Mechanisms in the hypersonic laminar near wake of a blunt body

A new theoretical framework, based on the analysis of Navier–Stokes solutions for the hypersonic laminar near wake of two-dimensional and axisymmetric blunt bodies, is presented. A semi-empirical relationship is derived between the free-stream Mach and Reynolds numbers and a characteristic wake Reynolds number. A control volume analysis was performed to assess the validity of some common assumptions used in the literature. Analysis of the momentum and vorticity equations is used to assess the dominant mechanisms of momentum transfer along and across the dividing streamline and centreline which enclose the near wake. An observed stagnation pressure gain along the dividing streamline is explained using the entropy transport equation, demonstrating an unbalance between entropy generation due to viscous dissipation and entropy diffusion. The rear-stagnation point flow is analysed using an analogy to a reversed flow jet which allows for the centreline Mach number to be solved. A new viscous–inviscid interaction theory is presented for the reattachment shock formation process for both planar and axisymmetric wakes. Finally, all of the sub-mechanisms are combined into an overall wake mechanism. The resulting equations constitute the first overall theoretical framework of the laminar near-wake mechanism including separation, reattachment, rear-stagnation point flow and dividing streamline stagnation pressure gain for both planar and axisymmetric near wakes. Scaling arguments are presented throughout the work for each of the key sub-mechanisms. Recommendations are made for how experimental and numerical results for the near wake should be presented. The equations and recommendations presented here are then used to perform a detailed disambiguation of laminar capsule studies in the literature.

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On the singular points in the laminar two-dimensional near wake flow field

Journal of Fluid Mechanics ◽

10.1017/s002211206800234x ◽

1968 ◽

Vol 33 (1) ◽

pp. 39-63 ◽

Cited By ~ 33

Author(s):

Sheldon Weinbaum

Keyword(s):

Stagnation Point ◽

Series Solution ◽

Wake Flow ◽

Navier Stokes ◽

Two Dimensional ◽

Near Wake ◽

Type Series ◽

Stagnation Points ◽

Insight Into ◽

Rear Stagnation Point

It is shown that useful information concerning the flow in the neighbourhood of the various separation and stagnation points in the laminar near wake of a blunt-based two-dimensional wedge can be learned from the locally valid Stokes type series solutions to the incompressible Navier-Stokes vorticity equation derived previously by Dean & Montagnon (1949) and Moffatt (1964). This theory, which is in qualitative agreement with the experiments of Hama (1967) and Donaldson (1967), shows that the flow separates from the base of a blunt-based body and not from its trailing edge. The series solution for the two-dimensional stagnation point is treated in detail and compared with Howarth's (1934) numerical solution in order to study the convergence and conditions for completeness of the Stokes type series solution. Finally, the wake rear stagnation point is examined to provide insight into the problem of wake closure.

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On the differential equation governing the rear stagnation point in magnetohydrodynamics and Goldstein's ‘backward’ boundary layers

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100042353 ◽

1967 ◽

Vol 63 (4) ◽

pp. 1327-1330 ◽

Cited By ~ 4

Author(s):

S. Leibovich

Keyword(s):

Differential Equation ◽

Boundary Value Problem ◽

Stagnation Point ◽

Boundary Layers ◽

Existence And Uniqueness ◽

Boundary Value ◽

Stagnation Point Flow ◽

Special Cases ◽

Rear Stagnation Point

AbstractExistence and uniqueness proofs for a boundary-value problem associated with a magnetohydrodynamic Falkner–Skan equation are presented. Relevant special cases of the problem herein considered include the magnetohydrodynamic rear stagnation point flow, and the non-magnetic ‘backward boundary layers’ of Goldstein(2).

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Unsteady MHD Rear Stagnation-Point Flow of a Hybrid Nanofluid with Heat Generation/Absorption Effect

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences ◽

10.37934/arfmts.87.1.4151 ◽

2021 ◽

Vol 87 (1) ◽

pp. 41-51

Author(s):

Nurul Amira Zainal ◽

Kohilavani Naganthran ◽

Roslinda Nazar

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Stagnation Point ◽

Heat Generation ◽

Stagnation Point Flow ◽

Hybrid Nanofluid ◽

Absorption Effect ◽

Suction Parameter ◽

The Impact ◽

Rear Stagnation Point

The study of unsteady flow is essential in various engineering systems, for instance, the periodic fluid motion and start-up process. Therefore, this numerical study focuses on examining the unsteady magnetohydrodynamics (MHD) rear stagnation-point flow in Al2O3-Cu/H2O hybrid nanofluid past a permeable stretching/shrinking surface with the impact of heat generation/absorption. By choosing a suitable similarity transformation, partial differential equations are transformed into a system of nonlinear ordinary differential equations and solved using the bvp4c function in the MATLAB package. The effects of the solution domain’s operating parameters are analysed, and dual solutions are observable as the sheet shrinks. It is found that the addition of the suction parameter escalates the heat transfer efficiency. Eventually, the existence of the unsteadiness parameter and the heat generation/absorption effect significantly encourage heat transfer deterioration.

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Oscillating stagnation point flow

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1982.0153 ◽

1982 ◽

Vol 384 (1786) ◽

pp. 175-190 ◽

Cited By ~ 20

Keyword(s):

Boundary Layer ◽

Stagnation Point ◽

High Frequency ◽

Stokes Equations ◽

Stagnation Point Flow ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Analytic Approximations ◽

Numerical Integrations ◽

Hiemenz Flow

A solution of the Navier-Stokes equations is given for an incompressible stagnation point flow whose magnitude oscillates in time about a constant, non-zero, value (an unsteady Hiemenz flow). Analytic approximations to the solution in the low and high frequency limits are given and compared with the results of numerical integrations. The application of these results to one aspect of the boundary layer receptivity problem is also discussed.

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Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate

Journal of Heat Transfer ◽

10.1115/1.4005742 ◽

2012 ◽

Vol 134 (6) ◽

Cited By ~ 11

Author(s):

Ali Shokrgozar Abbassi ◽

Asghar Baradaran Rahimi

Keyword(s):

Heat Transfer ◽

Strain Rate ◽

Flat Plate ◽

Stagnation Point ◽

Stagnation Point Flow ◽

Navier Stokes ◽

Variable Velocity ◽

Two Dimensional ◽

Flow And Heat Transfer ◽

Energy Equations

General formulation and solution of Navier–Stokes and energy equations are sought in the study of two-dimensional unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration toward main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces an unsteady two-dimensional flow in which the plate moves along z-direction with variable velocity and acceleration in general. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. Velocity and pressure profiles, boundary layer thickness, and surface stress-tensors along with temperature profiles are presented for different examples of impinging fluid strain rate, selected values of plate velocity, and Prandtl number parameter.

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Unsteady Reversed Stagnation-Point Flow over a Flat Plate

ISRN Applied Mathematics ◽

10.5402/2012/430432 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Vai Kuong Sin ◽

Chon Kit Chio

Keyword(s):

Laminar Flow ◽

Flow Field ◽

Asymptotic Solution ◽

Stagnation Point ◽

Stokes Equations ◽

Stagnation Point Flow ◽

Navier Stokes ◽

Two Dimensional ◽

Total Flow ◽

Navier Stokes Equations

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. Robins and Howarth (1972) stated that this is not true in neglecting the viscous terms within the total flow field. Viscous terms in this analysis are now included, and a similarity solution of two-dimensional reversed stagnation-point flow is investigated by solving the full Navier-Stokes equations.

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Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate

Journal of Fluids Engineering ◽

10.1115/1.3153366 ◽

2009 ◽

Vol 131 (7) ◽

Cited By ~ 14

Author(s):

Ali Shokrgozar Abbassi ◽

Asghar Baradaran Rahimi

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Flat Plate ◽

Stagnation Point ◽

Stokes Equations ◽

Three Dimensional ◽

Stagnation Point Flow ◽

Navier Stokes ◽

Dimensional Flow ◽

Flow And Heat Transfer

The existing solutions of Navier–Stokes and energy equations in the literature regarding the three-dimensional problem of stagnation-point flow either on a flat plate or on a cylinder are only for the case of axisymmetric formulation. The only exception is the study of three-dimensional stagnation-point flow on a flat plate by Howarth (1951, “The Boundary Layer in Three-Dimensional Flow—Part II: The Flow Near Stagnation Point,” Philos. Mag., 42, pp. 1433–1440), which is based on boundary layer theory approximation and zero pressure assumption in direction of normal to the surface. In our study the nonaxisymmetric three-dimensional steady viscous stagnation-point flow and heat transfer in the vicinity of a flat plate are investigated based on potential flow theory, which is the most general solution. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces a two-dimensional flow with different components of velocity on the plate. This situation may happen if the flow pattern on the plate is bounded from both sides in one of the directions, for example x-axis, because of any physical limitation. A similarity solution of the Navier–Stokes equations and energy equation is presented in this problem. A reduction in these equations is obtained by the use of appropriate similarity transformations. Velocity profiles and surface stress-tensors and temperature profiles along with pressure profile are presented for different values of velocity ratios, and Prandtl number.

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Unsteady MHD rear stagnation-point flow over off-centred deformable surfaces

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-04-2016-0160 ◽

2017 ◽

Vol 27 (7) ◽

pp. 1554-1570 ◽

Cited By ~ 7

Author(s):

Mustafa Turkyilmazoglu ◽

Kohilavani Naganthran ◽

Ioan Pop

Keyword(s):

Differential Equations ◽

Stagnation Point ◽

Design Methodology ◽

Flow Characteristics ◽

Stagnation Point Flow ◽

Content Type ◽

Flow Problems ◽

Deformable Surfaces ◽

Practical Implications ◽

Rear Stagnation Point

Purpose The purpose of this paper is to present both an analytical and a numerical analysis of the unsteady magnetohydrodynamic (MHD) rear stagnation-point flow over off-centred deformable surfaces. Design/methodology/approach The numerical MATLAB solver bvp4c suitable for routine boundary value problem is used for the set of ordinary differential equations reduced from the governing partial differential equations. Findings Multiple solutions are found for particular eigenvalues. The physical solution is computed by the help of a linear stability analysis. The authors have succeeded in discovering the second solutions, and it is suggested that these solutions are unstable and not physically realisable in practice. The current findings add to a growing body of literature on MHD stagnation-point flow problems. It is also found that the governing parameters have different effects on the flow characteristics. Practical implications Even though problems of steady MHD flows have been extensively studied for stagnation-point flows, limited findings can be found on the unsteady MHD rear stagnation-point flow over off-centred deformable surfaces. Originality/value The originality of this work is the application of a magnetic field on a time-dependent MHD rear stagnation-point flow over off-centred deformable surfaces.

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