Transient Boundary Layer Research Articles

Imaging the transient boundary layer on a free rotating disc.

This report presents a visual study of the transition process of the laminar boundary layer (BL) in a turbulent BL on a free rotating disc. The imaging is based on an experimental investigation that aimed to analyze the structure of the BL by relating it to the ratio between turbulent energy and vortex energy, the critical and the transient Reynolds numbers (Re), the vortex numbers and their dependence on Re, and on the distance from the rotating disc.

Thermal capacity effect on transient free convection adjacent to a vertical surface in a porous medium

In this paper we analyse how the presence of the thermal capacity of a vertical flat plate of finite thickness, which is embedded in a porous medium affects the transient free convection boundary-layer flow. At the time t = 0, the plate is suddenly loaded internally with a constant heat flux rate q″, so that a transient boundary-layer flow is initiated adjacent to the plate. Initially, the transient effects due to the imposition of the uniform heat flux rate at the plate are confined to a thin fluid region near to the surface and are described by a small time solution. These effects continue to penetrate outwards and eventually evolve into a new steady state flow. Analytical solutions have been derived for these transient (small time) and steady state (large time) flow regimes, which are then matched by a numerical solution of the full boundary-layer equations. It has been found that the non-dimensional fluid temperature (or fluid velocity) profiles are reduced when the thermal capacity effects, described by a parameter Q *, are reduced. For small values of Q *, the approach of these profiles to their steady state values is monotonic. However, for large values of Q *, the temperature profiles are observed to locally exceed (pass through a maximum value) the final steady state values at certain distances from the plate. In general, the maxima in the temperature profiles increase in size as Q * increases and the time taken to approach the steady state solutions increases significantly.

Convection mixte en régime transitoire de couche limite laminaire sur une plaque verticale

This work deals with transient laminar boundary layer along a vertical surface and system of equations is solved using finite difference implicite scheme. We show that the nature of the plate influence thermal and dynamical boundary layer thicknesses as well as the flow velocity. Moreover, we observe that a small perturbation of the velocity implies to flow laminar instabilities.

Dynamic neutron radiography in petrophysical application

For studying the microstructure of oil containing reservoirs a model experiment on Visingsö sandstone specimen was performed by dynamic neutron radiography. The characteristic features of the oil infiltration were visualized and analysed by image processing. Layered, laminated petrophysical structures, oil infiltration zones, residual heavy water region, transient boundary layers between them, non-absorbing thin friable segregations and porosity were disclosed.

The one-dimensional transient diffusional method: finite element adaptive solutions to convection-diffusion problems

The diffusional method, a new, simple and natural concept, is introduced for solving convection-diffusion equations. The inherent formulation leads to the variational scheme for one-dimensional steady-state problems; however, the formulation is general and can be directly used in multidimensional analysis. Additionally, a lumped capacitance (mass) matrix first-order time integration technique is presented that is unconditionally stable in its implicit form and conditionally stable for Courant numbers less than one in its explicit form. The explicit form is shown, by comparison with a two-step Taylor-Galerkin scheme, to present an excellent performance for solving transient boundary layer problems and Burger's non-linear equation. Because of dampening due to first order accuracy of the time integrator, the method is not well suited to solve advection dominated problems involving travelling waves at high Péclet numbers; in this respect, a brief analysis is made on the explicit form of the Taylor-Galerkin scheme. This work also presents a performance analysis of the method when used in conjunction with adaptive time stepping procedures. The resulting adaptive PMGV scheme works very well for boundary layer problems and for solving Burger's non-linear viscous and non-viscous equations.

PETROV-GALERKIN METHODS FOR THE TRANSIENT ADVECTIVE-DIFFUSIVE EQUATION WITH SHARP GRADIENTS

A Petrov–Galerkin formulation based on two different perturbations to the weighting functions is presented. These perturbations stabilize the oscillations that are normally exhibited by the numerical solution of the transient advective–diffusive equation in the vicinity of sharp gradients produced by transient loads and boundary layers. The formulation may be written as a generalization of the Galerkin Least-Square method.

Transient compressible boundary layer on a wedge impulsively set into motion

The development of a compressible boundary layer over a wedge impulsively set into motion is studied in this paper. The initial motion is independent of the leading edge effect and the solutions are those of a Rayleigh-type problem. The motion tends to an ultimate steady state of Falkner-Skan type. The equations governing the transient boundary layer from the initial steady state to the terminal steady-state change their character after certain time due to the leading edge effect and thereafter solution depends on both the end conditions. Numerical solutions are obtained through the second-order accuracy upwind scheme. The effects of the Falkner-Skan parameter and the surface temperature on the transient flow and heat transfer are also studied. It has been found that the flow separation does not occur form≧−0.0707 when θw = 1.5 (hot wall), andm≧−0.118 when θ0.5 (cold wall).

Convective Heat Transfer Enhancement Due to Intermittency in an Impinging Jet

An experimental investigation has been performed to study the effect of flow intermittency on convective heat transfer to a planar water jet impinging on a constant heat flux surface. Enhanced heat transfer was achieved by periodically restarting an impinging flow and thereby forcing renewal of the hydrodynamic and thermal boundary layers. Although convective heat transfer was less effective during a short period when flow was interrupted, high heat transfer rates, which immediately follow initial wetting, prevailed above a threshold frequency, and a net enhancement occurred. Experiments with intermittent flows yielded enhancements in convective heat transfer coefficients of nearly a factor of two, and theoretical considerations suggest that higher enhancements can be achieved by increasing the frequency of the intermittency. Enhancements need not result in an increased pressure drop within a flow system, since flow interruptions can be induced beyond a nozzle exit. Experimental results are presented for both the steady and intermittent impinging jets at distances up to seven jet widths from the stagnation line. A theoretical model of the transient boundary layer response is used to reveal parameters that govern the measured enhancements. A useful correlation is also provided of local heat transfer results for steadily impinging jets.

Transient natural convection over a heat generating vertical cylinder

A numerical solution for the transient natural convection over heat generating vertical cylinders of various thermal capacities and radii is presented. A fully implicit finite difference technique is used to solve the non-linear set of equations. The rate of propagation of the leading edge effect is given special consideration. It is found that this rate, predicted by the one-dimensional conduction solution, is slower than that resulting from the boundary layer solution. Also, it increases as the radius and thermal capacity of the cylinder decrease, and as the surface heat flux increases. The transient boundary layer thickness is found to exceed its steady-state value while the transient average heat transfer coefficient is found to reach a minimum, as low as 53% of its steady-state value for the highest value of the modified Grashof number studied. Excellent agreement with previous experimental steady-state data as well as with one-dimensional theoretical results is obtained.

Signatures of transient boundary layer processes observed with Viking

Transient penetration of plasma with magnetosheath origin is frequently observed with the hot plasma experiment on board the Viking satellite at auroral latitudes in the dayside magnetosphere. The injected magnetosheath ions exhibit a characteristic pitch angle/energy dispersion pattern, earlier reported for solar wind ions accessing the magnetosphere in the cusp regions. In contrast to the continuous plasma entry in the cusp, the events discussed here show temporal features which suggest a connection to transient processes at or in the vicinity of the magnetospheric boundary. A single event study confirms previously published observations that the injected ions flow essentially tailward with a velocity comparable to the magnetosheath flow and that the energy spectra inferred for the source population resemble magnetosheath spectra. Those ion injection structures, which were resolved by the Viking mass spectrometer, consist of protons. Based on a statistical study, it is found that these events are predominantly observed around 0800 and 1600 MLT, in a region populated both by ring current/plasma sheet particles and by particles whose source is the magnetosheath plasma. Magnetic field line tracing based on the Tsyganenko magnetic field model yields a scatter of the source locations around the mid‐latitude region of the magnetospheric boundary. The probability for these events to occur is highest when the interplanetary magnetic field (IMF) is confined to the ecliptic plane. The event occurrence frequency shows a dawn‐dusk asymmetry depending on the azimuthal direction of the IMF. The occurrence frequency is independent of the solar wind velocity but increases with increasing solar wind pressure. For radially directed IMF the probability for observing the events is generally higher than for azimuthally directed IMF. The difference is especially pronounced during times when the solar wind pressure is comparatively low. Some of the most prominent events are obviously associated with significant changes in solar wind plasma density. The connection of the events to transient impulsive solar wind/magnetosphere interaction processes, such as transient reconnection (FTE), impulsive plasma transfer, Kelvin Helmholtz instabilities, and solar wind pressure pulses, is discussed. A relation with transient reconnection can be excluded.

Convective heat transfer in conditions of a transient boundary layer at a cylinder in a transverse flow

A finite-difference method is proposed for solving the equations of the thermal boundary layer at a circular cylinder, and the results of calculating the heat transfer in transient flow conditions are presented.

Transient boundary layer effect in underground oil and gas reservoir depletion processes

Modern methods of exploiting underground deposits of oil and gas are characterized by conditions that vary slowly with time, which makes it possible to treat them over an extended period as near-equilibrium processes and use for their analysis the effective methods of perturbation theory. At the same time, during a brief initial period these systems display essentially nonequilibrium behavior leading to a transient boundary layer effect. For closed reservoir depletion problems a measure of the degree of nonequilibrium of the reservoir system is introduced and for real deposits shown to be small, the existence of a boundary layer is established, and the exterior and interior problems are formulated, together with the matching conditions. The general form of the exterior asymptotic behavior, in which the space variables and time are separated, is established and the initial parabolic system is reduced to a linear Poisson equation. Examples of problem solving are given.

Heat transfer in a transient boundary layer on a porous plate

We present the results of an experimental study and a procedure for calculation of the effect of intense injection of various coolants on stability loss in laminar flow and on heat transfer in a transient boundary layer on a porous plate in a longitudinal flow.

Transient Boundary Layers Between Porous Plates

Analysis is made of a transient, fully developed, laminar flow of an incompressible fluid in a porous, parallel-plate channel. The crossflow through the plates is uniform, but is allowed to vary with time. In addition to a pressure gradient due to pumping, the flow is also under the inducement of the motion of one of the plates. Numerical results are obtained through the (final or nonfinal) use of the finite Fourier sine transform. Asymptotic flow patterns showing transient boundary layers are investigated. Finally, the formation of the flow from the start is described in physical terms.

Parametric method of calculating a transient laminar boundary layer

A universal equation is derived for a transient laminar boundary layer in an incompressible fluid and is solved by numerical integration for certain values of the chosen parameters.

Exact numerical solutions for transient shear stress and boundary-layer induced pressure

Hypersonic flat plate under impulsive loads, calculating time dependent transient wall shear stress and boundary layer induced pressure

A Boundary-Layer Theory for Transient Viscous Losses in Turbulent Flow

A laminar boundary-layer model is proposed to account for viscous losses during the transient turbulent flow of a liquid in a tube. In this model, inviscid slug flow is assumed for the core and all viscous effects are assumed to occur in the boundary layer. The transient boundary-layer velocity distribution is determined as a function of a prescribed variation in core velocity and the associated pressure gradient. Both analytical and numerical solutions are presented. This transient flow information is used to calculate local and integrated energy dissipation rates which are then combined, with one-dimensional energy analyses. The result is a prediction of the decrease in pressure-wave magnitude due to viscous dissipation, and a comparison is made with experimental data for rapid flow extinction. Good agreement between the observed and predicted results is obtained.

Weak Shock Generation According to the Energy-Conserving Bhatnagar-Gross-Krook Kinetic Equation

The early-time, linearized impulsive piston problem is solved analytically for a gas obeying the energy-conserving Bhatnagar-Gross-Krook equation. The piston is adiabatic by reflecting particles specularly. Exact solutions for the density, mean velocity, and temperature are obtained as simple quadratures which are evaluated numerically. Flow features are related to the properties of certain “γ figures.” Density near the piston is found to rise and then fall as the early, near free-molecular flow converts to a transient thermal boundary layer and emerging viscous-acoustic front. A temperature maximum is observed traveling first at the isothermal sound speed and then slowing to half the adiabatic sound speed as the post-front profile flattens. Comparisons are made with a previous isothermal BGK study and with Moran and Shen's results for the linearized Navier-Stokes equations. Agreement with the latter results down to transition times proves the value of retaining high frequency components in a Navier-Stokes description of the flow.

An Analysis of Turbulent Free Convection Heat Transfer from a Vertical Surface

In the analysis of the turbulent free convection two different solutions are obtained ; one has a fundamental assumption that the temperature and velocity distributions in the boundary layer respectively take similar figures along the flow, and the other has a fundamental assumption that the laminar sublayer takes a Reynolds number 160. The former corresponds to the transient turbulent boundary layer and the latter to the ordinary turbulent boundary layer. Then referring to the experimental results, the most appropriate dimensionless heat transfer coefficients are represented.