Study of supersonic flows is of high interest for a wide variety of problems including design of high speed planes and other related applications [1]. This user tip presents a validation of numerical methods against experimental data.

Geometry Definition

The blunted cone-cylinder-flare geometry is presented in Figure 1. This configuration, designated HB-2, has been widely used to evaluate aerodynamic test facilities and consequently, a large quantity of experimental data are available [2].

Figure 1.   Blunted cone-cylinder-flare (HB-2)

Numerical Model

The geometry is discretized using a structured mesh. A 2D axisymmetrical model is built in order to reduce the CPU time requirements. The model contains 13 structured zones. On the solid walls, a boundary layer mesh has been used. The first element size close to the wall is equal to 2.0e-6 m. The total number of the cells is around 36,400.

Figure 2.  2D axisymmetric model

Numerical Results

The initial and boundary conditions used for the HB-2 model are the following :

• adiabatic walls on the solid boundaries,
• symmetry on the axis of symmetry,
• extrapolated exit condition,
• inflow/outflow condition on other outermost surface bounding the domain.

where Re_D is the Reynolds number, M is the Mach number, V is the velocity, T is the temperature, p is the pressure, r is the density, d is the diameter, and R is the specific gas constant. 

The simulation is done using the structured solver of CFD-FASTRAN. The Roe’s upwinding differencing scheme with min mod limiter is used. Steady state solution is obtained using the Point Jacobi fully implicit scheme. For the spatial discretization, high order numerical scheme is used. In Figure 3 we present the Mach number. The detached bow shock in front of the obstacle is well captured.

Figure 3.  Mach number on HB-2 model

The ratio between the static pressure on the wall and the pressure from the stagnation point function of x/L is represented in Figure 4.

Figure 4.  Comparison: Experiment (red) / CFD-FASTRAN (black)

Regarding the drag coefficient for HB-2 model, reference [3] presents the forbody axial-force coefficient (C_A) and the base axial force coefficient (C_Ab). The total axial force coefficient (C_At) is defined as :

C_At = total axial force / q_inf A

The comparison between numerical prediction and experimental measurements is good.

Regards,
Daniel Vinteler
CFD Support Manager - France 

REFERENCES

1. CFD-FASTRAN, Demo/Validation Manual, version 2004
2. Birch, T.J., Prince, S.A., Ludlow, D.K., Qin, N., “The application of parabolized Navier-Stokes solver to some hypersonic flow problems”, AIAA 2001-1753
3. Don Gray, J., Earl Lindsay, E., “Force Tests of Standard Hypervelocity Ballistic Models HB-1 and HB-2 at Mach 1.5 to 10 ” , NTIS, AD412651