Turbulent Flow Past Two-Body Configurations

Flows Around Bodies

Underlying Flow Regime 2-12

Test Case Study

Brief Description of the Study Test Case

A detailed description of the chosen test case (TC with L = 3.7D) is available at this link. So here we present only its brief overview.

A schematic of the airflow past the TC configuration is shown in Figure 1. The model is comprised of two cylinders of equal diameter aligned with the streamwise flow direction. The polar angle, ${\theta }$ , is measured from the upstream stagnation point and is positive in the clockwise direction.

Figure 1: Schematic of TC configuration [3]

Geometric and regime parameters defining the test case are summarized in Table 1.

**Table 1:** Flow parameters
Parameter	Notation	Value
Reynolds number	Re= $U_{0}D/\nu$	1.66×10⁵
Mach number	M	0.128
Separation distance	$L/D$	3.7
TC aspect ratio	$L_{z}/D$	12.4
Cylinder diameter	$D$	0.05715 m
Free stream velocity	$U_{0}$	44 m/s
Free stream turbulence intensity	$K$	0.1%

The principal measured quantities by which the success or failure of CFD calculations are to be judged are as follows:

Mean Flow
- Distributions of time-averaged pressure coefficient, $C_{p}\leq (p-p_{0})\geq (1/2\rho _{0}U_{0}^{2})$ , over the surface of both cylinders;
- Distribution of time-averaged mean streamwise velocity ${\left.\langle u\rangle /U_{0}\right.}$ along a line connecting the centres of the cylinders;
Unsteady Characteristics
- Distributions of the root-mean-square (rms) of the pressure coefficient over the surface of both cylinders;
- Power spectral density of the pressure coefficient (dB/Hz versus Hz) on the upstream cylinder at $\theta$ = 135°;
- Power spectral density of the pressure coefficient (dB/Hz versus Hz) on the downstream cylinder at $\theta$ = 45°;
Turbulence kinetic energy
- x – y cut of the field of time-averaged two-dimensional turbulent kinetic energy ${\text{TKE}}={\frac {1}{2}}\left(\langle u'u'\rangle +\langle \nu '\nu '\rangle \right)/U_{0}^{2}$ ;
- 2D TKE distribution along* y = 0;
- 2D TKE distribution along* x = 1.5 D (in the gap between the cylinders);
- 2D TKE distribution along* x = 4.45 D (0.75 D downstream of the centre of the rear cylinder).

All these and some other data are available on the web site of the BANC-I Workshop.

Test Case Experiments

A detailed description of the experimental facility and measurement techniques is given in the original publications [2-4] and available on web site of the BANC-I Workshop. So here we present only concise information about these aspects of the test case.

CFD Methods

Provide an overview of the methods used to analyze the test case. This should describe the codes employed together with the turbulence/physical models examined; the models need not be described in detail if good references are available but the treatment used at the walls should explained. Comment on how well the boundary conditions used replicate the conditions in the test rig, e.g. inflow conditions based on measured data at the rig measurement station or reconstructed based on well-defined estimates and assumptions.

Discuss the quality and accuracy of the CFD calculations. As before, it is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However the following points should be addressed: