Symmetry Boundary Conditions Research Articles

CFD Simulations of the Molten Salt Fast Reactor

The molten salt fast reactor (MSFR) is a fast-spectrum molten salt reactor concept, where the fuel salt flows freely through a toroidal core (2 m high × 2 m in diameter). The flow through this core is turbulent (Reynolds number ≈ 5 × 10 5 ) and presents several recirculation areas. Several thermal-hydraulic studies of the steady-state MSFR flow have been performed, where the thermal power distribution was fixed and the Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES) approaches were used. Different geometries were considered, from 1/16th of the core to the full core. The RANS simulations were performed first. The use of symmetry boundary conditions in these simulations had a very limited impact on the results while greatly speeding up the calculations. In the LES formulation, however, the symmetry boundary conditions had a large impact on the velocity and temperature fields, and so could not be used. While the RANS fields and the LES mean fields differed quite heavily, no particular hot spots appeared in the LES fields. Analysis of the LES temperature evolution in the center of the core revealed fluctuations of ± 20°C at a speed of 100°C·s−1.

Sidewall influence of varying free stream Mach number in ramp induced shock wave boundary layer interactions

This study investigates the three-dimensional (3D) effects introduced by the end walls for an aspect ratio of 1 in ramp-induced shock wave boundary layer interactions. The simulations are performed using a symmetry boundary condition in the spanwise direction at free-stream Mach numbers in 3D. The simulations are performed using an in-house compressible supersonic solver “OpenSBLIFVM”. Two free stream Mach numbers 2.5, and 3 are used in the current work, and the simulated results are compared with the aspect ratio 1 simulations by Mangalagiri and Jammy. The inflow is initialized with a similarity solution; its Reynolds number based on the boundary layer thickness is adjusted such that the Reynolds number at the start of the ramp is kept at 3×105 for all simulations. From the results, it is evident that the introduction of sidewalls resulted in a shorter centerline separation length when compared with the two-dimensional (2D) simulations. This contradicts the results at Mach 2 by Mangalgiri and Jammy where the vortex observed at Mach 2 in the central separation region disappeared with increasing free-stream Mach number. Additionally, the topology of interaction shifted from owl-like separation of the second kind to the first kind when the freestream Mach number increased from 2 to 2.5. It can be concluded that the interaction topology is crucial to the increase or decrease of the central separation length when compared to 2D simulations.

The voxelized photon Monte Carlo method for hypersonic radiation modeling

A novel method of solving for radiative energy transfer at hypersonic speeds, the voxelized photon Monte Carlo (voxPMC) method, is presented. The voxPMC method is implemented in the Discrete Adaptive Radiative Transport (DART) code and results are given for radiative heat transfer of Mach 9.6 flow over a cylinder. Simulation parameters for this method were tuned to determine requirements for accurate solutions, using benchmark results from NASA’s Nonequilibrium Radiative Transport and Spectra Program (NEQAIR). It was found that of the tuning parameters, the mesh resolution and number of simulated photon packets had the largest effect on the resulting solution accuracy. It was found that 108 photon packets, or 5 photon packets per smallest mesh cell dimension, produced accurate results. Voxel resolution refinement and optical boundary conditions were also tested and 2 voxels per smallest mesh cell dimension and an optical symmetry boundary condition produced results that aligned with those given by NEQAIR. Future work will determine if recommendations for these parameters hold for a wider range of applications. Loose coupling between flowfield results and radiation analysis resulted in radiative cooling, which smeared the shock gradients and led to a slight increase in convective heating at the stagnation point.

Effects of the Seal Wire on the Nonlinear Dynamics of the Aircraft Engine Turbine Blades

Abstract Complicated systems made of multiple components are known to be difficult to model, considering their solutions can change dramatically even with the slightest variations in conditions. Aircraft engines contain such complicated systems, and some components in aircraft engines' turbines can cause significant changes in the system's overall response. Hence, this study is focused on investigating the behavior of a turbine blade of an aircraft engine and the effects of the contact between the blade and the seal wire on the dynamics of the blade-disk system. The investigation is performed via various numerical simulations in time and frequency domains. One sector of the bladed disk is modeled using the finite element method with the lock plate and the seal wire imposing cyclic symmetry boundary conditions in the static, modal, and frequency domain forced response analyses. In time domain analyses, the cyclic symmetry is replaced with simplified displacement restricting boundary conditions. The time domain analysis contains steady-state forced responses of the system. The results show that contact with the seal wire is not a major source of nonlinearity and damping. The contacts with the lock plate contribute more to the vibration damping than the seal wire. However, compared to the contacts at the root of the blade, both components remain less significant with regard to frictional damping and nonlinearity.

Evaluation of the influence of the viscous sublayer on the mechanical stability of fuel plates under axial flow conditions

The current work aims to investigate the influence of the viscous sublayer on the mechanical stability of fuel element plates under axial flow conditions by means of two-way Fluid Structure Interaction (FSI) numerical simulations. The methodology adopted is that proposed by (Mantecón, 2019; Mantecón and Mattar Neto, 2018), who observed a transition from linear to non-linear behavior between the maximum deflection of the plates in their leading edge with the square of the velocity of the cooling fluid in the channel. The speed at which the transition is identified is the critical speed (Vc). In order to verify the influence of the viscous effects, the CFD domain was discretized from its viscous sublayer. As this approach greatly increases the computational cost, where the characteristics of the flow allowed, symmetry boundary conditions were used. In addition to this approach, it was decided to investigate the ability to solve the FSI problem in steady state. The obtained results confirmed that the boundary layer modeling is sufficient to determine the critical velocity. Furthermore, they also suggest that the steady-state approach and the application of symmetry boundary conditions, where possible, can be used in the design of new fuel elements, supporting traditional methods.

Electrochemical Model for a Three-Electrode Lead Acid Cell: Boundary Conditions for Asymmetric Configurations

A one-dimensional (1D) electrochemical model is developed for a lead-acid demonstration cell comprising two positive electrodes engaging a single negative electrode. Classical 1D models, which analyze a single repeat unit in a full battery, are extended to this non-standard configuration by considering additional porous electrode and electrolyte reservoir domains. The non-standard model necessitates appropriate boundary conditions to couple electrochemical variables in different domains, since symmetry boundary conditions typically employed at the current collector grids are no longer applicable. The modified model, with new boundary conditions, is simulated using standard techniques. Salient modeling and simulation differences compared to a standard lead-acid model are discussed, as are trends in predicted variables. The non-standard model predicts reduced polarization and more uniform utilization of the non-limiting electrodes, in addition to non-zero reaction currents and active material utilization in the terminal electrode faces, which are typically ignored in “unit-cell” analyses. This model is expected to be of substantial utility in guiding evaluations of new lead-acid battery designs through improved prediction of performance of such test configurations. The boundary conditions introduced herein are also useful for 1D modeling of non-standard configurations characterized by multiple, electrochemically interacting porous domains, particularly where spatial current distributions are initially unknown.

Conjugate Heat Transfer Model for an Induction Motor and Its Adequate FEM Model

The primary objective of the research presented in this paper was to design a methodology for analyzing the thermal field of an induction motor that would be of higher fidelity but less time- and cost-consuming and that would deal with air-cooled induction motors of all sizes. The complexity of the simulation is increased by the geometric asymmetry and by the asymmetric character of flow cooling the motor casing caused by the fan’s rotation. This increases demand, especially on computational resources, as creating a simplified numerical model using symmetry boundary conditions is impossible. The new methodology uses the existing findings from many partial articles and literature, which are modified into more accurate relationships suitable for predicting the external thermal field of induction motors. That way, we do not have to solve the thermal field by the conjugate heat transfer method, and it is possible to assess temperature gradients over the entire range. Furthermore, a new relationship between shear strain rate and thermal contact conductivity has been discovered that allows solving heat transfer of fluid adjacent to the internal walls of an induction motor at any location. That approach has not yet been published in the literature, so it can be considered a new method to simplify heat transfer simulation. An experimentally validated new methodology of the induction motor was performed. The so-called digital twin will be used for the virtual optimization of the new designs concerning minimizing losses and maximizing efficiency.

Fast Actuating Multi-Helically Heated Twisted and Coiled Polymer Actuator

The twisted and coiled polymer actuator (TCPA), promisingly used in wearable robots, soft exoskeletons and prosthesis, retains the advantages of convenience, high energy density, scalable stroke and hysteresis-free. However, as a thermal actuator, its dynamic response is still rather low, not only because of its convection improvable long cooling time, but also due to its long heating time. PID control is used to shorten TCPAs' rising time. However, this improvement is restricted by the upper limit of the heater temperature and has not substantially improve the poor heat conduction between nylon and heater. In addition, the high working current is also an important defect limiting TCPAs' application. In this work, we have revealed that the practical thermoelectric model of a TCPA obeys the law of heat transfer with Dirichlet condition. Under the consideration that TCPAs with symmetrical Dirichlet condition can effectively improve their heating performance, we have proposed a multi-helically heated twisted and coiled polymer actuator (MHTCPA). Through physical and simulated experiments, we verify that the MHTCPA has better actuating performance, requires less current, and that the symmetry of boundary conditions is the principal factor to improve the heating performance. Given the same power limit, the MHTCPA has a 20% smaller time constant, adopting a 24% smaller current to reach a 15% higher temperature and takes 50% less time to finish actuation. With the help of closed-loop control method, the actuation of the MHTCPA takes 83% less time compared previous TCPA. For the mechanical properties, the MHTCPA is still hysteresis-free but 25.8% stronger in lifting a 100-g weight.

A coupled approach to model wear effect on shrouded bladed disk dynamics

This paper deals with modelling the effect of wear on the dynamics of the shrouded bladed disk with frictional contacts at the shrouds and the contact interface evolution. Prediction of fretting wear commonly occurring at the contacts of turbomachinery components, and its impact on the dynamics is increasingly researched due to the components subjected to their structural limits for performance and operating at high loading conditions. Over a lifetime, the fretting wear at these contacts could alter the global dynamic response of these bladed disks from the designed operating point and could lead to high vibration amplitudes. This study implements a coupled static/dynamic harmonic balance method (HBM) with wear energy approach and an adaptive wear logic to study the impact on the steady-state nonlinear dynamic response. Firstly, the methodology is applied to a cantilever beam with a contact patch and then to a shrouded bladed disk with shroud contacts using cyclic symmetry boundary conditions. The novelty of the paper is to show the effect of wear on the dynamics with the changing contact pre-load using a coupled approach. A wear acceleration parameter vw,max is defined, and the impact of the choice of this parameter is discussed in detail on the computation time and the accuracy of results. The test cases demonstrate the impact of wear on the dynamic nonlinear response curves and the contact interface evolution for various scenarios.

Investigation on Heat Transfer Characteristics of Rectangular Channels With Internal Rough Surface Naturally Formed by Selective Laser Melting Three-Dimensional Printing

Abstract As a metal three-dimensional (3D) printing technology, selective laser melting (SLM) has been extensively applied to manufacture complex-shaped parts in industries. It is well known that the naturally formed surface by SLM processing is usually rough and irregular. The effects of the rough surface on heat transfer and fluid flow cannot be neglected when SLM is applied to fields such as heat exchangers and cooling equipment. In this paper, a novel bottom-up approach was proposed to build the naturally formed rough surface by SLM 3D printing. Numerical investigation on pressure loss and heat transfer characteristics of rectangular channels has been carried out based on the naturally formed rough model. Constant thermal boundary and symmetry boundary conditions were employed in the procedure of numerical computation. For comparison, a variety of typical surfaces with different roughness elements in previous studies have been introduced and analyzed. Results confirmed that the proposed rough surface modeling method was fully capable of descripting the real 3D-printed surface topography. Compared with the smooth surface, the heat transfer capacity of the 3D-printed rough channel was increased by 8.99%, while the pressure loss was increased by 25.02%. Additionally, 3D-printed rough surface had better overall thermal performance compared to rough surfaces with regular roughness element.

Multiplicity in an optimised kinematic dynamo

Multiplicity in optimal kinematic dynamos exists for certain types of symmetry classes and boundary conditions, at least near the lowest dynamo onset . Here we investigate the NNT type dynamo generated by steady flows with impermeable boundary conditions in a cube, where the letter N or T stands for pseudo-vacuum or superconducting boundary conditions along x, y, z directions, respectively. We find the top two of the three branches in the neighbourhood of have their growth rates crossed over at . Within each branch, the spatial structure of the optimal velocity field gradually shifts with respect to . At about above , the original optimal branch has developed distinct combinations of dominant Fourier modes. In contrast, the first suboptimal branch shows the least change in structure. We then follow the evolution of selected optimised solutions when varies until it becomes unstable. Specific modes in the flow that can destabilise the dynamo are identified. Within the range surveyed, we find that there can be one to two dynamo windows. All three branches generate a steady dynamo near , but the first suboptimal branch can generate an oscillatory dynamo at about eight times , and for both suboptimal branches, the growth rate reaches saturation approximately at . We find the two suboptimal branches create a more robust dynamo action supercritically.

Simulation of crack propagation in a thick-walled cylinder using XFEM

The integrity assessment to evaluate the safety margin of reactor pressure vessels (RPV) often considers only the crack initiation and excludes the crack propagation analysis. This contribution focuses on crack propagation analysis in RPV steels. The eXtended Finite Element (XFEM) method implemented in ABAQUS is applied to a thick-walled cylindrical specimen with a circumferential crack at the inner surface in order to simulate crack propagation in embrittled RPV subjected to Pressurized Thermal Shock (PTS). The thick-walled cylinder considered in this study was tested in the FALSIRE project, which results reported the crack opening displacement (COD) and the crack-arrest cycles occurring during the cooling down process. In order to simulate the cylinder with the XFEM, a reduced three-dimensional finite element (FE) model of a small sector (a slice of the cylinder) is used by applying cyclic symmetry boundary conditions. The COD evolution during the PTS transient is calculated and compared against the experimental COD. In the experiment, the COD shows several initiation-arrest-re-initiation cycles and final arrest. However, the results from the simulation show a smooth continuous increase of the COD indicating a progressive crack growth.

CFD analysis of added mass, damping and induced flow of isolated and cylinder-mounted heave plates at various submergence depths using an overset mesh method

Fluid–structure interaction processes of heave damping plates in forced vertical motion are investigated using a CFD numerical model. First, a single isolated disk is considered with two submergence depths, including a case where the disk is very close to the mean water level with d/D=1/12 (d is the submergence depth and D the diameter of the disk). Then, the case of a disk attached to a vertical cylinder is analyzed, corresponding to one leg of a semi-submersible floater. The open source software OpenFOAM® is used to model the flow around the disk and to extract the relevant hydrodynamic coefficients of the structures. The dynamics of the structure and induced flow and free surface waves are tackled with the overset mesh tool implemented in OpenFOAM®. Considering the rotational symmetry of the problem, an axisymmetry model is used with wedge symmetry boundary conditions. The results are compared with experimental measurements and linearized potential flow modeling approaches with empirical correction. The CFD results of the models of both structures predict well the experimental measurements, including large oscillation periods and various amplitudes of heaving motion, where the potential model results are deteriorated.

Numerical Study of Local Scour around a Submarine Pipeline with a Spoiler Using a Symmetry Boundary Condition

A two-dimensional numerical model for solving the Navier–Stokes equations was developed to investigate the local scour around a submarine pipeline with a spoiler. Both the suspended load and the bed load were considered in the present numerical model. The focus of the present study is to investigate the effects of the spoiler length on the hydrodynamic forces on the pipeline and the spoiler as well as the local scour around the submarine pipeline. The corresponding numerical results show that the mean drag coefficients of the pipeline and the spoiler increase with the increase of the spoiler length. As for the mean lift coefficient, a general decreasing trend with the increasing spoiler length is observed for the pipeline. However, the mean lift coefficient of the spoiler first increases and then decreases with the increasing spoiler length. In addition, it is found that a larger spoiler length leads to a deeper scour depth, and an empirical equation was proposed for predicting the non-dimensional scour depth of submarine pipelines with non-dimensional spoiler length based on the numerical results.

Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a semi-discrete entropy inequality under appropriate boundary conditions. In this work, we describe a discretization of viscous terms in the compressible Navier-Stokes equations which enables a simple and explicit imposition of entropy stable no-slip and reflective (symmetry) wall boundary conditions for discontinuous Galerkin (DG) discretizations. Specifically, we derive methods for imposing adiabatic no-slip and reflective (symmetry) boundary conditions for modal entropy stable DG formulations which preserve a semi-discrete entropy inequality. Numerical results confirm the robustness and accuracy of the proposed approaches.

Existence and structure of symmetric Beltrami flows on compact 3-manifolds

We show that for almost every given symmetry transformation of a Riemannian manifold there exists an eigenvector field of the curl operator, corresponding to a non-zero eigenvalue, which obeys the symmetry. More precisely, given a smooth, compact, oriented Riemannian 3-manifold (M¯,g) with (possibly empty) boundary and a smooth flow of isometries ϕt:M¯→M¯ we show that, if M¯ has non-empty boundary or if the infinitesimal generator is not purely harmonic, there is a smooth vector field X, tangent to the boundary, which is an eigenfield of curl and satisfies (ϕt)⁎X=X, i.e. is invariant under the pushforward of the symmetry transformation. We then proceed to show that if the quantities involved are real analytic and (M¯,g) has non-empty boundary, then Arnold's structure theorem applies to all eigenfields of curl, which obey a symmetry and appropriate boundary conditions. More generally we show that the structure theorem applies to all real analytic vector fields of non-vanishing helicity which obey some nontrivial symmetry. A byproduct of our proof is a characterisation of the flows of real analytic Killing fields on compact, connected, orientable 3-manifolds with and without boundary.

Boundary condition enforcement for renormalised weakly compressible meshless Lagrangian methods

This paper introduces a boundary condition scheme for weakly compressible (WC) renormalised first-order accurate meshless Lagrangian methods (MLM) by considering both solid and free surface conditions.A hybrid meshless Lagrangian method-finite difference (MLM-FD) scheme on prescribed boundary nodes is proposed to enforce Neumann boundary conditions. This is used to enforce symmetry boundary conditions and the implied Neumann pressure boundary conditions on solid boundaries in a manner consistent with the Navier-Stokes equation leading to the accurate recovery of surface pressures. The free surface boundary conditions allow all differential operators to be approximated by the same renormalised scheme while also efficiently determining free surface particles.The boundary conditions schemes are implemented for two renormalised MLMs. A WC smoothed particle hydrodynamics (SPH) solver is compared to a WC generalised finite difference (GFD) solver. Applications in both 2D and 3D are explored. A substantial performance benefit was found when comparing the WCGFD solver to the WCSPH solver with the WCGFD solver realising a maximum speedup in the range of three times over WCSPH in both 2D and 3D configurations. The solvers were implemented in C++ and used the NVIDIA CUDA 10.1 toolkit for the parallelisation of the solvers.

An updated Lagrangian framework for Isogeometric Kirchhoff–Love thin-shell analysis

We propose a comprehensive Isogeometric Kirchhoff–Love shell framework that is capable of undergoing large elasto-plastic deformations. Central to this development, we reformulate the governing thin-shell equations in terms of the mid-surface velocity degrees of freedom, accommodating the material response in the time-rate form while ensuring objectivity. To handle complex multipatch geometries, we propose a consistent penalty coupling technique for enforcing the continuity conditions at patch interfaces. Penalty is also employed to weakly enforce symmetry boundary conditions. A recently proposed non-local penalty contact is adopted as part of the formulation in order to handle complex dynamic crushing simulations. Numerical examples, ranging from static elasto-plastic shell benchmarks to highly dynamic crushing scenarios, validate the accuracy, efficiency and robustness of the proposed framework.

Investigation of the effects of geometrical parameters, eccentricity and perforated fins on natural convection heat transfer in a finned horizontal annulus using three dimensional lattice Boltzmann flux solver

PurposeThe purpose of this paper is to investigate the effects of geometrical parameters, eccentricity and perforated fins on natural convection heat transfer in a finned horizontal annulus using three-dimensional lattice Boltzmann flux solver.Design/methodology/approachThree-dimensional lattice Boltzmann flux solver is used in the present study for simulating conjugate heat transfer within an annulus. D3Q15 and D3Q7 models are used to solve the fluid flow and temperature field, respectively. The finite volume method is used to discretize mass, momentum and energy equations. The Chapman–Enskog expansion analysis is used to establish the connection between the lattice Boltzmann equation local solution and macroscopic fluxes. To improve the accuracy of the lattice Boltzmann method for curved boundaries, lattice Boltzmann equation local solution at each cell interface is considered to be independent of each other.FindingsIt is found that the maximum heat transfer rate occurs at low fin spacing especially by increasing the fin height and decreasing the internal-cylindrical distance. The effect of inner cylinder eccentricity is not much considerable (up to 5.2% enhancement) while the impact of fin eccentricity is more remarkable. Negative fin eccentricity further enhances the heat transfer rate compared to a positive fin eccentricity and the maximum heat transfer enhancement of 91.7% is obtained. The influence of using perforated fins is more considerable at low fin spacing although some heat transfer enhancements are observed at higher fin spacing.Originality/valueThe originality of this paper is to study three-dimensional natural convection in a finned-horizontal annulus using three-dimensional lattice Boltzmann flux solver, as well as to apply symmetry and periodic boundary conditions and to analyze the effect of eccentric annular fins (for the first time for air) and perforated annular fins (for the first time so far) on the heat transfer rate.

مدل سازی عددی و بهینه سازی هندسی اجکتور تک‌فاز مافوق صوت

In the present study, the performance of the 2D single-phase supersonic ejector with working fluid of air is simulated in ANSYS CFX. The aim is to investigate the velocity field, pressure distribution, primary nozzle flow regime, and entertainment ratio in different operational conditions. The primary pressure inlet with bar and the secondary inlet as an opening with bar at different outlet pressures are simulated. The turbulence model is used. The sidewalls are considered symmetry boundary conditions and the no-slip condition is applied to the ejector walls. Then, the ejector geometry is optimized using Multi-Objective Genetic Algorithm (MOGA) in order to reach greater efficiency. Optimization is performed considering geometric parameters including primary nozzle exit diameter, nozzle exit position, diameter, and length of the constant area section. Sensitivity analysis results show that the diameter of constant area section has major effect on the entertainment and pressure ratios as two objective functions. The nozzle exit position and external diameter of primary nozzle are the second and third dominant parameters that respectively influence the performance of the ejector, while the effect of constant area section length is negligible. Results indicate that by increasing the pressure ratio, the shock train moves upstream and at the design point, the last oblique shock is located in the exit of the constant area section, letting the remaining pressure recovery be done in the subsonic diffuser which reduces the pressure losses and increases the efficiency. Above the critical pressure ratio, due to the movement of the shock train to upstream weakening the shock strength, the suction pressure increases. Then, the pressure difference is reduced, leading to the lower secondary mass flow suction. The optimized ejector in the double choking condition has a % higher entertainment ratio and its operational range is enhanced by percent in comparison to the original geometry.