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Numerical solution of conjugate heat transfer (CHT) problems in multi-region domains is a challenging issue in terms of efficiency and stability due to inherent coupling between governing equations in separate sub-domains. This paper aims at comparing two distinct strategies for coupling energy equations at interface of regions: partitioned and monolithic. While the former enforces strong coupling via iterative procedures, the latter suggests simultaneous solution of energy equation throughout all regions at once. More precisely, the primary objective of this study is to compare computational costs for three finite volume- based CHT solvers which share a same method for handling pressure-velocity coupling in the fluid, i.e. semi-implicit projection method, and are distinguished from the coupling strategy for energy equation at interface of interacting sub-domains. The first method applies simultaneous solution of energy equation across all regions while second and third ones use separate solver for each region with difference in handling iterative loops. The accuracy and convergence rate of three algorithms are assessed via transient solution of conjugate free convection in fluid and conduction in vertical wall. Finally, it is concluded that, in contrast to partitioned solver in OpenFOAM for CHT problems, employing a separate loop to enforce energy-energy coupling per iteration, can be much more beneficial in terms of computational costs.

We consider a mathematical model for the interactions of an elastic body fully immersed in a viscous, incompressible fluid. The corresponding composite PDE system comprises a linearized Navier-Stokes system and a dynamic system of elasticity; the coupling takes place on the interface between the two regions occupied by the fluid and the solid, respectively. We specifically study the regularity of boundary traces (on the interface) for the fluid velocity field. The obtained trace regularity theory for the fluid component of the system -- of interest in its own right -- establishes, in addition, solvability of the associated optimal (quadratic) control problems on a finite time interval, along with well-posedness of the corresponding operator Differential Riccati equations. These results complement the recent advances in the PDE analysis and control of the Stokes-Lam\'e system.

Flexible inhibitors are generally used in solid rocket motors (SRMs) as a means to control the burning of propellant. Vortices generated by the flow of propellant around the flexible inhibitors have been identified as a driving source of instabilities that can lead to thrust oscillations in launch vehicles. Potential coupling between the SRM thrust oscillations and structural vibration modes is an important risk factor in launch vehicle design. As a means to predict and better understand these phenomena, a multidisciplinary simulation capability that couples the NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This capability is crucial to the development of NASA's new space launch system (SLS). This paper summarizes the efforts in applying the coupled software to demonstrate and investigate fluid-structure interaction (FSI) phenomena between pressure waves and flexible inhibitors inside reusable solid rocket motors (RSRMs). The features of the fluid and structural solvers are described in detail, and the coupling methodology and interfacial continuity requirements are then presented in a general Eulerian-Lagrangian framework. The simulations presented herein utilize production level CFD with hybrid RANS/LES turbulence modeling and grid resolution in excess of 80 million cells. The fluid domain in the SRM is discretized using a general mixed polyhedral unstructured mesh, while full 3D shell elements are utilized in the structural domain for the flexible inhibitors. Verifications against analytical solutions for a structural model under a steady uniform pressure condition and under dynamic modal analysis show excellent agreement in terms of displacement distribution and eigenmode frequencies. The preliminary coupled results indicate that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor. This insight could have profound implications for SRM and flexible inhibitor designs for current and future launch vehicles including SLS.

We consider the finite element method solving a fluid-solid interaction (FSI) problem in two dimensions. The original problem is reduced to an equivalent nonlocal boundary value problem through an exact Dirichlet-to-Neumann (DtN) mapping defined on an artificial boundary enclosing the solid. The solvability results are established for the corresponding variational problem and its modified form resulting from truncation of the DtN mapping. Regarding to the numerical solutions, we derive a priori error estimates involving the effects of both finite element discretization and infinite series truncation. Numerical examples are presented to illustrate the accuracy of numerical schemes and validate the theoretical results.

This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect approaches. Existence and uniqueness results for variational solutions of boundary integral equations equations are established. Since in all these boundary variational formulations, the hypersingular boundary integral operator associated with the time-harmonic Navier equation is a dominated integral operator, we also include a new regularization formulation for this hypersingular operator, which allows us to treat the hypersingular kernel by a wealkly singular kernel. Numerical examples are presented to verify and validate the theoretical results.

A new analysis procedure has been used to evaluate the propellant grain/flow stability of a new, five-segment Space Shuttle solid rocket booster. The fluid-structural interaction (FSI) analysis of the ETM-3 motor used PYTHON, a powerful programming language, and FEM BUILDER, a pre- and post processor developed by ATK Thiokol Propulsion under contract to the AFRL, to automatically couple the ABAQUS structural solver with FLUENT, the computational fluid dynamics (CFD) solver. This iterative process automatically used the results of one solver as the inputs to the other solver until convergence to a solution was obtained. The ETM-3 motor was basically an reusable solid rocket motor (RSRM) with an additional center segment added. The additional segment and greater nozzle diameter increased mass flow and mach number in the motor. Because of this harsher flow environment, it was necessary to conduct a detailed FSI analysis to ensure propellant grain stability against boot-strapping. This paper details the FSI analysis work done for ETM-3. The analyses conducted and documented in this report assumed linear elastic material behavior and steady state fluid behavior without time response in either the structural or fluid models.

The ETM-3 motor is basically an RSRM motor with an additional center segment added. The propellant burn rate was lowered to account for the additional surface area of the motor and the nozzle throat diameter was increase. The additional segment also increased mass flow and mach number in the motor. Because of this harsher flow environment, it was thought necessary to chamber the leading edges of every segment and conduct a detailed fluid/structural interaction (FSI) analysis to ensure propellant grain stability against boot-strapping. The analyses showed that the addition of the 3 inch radial by 24 inch axial chamber on the leading edges of the center/forward, center, center/aft, and aft segments was sufficient to give the ETM-3 motor stable grain displacements at much lower than expected propellant moduli. This report documents the FSI analysis work done for ETM-3. The analyses conducted and documented in this report assumed linear elastic material behavior and quasi-steady state fluid behavior without time response in either the structural or fluid models. Thus, the analyses represented only an approximation at a single snapshot in time. This led to selecting the largest chamfer size analyzed herein to get the biggest safety factor against boot-strapping.

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It is difficult to derive the solid--fluid transition from microscopic models. We introduce particle systems whose potentials do not decay with distance and calculate their partition function exactly using a method similar to that for lattice systems with infinite-range interaction. In particular, we investigate the behaviors of examples among these models, which become a triangular, body-centered cubic, face-centered cubic, or simple cubic lattice in low-temperature phase. The transitions of the first three examples are of the first order, and that of the last example is of the second order. Note that we define the solid phase as that whose order parameter, or Fourier component of the density, becomes nonzero, and the models we considered obey the ideal-gas law even in the solid phase.

This work outlines a unified multi-threaded, multi-scale High Performance Computing (HPC) approach for the direct numerical simulation of Fluid-Solid Interaction (FSI) problems. The simulation algorithm relies on the extended Smoothed Particle Hydrodynamics (XSPH) method, which approaches the fluid flow in a Lagrangian framework consistent with the Lagrangian tracking of the solid phase. A general 3D rigid body dynamics and an Absolute Nodal Coordinate Formulation (ANCF) are implemented to model rigid and flexible multi-body dynamics. The two-way coupling of the fluid and solid phases is supported through use of Boundary Condition Enforcing (BCE) markers that capture the fluid-solid coupling forces by enforcing a no-slip boundary condition. The solid-solid short range interaction, which has a crucial impact on the small-scale behavior of fluid-solid mixtures, is resolved via a lubrication force model. The collective system states are integrated in time using an explicit, multi-rate scheme. To alleviate the heavy computational load, the overall algorithm leverages parallel computing on Graphics Processing Unit (GPU) cards. Performance and scaling analysis are provided for simulations scenarios involving one or multiple phases with up to tens of thousands of solid objects. The software implementation of the approach, called Chrono::Fluid, is part of the Chrono project and available as an open-source software.

This work outlines a unified multi-threaded, multi-scale High Performance Computing (HPC) approach for the direct numerical simulation of Fluid-Solid Interaction(FSI) problems. The simulation algorithm relies on the extended Smoothed Particle Hydrodynamics (XSPH) method, which approaches the fluid flow in a Lagrangian framework consistent with the Lagrangian tracking of the solid phase. A general 3D rigid body dynamics and an Absolute Nodal Coordinate Formulation(ANCF) are implemented to model rigid and flexible multibody dynamics. The two way coupling of the fluid and solid phases is supported through use of Boundary Condition Enforcing (BCE) markers that capture the fluid-solid coupling forces by enforcing a no-slip boundary condition. The solid-solid short range interaction, which has a crucial impact on the small-scale behavior of fluid-solid mixtures, is resolved via a lubrication force model. The collective system states are integrated in time using an explicit, multi-rate scheme. To alleviate the heavy computational load, the overall algorithm leverages parallel computing on Graphics Processing Unit (GPU) cards. Performance and scaling analysis are provided for simulations scenarios involving one or multiple phases with up to tens of thousands of solid objects. The software implementation of the approach, called Chrono::Fluid, is part of the Chrono project and available as an open-source software.

In this paper we study a time-harmonic fluid-solid interaction model problem in one dimension. This is a Helmholtz-type system equipped with boundary and transmission conditions. We show the existence of a unique solution to this problem and study its stability and regularity properties. We analyze the convergence of finite element methods with respect to appropriate energy norms. Computational results are also presented.

One of the goals of the Weapons and Materials Research Directorate of the US Army Research Laboratory (ARL) is to develop propulsion technologies for future gun systems. This effort requires continued improvement of current guns which are already quite close to optimal, and the use of novel, high energy propellants and designs in future weapons. These new designs and propellants make use of next-generation concepts which are not yet well understood. For example, the electrothermal-chemical gun is a hybrid gun which uses a combination of chemical energy and electrical energy to accelerate the projectile. Liquid propellants are also under investigation, raising questions about, for example, the interaction between the liquid propellant (LP) and moving mechanical components in the regenerative liquid propellant gun (RLPG).

Fluid-solid interaction has been a challenging subject due to their strong nonlinearity and multidisciplinary nature. Many of the numerical methods for solving FSI problems have struggled with non-convergence and numerical instability. In spite of comprehensive studies, it has been still a challenge to develop a method that guarantees both convergence and stability. Our discussion in this work is restricted to the interaction of viscous incompressible fluid flow and a rigid body. We take the monolithic approach by Gibou and Min that results in an extended Hodge projection. The projection updates not only the fluid vector field but also the solid velocities. We derive the equivalence of the extended Hodge projection to the Poisson equation with non-local Robin boundary condition. We prove the existence, uniqueness, and regularity for the weak solution of the Poisson equation, through which the Hodge projection is shown to be unique and orthogonal. Also, we show the stability of the projection in a sense that the projection does not increase the total kinetic energy of fluid and solid. Also, we discusse a numerical method as a discrete analogue to the Hodge projection, then we show that the unique decomposition and orthogonality also hold in the discrete setting. As one of our main results, we prove that the numerical solution is convergent with at least the first order accuracy. We carry out numerical experiments in two and three dimensions, which validate our analysis and arguments.

Determination of mass flow rate in a solid rocket motor is critical in the design of a new motor due to its effect on the thrust produced. Fluidstructure interaction (FSI) effects between the combusting gases and propellant alter the motor chamber pressure and mass flow rate. To account for the FSI effects on mass flow rate in an expedited fashion, an automated method of coupling computational fluid dynamics (CFD) to finite element analysis (FEA) is explored. A propellant flap in a cross flow is analyzed. Comparisons are made between an analytical solution, a solely CFD solution, a manual FSI solution, and an automated FSI solution. The one-way FSI analysis, effectively the undeformed CFD solution, overpredicted the pressures and mass flow rates. The FSI analyses with twoway coupling provided a more accurate assessment of solid rocket motor internal ballistics

A computational method for solving nonlinear problems relating to impact and penetration of a rigid body into a fluid type medium is presented. The numerical techniques, based on the Marker-and-Cell method, gives the pressure and velocity of the flow field. An important feature in this method is that the force and displacement of the rigid body interacting with the fluid during the impact and sinking phases are evaluated from the boundary stresses imposed by the fluid on the rigid body. A sample problem of low velocity penetration of a rigid block into still water is solved by this method. The computed time histories of the acceleration, pressure, and displacement of the block show food agreement with experimental measurements. A sample problem of high velocity impact of a rigid block into soft clay is also presented.

In this paper, we present a computationally efficient method for including fluid-solid interactions into direct numerical simulations of the Navier-Stokes equations. This method is found to be as powerful as our earlier formulation [J. Comp. Phys., vol. 249: 243 (2015)], while outperforming the earlier method in terms of computational efficiency. The performance and efficacy of the presented method are demonstrated by computing contact angles of droplets at equilibrium. Furthermore, we study the instability of films due to destabilizing fluid-solid interactions, and discuss the influence of contact angle and inertial effects on film breakup. In particular, direct simulation results show an increase in the final characteristic length scales when compared to the predictions of a linear stability analysis, suggesting significant influence of nonlinear effects. Our results also show that emerging length scales differ, depending on a number of physical dimensions considered.

A capability to couple NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This paper summarizes the efforts in applying the installed coupling software to demonstrate/investigate fluid-structure interaction (FSI) between pressure wave and flexible inhibitor inside reusable solid rocket motor (RSRM). First a unified governing equation for both fluid and structure is presented, then an Eulerian-Lagrangian framework is described to satisfy the interfacial continuity requirements. The features of fluid solver, Loci/CHEM and structural solver, CoBi, are discussed before the coupling methodology of the solvers is described. The simulation uses production level CFD LES turbulence model with a grid resolution of 80 million cells. The flexible inhibitor is modeled with full 3D shell elements. Verifications against analytical solutions of structural model under steady uniform pressure condition and under dynamic condition of modal analysis show excellent agreements in terms of displacement distribution and eigen modal frequencies. The preliminary coupled result shows that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor.

In the nuclear fuel assembly, the mixing vanes are solid components which are attached to the spacer grid. These vanes would increase heat transfer rate from the fuel wall. The force induced by flow may expose the vanes to excessive stress and bending, which in turn, it impairs the mixing vanes. In order to improve the heat transfer rate and decrease the vibrational forces, vanes are usually positioned at a certain angle regarding to the flow axis. This study investigates displacement of vanes in three angles of 65, 70 and 75 degrees for a specific geometry using the fluid-solid interaction method. First, the fluid flow is solved using a Finite Volume Method (FVM) solver and the forces exposed by the flow to the vanes are estimated. Next, the displacement of the vanes due to the applied forces is calculated by the Finite Element Method (FEM). Comparison between calculated pressure drop in this study and experimental result show a difference less than 10%. The maximum pressure drop is occurred when the vanes have 65° angle. The most turbulence intensity is obtained at the angle of 75°. Also, according to the frequency estimation, it was observed that with increasing frequency the displacement's amplitude would decrease.