Unsteady Compressible Boundary Layer Research Articles

Reduced frequency effect on an unsteady compressible boundary layer over an oscillating supercritical airfoil

Boundary layer states, including laminar, turbulent, attached or separated, have significant effects on an airfoil operation and aerodynamic forces; especially as the boundary layer becomes turbulent or separated, the drag forces increase significantly. In the compressible flow and the transonic regime, when the compressibility effects and shock–boundary layer interaction are also considered, the flow field is so complicated that it cannot be easily investigated using the theoretical and computational methods. In this study boundary layer is investigated experimentally in several static angles of attack and also, during sinusoidal pitching motions at M ∞ = 0.65, Reynolds number of 9.202 million per meter, using multiple hot film and pressure sensors. Transition and relaminarization points, supersonic region, and shock formation are detected on the upper surface of the airfoil, and, the reduced frequency effect is investigated in dynamic case. It is worth mentioning that the low-range oscillation amplitudes and reduced frequencies used in this research led to quite different and interesting results that have not been considered in the other investigations dealing with oscillating airfoils.

Mechanism of unsteady aerodynamic heating with sudden change in surface temperature

The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.

Unsteady compressible boundary layer flow over a circular cone near a plane of symmetry

An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either inflow or outflow in the presence of suction. The flow is assumed to be steady at time t=0 and at t>0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer approximations have been solved by using an implicit finite-difference method. It is found that suction plays an important role in stabilising the fluid motion and in obtaining unique solution of the problem. The effect of the cross flow parameter is found to be more pronounced on the cross flow surface shear stress than on the streamwise surface shear stress and surface heat transfer. Beyond a certain value of the cross flow parameter overshoot in the cross flow velocity occurs and the magnitude of this overshoot increases with the cross flow parameter. The time variation of the streamwise surface shear stress is more significant than that of the cross flow surface shear stress and surface heat transfer. The suction and the total enthalpy at the wall exert strong influence on the streamwise and cross flow surface shear stresses and the surface heat transfer except that the effect of suction on the cross flow surface shear stress is small.

Slip flow and temperature jump on the impulsively started plate

The unsteady compressible boundary layer equations over an impulsively started flat plate are firstly solved subjected to velocity slip and temperature jump conditions. Comparisons are carried out with existing solutions. Then the conjugate problem for a slab of finite thickness is dealt, when the fluid dynamic field is coupled with the thermal field in the solid.

Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time.

Large injection rates on unsteady compressible boundary layer flow over cones at angles of attack

Three-dimensional unsteady laminar boundary layer near the planes of symmetry of sharp cones at angles of attack subject to large rates of injection is obtained numerically by using an implicit finite difference scheme in combination with the quasi-linearization technique. Several model gases are considered with Mach numbers, wall-to-total-enthalpy ratios, and cross-flow parameters spanning the ranges of main engineering interest. A detailed study has been made of the solutions in the symmetry plane, in order to increase the understanding of the problem. Various cases are considered, when the free-stream velocity and the surface mass transfer (injection) vary arbitrarily with time. The effects of viscous dissipation and the cross-flow parameter have also been discussed.

Unsteady compressible boundary layer flow on the stagnation line of an infinite swept cylinder

Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wall enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.

Large injection rates on unsteady compressible boundary layer flow over cones at angles of attack

Large injection rates on unsteady compressible boundary layer flow over cones at angles of attack

Unsteady laminar compressible boundary layers with vectored mass transfer and an applied magnetic field

This paper deals with the laminar unsteady compressible boundary layer flow of an electrically conducting viscous fluid at the stagnation point of an axi-symmetric blunt-nosed body with vectored mass transfer, non-zero dissipation parameter m( = u 2 s/2H c) and an applied magnetic field. The semi-similar solutions have been obtained numerically using an implicit finite difference scheme in combination with the quasi-linearization technique. The results have been obtained for (i) an accelerating/decelerating stream and (ii) a fluctuating stream. The skin-friction responds to the fluctuation in the free-stream more compared to the heat transfer. In presence of the magnetic field velocity overshoot occurs which gives rise to the point of inflexion in velocity profile and for small wall values of the total enthalpy, the point of inflexion arises in velocity and total enthalpy profiles which may cause instability in the flows but this can be avoided in certain circumstances. Skin friction can be reduced by applying vectored mass transfer more compared to the mass transfer applied normal to the surface. The results also show that the skin friction coefficient increases but Nusselt number decreases as the magnetic parameter M increases.

Numerical method for unsteady compressible boundary layers driven by compression or expansion wave

AbstractA numerical analysis is presented for the unsteady compressible laminar boundary layer driven by a compression or expansion wave. Approximate or series expansion methods have been used for the problems because of the characteristics of the governing equations, such as non‐linearity, coupling with the thermal boundary layer equation and initial conditions. Here a transformation of the governing equations and the numerical linearization technique are introduced to deal with the difficulties. First, the governing equations are transformed for the initial conditions by Howarth and semisimilarity variables. These transformations reduce the number of independent variables from three to two and the governing equations from partial to ordinary differential equations at the initial point. Next, the numerical linearization technique is introduced for the non‐linearity and the coupling with the thermal boundary layer equation. Because the non‐linear terms are linearized without sacrifice of numerical accuracy, the solutions can be obtained without numerical iterations. Therefore the exact numerical solution, not approximate or series expansion, can be obtained. Compared with the approximate or series expansion method, this method is much improved. Results are compared with the series expansion solutions.

Unsteady compressible boundary layer swirling flow in a nozzle and a diffuser

This paper presents the results of the study of unsteady swirling boundary-layer flow of compressible fluid in a nozzle and a diffuser when the free stream velocity, mass transfer and wall temperature vary arbitrarily with time. The set of coupled nonlinear partial differential equations governing the flow which involves three independent variables has been solved numerically using an implicit finite-difference scheme. Both the heat transfer and skin friction are strongly affected by the free stream velocity, variation of the density-viscosity product across the boundary layer, mass transfer and swirl parameter. However, the variation of the wall temperature with time strongly affects only the heat transfer. Also, separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction.

Analysis of unsteady compressible boundary layer flow via finite elements

This paper is concerned with the discrete formulation and numerical solution of unsteady compressible boundary layer flows using the Galerkin-finite element method. Linear interpolation functions for the velocity, density, temperature and pressure are used in the momentum equation and equations of continuity, energy and state. The coupled nonlinear finite element equations are approximated by a third order Taylor series expansion as temporal operator to integrate in time with Newton-Raphson type iterations performed until convergence within each time step. As an example, a boundary layer problem of a perfect gas behind a normal shock wave is solved. A comparison of the results with those by other method indicates a favorable agreement.

The Problem of an Unsteady Heat Transfer from Porous Flat Plate: Compressible Boundary Layer

We have obtained exact solutions in closed form for the unsteady compressible boundary layer's equations. The problem is initiated by moving the plate impulsively, and simultaneously raising its temperature. We have examined the effect on the motion in the boundary layer, far down from the leading edge, when, each quantity is independent of x. The transformation, suggested by Stewartson, is applied to change the independent variables (y, t) to (Y, t), and applying Laplace transform, we are able to solve the equations.

Unsteady compressible boundary layer for flow of gas in a tube.

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Similarity for unsteady compressible boundary layers.

Similarity for unsteady compressible boundary layers.

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.

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.