UFR 2-12 Test Case

Turbulent Flow Past Two-Body Configurations

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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 the web site of the BANC-I Workshop. So here we present only concise information about these aspects of the test case.

Figure 2: TC configuration in the BART facility [3]

Experiments have been conducted in the Basic Aerodynamic Research Tunnel (BART) at NASA Langley Research Center (see Figure 2). This is a subsonic, atmospheric wind-tunnel for investigation of the fundamental characteristics of complex flow-fields. The tunnel has a closed test section with a height of 0.711 m, a width of 1.016 m, and a length of 3.048 m. The span size of the cylinders was equal to the entire BART tunnel height, thus resulting in the aspect ratio L_z/D = 12.4. The free stream velocity was set to 44 m/s giving a Reynolds number based on cylinder diameter equal to 1.66 &times 10⁵ and Mach number equal to 0.128 (flow temperature T = 292 K).

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:

• What numerical procedures were used (discretisation scheme and solver)?

• What grid resolution was used? Were grid sensitivity studies carried out?

• Did any of the analyses check or demonstrate numerical accuracy?

• Were sensitivity tests carried out to explore the effect of uncertainties in boundary conditions?

• If separate calculations of the assessment parameters using the same physical model have been performed and reported, do they agree with one another?

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Contributed by: A. Garbaruk, M. Shur and M. Strelets — New Technologies and Services LLC (NTS) and St.-Petersburg State Polytechnic University

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