Test Case: NASA cylinders tandem

Coordinator: NTS.

Case description

Flow around a pair of cylinders in tandem shown in Fig.1 is considered.

Figure 1. Schematic of tandem cylinder flow

The two cylinders have identical diameters, D. Two cases with different separation distances between the cylinders axes, L, are investigated in experiments performed at NASA Langley Research Center [1-5]. The first case (large separation distance L=3.7D) is mandatory for ATAAC partners participating in this test case. The second case (small separation distance L=1.435D) is optional. In both cases the tandem arrangement is at nominally zero angle of attack so that the mean flow should be symmetric with respect to y=0 plane. However, in the experiments this is true only for the L/D=3.7 case, whereas for the L/D=1.435 case it turned out impossible to avoid some asymmetry. In the simulations, the asymmetry of the mean flow can be modeled via imposing a small (of the order of 1o) angle of attack [6].

The flow is at transitional Reynolds number Re=1.66 105 (based on free-stream velocity and cylinders diameter). However, in the experiments, in order to simulate the flow at high post-critical Reynolds numbers, the boundary layer at the front cylinder is tripped ahead of its separation. Due to this tripping the experimental surface pressure is very close to that from tests with Reynolds numbers above 4 million, which is an indication of a fully turbulent boundary layer separation. This justifies using the Fully Turbulent (FT) approach in the simulations.

It may be of interest for the test case participants that the mandatory case L/D=3.7 is planned on as a test case for a forthcoming “Workshop on airframe noise computations for benchmark configurations” organized by AIAA. Information about this workshop and particularly about the tandem cylinders test case is available on web sites:

Note, that the workshop organizers solicit for results of simulations that include both near-field aerodynamic data and predictions of noise radiated by the tandem arrangement. However but submissions with just the aerodynamic data are also be accepted.

Experimental parameters

Measurements of aerodynamic characteristics are performed in a closed section wind-tunnel. The cylinders in tandem are mounted vertically in the center of the tunnel.

Geometric parameters of the configuration and the flow characteristics are as follows.

  • Wind tunnel height H = 40 inch (1.016 m);
  • Wind tunnel width W = 28 inch (0.7112 m);
  • Cylinders diameter D= 2.25 inch (0.05715 m).
  • Separation distance between the cylinders axes:

L = 3.7 D (mandatory case);

L = 1.435 D (optional case);

  • Free-stream velocity =144 ft/s (44 m/s);
  • Mach number M∞ = 0.1285;
  • Reynolds number .

Available experimental data

These data include unsteady surface pressure measurements, detailed off-surface measurements of the flowfield using PIV technique, and hot-wire measurements in the wake of the rear cylinder. Refs. [4,5] present also acoustic measurements of radiated noise performed in an open-jet anechoic tunnel. Specifically, the following aerodynamic characteristics are presented in the available references:

  • Mean flow characteristics

Mean pressure coefficient on the surface of both cylinders as function of the angle measured clockwise from upstream stagnation point (see Fig.1).

Mean fields of velocity components, and , and spanwise vorticity, , in (x, y)-plane.

Mean streamlines in (x, y)-plane.

Profiles of mean velocity components and at several -values corresponding to the “gap” between the cylinders and to the wake of the rear cylinder.

Steamwise distribution of streamwise velocity in the mean flow symmetry plane between the cylinders and in the wake.

  • Instantaneous (x, y)-fields of spanwise vorticity corresponding to different stages of vortex-shedding process.
  • Off-surface turbulence characteristics

Fields of RMS of velocity components and 2D-TKE in (x, y)-plane.

Profiles of RMS of velocity components and at several -values corresponding to the “gap” between the cylinders and to the wake of the rear cylinder.

 Streamwise distribution in the mean flow symmetry plane between the cylinders and in the wake.

Streamwise velocity power spectra at point behind the rear cylinder ( is the -coordinate of the centroid of the rear cylinder).

  • Unsteady surface pressure characteristics for both cylinders

RMS of pressure coefficient RMSCp().

Power spectral density (PSD) of pressure at several values of angle .

Spanwise correlations of pressure at several values of angle .

Spanwise coherence of pressure at several values of angle (L/D=3.7 case) at frequency 178 Hz (primary shedding frequency).

Tar-archive with experimental data available as of September 4, 2009, can be downloaded from the following web site:

Recommended parameters for comparison with experiment

  • Time and span averaged pressure coefficient distributions for both cylinders.
  • Span averaged RMS of pressure coefficient distributions RMSCp() for both cylinders.
  • Time and span averaged fields in the x-y plane

velocity fields u(x, y), v(x, y).

RMS of velocity RMSu(x, y), RMSv(x, y).

2D-TKE (x, y).

Spanwise vorticity (x, y).

  • Profiles and streamwise distributions of time and span averaged parameters

Profiles of mean velocity components u(y), v(y) and 2D-TKE at (case L/D=3.7; “gap” between the cylinders) and at (both L/D=3.7 and L/D=1.435 cases; wake of the rear cylinder).

Streamwise distributions and at between the cylinders and in the wake.

  • Spectra

PSD of pressure (dB versus Hz) on the front cylinder at  = 135°.

PSD of pressure (dB versus Hz) on the rear cylinder at  = 45°.

PSD of streamwise velocity at point behind the rear cylinder.

The spectra should be computed for each individual z-section of the grid (or at least for several z-sections) and then sectional PSD should be averaged over z.

  • Correlations

Spanwise correlation of pressure versus on the front cylinder at  = 135°.

Spanwise correlation of pressure versus on the rear cylinder at  = 135°.

  • Instantaneous (x, y)-fields of spanwise vorticity corresponding to different stages of vortex-shedding process (for qualitative comparison with experiment).

Additional results requested to facilitate code-to-code comparison and evaluate statistical convergence of simulations

These results include (but are not limited to) the following data:

  • Primary shedding frequency based on the peak of PSD of surface pressure.
  • Time-history of running time-average of span-averaged drag and lift coefficient of both cylinders, and . Initial transient time-segment should not be accounted in the averaging process.
  • Final values of mean lift and drag of the cylinders.
  • Power spectral density of the unsteady lift and drag of the cylinders. The PSD spectra should be computed for each z-section of the cylinders and then the sectional PSD should be averaged over z.
  • Mean streamwise velocity and RMS of along obtained by averaging over two halves of the time-sample and over the whole time-sample (excluding the initial transient).

Recommended grids

NTS will provide sample structured multi-block (with face-to-face inter-block boundaries) grids in x-y-plane for both cases, L/D=3.7 and L/D=1.435, and values of corresponding grid steps in the spanwise direction . In these grids, it is assumed that side walls of the wind tunnel can be considered as slip ones, and so no grid clustering near these walls is performed.

Span-size of the experimental cylinder tandem is 12.4D. However, with available computational resources, such a large spanwise extent can be prohibitive. Based on experimental data on spanwise correlations of pressure, earlier simulations performed at NASA [6], and also experience gained in the course of DESider Project, minimum span-size of the computational domain Lz in the simulations of mandatory L/D=3.7 case should be 3D (with the use of periodic boundary condition in the spanwise direction). Therefore it is proposed to use as a standard span-size. Additional computations with larger are encouraged. Preliminary assessment of the minimum span-size for the optional L/D=1.435 case is .

Time interval of saving unsteady data for subsequent computations of spectra should allow resolution of frequencies up to 5 kHz. For the considered flow this means that it should be not larger than .

References

  1. Jenkins,L.N., Khorrami,M.R., Choudhari,M.M., and McGinley,C.B., “Characterization of Unsteady Flow Structures Around Tandem Cylinders for Component Interaction Studies in Airframe Noise,” AIAA-2005-2812, 2005.
  2. Jenkins,L.N., Neuhart,D.H., McGinley,C.B., Choudhari,M.M., and Khorrami,M.R., “Measurements of Unsteady Wake Interference Between Tandem Cylinders,” AIAA-2006-3202, 2006.
  3. Neuhart,D.H., Jenkins,L.N., Choudhari,M.M. and Khorrami,M.R., “Measurements of the Flowfield Interaction Between Tandem Cylinders,” AIAA-2009-3275, 2009.
  4. Lockard,D.P., Khorrami,M.R., Choudhari,M.M., Hutcheson,F.V., Brooks,T.F., and Stead,D.J., “Tandem Cylinder Noise Predictions,” AIAA-2007-3450, 2007.
  5. Lockard,D.P., Choudhari,M.M., Khorrami,M.R., Neuhart,D.H., Hutcheson,F.V., Brooks,T.F., and Stead,D.J., “Aeroacoustic Simulations of Tandem Cylinders with Subcritical Spacing,” AIAA-2008-2862, 2008.
  6. Khorrami, M.R., Lockard,D.P., Choudhari,M.M., Jenkins,L.N., Neuhart,D.H., and McGinley,C.B., “Simulation of Bluff Body Flow Interaction for Noise Source Modeling,” AIAA-2006-3203, 2006.