Thwaites' Method In Laminar Boundary Layer

1989 ◽  
pp. 5-13 ◽  
Author(s):  
Prof. Amer Nordin ◽  
Lim Chee Wah
Keyword(s):  
Boundary Layer ◽  
Coefficient Of Friction ◽  
Momentum Thickness ◽  
Flow Properties ◽  
Local Coefficient ◽  
Simple Boundary ◽  
Displacement Thickness ◽  
Different Types ◽  
Naca 0012 ◽  
Complex Curvature

Thwaites' method can be applied to find the boundary layer characteristics for either similar or nonsimilar flow for a variety of boundaries ranging from a simple flat plate (Blasius's Solution(1)) to a symmetrical airfoil. The flow properties to be determined include potential flow velocity distribution, displacement thickness, momentum thickness and coefficient of friction. Furthermore,the location of flow separation is readily obtainable from the numeric value of local coefficient of friction. Thwaites' Method is able to provide satisfactory approximate solution to different types of simple boundary as long as the flow is laminar and not separated. For a complex curvature such a an airfoil Thwaite' Method is yet to be tested. In this context, we will look into the applicability of Thwaites' Method for a particular symmetrical airfoil, NACA 0012.

Pohlhausen's Method for Three-Dimensional Laminar Boundary Layers

1951 ◽  
Vol 3 (1) ◽  
pp. 51-60 ◽  
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Three Dimensions ◽  
Momentum Thickness ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Good For ◽  
Layer Flow ◽  
Accelerated Flow

SummaryWild has extended to three dimensions the von Kármán-Pohlhausen method for the laminar boundary layer flow over a fixed obstacle and used the method for an infinite yawed elliptic cylinder in a stream. In this paper the method is tested in two ways (which may be called full-Pohlhausen and semi-Pohlhausen) for the case of an infinite yawed cylinder when the velocity outside the boundary layer over the surface normal to the generators is of the form U=cxm. The exact solution is known in this case.A table of the skin friction, displacement thickness and momentum thickness is given for various values of β [=2m/(m + 1)], and the agreement is found to be fairly good for β>0 (accelerated flow) but not so good for β<0 (retarded flow).)

Boundary Layers over Infinite Yawed Wings

1960 ◽  
Vol 11 (4) ◽  
pp. 333-347 ◽  
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Free Flow ◽  
Momentum Thickness ◽  
Displacement Thickness

SummaryA method of calculating turbulent boundary layers on infinite yawed wings is given, making use of a method of calculating turbulent boundary layers due to Spence and of an analogy between three-dimensional and axi-symmetric boundary layers. It is also shown that the displacement thickness is equal to that computed using chordwise components and that the streamwise momentum thickness is approximately equal to the chordwise momentum thickness. Shock-free flow and small boundary layer cross-flow are assumed.

Effects of Slip on the Flow Characteristics of Laminar Flat Plate Boundary-Layer

2006 ◽  
Author(s):  
Nanda K. Vedantam ◽  
Ramkumar N. Parthasarathy
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Boundary Layer Thickness ◽  
Computational Study ◽  
Slip Length ◽  
Flow Characteristics ◽  
Momentum Thickness ◽  
Displacement Thickness ◽  
Layer Flow ◽  
Control Volumes

A uniform stream of viscous fluid flowing past a flat plate with slip at the fluid-plate interface is considered. The aim of this investigation is to examine the effects of slip at the wall on the laminar boundary-layer flow characteristics. For this purpose, an analytical and a computational study were conducted. The analytical study is based on the Blasius similarity solution for laminar boundary-layer flow past a flat plate. In the computational study, the flow over a flat plate is modeled and solved (using FLUENT) by dividing the computational domain into small control volumes and discretizing and solving the governing equations around these control volumes. The slip at the fluid-solid interface is accounted for by the Navier boundary condition (NBC). Three cases are considered, wherein the slip boundary condition is incorporated in three different ways, i.e., by specifying the slip length, or the slip velocity, or by assuming the slip length to be a function of shear rate. The flow characteristics are evaluated for different amounts of slip. The wall shear stress, the skin-friction coefficient, and the drag coefficient decrease by about 38% when the nondimensional slip length is increased from zero (noslip) to 2. The boundary-layer thickness, the displacement thickness, and the momentum thickness also decrease with increase in slip. The reduction in displacement thickness is much greater (about 68%) than the boundary-layer thickness or the momentum thickness. An excellent agreement between the analytical and computational results is noticed.

Theory and application of two-dimension viscous hydraulic design of the ultra-low specific-speed centrifugal pump

2019 ◽  
Vol 234 (1) ◽  
pp. 58-71 ◽  
Author(s):  
Cong Wang ◽  
Yongxue Zhang ◽  
Hucan Hou ◽  
Zhiyi Yuan
Keyword(s):  
Boundary Layer ◽  
Centrifugal Pump ◽  
Diagnostic Model ◽  
Two Dimension ◽  
Cavitation Performance ◽  
Hydraulic Design ◽  
Displacement Thickness ◽  
Low Specific Speed ◽  
Specific Speed ◽  
Low Efficiency

Low efficiency and bad cavitation performance restrict the development of the ultra-low specific-speed centrifugal pump (ULSSCP). In this research, combined turbulent boundary layer theory with two-dimension design and two-dimension viscous hydraulic design method has been proposed to redesign a ULSSCP. Through the solution of the displacement thickness in the boundary layer, a less curved blade profile with a larger outlet angle was obtained. Then the hydraulic and cavitation performance of the reference pump and the designed pump were numerically studied. The comparison of performance of the reference pump calculated by the numerical and experimental results revealed a better agreement. Research shows that the average hydraulic efficiency and head of the designed pump improve by 2.9% and 3.3%, respectively. Besides, the designed pump has a better cavitation performance. Finally, through the internal flow analysis with entropy production diagnostic model, a 24.8% drop in head loss occurred in the designed pump.

scholarly journals A “Cold Path” for the Gulf Stream–Troposphere Connection

2017 ◽  
Vol 30 (4) ◽  
pp. 1363-1379 ◽  
Author(s):  
Benoît Vannière ◽  
Arnaud Czaja ◽  
Helen Dacre ◽  
Tim Woollings
Keyword(s):  
Boundary Layer ◽  
Gulf Stream ◽  
Surface Wind ◽  
Extratropical Cyclone ◽  
Convective Precipitation ◽  
Dynamical Response ◽  
Sst Front ◽  
Simple Boundary ◽  
Pressure Anomaly ◽  
Sst Gradient

Abstract The mechanism by which the Gulf Stream sea surface temperature (SST) front anchors a band of precipitation on its warm edge is still a matter of debate, and little is known about how synoptic activity contributes to the mean state. In the present study, the influence of the SST front on precipitation is investigated during the course of a single extratropical cyclone using a regional configuration of the Met Office Unified Model. The comparison of a control run with a simulation in which SST gradients were smoothed brought the following conclusions: a band of precipitation is reproduced for a single extratropical cyclone, and the response to the SST gradient is dominated by a change of convective precipitation in the cold sector of the storm. Several climatological features described by previous studies, such as surface wind convergence on the warm edge or a meridional circulation cell across the SST front, are also reproduced at synoptic time scales in the cold sector. Based on these results, a simple boundary layer model is proposed to explain the convective and dynamical response to the SST gradient in the cold sector. In this model, cold and dry air parcels acquire more buoyancy over a sharp SST gradient and become more convectively unstable. The convection sets a pressure anomaly over the entire depth of the boundary layer that drives wind convergence. This case study offers a new pathway by which the SST gradient can anchor a climatological band of precipitation.

The equation of similar profiles in boundary layer theory with strong blowing

1966 ◽  
Vol 294 (1437) ◽  
pp. 208-234 ◽  
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Main Part ◽  
Similarity Solutions ◽  
Boundary Layer Theory ◽  
Main Stream ◽  
Outer Solution ◽  
Boundary Layer Equations ◽  
Displacement Thickness ◽  
Complicated Form

This paper contains a study of the similarity solutions of the boundary layer equations for the case of strong blowing through a porous surface. The main part of the boundary layer is thick and almost inviscid in these conditions, but there is a thin viscous region where the boundary layer merges into the main stream. The asymptotic solutions appropriate to these two regions are matched to one another when the blowing velocity is large. The skin friction is found from the inner solution, which is independent of the outer solution, but the displacement thickness involves both solutions and is of more complicated form.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

Effect of plasma actuator in boundary layer on flat plate model with turbulent promoter

2017 ◽  
Vol 232 (16) ◽  
pp. 3001-3010
Author(s):  
James Julian ◽  
Harinaldi ◽  
Budiarso ◽  
Chin-Cheng Wang ◽  
Ming-Jyh Chern
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Aerodynamic Drag ◽  
Active Flow Control ◽  
Adverse Pressure Gradient ◽  
Plasma Actuator ◽  
Experimental Results ◽  
Plate Model ◽  
Displacement Thickness ◽  
Turbulent Promoter

This paper shows experimental results for velocity measurement in the boundary layer with the use of a flat plate model. The flat plate model is disrupted with a wire trip and the effect of the plasma actuator to alter the flow in the boundary layer is then observed. The purpose of this research is to characterize the performance of the plasma actuator in a no-flow condition and with the use of a 2 m/s flow and also to theoretically analyze the performance of actuator in the boundary layer namely, displacement thickness, momentum thickness, and energy thickness. This is all done to acquire a deeper understanding of the capabilities of plasma actuator as one of the alternative active flow control equipment and to increase the effect of aerodynamic drag reduction. One of the ways to decrease the aerodynamic drag is to manipulate the flow to have a low boundary layer thickness value in order to prevent an adverse pressure gradient from happening, which then may lead to the formation of a flow separation. From experimental results, it is known that plasma actuator could decrease the thickness of the boundary layer by 9 mm.

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