Compressible Laminar Boundary-layer Equations Research Articles

Numerical solution of the boundary-layer equations for a general aviation fuselage

Numerical solutions of the three-dimensional, compressible laminar boundary-layer equations for a general aviation fuselage are presented. The numerical procedure is second-order accurate and independent of the cross-flow velocity direction. Numerical results are presented for a Mach number and unit Reynolds number of 0.3 and 7 x 10 to the 6th/m, respectively, for angles of attack of 0 and 3 deg. Comparisons are made between results obtained using a general nonorthogonal curvilinear body oriented coordinate system and a streamline coordinate system. Axisymmetric analogue results are also compared with the three-dimensional solutions.

Linear instabilities in two-dimensional compressible mixing layers

Linear instability waves in supersonic shear layers are analyzed. Both viscous and inviscid disturbances are considered. The basic state is obtained by solving the compressible laminar boundary-layer equations or is specified by the hyperbolic tangent profile. The effects of the velocity ratio and temperature ratio are determined. The numerical results show that the maximum growth rate depends nonlinearly on the velocity ratio. The results also substantiate the convective Mach number as a compressibility parameter for mixing layers.

Some new methods for numerically solving the compressible laminar boundary layer equations

AbstractFour new methods are presented: a method of accelerating the truncation error convergence, a fourth and fifth order difference scheme for discretizing the normal partial derivatives, high order quadrature formulae for integrating a stream function and a third order implicit scheme for treating the streamwise partial derivatives. These are seen to be effective in finding solutions to the boundary layer equations in which the step sizes are adaptively altered to meet an error bound.

Semisimilar solutions of the unsteady compressible laminar boundary-layer equations

The theory of semisimilar solutions, previously developed for unsteady two-dimensional incompressible laminar boundary-layer flows, is extended to the case of compressible flows. A study is made of several flows for which semisimilar solutions are possible with a view of investigating the nature of compressible unsteady separation. The solutions obtained indicate that the Moore-Rott-Sears model for unsteady boundary-layer separation is valid for compressible as well as incompressible flow. In addition, the effects of Mach number and wall temperature on the moving separation point are determined.

Heat Transfer of the Critical Air Flow in a Nozzle : 4th Report, The Flow and Heat Transfer Characteristics of an Accelerated Transonic Air Flow in a Divergent Nozzle

This paper is concerned with the theoretical and experimental investigations of the accelerated critical air flow and heat-transfer characteristics in the divergent nozzles in which a sonic point exists midway between the inlet and the exit of nozzle fully taking into consideration the viscous effect. The compressible laminar boundary layer equations are solved numerically using a finite difference method, and a chart of the sonic line and the critical flow rate in a divergent nozzle are shown. The numerical solutions of the local and the mean Nusselt numbers of a critical nozzle are in good agreement with the experimental results. The range of critical divergent nozzles in which a laminar flow extends over the whole region of the nozzles is determined experimentally by the nozzle characteristic number and the divergent Reynolds number.

Heat Transfer of the Critical Air Flow in a Nozzle : 2nd Report; Experimental Study on Heat Transfer of the Critical Air Flow in a Nozzle with Parallel walls

The heat transfer of a critical flow in a small-sized has not been studied in detail, since the flow is too complicated. In this paper, the two-dimensional compressible laminar boundary layer equations in a parallel with heat transfer are solved numerically. The obtained results reveal that the two-dimensional critical flow patterns are classified by nozzle characteristic number xc. The local and mean heat transfer coefficients in the critical nozzles were calculated by defining an adiabatic wall temperature as gas temperature in reference. Especially, it is found that the local heat transfer coefficients rise sharply near the exit. The mean Nusselt numbers obtained numerically can be plotted on a single curve independent of the non-dimensional wall temperature θw, being arranged on the basis of modified characteristic Reynolds number Xcdw; furthermore they can be approximated by incompressible ones, if arranged on the basis of Xcdws-1 defined as the state of sonic point in the critical nozzle.

Compressible laminar boundary layers with suction on swept and tapered wings

In this paper we present a numerical method for solving the compressible laminar boundary-layer equations with suction on swept and tapered wings. The method employs an efficient two-point finite-difference method to solve the governing equations, and a very convenient similarity transformation which removes the wall normal velocity as a boundary condition and places it into the governing equations as a parameter. In this way the awkward nonlinear boundary condition which couples all the variables is avoided. To test and demonstrate the method, we present a sample calculation for a typical laminar-flow-control (LFC) wing.

On solutions of the compressible laminar boundary-layer equations and their behaviour near separation

A numerical solution of the two-dimensional compressible laminar boundary-layer equations up to the point of separation is presented. For a particular mainstream velocity distribution it is necessary to specify the surface temperature (or the heat flux across the surface), the suction velocity, the free-stream Mach number and the viscosity-temperature relationship for a solution to be generated. The effect upon the position of separation of a hot or cold wall and of varying the free-stream Mach number is given special emphasis. The variations of the skin friction, heat transfer and various boundary-layer thicknesses for compressible flow past a circular cylinder and for flow with a linearly retarded mainstream were found. The behaviour of the solutions close to separation is investigated. Known functions which model the skin friction and heat transfer are introduced and are used to match the numerical solutions with the Buckmaster (1970) expansions.

Approximate solution of the compressible laminar boundary-layer equations.

Approximate solution of the compressible laminar boundary-layer equations.

Similar solutions for the laminar mixing of reactive gases

Using the two-dimensional compressible laminar boundary-layer equations for a multicomponent gas mixture, the present analysis treats the mixing of two parallel reactive streams under the influence of an externally induced streamwise pressure gradient. The thermodynamic behavior of the gas mixture within the mixing region is specified by an empirical law that matches the density to its exact values at different points across the shear layer. In the analysis, it is assumed that the product of the density and viscosity is constant across the mixing layer, being only a function of its streamwise location. In addition, the usual assumptions of unit Prandtl number and Lewis numbers with either frozen or equilibrium chemistry specifying the state and composition of the gas mixture within the mixing layer are employed. Within the framework of these assumptions, similar solutions of the governing system of equations are obtained for various pressure gradients and velocity ratios of the two reactive streams.

Convection de la chaleur dans un gaz en régime laminaire dans le cas d'un gradient de pression et d'une température de paroi quelconques

A new transformation, generalizing Illingworth-Stewartson's, transforms the compressible laminar boundary layer equations to the incompressible boundary layer equations, for any external velocity and wall temperature distributions. For this, a reference enthalpy, generalizing Monaghan's formula, is employed; pressure gradient terms are neglected in the transformed equations. Comparison between results obtained thus and those obtained by Cohen and Reshotko by integrating the full equations shows that the velocity and temperature profiles are almost identical, at least when the wall temperature lies between half and twice the stagnation temperature. When the wall temperature decreases, the error rises while staying below 7.3 per cent, for example, in computing the heat transfer coefficient at a two-dimensional stagnation point with the gas Prandtl number equal to 1. When the wall temperature of an arbitrary body is small compared with the stagnation temperature, the heat-transfer rate at the wall is given by a formula differing slightly from that of Lees.