Two‐dimensional pseudo‐steady supersonic flow around a sharp corner

As indicated in section 111 of Courant and Friedrichs's book [Supersonic Flow and Shock Waves, Interscience, New York, 1948], a supersonic flow around a sharp corner, one of the most important elementary flows, is effected by a rarefaction wave. This paper is concerned with the local structural stability problem on such a wave of a three-dimensional (3-D) steady full Euler system. More concretely, we establish the local existence and stability of a 3-D incomplete expansion centered rarefaction wave when the perturbed supersonic incoming flow moves around a sharp corner whose fixed wall beyond the corner is of a perturbation with respect to some oblique half-plane. © 2010 Society for Industrial and Applied Mathematics.

Supersonic axisymmetric expansion flow is a typical and fundamental issue in gas dynamics. It plays a vital role in the high-speed external and internal flow fields regarding the contour design and performance evaluation of supersonic/hypersonic vehicles and their propulsion systems. The supersonic two-dimensional (2D) planar expansion flow is dominated by the well-known Prandtl–Meyer (P–M) theory. However, no similar explicit relation exists for the supersonic axisymmetric expansion flow, and only the computational fluid dynamics results could be employed at present. Therefore, this work focuses on developing the analytical solution of supersonic axisymmetric flow around a sharp convex corner on the basis of the generic gasdynamic functions in a newly established coordinate system for addressing the aforementioned issue. Theoretical derivations and numerical results prove that the flow deflection angle and Mach number in supersonic axisymmetric flow around a sharp convex corner obey the identical law to the 2D planar situation, that is, the P–M theory, while the local axisymmetric expansion fan is not the simple wave flow despite the conical flow. Meanwhile, the method of characteristics is employed to further explicate the intrinsic connection and difference between the 2D and axisymmetric sharp convex corner flow. The equivalence of sharp corner and curved surface flows with the identical deflection angle is discussed, and three limitations of the proposed analytical solution are clarified.

Automatic detection of oblique shocks and simple waves in schlieren images of two-dimensional supersonic steady flows

: A Navier-Stokes code to solve the aft end flow field of missile type configurations is presented. The consistently split linearized block implicit method of McDonald and Briley is employed in modified form to handle L-shaped domains with sharp reentrant corners. Appropriate boundary conditions are applied for the supersonic flow in particular at the outer boundary so that waves generated within the flow field are allowed to pass out of the computational domain without reflecting back into it. An adaptive grid option has been incorporated into the code and has been exercised by following the shear layer in a model backstep problem. Results are presented for the supersonic turbulent flow over a nozzle boattail configuration with and without jet exhaust and the results are compared with experiment. Calculations of the 2-D turbulent supersonic flow over a right angle back step with shear layer reattachment on a 20 deg ramp are also shown, and compared with experiments. The computation shows the qualitative physical behavior of the flows and there is generally good agreement with the experimental velocity profiles through most of the free shear layer and the ramp reattachment zone. (Author)

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.

A calculating method of shock wave oscillating frequency due to turbulent shear layer fluctuations in supersonic flow

This article is concerned with research on parallel pro cessing for chemically reactive supersonic flows. Effi ciency of autotasking and microtasking is examined for the problems of linear algebra and two-dimensional Euler equations with the finite element method. For microtasking, satisfactory improvements in speedup (2.63 for 4 CPUs and 1.67 for 2 CPUs) are achieved, with the load balance and the amount of parallelism being the dominant factors for the speedup. Autotask ing has advantages in providing automatic paralleliza tion, but it has been shown that in the solution of finite element Euler equations based on conventional algo rithms, parallelization by means of user's intervention is required for significant speedups (3.35 for 4 CPUs and 1.79 for 2 CPUs). A much better performance may be achieved with a combination of autotasking and microtasking. These results are verified from various example problems of linear algebra and supersonic diffuser flow field calculations with hydrogen-oxygen chemical reactions.

On the degeneration of supersonic flow due to interaction of centered compression and rarefaction waves: PMM, vol. 43, no. 1, 1979, pp. 45–50

Improved element-particle coupling strategy with δ-SPH and particle shifting for modeling sloshing with rigid or deformable structures

We present a new computational method that excites guided phonon modes in nanoscale waveguides at a specific frequency and wavenumber. The method uses nonequilibrium molecular dynamics and Fourier analysis of particle displacements to extract mode shapes from single frequency excitations consisting of superposed spatial modes. These mode shapes are used to excite the waveguide inlet boundary so that single phonon modes are generated in the structure. Mode shapes and phonon spectra for a silicon planar waveguide with rigid wall boundaries are calculated to demonstrate the viability of the technique. This method improves upon molecular dynamics techniques that activate all possible phonon modes and are thus not able to isolate the contribution of any single phonon excitation. Application of our method will enable the computational investigation of single phonon mode propagation in nanostructures of varying geometry.

The present dissertation deals with the application of an adaptive mesh hp-refinement method to the time-dependent compressible Euler equations describing the flow of an inviscid fluid. The physical simulation space is a two-dimensional channel with bump through which an ideal gas flows. A big advantage of the Euler equations is the applicability to different Mach regimes. Thus, smooth solutions and those containing discontinuities can be simulated. As the underlying numerical technique, a pseudo-spectral element method using least squares is used. The grid consists of rectangles that have to be transformed into curved deformed elements in the area of the bump. The h-refinement is realized by means of a quadtree and the p-refinement by means of a stepwise increase of the polynomial degree by 2, whereby hanging nodes can arise. Compared to previous research, the Euler equations are examined with respect to four different refinement criteria in combination with the hp-adaptive pseudo-spectral element method. The refinement criteria are the gradient criterion, two spectral criteria and an edge detection method. For a first determination of the suitability of the criteria for the h-refinement and for a validation of the pseudo-spectral element method, these are used for the solution of three steady state convection equations for which the exact solutions are known. Finally, the full method is applied to three test problems for the Euler equations. The flow through the channel is realized by a smooth subsonic flow, a transonic flow with a shock, and a supersonic flow that contains reflective shocks. Since no analytical solution is known, we compare our results to other works that consider stationary grids for these test cases. It turns out that the applied adaptive method refines the grid in the regions of the stagnation points and those that have discontinuities. Thus prior knowledge about the location of the problem areas is not necessary. A smaller number of elements and locally higher polynomial degrees reduce the sizes of the systems of equations to be solved.

Compact heat exchangers: by W.M. Kays and A.L. London. 156 pages, diagrams, [formula omitted], New York, McGraw-Hill Book Co., Inc., 1958. Price, $6.00

The results of parametric numerical experiments on the influence of heat and mass transfer on flow separation during the interaction of an oblique shock wave with a laminar boundary layer are presented. An implicit finite-volume algorithm for solving the Navier-Stokes equations for arbitrary coordinates, based on the Roe scheme for convective terms, is implemented. The second order of accuracy in space was provided by using the symmetric Jamecon flux limiter. The numerical algorithm was verified on the problems of transonic and supersonic laminar and turbulent flows when compared with experimental data.The study was carried out with the aim of comparative analysis of the possibilities of the flow separation control using heat and mass transfer with a streamlined surface under the same conditions of the shock wave/boundary layer interaction.Spatial pressure distributions, pressure and skin friction coefficient distributions along the plate, profiles of density, dynamic viscosity coefficient, longitudinal velocity components and momentum in the laminar boundary layer are presented. The main physical factors de-termining changes in the structure of the separation interaction under heat and mass transfer conditions were identified. The effect of heat transfer with the plate was manifested primarily in changes in the profiles of density and dynamic viscosity coefficient, which significantly de-pend on temperature. Removal of slowed particles from the boundary layer leads to a greater filling of the velocity profile by mass transfer with the practically constant value of the dy-namic viscosity coefficient on the surface. Based on the analysis of the results obtained, it was found that the main factor in pre-venting flow separation is the increase in the longitudinal component of the momentum dur-ing plate cooling by heat transfer and the removal of slowed particles by mass transfer. Therefore, despite the different physical nature of the impact, heat and mass transfer with the surface has a similar resulting effect on the size and structure of the supersonic separation zone.Using heat and mass transfer it is possible to prevent the occurrence of a separation zone in two-dimensional supersonic flows.

The results of numerical studies of the interaction of a detonation wave and an electron beam with supersonic reacting flows in channel of various configurations like channel with backward-facing step, symmetrical channel with abrupt expansion and channel with a cavity are presented. A mathematical technology has been created to implement such interaction based on the ANSYS Fluent software. The flow parameters at the outlet of the channel are compared for different channel configurations and ignition initiation ways. The possibility is shown to intensify the ignition in a supersonic flow by electron beams and pulsating detonation. The possibility is identified to use a cavity for stabilizing the combustion in a supersonic combustion chamber when exposed to a detonation wave.

A brief description of the flow field is given for the interaction of shock wave and laminar boundary layer on a compression corner in supersonic flow. A special sub-case—that of leadingedge laminar separation—is anafyzed by extension of Chapman's laminar mixing-laj^er theory. Results are tabulated for ranges of Mach number 1 < M0 < 10, and compression-corner angle 0 < /3 < 45°. A limited region of possible leading-edge laminar separation with an attached leading-edge shock (or in certain cases an expansion) followed by a second shock due to the reattachment flow is found to exist. Comparison with existing experimental data is found to be satisfactory in several cases.