Chapter 3 Results and Discussions
3.3 Aerodynamics Simulation with Different Mach numbers and Angles of Attack 14
3.3.1 Results in Different Mach Numbers and Attack Angles
By the result of the grid convergence test, we choose the mesh file with 300,000 grids to
simulate the cases with two kinds of Mach numbers M =3.01
00
= α =
, . And each kind
of case contains five kinds of attack angles , , , , and
. We also compare the results with experimental data and discuss the results with
different Mach numbers and attack angles. We also explain the physical meaning of each
coefficient.
3.3.1.1 Flow Conditions and Simulation Conditions
The flow conditions are shown in Table.III. The flows with two kinds of Mach numbers
01 .
=3
M , are all supersonic flow. So we can compare the shock wave between
different Mach number. We also can compare the shock wave between different angles of
attack. The simulation conditions are shown in Table.IV. Because we have already done
the grid convergence test, the simulation conditions are the same as the case of grid
convergence test. The residual of case’s criteria is also equal.
10 .
=5 M
3.3.1.2 Density, Pressure and Mach Number Distributions
The density, pressure and Mach number distribution are shown in Fig.3.7. We compare
the cases that involve two kinds of attack angles and . Their remainder of
attack angle is the biggest. It makes us more convenient to observe the difference between
them. We first observe the location of shock wave. The location of shock wave of the case
at is just in the top of nose, and the location of shock wave of the case at
leave the top of nose slightly to the windward side of wall. In the case at , all
changes of flow near the wall are axial symmetry include temperature, density, and
velocity. In the case at , there are different change between the windward side of
wall and the leeward side of wall--there are higher temperature, higher density, and lower
velocity in the windward side of wall then the leeward side of wall for example.
00
3.3.1.3 Coefficients of Axial-Force
freestream far-field, is the area of cross section, is the diameter of cylinder. When
the flow conditions are fixed, is affected by . In the same geometry form and
flow conditions, higher means that the axial-force of rocket is higher and the rock
need higher thrust to fly. We can observe that the change of axial-force coefficient is very
small between different attack angles. It is because the cases with less attack angle have
less influence on axial-force. There is almost no change of axial-force coefficient. The
results of simulation doesn’t include base flow region. In order to do some comparison, we
set to correct the axial-force. The error of the correctional axial-force
coefficients is less than 10%. In fact, is lower than . The correct change line of
should be between the line at between two kinds cases of Mach numbers. Although the case at has higher
velocity than the case at , the case at
, and also makes the higher normal-force coefficient in the cases at . 01
.
=3
M M =3.01
3.3.1.4 Coefficients of Normal-Force
The results of axial-force coefficient are shown in Fig.3.9. Cn is affected by Fn.
The HB-2 model is axial symmetry. If the attack angle of HB-2 model is zero, the
normal-force on wall of HB-2 model is also zero. When the angle of attack is larger, the
normal-force on wall of HB-2 model is also larger if other conditions like pressure, density,
velocity of flow are the same. We can observe that when the attack angle is bigger, the
coefficient is also bigger. The error in the case at is less then 9%. The errors in
other cases are all less than 5%. We do the comparison between two kinds cases of Mach
numbers. Although the case at
20
in the cases at is always higher than the pressure of wall in the cases at
. It makes the higher normal-force in the cases at 10
3.3.1.5 Coefficients of Pitching-Moment
The results of pitching-moment coefficient are shown in Fig.3.10. The minus sign
means the counterclockwise direction. is affected by and is affected by
and . The influence of on Cm is larger than . When the angle of attack
is larger, the total force that on wall of HB-2 model is also larger. It makes
Cm Mp
Fa
Mp
Fa Fn Fn
Pitching-Moment that on the wall of HB-2 model larger. It is also that we can observe by
the figure. The error in the case of M =5.10 and is about 40%. The error in the
case of and is about 20%. The other errors in these cases are less than
8%. Perhaps the reason that makes the larger error is separation happened at the leeward
side of wall.
3.3.1.6 Normal-Force Curve Slope
The results of the normal-force curve slope are shown in Fig.3.11. Cnα is defined
as the slope of normal-force coefficient at . When the rocket flies actually, the
normal-force curve slope affects the sensitivity of control. Precise control makes the
trajectory that we want to achieve the mission of flying. in the case at lower Mach
number is larger. When the Mach number is higher and the Reynolds number is almost no
change, the density is lower. The influence of density on normal-force is larger than
velocity on normal-force. So in the case at higher Mach number is lower than
in the case at lower Mach number. The errors in these cases are less than 5%.
=0
3.3.1.7 Center of Pressure Location
The results of center of pressure location are shown in Fig.3.12. XCP is defined as,
XCP =Cm Cn
We revise become the value that we get by taking the top of nose of HB-2 model as
the original point. The center of pressure location determines the stability of the rocket’s
flying directly. If the center of pressure location is more close to nose of rocket than the
center of gravity, the rocket is unstable while it is flying. If the center of pressure location
is farther from nose of rocket than the center of gravity, the rocket is stable while it is
flying. We can observe that when the attack angle is bigger and the center of pressure
location is also bigger. The center of pressure of the case at XCP
01 .
=3
M is large than it of
the case at . It is because the two kinds cases of Mach number have almost the
same , but in the case at
3.3.1.8 Comparison of Non-Dimensional Pressure Distributions
The results of pressure distribution are shown in Fig.3.13. The pressure is higher in the
nearby nose, it is probably P P0 =0.8~0.9. After pass 0.1, the pressure will
P . It is because the flow region near the wall just breaks away the shock
region and the velocity is higher to supersonic once again. The pressure rises a little bit
after pass 0.6. It is because the diameter of cylinder of HB-2 model is becomes
large and the velocity that perpendicular to the wall is also become large. So the pressure L
X /
rises a little bit after pass 0.6. The pressure in the case at are higher than
the pressure in the case at and . It is because there is cross flow effect.
The 3-D pressure distribution are shown in Fig.3.14.We can observe the cross flow effect.
The most errors in these cases are about 5%. A part of errors in the case at L
and are higher than 30%. It is because there is separation point, and the
separation point affects the flow, therefore the deviation is higher.
1800
φ =