A Study of Boundary-Layer Characteristics of Turbomachine Blade Rows and Their Relation to Over-All Blade Loss

1960 ◽  
Vol 82 (3) ◽  
pp. 588-592 ◽  
Author(s):  
Warner L. Stewart ◽  
Warren J. Whitney ◽  
Robert Y. Wong
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Surface Diffusion ◽  
Boundary Layer Thickness ◽  
Blade Surface ◽  
Loss Analysis ◽  
Blade Row ◽  
Momentum Boundary Layer ◽  
Turbomachine Blade ◽  
Blade Loss

This paper presents the results of a number of investigations concerned with the boundary-layer characteristics of turbomachine blade rows and their relation to the over-all blade loss. It is demonstrated how the over-all blade loss can be obtained from the momentum boundary-layer thickness. The momentum boundary-layer thickness is in turn shown to be correlated by flow Reynolds number and total blade surface diffusion. By assuming Zweifel’s form of blade-loading diagram the total blade surface diffusion parameter can be determined as a function of blade solidity and reaction across the blade row. Thus, this type of loss analysis enables an approximate predetermination of the over-all blade row loss as derived from fundamental boundary-layer concepts. In addition, it shows the effect on over-all blade loss of varying such design features as solidity and reaction.

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.

Effects of temperature-dependent viscosity and thermal conductivity on mixed convection flow along a magnetized vertical surface

2016 ◽  
Vol 26 (5) ◽  
pp. 1580-1592 ◽  
Author(s):  
Ashraf Muhammad ◽  
Ali J Chamkha ◽  
S Iqbal ◽  
Masud Ahmad
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Content Type ◽  
Variation Parameter ◽  
Momentum Boundary Layer

Purpose – The purpose of this paper is to report a numerical solution for the problem of steady, two dimensional boundary layer buoyant flow on a vertical magnetized surface, when both the viscosity and thermal conductivity are assumed to be temperature-dependent. In this case, the motion is governed by a coupled set of three nonlinear partial differential equations, which are solved numerically by using the finite difference method (FDM) by introducing the primitive variable formulation. Calculations of the coupled equations are performed to investigate the effects of the different governing parameters on the profiles of velocity, temperature and the transverse component of magnetic field. The effects of the thermal conductivity variation parameter, viscosity variation parameter, magnetic Prandtl number Pmr, magnetic force parameter S, mixed convection parameter Ri and the Prandtl number Pr on the flow structure and heat transfer characteristics are also examined. Design/methodology/approach – FDM. Findings – It is noted that when the Prandtl number Pr is sufficiently large, i.e. Pr=100, the buoyancy force that driven the fluid motion is decreased that decrease the momentum boundary layer and there is no change in thermal boundary layer is noticed. It is also noted that due to slow motion of the fluid the magnetic current generates which increase the magnetic boundary layer thickness at the surface. It is observed that the momentum boundary layer thickness is increased, thermal and magnetic field boundary layers are decreased with the increase of thermal conductivity variation parameter =100. The maximum boundary layer thickness is increased for =100 and there is no change seen in the case of thermal boundary layer thickness but magnetic field boundary layer is deceased. The momentum boundary layer thickness shoot quickly for =40 but is very smooth for =50.There is no change is seen for the case of thermal boundary layer and very clear decay for =40 is noted. Originality/value – This work is original research work.

scholarly journals The sensitivity of turbine cascade endwall loss to inlet boundary layer thickness

2019 ◽  
Vol 3 ◽  
pp. OEYMDE ◽  
Author(s):  
John Coull ◽  
Christopher Clark ◽  
Raul Vazquez
Keyword(s):  
Boundary Layer ◽  
Secondary Flow ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Flow Theory ◽  
Sensitivity Assessment ◽  
Blade Row ◽  
Turbine Cascades ◽  
Inlet Conditions ◽  
Is Design

The development of hub and casing boundary layers through a turbomachine is difficult to predict, giving rise to uncertainty in the boundary conditions experienced by each blade row. Previous studies in turbine cascades disagree on the sensitivity of endwall loss to such inlet conditions. This paper explores the problem computationally, by examining a large number of turbine cascades and varying the inlet boundary layer thickness. It is demonstrated that the sensitivity of endwall loss to inlet conditions is design dependent, and determined by the component of endwall loss associated with the secondary flow. This Secondary-Flow-Induced loss is characterised by a vorticity factor based on classical secondary flow theory. Designs that produce high levels of secondary vorticity tend to generate more loss and are more sensitive to inlet conditions. This sensitivity is largely driven by the dissipation of Secondary Kinetic Energy (SKE): thickening the inlet boundary layer causes the secondary vorticity at the cascade exit to be more dispersed within the passage, resulting in larger secondary flow structures with higher SKE. The effects are captured using a simple streamfunction model based on classical secondary flow theory, which has potential for preliminary design and sensitivity assessment.

EFFECTS OF BOUNDARY-LAYER THICKNESS ON UNSTEADY FLOW CHARACTERISTICS INSIDE OPEN CAVITIES AT SUBSONIC AND TRANSONIC SPEEDS

2012 ◽  
Vol 19 ◽  
pp. 206-213
Author(s):  
DANG-GUO YANG ◽  
JIAN-QIANG LI ◽  
ZHAO-LIN FAN ◽  
XIN-FU LUO
Keyword(s):  
Boundary Layer ◽  
Unsteady Flow ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Sound Pressure ◽  
Flow Characteristics ◽  
Open Cavity ◽  
Aerodynamic Noise ◽  
Sustained Oscillation ◽  
Cavity Depth

An experimental study was conducted in a 0.6m by 0.6m wind-tunnel to analyze effects of boundary-layer thickness on unsteady flow characteristics inside a rectangular open cavity at subsonic and transonic speeds. The sound pressure level (SPL) distributions at the centerline of the cavity floor and Sound pressure frequency spectrum (SPFS) characteristics on some measurement positions presented herein was obtained with cavity length-to-depth ratio (L/D) of 8 over Mach numbers (Ma) of 0.6 and 1.2 at a Reynolds numbers (Re) of 1.23 × 107 and 2.02 × 107 per meter under different boundary-layer thickness to cavity-depth ratios (δ/D). The experimental angle of attack, yawing and rolling angles were 0°. The results indicate that decrease in δ/D leads to severe flow separation and unsteady pressure fluctuation, which induces increase in SPL at same measurement points inside the cavity at Ma of 0.6. At Ma of 1.2, decrease in δ/D results in enhancing compressible waves. Generally, decrease in δ/D induces more flow self-sustained oscillation frequencies. It also makes severer aerodynamic noise inside the open cavity.

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Magnetohydrodynamics Williamson Fluid Comprising Gyrotactic Microorganisms Flows Through a Permeable Stretching Layer with Variable Fluid Properties

2020 ◽  
Vol 9 (4) ◽  
pp. 375-387
Author(s):  
Amit Parmar ◽  
Rakesh Choudhary ◽  
Krishna Agarwal
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Schmidt Number ◽  
Gyrotactic Microorganisms ◽  
Williamson Fluid ◽  
Non Linear ◽  
Fluid Properties ◽  
Variable Prandtl Number

The present study shows the impacts of Williamson fluid with magnetohydrodynamics flow containing gyrotactic microorganisms under the variable fluid property past permeable stretching sheet. Variable Prandtl number, mass Schmidt number, and gyrotactic microorganisms Schmidt number were all considered. The momentum, energy, mass, and microorganism equations’ governing PDEs are converted into nonlinear coupled ODEs and numerically solved with the bvp4c solver using suitable transformations. The main outcome of this study is that Williamson fluid parameter constantly decreases in velocity profile, however reverse effects can be shown in temperature profile. Also, M parameter and Kp parameter enhance the heat transfer rate, concentration rate and microorganisms boundary layer thickness but declines in momentum boundary layer thickness and velocity profile. The aim of this research is to see how velocity slide, temperature jump, concentration slip, and microorganism slip affect MHD Williamson fluid flow with gyrotactic microorganisms over a leaky surface embedded in spongy medium, with non-linear radiation and non-linear chemical reaction.

Freestream Flow Effects on Film Effectiveness and Heat Transfer Coefficient Augmentation for Compound Angle Shaped Holes

2017 ◽  
Author(s):  
Joshua B. Anderson ◽  
John W. McClintic ◽  
David G. Bogard ◽  
Thomas E. Dyson ◽  
Zachary Webster
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Layer Thickness ◽  
Film Cooling ◽  
Gas Turbines ◽  
Boundary Layer Thickness ◽  
Adiabatic Effectiveness ◽  
Compound Angle

The use of compound-angled shaped film cooling holes in gas turbines provides a method for cooling regions of extreme curvature on turbine blades or vanes. These configurations have received surprisingly little attention in the film cooling literature. In this study, a row of laid-back fanshaped holes based on an open-literature design, were oriented at a 45-degree compound angle to the approaching freestream flow. In this study, the influence of the approach flow boundary layer thickness and character were experimentally investigated. A trip wire and turbulence generator were used to vary the boundary layer thickness and freestream conditions from a thin laminar boundary layer flow to a fully turbulent boundary layer and freestream at the hole breakout location. Steady-state adiabatic effectiveness and heat transfer coefficient augmentation were measured using high-resolution IR thermography, which allowed the use of an elevated density ratio of DR = 1.20. The results show adiabatic effectiveness was generally lower than for axially-oriented holes of the same geometry, and that boundary layer thickness was an important parameter in predicting effectiveness of the holes. Heat transfer coefficient augmentation was highly dependent on the freestream turbulence levels as well as boundary layer thickness, and significant spatial variations were observed.

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