Mixed Convection on a Vertical Flat Plate With Transition and Separation

1990 ◽  
Vol 112 (1) ◽  
pp. 144-150 ◽  
Author(s):  
T. Cebeci ◽  
D. Broniewski ◽  
C. Joubert ◽  
O. Kural
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stability Theory ◽  
Separation Bubble ◽  
Boundary Layer Separation ◽  
Laminar Flows ◽  
Linear Stability Theory ◽  
Boundary Layer Equations ◽  
Heating And Cooling ◽  
Vertical Flat Plate

A numerical method has been developed and used to calculate the flow properties of laminar, transitional, and turbulent boundary layers on a vertical flat plate with heat transfer. The governing boundary-layer equations include a buoyancy-force term and are solved by a two-point finite-difference method due to Keller and results obtained for heating and cooling and, in the case of the laminar flows, for an isothermal surface corresponding to that of Merkin. Cooled plates with unheated sections can give rise to boundary-layer separation and reattachment and, on occasions, transition can occur within the separation bubble. Flows of this type have been examined with the inviscid-viscous interaction procedure developed by Cebeci and Stewartson and the location of transition obtained by the en method based on the linear stability theory for air with Pr = 1. Results are given in dimensionless form as a function of Reynolds number, Richardson number, and Prandtl number and quantify those parameters that give rise to separation. Consequences of the use of interaction and stability theory are examined in detail.

scholarly journals Joule Heating Effect on the Coupling of Conduction with Magnetohydrodynamic Free Convection Flow from a Vertical Flat Plate

2007 ◽  
Vol 12 (3) ◽  
pp. 307-316 ◽  
Author(s):  
M. A. Alim ◽  
Md. M. Alam ◽  
Abdullah Al-Mamun
Keyword(s):  
Boundary Layer ◽  
Surface Temperature ◽  
Flat Plate ◽  
Skin Friction ◽  
Joule Heating ◽  
Convection Flow ◽  
Boundary Layer Equations ◽  
Box Scheme ◽  
Implicit Finite Difference ◽  
Vertical Flat Plate

The present work describes the effect of magnetohydrodynamic (MHD) natural convection flow along a vertical flat plate with Joule heating and heat conduction. The governing boundary layer equations are first transformed into a non-dimensional form and resulting nonlinear system of partial differential equations are then solved numerically by using the implicit finite difference method with Keller box scheme. The results of the skin friction co-efficient, the surface temperature distribution, the velocity and the temperature profiles over the whole boundary layer are shown graphically for different values of the Prandtl number Pr (Pr = 1.74, 1.00, 0.72, 0.50, 0.10), the magnetic parameter M (M = 1.40, 0.90, 0.50, 0.10) and the Joule heating parameter J (J = 0.90, 0.70, 0.40, 0.20). Numerical values of the skin friction coefficients and surface temperature distributions for different values of Joule heating parameter have been presented in tabular form.

Instability and transition mechanisms induced by skewed roughness elements in a high-speed laminar boundary layer

2016 ◽  
Vol 805 ◽  
pp. 262-302 ◽  
Author(s):  
Gordon Groskopf ◽  
Markus J. Kloker
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Linear Stability ◽  
Stability Theory ◽  
High Speed ◽  
Roughness Element ◽  
Linear Stability Theory ◽  
Minor Importance ◽  
Roughness Elements ◽  
Second Mode

The disturbance evolution in a Mach-4.8 zero-pressure-gradient flat-plate boundary-layer flow altered by discrete three-dimensional roughness elements is investigated including a laminar breakdown scenario. Direct numerical simulation (DNS), as well as the biglobal linear stability theory based on two-dimensional eigenfunctions in flow cross-sections, are applied. Roughness elements with high ratios of spanwise width to streamwise length are compared at varying height and skewing angles with respect to the oncoming flow. For an oblique roughness, the element’s height is varied between 27 % and 68 % of the undisturbed boundary-layer thickness. Compared to a symmetric roughness element an obliquely placed element generates a more pronounced low-speed streak in the roughness wake. The linear stability analysis reveals the occurrence of eigenmodes that can be associated with the first and second modes in the flat-plate flow. At identical roughness height, larger amplification is found for the eigenmodes of the oblique set-up. The results are confirmed by unsteady DNS showing very good agreement with stability theory; transient-growth behaviour in the near wake of the roughness is of minor importance. The comparison of the results gained for adiabatic wind-tunnel flow conditions with those for atmospheric-flight conditions with wall cooling reveals significant differences in the wake vortex system with subsequent impact on the stability properties of the flow. The hot-flow cases are less unstable at identical roughness Reynolds numbers. A variation of the wall cooling shows that the roughness-wake first- and second-mode behaviour is similar to that of the flat-plate flow: wall cooling stabilizes the first-mode and destabilizes the second-mode instabilities of the roughness wake.

scholarly journals Large-eddy simulation of laminar transonic buffet

2018 ◽  
Vol 850 ◽  
pp. 156-178 ◽  
Author(s):  
Julien Dandois ◽  
Ivan Mary ◽  
Vincent Brion
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Separation Bubble ◽  
Oscillation Amplitude ◽  
Boundary Layer Separation ◽  
Stream Velocity ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Shock Oscillation ◽  
Transonic Buffet

A large-eddy simulation of laminar transonic buffet on an airfoil at a Mach number $M=0.735$, an angle of attack $\unicode[STIX]{x1D6FC}=4^{\circ }$, a Reynolds number $Re_{c}=3\times 10^{6}$ has been carried out. The boundary layer is laminar up to the shock foot and laminar/turbulent transition occurs in the separation bubble at the shock foot. Contrary to the turbulent case for which wall pressure spectra are characterised by well-marked peaks at low frequencies ($St=f\cdot c/U_{\infty }\simeq 0.06{-}0.07$, where $St$ is the Strouhal number, $f$ the shock oscillation frequency, $c$ the chord length and $U_{\infty }$ the free-stream velocity), in the laminar case, there are also well-marked peaks but at a much higher frequency ($St=1.2$). The shock oscillation amplitude is also lower: 6 % of chord and limited to the shock foot area in the laminar case instead of 20 % with a whole shock oscillation and intermittent boundary layer separation and reattachment in the turbulent case. The analysis of the phase-averaged fields allowed linking of the frequency of the laminar transonic buffet to a separation bubble breathing phenomenon associated with a vortex shedding mechanism. These vortices are convected at $U_{c}/U_{\infty }\simeq 0.4$ (where $U_{c}$ is the convection velocity). The main finding of the present paper is that the higher frequency of the shock oscillation in the laminar regime is due to a different mechanism than in the turbulent one: laminar transonic buffet is due to a separation bubble breathing phenomenon occurring at the shock foot.

An Accurate Calculation Method for Two-dimensional Incompressible Laminar Boundary Layers, Including Cases with Regions of Sharp Pressure Gradient

1977 ◽  
Vol 28 (3) ◽  
pp. 149-162 ◽  
Author(s):  
N Curle
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Calculation Method ◽  
Boundary Layer Separation ◽  
Pressure Gradients ◽  
Accurate Calculation ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Type Boundary

SummaryThe paper develops and extends the calculation method of Stratford, for flows in which a Blasius type boundary layer reacts to a sharp unfavourable pressure gradient. Whereas even the more general of Stratford’s two formulae for predicting the position of boundary-layer separation is based primarily upon an interpolation between only three exact solutions of the boundary layer equations, the present proposals are based upon nine solutions covering a much wider range of conditions. Four of the solutions are for extremely sharp pressure gradients of the type studied by Stratford, and five are for more modest gradients. The method predicts the position of separation extremely accurately for each of these cases.The method may also be used to predict the detailed distributions of skin friction, displacement thickness and momentum thickness, and does so both simply and accurately.

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