Two-dimensional Compressible Boundary Layer Research Articles

Boundary layer effects in He and Ar driven disk MHD generators

A two-dimensional compressible turbulent boundary layer model is adopted to predict the boundary layer characteristics of the 100 MW thermal input supersonic disk MHD generator walls for helium and argon under various enthalpy extraction conditions. The results show that the boundary layer thickness increases downstream in the channel for both argon and helium, and for helium, there occurs a boundary layer separation under high enthalpy extraction conditions. A slow variation of the Faraday current is observed through the boundary layer, while the Hall current decreases sharply, and the direction of the Hall current gets reversed in the vicinity of the insulator wall at the channel downstream end. This effect is observed to be more prominent for helium than for argon. The percentage of pressure loss through friction is found to be more for argon than for helium, while the heat loss is observed to be more for helium than for argon.

Iterative method for supersonic flow laminar boundary layer interaction in the presence of separation

The classical two-dimensional compressible boundary-layer equations supplemented by a relation describing the interaction of boundary layer with external inviscid flow (see, e.g., [1]) are treated as the governing equations in one of the methods to study the viscous-inviscid interaction. It is then necessary in the case of supersonic flow to specify certain downstream boundary conditions for the closure of the governing system, i.e., it is a boundary-value problem (e.g., [2]). The “shooting” technique for parameters at the beginning of the computational region to obtain the solution satisfying such a condition usually requires large computer time since the integral curves are highly sensitive to small changes in upstream boundary conditions. A more effective method is the algorithm of global relaxations of pressure distribution along the entire computational region [1]. A numerical method to compute supersonic interacting boundary layer in the presence of separation is presented in this paper.

A Theory for Fine Particle Deposition in Two-Dimensional Boundary Layer Flows and Application to Gas Turbines

A theory is presented to predict deposition rates of fine particles in two-dimensional compressible boundary layer flows. The mathematical model developed accounts for diffusion due to both molecular and turbulent fluctuations in the boundary layer flow. Particle inertia is taken into account in establishing the condition on particle flux near the surface. Gravitational settling and thermophoresis are not considered. The model assumes that the fraction of particles sticking upon arrival at the surface is known, and thus, treats it as a given parameter. The theory is compared with a number of pipe and cascade experiments, and a reasonable agreement is obtained. A detailed application of the model to a turbine is also presented. Various regimes of particle transport are identified, and the range of validity of the model is discussed. An order of magnitude estimate is obtained for the time the turbine stage can be operated without requiring cleaning.

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.

Unsteady two-dimensional and axisymmetric compressible boundary layers

The response of laminar compressible boundary layers to fluctuations of the skin of the body or the outer flow are studied via asymptotic expansions in powers of the amplitude parameter and the frequency of the oscillation. Oscillating outer pressure disturbances for compressible flows are considered for the first time and their effect to the energy equation and heat transfer is estimated. The analysis holds for both two dimensional and axisymmetric configurations.

On the curvature of compressible boundary layer flows near separation

Oswatitsch's analytical expression for the slope of a viscous flow separation or reattachment streamline is shown to be consistent with detailed experimental data on a supersonic boundary layer flow past a compression corner. An extension of his analysis is then given which yields a comparable new relation for the streamlinecurvature just above separation in either laminar or turbulent two-dimensional compressible boundary layer flows. This result is applied to examine the possible occurrence of Gortler streamwise vortices due to such curvature.

Solutions of unsteady compressible boundary-layer equations

AbstractThe unsteady two-dimensional compressible boundary layers have been studied by Sarma ((5)) assuming that the Prandtl number is unity and that the wall is in an arbitrary motion, the main stream being steady. In this paper the Prandtl number is taken to be an arbitrary parameter which need not be equal to unity, and it is assumed that the main stream velocity and temperature are perturbing about a steady mean, the wall being in an arbitrary motion. Solutions are obtained in two parts, one when the temperature gradient at the wall is perturbing about a zero mean and the other when the temperature of the wall is perturbing about a steady mean. Thus in this paper the theory given in Sarma ((5)) is made still more general. Following the work of Sarma ((4)–(6)) two types of solutions are developed in each part, one for large times and the other for small times.

Displacement thickness of the boundary layer with blowing.

Displacement thickness for two-dimensional or axisymmetric compressible boundary layer with blowing

A general theory of unsteady compressible boundary layers with and without suction or injection

AbstractThe theory of unsteady two-dimensional compressible boundary layers is studied in two parts. Part I deals with the solutions when the main stream is steady and the body is in an arbitrary motion while Part II deals with the solutions when the main stream is steady and the body is at rest with an arbitrary unsteady suction or injection perturbing about a zero mean. General methods of obtaining solutions are given when the coefficient of viscosity is proportional to temperature and the Prandtl number is unity. The main feature of the work in this paper lies in subjecting the equations to a transformation similar to that of Howarth and in linearization similar to that of Lighthill. Following the work of Sarma in incompressible flows two types of solutions are developed, one for large times and the other for small times. General expressions for the skin friction, the pressure ratio, the heat transfer and the difference between the normal coordinates of compressible and incompressible flows are obtained.

Turbulent Heat Transfer on Blunt-Nosed Bodies in Two-Dimensional and General Three-Dimensional Hypersonic Flow

Recent results obtained for three-dimensional laminar boundary la3^ers are extended to the turbulent case. I t is shown that in the presence of highly cooled surfaces and of moderate Mach Numbers of the outer stream, the crossflow and the pertaining Reynolds stresses in a general three-dimensional turbulent boundary layer are negligible even for large transverse pressure gradients. A correlation due to Mager between two-dimensional compressible and incompressible turbulent boundary layers is extended to the problem in question. From a study of the transformation and of its implications, a rapid method for the analysis of the boundary-layer flow under the subject conditions is established. In the absence of general three-dimensional data, a comparison with experiments and with the predictions of other known analyses is carried out for several axiS3^mmetric configurations; the results of the method presented here exhibit good agreement with the data. The range of validity of the cold wall approximation for general three-dimensional problems is estimated qualitatively on the basis of recent measurements in laminar flow, the argument being that , for either zero or favorable streamwise pressure gradients, smaller threedimensional effects are to be expected in a turbulent boundary layer, as compared to a laminar layer.