table below presents the primary setup configuration in non-dimensional units as used in the definitions file.
| Parameter | Value |
|---|---|
| L_DIMS | 2 |
| L_RESOLUTION | 8 |
| L_TIMESTEP | 0.0625 |
| L_BX | 20 |
| L_BY | 20 |
| L_RE | 300 |
| L_GEOMETRY_FILE | defined |
| L_INLET_ON | defined |
| L_FREESTREAM_TUNNEL | defined |
| L_NUM_LEVELS | 4 |
Figure 2 presents the drag and lift coefficient for the flat plate at different angles of incidence and results are compared with [1] showing excellent agreement.
INSERT FIGURE 2
[1] TAIRA, K., & COLONIUS, T. (2009). Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers. Journal of Fluid Mechanics, 623, 187-207. doi:10.1017/S0022112008005314