Strap-On Boosters Separation Analysis using Coupled Simulation of Constraint Dynamics and Time-Dependent CFD

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Introduction
Strap-on boosters are used to increase the payload capabilities of launch vehicles. Adding Boosters to the vehicle core makes the design and manufacture of launcher more complex. One of the important issues in the design and construction of these launchers is the safe booster separation from the core vehicle. Any unexpected instability in this section or any catastrophic collision and in general, any factor that prevents successful separation, can tend the entire mission to fail. Since the booster separation usually takes place in the dense atmosphere, in 1. PhD Student addition to the dynamic effect of ejection mechanisms, aerodynamic flow around the launch vehicle is also important [1]. Many researchers have investigated this field for several years. Meakin and Suhs of NASA Ames analyzed the solid booster (SRB) separation of a space shuttle with a Navier-Stokes solver, using a prescribed trajectory for dynamic analysis of body motion [2]. Lochan and Adimurthy analyzed the separation dynamics of strap-on boosters. They used wind tunnel data for the measurement of aerodynamic forces [3,21,22]. Lijewski and Suhs developed an unsteady technique for store separation from a delta wing [4]. In addition, Taylor et al. for the Titan IV with two boosters and Azevedo and Moraes for the AVLS launch vehicle with four boosters carried out similar analysis using steady-state aerodynamics without considering the relative motion of boosters [5,6]. Kim et al. were among the first researchers that used numerical dynamic-aerodynamic coupling to simulate strap-on boosters' separation [8]. They also had studied the effects of flow turbulence in booster separation [9]. In both recent cases, in accordance with conventional methods, dynamic mesh method (in aerodynamics) and the integrated dynamic code were used briefly and simply without any complex separation mechanisms for solving separation problems. In fact, the simulation was based on the aerodynamic analysis with an integrated simple 6DOF dynamic code. In other cases, separation mechanisms have to be prescribed in the calculations [9, 10, and 11]. Commercial flow solvers have been of great interest in separation analysis. FLUENT and OVERFLOW can be considered as good paragon of these solvers that have been frequently mentioned in the literature [9,12,13]. Both of these solvers utilize a 6DOF rigid body motion code with simple and prescribed separation mechanism, integrated into the unsteady Navier-Stokes (Euler) solver using an automated grid adaption method.
In the early 2000s, separation process was considered as one of the key technologies to develop the next generation of orbiter with reusability [12]. For this purpose, such software, like ConSep and Sepsim using ADAMS (Automatic Dynamic Analysis of Mechanical Systems) solver aided by wind tunnel results have been developed [13, 14, and 15]. In such software, complex full separation mechanisms can be modeled; but large aerodynamic coefficient databases are needed for calculation of aerodynamic effects on booster separation. In 2006, Pamadi et al. had examined the shuttle booster separation using Concep software and wind tunnel results at NASA [12]. In addition, this work had been done by the CFE/POST2 software [16]. In this software, notwithstanding the powerful dynamic analysis, aerodynamic modeling is incomplete and for example, unsteady effects of flow and boosters velocity effects are missed in analysis. Moreover, the aerodynamic databases are multidimensional and too large [12,21,22], and therefore, not suitable for developing new vehicle design. Based on what has been stated, the previous studies just focused on one of the dynamic or aerodynamic analysis using a brief form of the other (analysis) for completing their results. So, the separation analysis of strap-on boosters in atmosphere with consideration of complicated mechanisms (such as constrained dynamics) and unsteady aerodynamic effects was not mentioned in the open literature. This paper (in continuation of previous article by the authors [1]) is focused on developing a dynamic/aerodynamic coupled solver to simulate the separation of strap-on boosters' using constraint dynamics and time-dependent CFD. Therefore, two commercial solvers, MSC Adams and Ansys/Fluent are integrated together with an innovative Matlab/Simulink interface to constitute a powerful package that presents real-time dynamic/ aerodynamic coupled analysis. Independency of dynamic and aerodynamic solvers allows modeling of any complex separation dynamic mechanisms, while the unsteady flow analysis is implemented. Consequently, this method can simulate several multi-physic problems such as booster separation with more accuracy than conventional methods. For example, modeling of realtime joint separation in the presence of unsteady aerodynamics is proven. Also, the interface was validated by simulating a transonic store separation event compared with experimental data by the authors [19,20].

Problem Description
The 6DOF dynamics of separation of strap-on boosters from the fixed core using spring ejector mechanism and spherical joints is simulated. External geometry of the launch vehicle with springs and joints positions can be seen in Fig.1.

Launch Vehicle Aerodynamics with Strapon Boosters
In order to calculate the aerodynamic forces and moments, a numerical solution of unsteady flow with an implicit upwind accurate 3D Euler solver is used. A dynamic unstructured tetrahedral mesh adoption approach using a combination of spring-based smoothing [4] and local remeshing [5] is automatically employed in respect of bodies' motion and determining the location of new nodes. In this analysis, the entire field is divided into a total of about 900000 tetrahedral cells. A view of gridded domain can be seen in Fig. 2. Separation is done at an altitude of 21 km with 4728.9 Kpa gage pressure at Mach 1.6, and the airflow around the launch vehicle is assumed as perfect gas. Pressure distribution in the flow field around the launch vehicle and strap-on boosters before the separation are shown in Fig. 3.

Flow solver validation
To validate the flow solver, wind tunnel data of the Titan IV has been used (Fig. 4,5). In this test, the free stream Mach number is 1.6, with zero angle of attack and 36000 meters of separation height. In Fig. 4, the calculated pressure contour for Titan VI cross-section shows that good agreement between the numerical solution and wind tunnel results can be observed in most regions. Slight differences in connecting points of the core vehicle and boosters are because of a connecting cable in the windtunnel test [1].

Mesh Independence
Pressure changes in the longitudinal direction of the main body of the launch vehicle (before separation) have been calculated for different mesh sizes. Three samples of these changes can be seen in Fig. 6. The calculated pressures are roughly similar in both normal and fine cases, so the normal mesh size of about 900000 cells has been selected.

Boosters Separation Dynamics
The boosters' separation dynamics is derived using the constraint force equation (CFE) methodology. This method provides a framework to compute the internal forces and moments acting on two bodies with specified degrees of freedom and applies them as external forces and moments to each body. Then, the motion of each body can be simulated independently like multiple free bodies. Thus, CFE methodology provides the missing link to model the stage separation [17]. The equations of motion for each rigid body can be expressed with six scalar equations obtained from Newton's second law: . .
where the i subscripts represent the i th vehicle, and the j subscripts represent the j th local joint connection on the rigid body i. Fi and Ti represent the resultant external forces and torques, excluding constraint loads, mi is the vehicle mass,  i x is the linear acceleration of the mass center, I is the inertia dynamic with respect to the mass center of the vehicle i, ωi is the absolute angular velocity, and i   is the time rate of change of angular velocity.

Separation Mechanisms Model Separation Springs
The equation used to calculate the spring force: That K= spring stiffness C= viscous damping ratio R= spring displacement L0= spring initial length Fmax= spring initial length The characteristics of spring ejector mechanism can be seen in Fig. 555 and table 2, according to them, all of the springs are linear translational (stroke of 0.167 meters). These ejectors are separated from the launch vehicle at Fs= 450 N. Spring force, as a function of displacement is shown in Fig. 9:  Fig. 8, aftward springs (with maximum force of 1800 N) start working at approximately 0.15 second later than forward ones and after disconnection of related joints. In this simulation, the gravity is assumed 9.80665 m/s2 along the axis of the launch vehicle toward its end (+ x).

Spherical Constraint Joints Modeling
In this simulation, spherical constraint joints have been used to connect the boosters on the launch vehicle. For all of constraints, ball and socket attachments have been assigned. One of these attachments is connected to the booster (ball) and the other is connected to the core vehicle. The translational motion of spherical constraints has been limited in three dimensions, wherein there is no interference with the rotational motion. If A is pointed to the joint on the core and B pointed to the same location on the booster, one can obtain: The angle condition has been used to disconnect the two aftward attachments. When the relative angle between booster and vehicle body reaches to 1deg, the joints disconnect.  Fig. 9, the joints separation sequence and the sample forward and aftward springs are shown. The constraint (number) 3 is similar to the constraint 1, and the constraint 4 is similar to the constraint 2. As could be seen in Fig. 9, two upper constraints have been disconnected at the start of simulation (t=0.001 sec). The disconnection of two lower constraints has occurred when the relative angle between them reached to 10 deg (as shown in the lower segment of Fig. 9). It is noticeable that in the present plan, all of the constraints and springs have the same cross-sectional areas, so the corresponding spring of any constraints is not contributed to the solution until the separation of the constraint occurs. This fact results that, the operation of springs at the lower section, begins at t=0.09 sec. The block diagram of this solution could briefly be seen in the following graph (Fig.9). According to this algorithm, the code calculating the dynamic of the motion reports the position of vehicle to the flow solver, so the solver could derive the aerodynamic forces and moments in each time step. Then, this code calculates the linear and angular velocities of

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Strap-On Boosters Separation Analysis using Coupled Simulation … the vehicle, using the results of forces and moments. Consequently, the mesh in the next step is corrected. In this algorithm, both the dynamic and the aerodynamic solvers are connected to the main interface as two independent external functions (Fig.9, Fig.10).

Results
The results are given for the first 1.1 seconds of the motion, with aerodynamic effects and without it. All the graphs are plotted for the left booster and the right booster while the core vehicle is fixed. Without aerodynamic effects, there is no displacement in the z-direction and the motion is in xy plane. Considering that joints are active for approximately 0.15 seconds and spring ejectors 0.3, so in the case of no aerodynamic, velocity in separation direction(y) remains constant after 0.3 seconds.

Parametric Study
This section examines the path diagrams and some of the parameters affecting them, such as aerodynamic effects of flow on booster separation and some parameters like boosters mass, strength of spring ejectors, booster separation angle (joints separation). For this purpose, the separation mechanism is determined for the sample launch vehicle that its size and geometry and also flow characteristics around it was explained in the previous section. Simulation inputs are as follows. We call this simulation as the standard mode and the effect of parameters variations will be analyzed regarding the standard mode.

Simulation Inputs (Standard Mode)
Mass properties of the launch vehicle and two strap-on boosters:  In this case, the spherical joints in the forward section cutoff at 0.0001 seconds after separation. Therefore, the boosters begin to rotate about aft joints until the boosters reach the angle of 1 degree (about zaxis) and then aft joints separate from the core vehicle.

Comparison of Boosters Separation, with Different Mass
Separation simulation for boosters with 650 kg mass (approximately 30% of previous case) is also studied. With booster mass reduction, moment of inertia and angular velocities also increases. Due to the interaction of boosters' angle and velocity with aerodynamic effects, aerodynamic forces also increase, that can double the separation velocity. This can be seen in Fig. 12.

Comparison of Boosters Separation, Using Spring Ejectors with Different Power
In addition to the standard case, which is referred to in tables 1 and 2, the simulation is also performed using spring ejector mechanisms with different power, and the results can be seen in Fig. 11, it means: Fs= α Fstandard2, α=0, 1, 1.5, 3 According to Fig. 13 that shows the location of the strap-on boosters at 1.1 seconds after separation, the desirable effect of the spring power increase can be seen. In this figure, the nearest booster to the core is resulted from the case without ejector spring. Other three modes: standard mode, 1.5 and 3 times greater than standard mode are also shown in Fig. 13. According to this figure, power of selected spring ejectors in standard mode (according to table 2) is appropriate and also the safe separation is achieved without increasing the power. Pressure contour variation around the launch vehicle and boosters during strap-on boosters' separation is shown in Fig. 15 for the four mentioned modes. Force variations for these four modes with respect to time are shown in Fig. 14.

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Strap-On Boosters Separation Analysis using Coupled Simulation … ΔVz) in presence of aerodynamic effects and for spring mechanisms with different powers can be seen. According to these figures, the desirable effect of ejector power increasing in improving separation performance is observed. This is also seen in other diagrams. In Fig. 18, which is related to the linear acceleration, the fracture points represent joints' disconnection and a complete booster separation from launch vehicle. Also, angular velocities, aerodynamic forces and moments of separated boosters can be seen in figures 19, 20, and 21.

Comparison of Boosters Separation with Different Separation Angles Conditions (aft Joints Disconnection in Different Angles)
In addition to various spring ejector mechanisms, simulation for different separation angles has also been done. In the standard mode (according to figures 22 to 27), spherical joints in the upper section are cut at 0.001 seconds after separation, and consequently, boosters begin to rotate around the aft joints until the boosters reach to 1-degree angle (about z-axis) and aft joints separation. Fig. 22 shows the location of the strap-on boosters at 1.1 seconds after separation with different separation angle conditions. In this figure, the nearest booster to the core refers to standard mode (separation angle is 1-degree) and other two modes refer to 3 degree and 5 degree. Pressure contour variation during strap-on boosters' separation is shown in Fig. 24. Separation angle conditions that are shown due to delay of the lower joints' disconnection (increasing separation angle), and so aerodynamic forces increase on boosters and separation is improved. This is clearly observed in boosters' center of mass velocity diagrams (velocities are increasing in y-direction) in Fig. 26. As it can be seen in Fig. 23, the spring ejector mechanism is the same for all three cases that are mentioned before. In figures 25, 26, and 27, variations of relative distances of boosters center of mass with time (ΔX, ΔY), relative velocities (ΔVx, ΔVy) and relative accelerations (ΔAx, ΔAy) in presence of aerodynamic effects with different separation angels can be seen.

Conclusion
In this study, 6DOF strap-on boosters' separation from the launch vehicle was presented. In addition to spring ejector mechanisms and constraint joints, aerodynamic forces and moments were considered using coupled constraint dynamics and numerical aerodynamics. As mentioned, the strap-on boosters' separation from launch vehicle has already been studied in the literature. However, in all of the previous works, just one of the dynamics' motion or flow aerodynamics was simulated precisely, and the other was modeled simple or prescribed. Separation simulation methods in dense atmosphere can be classified in four summarized groups as can be seen in table 3.  According to table 3, the methods 1, 2, and 3 has already been used for separation simulation in dense atmosphere. For example, the method 3 can be performed in such software like FLUENT [7, 8, and 9], that the dynamics of motion and mechanisms are coupled as a UDF (user defined function) to flow solver. However, in this method, there is no possibility to model the full separation mechanisms (like joints, etc.). In this paper, according to method 4 in table3, the first version of the software code with name of IRASEP for real-time simulation of coupled dynamics and aerodynamics of constrained strap-on boosters from launch vehicle was presented. The ability of this interface software in connection of multi-body dynamics solver and the numerical aerodynamic solver has provided a high potential in separation simulation in the dense atmosphere. In this simulation, two time-dependent solvers of unsteady dynamics and aerodynamics are completely independent of each other and just exchange the information through an interface software. Thus, more accurate modeling of dynamic mechanisms in the presence of unsteady aerodynamics than conventional methods is possible. The accuracy of this numerical simulation was proved by real-time simulation of joints' separation in the presence of unsteady aerodynamics as an example which was not provided in any of the references so far. Considering the presented diagrams and separation animations, importance of aerodynamics effects in strap-on booster separation simulation in the mentioned conditions is quite evident.