Supersonic Flow over a Segmental Conic Body

Now let us consider an external supersonic flow of air over a segmental conic body. The general case is that the body is tilted at an angle of α with respect to the incoming flow direction.

The dimensions of the body whose longitudinal (in direction t, see Figure 1) and lateral (in direction n) aerodynamic drag coefficients, as well as longitudinal (with respect to Z axis) torque coefficient, were investigated in Ref. 1 are presented in Figure 2. They were determined from the dimensionless body sizes and the Reynolds number stated in Ref. 1.

Figure 1. Supersonic flow over a segmental conic body.

Figure 2. Model sketch dimensioned in centimeters.

The model of this body is shown in Figure 3.

Figure 3. The geometry model for calculating the 3D flow over the 3D segmental conic body with Flow Simulation.

To compare the Flow Simulation predictions with the experimental data of Ref. 1, the calculations have been performed for the case of incoming flow velocity of Mach number 1.7. The undisturbed turbulent incoming flow has a static pressure of 1 atm, static temperature of 660.2 K, and turbulence intensity of 1%. The flow Reynolds number of 1.7·106 (defined with respect to the body frontal diameter) corresponds to these conditions, satisfying the Ref. 1 experimental conditions.

To compare the flow prediction with the experimental data of Ref. 1, the calculations have been performed for the body tilted at α = 0°, 30°, 60°, 90°, 120°, 150° and 180° angles. To reduce the computational resources, the Z = 0 flow symmetry plane has been specified in all of the calculations. Additionally, the Y = 0 flow symmetry plane has been specified at α = 0° and 180°.

The calculations have been performed at result resolution level 6.

The comparison is performed on the following parameters:

  • longitudinal aerodynamic drag coefficient,



    where Ft is the aerodynamic drag force acting on the body in the t direction (see Figure 1), ρU2/2 is the incoming stream dynamic head, S is the body frontal cross section (being perpendicular to the body axis) area;

  • lateral aerodynamic drag coefficient,



    where Fn is the aerodynamic drag force acting on the body in the n direction (see Figure 1), ρU2/2 is the incoming stream dynamic head, S is the body frontal cross section (being perpendicular to the body axis) area;

  • on the longitudinal (with respect to Z axis) aerodynamic torque coefficient,



    where Mz is the aerodynamic torque acting on the body with respect to the Z axis (see Figure 1), ρU2/2 is the incoming stream dynamic head, S is the body frontal cross section (being perpendicular to the body axis) area, L is the reference length.

The calculation results compared with the experimental data from Ref. 1 are presented in Figure 4 and Figure 5.

Figure 4. The longitudinal and lateral aerodynamic drag coefficients predicted with Flow Simulation and measured in the experiments versus the body tilting angle.

From Figure 4, it is seen that the Flow Simulation predictions of both Cn and Ct are excellent.

As for the longitudinal aerodynamic torque coefficient (mz) prediction, it is also close to the experimental data of Ref. 1, especially if we take into account the measurements error.

Figure 5. The longitudinal aerodynamic torque coefficient predicted with Flow Simulation and measured in the experiments versus the body tilting angle.

To illustrate the quantitative predictions with the corresponding flow patterns, the Mach number contours are presented in Figure 6, Figure 7, and Figure 8. All of the flow patterns presented on the figures include both supersonic and subsonic flow regions. The bow shock consists of normal and oblique shock parts with the subsonic region downstream of the normal shock. In the head subsonic region the flow gradually accelerates up to a supersonic velocity and then further accelerates in the expansion fan of rarefaction waves. The subsonic wake region past the body can also be seen.

Figure 6. Mach number contours at α = 0°.

Figure 7. Mach number contours at α = 60°.

Figure 8. Mach number contours at α = 90°.

As the forward part becomes sharper, the normal part of the bow shock and the corresponding subsonic region downstream of it become smaller. In the presented pictures, the smallest nose shock (especially its subsonic region) is observed at α = 60°.