Global and Local Multidisciplinary Design Optimization of Expendable Launch Vehicles

Abstract

The paper presents engineering models, optimization algorithms and design results from a Multidisciplinary Design Optimization (MDO) research in the framework of ESA's PRESTIGE PhD program. The application focuses on the conceptual design of classical unmanned Expendable Launch Vehicles, and results are presented from sensitivity studies and validation tests on European launchers (Ariane-5 ECA and VEGA). Relatively simple models and a mixed global/local optimization approach allow obtaining reasonable results with limited computational effort. A critical analysis of the results also leads to the identification of the most critical modeling aspects to be improved to allow for early preliminary design applications. Nomenclature α = engine mixture ratio ε = nozzle expansion ratio θ = pitch angle ψ = yaw angle µ = mean value σ = standard deviation A e = nozzle exhaust area AoA = total angle of attack a = orbit semiaxiscore boosters configuration CpL = cost per launch e = orbit eccentricity GTOW = gross take-off weight i = orbit inclination I sp = specific impulse, nominal conditions (i.e. nozzle optimal expansion) 2 I sp,vac = specific impulse in vacuum I sp,sea = specific impulse at sea level L/D = length over diameter ratio LSP = launch success probability MR = Engine mixture ratio M = Mach number M prop = Propellant mass (usable propellant only) M dry = Dry mass = inert mass + unused propellants mass N s = number of stages N bs = number of booster sets N b,j = number of boosters for j-th boosters set n ax = axial acceleration p cc = chamber pressure PL = payload PLSF = payload scaling factor q dyn = dynamic pressure q heat = heat flux SET = single engine type configuration (i.e. same engine type for all stages) T nom = total thrust, nominal conditions (i.e. nozzle optimal expansion) T ,vac = total thrust in vacuum T sea = total thrust at sea level

Quantitative Assessment of Multidisciplinary Design Models for Expendable Launch Vehicles

“…The subsystem-level validation process showed a significant improvement in most of the disciplines, as can be evinced by the comparison of the results in Tables 1 and 4. Again, full results are detailed in [34], but it has to be remarked here how the accuracy in the assessments of propulsion and especially weight outputs was significantly increased. In terms of sensitivities, one-variable-at-atime analyses highlighted a significantly lower criticality of the inert masses with respect to the conceptual models.…”

“…During this phase, several tuning parameters specific to each disciplinary model were also calibrated, such as specific impulse loss coefficients or WER and CER parameters. The complete results are too extensive to be shown here, but full details are available in Castellini's Ph.D. dissertation [34]. A qualitative overview of the disciplinary accuracies is, however, given in the following text, with summarizing figures reported in Table 1.…”

“…These two aspects are described in more details in the following text, whereas numerous secondary enhancements to the propulsion models are reported in [34], covering both added functionalities (more fuels such as Russian kerosene vs rocket propellant one (RP-1), multiple thrust chambers, and extendable and submerged nozzles) and an improved accuracy (I sp loss for SP engines as a function of the expansion ratio and throat erosion, the detailed assessment of unused LP mass including an end-of-life propellant budget, and better tuning of the WERs).…”

“…Although the results are too lengthy to be shown here (see [34] for all the details), a few remarks are provided that are then directly used as inputs for the model enhancements described in the next section. On a disciplinary level, the MDA showed that the geometry calculations sensibly underestimate the lengths, especially for VEGA interstages, with nonnegligible effects on the weights.…”

“…Finally, the primary structural mass of all components can be assessed by a simple integration of the calculated thickness along the beam. This procedure, for which more details are provided in [34], is repeated for the core and all booster sets included in the architecture, accounting for the load transfer at the predefined attachment points. This allows an estimate of the optimal structural weight of all structural components.…”