**Multi-phyiscs and Multi-scale Modeling of a photo-responsive Liquid Crystal Elastomers**

Our research is to study fundamental field-coupled phenomena of adaptive materials and their integration into structures and devices. New methodologies that couple microstructure evolution with large deformation continuum mechanics are under investigation to unify a broad range of "smart" materials. Combinations of theory and numerical methods, including both determinstic and stochastic based models are being used to understand materials ranging from ferroelectric compositions, magnetostrictive compounds, shape memory alloys, and a number of functional elastomers and nanocomposites. These new methodologies are critical to advance the understanding of adaptive materials and facilitate the design of adaptive structures. The following example is a photo-responsive Azo-benzene LCN showing large bending due to the external light. Our current work is focused on understanding how liquid crystal domain structures create fast response, large deformation in the presence of polarized light and mechanical loads. Soft elasticity of a nematic phase liquid crystal elastomer is shown in the first image on the right. The image illustrates photoelastomer deformation from polarized light.

**Application of a cholesteric liquid crystal elastomer for aerodynamic applications and its physics on electromagnetic waves **

We are exploring the field-coupled properties of liquid crystal elastomers (LCEs) for integration into a number of adaptive structure applications. These materials exhibit a variety of fascinating properties including photomechanical coupling, shape memory, electrostriction, and chemically induced deformation. Our current work is focused on understanding how liquid crystal domain structures create fast response, large deformation in the presence of polarized light and mechanical loads. Soft elasticity of a nematic phase liquid crystal elastomer is shown in the first image on the right. This monodomain to polydomain transitions that explain soft elastic behavior. The second image illustrates photoelastomer deformation from polarized light. A cubic B-spline plate model was used to obtain high speed computations for nonlinear control applications.

**An efficient/effective fluid-structure interaction model development **

A new class of photomechanical liquid crystal networks (LCNs) has emerged, which generate large bending deformation and fast response times that scale with the resonance of the polymer films. Here, a numerical study is presented that describes the photomechanical structural dynamic behavior of an LCN in a fluid medium; however, the methodology is also applicable to fluid-structure interactions of a broader range of adaptive structures. Here, we simulate the oscillation of photomechanical cantilevers excited by light while simultaneously modeling the effect of the surrounding fluid at different ambient pressures. The photoactuated LCN is modeled as an elastic thin cantilever plate, and gradients in photostrain from the external light are computed from the assumptions of light absorption and photoisomerization through the film thickness. Numerical approximations of the equations governing the plate are based on cubic B-spline shape functions and a 2nd order implicit Newmark central scheme for time integration. For the fluid, three dimensional unsteady incompressible Navier-Stokes equations are solved using the arbitrary Lagrangian Eulerian (ALE) method, which employs a structured body-fitted curvilinear coordinate system where the solid-fluid interface is a mesh line of the system, and the complicated interface boundary conditions are accommodated in a conventional finite-volume formulation. Numerical examples are given which provide new insight into material behavior in a fluid medium as a function of ambient pressure.

**Development of efficient turbulent flow computation method using LES **

Simulation of turbulent flows at high Reynolds numbers is an important but difficult issue in engineering analysis and design. Our research is focused on the development of efficient turbulent flow computation method using a continuous RANS-LES model and a grid redistribution technique. A unified treatment of turbulent scales ranging from large energy containing eddies to small sub-grid scales is achieved by a continuous modeling function which is uniquely determined by a local mesh size and an integral length scale. With the mixing length assumption for calculation of the integral length scale in this function, the RANS computation is enforced in the wall layer of a turbulent flow and LES computation is enforced in the outer layer of it. The grid redistribution is introduced for the well-resolved turbulent flow results near the wall. Good simulation results for both mean flow and turbulence intensities in the turbulent pipe flow are achieved with the continuous RANSLES model. The figures shown below are the computation results in a turbulent pipe flow using the current method.

**Mesh refinement for complex geometry and for complicated flow computations **

An adaptive structured mesh redistribution method (ASMRM) that permits smooth transition from non-uniformly distributed boundary points to solution-adaptive interior points and enables the resolution of complex flow in the complex boundary region as well as away from the boundary is proposed. It is a variant of the traditional variational technique. It involves a combination of static and dynamic monitor functions, the former for mesh distribution in the vicinity of a complex boundary and the latter for mesh adaption with the evolving solution elsewhere. Its effectiveness is demonstrated on some example problems, and it is then applied to a chevron nozzle. The proposed method is shown to be capable of generating a mesh with a good balance of orthogonality and smoothness in the entire domain.

**Development of highly accurate discontinuous spectral element method for a comlex geometry **

Membrane wings are used both in nature and small aircraft as lifting surfaces. Separated flows are common at low Reynolds numbers and are the main sources of unsteadiness. Yet, the unsteady aspects of the fluidâ€“structure interactions of membrane airfoils are largely unknown.

The goal is to develop an understanding of fluid-structure interactions at low Reynolds number so that wing deformations can be altered for flow and flight control and to examine the ability of membrane wings in fixed wing applications to alter the flow characteristics. Dielectric Elastomer Membrane is used to control the tension in the membranes and hence the flexibility properties. The following figures represent experimental setup, operation principle, experimental and numerical results.

Computational Aeroacoustics

**Prediction of fine-scale and large-scale turbulent mixing noise in a supersonic jet **

Aircraft industry is a significant contributor to the US economy, boasting annual sales in excess of $36 billion and providing nearly a million jobs. To maintain our share of world market, improvement and advances in technology are critical. One area of great importance is the reduction of aircraft. The increasing demand for quiet, efficient and clean engines by airlines and the general public has prompted intense research effort on aerodynamically generated noise.

The present work is to effectively predict fine-scale and large-scale turbulent mixing noise from dual stream jets. The following figure represents the main dominant noise sources in a commercial airplane. To reduce the noise level, several methodologies has been applied, which are shown in the figure. Related to this issue, we performed numerical simulation for an acoustic liner, a dual-stream jet, and a chevron nozzle jet widely used for noise reduction recently. The bottom figures represent noise spectra generated by a dual steam nozzle without a plug in a highly subsonic condition.

**Impedance model development for the propagation of broadband noise **

An accurate and practical surface impedance boundary condition in the time domain has been developed for application to broadband-frequency simulation in aeroacoustic problems. To show the capability of this method, two kinds of numerical simulations are performed and compared with the analytical/experimental results: one is acoustic wave reflection by a monopole source over an impedance surface and the other is acoustic wave propagation in a duct with a finite impedance wall. Both single-frequency and broadband-frequency simulations are performed within the framework of linearized Euler equations. A high-order dispersion-relation-preserving finite-difference method and a low-dissipation, low-dispersion Rungeâ€“Kutta method are used for spatial discretization and time integration, respectively. The results show excellent agreement with the analytical/experimental results at various frequencies. The method accurately predicts both the amplitude and the phase of acoustic pressure and ensures the well-posedness of the broadband time-domain impedance boundary condition.

**Direct simulation of jet screech tone in a supersonic jet flow **

The purpose of this study is to perform direct simulation of jet screech tone in a supersonic jet flow and to show that the jet screech noise can be obtained using URANS approach by an aeroacoustic feedback loop mechanism. Mode transition of the axi-symmetric screech tone in the low supersonic Mach number range from 1.0 to 1.20 is numerically analyzed. The axi-symmetric Navier-Stokes equations and the k-e turbulence model are solved in the cylindrical coordinate system. The dispersion-relation-preserving(DRP) scheme is applied for space discretization and the optimized four levels marching method are used for time integration. At low supersonic Mach numbers with an axi-symmetric A1 mode in the simulation. it is shown that acoustic propagation due to the nonlinear effects is seen in the lateral direction and the screech tone frequency is the same as the vortex passing frequency due to the generation of intense large-scale vortical motions.

**Understanding of flow physics and impulsive noise generation characteristics **

A numerical study of a complex muzzle blast flow field is performed to understand the evolution of muzzle flow structures and to examine the sound wave generation mechanisms in the near field. The axisymmetric Euler equations are solved by a dispersion-relation-preserving (DRP) finite-difference scheme with 4th order accurate spatial discretization and an optimized four-level marching method for time integration. The analysis of vortex dynamics based on the vorticity transport equation shows that the dilatation term contributes more than the baroclinic term to vorticity generation and deformation. The motion of the vortex structures is found to be similar in the cases studied here: the main vortex formation, additional vortex generation and their interactions. The Helmholtz decomposition and acoustic perturbation equations are used to analyze the sound generation mechanism in the muzzle flow. The most significant sound source term is identified and the dominant sound generation phenomenon is shown to occur near the vortex ring region and not in the shocked jet flow.