[EN] The main objective of this work is the modeling of diesel sprays under engine conditions, including the atomization, transport and evaporation processes pivotal in the diesel spray formation and its development. For this purpose, an Eulerian single fluid model, embedded in a RANS environment, is implemented in the CFD platform OpenFOAM. The modeling approach implemented here is based on the ⅀-Y model. The model is founded on the assumption of flow scales separation. In actual injection systems, it can be assumed that the flow exiting the nozzle is operating at large Reynolds and Weber numbers and thus, it is possible to assume a separation of features such as mass transport (large scales) from the atomization process occurring at smaller scales. The liquid/gas mixture is treated as a pseudo-fluid with variable density and which flows with a single velocity field. Moreover, the mean geometry of the liquid structures can be characterized by modeling the mean surface area of the liquid-gas interphase per unit of volume. Additionally, an evaporation model has been developed around the particular characteristics of the current engine technologies. This means that vaporization process is limited by fuel-air mixing rate and fuel droplets evaporate as long as there is enough air for them to heat up and vaporize. Consequently, the evaporation model is based on the Locally Homogeneous Flow (LHF) approach. Under the assumption of an adiabatic mixing, in the liquid/vapor region, the spray is supposed to have a trend towards adiabatic saturation conditions and to determine this equilibrium between phases Raoult's ideal law is considered. Finally, the spray model is coupled with an advanced combustion model based on approximated diffusion flames (ADF), which reduces the computational effort especially for complex fuels and is a natural step for modeling diesel sprays. First, the model is applied to a basic external flow case under non-vaporizing conditions, extremely convenient due to both the experimental database available and the symmetric layout which allows important simplification of the modeling effort. Good agreement between computational results and experimental data is observed, which encourages its application to a more complex configuration. Secondly, the model is applied to the "Spray A" from the Engine Combustion Network (ECN), under non-vaporizing conditions, in order to reproduce the internal structure of diesel sprays as well as to produce accurate predictions of SMD droplets sizes. Finally, vaporizing "Spray A" studies are conducted together with the baseline reacting condition of this database. The calculated spray penetration, liquid length, spray velocities, ignition delay and lift-off length are compared with experimental data and analysed in detail. / [ES] El objetivo principal de este trabajo es el modelado de chorros diésel en condiciones de motor, incluyendo los fenómenos de atomización, transporte y evaporación fundamentales en la formación y desarrollo del chorro. Para este fin, se implementa un modelo de spray euleriano de tipo monofluido en un entorno RANS en la plataforma CFD OpenFOAM. El enfoque de modelado aplicado aquí sigue la idea de un modelo del tipo ⅀-Y. El modelo se fundamenta en la hipótesis de separación de escalas del flujo. En los sistemas de inyección actuales, es posible asumir que el flujo que sale de la tobera opera a altos números de Reynolds y Webber y por tanto, es posible considerar la independencia de fenómenos como el transporte de masa (grandes escalas del flujo) de los procesos de atomización que ocurren a escalas menores. La mezcla líquido/gas se trata como un pseudo-fluido con densidad variable y que fluye según un único campo de velocidad. Además, la geometría promedio de las estructuras de líquido se puede caracterizar mediante el modelado de la superficie de la interfase líquido/gas por unidad de volumen. Completando el modelo de chorro, se ha desarrollado un modelo de evaporación alrededor de las características particulares de las tecnologías actuales de los motores. Esto supone que el proceso de evaporación está controlado por mezcla aire-combustible y las gotas de combustible se evaporan siempre que exista suficiente aire para calentarlas y evaporarlas. Debido a esto, el modelo de evaporación implementado está basado en el enfoque de Flujos Localmente Homogéneos (LHF). Considerando una mezcla adiabática, en la región líquido/vapor, se supone que el chorro tiende a las condiciones adiabáticas de saturación y para determinar este equilibrio entre fases, se utiliza la ley ideal de Raoult. Finalmente, el modelo de chorro se acopla con un modelo avanzado de combustión basado en llamas de difusión aproximadas (ADF), que reduce el coste computacional especialmente para combustibles complejos y supone el paso lógico en el desarrollo del modelo para simular chorros diesel. En primer lugar, el modelo se aplica al cálculo de un caso básico de flujo externo no evaporativo, muy adecuado tanto por la extensa base de datos experimentales disponible como por la simetría geométrica que presenta, permitiendo una importante simplificación de la simulación. Los resultados obtenidos presentan un buen acuerdo con los experimentos, lo cual estimula su aplicación en configuraciones más complejas. En segundo lugar, el modelo se aplica al cálculo del "Spray A" del Engine Combustion Network (ECN), no evaporativo, para reproducir la estructura interna del chorro diesel así como predecir tamaños de gota (SMD) de forma precisa. Finalmente, se realizan estudios evaporativos del "Spray A" junto con la condición nominal reactiva de esta base de datos. La penetración de vapor, la longitud líquida, velocidad, el tiempo de retraso y la longitud de despegue de llama calculados se comparan con los datos experimentales y se analizan en detalle. / [CA] L'objectiu principal d'aquest treball és el modelatge de dolls dièsel en condicions de motor, incloent els fenòmens d'atomització, transport i evaporació fonamentals en la formació i desenvolupament del doll. Amb aquesta finalitat, s'implementa un model de doll eulerià de tipus monofluid en un entorn RANS a la plataforma CFD OpenFOAM. L'enfocament de modelatge aplicat ací segueix la idea d'un model del tipus ⅀-Y. El model es fonamenta en la hipòtesi de separació d'escales del flux. En els sistemes d'injecció actuals, és possible assumir que el flux que surt de la tovera opera a alts nombres de Reynolds i Webber, i per tant és possible considerar la independència de fenòmens com el transport de massa (grans escales del flux) dels processos d'atomització que ocorren a escales menors. La mescla líquid / gas es tracta com un pseudo-fluid amb densitat variable i que flueix segons un únic camp de velocitat. A més, la geometria mitjana de les estructures de líquid es pot caracteritzar mitjançant el modelatge de la superfície de la interfase líquid / gas per unitat de volum. Completant el model, s'ha desenvolupat un model d'evaporació al voltant de les característiques particulars de les tecnologies actuals dels motors. Això suposa que el procés d'evaporació està controlat per la mescla aire-combustible i les gotes de combustible s'evaporen sempre que hi hagi suficient aire per escalfar i evaporar. A causa d'això, el model d'evaporació implementat està basat en el plantejament de fluxos Localment Homogenis (LHF). Considerant una mescla adiabàtica, a la regió líquid / vapor, se suposa que el doll tendeix a les condicions adiabàtiques de saturació i per determinar aquest equilibri entre fases, s'utilitza la llei ideal de Raoult. Finalment, el model de doll s'acobla amb un model avançat de combustió basat en flamelets de difusió aproximades (ADF), que redueix el cost computacional especialment per a combustibles complexos i suposa el pas lògic en el desenvolupament del model per simular dolls dièsel. En primer lloc, el model s'aplica al càlcul d'un cas bàsic de flux extern no evaporatiu, molt adequat tant per l'extensa base de dades experimentals disponible com per la simetria geomètrica que presenta, permetent una important simplificació de la simulació. Els resultats obtinguts presenten un bon acord amb els experiments, la qual cosa estimula la seva aplicació en configuracions més complexes. En segon lloc, el model s'aplica al càlcul del "Spray A" no evaporatiu de la xarxa Engine Combustion Network (ECN), per reproduir l'estructura interna del doll dièsel així com predir mides de gota (SMD) de forma precisa. Finalment, es realitzen estudis evaporatius del "Spray A" juntament amb la condició nominal reactiva d'aquesta base de dades. La penetració de vapor, la longitud líquida, velocitat, el temps de retard i la longitud d'enlairament de flama calculats es comparen amb les dades experimentals i s'analitzen en detall. / Pandal Blanco, A. (2016). Implementation and Development of an Eulerian Spray Model for CFD simulations of diesel Sprays [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/68490

This research used computational fluid dynamics (CFD) to examine the behavior of airborne droplets released during respiratory events. The CFD model utilizes an Eulerian-Lagrangian approach, with turbulence resolved using the Spalart-Allmaras detached eddy simulation. The first part investigates airborne transmission and how modifying saliva during a sneeze impacts this process. The study employs CFD to simulate these respiratory events in a ventilated room. It finds that larger droplets alone are insufficient for droplet settling due to secondary breakdown processes. Modifiers that increase the Ohnesorge number show resistance to aerosolization from secondary breakup, resulting in more droplets with high settling rates, reducing their likelihood of airborne transmission. Another effective modifier reduces saliva content. The second part of the research develops a linear algebraic function to represent the near-field dispersion of droplets formed during respiratory events. This model facilitates the examination of flow interaction among various sources in different environments without requiring computationally expensive CFD simulations. The final part of the research involves developing a numerical Wells curve considering droplet evaporation, buoyancy, turbulence, breakup, and collision. The study also examines the effect of relative humidity on airborne transmission, finding that higher relative humidity slows the evaporation rate, which typically promotes faster droplet settling. Overall, these findings offer promising strategies for preventing spread of airborne transmission, highlighting the potential of saliva modification and advanced modeling techniques in public health interventions.

In the current age of space exploration, the push to reach further to deep space presents a greater need for analysis and verification and validation of rocketry components in the space environment. Due to the nature of space, firings of rocket thrusters in space is a multi-regime problem. With the low density, pressure, and temperature of the environment, the resultant plume structure, seeded with unburnt fuel droplets, extends up to multiple orders of magnitude in distance as compared to a plume structure in the Earth’s atmosphere. The frozen droplets, or particles, create concerns including surface contamination and erosion, calling a cause for study and model development to understand particle behavior in this multi-regime environment. This work intends to develop a model to analyze and understand multiphase flow and particle behavior in this environment utilizing the lower fidelity, but more computationally efficient, RANS turbulence modeling. Particle properties are compared against a regime-defining parameter to understand the trends in behavior. Finally, the work closes out on a preliminary look into implementing fully reacting flow chemistry for the multiphase flow. These results and progress are promising in developing an efficient model that may be integrated into a hybrid model to better predict particle behavior and dispersion in this multi-regime environment.

Cette thèse se situe au carrefour de la combinatoire énumérative, algébrique et bijective. Elle se consacre d’une part à traduire des problèmes algébriques en des problèmes combinatoires, et inversement, utilise le formalisme algébrique pour traiter des questions combinatoires.Après un rappel des notions classiques de combinatoire et de structures algébriques, nous abordons l’étude des tableaux de dominos décalés, qui sont des objets combinatoires définis dans le but de mieux comprendre la combinatoire des fonctions symétriques P et Q de Schur. Nous donnons la définition de ces tableaux et nous démontrons qu'ils sont en bijection avec les paires de tableaux de Young décalés. Cette bijection nous permet de voir ces objets comme des éléments du super monoïde plaxique décalé, qui est l'analogue décalé du super monoïde plaxique de Carré et Leclerc. Nous montrons aussi que ces tableaux décrivent un produit de deux fonctions P de Schur et en prenant un autre type de tableaux de dominos décalés, nous décrivons un produit de deux fonctions Q de Schur. Nous proposons aussi deux algorithmes d'insertion pour les tableaux de dominos décalés, analogues aux algorithmes d'insertion mixte et d'insertion gauche-droit de Haiman. Toujours dans le domaine de la combinatoire bijective, nous nous intéressons dans la deuxième partie de notre travail à des bijections en lien avec des statistiques sur les permutations et les nombres eulériens.Dans cette deuxième partie de thèse, nous introduisons l'unimodalité des suites finies associées aux différentes directions dans le triangle eulérien. Nous donnons dans un premier temps une interprétation combinatoire ainsi que la relation de récurrence des suites associées à la direction (1,t) dans le triangle eulérien, où t≥1. Ces suites sont les coefficients de polynômes appelés les polynômes eulériens avec succession d'ordre t, qui généralisent les polynômes eulériens. Nous démontrons par une bijection entre les permutations et des chemins nord-est étiquetés que ces suites sont log-concaves et donc unimodales. Puis nous prouvons que les suites associées aux directions (r,q), où r est un entier positif et q est un entier, tel que r+q≥0, sont aussi log-concaves et donc unimodales / This thesis is at the crossroads of enumerative, algebraic and bijective combinatorics. It studies some algebraic problems from a combinatorial point of view, and conversely, uses algebraic formalism to deal with combinatorial questions.After a reminder about classical notions of combinatoics and algebraic structures, We introduce new combinatorial objects called the shifted domino tableaux, these objects can be seen as a shifted analog of domino tableaux or as an extension of shifted Young tableaux. We prove that these objects are in bijection with pairs of shifted Young tableaux. This bijection shows that shifted domino tableaux can be seen as elements of the super shifted plactic monoid, which is the shifted analog of the super plactic monoid. We also show that the sum over all shifted domino tableaux of a fixed shape describe a product of two P-Schur functions, and by taking a different kind of shifted domino tableaux we describe a product of two Q-Schur functions. We also propose two insertion algorithms for shifted domino tablaux, analogous to Haiman's left-right and mixed insertion algorithms. Still in the field of bijective combinatorics, we are interested in the second part of our work with bijections related to statistics on permutations and Eulerian numbers.In this second part of this thesis, we introduce the unimodality of finite sequences associated to different directions in the Eulerian triangle. We first give a combinatorial interpretations as well as recurrence relations of sequences associated with the direction (1, t) in the Eulerian triangle, where t≥1. These sequences are the coefficients of polynomials called the t-successive eulerian polynomials, which generalize the eulerian polynomials. We prove using a bijection between premutations and north-east lattice paths that those sequences are unomodal. Then we prove that the sequences associated with the directions (r, q), where r is a positive integer and q is an integer such that r + q ≥ 0, are also log-concave and therefore unimodal

En 2010 Chung, Graham et Knuth ont démontré une remarquable identité symétrique sur les nombres eulériens et posé le problème de trouver un q-analogue de leur identité. En utilisant les q-polynômes eulériens introduits par Shareshian-Wachs, nous avons pu obtenir une telle q-identité. La preuve bijective que nous avons imaginée, nous a permis ensuite de démontrer d'autres q-identités symétriques, en utilisant un modèle combinatoire dû à Foata-Han. Entre temps, Hyatt a introduit les fonctions quasisymétriques eulériennes colorées afin d'étudier la distribution conjointe du nombre d'excédances et de l'indice majeur sur les permutations colorées. En appliquant le Decrease Value Theorem de Foata-Han, nous donnons d'abord une nouvelle preuve de sa formule principale sur la fonction génératrice des fonctions quasisymétriques eulériennes colorées, puis généralisons certaines identités eulériennes symétriques, en les exprimant comme des identités sur les fonctions quasisymétriques eulériennes colorées. D'autre part, en prolongeant les travaux récents de Savage-Visontai et Bec-raun, nous considérons plusieurs q-polynômes de descente des mots signés. Leurs fonctions génératrices factorielles et multivariées sont explicitement calculées. Par ailleurs, nous montrons que certains de ces polynômes n'ont que des zéros réels. Enfin, nous étudions la fonction génératrice diagonale des nombres de Jacobi Stirling de deuxième espèce, en généralisant des résultats analogues pour les nombres de Stirling et Legendre-Stirling de deuxième espèce. Il s'avère que cette fonction génératrice est une série rationnelle dont le numérateur est un polynôme à coefficients entiers positifs. En appliquant la théorie des P-partitions de Stanley nous trouvons des interprétations combinatoires de ces coefficients / In 2010 Chung-Graham-Knuth proved an interesting symmetric identity for the Eulerian numbers and asked for a q-analog version. Using the q-Eulerian polynomials introduced by Shareshian-Wachs we find such a q-identity. Moreover, we provide a bijective proof that we further generalize to prove other symmetric qidentities using a combinatorial model due to Foata-Han. Meanwhile, Hyatt has introduced the colored Eulerian quasisymmetric functions to study the joint distribution of the excedance number and major index on colored permutations. Using the Decrease Value Theorem of Foata-Han we give a new proof of his main generating function formula for the colored Eulerian quasisymmetric functions. Furthermore, certain symmetric q-Eulerian identities are generalized and expressed as identities involving the colored Eulerian quasisymmetric functions. Next, generalizing the recent works of Savage-Visontai and Beck-Braun we investigate some q-descent polynomials of general signed multipermutations. The factorial and multivariate generating functions for these q-descent polynomials are obtained and the real rootedness results of some of these polynomials are given. Finally, we study the diagonal generating function of the Jacobi-Stirling numbers of the second kind by generalizing the analogous results for the Stirling and Legendre-Stirling numbers of the second kind. It turns out that the generating function is a rational function, whose numerator is a polynomial with nonnegative integral coefficients. By applying Stanley’s theory of P-partitions we find combinatorial interpretations of those coefficients

The evolution of numerical methods and computational facilities allow re- searchers to explore complex physical phenomenons such as multiphase flows. The specific regime of incompressible, turbulent, bubbly two-phase flow (where a car- rier fluid is infused with bubbles or particles) is also receiving increased attention due to it’s appearance in major industrial processes. The main challenges arise from coupling individual aspects of the physics into a unified model and to provide a robust numerical framework. The presented work aimed at to achieve the second part by employing the most frequently used dispersed two-phase flow model and another incompressible, turbulent single phase solver as a base flow provider for coupled Lagrangian or surface tracking tools. Among the numerical techniques, the finite element method is a powerful can- didate when the need arises for multiphysics simulations (for example coupling with an electrochemical module) where the counterpart has a node based ap- proach. Stabilization schemes such as PSPG/SUPG/BULK provide remedies for the pressure decoupling and the inherent instability of the central discretization when applied for convective flow problems. As an alternative to unsteady solvers based upon an explicit or a fully im- plicit nonlinear treatment of the convective terms, a semi-implicit scheme results in a method of second order accurate in both space and time, has absolute linear stability and requires only a single or two linear system solution per time step. The application of the skew symmetric approach to the convective term further stabilizes the solution procedure and in some cases it even prevents divergence. The Eulerian-Eulerian two-phase flow model poses various issues to be over- come. The major difficulty is the density ratio between the phases; for an ordinary engineering problem it is in the order of thousands or more. The seemingly minus- cule differences in the formulation of the stabilizations can cause very different end results and require careful analysis. Volume fraction boundedness is of concern as well, but it is treatable by solving for its logarithm. Since the equations allow jumps (even separation of the phases) in the volume fraction field, discontinuity capturing techniques are also needed. Besides the standard ’spatial’ stabilization temporal smoothing is also necessary, otherwise the limitation in time step size becomes too stringent. Designing a flow solver is one side of the adventure, but verification is equally important. Comparison against analytical solution (such as the single and two- phase Taylor-Green testcase) provides insight and confirmation about the mathe- matical and physical properties. Meanwhile comparing with real life experiments prove the industrialization and usability of a code, dealing with low quality meshes and effective utilization of computer clusters. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Die Dynamik von elastischen Membranen, Kapseln und Schalen hat sich zu einem aktiven Forschungsgebiet in der simulationsgestützten Physik und Biologie entwickelt. Die dünne Oberfläche dieser elastischen Materialien ermöglicht es, sie effizient als Hyperfläche zu approximieren. Solche Oberflächen reagieren auf Dehnungen in Oberflächenrichtung und Verformungen in Normalenrichtung mit einer elastischen Kraft. Zusätzlich können Oberflächenspannungskräfte auftreten. In dieser Arbeit präsentieren wir eine neuartige Arbitrary Lagrangian-Eulerian (ALE) Methode um solche in (Navier-Stokes) Fluiden eingebetteten elastischen Schalen zu simulieren. Dadurch, dass das Gitter an die elastische Oberfläche angepasst ist, kombiniert die vorgeschlagene Methode hohe Genauigkeit mit Effizienz in der Berechnung der Lösungen. Folglich kann man die Simulationen mit einer verhältnismäßig geringen Gitterauflösung durchführen. Der Fokus dieser Arbeit liegt bei achsensymmetrischen Formen und Strömungen, wie sie bei vielen biophysikalischen Anwendungen zu finden sind. Neben einer allgemeinen dreidimensionalen Beschreibung formulieren wir achsensymmetrische Kräfte auf der Oberfläche, für welche wir eine Diskretisierung mit der Finite Differenzen Methode vorschlagen, welche an eine Finite-Elemente Methode für die umgebenden Fluide gekoppelt ist. Weiterhin entwickeln wir eine Strategie zur impliziten Kopplung der Kräfte, um Zeitschrittrestriktionen zu reduzieren. In verschiedenen numerischen Tests werden wir zeigen, dass akkurate Ergebnisse schon in einer Größenordnung von Minuten auf einer Single-Core CPU erreicht werden können. Die Methode wurde in drei aktuellen Anwendungen verwendet, wobei mindestens zwei davon nach unserer Kenntnis im Moment mit keiner anderen numerischen Methode simuliert werden können: Zunächst präsentieren wir Simulationen von biologischen Zellen, die im Zuge eines RT-DC (Real-Time Deformability Cytometry) Experiments durch einen schmalen mikrofluidischen Kanal advektiert und dabei verformt werden. Danach zeigen wir die Ergebnisse erster Simulationen der uniaxialen Kompression biologischer Zellen zwischen zwei parallelen Platten im Zuge eines AFM Experiments. Schließlich präsentieren wir Resultate erster Simulationen von neuartigen mikroschwimmenden Schalen, welche lediglich durch äußere Einflüsse (wie z.B. Ultraschall), zum Schwimmen angeregt werden können. / The dynamics of membranes, shells, and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface, which exhibits an elastic response to in-plane stretching and out-of-plane bending, possibly accompanied by a surface tension force. In this work, we present a novel arbitrary Lagrangian-Eulerian (ALE) method to simulate such elastic surfaces immersed in Navier-Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can therefore be resolved with relatively few grid points. The focus of this work is on axisymmetric shapes and flow conditions, which are present in a wide range of biophysical problems. Next to a general three-dimensional description, we formulate axisymmetric elastic surface forces and propose a discretization with surface finite-differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. Several numerical test cases show that accurate results can be achieved at computational times on the order of minutes on a single core CPU. Three state-of-the-art applications are demonstrated, where to our knowledge at least two of them cannot be simulated with any other numerical method so far. First, simulations of biological cells being advected through a microfluidic channel and therefore being deformed during an RT-DC (Real-Time Deformability Cytometry) experiment are presented. Then, the uniaxial compression of the cortex of a biological cell during an AFM experiment is investigated. Finally, we present the results of first simulations of the observed shape oscillations of novel microswimming shells which can be locomoted by exterior influences (e.g. ultrasound waves) only.

In the semestral thesis is given basic methods of non-contact measurement heart rate. There is explained Eulerian video magnification method deals with the visualization of the pulse in the videosequence of face. The semestral thesis describes algorithm Viola-Jones face detection in images and algorithm Kanade-Lucas-Tomasi for tracking faces in the videosequence. Part of the work includes design and realization of measurement. There is explained realization of the program and documented execution results, which are discussed. From the results it is designed to guide for optimal recording.

Interactions between three immiscible phases, including incompressible viscoelastic structures and fluids, form standard constellations for countless scenarios in natural science. The complexity of many such scenarios has motivated various research efforts in scientific computing. This work presents novel numerical approaches for two specific of these ternary fluid-structure interaction constellations. The potential of these approaches is demonstrated by diverse applications. First, a phase field model is developed describing the interaction between a fluid and a viscoelastic solid. For this purpose, a Navier-Stokes-Cahn-Hilliard system is considered together with a hyperelastic neo-Hookean model. Based on this, an arbitrary Lagrangian-Eulerian (ALE) method is implemented to simulate the indentation of the solid material in the context of atomic force microscopy, capable of predicting physical parameters. Next, the second approach is developed to describe the interaction between a two-phase fluid and a viscoelastic solid, where fluid and solid are defined on separate domains but aligned at the interface between them. The previously introduced phase field model is used to represent the fluid and an ALE method is used for the motion of the grid, where the fluid-solid interface moves with flow velocity. A unified system is solved in all subdomains, which includes both the balance of mass and momentum and the balance of forces at the fluid-solid interface. Simulations of static and dynamic soft wetting are subsequently presented, in particular a contact line moving over a substrate with oscillating stick-slip behavior. This work combines the advantages of phase field and ALE methods for meaningful simulations and emphasizes validity and numerical stability in all approaches.

In multibody systems, mechanical components (bodies) can be assumed rigid (non-deformable), if their deformation is negligible. For components with non-negligible deformations several methods were developed to represent their deformation. The most widely used method is the floating frame of reference. In this formulation the deformable body is represented by a finite element model whose deformation is described with respect to a local body-fixed frame. Unfortunately, finite element models can include many degrees-of-freedom, which stand in contradiction to the requirements of multibody dynamics. System truncation is therefore inevitable to support computational efficiency. The use of modal data in representing a deformable body is well understood in the multibody community. By truncating modes associated with higher frequencies, the total degrees-of-freedom of the deformable body can be reduced while preserving its dynamic eigen-properties. However, since the finite element model may be in contact with other moving bodies, the reduction technique needs to address the issue of moving boundary conditions. The component mode synthesis reduction methods are such techniques that describe the deflection of all the nodes as a superposition of different types of modes. However, it is limited in the fact that the nodes in contact need to remain in contact throughout a simulation. In some applications these nodes may change, i.e. a node that is in contact with another body or the ground at one instant may become free at the next instant. The present methodologies in multibody modeling of a deformable body with modal data have not yet addressed the issue of changing contact nodes. This research highlights the usefulness of orientation invariant characteristics of some deformable bodies. It proposes to define orientation invariant degrees-of-freedom of the reduced model in Eulerian space, while the remaining degrees-of-freedom are defined in Lagrangian space. In some circumstances, this approach can resolve the issue of changing contact nodes. The combination of Eulerian and Lagrangian formulation for component mode synthesis reduced finite element models is a new concept in deformable multibody dynamics.