A parametric method of solving laminar boundary layer equations with a longitudinal pressure gradient in an equilibrium-dissociated gas

1966 ◽  
Vol 10 (2) ◽  
pp. 95-100 ◽  
Author(s):  
N. V. Krivtsova
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Laminar Boundary Layer ◽  
Parametric Method ◽  
Longitudinal Pressure Gradient ◽  
Boundary Layer Equations

scholarly journals The laminar boundary layer in compressible flow

1948 ◽  
Vol 241 (827) ◽  
pp. 1-69 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Incompressible Fluid ◽  
Laminar Boundary Layer ◽  
Compressible Fluid ◽  
Early Stage ◽  
General Structure ◽  
Main Stream ◽  
Boundary Layer Equations ◽  
Independent Variable

The paper is concerned with the integration of the laminar boundary-layer equations for a compressible fluid and is in three parts. In Part I the boundary-layer equations for a compressible fluid are derived, reduced to nondimensional form, and their relation to the corresponding equations for an incompressible fluid discussed. Methods of integrating them are considered, and it is shown that, provided there is no pressure gradient in the main stream, the methods employed for incompressible flow are of practical value. If there is a pressure gradient, then the complications introduced by compressibility are such that general algebra must cease and numerical integration take its place at an early stage. This means that approximate methods (such as Pohlhausen’s) of calculating separation lose their simplicity, and there are indications that their accuracy will also suffer; so it is natural to consider the practicability of direct integration of the equations, probably by series expansions. In Part II, suitable expansions in one independent variable with coefficients which are functions of the other are obtained. It is found that the independent variables can be so chosen that the differential equations for the coefficients in the expansions have the same general structure as for an incompressible fluid. The boundary conditions and the limiting forms of the equations for zero Mach number are investigated. The application of iterative methods to the equations is discussed. In Part III the ENIAC is briefly described, and the methods of applying it to obtain solutions of the equations derived in Part II are described in some detail. It is shown that, by proper choice of independent variable, the results for zero pressure gradient can be put into a form in which they vary only slowly with Linear interpolation in between the tabulated values will thus provide reliable first estimates of these quantities, and the accuracy can be improved, if required, by an iterative process. Tables of results are given.

Turbine Cascade Flow Control Using a “Wake Filling” Pulsed Plasma Actuator

2005 ◽  
Author(s):  
H. Perez-Blanco ◽  
Robert Van Dyken ◽  
Aaron Byerley ◽  
Tom McLaughlin
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Laminar Boundary Layer ◽  
Separation Bubble ◽  
Adverse Pressure Gradient ◽  
Suction Side ◽  
Plasma Actuator ◽  
Pulsed Plasma ◽  
Power Cost ◽  
Hot Film

Separation bubbles in high-camber blades under part-load conditions have been addressed via continuous and pulsed jets, and also via plasma actuators. Numerous passive techniques have been employed as well. In this type of blades, the laminar boundary layer cannot overcome the adverse pressure gradient arising along the suction side, resulting on a separation bubble. When separation is abated, a common explanation is that kinetic energy added to the laminar boundary layer speeds up its transition to turbulent. In the present study, a plasma actuator installed in the trailing edge (i.e. “wake filling configuration”) of a cascade blade is used to excite the flow in pulsed and continuous ways. The pulsed excitation can be directed to the frequencies of the large coherent structures (LCS) of the flow, as obtained via a hot-film anemometer, or to much higher frequencies present in the suction-side boundary layer, as given in the literature. It is found that pulsed frequencies much higher than that of LCS reduce losses and improve turning angles further than frequencies close to those of LCS. With the plasma actuator 50% on time, good loss abatement is obtained. Larger “on time” values yield improvements, but with decreasing returns. Continuous high-frequency activation results in the largest loss reduction, at increased power cost. The effectiveness of high frequencies may be due to separation abatement via boundary layer excitation into transition, or may simply be due to the creation of a favorable pressure gradient that averts separation as the actuator ejects fluid downstream. Both possibilities are discussed in light of the experimental evidence.

The Critical Height of Distributed Roughness to Cause Boundary Layer Transition

1959 ◽  
Vol 63 (588) ◽  
pp. 722-722
Author(s):  
R. L. Dommett
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Boundary Layer ◽  
Boundary Layer Transition ◽  
Critical Height ◽  
Layer Transition ◽  
Local Conditions ◽  
Additional Advantage ◽  
Boundary Layer Equations ◽  
General Method

It has been found that there is a critical height for “sandpaper” type roughness below which no measurable disturbances are introduced into a laminar boundary layer and above which transition is initiated at the roughness. Braslow and Knox have proposed a method of predicting this height, for flow over a flat plate or a cone, using exact solutions of the laminar boundary layer equations combined with a correlation of experimental results in terms of a Reynolds number based on roughness height, k, and local conditions at the top of the elements. A simpler, yet more general, method can be constructed by taking additional advantage of the linearity of the velocity profile near the wall in a laminar boundary layer.

scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

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