Turbulent Flow Past Two-Body Configurations

Flows Around Bodies

Underlying Flow Regime 2-12

Evaluation

Comparison of CFD Calculations with Experiments

This section is organized as follows. First (Section 6.1), results of some sensitivity studies are presented and briefly discussed. These include evaluation of such effects as span-size of the domain, compressibility, time sample used for computing the mean flow and turbulent statistics, and numerical dissipation of the method used. Then, in Section 6.2, a comparison with the experimental data is shown for the main body of simulations carried out within the ATAAC project with the use of the physical and computational problem setups outlined in Section 5.

RESULTS OF SENSITIVITY STUDIES

Effect of span size of domain

As mentioned in Section 4, the aspect ratio of the CT configuration L_z/ D in the BART facility is equal to 12.4. Strictly speaking this demands carrying out simulations exactly at this value of L_z/ D and imposing no-slip boundary conditions on the floor and ceiling of the test section (see Figure 2). However such simulations would be very expensive. Considering this and, also, recommendations of the BANC-I Workshop based on simulations at different L_z/ D with periodic boundary conditions in the spanwise directions, most of the simulations in the ATAAC project were performed at L_z/ D = 3 assuming spanwise periodicity. In order to get an idea on how strong the effect of such a simplification could be, NTS conducted a series of simulations at different L_z/ D. Some results of these simulations are presented below ^[1]

Figure 4 compares flow visualisations from the SA DDES carried out in the "mandatory" (L_z/ D = 3) and the widest of the considered domains (L_z/ D = 16) in the form of instantaneous isosurface of the magnitude of the second eigenvalue of the velocity gradient tensor or "swirl" quantity, λ₂. The figure is reassuring in the sense that it visibly displays that the narrow-domain simulation resolves not only fine-grained turbulent eddies but also large, nearly coherent, structures and exhibits all the complex flow features observed in the visualization of the wide-domain simulation, except for the initial region of the free shear-layer separated from the upstream cylinder, where a noticeable difference between the two flow-visualizations is observed.


Figure 4: Isosurface of λ₂ = 4.0(U₀ /D ) from incompressible SA DDES at L_z = 3D and 16D.

As a result, sensitivity of predictions of the major characteristics of the flow in the wake of the downstream cylinder to the value of L_z/D turns out to be marginal (see Figure 5 and Table 4). At the same time, as seen in Figure 6, the flow features directly related to the details of the flow past the upstream cylinder (its boundary layers separation and shear-layers roll-up) vary with L_z/D variation rather significantly. Other than that, Figures 5, 6 suggest that the effect of L_z/D within different turbulence modelling approaches is different and is stronger pronounced for IDDES than for DDES. These findings should be kept in mind when analyzing agreement with the experiment of the simulations carried out at L_z/D = 3 with the use of different approaches to turbulence representation presented in the next section.


Figure5: Effect of L_z/D on centreline distributions of mean velocity and 2D kinetic energy in the wake of the downstream cylinder (left and middle frames respectively) and on rms of pressure coefficient on the downstream cylinder (right) from incompressible SA DDES and SA IDDES of NTS.

**Table 4:** Effect of modelling approach and span-size of computational domain on the global shedding frequency.
	Shedding frequency, Hz
DDES, L_z = 3D	188
DDES, L_z = 16D	188
IIDDES, L_z = 3D	192
IIDDES, L_z = 16D	192


Figure6: Effect of L_z/D on centreline distributions of mean velocity and 2D kinetic energy in the gap between cylinders (left and middle frames respectively) and on rms of pressure coefficient on the upstream cylinder (right) from incompressible SA DDES and IDDES of NTS.

↑ The simulations at L_z/ D = 16 were conducted with the use of resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357.

Compressibility effects

Considering that TUB simulations were carried out under assumption of incompressible flow and BTU and DLR performed compressible simulation at the experimental value of the Mach number (M = 0.128), it was important to find out how strongly this could affect the obtained results. In order to gain this knowledge NTS has carried out IDDES simulations both in the framework of incompressible and compressible problem statements. Results of these two simulations for the quantities which were found to be most sensitive to L_z/D (see Figure 6) are shown in Figure 7. They suggest that the role of the effects of compressibility in the considered flow is negligible.


Figure7: Comparison of results of SA IDDES at L_z/D = 3 carried out in incompressible and compressible (M = 0.128) modes. Left and middle frames: centreline distributions of mean velocity and 2D kinetic energy in the gap between cylinders; right frame: rms of pressure coefficient on the upstream cylinder.

Effect of time sample

This effect has been shown to be very strong for nominally 2D bodies with massive separation in many previous DES and LES studies. This is not surprising, since such flows typically have large scale coherent vortices in a vortex street pattern overlaid with finer random turbulent fluctuations at higher frequencies and random modulation and intermittency at frequencies lower than the vortex shedding one. This is true for the TC flow as well (see Figure 4), which dictates a need of rather long time samples for getting statistically representative mean flow characteristics and especially turbulence statistics. In order to exclude or at least minimize the effect of insufficient time sample when comparing results of different simulations, NTS has carried out a time-sample sensitivity study of the SA DDES of the TC flow. Its outcome is presented in Figure 8 and in Table 5. One can see that the time sample of about 150 convective time units (D / U₀) is sufficient to obtain a reliable statistics not only for the mean drag but also for rms of the pressure coefficient. Exactly this value was recommended as a minimum one within the ATAAC project.


Figure8: Effect of time sample on running time average of the drag coefficient (left frame) and rms of pressure coefficient on the surface of upstream (middle frame) and downstream (right frame) cylinders of tandem at L_z/D = 3 from incompressible SA IDDES

**Table 5:** Effect of time sample on time average of integral of TC configuration
Time, Convective time units (D/U₀)	C_D upstream cylinder	C_D downstream cylinder
100	0.501	0.410
200	0.510	0.403
300	0.505	0.404

Effect of numerical dissipation

In order to evaluate this effect, NTS has carried compressible SA IDDES of the flow at L_z = 3D on the mandatory grid with the use of different approximations of the inviscid fluxes, F_inv, available in the NTS code. All these approximations are based on the weighted upwind-biased (F_upw ) and central (F_ctr ) schemes