Preliminary Study on Side-Wall Boundary Layers in Transonic Shock Tube Airfoil Testing

2008 ◽  
Author(s):  
Masashi Kashitani ◽  
Yutaka Yamaguchi ◽  
Eisaku Sunahara ◽  
Hideki Kitano
Keyword(s):  
Shock Tube ◽  
Boundary Layers ◽  
Side Wall ◽  
Transonic Shock ◽  
Wall Boundary ◽  
Preliminary Study

Correction: A Preliminary Study on Transonic Shock Tube Airfoil Flows with Gurney Flap by utilizing PDI

2020 ◽  
Author(s):  
Masashi Kashitani ◽  
Masato Taguchi ◽  
Nguyen T. Duong ◽  
Akinori Oomori ◽  
Masanori Nishiyama ◽  
...  
Keyword(s):  
Shock Tube ◽  
Transonic Shock ◽  
Gurney Flap ◽  
Preliminary Study

On source-sink flows in a rotating fluid

1968 ◽  
Vol 32 (4) ◽  
pp. 737-764 ◽  
Author(s):  
R. Hide
Keyword(s):  
Boundary Layers ◽  
Normal Component ◽  
Fluid Motion ◽  
Side Wall ◽  
General Point ◽  
Main Body ◽  
End Effects ◽  
Wall Boundary ◽  
Side Walls ◽  
Source Sink

An incompressible fluid fills a container of fixed shape and size and of uniform cross-section in the (x, y)-plane, themrigid side walls and the two rigid end walls being in contact with the fluid. Here (x, y, z) are the Cartesian co-ordinates of a general point in the frame of reference in which the container is stationary. Fluid is withdrawn from the container atQcm3/sec via certain permeable parts of the side walls and replaced at the same steady rate via other permeable parts of the side walls. As, by hypothesis, the vorticity of the entering and leaving fluid relative to the container is zero, the concomitant fluid motion within the container, Eulerian velocityu= −∇ϕ − ∇ ×A, is irrotational when the container is stationary in an inertial frame. The present paper is concerned with the effects onuof uniform rotation of the whole system with angular velocity Ω about thez-axis when the normal component ofuon the side walls is independent ofz.In the simplest conceivable case,D≡zu−zlis infinite (butD/Qremains finite). End effects are then negligible anduis everywhere independent ofz.The solenoidal component ofu, − ∇ ×A, corresponds tojgyres, one for each of thejirreducible sets of circuits across which the net flow of fluid does not vanish that can be drawn within them-ply connected region bounded by the side walls. While ∇ϕ, which satisfies ∇2ϕ = 0, depends onQbut not on Ω,jandv(the coefficient of kinematic viscosity), ∇ ×Adepends on all these quantities but vanishes identically whenjΩ = 0. WhenjΩ ≠ 0 butv→ 0, ∇2A+ 2Ω, the absolute vorticity, tends to zero everywhere except in certain singular regions near the bounding surfaces, where boundary layers form.End effects cannot be ignored whenDis finite. WhenDis independent ofxandyand equal toD0(say) and Ω is sufficiently large for the boundary layers on the end walls to be of the Ekman type, 95% thickness δ = 3(v/Ω)½(δ [Lt ]D0), the end effects that then arise are only confined to these boundary layers whenj= 0. Whenj≠ 0 boundary-layer suction influences the flow everywhere; thus ∇2Aand ∇ϕ (but not ∇ ×A) are reduced to zero in the main body of the fluid, the regions of non-zero ∇ϕ and ∇2Abeing the Ekman boundary layers on the end walls and boundary layers of another type, 95% thickness δs(typically greater than δ), on the side walls. A theoretical analysis of the structure of these boundary layers shows that non-linear effects, though unimportant in the end-wall boundary layers, can be significant and even dominant in the side-wall boundary layers. The analysis of an axisymmetric system, whose side walls are two coaxial cylinders, suggests an approximate expression for Δs. WhenDis not everywhere independent ofxandy,non-viscous end effects arise which produce relative vorticity in the main body of the fluid even whenj= 0.Experiments using a variety of source-sink distribution generally confirm the results of the theory, show that instabilities of various kinds may occur under certain circumstances, and suggest several promising lines for future work.

Boundary-layer structure in a shock-generated plasma flow: Part 2. Experiments using a new quantitative schlieren technique

1968 ◽  
Vol 2 (2) ◽  
pp. 243-255 ◽  
Author(s):  
Stellan Knöös
Keyword(s):  
Boundary Layer ◽  
Shock Tube ◽  
Boundary Layers ◽  
Layer Structure ◽  
Argon Plasma ◽  
Side Wall ◽  
Plasma Boundary ◽  
Spherical Mirror ◽  
Schlieren Technique ◽  
Wall Boundary Layer

The shock-tube side-wall boundary layer in a 1 eV, high-density argon plasma was studied experimentally using anew, simple, quantitative schlieren technique. The angular refraction of light which enters the shock-tube test section parallel to a side wall and passes through typically 1 mm thick boundary layers was determined in two separate wavelengths. This was done by measuring the displacements of two shadows formed by two thin wires placed in the point source light, which is reflected non-centrally by a concave spherical mirror. The experiments were of exploratory nature only, but clearly demonstrated the feasibility of the new technique in analysing plasma-boundary-layer flows. Measured electron density profiles in the high-temperature region of the sidewall boundary layers agreed within experimental errors with those calculated from the equilibrium-boundary-layer theory.

Ionizing argon boundary layers. Part 2. Shock-tube side-wall boundary-layer flows

1979 ◽  
Vol 91 (4) ◽  
pp. 679-696 ◽  
Author(s):  
W. S. Liu ◽  
I. I. Glass
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Shock Tube ◽  
Flat Plate ◽  
Electron Number Density ◽  
Side Wall ◽  
Number Density ◽  
Electron Number ◽  
Wall Boundary ◽  
Wall Boundary Conditions

A combined experimental and theoretical investigation was conducted on the shock-tube side-wall ionizing boundary-layer induced by a shock wave moving into argon. The dual-wavelength interferometric boundary-layer data were obtained by using a 23 cm diameter Mach—Zehnder interferometer with the 10 × 18 cm Hypervelocity Shock Tube at initial shock Mach numbers of 13 and 16, an initial pressure of 5 torr and a temperature of 300° K. The plasma density and electron number density in the boundary layer were measured and compared with numerical profiles obtained by using an implicit finite-difference scheme for a two-temperature, chemical non-equilibrium, laminar boundary-layer flow in ionizing argon. The analysis included the variations of transport properties based on elastic-scattering cross-sections, effects of chemical reactions, radiation-energy losses and electron-sheath wall boundary conditions. Considering the difficulties involved in such complex plasma flows, satisfactory agreement was obtained between the analyses and experiments. A comparison was made with the flat-plate case and despite the very different velocity boundary conditions at the wall for the two flows the experimental data appear to be quite similar. The experimental bump in the profile of electron number density which was found in the flat-plate case was not found in the side-wall case. Comparisons and discussions of the results for the different types of boundary layer are presented, including a comparison between experimentally derived and analytical plasma-temperature profiles.

Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 2. Variable-area rectangular ducts with conducting sides

1971 ◽  
Vol 46 (4) ◽  
pp. 657-684 ◽  
Author(s):  
J. S. Walker ◽  
G. S. S. Ludford ◽  
J. C. R. Hunt
Keyword(s):  
Magnetic Field ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Side Wall ◽  
Transverse Magnetic ◽  
Reverse Direction ◽  
Wall Boundary ◽  
Strong Transverse ◽  
Side Walls ◽  
The Magnetic Field

In this paper the general analysis, developed in part 1, of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section. It is found that, with the magnetic field parallel to one pair of the sides, the essential problem is the analysis of the boundary layers on these (side) walls. Assuming that they are highly conducting and that those perpendicular to the magnetic field are non-conducting, the flow is found to have some interesting properties: if the top and bottom walls diverge, the side walls remaining parallel, then an O(1) velocity overshoot occurs in the side-wall boundary layers; but if the top and bottom walls remain parallel, the side walls diverging, these boundary layers have conventional velocity profiles. The most interesting flows occur when both pairs of walls diverge, when it is found that large, 0(M½), velocities occur in the side-wall boundary layers, either in the direction of the mean flow or in the reverse direction, depending on the geometry of the duct and the external electric circuit!The mathematical analysis involves the solution of a formidable integral equation which, however, does have analytic solutions for some special types of duct.

Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 3. Variable-area rectangular ducts with insulating walls

1972 ◽  
Vol 56 (1) ◽  
pp. 121-141 ◽  
Author(s):  
J. S. Walker ◽  
G. S. S. Ludford ◽  
J. C. R. Hunt
Keyword(s):  
Magnetic Field ◽  
Boundary Layers ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Flow Direction ◽  
Three Dimensional ◽  
Side Wall ◽  
Transverse Magnetic ◽  
Wall Boundary ◽  
Strong Transverse

The general analysis developed in Parts 1 and 2 of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section, the walls of which are electrically non-conducting. A dramatically different flow is found in this case from that studied in Part 2, where the side walls parallel to the magnetic field were highly conducting. Now it is found that the core velocity normalized with respect to the mean velocity is of O(M−½) while the velocity in the side-wall boundary layers is of O(M½), so that these boundary layers carry most of the flow. The problem of entry is solved by analysing the change from fully developed Hartmann flow in a rectangular duct to the flow in the diverging duct. It is found that the disturbance in the upstream duct decays exponentially. The analysis of the side-wall boundary layers is more difficult than that in Part 1 on account of the different boundary conditions and requires the solution of two coupled integro-differential equations. Numerical solutions are obtained for a duct whose width increases linearly in the flow direction.

A Preliminary Study on Transonic Shock Tube Airfoil Flows with Gurney Flap by utilizing PDI

2020 ◽  
Author(s):  
Masashi Kashitani ◽  
Masato Taguchi ◽  
Nguyen T. Duong ◽  
Akinori Oomori ◽  
Masanori Nishiyama ◽  
...  
Keyword(s):  
Shock Tube ◽  
Transonic Shock ◽  
Gurney Flap ◽  
Preliminary Study

scholarly journals Boundary Layer Effects on the Transonic Flow in a Straight Turbine Cascade

1992 ◽  
Author(s):  
M. Štastný ◽  
P. Šafařík
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Transonic Flow ◽  
Side Wall ◽  
Suction Side ◽  
Exit Angle ◽  
Turbine Cascade ◽  
Wall Boundary ◽  
2D Flow

The analysis presented here deals with two subjects related to the transonic flow in a straight turbine cascade: 1) turbulization of the suction side boundary layer and its subsequent development along the profile 2) influence of side wall boundary layers on cascade flows. The turbulization effect of supersonic compression on the boundary layers which accompany transonic expansion on the suction side of the profile is investigated by independent methods. Both the experimental results and the calculation confirm the loss of stability of the laminar boundary layer and its subsequent transition into turbulence in the region of an adverse pressure gradient. Also the possibility of reverse transition of turbulent boundary layer in a subsequent strong favourable pressure gradient is investigated. The contraction effect of the wind tunnel side wall boundary layers is expressed by means of the AVDR factor over a wide range of flow regimes determined by the incidence angle and the Mach number. A correction of the exit flow angle from the cascade is made to obtain a purely 2D flow although it is apparent that the measured exit angle values and the exit angle obtained for a 2D flow differ considerably.

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