Previous Work Status
Initial Version of Missile-SIM for Performance evaluation
Aerodynamic Validation of Missile-SIM for Trajectory
AIM-120C Study using Missile-SIM : Part 1 - Sensitivity
AIM-120C Study using Missile-SIM : Part 2 - Launch Condition
AIM-120C Study using Missile-SIM : Part 2 - Launch Condition - revision
Patch note of Missile-SIM : Guidance Algorithm is added w/ Real-Time plot
My Missile-SIM is about to update part for variable ISP depending on the free-stream condition. It means air-breathing engine can be a new feature of the simulation.
Air-breathing engines for the missiles have three major categories
1. Turbo-jet or fan : Subsonic or low supersonic cruise missiles like AGM-86 or Stormshadow
2. Ramjet : Compressing air through shock and combustion in subsonic for Meteor or ASMP
3. Scram-jet : Compressing air w/ combustion in supersonic for X-51 or new developing missiles
Those options make Missile-SIM as universal tool for the missile-trajectory simulation, however getting ISP value from the parametric condition and achieving precise drag value with inlet are not easy task.
1. Getting ISP value from free-stream and parametric engine condition.
2. Getting precise drag value w/ inlet
This part explains W.I.P status of these two tasks.
1. ISP value for each type of the engine
1) ISP of Turbojet [1]
Thrust Mach1 1
ISP = -------------- * ------------ * ----------
(P*A*gam*M) g f/a
(f/a = fuel to air ratio
Mach1 = speed of M1)
2) ISP of Ramjet [1]
Term_A * Term_B
ISP = ----------------------------
Term_C * Term_D
Term_A = Mach1 * Hfc / (g*c_p*T)
Term_B = M * ((T4T0/(1+((gam-1)/2)*M^2))^(1/2) - 1)
Term_C = 1+((gam-1)/2)*M^2
Term_D = T4T0/Term_C - 1
(c_p = specific heat of air
T4T0 = ratio of T4 and T0 - combustion to free-stream
Hfc = fuel heat value)
T4T0 = 1 + ((gam-1)/2)*M^2 + Hfc*f/a/(c_p*temp)
3) ISP of Scramjet [2]
M*Mach1
ISP = -------------- * ((1+Term_A*Term_B)^(1/2) - 1)
g
Term_A = 2*(H3H0-1)/((gam-1)*M^2)
Term_B = Hfc/H3H0 - 1
(f/a = fuel to air ratio
H3H0 = Enthalpy ratio of compression)
2. CFD with inlet of engine
Design of inlet for the engine in supersonic is highly sophisticated work; I tested two-dimensional inlet before the three-dimensional inlet for the missile is configured. Few or more shock including external and internal compression ramps are used to slow down the free-stream for the combustion.
Estimation of the flow characteristics (pressure, temperature, Mach number etc) are given by the equations as shown below Fig. 1, while rough design including angle of ramps and position of lips can be determined by the equations. However, the fully matured design of the inlet should take account effect of flow separation, thickness of the boundary layer for several speed, mass-flow condition(throttle), and AoA conditions.
Fig. 1 Prediction equation and structure of shock for two-dimensional ramp (external and internal)
As the example model of the inlet, I tried to design very rough model of ramjet missile having three-ramp; the design is to estimate the drag of the meteor style air-to-air missile. (But, still, there is no kind of reference of that model, it is pure imagination)
CFD for this design and analysis is very rough because I have only limited resource to calculate the inlet. Then, only small number of grid is used for this calculation below. From low speed(M2) to high speed(M6), slow down of the ramp is not enough to make flow subsonic speed, then, the internal combustion mode of the jet become scramjet. The intended Mach number for this inlet is in between M3 and M4 like Meteor missile.
At M2 or 3, shock is located at the outside of the lip, while the end of the shock goes to exact lip of the inlet at M4. However, there are already separation around the corner of the ramp which means smooth shock inlet without flow separation is not easy as two dimensional theory. Indeed, flow structure after the separation is not intended as designer wanted to.
At M6, shock train structure follows start of the inlet which is usually observed in scramjet combustion. When the more resource is available for me, I want to do more serious design for the supersonic/hypersonic inlet. Next part will deal with the Meteor missile DB CFD result while other series for the hypersonic aerodynamics will be written.
Fig. 2 Two dimensional result - M2, AoA0 (from top to bottom; pressure, velocity)
Fig. 3 Two dimensional result - M2, AoA5 (from top to bottom; pressure, velocity)
Fig. 4 Two dimensional result - M3, AoA0 (from top to bottom; pressure, velocity)
Fig. 5 Two dimensional result - M3, AoA5 (from top to bottom; pressure, velocity)
Fig. 6 Two dimensional result - M4, AoA0 (from top to bottom; pressure, velocity)
Fig. 7 Two dimensional result - M4, AoA5 (from top to bottom; pressure, velocity)
Fig. 8 Two dimensional result - M6, AoA0 (from top to bottom; pressure, velocity)
Fig. 9 Two dimensional result - M6, AoA5 (from top to bottom; pressure, velocity)
[1] AIAA series, Tactical Missile Design, 2nd Edition
[2] Segal, C., The Scramjet Engine: Processes and Characteristics, Cambridge series
