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.

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.

Research on Turbulent Boundary Layer Development of Hydraulic Jump Region with the Theory of Plane Adhesive Wall Jet Flow

2012 ◽  
Vol 212-213 ◽  
pp. 1141-1146
Author(s):  
Zhi Chang Zhang ◽  
Ruo Bing Li ◽  
Ying Zhao ◽  
Ming Huan Fu
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Hydraulic Jump ◽  
Rectangular Channel ◽  
Jet Flow ◽  
Wall Jet ◽  
Boundary Layer Development ◽  
Wall Jet Flow ◽  
Momentum Integral ◽  
Layer Development

【Objective】The calculation of turbulent boundary layer development in hydraulic jump region is put forwarded.【Method】According to the analysis of predecessors’ researches about plane adhesive wall jet flow of rectangular channel, Based on the momentum integral equation of turbulent boundary layer and the velocity distribution formula of adhesive wall jet flow, turbulent boundary layer development of hydraulic jump region in rectangular channel is researched.【Result】Formulas of the development of boundary layer in hydraulic jump region and drag coefficient are obtained, the accuracy of equations are verified by the example. 【Conclusion】The calculation has enlightened effect on the hydraulic characteristics of hydraulic jump.

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.

Turbulence Stimulation and the Initial Boundary-Layer Development on Two Ship Forms

1982 ◽  
Vol 26 (03) ◽  
pp. 166-175
Author(s):  
A.J. Smits
Keyword(s):  
Boundary Layer ◽  
Initial Boundary ◽  
Skin Friction Coefficient ◽  
Total Drag ◽  
Virtual Origin ◽  
Boundary Layer Development ◽  
Approximate Form ◽  
Momentum Integral ◽  
Layer Development ◽  
Inappropriate Choice

Inappropriate tripping devices may either not promote transition effectively or cause significant distortion of the initial boundary-layer development. By reexamining data for reflex geosims of Lucy Ashton and a small 0.80-CB tanker it is shown that this distortion can readily occur. To compare the boundary-layer development near the bow of a ship model under different test conditions the relative position of the virtual origin must remain constant. The concept of a virtual origin is considered using an approximate form of the momentum integral equation and it is found that locating the virtual origin is a highly ambiguous process, and therefore it becomes difficult to decide if the virtual origin remains constant or not. To compare and extrapolate total drag results, a correction for the virtual origin position is usually applied. For two widely different ship forms it is shown that the total skin friction coefficient is relatively insensitive to a poor estimate of the virtual origin position and an inappropriate choice of stimulator.

Boundary-layer development on the afterbody of an engine nacelle

1985 ◽  
Vol 158 ◽  
pp. 23-46
Author(s):  
Eugene Lai ◽  
L. C. Squire
Keyword(s):  
Boundary Layer ◽  
Pressure Distribution ◽  
Reynolds Shear Stress ◽  
The Body ◽  
Turbulence Structure ◽  
Boundary Layer Development ◽  
Dimensional Boundary ◽  
Momentum Integral ◽  
Engine Nacelle ◽  
Layer Development

Measurements have been made of the pressure distribution and turbulent-boundary-layer development on the afterbody of a model engine nacelle with a jet exhausting from the base and with the jet replaced by a parallel solid sting. It was found that the effect of replacing the jet by a solid body was to increase the pressure recovery over the afterbody and hence give a lower drag than with the jet. These changes in the pressure distribution affected the boundary-layer development and turbulence structure by different methods based on a momentum integral equation and the kinetic equation for the turbulence. Both methods approximately incorporate the effects of convergence and divergence of the flow caused by changes in transverse curvature of the surface. Neither method was completely satisfactory for the prediction of the overall boundary-layer development.It was also found that, near the tail of the model, where the body radius is decreasing rapidly, the Reynolds shear stress was much lower than it would be in a two-dimensional boundary layer with the same pressure gradient. Calculations and analysis based on earlier work show that this reduction is directly related to the rates of strain associated with the convergence of the streamlines over the afterbody.

A boundary layer developing in an increasingly adverse pressure gradient

1974 ◽  
Vol 66 (3) ◽  
pp. 481-505 ◽  
Author(s):  
A. E. Samuel ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Adverse Pressure Gradient ◽  
Momentum Balance ◽  
Mean Flow ◽  
Law Of The Wall ◽  
Centre Line ◽  
Boundary Layer Development ◽  
Momentum Integral ◽  
Layer Development

This paper deals with a survey of mean flow and fluctuating quantities in a turbulent boundary layer developing on a smooth wall in a pressure domain P(x), where both dP/dx and d2P/dx2 are positive (increasingly adverse). The two-dimensional nature of the flow field was checked by momentum balance, as well as velocity traverses either side of the working section centre-line. Using the integrated form of the momentum integral equation, it was found that the skinfriction term and the summed momentum and pressure terms differed by at most 19%; but for the majority of measuring points they differed by less than 14%. The off-centre-line velocity profiles were indistinguishable from those taken on the centre-line. The flow field was also surveyed for fluctuating components $(\overline{u^2_1})^{\frac{1}{2}}, (\overline{u^2_2})^{\frac{1}{2}}, (\overline{u^2_3})^{\frac{1}{2}}$, and $\overline{u_1u_2}$, as well as for u1 spectra. Wherever possible, the results were compared with existing models of boundary-layer development. These comparisons indicated that the only all-embracing model for boundary-layer development is the law of the wall.

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.

Some Boundary Layer-Porous Wall Coupling Effects in Laminar Flows With Surface Injection

1970 ◽  
Vol 92 (3) ◽  
pp. 257-266
Author(s):  
D. A. Nealy ◽  
P. W. McFadden
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Balance ◽  
Transfer Problem ◽  
Porous Wall ◽  
Laminar Flows ◽  
Stream Velocity ◽  
Axial Conduction ◽  
Boundary Layer Development ◽  
Layer Development

Using the integral form of the laminar boundary layer thermal energy equation, a method is developed which permits calculation of thermal boundary layer development under more general conditions than heretofore treated in the literature. The local Stanton number is expressed in terms of the thermal convection thickness which reflects the cumulative effects of variable free stream velocity, surface temperature, and injection rate on boundary layer development. The boundary layer calculation is combined with the wall heat transfer problem through a coolant heat balance which includes the effect of axial conduction in the wall. The highly coupled boundary layer and wall heat balance equations are solved simultaneously using relatively straightforward numerical integration techniques. Calculated results exhibit good agreement with existing analytical and experimental results. The present results indicate that nonisothermal wall and axial conduction effects significantly affect local heat transfer rates.

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