Aerospace Science and Technology 39 (2014) 491–500 Contents lists available at ScienceDirect Aerospace Science and Technology www.elsevier.com/locate/aescte EUCLID satellite: Development of a lumped parameter model for sloshing description M. Lazzarin ∗,1 , M. Biolo 2 , A. Bettella 3 , M. Manente 3 , R. Da Forno 3 , D. Pavarin 3 CISAS – Padova, Italy a r t i c l e i n f o a b s t r a c t Article history: Received 15 April 2014 Received in revised form 27 May 2014 Accepted 31 May 2014 Available online 2 July 2014 Keywords: Lumped parameter model Sloshing Liquid propellant tank This paper presents a research work estimating the impact of propellant sloshing on the pointing-stability of the EUCLID satellite, for a pre-design phase of the project. The analysis is carried out by means of a simplified lumped parameter model describing the fluid system. This model allows the identification of forces and angular moments due to liquid movement under different acceleration conditions, and for different fill levels of the reservoir. The lumped model is calibrated by means of CFD simulations to determine the correct values to be attributed to the different coefficients. For this work, two tank fill ratios have been considered: 22 and 50%, with an elastomeric and deformable bladder. The results of the lumped models are compared with the CFD output obtained using the same acceleration profile, and corresponding to the same fill level. The study shows that using CFD to calibrate the lumped parameter model is a promising technique, which can be applied at a preliminary design stage, to reduce development costs and time. This work is intended as the prosecution of the first study about sloshing by the same authors, which was aimed at representing bladdered tanks using computational fluid dynamics without recurring to fluid–structure interaction techniques. Here, a new method for the calibration of the traditional sloshing lumped model, based on computational fluid dynamics instead of real experiments, is proposed and applied to a specific fluid system. This procedure can result in a consistent reduction of the experiments costs.  2014 Elsevier Masson SAS. All rights reserved. 1. Introduction Many tests and experiments have been performed since the 1960s to study sloshing in tanks of different shapes. NASA assessed the influence of the amplitude of the applied acceleration, bladder thickness and tank radius [6,1] on damping. Afterwards, analytical and simplified lumped parameter models were developed to de- scribe the slosh behaviour of a fluid [2]. These models have been illustrated in many papers and documents, but no specific docu- mentation is available about bladder modelling. Additionally, it is possible to create lumped models which need to be calibrated, to correctly estimate the damping, sloshing mass and inertial mass contribution [7]. This work illustrates a new idea for lumped sloshing models calibration, which is based on CFD simulations instead of real ex- * Corresponding author. E-mail address: marta.lazzarin@unipd.it (M. Lazzarin). 1 Aerospace Engineer, PhD. 2 Aerospace Engineer, Weir Gabbioneta s.r.l. 3 Mechanical Engineer, PhD. perimental testing. The major advantage of this new approach pro- posed for the pre-design phase is connected to the reduction of the time required to calibrate the model, because it is no longer necessary to develop a complete test facility for sloshing charac- terisation. Moreover, a consistent reduction in the costs for the experiments development also applies. This paper also presents the application of this calibration tech- nique to two lumped parameter models created to describe the sloshing-induced-perturbations of the highly-stable EUCLID satel- lite. The liquid propellant response to the external accelerations obtained with the lumped model is compared to the output of the corresponding CFD simulation, for each of the two fill lev- els considered in this study. The paper is organized as follows: a first section introduces the lumped model used, and a second sec- tion introduces the idea proposed for model calibration. The setup required for CFD simulations is only briefly described, as it has already been fully illustrated by the authors [3]. Finally, the assess- ment done comparing the lumped model results to the CFD results on the EUCLID case is reported. The data used for the acceleration profiles only refers to a preliminary design of the satellite and its behaviour. http://dx.doi.org/10.1016/j.ast.2014.05.014 1270-9638/ 2014 Elsevier Masson SAS. All rights reserved.