Thin-layer approximation for three-dimensional supersonic corner flows

AIAA Journal ◽  
1980 ◽  
Vol 18 (12) ◽  
pp. 1544-1546 ◽  
Author(s):  
C. M. Hung ◽  
Seth S. Kurasaki
Keyword(s):  
Thin Layer ◽  
Three Dimensional ◽  
Thin Layer Approximation ◽  
Corner Flows

Microstructures of Low Angle Boundaries of the Second Generation Single Crystal Superalloy DD6

2011 ◽  
Vol 284-286 ◽  
pp. 1584-1587
Author(s):  
Zhen Xue Shi ◽  
Jia Rong Li ◽  
Shi Zhong Liu ◽  
Jin Qian Zhao
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Scanning Electron Microscope ◽  
Thin Layer ◽  
Single Crystal ◽  
Second Generation ◽  
Three Dimensional ◽  
Single Crystal Superalloy ◽  
Transition Electron ◽  
Scanning Electron

The specimens of low angle boundaries were machined from the second generation single crystal superalloy DD6 blades. The microstructures of low angle boundaries (LAB) were investigated from three scales of dendrite, γ′ phase and atom with optical microscopy (OM), scanning electron microscope (SEM), transition electron microscope (TEM) and high resolution transmission electrion microscopy (HREM). The results showed that on the dendrite scale LAB is interdendrite district formed by three dimensional curved face between the adjacent dendrites. On the γ′ phase scale LAB is composed by a thin layer γ phase and its bilateral imperfect cube γ′ phase. On the atom scale LAB is made up of dislocations within several atom thickness.

Fabrication of thin-layer matrigel-based constructs for three-dimensional cell culture

2018 ◽  
Vol 35 (1) ◽  
pp. e2733 ◽  
Author(s):  
Kristin Robin Ko ◽  
Meng-Chiao Tsai ◽  
John P. Frampton
Keyword(s):  
Cell Culture ◽  
Thin Layer ◽  
Three Dimensional ◽  
Dimensional Cell

Comparison of Numerical and Experimental “Conical” Flow Fields in Supersonic Corners with Compression and/or Expansion

1977 ◽  
Vol 28 (4) ◽  
pp. 293-306 ◽  
Author(s):  
D A Anderson ◽  
R K Nangia
Keyword(s):  
Flow Field ◽  
Numerical Method ◽  
Three Dimensional ◽  
Solid Surfaces ◽  
Supersonic Stream ◽  
Conical Flow ◽  
Wave Interactions ◽  
Surface Deflection ◽  
Corner Flows ◽  
General Influence

SummaryThe flow field produced by the intersection of two plane solid surfaces in a supersonic stream is a complex interference flow. These flows can be fully compressive, fully expansive or of mixed compression-expansion nature. This paper presents a comparison of the flow field structure in an axial corner obtained experimentally with that predicted numerically by using a shock-capturing finite-difference method. The effect of sweep and surface deflection are evaluated and the general influence of each is presented for the three classes of corner flows. The results of this study show that the numerical method is a valuable aid in understanding the flow structure for simple configurations. In addition confidence in the numerical method is gained for use in solving the more general three-dimensional configurations where the flow is non-conical and several wave interactions may be present.

Flow along streamwise corners revisited

2003 ◽  
Vol 476 ◽  
pp. 223-265 ◽  
Author(s):  
A. RIDHA
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Three Dimensional ◽  
Numerical Results ◽  
Intermediate Layers ◽  
Concave Corner ◽  
Dimensional Boundary ◽  
Streamwise Pressure Gradient ◽  
Corner Flows ◽  
Corner Layer

In this paper we investigate the three-dimensional laminar incompressible steady flow along a corner formed by joining two similar quarter-infinite unswept wedges along a side-edge. We show that a four-region construction of the potential flow arises naturally for this flow problem, the formulation being generally valid for a corner of an arbitrary angle (π−2α), including the limiting cases of semi- and quarter-infinite flat-plate configurations. This construction leads to five distinct three-dimensional boundary-layer regions, whereby both the spanwise length and velocity scales of the blending intermediate layers are O(δ), with Re−1/2 [Lt ] δ [Lt ] 1, Re being a reference Reynolds number supposed to be large. This reveals crucial differences between concave and convex corner flows. For the latter flow regime, the corner-layer motion is shown to be mainly controlled by the secondary flow which effectively reduces to that past sharp wedges with solutions being unique and existing only for favourable streamwise pressure gradients. In this regime, the corner-layer thickness is shown to be O(Re−0.5+α/π/δ2α/π), −½π [les ] α [les ] 0, which is much smaller than O(Re−1/2) for concave corner flows.Crucially, our numerical results show conclusively that, for α ≠ 0, closed streamwise symmetrically disposed vortices are generated inside the intermediate layers, confirming thus the prediction made by Moore (1956) for a rectangular corner, which has so far remained unconfirmed in the literature.For almost planar corners, three-dimensional corner boundary-layer features are shown, as in (Smith 1975), to arise when α ∼ O(1/ln Re). On the other hand, we show that the flow past a quarter-infinite flat plate would be attained when both values of the streamwise pressure gradient and external corner angle (π+2α) become O(1/ln Re) or smaller.Numerical results for all these flow regimes are presented and discussed.

scholarly journals Generalized impedance boundary conditions and shape derivatives for 3D Helmholtz problems

2016 ◽  
Vol 26 (10) ◽  
pp. 1995-2033 ◽  
Author(s):  
Djalil Kateb ◽  
Frédérique Le Louër
Keyword(s):  
Thin Layer ◽  
Three Dimensional ◽  
Transmission Problem ◽  
Impedance Boundary Condition ◽  
Constant Thickness ◽  
Laplacian Operator ◽  
Shape Sensitivity ◽  
Impedance Boundary ◽  
First Order ◽  
Exterior Boundary

This paper is concerned with the shape sensitivity analysis of the solution to the Helmholtz transmission problem for three-dimensional sound-soft or sound-hard obstacles coated by a thin layer. This problem can be asymptotically approached by exterior problems with an improved condition on the exterior boundary of the coated obstacle, called generalized impedance boundary condition (GIBC). Using a series expansion of the Laplacian operator in the neighborhood of the exterior boundary, we retrieve the first-order GIBCs characterizing the presence of an interior thin layer with a constant thickness. The first shape derivative of the solution to the original Helmholtz transmission problem solves a new thin layer transmission problem with non-vanishing jumps across the exterior and the interior boundary of the thin layer. We show that we can interchange the first-order differentiation with respect to the shape of the exterior boundary and the asymptotic approximation of the solution. Numerical experiments are presented to highlight the various theoretical results.

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