BALLISTIC PHASE PERFORMANCE MODEL FOR COLD GAS ATTITUDE CONTROL IN CRYOGENIC UPPER STAGES

During the ballistic phase of a cryogenic upper stage, attitude and orbit control are usually performed by a cold gas thruster system. Since the thruster inlet pressure is driven by the propellant tank ullage conditions, a su©cient pressure regeneration rate has to be assured to compensate the pressure decrease during thruster activation. The coupling between the thruster activation sequence, stage kinematics, and thermal environment is essential for the performance prediction of cold gas systems. An iteration loop using a statistical model considering the thruster activation sequence is applied. For detailed ¦nal analysis, an EcosimPro model is used, including three-dimensional (3D) CFD (computational §uid dynamics) sloshing analysis and all relevant boundary conditions.

During the ballistic phase of a cryogenic upper stage, attitude and orbit control are usually performed by a cold gas thruster system. Since the thruster inlet pressure is driven by the propellant tank ullage conditions, a su©cient pressure regeneration rate has to be assured to compensate the pressure decrease during thruster activation. The coupling between the thruster activation sequence, stage kinematics, and thermal environment is essential for the performance prediction of cold gas systems. An iteration loop using a statistical model considering the thruster activation sequence is applied. For detailed ¦nal analysis, an EcosimPro model is used, including three-dimensional (3D) CFD (computational §uid dynamics) sloshing analysis and all relevant boundary conditions. NOMENCLATURE c pl Speci¦c heat of liquid, J/(kg·K) C sf Surface factor C

INTRODUCTION
During lifto¨the Ariane 5 launcher is propelled by two solid boosters and the main cryogenic stage. In the course of the ascent phase, the solid boosters and, subsequently, the main stage are separated (Fig. 1). Being the last stage, ESC-A (Etage Sup‚ erieur Cryotechnique Type A) completes the mission by performing a last boost and ejecting the satellites in their speci¦c orbit after engine shutdown (H3).

Figure 1 Ariane 5 mission sequence (illustration by Arianespace)
The ESC-A has a diameter of 5.4 m and consists of two propellant tanks for liquid hydrogen (LH 2 ) and liquid oxygen (LOx) with a volume of 39.4 m 3 and 11.4 m 3 , respectively. A cold gas system is used to provide linear acceleration as well as attitude and roll control during the ballistic phase (also called SCAR (Système de Contr ole d£Attitude et Roulis) phase).
The system splits into hydrogen and oxygen side, which both consist of piping connecting the cryogenic propellant tanks and thruster assemblies. During the ballistic phase, both tanks contain liquid and gaseous residuals. After the engine shutdown, the liquid phases are a volumetrically small part, most of the volume is ¦lled with gas.
Attitude and roll control is provided by the GH 2 SCAR system, which consists of four blocks with three nozzles each. Linear acceleration, as needed for distancing and positioning maneuvers, is provided by the oxygen purge and balancing nozzles. The blowout of gaseous oxygen parallel to the stage x-axis is controlled by the S34 valve. Due to di¨erent lever arms relative to the stage center of gravity (CoG), the oxygen thrusters are not identical in terms of geometry.
To ensure the su©cient performance of the cold gas thrusters according to the mission pro¦le, the pressure evolution in the propellant tank ullage has to be predicted. This paper describes the iteration loop of thruster activation sequence and provided thrust applying a simpli¦ed statistical MATLAB model. Furthermore, the setup of a one-dimensional (1D) EcosimPro system model comprising 3D sloshing e¨ects is described based on the preceding fundamental research [1,2]. In the perimeter of this paper, only the LH 2 circuit is presented.

ARIANE 5 CRYOGENIC UPPER STAGE SYSTEM OVERVIEW
To facilitate the understanding of the overall problems connected to the ballistic phase performance prediction, this section gives an overview of the general technical concepts used in the Ariane 5 cryogenic upper stage functional propulsion system (FPS). The FPS can be divided into the independent LOx and LH 2 circuits with their respective helium pressurization systems, propellant tanks, §uid control equipment, and ACS (attitude control system) components.
The primary component of the hydrogen circuit ( Fig. 2) is the hydrogen tank with a diameter of 5.4 m and a volume of 39.4 m 3 . The single turbopump feedline inlet is located in the tank lower dome section, causing for a small geometrical LH 2 residual after engine shutdown. For the initial tank prepressurization, gaseous helium is used, leading to a volumetrically small helium fraction in the ullage gas composition. During the propelled ascent phase, the tank ullage pressure is regulated via a hydrogen bleed §ow from the engine cooling system, leading to a relatively hot ullage (approximately 140 K) consisting almost entirely of gaseous hydrogen (GH 2 ). During the ballistic phase, the turbopump feed and the GH 2 repressurization valve are closed and the ullage gas is used in the 12 cold gas thrusters for attitude control. The pressure loss due to thruster activation is regenerated by the natural evaporation of the geometrical LH 2 residual.
The primary component of the oxygen circuit (Fig. 3) is the oxygen tank with a diameter of 2.6 m and a volume of 11.4 m 3 . The turbopump feedline inlet is located in the bottom center of the tank; so, the LOx residual is driven primarily by diphasic and thermal residuals. During ascent, the tank is pressurized only by gaseous helium from a single high pressure helium tank. After engine shutdown, natural evaporation rates are the driving part in the tank pressure regeneration. The tank ullage consists of a mixture of gaseous helium and oxygen with a de¦ned strati¦cation under accelerated conditions. This mixture ratio plays a major role in the LOx thruster performance prediction. The LOx thrusters are used both for tank pressure regulation and axial acceleration. To compensate induced torques due to the thruster position relative to the stage CoG, the nozzles are not identical in terms of geometry.

BALLISTIC PHASE PERFORMANCE PREDICTION
In the case of ESC-A acceleration in §ight direction (e. g., during boost phase), the propellant is settled at the tank bottom next to the draining outlet. Due to the settled propellant position, the wetted surface areas and, in consequence, the propellant tank conditions are well known. During the ballistic phase, attitude control maneuvers are performed to place the payloads in their transfer orbits. In this phase, all occurring accelerations are induced by the SCAR, respectively, LOx-purging-system, requiring a certain  Figure 4 illustrates an example of settled and sloshing propellant [3].
At a ¦rst glance, the cold gas thruster activation leads to a pressure decrease in the propellant tank. In addition, the alternating states of acceleration and micro-gravity lead to movements of the residual propellant and oxidizer, which cause casual sloshing. With liquid particles moving freely through the ullage volume and increasing the free liquid surface, higher evaporation rates are achieved, leading to disturbances in the ullage pressure. Figure 5 shows the ullage pressure evolution of the LH 2 tank. After engine §ameout, a signi¦cant pressure drop is visible caused by a stage slewing ma- Figure 5 Liquid hydrogen ullage pressure evolution neuver, which leads to propellant sloshing. The pressure is regenerating until the next pressure drop is induced. Over the entire ballistic phase, the cooling of the tank structure due to sloshing cannot be compensated by the thermal environment. In consequence, the ¦nal pressure regeneration level is decreasing (cf. slope illustrated in Fig. 5).
The pressure evolution in the propellant tank is primarily driven by the evaporation rate of the respective liquid (dependent on the boiling mode) and the gas expulsion through the SCAR. While the mechanisms of the gas expulsion as function of the ullage pressure are relatively well understood, the mechanisms behind the boiling mode are depending on a large range of uncertain parameters connected to the overall system design.
The hydromechanical e¨ects contain all reactions induced by the change of the kinetic state of the stage, bounded by the overall tank, line, and nozzle geometry and the properties of the respective residual §uids. The movement of the §uid and interactions with walls, bulkheads, baªes, and other installations change the absolute free liquid surface, leading to modi¦cations in evaporation rates. Furthermore, the inertia of the moving liquids may disturb the motion of the stage itself leading to additional corrective maneuvers.

ANALYSIS WORK FLOW
A ballistic phase performance prediction has to cover the complex e¨ects of thermo-and hydrodynamics as well as the interaction with stage kinetics, involving various engineering disciplines and models. To increase the analysis performance by decreasing cycle time and costs, the work §ow is separated into a rough iteration loop and an accurate §ight prediction model (Fig. 6). The work §ow is initiated by the de¦nition of the speci¦c mission phases and the generation of corresponding SCAR activation sequences.
Due to the fact that the activation pro¦les a¨ect the tank ullage pressure evolution and, in consequence, the thrust level, a consistent mission pro¦le has to be ensured. Therefore, an iterative process of several loops could be necessary for nonstandard missions. A rough numerical model is su©cient because at this point, iteration speed is more important than a high accuracy level. This model is based on a statistical approach and is described later in this paper.
When the iterative loop is successful, i. e., the mission pro¦le with corresponding thruster activation pro¦les as well as thrust levels and tank ullage pressure evolution are consistent, more accurate numerical models are used for ¦nal ballistic phase performance prediction. Due to the consideration of the wide range of physical e¨ects and boundary conditions, the calculation duration is signi¦cantly increased in comparison with the rough statistical model.

STATISTICAL PERFORMANCE MODEL
A wide range of parameters has to be respected in the estimation of the depressurization and regeneration behavior. To limit the analysis e¨ort, it has to be demonstrated that these e¨ects are statistically covered by the number of performed §ights and can be simulated in a statistical model by simple correlation mechanisms. For the model, the two main e¨ects, the thermal environment and the stage movement, are taken into account and examined in terms of impact.

Numerical Model
A numerical model for the simulation of the LH 2 ullage pressure was set up in MATLAB. The model makes three basic assumptions: (1) the pressure loss caused by thruster activations can be described as exponential function driven by the parameter activation time t and the number of active nozzles n. Further, major in §uences include the stage acceleration and the point in mission time, resembling the mass of liquid residuals; (2) the pressure regeneration in-between thruster activations can be described as exponential function driven by the parameter regeneration time t. Further, major in §uences include the stage acceleration and the point in mission time, resembling the mass of liquid residuals; and (3) the optimization of the given set of parameters and the validation with a su©cient number of in- §ight measurements will cover all unexpected, rare or random, e¨ects. It is assumed that the majority of possible unexpected e¨ects have been observed during the previous ESC-A §ights.
At the beginning of the development process, §ight data have been used to derive and ¦t the basic equations from in- §ight measurements of pressure slopes. After that, the modi¦cation parameters have been identi¦ed and optimized using several optimization approaches. Hereafter, the results of this development process are presented.
During a depressurization phase (n > 0), the ullage pressure P i for timestep i is depending on a number of di¨erent time-and event-correlating factors. The depressurization slope can be described by following equation: The ullage pressure at timestep i is de¦ned by the ullage pressure P 0 at t = 0 (start of depressurization) and several statistical modi¦ers. C x is a factor describing the stage acceleration with the assumption that the acceleration leads to propellant settling and, thus, to a higher evaporation rate due to better coupling, less ullage cooling due to reduced liquidgas interface and bubble transport during boiling. As a consequence for the model, the factor reduces the pressure loss during acceleration and varies between C x = 1 for the non-and C x > 1 for the accelerated states.
The nozzle mass §ow factor M n represents the correlation between nozzle mass §ow, §ow speed, and number of activated nozzles n, driven by the system speci¦c parameters (friction, pipe length, temperature, and diameters). The respective numbers for 1 to 12 parallel activated nozzles are de¦ned on the system side and are taken from a look-up table.
Finally, the depressurization factor S d covers the reduction in liquid residuals due to evaporation and blowout. Since the total mass of the residual liquid is not constant for di¨erent missions, the factor is only assumed to be mission time dependent with S d = 1 for t = 0 and S d < 1 for t > 0. The factors d 1 to d 4 are derived from the initial setup of the depressurization equation and are optimized ¦rst before all other parameters. Factor d 5 biases a slight o¨set in the starting parameter since for small t, the equation returns P i > P 0 .
During a regeneration phase (n = 0), the ullage pressure P i for timestep i can be described by the following equation: The regeneration factor S r covers again the reduction in liquid residuals due to evaporation and blowout. The factor is again only assumed to be mission time dependent with S r = 1 for t = 0 and S r < 1 for t > 0. The factors r 1 to r 4 are derived from the initial setup of the regeneration equation and are optimized ¦rst before all other parameters. During development, it was observed that the impact of acceleration on the regeneration rate can be neglected.

Model Parameter Optimization
With the setup of the simpli¦ed pressurization model, several unknown variables are introduced and have to be ¦tted to the §ight data. Since the given 18 parameters are not well known, they will undergo several optimization loops. The basic aim of these loops is to generate a model that is able to reproduce the pressure slope for a given SCAR activation pro¦le without taking into account the e¨ects caused by potential sloshing e¨ects.
The optimization is considered successful when the mean deviation between the slopes of the measured tank ullage pressure and the respective predicted pressure reaches a minimum. All deviations between model and physical measurement are then considered to be caused by modeling-or sloshing e¨ects and will be treated later. To optimize the prediction model, a Monte-Carlo-based multiple stage simplex algorithm is used. The regular break criterion is set by a deviation corridor and has to be adapted iteratively.

Model Performance
After performing the optimization loop, the overall model precision for 34 ESC-A §ights is 4.43% ± 3.18%. The overall calculation time for one simulation is between 0.7 and 0.95 s depending on the number of SCAR activations and ballistic phase durations.
Several observations have been made. The most important ¦nding is that eventual sloshing of the liquid residuals in the tank takes place on a scale, which is well covered by the statistical analysis of the re-and depressurization slopes. Figure 7 illustrates exemplarily the LH 2 tank ullage pressure calculated by the statistical approach in comparison to the §ight measurements for a ballistic §ight. Even if the initial sloshing event and the pressure slope during the ballistic phase are well covered by the simpli¦ed model, a single excessive pressure drop after ∼ 150 s leads to an o¨set. The maximum deviation for this §ight is ∼ 200 mbar.
Only on two instances, a macroscopic impact of liquid sloshing on the tank ullage pressure could be observed. For nonstandard missions, the performance of the algorithm is rather good due to the statistical character of the parameters.

EcosimPro PERFORMANCE MODEL
EcosimPro is a simulation environment designed by Empresario Agrupados International for modeling physical processes based on di¨erential-algebraic equations and discrete events. The modeling process is based on the EcosimPro modeling language EL which is used to design various types of single components that can be connected to a complex physical system. Due to the limitation to zeroand one-dimensional models, complex systems with long physical time durations, such as the ballistic §ight phase of the upper stage, require a system analysis tool with limited dimensions and discretization.

Model Setup
The EcosimPro model of the ballistic phase aims to give a realistic view of the propellant behavior in the tanks during the ballistic §ight. Therefore, the LH 2 cold gas system has to be simulated with respect to variable heat loads and sloshing e¨ects due to the upper stage maneuvers. The model is set up using the ESPSS library [4] at version 2.4 under EcosimPro 5.4 and consists of the tank model which takes account of the sloshing e¨ects, the feed line system with its hydraulic boundary conditions, several time dependent valve control regulators, and the SCAR system thrusters. Tank walls and insulation layers de¦ne thermal capacities and conductivities of the tank and, thus, heat §uxes induced by a time variable thermal environment (Fig. 8).
Sensitivity analyses have identi¦ed a signi¦cant impact of the boiling model parameters on the depressurization and pressure regeneration behavior during the ¦rst sloshing event after engine §ameout. Boiling as well as condensation e¨ects are respected in the tank component. The time step size is adjusted by the transient solver, depending primarily on the thruster activation events.

Boundary Conditions
The numerical model for ballistic phase analysis requires a set of boundary conditions. Heat §uxes are taken from the generic thermal environment, which includes sink temperatures, solar and albedo §uxes speci¦c for each tank part. These are the upper dome (exposed to stage structure), cylindrical part and lower dome (deep space / Earth / Sun) and inner dome (LOx tank). They are depending on time and generic thermal scenario (hot, reference, and cold cases).
The simulation starts at engine shutdown. Thus, the residual mass with pressure and temperature of the liquid and gas phase are inputs. Thruster activations of the SCAR de¦ne the outgoing mass §ow. In addition, the accelerations of the stage are used as input and are required to compute the heat transfer coe©cients.
The wetted surfaces between liquid and gas (LG) and liquid and wall (LW) are computed by the use of the CFD tool Flow3D based on the SCAR activation pro¦les, respectively, torques, the stage mass, and inertia as well as the propellant residual mass [5]. According to Fig. 6, these 3D CFD results are inputs of the EcosimPro system model.

Implementation of Three-Dimensional Data in the One-Dimensional System Model
In the Flow3D CFD tool, the propellant tank is represented by a 3D geometry and a Cartesian numerical mesh. In consequence, the CFD analysis output, linked to the numerical discretization, has a 3D format as well. Each mesh cell contains the information of its position in the propellant tank and for each of the two interfaces (LG and LW) the wetted surface fraction for each cell face. This set of output values is provided for each numerical cell at each analysis time step.
In contrast to the 3D Flow3D format, the system model in EcosimPro is limited to a 1D discretization. The propellant tank is divided into slices along the tank symmetry axis, representing the numerical nodes. For the transformation from three dimensions to one dimension, a MATLAB script is used.
The LG interface areas of each CFD cell are summed up for each time step. For the LW interface, the CFD cells have to be assigned to the EcosimPro node according to their position on the tank symmetry axis. For each EcosimPro node and each time step, the sum of the corresponding CFD values is built. In consequence, the full set of 3D values is reduced to a single value for the LW wetted surface area for each EcosimPro node and one single value for the LG interface area for the complete §uid compartment.

Figure 9
Transformation of 3D CFD results into 1D EcosimPro model inputs Figure 9 presents a schematic illustration of the transformation of 3D CFD data into the 1D EcosimPro model format. The complex LH 2 tank geometry, comprising tank internal equipment such as pressurization line and draining collector, is simpli¦ed to a numerical model (picture at the left-hand side). The 3D sloshing analysis is performed by an appropriate CFD model using a Cartesian numerical mesh (picture in the center). All 3D sloshing data are transformed to ¦t the sliced EcosimPro model (picture on the right-hand side).

Model Parameter Correlation
Even if the boundary conditions are well-de¦ned, a large set of model inherent parameters a¨ects the accuracy and robustness of the numerical solution. The EcosimPro ESPSS tank component applies an empirical boiling model covering the pool boiling regimes de¦ned by the Nukiyama curve. Sensitivity analyses have highlighted the impact of these empirical boiling model parameters on the depressurization and regeneration rates.
Thus, correlation loops with four representative ESC-A §ight data measurements are performed. Therefore, four Ariane 5 ESC-A launches were selected, representing a family of ballistic phase mission pro¦le. Especially, the LH 2 pressure evolution and cold gas system activations are similar. An additional mission with an extended ballistic phase (V173/L533) is also considered.
Parameters for the major sloshing phase (engine shutdown + 250 s) were optimized regarding the hot, cold, and reference cases. Since the exact heat §uxes remain unknown, they can only be estimated by exposure time to sun radiation. Nevertheless, best correlations were reached for the hot case. These optimizations of the boiling parameters C sf , f boi , and r from the Rhosenowcorrelation [6] were done manually: A reasonable implementation of §uid velocities calculated by CFD sloshing analyses did not show improvements. It seems that the implementation methodology a¨ecting the heat transfer mechanisms do not match the real LH 2 movements. Thus, a common set of boiling parameters was computed by the optimization approach without velocity implementation. Consequentially, further investigations could decrease deviations which are already below 5%.

Model Performance
The time needed for the simulation of one §ight (from engine shutdown until stage passivation) is between 3600 and 8000 s depending on the mission duration. Partly simulated scenarios (e. g., only sloshing phase) are possible for a known initial status. It has to be noted that the total analysis duration is driven by the complex CFD sloshing analysis providing the required EcosimPro inputs, not covered by the stated simulation duration.
For the complete ballistic phase, the deviations are below 5%. In Fig. 10, the numerical analysis by EcosimPro and the §ight measurement are compared for one exemplary §ight. The ¦rst 200 s, which are in the range of model parameter optimization, re §ect the §ight measurements very well. Even if the calculated pressure evolution has an excessive pressure regeneration after 200 s, the maximum deviation is below 120 mbar for this §ight.
The §ight prediction accuracy by EcosimPro is a¨ected by the quality of the required input data. Even if the CFD sloshing analysis, based on SCAR activation pro¦les, delivers §ight speci¦c data, other inputs are based on generic de¦nitions (e. g., thermal environment). To further increase the accuracy and robustness of the EcosimPro §ight prediction model, additional analysis and workarounds for nonstandard missions have to be performed. Additional §ights with an extended ballistic phase will be a source of enhanced model correlations.

CONCLUDING REMARKS
A performance model is required to ensure su©cient cold gas attitude control performance during long ballistic phase, e. g., for future launchers. Due to the coupling between thruster activation sequence, stage kinematics, and thermal environment, a dedicated work §ow with iteration loops involving several tools and engineering disciplines was established.
To increase the performance of the initial coherence loop, a simpli¦ed model was implemented in MATLAB. The depressurization and regeneration due to sloshing was considered by a statistical approach limiting the number of required inputs. For standard mission phases, covered by §ight experience, this model shows a su©cient accuracy by short calculation times.
For ¦nal and detailed analysis, an EcosimPro model comprising all relevant boundary conditions was set up. Especially, the implementation of 3D propellant sloshing e¨ects (extracted from CFD calculations) into the 1D system model leads to a signi¦cant increase of accuracy and robustness also for nonstandard missions and future launcher design. For further improvements of analysis accuracy, additional correlations and sensitivity analyses with §ight measurements will be performed in future.

PROPOSAL OF FUTURE ACTIVITIES
In addition to the already mentioned extension of underlying §ight measurements, further areas of improvement are identi¦ed for ballistic phase performance prediction modeling.
For §ight prediction, generic data, e. g., hot, reference, and cold cases for the thermal environment, are de¦ned and applied. These generic de¦nitions cover all probable mission scenarios and ensure a high level of con¦dence by a limited analysis e¨ort. However, the application of these worst case conditions, usually, does not represent the real §ight conditions. Here, simpli¦ed models for more detailed §ight condition prediction and input generation are required.
As shown in Eq. (1), the heat transfer mechanisms have a signi¦cant impact on the LH 2 evaporation and, in consequence, pressure regeneration. During the ballistic phase, the upper stage is under microgravity condition. In case of cold gas thruster activation (e. g., S34), acceleration occurs. Furthermore, the propellant movement due to sloshing overlays the empirically determined heat transfer coe©cients. It might be reasonable that a more detailed consideration of heat transfer mechanisms of sloshing liquids under di¨erent acceleration conditions is required.
During the whole performance prediction process, interfaces between di¨erent engineering disciplines and tools exist. In the frame of the analysis work §ow de¦nition, the interfaces and data exchange formats are already de¦ned (cf. Fig. 6). MATLAB scripts are used for data treatment reducing the data handling e¨ort. An integrated system analysis approach, integrating all relevant tools and covering the data handling in-between, would decrease the analysis loop duration and would further increase the performance prediction accuracy and robustness.