Grid Aspect Ratio Research Articles

Analysis of ansys fluent for Wall-Modeled Large-Eddy Simulation of Turbulent Channel Flow

Abstract This study assesses the accuracy of ansysfluent 19.2, a commonly employed general-purpose finite volume solver, in the context of wall-modeled large-eddy simulation for turbulent channel flow at a moderate Reynolds number, Reτ=2000. The sensitivity of the solution to variations in grid resolution, aspect ratio, grid arrangement (collocated versus staggered), and subgrid-scale (SGS) model is analyzed and contrasted to results from a corresponding direct numerical simulation (DNS) and a mixed pseudospectral and finite differences solver. Results indicate good convergence of first- and second-order statistics from the staggered grid setups as the grid is refined, whereas no clear trend is observed in cases with collocated grid setups. Velocity spectra show a lack of an apparent inertial range trend and rapid decay of energy density at high wavenumbers, with a spurious energy pile-up near the cutoff wavenumber indicating the presence of unphysical oscillations in the velocity fields. Grid refinement strengthens such oscillations in collocated grid setups and reduces them in staggered grid setups. Two-point streamwise velocity autocorrelation maps reveal an underprediction of turbulent structure size. In contrast, cross-stream autocorrelations agree with corresponding curves from direct numerical simulation, showing signatures of alternating high- and low-momentum streaks in the logarithmic layer.

Improvements for the DDES model with consideration of grid aspect ratio and coherent vortex structures

The delayed detached eddy simulation (DDES) model has achieved great success in simulations of massive separations, but has been found to significantly delay the Kelvin-Helmholtz (K-H) instability in weak separations due to the “grey area” problem. A new DDES model was proposed by considering the grid aspect ratio and local coherent vortex structures, named the DDES with an adaptive grid-scale and adaptive coefficient (DDES-AGAC). The DDES-AGAC model was examined in detail by computing four typical types of turbulent flows: fully attached turbulent boundary layer, massive separation, weakly unstable flow with a fixed separation point, and weak separation over a smooth surface due to pressure gradient. The results confirm the advantages of the new DDES-AGAC model over the standard DDES. It exhibits high efficiency and insensitivity to spanwise or circumferential grid spacing in flow simulations of quasi-three-dimensional flows. For the weakly unsteady separation, it helps to accelerate the rapid switch from Reynolds-averaged Navier-Stokes equations to large eddy simulation, unlock the K-H instability in the shear layer, and hence accurately resolve the turbulent structures, profiles of velocity and turbulent kinetic energy, and spectra in the separation regions. Furthermore, it does not result in a noticeable drag or skin friction reduction in the fully attached flow simulations. The DDES-AGAC model is expected to be widely used in simulations of engineering flows with separations.

Numerical study for slamming loads on the bow of a ship-type FPSO model under breaking waves

Numerical analyses were performed to investigate the characteristics of the slamming impact loads on the bow-flare of a ship-type floating production storage and offloading (FPSO) model under breaking waves. To estimate the slamming impact load, a series of breaking wave simulations was performed. From 2D wave flume tests, the grid aspect ratio, convection scheme, turbulence model, effect of surface tension, and grid dependencies were investigated. Through a series of numerical simulations, the grid system and numerical schemes were determined, and the slamming impact load simulations were conducted. It could be observed that the slamming impact loads and motions of the FPSO model in the numerical simulations were in good agreement with the experimental results. In order to investigate the relation between the slamming impact load and free motion of the FPSO model, the breaking impact simulations were performed under fixed positions and the free motion of the FPSO model. From the results, the relation between the relative angle and slamming impact load, as well as the relation between the position of the FPSO model and impulse response, are discussed.

Advancing high-speed flow simulations: SAUSM – an innovative hybrid numerical scheme for shock stability and accuracy

This paper introduces a novel hybrid numerical method, SAUSM, designed for accurate and robust simulation of compressible flows governed by the Euler equations. While the AUSM[Formula: see text] scheme provides proper resolution of smooth flow features, it is susceptible to anomalies, particularly the carbuncle phenomenon near strong shock discontinuities. Conversely, the AUFS scheme offers inherent stability in capturing shocks; however, it lacks the accuracy of AUSM[Formula: see text] in smooth regions. The proposed SAUSM method combines AUSM[Formula: see text] and AUFS through an adaptive weighting function, facilitating a seamless transition between the schemes. This approach preserves the accuracy of AUSM[Formula: see text] in smooth regions while ensuring robust shock-capturing capabilities near discontinuities. The effectiveness of the SAUSM method is rigorously demonstrated through a comprehensive suite of progressively complex test cases. Numerical experiments demonstrate SAUSM’s proficiency in resolving intense shock patterns and discontinuities without introducing anomalies. In the selected test cases, SAUSM agrees with reference solutions and effectively mitigates anomalies observed in AUSM[Formula: see text], including kinked Mach stems. In the challenging test case involving hypersonic blunt body flow over a cylinder, SAUSM adapts dissipation effectively by utilizing its adaptive weighting function to generate smooth pressure distributions, thereby eliminating the carbuncle instability linked to AUSM[Formula: see text] when applied to a high aspect ratio grid. The consistent formulation of flux splitting and the adaptive weighting in SAUSM prevent excessive dissipation away from discontinuities, thus preserving accuracy comparable to that of exact Riemann solvers. Consequently, SAUSM emerges as a promising and innovative approach to accurately and robustly simulate a wide range of compressible Euler flows. The comprehensive results obtained from the validation tests firmly establish SAUSM as a highly effective general-purpose technique for computational fluid dynamics in academic research.

A unification of least-squares and Green–Gauss gradients under a common projection-based gradient reconstruction framework

We propose a family of gradient reconstruction schemes based on the solution of over-determined systems by orthogonal or oblique projections. In the case of orthogonal projections, we retrieve familiar weighted least-squares gradients, but we also propose new direction-weighted variants. On the other hand, using oblique projections that employ cell face normal vectors we derive variations of consistent Green–Gauss gradients, which we call Taylor–Gauss gradients. The gradients are tested and compared on a variety of grids such as structured, locally refined, randomly perturbed, unstructured, and with high aspect ratio. The tests include quadrilateral and triangular grids, and employ both compact and extended stencils, and observations are made about the best choice of gradient and weighting scheme for each case. On high aspect ratio grids, it is found that most gradients can exhibit a kind of numerical instability that may be so severe as to make the gradient unusable. A theoretical analysis of the instability reveals that it is triggered by roundoff errors in the calculation of the cell centroids, but ultimately is due to truncation errors of the gradient reconstruction scheme, rather than roundoff errors. Based on this analysis, we provide guidelines on the range of weights that can be used safely with least squares methods to avoid this instability.

Preconditioned central moment lattice Boltzmann method on a rectangular lattice grid for accelerated computations of inhomogeneous flows

Convergence acceleration of flow simulations to their steady states at lower Mach numbers can be achieved via preconditioning the lattice Boltzmann (LB) schemes that alleviate the associated numerical stiffness, which have so far been constructed on square lattices. We present a new central moment LB method on rectangular lattice grids for efficient computations of inhomogeneous and anisotropic flows by solving the preconditioned Navier–Stokes (PNS) equations. Moment equilibria corrections are derived via a Chapman–Enskog analysis for eliminating the truncation errors due to grid-anisotropy arising from the use of the rectangular lattice and the non-Galilean invariant cubic velocity errors resulting from an aliasing effect on the standard D2Q9 lattice for consistently recovering the PNS equations. Such corrections depend on the diagonal components of the velocity gradients, which are locally obtained from the second order non-equilibrium moments and parameterized by an associated grid aspect ratio r and a preconditioning parameter γ, and the speed of sound in the collision model is naturally adapted to r via a physically consistent strategy. We develop our approach by using a robust non-orthogonal moment basis and the central moment equilibria are based on a matching principle, leading to simpler expressions for the corrections for using the rectangular grids and for representing the viscosities as functions of the relaxation parameters, r and γ, and its implementation is modular allowing a ready extension of the existing LB schemes based on the square lattice. Numerical simulations of inhomogeneous and anisotropic shear-driven bounded flows using the preconditioned rectangular central moment LB method demonstrate the accuracy and significant reductions in the numbers of steps to reach the steady states for various sets of characteristic parameters.

High-order compact finite volume schemes for solving the Reynolds averaged Navier-Stokes equations on the unstructured mixed grids with a large aspect ratio

In this paper, high-order compact finite volume schemes on the unstructured grids based on the variational reconstruction are developed to solve the Reynolds averaged Navier-Stokes equations closed by the Spalart-Allmaras one-equation turbulence model. Encouraging progress is made in addressing the following two challenging problems: reducing the numerical errors on the large aspect ratio grids and avoiding the negative turbulent viscosity associated with the high-order methods. On grids with large aspect ratios, a three-step procedure is designed to optimize the functional parameters of variational reconstruction. In addition, an exponential decay procedure is proposed to cure the negative turbulent viscosity problem of the Spalart-Allmaras model. The exponential decay procedure has the advantage of being able to be used with any spatial discretization method and with the implicit temporal discretization. Numerical tests show significant benefits of the high-order schemes in predicting the skin frictions, capturing some important flow structures, and achieving grid-independent solutions. The numerical tests also show that the proposed schemes are sufficiently robust for practical applications.

Optimization of Numerical Methods for Transforming UTM Plane Coordinates to Lambert Plane Coordinates

The rapid transformation from UTM (Universal Transverse Mecator) projection to Lambert projection helps to realize timely merging, inversion, and analysis of high-frequency partitioned remote sensing images. In this study, the transformation error and the efficiency of the linear rule approximation method, the improved linear rule approximation method, the hyperbolic transformation method, and the conformal transformation method were compared in transforming the coordinates of sample points on WGS84 (The World Geodetic System 1984)-UTM zonal projections to WGS84-Lambert projection coordinates. The effect of the grid aspect ratio on the coordinate transformation error of the conformal transformation method was examined. In addition, the conformal transformation method-based error spatial pattern of the sample points was analyzed. The results show that the conformal transformation method can better balance error and efficiency than other numerical methods. The error of the conformal transformation method is less affected by grid size. The maximum x-error is less than 0.36 m and the maximum y-error is less than 1.22 m when the grid size reaches 300 km × 300 km. The x- and y-error values decrease when square grids are used; namely, setting the grid aspect ratio close to 1 helps to weaken the effect of increasing grid area on the error. The dispersion of the error distribution and the maximum error of sample points both decrease relative to their minimum distance to the grid edge and stabilize at a minimum distance equal to 70 km. This study can support the rapid integration of massive remote sensing data over large areas.

Realism of Lagrangian Large Eddy Simulations Driven by Reanalysis Meteorology: Tracking a Pocket of Open Cells Under a Biomass Burning Aerosol Layer.

An approach to drive Lagrangian large eddy simulation (LES) of boundary layer clouds with reanalysis data is presented and evaluated using satellite (Spinning Enhanced Visible and Infrared Imager, SEVIRI) and aircraft (Cloud‐Aerosol‐Radiation Interactions and Forcing, CLARIFY) measurements. The simulations follow trajectories of the boundary layer flow. They track the formation and evolution of a pocket of open cells (POC) underneath a biomass burning aerosol layer in the free troposphere. The simulations reproduce the evolution of observed stratocumulus cloud morphology, cloud optical depth, and cloud drop effective radius, and capture the timing of the cloud state transition from closed to open cells seen in the satellite imagery on the three considered trajectories. They reproduce a biomass burning aerosol layer identified by the in‐situ aircraft measurements above the inversion of the POC. Entrainment of aerosol from the biomass burning layer into the POC is limited to the extent of having no impact on cloud‐ or boundary layer properties, in agreement with the CLARIFY observations. The two‐moment bin microphysics scheme used in the simulations reproduces the in‐situ cloud microphysical properties reasonably well. A two‐moment bulk microphysics scheme reproduces the satellite observations in the non‐precipitating closed‐cell state, but overestimates liquid water path and cloud optical depth in the precipitating open‐cell state due to insufficient surface precipitation. A boundary layer cold and dry bias occurring in LES can be counteracted by reducing the grid aspect ratio and by tightening the large scale wind speed nudging towards the surface.

Detailed investigation of subgrid scale models in large-eddy simulation using high aspect-ratio grid spacing

In large eddy simulation (LES), we generally use information of the grid width in representing a filter width (Δ) to evaluate a subgrid scale (SGS) model. In practical applications, however, the grid widths are largely different in the streamwise and cross-streamwise directions, resulting in grid cells having high aspect ratios. In such a case, we often adopt the cube root of the grid-cell volume for the filter width; i.e., Δ=(ΔxΔyΔz)1/3 in the Cartesian grid system. Although this has been regarded as a standard way to determine the filter width, its superiority over other strategies, such as using the maximum width in all directions (i.e., Δ=max(Δx,Δy,Δz)), has not always been made clear. In this paper, to investigate the effect of the definition of a filter width on the prediction accuracy of an SGS model, we report on a priori tests of several SGS models using highly resolved LES data of a backward-facing step flow. We focus particularly on the model performance in the shear layer downstream of a step, where there exists a strong velocity gradient and the aspect ratio of a grid cell is high despite the region being far from wall surfaces. This investigation enables us to distinguish the effect of the grid aspect ratio from that of near-wall damping. We make the important finding that the cube root of a grid-cell volume is not always appropriate for the filter width. To evaluate an SGS model properly, the effect of a grid width in one direction much smaller than in other directions must be excluded in determining the filter width.

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

Local Banking to 45°: Axis Grid Generation for Line Charts

<p indent=0mm>Axis grid is a basic reference structure that assists people in reading line charts. In this paper, we focus on axis labels that help people perceive slopes in line charts. A series of user studies are conducted to explore the influence of local aspect ratio on the task of slope estimation in line charts. We evaluate the influence of different experimental conditions by calculating the errors between the user estimated slope and the ground truth. The results show that appropriate grid density and squarified grid aspect ratio increase the estimation accuracy of line segment slopes. Accordingly, we propose a new algorithm for generating axis grid considering the maximal label, the minimal label and label intervals for line charts. Following the previous criteria of simplicity, coverage and overlap, our algorithm applies the squarifed local aspect ratio to the joint optimization of the tick marks of both horizontal and vertical axis to generate aesthetic axis grid that helps increase graphical perception accuracy.

Central moment lattice Boltzmann method on a rectangular lattice

Simulating inhomogeneous flows with different characteristic scales in different coordinate directions using the collide-and-stream based lattice Boltzmann methods (LBMs) can be accomplished efficiently using rectangular lattice grids. We develop and investigate a new rectangular central moment LBM based on a non-orthogonal moment basis and involving multiple relaxation times. The equilibria to which the central moments relax under collision in this approach are obtained from matching with those corresponding to the continuous Maxwell distribution. A Chapman–Enskog analysis is performed to derive the correction terms to the second order moment equilibria involving the grid aspect ratio and velocity gradients that restore the isotropy of the viscous stress tensor and eliminate the non-Galilean invariant cubic velocity terms in the resulting hydrodynamical equations. A special case of this rectangular formulation involving the raw moments is also constructed. The resulting schemes represent a considerable simplification, especially for the transformation matrices and isotropy corrections, and improvement over the existing lattice Boltzmann schemes based on raw moments on rectangular lattice grids that use orthogonal moment basis. Numerical validation study of both the proposed rectangular LBMs for a variety of benchmark flows is performed, which shows good accuracy at various grid aspect ratios. The ability of our proposed schemes to simulate flows at relatively low grid aspect ratios and higher Reynolds numbers than considered in prior approaches is demonstrated. Furthermore, simulations reveal the superior stability characteristics of the rectangular central moment LBM over that based on raw moments in handling shear flows at lower viscosities and/or higher characteristic velocities. In addition, computational advantages of using our rectangular LB formulation in lieu of that based on the square lattice are shown.

Viscous liquid-liquid wetting and dewetting of textured surfaces.

We experimentally investigate the spreading and receding behavior of small water droplets immersed in viscous oils on grid-patterned surfaces using synchronized bottom and profile views. In particular, the evolution of apparent advancing and receding contact angles of droplets fed at constant flow rate is studied as a function of grid surface coverage and height for a wide range of external phase viscosity. Detailed examination of droplet aspect ratio during inflation process provides an averaging method for characterization of quasi-static advancing angles on heterogeneous surfaces. Droplets spreading in partial Cassie state on planar microfluidic grids are also shown to capture oil patches that further evolve into trapped oil droplets depending on grid aspect ratio. The natural retraction velocity of thin water films is examined based on external phase velocity and regime maps of trapped droplets are delineated based on control parameters.

The ghost fluid method for OpenFOAM: A comparative study in marine context

The open source CFD library OpenFOAM is utilized to implement the ghost fluid method (GFM). The implemented solver GFMFoam is compared against the standard volume-of-fluid (VOF) solver interFoam in OpenFOAM. For both VOF solvers, the scalar transport equation is solved similarly but the discretization of the momentum and continuity equations differ between GFMFoam and interFoam. The two methods are compared in four test cases with mild surface deformation. First, the GFM implementation is validated. Second, the results on a 2 d interface shear layer highlight the importance of the viscous term treatment in the GFM. Third, the model scale Wiggley hull results indicate that the GFMFoam is more sensitive to the grid aspect ratio and resolution than interFoam but the viscous resistance is better predicted. Also, GFMFoam is shown to be less sensitive to numerical ventilation than interFoam. Fourth, the results from the Hamburg Test Case indicate a total resistance prediction within 1% when evaluated against reference data at model scale and 10% at full scale. Based on the steady state test cases of the present study, GFMFoam has moderate benefits over interFoam but it does not clearly outperform interFoam.

Deep ultraviolet excimer laser processing for the micro via hole on semiconductor package

Moore's law has almost reached the limit of resolution on semiconductor die and, therefore, multidie packaging is one of the alternative solutions. Substrate materials currently use organic build-up films and silicon substrates [through silicon via (TSV)] in applications. But recently, organic films, too, have reached the resolution limit, and TSV is expensive. In this situation, nonalkali glass (glass) and fused silica (SiO2) substrates are expected to be good alternatives in high-frequency signal transfer applications like 5G telecommunication. But the via holes are hard to process with less defects (tips and cracks) on the glass and SiO2 substrates. Deep ultraviolet (DUV) excimer laser ablation is expected to have a finer (&amp;lt;10 μm) resolution with a shorter wavelength (248–193 nm) and also hard material processing with a higher photon energy (5–6.4 eV). Therefore, the authors have explored the application of the DUV excimer laser ablation process for a via hole on hard materials like glass and SiO2 substrates. In this study, they have investigated the via hole quality through the DUV excimer laser ablation process. The results show the possibilities of micromachining on both glass and SiO2 substrates. The authors have succeeded by achieving a value of &amp;lt;50 μm through the via hole grid aspect ratio of 6 on the glass substrate without any significant defects. As the ablation rate is quite an affordable value, DUV excimer lasers are expected to play a crucial role in the next-generation manufacturing process for semiconductor packages. The authors also investigate the SiO2 substrate with DUV excimer lasers.

Evaluating Implementations of the Immersed Boundary Method in the Weather Research and Forecasting Model

AbstractThe terrain-following coordinate system used by many atmospheric models can cause numerical instabilities due to discretization errors as resolved terrain slopes increase and the grid becomes highly skewed. The immersed boundary (IB) method, which does not require the grid to conform to the terrain, has been shown to alleviate these errors, and has been used successfully for high-resolution atmospheric simulations over steep terrain, including vertical building surfaces. Since many previous applications of IB methods to atmospheric models have used very fine grid resolution (5 m or less), the present study seeks to evaluate IB method performance over a range of grid resolutions and aspect ratios. Two classes of IB algorithms, velocity reconstruction and shear stress reconstruction, are tested within the common framework of the Weather Research and Forecasting (WRF) Model. Performance is evaluated in two test cases, one with flat terrain and the other with the topography of Askervein Hill, both under neutrally stratified conditions. WRF-IB results are compared to similarity theory, observations, and native WRF results. Despite sensitivity to the location at which the IB intersects the model grid, the velocity reconstruction IB method shows consistent performance when used with a hybrid RANS/LES surface scheme. The shear stress reconstruction IB method is not sensitive to the grid intersection, but is less consistent and near-surface velocity errors can occur at coarse resolutions. This study represents an initial investigation of IB method variability across grid resolutions in WRF. Future work will focus on improving IB method performance at intermediate to coarse resolutions.

Development of multi-component generalized sphere function based gas-kinetic flux solver for simulation of compressible viscous reacting flows

In this paper, a multi-component generalized sphere function based gas-kinetic flux solver is developed for simulation of compressible viscous reacting flows. This work is inspired by the existing simplified gas-kinetic schemes, which use the circular or sphere function to develop single-component gas-kinetic flux solvers. The present solver applies the finite volume method to discretize the multi-component Navier-Stokes equations and evaluate the numerical flux at the cell interface by using the local solution of Boltzmann equation. In order to unify the existing circular and sphere functions, a generalized sphere function is derived from a reduced Maxwellian distribution function by assuming that all the particles are concentrated on an N-dimensional sphere. The present solver is then developed by integrating the generalized sphere function on the sphere surface. To obtain a multi-component solver, the mass fraction from both sides of the cell interface is used to compute the densities of different species. Considering the different physical properties of the species, the internal energy is computed by enthalpy, and the temperature at the cell interface is obtained by Newton iteration. In addition, to control the numerical dissipation, which is relevant to the grid aspect ratio and the chemical reaction, an improved switch function is introduced. Several benchmark problems are simulated to validate the present solver. It is shown that the developed flux solver has a satisfied performance for simulation of multi-component compressible viscous reacting flows.

Development of multicomponent lattice Boltzmann flux solver for simulation of compressible viscous reacting flows.

In this paper, the multicomponent lattice Boltzmann flux solver (LBFS) is developed for simulation of two-dimensional compressible viscous reacting flows. This work is based on the existing LBFS for simulation of single-component compressible flows. The present solver applies the finite volume method to discretize the multicomponent Navier-Stokes equations and evaluates the numerical flux at the cell interface by local solution of the lattice Boltzmann equation. To evaluate numerical flux, the original non-free parameter D1Q4 model in the existing LBFS is extended to the multicomponent counterpart in which the total density at the cell interface is computed directly by summing the density distribution functions, and the densities of different species are calculated from the mass fractions at the left and right sides of cell interface. The internal energy is evaluated from the enthalpy which considers the different physical properties of the species, and the temperature at the cell interface is obtained by Newton iteration. In addition, an improved switch function which takes into account the reacting effects and aspect ratio of the grid is introduced to control the numerical dissipation. Several benchmark problems are simulated to validate the present multicomponent LBFS. It is shown that the present solver is carbuncle-free for the unfavorable aspect ratio grid in the test cases here and has a satisfied performance for simulation of multicomponent compressible viscous reacting flows.

Constitutive modeling for the simulation of the superplastic forming of TA15 titanium alloy

Titanium alloy, TA15, has a high strength-to-weight ratio, high weldability, and superior creep resistance at high temperatures up to 550 °C. TA15 is difficult to deform, especially for forming complex-shaped large-scale web–rib components, due to its low plasticity, large inhomogeneous deformation and narrow processing window. The objective of this research is to model the superplastic mechanisms in TA15 alloy with equiaxed, fine grain structure, and applying the proposed constitutive model to investigate the maximum grid aspect ratio, that can be achieved in superplastic forming (SPF), for a TA15 sheet with an initial thickness of 1.2 mm. Thermo-mechanical tensile tests are conducted first to characterize the superplastic behavior of the material in the temperature range of 880– 940 °C and the strain-rate of 0.0005–0.01 s−1. A set of mechanism-based unified visco-plastic constitutive equations has been proposed and calibrated based on the results of stress-strain data. A gradient-based optimization method is applied for the calibration of constitutive equations. The constitutive model is incorporated into FEA code through creep subroutine to check the validity of the proposed material model against the experimental SPF test of a multi-box die. Predicted sheet thickness and thinning in a die entry radius region at the end of forming are examined in detail. Preliminary results show a good agreement between the computational and experimental results.