Experimental Investigation of the Laminar Boundary Layer Flow on a Rotating Wavy Disk

2016 ◽  
Author(s):  
Christian Helcig ◽  
Christian Teigeler ◽  
Stefan aus der Wiesche
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Similar Solution ◽  
Surface Shape ◽  
Self Similar Solution ◽  
Self Similar ◽  
Layer Flow

Since nearly one century, the flow on a flat rotating disk has provided the paradigm for studying rotating flows. For the laminar flow regime, a self-similar solution was obtained by von Kármán [6] in 1921, and a rather special feature of his exact solution of the Navier-Stokes equation is a constant boundary layer thickness not depending on the radial coordinate. A substantial modification of this canonical configuration is given by a wavy disk with a sinusoidal surface shape. Although axis-symmetric, no exact solution for the laminar flow on a wavy disk is known so far. In this study, detailed measurements of the velocity profiles were performed within the laminar boundary layer flow on a wavy disk. Based upon the experimental data, the potential of a self-similar solution approach for describing the resulting flow field was assessed. It was found that such an approach is useful for approximating the far-field solution but systematic deviations were observed in the vicinity of the disk origin.

Numerical Simulation of Laminar Boundary Layer Flow Over a Horizontal Flat Plate in External Incompressible Viscous Fluid

2021 ◽  
Author(s):  
Ali Belhocine ◽  
Nadica Stojanovic ◽  
Oday Ibraheem Abdullah
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Solution Procedure ◽  
Dimensionless Temperature ◽  
Plane Plate ◽  
Fluid Properties ◽  
Layer Flow

In this paper, steady laminar boundary layer flow of a Newtonian fluid over a flat plate in a uniform free stream was investigated numerically when the surface plate is heated by forced convection from the hot fluid. This flow is a good model of many situations involving flow over fins that are relatively widely spaced. All the solutions given here were with constant fluid properties and negligible viscous dissipation for two-dimensional, steady, incompressible laminar flow with zero pressure gradient. The similarity solution has shown its efficiency here to transform the governing equations of the thermal boundary layer into a nonlinear, third-order ordinary differential equation and solved numerically by using 4th-order Runge-Kutta method which in turn was programmed in FORTRAN language. The dimensionless temperature, velocity, and all boundary layer functions profiles were obtained and plotted in figures for different parameters entering into the problem. Several results of best approximations and expressions of important correlations relating to heat transfer rates were drawn in this study of which Prandtl’s number to the plate for physical interest was also discussed across the tables. The same case of solution procedure was made for a plane plate subjected to other thermal boundary conditions in a laminar flow. Finally, for the validation of the treated numerical model, the results obtained are in good agreement with those of the specialized literature, and comparison with available results in certain cases is excellent.

scholarly journals The Convective Instability of Boundary-Layer Flows Over Rotating Spheroids

2009 ◽  
Author(s):  
A. Samad ◽  
S. J. Garrett
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Convective Instability ◽  
Laminar Flows ◽  
Type I ◽  
Rotating Sphere ◽  
Flow Equations ◽  
Layer Flow

The continuous development of spinning projectiles and other industrial applications has led to the need to understand the laminar boundary-layer flow and subsequent onset of transition over the general family of rotating spheroids. We begin by finding the laminar boundary-layer flow over a general spheroid. In particular, we distinguish between prolate and oblate spheroids and use an appropriate spheroidal coordinate system in each case. The laminar-flow equations are established for each family of spheroid rotating in otherwise still fluid. An eccentricity parameter e is used to distinguish particular bodies within the oblate or prolate families. In each case, setting e = 0 reduces the equations to those already established by Howarth [2] and Banks [4] for the rotating sphere. In this preliminary study the laminar-flow equations at each latitude are solved by extending the original series solutions due to Howarth and Banks for the rotating sphere. The laminar flows obtained are consistent with established results for the rotating sphere as e tends to zero, and tend to the von Ka´rma´n [5] solution for the rotating disk as the latitude is reduced close to the nose. Analyses of the convective instability are performed on the rotating prolate family. These extend the linear analyses previously published by Malik, Lingwood and Garrett & Peake [6–10] on related geometries. An investigation into the relative importance of type I (crossflow) and type II (streamline curvature) modes is also presented. At low latitudes increasing eccentricity has negligible effects on the stability characteristics of the flow. However as the latitude increases, eccentricity is seen to lower the upper (type I) branch of the neutral curve, reducing the region of instability.

Keel Design for Low Viscous Drag

1987 ◽  
Author(s):  
Clifford J. Obara ◽  
C. P. van Dam
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Laminar Boundary Layer ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Viscous Drag ◽  
Hydrodynamic Characteristics ◽  
Sweep Angle ◽  
Layer Transition ◽  
Layer Flow

In this paper, foil and planform parameters which govern the level of viscous drag produced by the keel of a sailing yacht are discussed. It is shown that the application of laminar boundary-Layer flow offers great potential for increased boat speed resulting from the reduction in viscous drag. Three foil shapes have been designed and it is shown that their hydro­dynamic characteristics are very much dependent on location and mode of boundary-Layer transition. The planform parameter which strongly affects the capabilities of the keel to achieve laminar flow is lea ding-edge sweep angle. The two significant phenomena related to keel sweep angle which can cause premature transition of the laminar boundary layer are crossflow instability and turbulent contamination of the leading-edge attachment line. These flow phenomena and methods to control them are discussed in detail. The remaining factors that affect the maintainability of laminar flow include surface roughness, surface waviness, and freestream turbulence. Recommended limits for these factors are given to insure achievability of laminar flow on the keel. In addition, the application of a simple trailing-edge flap to improve the hydrodynamic characteristics of a foil at moderate-to-high leeway angles is studied.

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