Numerical Modeling and Visualization of Supersonic Tip Vortices

In this paper we present an analysis and comparison of two streamwise supersonic vortices interaction with using the methods of maximum vorticity and the ?2-criterion. Mach number of incoming flow was M? = 3. A pair of vortices was generated by two coaxial straight wings with sharp leading, tip and trailing edges. Two configurations are considered: a pair of counter-rotating vortices and a pair of co-rotating vortices. In the case of counterrotating vortices the wings attack angle was 10 degrees. In the case of co-rotating vortices the attack angle of one of the wings was 10 degrees, the attack angle of other one was -10 degrees. Numerical data were obtained in the domain of 10 wing chords downstream from a wings axis by a computational model based on the URANS equations with SA turbulence model. Numerical simulations were performed on the hybrid supercomputing system K-60 at the Keldysh Institute of Applied Mathematics RAS using the developed software package ARES for 3D turbulent flows modeling on high performance computing systems. The main simulation was performed on 224 cores. The simulations were carried out on unstructured grids with hexagonal cells.

A three -dimensional steady flowfield generated by transverse sonic injection into a supersonic flow was simulated by solving the Favre -averaged Navier -Stokes equations using the weighted essentially nonoscillatory (WENO) schemes and Jones -Launder k-� turbulence model. Both two -dimensional and three -dimensional results are given. The two -dimensional results agree well with the experiment. Three -di mensional results indicate that there are four pairs of vortices around the secondary injection. In the upstream of the square injection there exist two main recirculation regions and the primary vortex induces the horseshoe vortex region. After the second ary injection flow ejects from the square hole, it is forced by the supersonic main flow and then it become s a pair of counter rotation vortices towards downstream. In the downstream there is a low -pressure region that conduces a pair of helical vortices.

Thematic mapping and scientific visualization are two dedicated areas for visualizing a wide range of domain-specific data sets. From a general perspective, thematic mapping and scientific visualization reveal large overlaps in terms of visualization methods. However, these two disciplines are shaped by different driving forces and usage purposes. Accordingly, the concerns involved in the thematic mapping workflow that ranges from data source, data processing to map design principles may be quite different from those for scientific visualization and vice versa. Although some interdisciplinary researches between general mapping and scientific visualization have been conducted, little knowledge about the differences and commonalities between thematic mapping and scientific visualization is available. This research work is devoted to an in-depth comparative study with the aim to bridge these two disciplines by identifying their methodological strengths and synergetic effects. Comparison results show that thematic mapping goes steps further than scientific visualization in terms of data preprocessing, while scientific visualization relies more on the capability of users to visually process the data by themselves. We believe that scientific visualization can very well profit from thematic mapping methods to achieve some communication effects while thematic mapping can be very well extended to embrace some scientific visualization methods for the hotspot explorations.

New exact spatially localized stationary solutions on the background of a zonal flow are found for the (3 + 1)-dimensional nonlinear non-dissipative quasi-geostrophic potential vorticity equation (Charney–Obukhov equation), which describes Rossby waves and vortices in an exponentially stratified fluid. The three solutions are presented. They include solutions with spherically and cylindrically symmetric cores, as well as partial superposition of these solutions. The nonlinear boundary conditions with a flat bottom and a rigid lid generate an infinite discrete set of baroclinic modes for each solution. For the analytical assessment of the vertical localization of vortices, the condition of maximum total vorticity is used. The solutions show that for a given value of the velocity of stationary motion V, vortices may not exist, or there may be one, two or more vortices localized at different heights and having the same velocity V. All vortices described by the solutions consist of a continuous sequence of the eddy chains, extended along the zonal direction and having an inclination to the horizon in the meridional plane. A pair of vortices in the baroclinic dipole appears and disappears when the velocity V passes through neutral points. In the dipole, the eddy chains belonging to different vortices typically have different inclinations in the meridional plane. The magnitudes of these inclinations can vary from zero to several degrees. The baroclinic dipole generated by the solution with the spherically symmetric core has a “pocket” capable of carrying warm or cold fluid depending on the polarity of the eddies in the dipole.

A numerical study of a dual-mode combustor has been conducted to investigate the effect of the flow Mach number on both mixing and combustion processes using unstructured grids. A wall-mounted parallel injector ramp has been selected as the fuel injector. Results are obtained with swept and unswept raised ramps. Numerical results are presented for non reacting flows as well as for reacting flows. A constant area duct (isolator) of 30 H in length is placed before the swept ramp in the non reacting flows case. In the reacting flows case, a short isolator of 10 H in length has been placed before the unswept ramp. A three-dimensional model for the combustor configuration has been used. Numerical results are obtained using an existing finite volume CFD code with unstructured grids with size of about 400,000 cells. Results for both non reacting and reacting flows show that increasing the flow Mach number decreases the mixing rate. Also, significant decrease in total pressure is observed as a result of increasing the flow Mach number.

An experimental investigation has been made on the interaction process between a boundary layer and longitudinal vortices. Comparable experimental conditions were set up for two types of vortex pair, namely, common-flow up (cfu) and common-flow down (cfd) and results obtained from two conditions were compared. The longitudinal vortex pair moves away from the wall in a faster rate in case of cfu. Spanwise spreading rate of two longitudinal vortex paths is larger in case of cfd. The decay of maximum longitudinal vorticity is slower in case of cfd. At the symmetrical plane between two vortices, the interaction between longitudinal vortex makes closely distributed mean velocity contour lines and higher skin-friction coefficient in case of cfd. Otherwise, in case of cfu the interaction makes widely distributed mean velocity contour lines and low skin-friction coefficient. Effect of extra rate of strain involved in momentum integral equation is applied to explain behaviors of boundary layer in the two cases.

Crosswind shear can influence the trailing vortex trajectories significantly, according to both field measurement and numerical simulations. Point vortex models are used in this paper to study the fluid dynamic mechanism in the interactions between trailing vortex pair and shear layers. It has been shown that the shear-layer deformation causes the vortex descent history difference in the two vortices of the vortex pair. When a shear layer is below the vortex pair with the same sign as the left vortex, the right vortex descends less than the left vortex. When the same shear layer is above the vortex pair, the right vortex descends more. The descent altitudes of the two vortices are the same when they go through a constant, non-deformed shear layer. Those trends are in agreement with Navier-Stokes simulations.

The efficient reconstruction and artifact-free visualization of surfaces from measured real-world data is an important issue in various applications, such as medical and scientific visualization, quality control, and the media-related industry. The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions. Our methods show that these models are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data. We create a new quasi-interpolating operator which for the first time solves the problem of finding a globally C1-smooth quadratic spline approximating data and where no tetrahedra need to be further subdivided. In addition, we devise a new projection method for point sets arising from a sufficiently dense sampling of objects. Compared with existing approaches, high-quality surface triangulations can be generated with guaranteed numerical stability. Keywords. Piecewise polynomials; trivariate splines; quasi-interpolation; volume data; GPU ray casting; surface reconstruction; point set surfaces

Unstructured grids are extensively used in modern computational solvers and, thus, play an important role in scientific visualization. They come in many different types. One of the most general types are non-convex meshes, which may contain voids and cavities. The lack of convexity presents a problem for several algorithms, often causing performance issues.

Computational simulations for complex geometries nowadays often deal with unstructured grids. That’s why scientific visualization must also be extended to these grid types. A visualization system is presented which works with any type of unstructured grids, i.e. arbitrary polygonal and polyhedral grids. Results from finite volume (cell-centered) and finite element methods can be visualized. Additionally time-dependent data can be processed and interpolation between time steps is possible. This data may be transfered directly from a simulation program and therefore on-line visualized. To integrate this task into a computational simulation an object-oriented interface is presented which allows an easy connection of simulation and visualization.

This paper discusses an analytical/numerical model developed to describe the behavior of gaseous jets injected transversely into a subsonic (but compressible) crossflow. The cross section of the jet is modeled as an inviscid, compressible vortex pair, consistent with experimental observations of the transverse jet cross section. The numerically computed behavior of the vortex pair is used as an input to mass and momentum balances along the jet, forming a model that describes the trajectory, entrainment, and mixing of jets injected into subsonic crossflows in the range 0.15 < Mx < 0.8. Theoretical predictions of jet trajectories are compared with limited experimental data, yielding accuracy within 10%. Because very short computational times are required for this model, it could serve as an excellent design tool for perfectly expanded or slightly underexpanded jets in subsonic crossflow. Nomenclature B = constant used in defining jet cross-sectional area d = jet orifice diameter Fy = dimensionless force tending to separate vortices due to compressibility associated with vortex pair Fyp = dimensionless force tending to separate vortices due to

Correlation measurements have been made on large scale models placed in wind tunnels. The correlation has been taken between surface pressures and farfield radiated sound. The technique permits one to find the amount of sound radiated by a surface even when that sound is up to 20 dB and more below the ambient noise in the operating wind tunnel. These techniques have strongly suggested that the major source of radiated airframe noise is at the outboard edges of deployed aircraft flaps. Measurements have been made to determine the dependence upon flow Mach number, upon angle, and upon the various flap‐surface positions. A theoretical model has been devised using a vortex (and its image) embedded in a potential flow about a corner. The theory has but one adjustable parameter; all computations can be made on a hand calculator. The radiated sound is found using the Curie theory. The effects of many vortices are included. The predicted, radiated sound matches the correlation‐measured sound to within 3 dB for mo...

A nonlinear system with boundary-initial value conditions of convection–diffusion partial differential equations is presented to describe incompressible nuclear waste disposal contamination in porous media. The flow pressure is determined by an elliptic equation, the concentrations of brine and radionuclide are formulated by convection–diffusion equations, and the transport of temperature is defined by a heat equation. The pressure appears in convection–diffusion equations and heat equation in the form of Darcy velocity and controls the physical processes. The fluid pressure and velocity are solved by the conservative mixed volume element and the computation accuracy of Darcy velocity is improved one order. A combination method of the mixed volume element and the approximation of characteristics is applied to solve the brine and heat, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computation stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. Larger time-steps along the characteristics are shown to result in smaller time-truncation errors than those resulting from standard methods. The mixed volume element method has the property of conservation on each element and it can obtain numerical solutions of the brine and adjoint vectors. The radionuclide is solved by a coupled method of characteristics and fractional step difference. The computational work is reduced greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and using the algorithm of speedup. Using numerical analysis of priori estimates of differential equations, we demonstrate an optimal second order estimate in $$l^2$$ norm. Numerical data are appropriate with the scheme and it is shown that the method is a powerful tool to solve the well-known problems in porous media.

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate-a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Exact solutions of the Navier–Stokes equations describing the interaction of streamwise vortices with a rigid surface are utilized to develop a conceptual model for the surface pressure spectrum associated with the wall region of a turbulent boundary layer. The evolution of single as well as pairs of coherent streamwise vortices, which principally govern the production of turbulence in the wall region, is considered in the presence of local straining flow induced by larger, outer-layer eddies. The surface pressure signatures of the coherent vortex motion and the associated power spectrum of the pressure are examined. Based on the results of the exact solutions, the surface pressure spectrum of an ensemble of independent coherent structures is modeled using the assumption of ergodicity in the manner described by Townsend and Lundgren for homogeneous turbulence. The free parameters in the model are estimated through comparison with available results from experiments and numerical simulations. The model, especially the one involving pairs of streamwise vortices, predicts the high frequency and high spanwise wave number range of the surface pressure spectrum quite well. Further, the probability density function of surface pressure associated with the model compares well with experimental results. Interestingly, the model also suggests that the contribution of the viscous interaction to low wave number spectral elements accounts for the discrepancy between experimental observations at such wave numbers and the prediction of the Kraichnan–Phillips theorem.