Boundary-layer development at a two-dimensional rear stagnation point

1972 ◽  
Vol 56 (1) ◽  
pp. 161-171 ◽  
Author(s):  
A. J. Robins ◽  
J. A. Howarth
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Initial Value ◽  
Boundary Layer Development ◽  
Leading Term ◽  
Layer Development ◽  
Rear Stagnation Point ◽  
Good Agreement

This paper examines the nature of the development of two-dimensional laminar flow of an incompressible fluid at the rear stagnation point on a cylinder which is started impulsively from rest. Proudman & Johnson (1962) first examined this type of flow, andobtainedasimilarity solution of the inviscid form of the equations of motion. This solution describes the nature of the flow at large distances from the surface, for large times after the start of the motion. Here, the flow at the rear stagnation point is examined in greater detail. The solution found by Proudman & Johnson constitutes the leading term in an asymptotic expansion, valid for large times. Further terms in this expansion are now calculated, and the method of matched asymptotic expansions is used to obtain an inner solution describing the flow near the surface. A numerical integration of the full initial-value problem gives good agreement with the analytical solution.

The flow at a rear stagnation point is eventually determined by exponentially small values of the velocity

1985 ◽  
Vol 157 ◽  
pp. 1-16 ◽  
Author(s):  
Leon L. van Dommelen ◽  
Shan Fu Shen
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Matching Rule ◽  
Rotational Perturbation ◽  
Boundary Layer Development ◽  
Perturbation Velocity ◽  
Asymptotic Matching ◽  
Layer Development ◽  
Rear Stagnation Point ◽  
Exponentially Small

It is suggested that current conceptions about unsteady rear-stagnation-point flow do not fully describe the physics, since they show discrepancies from recent numerical results. The previously neglected exponentially small rotational perturbation velocity above the boundary-layer proves to have a dominating influence on the final boundary-layer development. An asymptotic analysis reveals possible difficulties for common computational schemes for viscous flows. Failure of the usual asymptotic matching rule in the analysis is in accordance with Fraenkel's warning on logarithmic expansions.

Measurements of the Boundary Layer Development along a Turbine Blade with Rough Surfaces

1980 ◽  
Vol 102 (4) ◽  
pp. 978-983 ◽  
Author(s):  
K. Bammert ◽  
H. Sandstede
Keyword(s):  
Boundary Layer ◽  
Rough Surfaces ◽  
Chord Length ◽  
Smooth Surfaces ◽  
Turbine Cascade ◽  
Boundary Layer Development ◽  
Turbine Cascades ◽  
Layer Development ◽  
Good Agreement

During the operation of turbines the surfaces of the blades are roughened by corrosion, erosion and deposits. The generated roughness is usually greater than that produced by manufacture. The quality of the blade surfaces determines the losses of energy conversion in turbine cascades to a great extent. The loss coefficient can be found theoretically by a boundary layer calculation. For rough surfaces there are no boundary layer measurements along the profiles of a turbine cascade. Therefore in a cascade wind tunnel measurements of the boundary layer development were carried out. The chord length of the blades was 175 mm. The cascade represented a section through the stator blades of a 50 percent reaction gas turbine. For smooth surfaces and three different roughnesses up to 3.3 · 10−3 (equivalent sand roughness related to chord length) the boundary layers were measured. The momentum thickness is up to three times as great as that on smooth surfaces. Especially in regions with decelerated flow the effects of roughness are high. A rough surface causes a rise of the friction factor and a shift of the transition of laminar to turbulent flow. The results of the measurements are shown. Correction factors are worked out to get good agreement between measurement and calculation according to the Truckenbrodt theory.

Approximate Analysis of Transient Laminar Boundary-Layer Development

1968 ◽  
Vol 90 (4) ◽  
pp. 452-456 ◽  
Author(s):  
J. A. Schetz ◽  
Sin K. Oh
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Development Time ◽  
Constant Density ◽  
Boundary Layer Development ◽  
New Type ◽  
Momentum Integral ◽  
Layer Development ◽  
Surrounding Fluid ◽  
Good Agreement

Transient development of the boundary layer on a flat plate following the impulsive start of motion of the surrounding fluid is analyzed approximately. The Howarth-Dorodnitzin transformation and a Crocco Integral are used to relate the temperature field to the approximate velocity field which is obtained in a “constant density” plane. The solution for the velocity field is determined using the unsteady Momentum Integral equation with a new type of profile. Expressions for the boundary-layer development time and model surface temperature at the end of the development time are presented. Good agreement with a roughly determined experimental flow development time is achieved.

Turbulent Boundary Layer Development in the Presence of Small Isolated Two-Dimensional Surface Discontinuities

1989 ◽  
Vol 111 (4) ◽  
pp. 472-477 ◽  
Author(s):  
D. J. Cockrell ◽  
H. H. Nigim ◽  
M. A. Alhusein
Keyword(s):  
Boundary Layer ◽  
Two Dimensional ◽  
Integral Boundary ◽  
Aircraft Wings ◽  
Boundary Layer Development ◽  
Predictive Role ◽  
Engineering Significance ◽  
Prediction Techniques ◽  
Surface Discontinuities ◽  
Layer Development

Discontinuities in surfaces over which fluids flow can occur in a variety of situations. One of contemporary engineering significance is that which arises on aircraft wings, where the wing forms a junction with an auxiliary lifting surface. Such discontinuities are often two-dimensional and may well be small, lying within the logarithmic regions of the turbulent boundary layers in which they are immersed. In this paper such surface discontinuities are idealized into shapes whose drag coefficients, when they have been isolated from their surrounding surfaces, have been previously determined and tabulated. By making appropriate assumptions about the boundary layer characteristics in the vicinity of the discontinuities and then adopting appropriate integral boundary layer prediction techniques, methods are developed for continuing the boundary layer prediction process across them and then downstream of them. These computations compare well with experimental results, even for comparatively large discontinuities and the technique is recommended for use in a predictive role.

Stabilizing and Destabilizing Effects of Coriolis Force on Two-Dimensional Laminar and Turbulent Boundary Layers

1979 ◽  
Vol 101 (1) ◽  
pp. 23-29 ◽  
Author(s):  
H. Koyama ◽  
S. Masuda ◽  
I. Ariga ◽  
I. Watanabe
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Coriolis Force ◽  
Stable Boundary Layer ◽  
Numerical Evaluation ◽  
Critical Reynolds Number ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Boundary Layer Development ◽  
Layer Development

To investigate the effects of Coriolis force on two-dimensional laminar and turbulent boundary layers, quantitative experiments were performed. A numerical evaluation was also carried out utilizing the Monin-Oboukhov coefficient including the effect of rotation. From the experimental results, the boundary layer development was found to be promoted on the unstable side and suppressed on the stable side, in comparison with the case of zero-rotation. In the stable boundary layer, the critical Reynolds number for relaminarization was observed to increase as rotation number was decreased. Calculated results were seen to predict the stabilizing effect of Coriolis force fairly well.

Turbulent Boundary-Layer Development on a Two-Dimensional Aerofoil with Supercritical Flow at low Reynolds Number

1982 ◽  
Vol 33 (2) ◽  
pp. 174-198 ◽  
Author(s):  
C.J. Baker ◽  
L.C. Squire
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Turbine Blade ◽  
Side Wall ◽  
Two Dimensional ◽  
Supercritical Flow ◽  
Boundary Layer Development ◽  
Wide Range ◽  
Layer Development

SummaryDetailed measurements have been made of the boundary-layer development on a small two-dimensional aerofoil with supercritical flow and a weak shock wave, together with similar measurements on the tunnel side wall opposite the aerofoil surface. The Reynolds number of the test is similar to that found in the turbines of jet engines and there is a strong favourable pressure gradient ahead of the interaction of the shock with the boundary layer as often occurs in turbine blade passages. However, whereas the boundary layer on the aerofoil is thin and of the same thickness as that on a turbine blade, the thicker boundary layer on the wall is more typical of that on the hub or casing. The experimental results are compared with results from a wide range of calculation methods. One interesting conclusion from these comparisons is the fact that prediction methods which perform well for the thin boundary layers on the aerofoil do not necessarily perform as well for the thicker boundary layers on the wall.

Boundary-layer growth at a three-dimensional rear stagnation point

1975 ◽  
Vol 67 (2) ◽  
pp. 289-297 ◽  
Author(s):  
J. A. Howarth
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Similarity Solutions ◽  
Layer Growth ◽  
Initial Value ◽  
Stagnation Points ◽  
Boundary Layer Growth ◽  
Rear Stagnation Point

The theory of boundary-layer growth at a rear stagnation point, first presented by Proudman & Johnson, is here extended to cover fully three-dimensional rear stagnation points. Supporting numerical solutions of the full initial-value problem establish the relevance of the in viscid similarity solutions obtained.

Assessing the Influence of Aerosol on Radiation and Its Roles in Planetary Boundary Layer Development

2021 ◽  
Vol 35 (2) ◽  
pp. 384-392
Author(s):  
Zhigang Cheng ◽  
Yubing Pan ◽  
Ju Li ◽  
Xingcan Jia ◽  
Xinyu Zhang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Planetary Boundary Layer ◽  
Boundary Layer Development ◽  
Layer Development

Numerical Simulation of Turbine Blade Boundary Layer and Heat Transfer and Assessment of Turbulence Models

1997 ◽  
Vol 119 (4) ◽  
pp. 794-801 ◽  
Author(s):  
J. Luo ◽  
B. Lakshminarayana
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Bypass Transition ◽  
Boundary Layer Development ◽  
Low Reynolds ◽  
Layer Development

The boundary layer development and convective heat transfer on transonic turbine nozzle vanes are investigated using a compressible Navier–Stokes code with three low-Reynolds-number k–ε models. The mean-flow and turbulence transport equations are integrated by a four-stage Runge–Kutta scheme. Numerical predictions are compared with the experimental data acquired at Allison Engine Company. An assessment of the performance of various turbulence models is carried out. The two modes of transition, bypass transition and separation-induced transition, are studied comparatively. Effects of blade surface pressure gradients, free-stream turbulence level, and Reynolds number on the blade boundary layer development, particularly transition onset, are examined. Predictions from a parabolic boundary layer code are included for comparison with those from the elliptic Navier–Stokes code. The present study indicates that the turbine external heat transfer, under real engine conditions, can be predicted well by the Navier–Stokes procedure with the low-Reynolds-number k–ε models employed.

Sign in / Sign up

Export Citation Format

Share Document