Oscillations of a gas in a closed tube near half the fundamental frequency

1987 ◽  
Vol 183 ◽  
pp. 147-161 ◽  
Author(s):  
R. Althaus ◽  
H. Thomann
Keyword(s):  
Boundary Layer ◽  
Fundamental Frequency ◽  
Atmospheric Pressure ◽  
Nonlinear Effects ◽  
Viscous Effects ◽  
Sinusoidal Motion ◽  
Closed Tube ◽  
Resonant Part ◽  
Theoretical Results ◽  
Good Agreement

The oscillations are driven by the sinusoidal motion of a piston at one end of the tube. Near half the fundamental frequency the first overtone, driven by nonlinear effects, becomes resonant. For small boundary-layer friction the amplitude of this resonant part is comparable with the non-resonant acoustic solution and shocks are formed. Theoretical results are compared with pressure signals measured at the closed end of the tube. The viscous effects are large for air at atmospheric pressure and the nonlinear effects remain small. Experiments with xenon, sulphurhexafluoride (SF6) and Freon RC-318 (C4F8) were therefore conducted and shocks formed as predicted. The comparison of the nonlinear theory by Keller (1975) with the experiments shows very good agreement.

A Boundary-Layer Theory for Transient Viscous Losses in Turbulent Flow

1970 ◽  
Vol 92 (4) ◽  
pp. 865-873 ◽  
Author(s):  
D. J. Wood ◽  
J. E. Funk
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Numerical Solutions ◽  
Transient Flow ◽  
Viscous Effects ◽  
Viscous Losses ◽  
Rapid Flow ◽  
Flow Information ◽  
Layer Velocity ◽  
Good Agreement

A laminar boundary-layer model is proposed to account for viscous losses during the transient turbulent flow of a liquid in a tube. In this model, inviscid slug flow is assumed for the core and all viscous effects are assumed to occur in the boundary layer. The transient boundary-layer velocity distribution is determined as a function of a prescribed variation in core velocity and the associated pressure gradient. Both analytical and numerical solutions are presented. This transient flow information is used to calculate local and integrated energy dissipation rates which are then combined, with one-dimensional energy analyses. The result is a prediction of the decrease in pressure-wave magnitude due to viscous dissipation, and a comparison is made with experimental data for rapid flow extinction. Good agreement between the observed and predicted results is obtained.

Laminar Free Convection From a Downward-Projecting Fin

1968 ◽  
Vol 90 (1) ◽  
pp. 63-70 ◽  
Author(s):  
G. S. H. Lock ◽  
J. C. Gunn
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Prandtl Number ◽  
Experimental Program ◽  
Boundary Layer Problem ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Good Agreement ◽  
Quiescent Fluid

A theoretical analysis of conduction through and free convection from a tapered, downward-projecting fin immersed in an isothermal quiescent fluid is presented. The problem is solved by assuming quasi-one-dimensional heat conduction in the fin and matching the solution to that of the convection system, which is treated as a boundary layer problem. For an infinite Prandtl number, solutions are derived which take the form of a power law temperature distribution along the fin. The effect of this power (n) on heat transfer, drag, and the corresponding boundary layer profiles is discussed. It is shown that n is independent of the fin profile and dependent on a single nondimensional group χ. The theoretical results for infinite Prandtl number are compared with corresponding results derived from previous work using a Prandtl number of unity. The effect of Prandtl number on the determination of n and consequently the fin effectiveness is found to be extremely small. The results of an experimental program are also presented. These consist of temperature profiles and the n — χ relation for different fin geometries and surrounding fluids. Comparison with the theoretical predictions reveals good agreement.

On transition in a separated laminar boundary layer

1966 ◽  
Vol 25 (4) ◽  
pp. 683-704 ◽  
Author(s):  
Peter Freymuth
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Reynolds Numbers ◽  
Flow Parameters ◽  
Hydrodynamic Stability Theory ◽  
Basic Equations ◽  
High Reynolds ◽  
Theoretical Results ◽  
Good Agreement ◽  
Small Disturbances

This paper deals with the growth of small disturbances in a separated laminar boundary layer for high Reynolds numbers as a function of the dimensionless flow parameters. Using a hot-wire technique, the experiments show that spatially growing disturbances are only affected by the Strouhal number. Thus the basic equations of the process become relatively simple. The experiments show good agreement with theoretical results obtained by means of hydrodynamic stability theory for spatially growing disturbances.

Resonant oscillations in closed tubes: the solution of Chester's equation

1976 ◽  
Vol 77 (2) ◽  
pp. 279-304 ◽  
Author(s):  
Jakob Keller
Keyword(s):  
Boundary Layer ◽  
Main Part ◽  
Shock Strength ◽  
Number Of Solutions ◽  
Resonant Frequencies ◽  
Sinusoidal Motion ◽  
Closed Tube ◽  
Arbitrary Strength ◽  
Frictional Effects ◽  
Inviscid Case

A closed tube is considered in which the oscillations of a gas column are driven by the sinusoidal motion of a piston. The case where the frequency of the gas column in the tube lies near one of its resonant frequencies is of special interest. The aim of this paper is to extend the theory of Chester (1964), who has given solutions in the inviscid case and for very small boundary-layer friction, to cases of frictional effects of arbitrary strength. This is done by means of a combination of analytical and numerical methods. Different methods are applied for different strengths of the boundary-layer friction. The cases where the influence of the Stokes boundary layer is either very strong or very weak are not especially difficult to treat. The main part of this paper considers cases of intermediate friction, i.e. when the shock strength has grown rather small owing to the influence of the Stokes boundary layer. To obtain an overall view of the phenomena which occur in the Merent regions, a number of solutions have been calculated.

Identification of Vibration of Cooler Tubes With Tube-to-Baffle Impacts

1998 ◽  
Vol 120 (2) ◽  
pp. 419-425 ◽  
Author(s):  
S. C. N. Wong ◽  
J. K. T. Chan
Keyword(s):  
Piecewise Linear ◽  
Nonlinear Effects ◽  
Site Investigation ◽  
Power Station ◽  
Piecewise Linear System ◽  
System Method ◽  
Spring Type ◽  
Theoretical Results ◽  
Tube Structure ◽  
Good Agreement

A random series of impacts method was introduced for vibration test on tube bundles of coolers. A non-normal Poisson process was employed to establish a model for the method. Experimental analysis of the forcing functions showed good agreement with the model. The method was found to be appropriate for extracting modal parameters of such tube structure. Site investigation on power station coolers proved this method to be convenient and reliable. Tube-to-baffle impactions created nonlinear effects which were shown to be of hard-spring type. A piecewise linear system method was used to handle such situation. The theoretical results were closely correlated with the experimental results.

Investigating the Nonlinear Optical Response of Pepper Oil under Low Power Irradiation with Continuous Wave Visible Laser Beam

2020 ◽  
pp. 131-138
Keyword(s):  
Refractive Index ◽  
Nonlinear Refractive Index ◽  
Nonlinear Optical ◽  
Continuous Wave ◽  
Diffraction Integral ◽  
Visible Laser ◽  
Limiting Property ◽  
Kirchhoff Diffraction Integral ◽  
Theoretical Results ◽  
Good Agreement

The nonlinear optical properties of pepper oil are studied by diffraction ring patterns and Z-scan techniques with continuous wave beam from solid state laser at 473 nm wavelength. The nonlinear refractive index of the sample is calculated by both techniques. The sample show high nonlinear refractive index. Based on Fresnel-Kirchhoff diffraction integral, the far-field intensity distributions of ring patterns have been calculated. It is found that the experimental results are in good agreement with the theoretical results. Also the optical limiting property of pepper oil is reported. The results obtained in this study prove that the pepper oil has applications in nonlinear optical devices.

Studies of local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) crystals

2021 ◽  
Vol 76 (4) ◽  
pp. 299-304
Author(s):  
Fu Chen ◽  
Jian-Rong Yang ◽  
Zi-Fa Zhou
Keyword(s):  
Crystal Field ◽  
Elongation Ratio ◽  
Paramagnetic Resonance ◽  
Local Structures ◽  
Epr Parameters ◽  
Structure Constants ◽  
Crystal Field Parameters ◽  
Electron Paramagnetic ◽  
Theoretical Results ◽  
Good Agreement

Abstract The electron paramagnetic resonance (EPR) parameters (g factor g i , and hyperfine structure constants A i , with i = x, y, z) and local structures for Cu2+ centers in M2Zn(SO4)2·6H2O (M = NH4 and Rb) are theoretically investigated using the high order perturbation formulas of these EPR parameters for a 3d 9 ion under orthorhombically elongated octahedra. In the calculations, contribution to these EPR parameters due to the admixture of d-orbitals in the ground state wave function of the Cu2+ ion are taken into account based on the cluster approach, and the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the studied EPR parameters with the local structures of the Cu2+ centers. Based on the calculations, the Cu–H2O bonds are found to suffer the axial elongation ratio δ of about 3 and 2.9% along the z-axis, meanwhile, the planar bond lengths may experience variation ratio τ (≈3.8 and 1%) along x- and y-axis for Cu2+ center in (NH4)2Zn(SO4)2·6H2O and Rb2Zn(SO4)2·6H2O, respectively. The theoretical results show good agreement with the observed values.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

Heat Transfer Committee and Turbomachinery Committee Best Paper of 1996 Award: The Path to Predicting Bypass Transition

1997 ◽  
Vol 119 (3) ◽  
pp. 405-411 ◽  
Author(s):  
R. E. Mayle ◽  
A. Schulz
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Energy Equation ◽  
Free Stream ◽  
Bypass Transition ◽  
Turbulence Level ◽  
Free Stream Turbulence ◽  
Energy Profiles ◽  
Computer Codes ◽  
Good Agreement

A theory is presented for calculating the fluctuations in a laminar boundary layer when the free stream is turbulent. The kinetic energy equation for these fluctuations is derived and a new mechanism is revealed for their production. A methodology is presented for solving the equation using standard boundary layer computer codes. Solutions of the equation show that the fluctuations grow at first almost linearly with distance and then more slowly as viscous dissipation becomes important. Comparisons of calculated growth rates and kinetic energy profiles with data show good agreement. In addition, a hypothesis is advanced for the effective forcing frequency and free-stream turbulence level that produce these fluctuations. Finally, a method to calculate the onset of transition is examined and the results compared to data.

Explanation of the Influence of Inflow Air Content on the Lift of Cavitating Hydrofoils

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Eduard Amromin
Keyword(s):  
Experimental Data ◽  
Theoretical Study ◽  
Lift Coefficient ◽  
Cavity Surface ◽  
Air Bubbles ◽  
Incoming Flow ◽  
Fluid Density ◽  
Air Content ◽  
Theoretical Results ◽  
Good Agreement

According to several known experiments, an increase of the incoming flow air content can increase the hydrofoil lift coefficient. The presented theoretical study shows that such increase is associated with the decrease of the fluid density at the cavity surface. This decrease is caused by entrainment of air bubbles to the cavity from the surrounding flow. The theoretical results based on such explanation are in a good agreement with the earlier published experimental data for NACA0015.

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