Asymptotic Theory of Separated Flows

Sychev, Vladimir V.; Ruban, Anatoly I.; Sychev, V. V.; Korolev, Georgi L.; Maroko, Elena V.

doi:10.1017/cbo9780511983764

Cited by 156 publications

(149 citation statements)

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“…In Sychev et al (1998), different approaches are described to solve these kind of problems. Our method consists of using finite differences in the x-direction (stream-wise direction) and Chebyshev collocation method in the y-direction (wall normal direction) using the technique as described in Korolev et al (2002), Logue (2008).…”

Section: Numerical Methods To Solve the Non-linear Problemmentioning

confidence: 99%

Subsonic flow past localised heating elements in boundary layers

Aljohani

Gajjar

2017

J. Fluid Mech.

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The problem of subsonic flow past micro-electro-mechanical-type (MEMS-type) heating elements placed on a flat surface, where the MEMS devices have hump-shaped surfaces, is investigated using triple deck theory. The compressible Navier-Stokes equations supplemented by the energy equation are considered in the limit that the Reynolds number is large. The triple deck problem is formulated and the linear and non-linear analysis and results are presented. The current work is a generalisation of the problem discussed by (Koroteev & Lipatov 2012, 2013 where the MEMS devices have flat shaped surfaces. The results show the hump-shaped heating elements enhance large drops in pressure and peaks and troughs in the skin-friction over the centre of the hump as compared to the flat shaped devices which may be useful for controlling the flow.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfmkeywords.pdf for the full list)

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Section: Numerical Methods To Solve the Non-linear Problemmentioning

confidence: 99%

Subsonic flow past localised heating elements in boundary layers

Aljohani

Gajjar

2017

J. Fluid Mech.

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“…Boundary conditions include the following: Flow velocity is tangential at the body surface, pressure in the wake and along the free streamlines is equal to the far-field pressure, and the separation points are prescribed. Our simulation is not expected to apply near separation (22) but is robust provided that the high-curvature corner is confined to the wake. We therefore place the separation points upstream of the corner by 2% of the perimeter length and find consistent results if this value is doubled or halved.…”

Section: Methodsmentioning

confidence: 99%

Sculpting of an erodible body by flowing water

Ristroph

Moore

Childress

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

112

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Erosion by flowing fluids carves striking landforms on Earth and also provides important clues to the past and present environments of other worlds. In these processes, solid boundaries both influence and are shaped by the surrounding fluid, but the emergence of morphology as a result of this interaction is not well understood. We study the coevolution of shape and flow in the context of erodible bodies molded from clay and immersed in a fast, unidirectional water flow. Although commonly viewed as a smoothing process, we find that erosion sculpts pointed and cornerlike features that persist as the solid shrinks. We explain these observations using flow visualization and a fluid mechanical model in which the surface shear stress dictates the rate of material removal. Experiments and simulations show that this interaction ultimately leads to selfsimilarly receding boundaries and a unique front surface characterized by nearly uniform shear stress. This tendency toward conformity of stress offers a principle for understanding erosion in more complex geometries and flows, such as those present in nature.R eflecting on his scientific discoveries, Isaac Newton compared himself to a boy on the seashore who marvels at having found a yet smoother stone (1). For pebbles and mountains alike, our curiosity about natural sculptures stems perhaps from the realization that these shapes reflect countless incremental events acting over eons. Morphology is often the only clue available as we attempt to reconstruct the physical history of the Earth as well as of our neighboring worlds (2-6). Recreating geologically inspired situations in the laboratory offers an opportunity to connect the development of structures to the underlying processes at work (7). This approach has been used to study phenomena across many scales, for example, the rounding of rocks by abrasion (8), the formation of rivers (9) and drainage channels (10), and the drift of continental plates driven by mantle convection (11).Rather than mimic a particular geological scenario, we conduct experiments that isolate a central aspect common to all erosive processes: the interdependent evolution of shape and flow (3). As described in Methods, we study the erosion of soft clay bodies by fast-flowing water, allowing us to witness what is an intractably slow process in nature. We consider unidirectional flow and canonical initial geometries-a thin flat bed of clay, a cylinder, and a sphere-with an eye toward informing mathematical models that intimately link the coevolving flow and shape (12, 13). Our experiments typically involve centimeter-scale bodies immersed in flows of 40-70 cm/s, yielding high Reynolds numbers of order 10 4 . Importantly, the solid boundaries recede at rates (approximately centimeters per hour) that are many orders slower than the flow speed, preserving the large separation of time-scales characteristic of natural erosion.Considering first the case of a 3D body, we form a clay sphere of diameter 4.9 cm and support it within a water tunnel with a cro...

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“…As far as separation phenomena are concerned, the theory has been extended to describe boundary-layer separation from a smooth body surface in incompressible fluid flow, supersonic flow separation provoked by a shock wave impinging upon the boundary layer, incipient and large-scale separations at angular points of the body contour both in subsonic and supersonic flows, separation at the trailing edge of a thin aerofoil appearing as a result of increase of the angle of attack or the aerofoil thickness, leading-edge separation, separation of the boundary layer in hypersonic flow on a hot or cold wall, separation provoked by a wall roughness, etc. ; see Sychev et al (1998) and references therein. However, summarizing the results of a century long effort in this field, we have to admit that despite the significance of the progress made, many aspects of the theory of separated flows remain unresolved.…”

Section: Introductionmentioning

confidence: 99%

Once again on the supersonic flow separation near a corner

2002

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Laminar boundary-layer separation in the supersonic flow past a corner point on a rigid body contour, also termed the compression ramp, is considered based on the viscous-inviscid interaction concept. The 'triple-deck model' is used to describe the interaction process. The governing equations of the interaction may be formally derived from the Navier-Stokes equations if the ramp angle θ is represented as θ = θ 0 Re −1/4 , where θ 0 is an order-one quantity and Re is the Reynolds number, assumed large. To solve the interaction problem two numerical methods have been used. The first method employs a finite-difference approximation of the governing equations with respect to both the streamwise and wall-normal coordinates. The resulting algebraic equations are linearized using a Newton-Raphson strategy and then solved with the Thomas-matrix technique. The second method uses finite differences in the streamwise direction in combination with Chebychev collocation in the normal direction and Newton-Raphson linearization.Our main concern is with the flow behaviour at large values of θ 0 . The calculations show that as the ramp angle θ 0 increases, additional eddies form near the corner point inside the separation region. The behaviour of the solution does not give any indication that there exists a critical value θ * 0 of the ramp angle θ 0 , as suggested by Smith & Khorrami (1991) who claimed that as θ 0 approaches θ * 0 , a singularity develops near the reattachment point, preventing the continuation of the solution beyond θ * 0 . Instead we find that the numerical solution agrees with Neiland's (1970) theory of reattachment, which does not involve any restriction upon the ramp angle.

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Asymptotic Theory of Separated Flows

Cited by 156 publications

References 0 publications

Subsonic flow past localised heating elements in boundary layers

Subsonic flow past localised heating elements in boundary layers

Sculpting of an erodible body by flowing water

Once again on the supersonic flow separation near a corner

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