Experiments on Supersonic Boundary-Layer Separation in Three Dimensions

1975 ◽  
Vol 42 (2) ◽  
pp. 289-294 ◽  
Author(s):  
W. D. Bachalo
Keyword(s):  
Three Dimensional ◽  
Cross Flow ◽  
Separated Flow ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Supersonic Boundary Layer ◽  
Three Dimensions ◽  
Pressure Gradients ◽  
Flat Plates ◽  
Relationship Of

A detailed experimental study of three-dimensional separation in supersonic flow is described. Three-dimensional wedges affixed to flat plates were used to generate the flow fields that were used to examine the relationship of cross flow to the extent of separation. Models with strong transverse pressure gradients resulted in a diminished extent of separation about the model plane of symmetry but demonstrated expansive growth of separation to a limit with distance from the plane of symmetry. A secondary flow region was found embedded in the separated flow.

Three-dimensional X-ray diffraction imaging of process-induced dislocation loops in silicon

2011 ◽  
Vol 44 (3) ◽  
pp. 526-531 ◽  
Author(s):  
David Allen ◽  
Jochen Wittge ◽  
Jennifer Stopford ◽  
Andreas Danilewsky ◽  
Patrick McNally
Keyword(s):  
Semiconductor Industry ◽  
Three Dimensional ◽  
Crystal Defects ◽  
Three Dimensions ◽  
Dimensional Structure ◽  
Dislocation Loops ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Imaging ◽  
Relationship Of

In the semiconductor industry, wafer handling introduces micro-cracks at the wafer edge and the causal relationship of these cracks to wafer breakage is a difficult task. By way of understanding the wafer breakage process, a series of nano-indents were introduced both into 20 × 20 mm (100) wafer pieces and into whole wafers as a means of introducing controlled strain. Visualization of the three-dimensional structure of crystal defects has been demonstrated. The silicon samples were then treated by various thermal anneal processes to initiate the formation of dislocation loops around the indents. This article reports the three-dimensional X-ray diffraction imaging and visualization of the structure of these dislocations. A series of X-ray section topographs of both the indents and the dislocation loops were taken at the ANKA Synchrotron, Karlsruhe, Germany. The topographs were recorded on a CCD system combined with a high-resolution scintillator crystal and were measured by repeated cycles of exposure and sample translation along a direction perpendicular to the beam. The resulting images were then rendered into three dimensions utilizing open-source three-dimensional medical tomography algorithms that show the dislocation loops formed. Furthermore this technique allows for the production of a video (avi) file showing the rotation of the rendered topographs around any defined axis. The software also has the capability of splitting the image along a segmentation line and viewing the internal structure of the strain fields.

Optimization Analysis on Gyroscope’s Three Dimensions Complicated Motion and Lash-Force

2014 ◽  
Vol 945-949 ◽  
pp. 581-586
Author(s):  
Wen Li Yang ◽  
Xiang Hui Lu
Keyword(s):  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Optimization Analysis ◽  
Motion Equations ◽  
Sliding Motion ◽  
Motion State ◽  
Motion Characteristics ◽  
Force Time ◽  
Relationship Of

The complicated motion of the gyroscope includes the rotation, the precession, the nutation and the sliding motion which are coupled, and it is affected by the lash-force by the whip. Taking the gyroscope which is moving stably as the research subject, according to the motion characteristics of the gyro’s rotation and precession, the gyro is assumed to be the two-force bar, and the coupled relationship of the gyroscope is analyzed quantitatively. The three-dimensional complicated motion in the different categories is analyzed. The nonlinear differential equations in the different categories is derived and linearized by the minor variables method, and then the three-dimensional motion equations on the rotation, precession, nutation and slipping of the gyroscope in the different categories is established. Take the big gym gyroscope as the example, the influence of the force, time and position of the whip on the motion state of the gyroscope is analyzed in detail, and provides the basis for the design of the gyroscope.

The Calculation of Three-Dimensional Turbulent Boundary Layers: Part I: Flow over the Rear of an Infinite Swept Wing

1967 ◽  
Vol 18 (1) ◽  
pp. 55-84 ◽  
Author(s):  
N. A. Cumpsty ◽  
M. R. Head
Keyword(s):  
Essential Feature ◽  
Three Dimensional ◽  
Cross Flow ◽  
Stream Velocity ◽  
Pressure Gradients ◽  
Swept Wing ◽  
Form Parameter ◽  
Method Of Calculation ◽  
Flow Profiles ◽  
Momentum Integral

SummaryA method of calculation has been developed in which all terms in the momentum integral equations in the streamwise and cross-flow directions are taken into account so that no restriction to small cross-flows is imposed. The essential feature of the method is the use of an entrainment equation which enables the development of the streamwise form parameter to be calculated along with the streamwise and cross-flow momentum thicknesses. Mager’s quadratic expression is used to relate streamwise and cross-flow profiles. The method has been applied to the idealised case of an infinite swept wing with free-stream velocity over the forward part of the chord and a linear adverse velocity gradient over the rear. The position of separation, the directions of the surface streamlines and the development of streamwise and cross-flow profiles have been calculated for a series of angles of sweep and for adverse pressure gradients of varying severity.

DNS of Expansion Ratio Effects on Three-Dimensional Unsteady Separated Flow and Heat Transfer Around a Downward Step

2005 ◽  
Author(s):  
Aya Kito ◽  
Kazuaki Sugawara ◽  
Hiroyuki Yoshikawa ◽  
Terukazu Ota
Keyword(s):  
Heat Transfer ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Side Wall ◽  
Separated Flow ◽  
Flow Region ◽  
Expansion Ratio ◽  
Mean Velocity ◽  
Flow And Heat Transfer ◽  
Channel Expansion

The direct numerical simulation methodology was employed to analyze the unsteady features of a three-dimensional separated flow and heat transfer around a downward step in a rectangular channel, and to clarify systematically the channel expansion ratio effects upon them. Numerical calculations were carried out using the finite difference method. The Reynolds number Re based on the mean velocity at inlet and the step height was varied from 300 to 1000. The channel expansion ratio ER is 1.5, 2.0 and 3.0 under a step aspect ratio of 36.0. It is found that the flow is steady upto Re = 500 but becomes sensibly unsteady at Re = 700 for all the three expansion ratios. In the case of ER = 2.0, the separated shear layer is most unstable. In the case of ER = 1.5, the longitudinal vortices formed near the side walls of channel are strongest. Nusselt number reaches its maximum in the reattachment flow region and also in the neighborhood of the side wall, and their locations depend greatly upon ER and Re.

Three Dimensional Numerical Modelling of Staggered Tube Bundle Turbulent Crossflow in Duct

2005 ◽  
Author(s):  
Ahad Ramezanpour ◽  
Hassan Shirvani ◽  
Ramin Rahmani ◽  
Iraj Mirzaee
Keyword(s):  
Nusselt Number ◽  
Numerical Study ◽  
Tube Bundle ◽  
Three Dimensional ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Wall Function ◽  
Flat Plates ◽  
Geometrical Characteristics ◽  
Commercial Code

A numerical study has been conducted to investigate the three dimensional (3D) staggered tube bundle turbulent cross flow confined between two parallel flat plates using RNG k-ε model and standard wall function utilizing commercial code FLUENT. The maximum Reynolds numbers of 1000, 5000, and 50000 and the distance between plates of H = 3, 5, 10, 15, and 20 mm have been considered. The arrangement of the staggered tube bundle is fix with geometrical characteristics of Sn/D = 1.5 and Sp/D = 1.2 which has been found optimum in previous two-dimensional studies. The constant temperature of 360K on tubes, constant inlet flow and plates’ temperature of 300K have been set as the boundary conditions. The global Nusselt number, friction factor for the dissimilar Reynolds numbers, distance between plates, local Nusselt number and different angles on first and third tubes have been evaluated.

Viscous flow over a cone at moderate incidence. Part 2. Supersonic boundary layer

1973 ◽  
Vol 59 (3) ◽  
pp. 593-620 ◽  
Author(s):  
T. C. Lin ◽  
S. G. Rubin
Keyword(s):  
Boundary Layer ◽  
Viscous Flow ◽  
Three Dimensional ◽  
Cross Flow ◽  
Lateral Diffusion ◽  
Supersonic Boundary Layer ◽  
Half Angle ◽  
Local Shear ◽  
Sharp Cone ◽  
Good Agreement

A finite-difference method recently developed to study three-dimensional viscous flow is applied here to the supersonic boundary layer on a sharp cone at moderate angles of incidence (α/θ [les ] 2, angle of attack α, cone half-angle θ). The present analysis differs from previous investigations of this region in that (i) boundary-layer similarity is not assumed, (ii) the system of governing equations incorporates lateral diffusion and centrifugal force effects, and (iii) an improved numerical scheme for three-dimensional viscous flows of the type considered here is used. Solutions are shown to be non-similar at the separation streamline with local shear-layer formation. Detailed flow structure, including surface heat transfer, boundary-layer profiles and thickness, and the formation of swirling pairwise symmetric vortices, associated with cross-flow separation, are obtained. Good agreement is obtained between the present theoretical results and the existing experimental data.

Boundary-layer separation of rotating flows past surface-mounted obstacles

1992 ◽  
Vol 237 ◽  
pp. 343-371 ◽  
Author(s):  
K. J. Richards ◽  
D. A. Smeed ◽  
E. J. Hopfinger ◽  
G. Chabert D'Hières
Keyword(s):  
Flow Separation ◽  
Three Dimensional ◽  
Separated Flow ◽  
Boundary Layer Separation ◽  
Critical Value ◽  
Complex Stress ◽  
Rotating Fluid ◽  
Separation Line ◽  
Maximum Value ◽  
The Hill

This paper describes laboratory experiments on the flow over a three-dimensional hill in a rotating fluid. The experiments were carried out in towing tanks, placed on rotating tables. Rotation is found to have a strong influence on the separation behind the hill. The topology of the separation is found to be the same for all the flows examined. The Rossby number R in the experiments is of order 1, the maximum value being 6. The separated flow is dominated by a single trailing vortex. In the majority of cases the surface stress field has a single separation line and there are no singular points. In a few experiments at the highest Rossby numbers the observations suggest more complex stress fields but the results are inconclusive.A criterion for flow separation is sought. For values of D/L > 1, where D is the depth of the flow and L the lengthscale of the hill, separation is found to be primarily dependent on R. At sufficiently small values of R separation is suppressed and the flow remains fully attached.Linear theory is found to give a good estimate for the critical value of R for flow separation. For hills with a moderate slope (slope ≤ 1) this critical value is around 1, decreasing with increasing slope. It is postulated that the existence of a single dominant trailing vortex is due to the uplifting and subsequent turning of transverse vorticity generated by surface pressure forces upstream of the separation line.

Modeling of Three-Dimensional Flow in Turning Channels

1984 ◽  
Vol 106 (3) ◽  
pp. 682-691 ◽  
Author(s):  
I. M. Khalil ◽  
H. G. Weber
Keyword(s):  
Stokes Equations ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Curved Channels

The structure of developing flows inside curved channels has been investigated numerically using the time-averaged Navier Stokes equations in three dimensions. The equations are solved in primitive variables using finite difference techniques. The solution procedure involves a combination of repeated space-marching integration of the governing equations and correction for elliptic effects between two marching sweeps. Type-dependent differencing is used to permit downstream marching even in the reverse-flow regions. The procedure is shown to allow efficient calculations of turbulent flow inside strongly curved channels as well as laminar flow inside a moderately curved passage. Results obtained in both cases indicate that the flow structure is strongly controlled by local imbalance between centrifugal forces and pressure gradients. Furthermore, distortion of primary flow due to migration of low momentum fluid caused by secondary flow is found to be largely dependent on the Reynolds number and Dean number. Comparison with experimental data is also included.

Flow Characterization of a Three-Dimensional Separated Annular Diffuser

2009 ◽  
Author(s):  
Jason J. Dunn ◽  
Mark Ricklick ◽  
J. S. Kapat
Keyword(s):  
Vertical Wall ◽  
Three Dimensional ◽  
Separated Flow ◽  
Outer Wall ◽  
Reynolds Numbers ◽  
Pressure Gradients ◽  
Cfd Models ◽  
Flow Characterization ◽  
Annular Diffuser

Experiments were performed on two annular diffusers to characterize the flow separation along the outer wall. Both diffusers had the same fully developed inlet flow condition, however, the expansion of the two diffusers differed such that one diffuser replicated a typical compressor discharge diffuser found in a real machine while the other would create a natural separated flow along the outer wall. Both diffusers were tested at two Reynolds numbers, 5×104 and 1×105, with and without a vertical wall downstream of the exit to replicate the dump diffuser that re-directs the flow from the compressor outlet to the combustor. It was shown that the separation happens quite quickly within the diffuser after which the pressure recovery remains fairly constant. The results also further validate claims that CFD models can not accurately predict flows with high adverse pressure gradients.

scholarly journals Calculation of the Maximum Number of Cutting Finite Fields in the Multi-dimensions

2017 ◽  
Vol 9 (4) ◽  
pp. 49
Author(s):  
Erick C. Huang ◽  
Sharon S. Huang ◽  
Cheng-Hua Tsai
Keyword(s):  
General Formula ◽  
Finite Fields ◽  
Original Problem ◽  
Three Dimensional ◽  
Maximum Amount ◽  
Three Dimensions ◽  
Infinite Plane ◽  
Euler’S Formula ◽  
Relationship Of

The original problem that serves as a basis for this project comes from an American contest (PUMaC, 2014) regarding the maximum amount of enclosed spaces given a limited number of cuts on an infinite plane. In this study, we explore the same problem and extend it in the context of m dimensions given n (m-1) dimensional cuts using the recursive relationship of finite cuts and enclosed spaces in lower dimensions. Once the general formula of f(m,n) was proven for dimensions, an Euler’s inspired formula was used to check the accuracy of the formula in two and three dimensions. The Euler’s formula also allowed us to derive the formula for the maximum number of unenclosed spaces in three-dimensional F(3, n). The results are as follows:

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