Finite element analysis of fluid flows with moving boundary

The objective of the present study is to analyze the fluid flow with moving boundary using a finite element method. The algorithm uses a fractional step approach that can be used to solve low-speed flow with large density changes due to intense temperature gradients. The explicit Lax-Wendroff scheme is applied to nonlinear convective terms in the momentum equations to prevent checkerboard pressure oscillations. The ALE (Arbitrary Lagrangian Eulerian) method is adopted for moving grids. The numerical algorithm in the present study is validated for two-dimensional unsteady flow in a driven cavity and a natural convection problem. To extend the present numerical method to engine simulations, a piston-driven intake flow with moving boundary is also simulated. The density, temperature and axial velocity profiles are calculated for the three-dimensional unsteady piston-driven intake flow with density changes due to high inlet fluid temperatures using the present algorithm. The calculated results are in good agreement with other numerical and experimental ones.     

Unsteady shock waves in supersonic nozzles

The present paper describes the numerical and experimental results on unsteady nozzle flows induced by nonstationary shock waves. The two-dimensional Navier-Stokes equations are numerically solved using the upwind TVD finite-difference scheme of the Harten-Yee type. For the purpose of computational visualization of shock waves in transient nozzle starting process, computer shadow graphs are developed based on the principle of the optical shadowgraph. Visualization experiments employing a conventional shock tube are also performed. Comparison of numerical and experimental results shows satisfactory agreement. Furthermore, the steady flow establishment process around an airfoil model installed inside the nozzle is numerically investigated. The simulated results successfully reveal the unsteady viscous flow structure around the model.     

Development of a 2-D flow solver on unstructured and adaptive Cartesian meshes

A two-dimensional flow solver using mixed grids has been developed for accurate and efficient simulation of steady and unsteady flow fields. The flow solver was cast to accommodate two different topologies of computational meshes: unstructured triangular meshes in the near-body region such that complex geometric configurations can be easily modeled, while unstructured adaptive Cartesian meshes are utilized in the off-body region to resolve the flow more accurately with less numerical dissipation by adopting a spatially high-order accurate scheme and solution-adaptive mesh refinement technique. The unstructured adaptive Cartesian meshes can be generated automatically and allow to handle data efficiently via quad-tree data structures. A chimera mesh approach has been employed to link the two flow regimes adopting each mesh topology. A second-order accurate vertex-centered scheme and a 3^rd- or 5^th-order accurate cellcentered WENO scheme has been utilized in the near-body region and in the off-body region, respectively. Validations were made for the unsteady inviscid vortex convection and the steady and unsteady turbulent flows over an NACA0012 airfoil, and the results were compared with other computational and experimental results.     

A semi-implicit method for the analysis of two-dimensional fluid flow with moving free surfaces

Flow with moving free surfaces is analyzed with an the Eulerian coordinate system. This study proposes a semi-implicit filling algorithm using VOF in which the PLIC (Piecewise Linear Interface Calculation)-type interface reconstruction method and the donor-acceptor-type front advancing scheme are adopted. Also, a new scheme using extrapolation of the stream function is proposed to find the velocity of the node that newly enters the computational domain. The effect of wall boundary conditions on the flow field and temperature field is examined by numerically solving a two-dimensional casting process.     

Numerical assessment of turbulent models at a critical regime on unstructured meshes

The present study mainly aims to investigate the performances of different turbulent models for the flow simulation around a circular cylinder at a critical Reynolds number regime (Re = 8.5×10⁵, Tu = 0.7%). A hybrid RANS/LES model (SAS model), a correlation-based transition model ( $\gamma - \widetilde{\operatorname{Re} }_{\theta t} $ model), and a fully turbulent RANS model (SST model) were used to simulate various flow features, such as laminar-turbulence transition inside the boundary layer and the unsteady vortex shedding in the wake region, and their feasibilities for the flow simulation at a critical Reynolds number regime were demonstrated. A vertex-centered finite-volume method was used to discretize the incompressible Navier-Stokes equations, and an unstructured mesh technique was used to discretize the computational domain. The inviscid fluxes were evaluated using 2^nd-order Roe??s flux difference splitting, and the viscous fluxes were computed based on central differencing. A dual time-stepping method and the Gauss-Seidel iteration were used for unsteady time integration. The parallelization strategy using METIS and MPI libraries was used to reduce computational costs. The unsteady characteristics and the time-averaged quantities of the flow fields were compared between turbulent models. The numerical results were also compared with experimental results. The turbulent models showed quite different results at the critical regime because of the different abilities of each model to predict various flow features, such as laminar-turbulence transition and unsteady vortex shedding.     

A non-linear integrated aeroelasticity method for the prediction of turbine forced response with friction dampers

The aim of this paper is to describe an integrated aeroelasticity model for turbine blade forced response predictions. Such an approach requires a successful integration of the unsteady aerodynamics with non-linear structural dynamics, the latter arising from the use of root friction dampers to dissipate energy so that the response levels can be kept as low as possible. The inclusion of friction dampers is known to raise the resonant frequencies by up to 20% from the standard assembly frequencies, a shift that is not known prior to the aeroelasticity calculations because of its possible dependence on the unsteady excitation. An iterative procedure was therefore developed in order to determine the resonance shift under the effects of both unsteady dynamic loading and non-linear friction dampers. The iterative procedure uses a viscous, non-linear time-accurate flow representation for evaluating the aerodynamic forcing, a look-up table for determining the aerodynamic boundary conditions at any speed, and a time-domain friction damping module for resonance tracking. The methodology was applied to a high-pressure turbine rotor test case where the resonances of interest were due to first torsion and second flap blade modes under 40 engine-order excitation. The forced response computations were conducted using a multi-bladerow approach in order to avoid errors associated with “linking” single bladerow computations since the spacing between the bladerows was relatively small. Three friction damper elements, representing one actual friction damper, were used for each rotor blade. The number of rotor blades was decreased by 2–90 to obtain a cyclic sector of 4 stator and 9 stator blades. Such a route allowed the analysis to be conducted on a much smaller domain, hence reducing the computational effort significantly. However, the stator blade geometry was skewed in order to adjust the mass flow rate. Frequency shifts of 3.2% and 20.0% were predicted for the 40 engine-order resonances in torsion and bending modes, respectively. The predicted frequency shifts and the dynamic behaviour of the friction dampers were found to be within the measured range. Furthermore, the measured and predicted blade vibration amplitudes showed a good agreement with available experimental data, indicating that the methodology can be applied to typical industrial problems.     

高速列车单车通过隧道压力波的研究

采用计算流体力学的数值计算方法对基于三维、瞬态、可压缩Navier-Stokes方程和κ-ε两方程紊流模型进行求解,模拟高速列车单车通过隧道时列车外流场的特性,分析高速列车单车通过隧道的压力波特性及阻力变化规律。结果表明列车单车通过隧道的压力波最小负压值与速度为二次函数的关系,列车阻力主要由压差阻力构成。研究结果可为解决隧道空气动力学问题提供参考依据。     

A numerical simulation of train-induced unsteady airflow in a tunnel of Seoul subway

This study has been conducted to investigate numerically the characteristics of train-induced unsteady airflow in a subway tunnel. A three-dimensional numerical model using the dynamic layering method for the moving boundary of a train is applied. The validation of the present study has been carried out against the experimental data obtained by Kim and Kim [1] in a model tunnel. After this, for the geometries of the tunnel and subway train which are very similar to those of the Seoul subway, a three-dimensional unsteady tunnel flow is simulated. The predicted distributions of pressure and air velocity in the tunnel as well as the time series of mass flow rate at natural ventilation ducts reveal that the maximum exhaust mass flow rate of air through the duct occurs just before the frontal face of a train reaches the ventilation duct, while the suction mass flow rate through the duct reaches the maximum value just after the rear face of a train passes the ventilation duct. The results of this study can be utilized as basic data for optimizing the design of tunnel ventilation systems.     

Numerical study on characteristics of ship wave according to shape of waterway section

The ship wave phenomena in the restricted waterway were investigated by a numerical analysis. The Euler and continuity equations were employed for the present study. The boundary fitted and moving grid system was adopted to enhance the computational efficiency. The convective terms in the governing equations and the kinematic free surface boundary condition were solved by the Constrained Interpolated Profile (CIP) algorithm in order to solve accurately wave heights in far field as well as near field. The advantage of the CIP method was verified by the comparison of the computed results by the CIP and the Maker and Cell (MAC) method. The free surface flow simulation around Wigley hull was performed and compared with the experiment for the sake of the validation of the numerical method. The present numerical scheme was applied to the free surface simulation for various canal sections in order to understand the effect of the sectional shape of waterways on the ship waves. The wave heights on the side wall and the shape of the wave patterns with their characteristics of flow are discussed. Key Words: Ship Wave, Shallow Water, Waterway, Constrained Interpolated Profile (CIP) Algorithm     

Passive prandtl-meyer expansion flow with homogeneous condensation

Prandtl-Meyer expansion flow with homogeneous condensation is investigated experimentally and by numerical computations. The steady and unsteady periodic behaviors of the diabatic shock wave due to the latent heat released by condensation are considered with a view of technical application to the condensing flow through steam turbine blade passages. A passive control method using a porous wall and cavity underneath is applied to control the diabatic shock wave. Two-dimensional, compressible Navier-Stokes with the nucleation rate equation are numerically solved using a third-order TVD (Total Variation Diminishing) finite difference scheme. The computational results reproduce the measured static pressure distributions in passive and no passive Prandtl-Meyer expansion flows with condensation. From both the experimental and computational results, it is found that the magnitude of steady diabatic shock wave can be considerably reduced by the present passive control method. For no passive control, it is found that the diabatic shock wave due to the heat released by condensation oscillates periodically with a frequency of 2.40 kHz. This unsteady periodic motion of the diabatic shock wave can be completely suppressed using the present passive control method.     

Investigations on the exterior flow field and the efficiency of the muzzle brake

Numerical investigations of the projectile launch process with different muzzle brakes have been performed in a nearly realistic situation. Both two- and three-dimensional unsteady Euler equations are used as the governing equations. The hybrid Roe type scheme is employed to solve the flow fields with strong blast waves, and structured dynamic mesh technique is used for describing projectile motion. Based on the numerical solutions, the flow structures of a bare muzzle, the three-way and multi-hole muzzle brakes have been described, respectively, which agree well with our previous experimental shadowgraphs. Moreover, the efficiency of the three-way muzzle brake is calculated, which is also comparable to the corresponding experimental value. Our results showed that the numerical simulation can be a useful and efficient way for the design of new muzzle brakes.     

Time-dependent characteristics of the nonequilibrium condensation in subsonic flows

High-speed moist air or steam flow has long been of important subject in engineering and industrial applications. Of many complicated gas dynamics problems involved in moist air flows, the most challenging task is to understand the nonequilibrium condensation phenomenon when the moist air rapidly expands through a flow device. Many theoretical and experimental studies using supersonic wind tunnels have devoted to the understanding of the nonequilibrium condensation flow physics so far. However, the nonequilibrium condensation can be also generated in the subsonic flows induced by the unsteady expansion waves in shock tube. The major flow physics of the nonequilibrium condensation in this application may be different from those obtained in the supersonic wind tunnels. In the current study, the nonequilibrium condensation phenomenon caused by the unsteady expansion waves in a shock tube is analyzed by using the two-dimensional, unsteady, Navier-Stokes equations, which are fully coupled with a droplet growth equation. The third-order TVD MUSCL scheme is applied to solve the governing equation systems. The computational results are compared with the previous experimental data. The time-dependent behavior of nonequilibrium condensation of moist air in shock tube is investigated in details. The results show that the major characteristics of the nonequilibrium condensation phenomenon in shock tube are very different from those in the supersonic wind tunnels.     

Periodic transonic flow simulation using fourier-based algorithm

The present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady Euler and Navier-Stokes equations, using time spectral method (TSM) and compares it with the traditional methods like BDF and explicit structured adaptive grid method. The TSM uses a Fourier representation in time and hence solves for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. The TSM has been validated with 2D external aerodynamics test cases. These test cases are NACA 64A010 (CT6) and NACA 0012 (CT1 and CT5) pitching airfoils. Because of turbulent nature of flow, Baldwin-Lomax turbulence model has been used in viscous flow analysis with large oscillation amplitude (CT5 type). The results presented by the TSM are compared with experimental data and the two other methods. By enforcing periodicity and using Fourier representation in time that has a spectral accuracy, tremendous reduction of computational cost has been obtained compared to the conventional time-accurate methods. Results verify the small number of time intervals per pitching cycle (just four time intervals) required to capture the flow physics with small oscillation amplitude (CT6) and large oscillation amplitude (CT5) as compared to the other two methods.     

The self-induced oscillations of the under expanded jets impinging upon a cylindrical body

The present study addresses the flow characteristics involved in the self-induced oscillations of the underexpanded jet impinging upon a cylindrical body. Both experiment and computational analysis are carried out to elucidate the shock motions of the self-induced oscillations and to find the associated major flow factors. The underexpanded sonic jet is made from a nozzle and a cylindrical body is placed downstream to simulate the impinging jet upon an obstacle. The computational analysis using TVD scheme is applied to solve the axisymmetric, unsteady, inviscid governing equations. A Schlieren system is employed to visualize the self-induced oscillations generated in flow field. The data of the shock motions are obtained from a high-speed video system. The detailed characteristics of the Mach disk oscillations and the resulting pressure variations are expatiated using the time dependent data of the Mach disk positions. The mechanisms of the self-induced oscillations are discussed in details based upon the experimental and computational results.     

An efficient correction storage scheme for unsteady flows

An efficient correction storage scheme on a structured grid is applied to a sequence of approximate Jacobian systems arising at each time step from a linearization of the discrete nonlinear system of equations, obtained by the implicit time discretization of the conservation laws for unsteady fluid flows. The contribution of freezing the Jacobian matrix to computing costs is investigated within the correction storage scheme. The performance of the procedure is exhibited by measuring CPU time required to obtain a fully developed laminar vortex shedding flow past a circular cylinder, and is compared with that of a collective iterative method on a single grid. In addition, some computed results of the flow are presented in terms of some functionals along with measured data. The computational test shows that the computing costs may be saved in favor of the correction storage scheme with the frozen Jacobian matrix, to a great extent.     

Numerical investigation of the three-dimensional dynamic process of sabot discard

The sabot discard process of an armor-piercing, fin-stabilized discarding sabot (APFSDS) is crucial for the flight stability of the projectile. In this paper, the sabot discard behavior after projectile ejection from the muzzle is investigated at Mach number 4.0 and angle of attack of 0°. 3D compressible equations implemented with a dynamic unstructured tetrahedral mesh are numerically solved with a commercial computational fluid dynamics (CFD) code (FLUENT 12.0). Six-degrees-of-freedom (6DOF) rigid-body motion equations is solved with the CFD results through a user-defined function to update the sabot trajectory at every time step. A combination of springbased smoothing and local re-meshing is employed to regenerate the meshes around the sabot and describe its movement at each time step. Computational results show three different separation processes during the sabot discard process. Furthermore, the aerodynamic forces of APFSDS are calculated, and the trajectories of the three sabots are illustrated through the numerical solution of 6DOF equations. The results of the present study agree well with typical experimental results and provide detailed parameters that are important for analyzing the stability of the projectile. The present computations confirm that the numerical solution of the governing equations of aerodynamics and 6DOF rigid-body equations are a feasible method to study the sabot discard processes of APFSDS.     

Three-dimensional computations of the impulsive wave discharged from a duct

A sudden discharge of mass flow from the exit of a duct can generate an impulsive wave, generally leading to undesirable noise and vibration problems The present study develops an understanding of unsteady flow physics with regard to the impulsive wave discharged from a duct, using a numerical method A second order total variation diminishing scheme ts employed to solve three-dimensional, unsteady, compressible Euler equations Computations are performed for several exit conditions with and without ground and wall effects under a change in the Mach number of an initial shock wave from 11 to 15 The results obtained show that the directivity and magnitude of the impulsive wave discharged from the duct are significantly influenced by the initial shock Mach number and by the presence of the ground and walls     

A numerical method of analysis for the mushrooming of flat-ended projectiles impinging on a flat rigid anvil

The theories of Taylor, and Lee and Tupper use conservation of momentum across the plastic wave front to determine the strain distribution in a flat ended projectile impinging on a flat rigid anvil. In Hawkyard's theory conservation of energy is used across the plastic wave and some account of projectile strain hardening is incorporated. The present study replaces the projectile with a lumped parameter model which consists of a number of concentrated masses connected to each other by massless links. The equation of motion is applied to each concentrated mass and a solution for the dynamic behaviour of the connected mass system is obtained using a numerical technique. This method of approach is capable of incorporating the effects of material strain hardening and strain rate on the final shape of the projectile, it enables the distribution of strain in the projectile to be determined.     

Unsteady viscous flow model on moving the domain through a stenotic artery

An unsteady Navier-Stokes (N-S) solver based on the method of operator splitting and artificial compressibility has been studied for the moving boundary problem to simulate blood flow through a compliant vessel. Galerkin finite element analysis is used to discretize the governing equations. The model has been applied to a time-varying computational domain (two-dimensional tube) as a test case for validation. Consideration has been given to retaining the space conservation property. The same code is then applied to a hypothetical critical high-pressure gradient over a short length of blood vessel based on the spring and dashpot model. The governing equation for the blood vessel is based on two-dimensional dynamic thin-shell theory that takes into account the curvature of the stenotic portion of the vessel. Progressing the solution towards steady state is considered, as the main objective is to show the viability of the current technique for fluid/structure interactions. Preliminary results of the wall velocity and displacement based on steady state prediction agree well with data in the literature. Results, such as the streamlines, wall pressures and wall shear stress depict the possible progression of arterial disease.     

Unsteady aerodynamic loads on high speed trains passing by each other

In order to study unsteady aerodynamic loads on high speed trains passing by each other 350km/h, three-dimensional flow fields around trains during the crossing event are numerically simulated using three-dimensional Euler equations. Roe’s FDS with MUSCL interpolation is employed to simulate wave phenomena. An efficient moving grid system based on domain decomposition techniques is developed to analyze the unsteady flow field induced by the restricted motion of a train on a rail. Numerical simulations of the strain passing by on the double-track are carried out to study the effect of the train nose-shape, length and the existence of a tunnel on the crossing event. Unsteady aerodynamic loads-a side force and a drag force-acting on the train during the crossing are numerically predicted and analyzed. The side force mainly depends on the nose-shape, and the drag force depends on tunnel existence. Also. a push-pull (i.e. impluse force) force successively acts on each car and acts in different directions between the neighborhood cars. The maximum change of the impulsive force reaches about 3 tons. These aerodynamic force data are absolutely necessary to evaluate the stability of high speed multi-car trains. The results also indicate the effectiveness of the present numerical method for simulating the unsteady flow fields induced by bodies in relative motion.