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Unsteady turbulent flow simulations were performed based on the Reynolds-averaged Navier–Stokes (RANS) equations to investigate flow oscillation due to three-dimensional (3D) configuration of a Mach 1.5 supersonic open cavity flow with a length-to-depth ratio of 3. Two-dimensional (2D) and 3D unsteady simulation results were analyzed and compared with experimental data and Rossiter’s empirical prediction data. The three-dimensional cavity width-to-depth ratio (W/D) was 1, 3.8 and 7.6. Computational results indicated that pressure oscillation in the 2D flow was generated by a single-flow structure, whereas a multiple-flow structure generated multiple oscillation peaks in the 3D flow. The flow structure in the 3D cavity was investigated. For the 2D flow case, the cavity internal pressure wave was directly synchronized with the free shear layer. In the 3D flow case, an unstable spanwise flow due to the sidewall was observed. This spanwise fluctuation produced additional pressure oscillations coupled with the streamwise internal pressure wave. The numerical results indicate that the spanwise flow reduces the propagation speed of the internal pressure waves and the intensity of the corresponding pressure fluctuation.

In this paper, we present a computational aeroelastic analysis of flexible flapping wings in the vicinity of solid walls. The wall effects change the aerodynamic forces and moments of the wings, and thus the aeroelastic behavior. The numerical simulation is carried out using a fluid–structure interaction framework by coupling the computational fluid dynamics and computational structural dynamics. A preconditioned Navier–Stokes solver based on a finite volume method is used for the aerodynamic analysis. The structural analysis is performed using a nonlinear structural model based on a geometrically exact beam formulation. The method is validated using previous numerical and experimental results. The aeroelastic characteristics of the flexible wings with and without the walls are computed and compared.

This paper presents numerical analyses of lateral jets in supersonic cross flows on a flat plate and on a generic missile. The freestream Mach number is 4 for the flat plate and 3 for the missile, and the jets are sonic for both cases. The numerical results are validated with wind tunnel data such as Schlieren images and surface pressure distributions. The flow structure due to the jet interaction with the supersonic free-stream is examined in terms of the vortex structure. A 3-dimensional compressible RANS solver is used for the study. To describe the effects of high temperature, a thermally perfect gas is assumed. When high temperature is applied, the shock structure changes, which affects the separation region and recirculation zone. Next, the effects of turbulence models on the jet interaction flow are investigated. The Spalart–Allmaras, Menter's shear-stress transport k–ω, Huang and Coakley's k–e, and Coakley's q–ω models are used to analyze the flows. The differences in pressure distribution among the turbulence models are larger in the case of the flat plate than the missile. In addition, several numerical flux functions are compared to investigate their effects on the jet interaction: the Roe scheme with Sanders's H-correction, RoeM scheme, and the HLLE scheme. Although the HLLE scheme shows a little difference at the indent of the barrel shock, the three numerical flux schemes give similar C P distributions on the wall.

In this paper, numerical simulations are performed on the lock-in phenomena of vortex induced vibration(VIV) of a two dimensional cylinder. A deforming grid as well as a rigidly moving grid are used to simulate the movement of the cylinder. The grid deformation is accomplished by the linear spring analogy. Converged solutions, which are obtained by controling the grid size and the non-dimensional time step, are used for comparison and validation of the analysis results. Moreover, the efficiency and the accuracy of the coupling methods for fluid-structure interaction are examined.

Realistic computations of flows induced by synthetic jets in multiple flow conditions are studied with an unsteady preconditioned Reynolds-averaged Navier–Stokes solver with deforming meshes. Deforming meshes suitable for structured grid systems are used to simulate the motion of diaphragms driven at a given frequency.With deforming meshes, a boundary-conditionmodel is not necessary for synthetic jet calculations. To obtain time-accurate solutions with a grid system under deformation, the geometric conservation law is employed. Numerical calculations of three cases of the Langley Research Center Workshop Computational Fluid Dynamics Validation of Synthetic Jets and Turbulent Separation Control workshop are carried out, and the computational results are compared with the experimental data. The results indicate the effectiveness of the current method in synthetic jet flow computations.

This paper presents computations of the dynamic derivatives of three dimensional flight vehicle configurations using CFD. The pitch dynamic derivatives are computed from the pitch sinusoidal motion, while the roll damping is computed based on steady state calculation using a non-inertial frame method. The Basic Finner and the SDM(Standard Dynamic Model) are chosen for the benchmark tests against other numerical and experimental results. For the flow calculations, a 3-D Euler solver that can be run both on the non-inertial frame and on the inertial frame is developed. A dual-time stepping method is applied for the unsteady time accurate simulations. A good agreement of pitch-roll dynamic derivatives with previously published numerical results and the experimental results is observed.

This paper investigates the convergence characteristics of the modified artificial compressibility method proposed by Turkel. In particular, a focus is mode on the convergence characteristics due to variation of the preconditioning factor (αu) and the artificial compressibility ( β) in conjunction with an upwind method. For the investigations, a code using the modified artificial compressibility is developed. The code solves the axisymmetric incompressible Reynolds averaged Navier-Stokes equations. The cell-centered finite volume method is used in conjunction with Roe’s approximate Riemann solver for the inviscid flux, and the central difference discretization is used for the viscous flux. Time marching is accomplished by the approximated factorizationalternate direction implicit method. In addition, Menter’s k-ω shear stress transport turbulence model is adopted for analysis of turbulent flows. Inviscid, laminar, and turbulent flows are solved to investigate the accuracy of solutions and convergence behavior in the modified artificial compressibility method. The possible reason for loss of robustness of the modified artificial compressibility method with αu >1.0 is given.

A numerical simulation of flows in an axisymmetric supersonic inlet with bleed regions is performed. An existing code which solves the Reynolds Averaged Navier-Stokes equations and the two-equation turbulence model equations is converted into an axisymmetric code. In addition, a bleed boundary condition model has been applied to the code. In this paper, the modified code is validated by comparing numerical results against experimental data and other computational results for flows on a bump and over an oblique shock with bleed region. Using the code, numerical simulation is performed for the flows in an inlet with multiple bleed regions.

The Preissmann slot model is one of the most widely used models to conceptualize both free-surface and pressurized flows in urban drainage systems. Despite its simplicity and wide range of applications, numerical solutions of the Preissmann slot model suffer from the spurious oscillations, especially when flow conditions switch from free-surface flow to pressurized flow. To overcome this problem, a new hybrid numerical flux solver of the Preissmann slot model is proposed herein, in which the upwind flux solver is combined with the centered flux solver. Numerical experiments are conducted for multiple flow conditions such as typical filling, pipe-filling, and transition-flow conditions. The numerical results indicate that the proposed scheme generally outperforms the conventional flux schemes for various hydraulic conditions and wave velocities. The proposed scheme should be useful to further enhance integrated urban water modeling in which transient mixed flow conditions significantly impact the simulation accuracy during extreme floods.

A numerical procedure for aerodynamic load analysis of long span bridges is presented. The preconditioned Reynolds averaged Navier-Stokes equations are adopted to compute flows over the bridges. To capture the turbulent characteristics of the flows, two equation turbulence models, Coakley’s q − ω model and Menter’s k − ω SST model, are used to compute the turbulent viscosity. A dual time stepping method in conjunction with the AF-ADI method is used to advance the solution in time. A loosely coupled method of the preconditioned RANS equations with the turbulence model equations is employed for fast computation without losing numerical stability. The numerical method for the aerodynamic load analysis is verified against well-known benchmark problems. Aerodynamic loads of two real bridges are computed with the method to demonstrate the usefulness of the method.

Euler codes or Navier-Stokes codes for compressible flows suffer severe degradation in convergence as Mach number approaches zero. The convergence problem arose from the wide disparity in characteristic speeds can be solved using preconditioning methods without large modifications. In this paper, a preconditioned RANS(Reynolds Averaged Navier-Stokes) solver is developed for analysis of low Mach number flows. In order to validate the method, computational examples are chosen and the results are compared with the experimental data and the existing computed results showing a good accuracy and convergence characteristics for steady inviscid, laminar and turbulent flows at low Mach number.

The flow characteristics on and around an airfoil at moderate Reynolds number are studied to understand the generation mechanism of tonal noise from a symmetrical airfoil NACA0018 in a uniform flow. The separation and reattachment of the flow on the airfoil surface are evaluated from the liquid-crystal visualization and the velocity field across the boundary layers over the airfoil are measured by particle image velocimetry (PIV). These results indicate that the separation and reattachment points of laminar boundary layers over the airfoil move along the airfoil surface, depending on the angle of attack variations. When the airfoil is inclined at a small attack angle to meet with the condition of tonal noise generation, the boundary layer on the pressure surface experiences the separation along the surface and reattaches near the trailing edge of the airfoil. Then, the periodic vortex structure is generated over the pressure surface near the trailing edge, which is followed by the formation of periodic vortex shedding in the airfoil wake. With further increase in attack angle, the flow over the suction surface separates near the leading edge of the airfoil and the boundary layer on the pressure surface keeps fully attached flows on the airfoil surface, resulting in the disappearance of tonal noise.

Two methods for coupling the Reynolds-averaged Navier–Stokes equations with the q–ω turbulence model equations on structured grid systems have been studied; namely a loosely coupled method and a strongly coupled method. The loosely coupled method first solves the Navier–Stokes equations with the turbulent viscosity fixed. In a subsequent step, the turbulence model equations are solved with all flow quantities fixed. On the other hand, the strongly coupled method solves the Reynolds-averaged Navier–Stokes equations and the turbulence model equations simultaneously. In this paper, numerical stabilities of both methods in conjunction with the approximated factorization-alternative direction implicit method are analysed. The effect of the turbulent kinetic energy terms in the governing equations on the convergence characteristics is also studied. The performance of the two methods is compared for several two- and three-dimensional problems. Copyright © 2005 John Wiley & Sons, Ltd.

When growing large single crystals from a melt, it is desirable to minimize thermally induced convection effects so that solidification is achieved predominantly by thermal conduction. It is expected that under such conditions any impurities that originate from the walls of the crucible will be less likely to migrate into the mushy region and consequently deposit in the crystal. It is also desirable to achieve a distribution of the dopant in the crystal that is as uniform as possible. A finite volume method and a least-squares spectral finite element method were used to develop accurate computer codes for prediction of solidification from a melt under the influence of externally applied magnetic fields. A hybrid constrained optimization algorithm and a semi-stochastic self-adapting response surface optimizer were then used with these solidification analysis codes to determine the distributions of the magnets that will minimize the convective flow throughout the melt or in desired regions of the m...

In a flapping wing micro air vehicle (MAV), inspired by an organism of either insects or birds, flexibility of the wing structure induces a crucial effect upon the vehicle performance. Thus, in an analysis upon the flapping wing MAV, coupling between aerodynamics and structural dynamics considering the wing flexibility will be a critical component. This paper presents an accurate computational approach to simulate a flapping wing by coupling between CFD and CSD. Non-linear structural analysis based on the geometrically exact beam formulation was used. Such non-linear beam analysis was coupled with preconditioned Navier-Stokes solutions. For a grid deformation in the aerodynamic analysis, the mesh shearing methodology was used. A coupling between the structural and aerodynamic analyses was conducted by adopting the implicit coupling approach. After that, an aeroelastic analysis was performed and the results are compared with the experimental results. However, the flapping wing configuration is not slender in reality and their vein section geometry is complex generally. Thus, to consider those features, the finite element analysis, beam and shell, based on a co-rotational (CR) theory was developed in parallel. Currently, the CR beam analysis with a warping DOF was developed and validated by comparing it with NASTRAN in static condition.

Numerical simulations of flows around Nagashima et al.'s supersonic inlet with three exit configurations are performed to determine the effects of exit configurations on inlet buzz. Two exits are axisymmetric configurations with different locations, and the other is a 3-D configuration exit with several holes. The supersonic inlet used in the simulations is an external compression type, and axisymmetric except the exit. Three-dimensional simulations are carried out using a Reynolds-averaged Navier-Stokes (RANS) solver with the SpalartAlmaras turbulence model. Results with two axisymmetric exit configurations indicate that the amplitude of the pressure oscillation and the dominant frequency are larger than those of the experimental data. On the other hand, the result with the 3-D configuration exit shows that both the pressure history and the dominant frequency are good agreement with experimental data.

This paper describes a computational study of the prediction of stability derivatives for the standard dynamic model(SDM) using three-dimensional Euler and Reynolds-averaged Navier-Stokes(RANS) computation fluid dynamics(CFD) solvers. Directional and longitudinal stability derivatives are computed in pitch and yaw harmonic oscillations, and a dual time stepping method is applied to evaluate time-accurate solutions. Lateral derivatives are evaluated by a steady state method in a non-inertial reference frame. Source terms due to the transformation of the governing equations to the non-inertial coordinate are added for the steady state method. Simulations are performed at various flight conditions in terms of Mach numbers, angles of attack, and oscillation amplitudes. The simulations show that the nonlinear characteristics of the stability derivatives appear at high angles of attack as well as in the transonic region.

A mathematical model and an explicit finite-difference iterative integration algorithm for two-dimensional laminar steady flow and solidification of an incompressible, viscous, electrically conducting but neutrally charged melt containing electrically charged panicles and exposed to an externally applied electrostatic field were developed. The system of governing electrohydrodynamic equations was derived from a combination of Maxwell's equations and the Navier-Stokes equations, including thermally induced buoyancy, latent heat release, and Joule heating, while accounting for the mushy region. Physical properties were treated as arbitrarily temperature-dependent. Numerical results demonstrate the existence of strong electrothermoconvective motion in the melt and quantify its influence on the amount of accrued solid, deposition pattern of the electrically charged particles inside the accrued solid, and the melt/solid interface shape.

The realistic computations of three dimensional flows induced by a synthetic jet in a couple of flow conditions are studied with the unsteady preconditioned Reynolds averaged Navier-Stokes equations with deforming mesh. Deforming mesh suitable for structured grid systems is used to simulate the motion of a diaphragm driven at a given frequency. By using the deforming mesh, there is no need for a boundary condition model for the synthetic jet calculation. In order to obtain time accurate solutions with grid system under deformation, GCL (Geometric Conservation Law) is employed. Numerical calculations of the cases 1 and 2 of the CFDVAL2004 workshop are carried out, and their results are compared with the experimental data. The computational results of case 1 using the full three-dimensional geometry are also compared with the results of the two dimensional calculations. Computational results enable us to understand qualitatively as well as quantitatively the evolution of the turbulent eddies out of the slot and inside the cavity during the expulsion and suction phases. The results indicate the effectiveness of the current method in threedimensional synthetic jet flow computations.

In this study, two commonly used numerical methods for the analysis of incompressible flows (or low Mach number flows), Chorins’ artificial compressibility method and Wiess and Smith’s preconditioning method are compared. Also, the convergence characteristics of two methods are numerically investigated for two-dimensional laminar and turbulent flows. Although the two methods have similar governing equations, the eigensystems and other details are very different. The eigensystems of the artificial compressibility method and the preconditioning method are analytically examined. An artificial compressibility code that solves the incompressible RANS (Reynolds Averaged Navier-Stokes) equations is newly developed for the study. An artificial compressibility code and a well-verified existing low Mach number code uses Roe’s approximate Riemann solver in conjunction with a cell centered finite volume method. Using MUSCL extrapolation with nonlinear limiters, 2nd order spatial accuracy is achieved while maintaining TVD (total variation diminishing) property. AF-ADI (approximate factorization-alternate direction implicit) method is used to get the steady solution for both codes. Menter’s k–ω SST turbulence model is used for the analysis of turbulent flows. Navier-Stokes equations and the turbulence model equations are solved in a loosely coupled manner.Copyright © 2011 by KSME

Numerical simulations of 3D aircraft configurations are performed in order to understand the effects that turbulence models have on the aerodynamic characteristics of an aircraft. An in-house CFD code that solves 3D RANS equations and 2-equation turbulence model equations is used for the study. The code applies Roe’s approximated Riemann solver and an AF-ADI scheme. Furthermore van Leer’s MUSCL extrapolation with van Albada’s limiter is adopted. Various versions of Menter’s k-omega SST turbulence models as well as Coakley’s q-omega model are incorporated into the CFD code. Menter’s k-omega SST models include the standard model, the 2003 model, the model incorporating the vorticity source term, and the model containing controlled decay. Turbulent flows over a wing are simulated in order to validate the turbulence models contained in the CFD code. The results from these simulations are then compared to computational results of the 3rd AIAA CFD Drag Prediction Workshop. Moreover, numerical simulations of the DLR-F6 wing-body and wing-body-nacelle-pylon configurations are conducted and compared to computational results of the 2nd AIAA CFD Drag Prediction Workshop. Especially, the aerodynamic characteristics as well as flow features with respect to the turbulence models are scrutinized. The results obtained from each simulation incorporating Menter’s k-omega SST turbulence model variations are compared with one another.Copyright © 2011 by KSME

This work deals with the development of a numerical algorithm for the prediction of magnetic force lines inside a flowing solidifying melt with the ultimate purpose of simulating and controlling alignment of short nickel-coated fibers during the curing process in composites. A complete mathematical model and an accompanying computer program have been developed for the simulation of a steady laminar flow of an incompressible fluid with strong heat transfer (involving solidification) and a strong superimposed magnetic field. An extended form of the Boussinesq approximation allowing for temperature-dependent physical properties of the fluid and the solid including latent heat of phase change was incorporated. This formulation simultaneously predicts detailed velocity, pressure, and temperature fields in the moving fluid while capturing the forming solid phase by using a single computer code. The same code can simulate the reverse process of thawing or melting of the solid phase. The computed sample configurations involve a two-dimensional closed container, a straight and a U-shaped channel, and a passage of an arbitrary shape. It was found that the presence of an external steady magnetic field: (a) diminishes flow field vorticity, (b) causes higher velocity gradients within the boundary layers, (c) is able to orient magnetized fibers along the lines of local magnetic lines of forces.

A complete three-dimensional mathematical model has been developed governing the steady, laminar flow of an incompressible fluid subjected to a magnetic field and including internal heating due to the Joule effect, heat transfer due to conduction, and thermally induced buoyancy forces. The thermally induced buoyancy was accounted for via the Boussinesq approximation. The entire system of eight partial differential equations was solved by integrating intermittently a system of five fluid flow equations and a system of three magnetic field equations and transferring the information through source-like terms. An explicit Runge-Kutta time-stepping algorithm and a finite difference scheme with artificial compressibility were used in the general non-orthogonal curvilinear boundary-conforming co-ordinate system. Comparison of computational results and known analytical solutions in two and three dimensions demonstrates high accuracy and smooth monotone convergence of the iterative algorithm. Results of test cases with thermally induced buoyancy demonstrate the stabilizing effect of the magnetic field on the recirculating flows.

A mathematical model governing steady laminar flow of an incompressible fluid subjected to a steady magnetic field including internal heating due to Joule effect, heat transfer due to conduction and convection, and thermally induced buoyancy forces has been developed. The thermal buoyancy was accounted for via Boussinesq approximation. To demonstrate effects of the Lorentz and Joule heating on the blood flow, two configurations have been chosen. The first configuration consists of a closed rectangular container (two-dimensional), and the second is a three-dimensional pipe with rectangular cross section. Results of test cases with and without applied magnetic field demonstrate influence of the magnitude of the magnetic field on the recirculating blood flow instability. >

A mathematical model for three-dimensional laminar steady flow of an incompressible viscous neutrally charged carrier fluid mixed with an electrically charged fluid is presented. All magnetic fields are neglected. Thermally induced buoyancy is incorporated via Boussinesq approximation while including Joule heating effects. Numerical results demonstrate the detrimental effects of numerical dissipation on the accuracy of the solution. Bending of a stream of charged particles under the influence of an electric field and an electrohydrodynamic instability are demonstrated. >