Discussion: “A Family of Hodograph Models for the Cross Flow Velocity Component of Three-Dimensional Turbulent Boundary Layers” (Shanebrook, J. R., and Hatch, D. E., 1972, ASME J. Basic Eng., 94, pp. 321–329)

1972 ◽  
Vol 94 (2) ◽  
pp. 331-331
Author(s):  
R. G. Bradley
Keyword(s):  
Flow Velocity ◽  
Boundary Layers ◽  
Velocity Component ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Cross Flow Velocity ◽  
The Cross

A Family of Hodograph Models for the Cross Flow Velocity Component of Three-Dimensional Turbulent Boundary Layers

1972 ◽  
Vol 94 (2) ◽  
pp. 321-329 ◽  
Author(s):  
J. R. Shanebrook ◽  
D. E. Hatch
Keyword(s):  
Flow Velocity ◽  
Boundary Layers ◽  
Velocity Component ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Flow Profiles ◽  
Rectangular Channels ◽  
Cross Flow Velocity ◽  
The Cross

A family of hodograph models for the cross flow velocity component of three-dimensional, turbulent boundary layers is presented. The principal advantage of this family is its flexibility which allows a wide variety of possible shapes for the hodograph. An integral method based on this family is developed and applied to data obtained in curved, rectangular channels. For the cases treated, the method gives acceptable results for cross flow profiles with and without flow reversal. Suggestions for refining the method are given.

Cross Flows in Bounded Three-Dimensional Turbulent Boundary Layers

1973 ◽  
Vol 15 (4) ◽  
pp. 274-284 ◽  
Author(s):  
J. H. Horlock
Keyword(s):  
Experimental Data ◽  
Flow Velocity ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Cross Flow Velocity ◽  
Flow Through ◽  
Bounding Surfaces ◽  
Analytical Expressions

A study is made of the flow normal to the mainstream direction (cross flow) that takes place in three-dimensional ‘bounded’ turbulent boundary layers near a wall, i.e. boundary layers restricted by the presence of bounding surfaces normal to that wall. Such boundary layers are present in the flow through rows of blades in a turbo machine. Analytical expressions for the cross-flow velocity profiles are derived for these ‘bounded’ boundary layers and are compared with experimental data.

An Approach to Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Author(s):  
A. D. Carmichael
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Basic Assumption ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Factor H ◽  
Simple Method ◽  
The Cross

A relatively simple method for predicting some of the characteristics of three-dimensional turbulent boundary layers is presented. The basic assumption of the method is that the cross-flow is small. An empirical correlation of a basic shape factor of the cross-flow boundary layer against the streamwise shape factor H is provided. This correlation, together with data for the streamwise boundary layer, is used to predict the cross flow. The solution is very sensitive to the accuracy of the streamwise boundary-layer data which is predicted by conventional two-dimensional methods.

Mathematical and Physical Simulation of the Cross-Flow Velocity Pulsation Effect on the Flame Structure during the Diffusion Mode of Methane Combustion

2020 ◽  
pp. 65-84
Author(s):  
K.Yu. Arefyev ◽  
K.V. Fedotova ◽  
A.I. Krikunova ◽  
V.A. Panov
Keyword(s):  
Mathematical Model ◽  
Flow Velocity ◽  
Stokes Equations ◽  
Flame Structure ◽  
Cross Flow ◽  
Methane Combustion ◽  
Velocity Pulsation ◽  
Diffusion Mode ◽  
Cross Flow Velocity ◽  
The Cross

The paper presents the results of calculation and experimental studies of the diffusion combustion of methane in the air cross-flow. We developed a mathematical model for describing a diffusion air-methane flame, the model being based on solving a system of averaged Navier --- Stokes equations in an unsteady setting. To calculate the combustion processes, we used the flamelet models and eddy dissipation concept (EDC) model. The mathematical model was supplemented by a detailed kinetic mechanism consisting of 325 elementary reactions involving 53 substances. Furthermore, we carried out calculations and comparative analysis of the flame characteristics using various turbulence models: k − ε, k − ω SST and Transition SST. The study introduces a diagram of the experimental setup for physical modeling of methane combustion in the air cross-flow, and presents the results of the calculation and experimental study of the cross-flow velocity pulsation effect on the flame structure, as well as the efficiency of methane combustion in the diffusion mode. We obtained data on temperature and concentration fields at pulsation frequencies of 0--100 Hz. Findings of research show that for the case under consideration, stable combustion occurs at pulsation frequencies of 0--90 Hz. The maximum observed flame lift-off is 3.2 times the diameter of the burner nozzle

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.

Three-dimensional laminar boundary layers in crosswise pressure gradients

1974 ◽  
Vol 66 (4) ◽  
pp. 641-655 ◽  
Author(s):  
J. H. Horlock ◽  
A. K. Lewkowicz ◽  
J. Wordsworth
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Laminar Boundary Layers ◽  
The Cross

Two attempts were made to develop a three-dimensional laminar boundary layer in the flow over a flat plate in a curved duct, establishing a negligible streamwise pressure gradient and, at the same time, an appreciable crosswise pressure gradient.A first series of measurements was undertaken keeping the free-stream velocity at about 30 ft/s; the boundary layer was expected to be laminar, but appears to have been transitional. As was to be expected, the cross-flow in the boundary layer decreased gradually as the flow became progressively more turbulent.In a second experiment, at a lower free-stream velocity of approximately 10 ft/s, the boundary layer was laminar. Its streamwise profile resembled closely the Blasius form, but the cross-flow near the edge of the boundary layer appears to have exceeded that predicted theoretically. However, there was a substantial experimental scatter in the measurements of the yaw angle, which in laminar boundary layers is difficult to obtain accurately.

Critical Velocity of a Non-Linearly Supported Multi-Span Tube Bundle

2006 ◽  
Author(s):  
M. K. Au-Yang ◽  
J. A. Burgess
Keyword(s):  
Flow Velocity ◽  
Critical Velocity ◽  
Tube Bundle ◽  
Normal Modes ◽  
Cross Flow ◽  
Time History ◽  
Tube Bundles ◽  
Cross Flow Velocity ◽  
The Cross ◽  
The Time Domain

The phenomenon of fluid-elastic instability and the velocity at which a heat exchanger tube bundle becomes unstable, known as the critical velocity, was discovered and empirically determined based upon single-span, linearly supported tube bundles. In this idealized configuration, the normal modes are well separated in frequency with negligible cross-modal contribution to the critical velocity. As a result, a critical velocity can be defined and determined for each mode. In an industrial heat exchanger or steam generator, not only do the tube bundles have multiple spans, they are also supported in over-sized holes. The normal modes of a multi-span tube bundle are closely spaced in frequency, and the non-linear effect of the tube-support plate interaction further promotes cross-modal contribution to the tube responses. The net effect of cross-modal participation in the tube vibration is to delay the instability threshold. Tube bundles in industrial exchangers often have critical velocities far above what were determined in the laboratory based upon single-span, linearly supported tube bundles. In this paper, the authors attempt to solve this non-linear problem in the time domain, using a time history modal superposition method. Time history forcing functions are first obtained by inverse Fourier transform of the power spectral density function used in classical turbulence-induced vibration analyses. The fluid-structure coupling force, which is dependent on the cross-flow velocity, is linearly superimposed onto the turbulence forcing function. The tube responses are then computed by direct integration in the time domain. By gradually increasing the cross-flow velocity, a threshold value is obtained at which the tube response just starts to diverge. The value of the cross-flow velocity at which the tube response starts to diverge is defined as the critical velocity of this non-linearly supported, multi-span tube bundle.

scholarly journals Trajectory of a synthetic jet issuing into high-Reynolds-number turbulent boundary layers

2018 ◽  
Vol 856 ◽  
pp. 531-551 ◽  
Author(s):  
Tim Berk ◽  
Nicholas Hutchins ◽  
Ivan Marusic ◽  
Bharathram Ganapathisubramani
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
High Reynolds Number ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Synthetic Jet ◽  
Actuation Frequency ◽  
The Cross ◽  
High Reynolds

Synthetic jets are zero-net-mass-flux actuators that can be used in a range of flow control applications. For some applications, the scaling of the trajectory of the jet with actuation and cross-flow parameters is important. This scaling is investigated for changes in the friction Reynolds number, changes in the velocity ratio (defined as the ratio between the mean jet blowing velocity and the free-stream velocity) and changes in the actuation frequency of the jet. A distinctive aspect of this study is the high-Reynolds-number turbulent boundary layers (up to $Re_{\unicode[STIX]{x1D70F}}=12\,800$) of the cross-flow. To our knowledge, this is the first study to investigate the effect of the friction Reynolds number of the cross-flow on the trajectory of an (unsteady) jet, as well as the first study to systematically investigate the scaling of the trajectory with actuation frequency. A broad range of parameters is varied (rather than an in-depth investigation of a single parameter) and the results of this study are meant to indicate the relative importance of each parameter rather than the exact influence on the trajectory. Within the range of parameters explored, the critical ones are found to be the velocity ratio as well as a non-dimensional frequency based on the jet actuation frequency, the cross-flow velocity and the jet dimensions. The Reynolds number of the boundary layer is shown to have only a small effect on the trajectory. An expression for the trajectory of the jet is derived from the data, which (in the limit) is consistent with known expressions for the trajectory of a steady jet in a cross-flow.

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