Higher Order Boundary Layer Theory Research Articles

Optimal coordinates for higher-order boundary-layer theory

The optimal coordinates for higher-order boundary-layer theory are derived using an extension of Kaplun’s approach. They are applicable to any approximation order and become small-parameter dependent beginning with the second-order boundary-layer problem. The new result is consistent with an earlier methodology that led to the same results. Two boundary-layer solutions from the literature confirm the new rule. The optimal coordinates will be valuable for analytical investigations of the Navier–Stokes equations as well as for new approaches to developing grid schemes for CFD.

The influence of higher-order effects on the linear instability of thermal boundary layer flow in porous media

We examine the instability of free convective boundary layer flows in porous media. The medium is bounded by two semi-infinite plane surfaces forming a wedge of angle α. One of the surfaces is heated uniformly and the other is either cold or insulated. The basic flow used in the analysis is the most accurate obtainable by means of higher order boundary layer theory. In general, the critical distance from the leading edge beyond which disturbances grow is found to be strongly dependent on the outer flow field. The only exception to this arises when the heated surface is close to the vertical and if the wedge is not too close to either 0° or 360°. The main implication of this paper is that instability occurs too close to the leading edge for the basic flow to be represented adequately either by the leading order boundary layer theory used in previous papers, or by even the most accurate higher order theory obtained using matched asymptotic expansions.

Pressure gradients due to gas expansion in the boundary layer combustion of a condensed fuel

Ignition and combustion of a condensed fuel in a gaseous high temperature oxidizing boundary layer flow is analyzed on the basis of higher order boundary layer theory. First order effects due to displacement thickness are taken into account and the pressure gradients generated in the outer potential flow are included in the numerical solution of the governing equations. The strong positive pressure gradients which are induced by expansion in front of the flame generate a low velocity region which facilitates a longitudinal diffusion of heat and mass.

Calculation of Ship Viscous Resistance and Its Application

A method is described for representing ship hull forms by use of the exponential splines and viscous resistance calculations based on a higher-order boundary layer theory. Higher order terms retained in the boundary layer equations were examined on the basis of the flow characteristics measured near the stern for an 8-meter-long ship model. The higher order boundary layer equations are solved by the integral method, and then frictional and viscous pressure resistance components are calculated separately by integrating wall shear stress and pressure over the hull surface to obtain explicitly the correlation between hull form and viscous resistance components. From comparison between calculations and measurements, it is found that the method predicts the viscous resistance of full form ships with allowable accuracy and can become a useful tool for systematic investigations of various ship forms in the course of hull form design.

Minimization of Total Resistance of a Surface-Piercing Vertical Strut

An attempt was made to obtain a surface-piercing vertical strut with minimum total resistance by means of nonlinear programming under the constraints that the beam and water plane area of the strut were kept constant. The objective function in the nonlinear programming is the sum of wave-making resistance calculated by Michell's integral and viscous resistance calculated by a higher order boundary layer theory taking the longitudinal curvature effect into consideration.In the minimization process, the strut form with minimum wave-making resistance was used as an initial form. It is a characteristic that the strut form of minimum total resistance has a fine shape near the trailing edge and the fore body has a similar shape as that of the body of minimum wave-making resistance. In the minimization process, it is shown that the viscous pressure resistance is reduced largely whereas the wave-making resistance is increased a little and frictional resistance is kept almost unchanged.

Determination of Resistance forward of an Arbitrary Cross Section of Slow Ships by Means of Velocity Measurements

In order to know the contribution of local hull geometry to the resistance of slow full ships, a calculation formula was derived to determine the resistance acting on the hull surface forward of an arbitrary transverse cross section. In determining the resistance use was made of the results of flow measurement at the transverse cross section outside of a ship model.This formula was applied to the two full ship models whose wave resistances were negligibly small. The results of the calculation were found to agree with those based on a higher order boundary layer theory which takes into account pressure variation across the boundary layer. Resistance determined at the control surface right after a ship model was also comparable with towing test result.Applicability of the present method was thus found to be promising, though there exists a room for improvement.

Calculation of Viscous Pressure Resistance of Ships Based on a Higher Order Boundary Layer Theory

Calculation of Viscous Pressure Resistance of Ships Based on a Higher Order Boundary Layer Theory

The steady streaming induced by a vibrating cylinder

In this paper we apply the techniques of higher-order boundary-layer theory to study the steady streaming induced in the neighbourhood of a cylinder which vibrates harmonically, perpendicular to its generators, in an unbounded fluid. The theoretical predictions are compared with the results of experiments performed at high streaming Reynolds numbers. Improved agreement between theory and experiment is achieved although unresolved discrepancies remain.

Numerical methods for nonreacting and chemically reacting laminar flows - Tests and comparisons

Equilibrium, nonequilibrium, and ideal gas (7 = 1.4) laminar boundary layers and viscous shock layers over a 10°-half-angle hyperboloid, 50 nose-radii long, have been computed by several investigators for three 20,000-fps cases, one at 100,000 ft altitude and two at 250,000 ft. Their predictions of skin-friction and heat-transfer coefficients and displacementthickness distributions over the body, as well as property profiles across the layer at the ends of the body, are compared. The conditions were chosen to test the ability of the numerical methods to predict nonequilibrium viscous-layer flows near and far from chemical equilibrium and the applicability of boundary-layer theory at low-Reynolds-number conditions. Results show that recently developed finite-difference methods can be used to compute finite rate, chemically reacting flows near chemical equilibrium, and iterations of implicit finite-difference solutions are required for accurate results. At 250,000 ft altitude, higher-order boundary-layer theory is not adequate and a fully viscous shock-layer technique must be used. At the higher altitude, stagnation heat transfer is strongly affected by shock slip.