Unsteady Laminar Boundary Layer Research Articles

Studies on boundary-layer separation in unsteady flows using an integral method

A new two-parameter integral method is presented which is applicable to unsteady two-dimensional laminar boundary layers whether they are separated or not. The governing equations consist of three moments of the boundary-layer equation, and the assumed velocity profiles are those of unsteady trailing-edge flow and Falkner-Skan flow with slip. The governing equation system being hyperbolic, the spontaneous generation of a singularity associated with unsteady separation is confirmed as the focusing of characteristics. The obtained results of the boundary-layer quantities as well as the generation of separation singularity are in good agreement with those of exact methods (e.g. van Dommelen & Shen 1980) for starting flows of cylinders.

Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point

The flow, heat and mass transfer on the unsteady laminar incompressible boundary layer in micropolar fluid at the stagnation point of a 2-dimensional and an axisymmetric body have been studied when the free stream velocity and the wall temperature vary arbitrarily with time. The partial defferential equations governing the flow have been solved numerically using a quasilinear finite-difference scheme. The skin friction, microrotation gradient and heat transfer parameters are found to be strongly dependent on the coupling parameter, mass transfer and time, whereas the effect of the microrotation parameter on the skin friction and heat transfer is rather weak, but microrotation gradient is strongly affected by it. The Prandtl number and the variation of the wall temperature with time affect the heat-transfer very significantly but the skin friction and micrortation gradient are unaffected by them.

Numerical Analysis of Unsteady Laminar Boundary Layers with Separation Using One-Parameter Integral Method (2nd Report, Application to an Elliptic Cylinder)

前報で提案したはく離を伴う非定常層流境界層の1パラメータ積分法による数値解法を用いて瞬間的に動き出すだ円柱上の非定常境界層を解析し排除厚,形状係数,壁面摩擦の時間的変化とはく離再付着点の軌跡を求めた.この軌跡は既知の厳密解の結果とよく一致しており本計算法のような積分法によってもはく離泡の形成と成長,それらの合体によって失速にいたる過程を簡便に解析することができることを示した.

Heat and mass transfer in unsteady compressible axisymmetric stagnation point boundary layer flow over a rotating body

The study deals with the unsteady laminar compressible stagnation-point boundary layer flow over a rotating body of revolution (sphere) with mass transfer when the free-stream velocity, the rotation of the body, the surface mass transfer, and the wall temperature vary arbitrarily with time. The rotation of a body is found to exert a strong influence on the skin friction, but its effect on the heat transfer is comparatively weak. On the other hand, the effect of the variation of the wall temperature with time on the heat transfer is appreciable; the skin friction, however, is affected only slightly by it. The variation of the density-viscosity product across the boundary layer has a strong effect on both the skin friction and the heat transfer. Suction serves to increase the skin friction and heat transfer, but injection does the reverse. A velocity overshoot is found in the longitudinal velocity profiles which increases as the rotation of the body increases.

Instant Nonsimilarity Solutions of Unsteady Laminar Boundary-Layer Heat Transfer

Instant Nonsimilarity Solutions of Unsteady Laminar Boundary-Layer Heat Transfer

Free convection and mass transfer effects on the unsteady laminar boundary-layer accelerated flow past a vertical porous limiting surface with uniform suction

An analysis of the mass transfer and free convection effects on the unsteady laminar accelerated flow of a viscous incompressible fluid past an infinite vertical porous limiting surface is presented when the free stream is accelerated and the limiting surface temperature and concentration changes with step-wise variations. Expressions for velocity and skin-friction are obtained by using Laplace transform, when the Prandtl number and the Schmidt number are equal to one. Graphs showing variations of velocity and skin-friction, for different values of Gr (Grashof number) and Gc (modified Grashof number) are plotted, and the results of them are discussed.

Implicit noniterative schemes for unsteady boundary layers

In order to solve unsteady boundary layers it is necessary to use fast and stable methods; implicit methods are therefore very useful. To overcome the iterative procedure related to the nonlinear system of equations, a linearization procedure should be employed. In this paper the method developed by Beam and Warming has been applied for both time and streamwise directions. Due to the time-dependent coordinate transformation and to the nonlinearity, the Beam-Warming algorithm does not retain a large number of time-differencing schemes. The method has been applied to unsteady laminar boundary layers and the solutions compared with the analytical and experimental results.

The spontaneous generation of the singularity in a separating laminar boundary layer

The question whether solutions of the unsteady laminar boundary layer equation may turn singular spontaneously has been in dispute lately. By a case study, here a numerical proof is given that the spontaneous generation of a singularity does indeed occur, thus settling the point. The proof is achieved by abandoning the usual Eulerian boundary layer coordinates in favor of Lagrangian coordinates. The singularity then occurs at a stationary point, the presence of which can be ascertained numerically without ambiguity.

Wall Friction and Local Heat Transfer in Oscillatory Flow : Two-dimensional Unsteady Laminar Boundary Layer on a Flat Plate

Wall friction and local heat transfer in an oscillating laminar boundary layer over a flat plate with an unheated starting length are theoretically analyzed. In the analysis, the power series solutions are derived for velocity and temperature distributions in three frequency regions, that is, low frequency (ω*<1), intermediate frequency (1<ω*<1/K), response of a hot film sensor is clarified theoretically. Especially it is shown that the amplitude of heat transfer oscillation with an unheated starting length increase with frequency at low and intermediate regions, and the phase angle is in advance of free stream oscillation at these frequency regions.

Numerical solutions for unsteady laminar boundary layers behind blast waves

Numerical solutions are obtained for plane (σ=0) and axisymmetric (σ=1) laminar boundary layers induced by blast waves of the form xs∼t2/(σ+3), where xs is the distance of the blast wave from the blast origin; t is time; and σ̄ is 0, 1, or 2 for plane, cylindrical, and spherical waves, respectively. Explicit dependence on time is eliminated by a similarity transformation. The entire region between the shock (x=xs) and the blast origin (x=0) is considered, except for a small region near x=0 where the equations are singular. Numerical results are presented for ideal air with σ̄=0, σ=0; σ̄=1, σ=0; σ̄=1, σ=1; and ⩽=2, σ=1. Wall shear and heat transfer are found to increase with ξ=1 −x/xs at a rate faster than that indicated by previous solutions for the flow directly behind the shock (ξ2<<1). The results are applicable in the laminar boundary layer region, p∞xs?O (10−1) atm‐cm, where p∞ is ambient pressure.

Numerical analysis of unsteady compressible laminar boundary layer flow

Abstract The unsteady compressible laminar boundary layer flow on an arbitrary cylinder due to an incident stream whose velocity varies arbitrarily with time is considered. The method presented is based on the separation between the convective and diffusive quantities. By defining some new variables, the splitting appears rather naturally, and the initialisation problem can be solved without difficulty. The transformed equations are solved with the help of a semi-implicit finite difference scheme which is unconditionally linearly stable. The computations have been applied to flows past a cylinder with constant and fluctuating free-stream velocities.

The collision of unsteady laminar boundary layers

The boundary-layer growth near the equator of an impulsively rotated sphere is considered numerically and analytically. The numerical work is highly suggestive of the presence of a singularity at a finite time at which two of the velocity components and the swirl displacement thickness become infinite. Details of an analytic investigation are presented which is consistent with the gross features of the numerical results. Brief consideration is also given to the flow near the equators of impulsively rotated spheroids and it is shown that the relevant boundary-layer equations for this class of bodies can be written in the same form as those for the sphere.

Heat transfer in unsteady laminar boundary layers at an incompressible three-dimensional stagnation flow

Heat transfer in unsteady laminar boundary layers at an incompressible three-dimensional stagnation flow

Nouvelle approche numerique des solutions de la couche limite laminaire incompressible en regime non-stationnaire autour d'une paroi cylindrique elliptique mise en impulsion brutale

The equations of the unsteady incompressible laminar boundary layers about circular and elliptic cylinders started impulsively from rest are solved, after an original coordinate transformation, with the help of a semi-implicit difference scheme linearly stable without conditions. The knowledge of the phenomenon results only from that of the flow characteristics at the initial time; this makes mandatory the use of an analytical method of the Blasius type. When the ratio of the semi-axes of the elliptic cylinder becomes infinite, the present method gives the solution of the stagnation flow. When the flow presents a separation point in the steady state (circular cylinder), a criterion for stopping computation is proposed. It may be noted that to obtain the stagnation flow, we can continue the computations as far as possible and a steady solution is found with excellent accuracy.

Laminar forced convection in wedge flow with separation

Abstract A perturbation method is used to study the steady and unsteady laminar boundary layer heat transfer from a wedge with separation for a step‐discontinuity in the surface temperature. The analytic solutions obtained can be used to calculate the steady and unsteady heat transfer rate with arbitrary surface temperature. The effects of the Prandtl number on the temperature distribution and the heat transfer rate are discussed in detail. The solution is valid for large or moderate Prandtl number.

An Unsteady Laminar Boundary Layer with Separation and Reattachment

An Unsteady Laminar Boundary Layer with Separation and Reattachment

Laminar Shear Layer Due to a Thin Flat Plate Oscillating With Zero Mean Velocity

A numerical solution of the unsteady laminar boundary layer equations is described for the flow due to a semi-infinite plate, sinusoidally oscillating with zero mean velocity. The plate periodically reverses its direction of motion with no net translation. The solution treats the region intermittently occupied by the plate as a thin symmetric wake. A time-centered two-step implicit finite-difference scheme was used with upwind differencing and a variable spatial grid to obtain the numerical results. Results are presented for velocity profiles and surface shear stress as a function of position and time.

Similarity solutions of unsteady laminar incompressible boundary layer equations for flow, heat and mass transfer in non-Newtonian fluids around axisymmetric bodies

The possible existence of similarity solutions for the unsteady three-dimensional boundary layer flows with heat and mass transfer around stationary axisymmetric bodies which are fully immersed in purely viscous moving non-Newtonian fluids has been searched in general by the application of transformations, involving a single linear parameter. In particular, the cases involving rotational flows around stationary bodies and rotating bodies have been discussed as corollaries of the main analysis. The main analysis shows that the similarity solutions are possible only for the bodies for which $$\bar r \propto \bar x^n $$ where $$\bar r$$ is a cross-sectional radius; and $$\bar x$$ is the longitudinal distance from the nose point to the cross section. In case of rotating bodies, similarity solutions exist only for cones and disks. The analysis, as an example, has successfully been applied to the Powell-Eyring model. It is seen that for the same rate of shear, expenditure of energy for maintaining the rotation of the solid body is comparatively higher for a flow with a higher Eyring number where the Eyring numberEy=1/µBE. µ, B, andE are the material functions of the Powell-Eyring fluid.

Transient response of a solar regenerator

Since a solution-air solar regenerator is exposed continuously to varying insolation, the instantaneous transfer process can be significantly different from quasisteady conditions. In the present analysis the first order deviations of the instantaneous conditions from the quasisteady conditions have been considered by solving the governing unsteady laminar boundary layer equations. The results show that early in the morning and late in the evening the instantaneous values are different from quasisteady values, but the deviation is insignificant for ±2 hours from noon, particularly for mass transfer coefficients, which determine the performance of the regenerator. The study further reveals that the ratio of solution velocity to air velocity also influences the performance of the regenerator.

The Unsteady Laminar Boundary Layer on Cylinders in Translational Oscillation : The Case in which the Influence of Wake Vortices is Disregarded

The Unsteady Laminar Boundary Layer on Cylinders in Translational Oscillation : The Case in which the Influence of Wake Vortices is Disregarded