Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described

[Research activities in applied mathematics, fluid mechanics, and computer science]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995

Modeling Acoustic Microfluidic Phenomena in Unconventional Geometries

In this work, the performance of a piezoelectrically-actuated ultrasonic droplet generator is analyzed by modeling the harmonic response of a two-dimensional representation of the device cross-section. Observed vibrational and acoustic resonances provide insight into optimal design conditions to achieve efficient, robust droplet ejection. Numerical simulations highlight the importance of the coupled electrical and mechanical behavior of the resonator assembly and show that elastic modes can effectively amplify or dampen acoustic modes within the fluid chamber. Experimentally-validated modeling results guide development of an optimization strategy to further improve device performance. In addition, the standing acoustic field that is the focus of the harmonic response model is incorporated into a custom simulation of the acoustophoretic migration of microparticles. Particles achieve terminal distributions at pressure nodes in the quiescent fluid, exhibiting remarkable agreement with experimental observations. The migratory speed of microparticles in a simple rectangular fluid chamber geometry has been shown to be inversely proportional to the square of the particle radius. Here, this relationship is confirmed for particle migration in more complex acoustic microfluidic geometries

Modeling Acoustic Microfluidic Phenomena in Unconventional Geometries

In this work, the performance of a piezoelectrically-actuated ultrasonic droplet generator is analyzed by modeling the harmonic response of a two-dimensional representation of the device cross-section. Observed vibrational and acoustic resonances provide insight into optimal design conditions to achieve efficient, robust droplet ejection. Numerical simulations highlight the importance of the coupled electrical and mechanical behavior of the resonator assembly and show that elastic modes can effectively amplify or dampen acoustic modes within the fluid chamber. Experimentally-validated modeling results guide development of an optimization strategy to further improve device performance. In addition, the standing acoustic field that is the focus of the harmonic response model is incorporated into a custom simulation of the acoustophoretic migration of microparticles. Particles achieve terminal distributions at pressure nodes in the quiescent fluid, exhibiting remarkable agreement with experimental observations. The migratory speed of microparticles in a simple rectangular fluid chamber geometry has been shown to be inversely proportional to the square of the particle radius. Here, this relationship is confirmed for particle migration in more complex acoustic microfluidic geometries

Institute for Computational Mechanics in Propulsion (ICOMP) fourth annual review, 1989

The Institute for Computational Mechanics in Propulsion (ICOMP) is operated jointly by Case Western Reserve University and the NASA Lewis Research Center. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1989 are described

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is operated by the Ohio Aerospace Institute (OAI) and the NASA Lewis Research Center in Cleveland, Ohio. The purpose of ICOMP is to develop techniques to improve problem-solving capabilities in all aspects of computational mechanics related to propulsion. This report describes the accomplishments and activities at ICOMP during 1993

에너지흐름해석법을 이용한 다공성 재료 내 에너지 전달에 관한 연구

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계항공공학부, 2022. 8. 강연준.본 연구에서는 열전도 상사를 기반으로 고주파 대역에서 주로 감쇠가 작은 구조물의 응답을 예측하기 위하여 활용된 에너지 흐름해석법 (energy flow analysis, EFA)를 기반으로, 다공성 재료 내부의 에너지 전달을 나타내는 에너지 지배방정식을 제안한다. 연구의 서두에서는 에너지 모델 개발에 필요한 에너지 표현식을 도출하기 위하여 Biot 이론을 바탕으로, 다공성 재료의 energy-conservation-dissipation corollary를 유도하였다. 해당 기법의 활용 가능성을 검토하기 위하여, 등가유체모델을 이용하여 음향학적 응답의 기술이 비교적 용이한 rigid 및 limp형 다공성 재료에 대하여 EFA기법을 우선적으로 적용하였다. 수직 및 사입사하는 음파에 의해 재료 내부에 전달되는 균질파 (homo-geneous) 및 비균질파(nonhomogeneous)의 에너지 전달을 기술하는 지배방정식을 유도하였으며, 구조물의 에너지 모델에 사용되는 군속도와 손실계수가 에너지속도와 등가손실 계수로 치환됨을 확인하였다. 또한 등가유체모델 활용에 있어 요구되는 고체상의 강체특성이 frame-borne 파동의 감쇠 효과를 저감시킴으로써, airborne 파동만을 고려하는 강체에너지 모델의 활용범위가 제한됨을 확인하였다. 마지막으로, 탄성다공재료의 에너지 모델을 유도하기 위하여 고체상과 유체상의 탄성계수 및 유효밀도와 파동의 종류에 따른 두 상(phase)간의 상대운동을 고려하여 등가종체적계수와 밀도를 정의하였다. 해당 등가 물성은 유체모델의 등가체적계수 및 등가밀도와 유사한 역할을 하며 이를 기반으로 파동의 종류에 따른 에너지 거동을 체적 평균 관점에서 기술하였다. 이를 통해 탄성다공재료 내부를 통해 전달되는 두 종의 종파와 단일 횡파의 에너지 분포를 예측하는 에너지 모델을 유도할 수 있었으며, 다공성 재료가 두 패널사이의 장착되는 조건에서 에너지 모델의 정확도를 평가하였다. 최종적으로, Biot이론을 기반으로 예측한 에너지 분포 결과와 비교함으로써 고주파 범위에서 제안한 모델의 유효성을 확인하였다.This study proposes energy governing equations in the form of heat conduction laws to represent energy propagation in porous materials within the framework of energy flow analysis (EFA), which has been widely applied to a variety of structure to predict vibrational responses at high frequencies based on a heat conduction analogy. At the beginning of work, the energy-conservation-dissipation corollary for porous materials is discussed based on the Biot theory for deriving energy expressions required to develop energy models. The heat conduction approach is first applied to the rigid- and limp-frame porous materials, whose acoustic reponses can be described using equivalent fluid models. The resulting energy equations, which characterize energy propagation behaviors of homogeneous and inhomogenous waves in a space-averaged sense, are similar to those in classical EFA with the differences that the energy velocity and effective loss factor, respectively, are used in place of the group velocity and loss factor included in the energy models for structures. The capabilities of the energy models are demonstrated using configuration in which the porous layer placed on a hard wall is subject to normal and oblique incident sound waves. The results of the numerical simulations show that from an energy perspective, the use of the rigid-frame energy model is more resticitive than that of the limp-frame model due to the presence of the frame-borne wave, whose ampltiude can be less attenuated than airborne waves. For the derivation of energy models for poroelastic materials, the equivalent longitudinal bulk modulus and density are defined based on the elastic and inertial coefficient of the frame and interstitial fluid and the relative motion between them. They play similar roles to those of the equivalent bulk modulus and density of the equivalent fluid models for rigid- and limp-frame porous materials and are used to describe the energy behavior of each propagating mode in terms of the volume-averaged variables. The resulting energy models describe the energy propagation carried by the two dilatational waves and one shear wave. Their capabilities are demonstrated in cases where a poroelastic layer is used to fill the space between two panels. The prediction results of energy models are in good agreement with the exact energy distributions of each wave calculated from Biot's displacement formulation at high frequencies.I. INTRODUCTION 1 II. ISOTROPIC ELASTIC POROUS MATERIAL THEORY 13 2.1 Introduction 13 2.2 Stress-strain relations 15 2.3 Dynamic equations 18 2.4 Wave equations 20 III. REPRESENTATIONS OF ENERGY QUANTITIES FOR POROUS MATERIALS 25 3.1 Introduction 25 3.2 Derivation of energy conservation corollary 27 3.2.1 A porous elastic solid containing an ideal fluid 27 3.2.2 A porous viscoelastic solid containing a thermoviscous fluid 34 IV. ENERGY MODELS FOR RIGID- AND LIMP-FRAME POROUS MATERIALS 44 4.1 Introduction 44 4.2 Equivalent fluid models 46 4.2.1 Equivalent bulk modulus and density 46 4.2.2 Energy field representations 52 4.3 Development of energy models for homogeneous waves 56 4.3.1 Classical energy flow models 56 4.3.2 Derivation of energy relationships 59 4.3.2.1 A general propagative approach 59 4.3.2.2 A local average-based approach 63 4.3.2.3 A modeling approach for porous materials 65 4.3.3 Energy governing equations 68 4.4 Development of energy models for inhomogeneous waves 70 4.4.1 Partial energy relationships 71 4.4.2 Energy governing equations 73 4.5 Numerical examples and discussion 74 V. ENERGY MODELS FOR ELASTIC POROUS MATERIALS 101 5.1 Introduction 101 5.2 Concept of equivalent longitudinal bulk modulus and density 103 5.2.1 Energy quantities representations 103 5.2.2 Dispersion relationships 107 5.3 Energy models for homogeneous waves 110 5.3.1 Partial energy relationships 110 5.3.2 Energy governing equations 113 5.3.3 Performance of energy models 115 5.3.3.1 Evaluation criteria 115 5.3.3.2 Interference coefficients 119 5.4 Energy models for inhomogeneous waves 124 5.4.1 Dilatational waves 125 5.4.2 Shear waves 129 5.5 Numerical examples and discussion 132 VI. CONCLUSION AND RECOMMENDATIONS 160 REFERENCES 164 Appendix A – Finite element formulation of energy equations 172 국 문 초 록 180박

Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discuss some general conceptual differences between the two approaches. Second, a detailed study of both models is proposed, where differences are made evident at the aid of deriving a hypoelastic-type model corresponding to the hyperelastic model and a particular equation of state used in this paper. Third, using the same high order ADER Finite Volume and Discontinuous Galerkin methods on fixed and moving unstructured meshes for both models, a wide range of numerical benchmark test problems has been solved. The numerical solutions obtained for the two different models are directly compared with each other. For small elastic deformations, the two models produce very similar solutions that are close to each other. However, if large elastic or elastoplastic deformations occur, the solutions present larger differences.Comment: 14 figure

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science