Dynamics of Slender Tapered Beams With Internal or External Axial Flow—Part 1: Theory

1979 ◽  
Vol 46 (1) ◽  
pp. 45-51 ◽  
Author(s):  
M. J. Hannoyer ◽  
M. P. Paidoussis
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Thickness ◽  
Equations Of Motion ◽  
Axial Flow ◽  
Internal Flow ◽  
External Flow ◽  
High Flow ◽  
Flow Passage ◽  
Flow Part ◽  
Surrounding Fluid

This paper develops a general theory for the dynamics of slender, nonuniform axisymmetric beams subjected to either internal or external flow, or to both simultaneously. The effect of the boundary layer of the external flow is taken into account in the formulation. Typical solutions of the equations of motion are presented for cantilevered conical beams in external flow and for beams with a conical internal flow passage. Such systems lose stability at sufficiently high flow velocity, internal or external, either by flutter or by buckling. The effect of several parameters is investigated. For internal flow, the internal and external shape, whether uniform or conical, and the density of the surrounding fluid have sometimes unexpected effects on stability; e.g., tubular beams lose stability at lower internal flow when immersed in water than when in air. For external flow the effects of conicity, free end shape and boundary-layer thickness are investigated; the latter has a strong stabilizing influence, such that simple theory neglecting this effect results in serious error.

Dynamics of Slender Tapered Beams With Internal or External Axial Flow—Part 2: Experiments

1979 ◽  
Vol 46 (1) ◽  
pp. 52-57 ◽  
Author(s):  
M. J. Hannoyer ◽  
M. P. Paidoussis
Keyword(s):  
Axial Flow ◽  
Internal Flow ◽  
Quantitative Agreement ◽  
External Flow ◽  
Critical Conditions ◽  
Experimental Program ◽  
Water Tunnel ◽  
Elastic Instabilities ◽  
Theoretical Predictions ◽  
Flow Part

This paper describes the experimental program which was conducted in parallel with the theoretical investigation presented in Part 1 of this study. Experiments were conducted in a special water tunnel with silicone rubber cantilevers which, in the case of external flow, were truncated cones, the free ends of which were streamlined; in the case of internal flow the beams were tubular, conical inside, and either conical or cylindrical outside, immersed either in still air or water. Experiments were also conducted with uniform tubular cylinders, and some with simultaneous internal and external axial flow. Qualitatively these experiments support theoretical predictions very well. The critical conditions for the various fluid-elastic instabilities which these systems can develop were measured and compared with theory. Quantitative agreement ranged from excellent to fair, the former for internal flow in conical tubes, and the latter for very slender cones in external flow.

Effect of Transverse Curvature on Turbulent-Boundary-Layer Characteristics

1958 ◽  
Vol 2 (04) ◽  
pp. 33-51
Author(s):  
Yun-Sheng Yu
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Shearing Stress ◽  
Transverse Curvature ◽  
Similarity Laws

Tests made on the turbulent boundary layer on a circular cylinder in axial flow at zero pressure gradient are described. From the measurements, similarity laws of the velocity profile are formulated, and various boundary-layer characteristics are evaluated and compared with the flatplate results. It is found that the effect of transverse curvature is to increase the surface shearing stress and to decrease the boundary-layer thickness, and that the latter variation is more pronounced than the former.

Effects of the Inlet Boundary Layer Thickness on the Flow and Loss Characteristics in an Axial Compressor

2005 ◽  
Author(s):  
Minsuk Choi ◽  
Junyoung Park ◽  
Jehyun Baek
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Axial Compressor ◽  
Internal Flow ◽  
Total Loss ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Suction Surface ◽  
Tip Leakage

A three-dimensional computation was conducted to understand effects of the inlet boundary layer thickness on the internal flow and the loss characteristics in a low-speed axial compressor operating at the design condition (φ = 85%) and near stall condition (φ = 65%). At the design condition, independent of the inlet boundary layer thickness, flows in the axial compressor show similar characteristics such as the pressure distribution, size of hub corner-stall, tip leakage flow trajectory, limiting streamlines on the blade suction surface, etc. But, as the load is increased, for the thick inlet boundary layer at hub and casing, the hub corner stall grows to make a large separation region between the hub and suction surface, and the tip leakage flow is more vortical than that observed in the case with thin inlet boundary layer and has the critical point where the trajectory of the tip leakage flow is suddenly turned to the downstream. For the thin inlet boundary layer, the hub corner stall decays to form the thick boundary layer from hub to midspan on the suction surface owing to the blockage of the tip leakage flow and the tip leakage flow leans to the circumferential direction more than at the design condition. In addition to these, the severe reverse flow, induced by both boundary layers on the blade surface and the tip leakage flow, can be found to act as the blockage of flows near the casing, resulting in a heavy loss. As a result of these differences of the internal flow made by the different inlet boundary layer thickness, the spanwise distribution of the total loss is changed dramatically. At the design condition, total pressure losses for two different boundary layers are almost alike in the core flow region but the larger losses are generated at both hub and tip when the inlet boundary layer is thin. At the near stall condition, however, total loss for thick inlet boundary layer is found to be greater than that for thin inlet boundary layer on most of the span except the region near the hub and casing. In order to analyze effects of inlet boundary layer thickness on total loss in detail, total loss is scrutinized through three major loss categories available in a subsonic axial compressor such as profile loss, tip leakage loss and endwall loss.

A Numerical Investigation Into the Sources of Endwall Loss in Axial Flow Turbines

2012 ◽  
Author(s):  
John Denton ◽  
Graham Pullan
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Turbine Cascade ◽  
Plane Model ◽  
Blade Row ◽  
Axial Turbines ◽  
Different Sources ◽  
Good Agreement

Endwall loss, often termed “secondary loss”, in axial turbines has been intensively studied for many years, despite this the physical origin of much of the loss is not really understood. This lack of understanding is a serious impediment to our ability to predict the loss and to the development of methods for reducing it. This paper aims to study the origins of the loss by interrogating the results from detailed and validated CFD calculations. The calculation method is first validated by comparing its predictions to detailed measurements in a turbine cascade. Very good agreement between the calculations and the measurements is obtained. The solution is then examined in detail to highlight the sources of entropy generation in the cascade, several different sources of loss are found to be significant. The same blade row is then used to study the effects of the of the inlet boundary layer thickness on the loss. It is found that only the inlet boundary layer loss and the mixing loss vary greatly with inlet boundary layer thickness. Finally a complete 50% reaction stage, with identical stator and rotor blade profiles, is examined using both steady calculations, with a mixing plane model, and the time average of unsteady calculations. It is found that the endwall flow in the rotor is completely different from that in the stator. Because of this it is considered that results from endwall flow and loss measurements in cascades are of limited relevance to the endwall flow in a real turbine. The results are also used to discuss the validity of the mixing plane model.

Calculation of the axisymrnetric boundary layer on a long thin cylinder

1980 ◽  
Vol 372 (1751) ◽  
pp. 555-564 ◽  
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansion ◽  
Skin Friction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Thin Cylinder ◽  
Residual Series ◽  
Convergent Expansion ◽  
Significant Figures

The laminar boundary layer in axial flow along a long thin cylinder is investigated, following Seban & Bond (1951), by expanding in powers of a variable £ that represents the ratio of the boundary layer thickness to the cylinder radius. The resulting series for the skin friction r, of which 20 terms are calculated, is analysed, and, by working in terms of the inverse series, for r _1, the radius of convergence is estimated to be £ = 0.37416. An Euler transformation then yields a more convergent expansion in terms of a new variable By using the known asymptotic expansion of r for large £, we deduce how t—1 behaves near 2 = 1 , and extraction of the leading terms leaves an even more convergent residual series. Although neither the original series nor the asymptotic expansion give very accurate results over the substantial range 0-2 < £ < 100, the present analysis gives r to about six, or more, significant figures throughout the range. Similar success is achieved in calculating the displacement area.

An Analysis of Axisymmetric Turbulent Flow Past a Long Cylinder

1972 ◽  
Vol 94 (1) ◽  
pp. 200-204 ◽  
Author(s):  
F. M. White
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Small Radius ◽  
Law Of The Wall ◽  
Curvature Effects ◽  
Flow Past ◽  
Long Cylinder

An analysis is presented which predicts the properties of an arbitrarily thick turbulent boundary layer for incompressible axial flow past a long cylinder. The approach makes use of a modified form of the law-of-the-wall, deduced by G. N. V. Rao, which properly accounts for transverse curvature effects. Using this law, the theory which follows is equivalent to an exact solution to the axisymmetric equations of continuity and momentum for zero pressure gradient. Numerical results show that curvature increases skin friction and overall drag and decreases the boundary layer thickness and the integral thicknesses. The velocity profile is flattened and the shape factor approaches unity at large curvature. Comparison with several sources of friction data show better overall agreement than previous theories, except for an unexplained discrepancy with data for moving nylon fibers at very small radius Reynolds numbers.

Nonlinear Dynamics of an Extensible Flexible Pipe Conveying Fluid and Subjected to External Axial Flow

2011 ◽  
Author(s):  
F. A. Ghaith ◽  
Y. A. Khulief
Keyword(s):  
Nonlinear Equations ◽  
Linear Models ◽  
Numerical Solutions ◽  
Plug Flow ◽  
Axial Flow ◽  
Internal Flow ◽  
External Flow ◽  
Pipe Conveying Fluid ◽  
Flexible Pipe ◽  
Conveying Fluid

In this paper, the nonlinear equations representing the dynamics of a slender flexible pipe conveying fluid and subjected to external axial flow are formulated using the extended Hamilton’s principle. The internal flow is assumed to be steady, fully developed turbulent and approximated by a plug flow, while the external flow is represented by the induced hydrodynamic forces associated with friction, hydrostatic and inviscid components. The pipe centerline is considered to be extensible, and hence two coupled nonlinear equations of motion associated with longitudinal and transverse displacements are derived to describe the dynamics of the system. The developed model takes into account the fluid pressurization force and the tension in the pipe, which may be externally applied or associated with the frictional forces. For verification purpose, comparisons were performed, wherein the developed formulation was reduced to some published linear models. Numerical solutions were obtained for a case study of a double-pipe heat exchanger, wherein the effects of internal flow, external flow, flowrate, and radial gap on the dynamic characteristics of the system were addressed.

The development of horizontal boundary layers in stratified flow. Part 1. Non-diffusive flow

1970 ◽  
Vol 42 (3) ◽  
pp. 497-511 ◽  
Author(s):  
R. E. Kelly ◽  
L. G. Redekopp
Keyword(s):  
Boundary Layer ◽  
Equations Of Motion ◽  
Boussinesq Equations ◽  
Stratified Flow ◽  
Relative Magnitude ◽  
Dimensional Parameter ◽  
Horizontal Boundary ◽  
Basic Parameters ◽  
Flow Part ◽  
Two Parameters

The development of the boundary layer on the upper surface of a horizontal flat plate in a non-diffusive, stratified flow is described. It is shown that the flow can be characterized by two basic parameters, the Reynolds (RL) and Russell (RuL) numbers, and that, depending on the relative magnitude of these two parameters, three different régimes of flow can be defined. The delineation of these régimes and the description of the flow in each of them is obtained by deriving a uniformly valid first approximation to the Boussinesq equations of motion for a flow contained in the two-dimensional parameter spaceRuL> 0,RL> 1. The critical stratification for the self-blocking of a horizontal boundary layer is shown to be given by the conditionRuL=O(RL½).

scholarly journals Design and Verification for Hypersonic Aerodynamic Model with Duct of Internal and External Flow Decoupling

2015 ◽  
Vol 9 (12) ◽  
pp. 202
Author(s):  
Zejiang Wang ◽  
Wenping Song ◽  
Jin Jiang ◽  
Huiyong Zhao ◽  
Yong Zhang
Keyword(s):  
Circular Cross Section ◽  
Wind Tunnel Test ◽  
Internal Flow ◽  
Test System ◽  
External Flow ◽  
Design Technique ◽  
Aerodynamic Model ◽  
Component Strain ◽  
Flow Part ◽  
Key Techniques

<p class="zhengwen"><span lang="EN-GB">In order to develop the design techniques for the hypersonic aerodynamic testing model with duct system of internal flow and external flow decoupling, this research used a circular cross section air-breathing hypersonic cruise vehicle model, explored the model design technique for internal flow and external flow separated from each other, the design technique and the seal technique for the clearance between the internal flow part and the external flow part, the design technique of ring type six-component strain-gauge balance and so on. A wind tunnel test was conducted at mach 6. The results of the test indicate that, the design of the internal flow and external flow decoupling test system is successful to get credible test data. It have been mastered that the key techniques for the test system design of internal flow and external flow decoupling.</span></p>

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