A Momentum Integral Solution of a Three-Dimensional Turbulent Boundary Layer

1972 ◽  
Vol 94 (4) ◽  
pp. 795-800
Author(s):  
F. J. Pierce ◽  
W. F. Klinksiek
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Strong Dependence ◽  
Three Dimensional ◽  
Integral Solution ◽  
Edge Condition ◽  
Integral Methods ◽  
Flow Parameters ◽  
Layer Flow ◽  
Momentum Integral

The results of a momentum integral solution of the three-dimensional turbulent boundary layer on the confining wall of an impinging jet are presented. This geometry provides a boundary layer where large gradients in the streamwise and especially the transverse direction occur and hence is a severe test of momentum integral methods. The solution utilizes the Head entrainment function and the Ludwieg and Tillmann wall shear law, with no restriction on cross flows. An extensive comparison with experimental results show good to moderate agreement in the integrated flow parameters, with a strong dependence on the free-stream or edge condition to the boundary layer flow.

Turbulent Boundary Layer Flow on the End Wall of a Cylindrical Vortex Chamber

1975 ◽  
Vol 189 (1) ◽  
pp. 305-315 ◽  
Author(s):  
T. J. Kotas
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Vortex Chamber ◽  
Cylindrical Vortex ◽  
Layer Flow ◽  
Momentum Integral ◽  
End Wall

A presentation of some measurements of velocities in the turbulent boundary layer on the end wall of a vortex chamber. These show that the boundary layer flow is three-dimensional with large inward radial velocities. Consequently, most of the fluid entering the vortex chamber passes into the central region through the boundary layers on the end walls rather than the main space of the vortex chamber. A momentum integral solution is used to obtain an estimate of the radial flow through the end-wall boundary layers. A comparison of the theoretical curves with the experimental results gives support to the main assumptions used in the solutions.

The Calculation of Three-Dimensional Turbulent Boundary Layers: Part II: Attachment-Line Flow on an Infinite Swept Wing

1967 ◽  
Vol 18 (2) ◽  
pp. 150-164 ◽  
Author(s):  
N. A. Cumpsty ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Cross Flow ◽  
Swept Wing ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow ◽  
Momentum Integral ◽  
Attachment Line

SummaryAn earlier paper described a method of calculating the turbulent boundary layer flow over the rear of an infinite swept wing. It made use of an entrainment equation and momentum integral equations in streamwise and cross-flow directions, together with several auxiliary assumptions. Here the method is adapted to the calculation of the turbulent boundary layer flow along the attachment line of an infinite swept wing. In this case the cross-flow momentum integral equation reduces to the identity 0 = 0 and must be replaced by its differentiated form. Two alternative approaches are also adopted and give very similar results, in good agreement with the limited experimental data available. It is found that results can be expressed as functions of a single parameter C*, which is evidently the criterion of similarity for attachment-line flows.

Turbulent boundary-layer flow on a rotating disk

1969 ◽  
Vol 37 (1) ◽  
pp. 129-147 ◽  
Author(s):  
T-S. Cham ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Rotating Disk ◽  
Circumferential Velocity ◽  
Auxiliary Equation ◽  
Two Dimensional ◽  
Free Air ◽  
Radial Profiles ◽  
Layer Flow ◽  
Momentum Integral

Calculations have been made of the development of the turbulent boundary layer on a disk rotating in free air, using circumferential and radial momentum-integral equations and an auxiliary equation of entrainment. In the calculations, circumferential velocity profiles are represented by Thompson's (1965) two-parameter family, while radial profiles are given by Mager's (1952) quadratic expression. The circumferential component of skin friction follows from the use of Thompson's profile family for the circumferential velocity. The entrainment, in dimensionless form, is assumed to be determined uniquely by the circumferential velocity profile in the same way as was proposed by Head (1958) for a two-dimensional turbulent boundary layer.Detailed measurements have been made of the development of the turbulent boundary layer on the rotating disk, and the calculations are found to be in excellent agreement with the results when a suitable adjustment is made to Head's two-dimensional entrainment curve.

Calculation of the three-dimensional turbulent boundary layer in the vessel’s bow and midship area by the integral method

2021 ◽  
Author(s):  
T.G. Artyushina
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Mathematical Models ◽  
Integral Method ◽  
Three Dimensional ◽  
Physical Modelling ◽  
Limited Range ◽  
Differential Method ◽  
Friction Resistance ◽  
Integral Methods

The quality of technical solutions applied in ship design and construction is substantially determined by the validity of viscous flow parameters, especially in the vicinity of thrusters. The influence of shapes on velocity, pressure and turbulence distribution can be assessed by physical experimentation. Along with undeniable advantages, physical modelling has a number of disadvantages: high labour input and cost, limited range of parameters variation (e.g. Reynolds numbers), difficulty in separating the influence of individual factors. Therefore, the development of mathematical models and numerical calculation schemes based on them is extremely relevant. Calculation of friction resistance and calculation of the velocity field in the vicinity of a vessel comes down to the calculation of its boundary layer and trace parameters. Current mathematical models with a planar representation, i.e. working with projections rather than real curves, do not give an accurate description. This has led to the need for a mathematical model that can address all of the required characteristics of a three-dimensional turbulent boundary layer. Both differential and integral methods are used to calculate three-dimensional boundary layers. The model is capable of calculating the characteristics of the spatial boundary layer in the stern and the viscous wake, in the bow and in the middle of the vessel. The model is quite versatile: it has been successfully used both for computing the boundary layer characteristics in the bow and midship area by the integral method based on the thick boundary layer concept, and for computing the turbulent flow in the stern and viscous wake by the differential method based on the partial parabolic concept using the k-ε turbulence model. In this paper we will elaborate on the integral method calculation.

Investigation of Turbulent Flow Behavior in a Heated Boundary Layer

2019 ◽  
Author(s):  
Kadeem Dennis ◽  
Kamran Siddiqui
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Mixed Convection ◽  
Turbulent Flow ◽  
Flow Regime ◽  
Three Dimensional ◽  
Convection Flow ◽  
Buoyant Force ◽  
Layer Flow ◽  
Flow Inertia

Abstract The boundary layers are known to play key roles in many engineering systems. The hydrodynamic boundary layer found in these systems is often turbulent in nature and heat transfer is involved which further increases flow complexity due to the influence of buoyancy. One of the constituent layers of the turbulent boundary layer, the inner layer, has been established as home to key dynamical turbulent phenomena which can be influenced by the buoyant force. In the mixed convection flow regime, flow inertia and buoyant force are on the same order of magnitude. In this regime, buoyant thermals rising from the wall interact with the inertia-driven turbulent flow field resulting in highly complex three-dimensional flow dynamics. Past research studies conducted in this flow regime have been mostly computational in nature with little experimental work. The current knowledge on the impact of the relative contributions by the buoyant force and flow inertia on turbulent phenomena in the mixed convection flow regime is very limited. This study reports on an investigation into the turbulent flow phenomena present in mixed convection turbulent boundary layer flow over a heated smooth horizontal flat plate. Experiments were performed in a closed loop wind tunnel where the turbulent boundary layer was heated from below. The multi-plane particle image velocimetry (PIV) technique was used to capture two-dimensional velocity fields over two planes with respect to the flow direction. Experiments were conducted over a range of Richardson numbers (Ri) between 0.0 and 2.0 to control the relative contribution of the buoyant force with respect to flow inertia. The measured velocity fields are used to describe the influence of buoyancy on the three-dimensional turbulent boundary layer flow.

Sign in / Sign up

Export Citation Format

Share Document