GLOBAL MULTIDIMENSIONAL SHOCK WAVE FOR THE STEADY SUPERSONIC FLOW PAST A THREE-DIMENSIONAL CURVED CONE

2006 ◽  
Vol 04 (02) ◽  
pp. 101-132 ◽  
Author(s):  
ZHOUPING XIN ◽  
HUICHENG YIN
Keyword(s):  
Shock Wave ◽  
Boundary Condition ◽  
Supersonic Flow ◽  
Global Existence ◽  
Three Dimensional ◽  
Flow Equation ◽  
Flow Past ◽  
Existence And Stability ◽  
Whole Space ◽  
Steady Potential

In this paper, we establish the global existence and stability of a multidimensional conic shock wave for three-dimensional steady supersonic flow past an infinite cone. The flow is assumed to be hypersonic and described by a steady potential flow equation. Under an appropriate boundary condition on the curved cone, we show that a pointed shock attached at the vertex of the cone will exist globally in the whole space.

scholarly journals Laminar buffet and flow control

2019 ◽  
Vol 234 (1) ◽  
pp. 124-139 ◽  
Author(s):  
V Brion ◽  
J Dandois ◽  
R Mayer ◽  
P Reijasse ◽  
T Lutz ◽  
...  
Keyword(s):  
Shock Wave ◽  
Separation Bubble ◽  
Control Strategies ◽  
Three Dimensional ◽  
Low Frequency ◽  
Frequency Component ◽  
High Frequency Component ◽  
Mean Flow ◽  
Flow Past ◽  
The Impact

An experimental investigation of the transonic flow past the laminar OALT25 airfoil has been conducted to analyze the impact of laminar flow upon the shock wave dynamics and the existence of a laminar buffet like phenomenon. Tests have been carried out at freestream Mach numbers varying in the range of 0.7–0.8, angle of attack from 0.5° to 4°, and with two tripping configurations at the upper surface of the wing. The (airfoil) chord based Reynolds number is about three million. Results obtained from pressure taps and sensors measurements, as well as Schlieren visualizations of the flow reveal the presence of a laminar buffet phenomenon in sharp contrast with the turbulent phenomenon, as it features a freestream- and chord-based normalized frequency of about unity while turbulent buffet occurs for a frequency close to 0.07 (Jacquin et al., AIAA J 2009; 47). A low-frequency mode, at a frequency of about 0.05 is also present in the laminar situation, notably lower than the high-frequency component. The latter exhibits strong oscillations of the shock foot and vertical wavelike deformations of the shock wave and the former moves the shock back and forth over a small portion of chord, quite similar to the turbulent phenomenon. The mean flow past the laminar wing is characterized by a laminar separation bubble under the shock foot, which likely contributes much to the novel dynamics revealed by the present experiments. Two control strategies of the unsteady shock wave are implemented, one consisting of three-dimensional bumps and one consisting of steady jets blowing transversely to the freestream. It is found that bumps provide a significant reduction of the buffet intensity in the laminar situation. The jets are able to completely remove the flow unsteadiness in both laminar and turbulent conditions.

A new approach to problems of shock dynamics Part 2. Three-dimensional problems

1959 ◽  
Vol 5 (3) ◽  
pp. 369-386 ◽  
Author(s):  
G. B. Whitham
Keyword(s):  
Shock Wave ◽  
Supersonic Flow ◽  
Three Dimensional ◽  
Functional Relation ◽  
Plane Shock Wave ◽  
Plane Shock ◽  
Special Choice ◽  
Approximate Theory ◽  
Symmetrical Body ◽  
The Stability

This paper gives the extension of the approximate theory developed in Part 1 (Whitham 1957) to three-dimensional problems. The basic equations are derived in §1, using the original assumption of a functional relation between the strength of the shock wave at any point and the area of the ray tube. An analogy with steady supersonic flow is found. For the diffraction of a plane shock wave by an obstacle, the equations and boundary conditions are exactly the same as those for steady supersonic potential flow past that obstacle, with a special choice of the density-speed relation. The successive positions of the shock wave are the equipotential surfaces of the supersonic flow. The 'shock-shocks’ introduced in Part 1, i.e. discontinuities in the slope and Mach number of the shock wave, correspond to the steady oblique shock waves in the supersonic flow problem. They arise when Mach reflexion occurs.In §2 the theory is applied in detail to the diffraction of a plane shock wave by a cone. Then, in §3, a small perturbation theory is applied to the two typical problems of (i) diffraction by a slender axi-symmetrical body of general shape, and (ii) the stability of a plane shock. Many further applications would be possible and some brief comments on these are made in §4.

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