The Effect of Froude Number on Entrainment in Two-Dimensional Line Plumes

1981 ◽  
Vol 103 (3) ◽  
pp. 471-477 ◽  
Author(s):  
W. F. Phillips
Keyword(s):  
Froude Number ◽  
Large Distance ◽  
Universal Constant ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Development Length ◽  
High Discharge ◽  
Entrainment Coefficient ◽  
Theoretical Results

Theoretical results are presented which predict the entrainment coefficient in a forced plume as a function of the local Froude number. The model does not require any external specification of the velocity and temperature profiles. The Froude number for any plume, in a motionless isothermal ambient, approaches a universal constant, at a large distance above the source. However, it is shown here that the development length for the Froude number, in plumes with high discharge Froude number, is of the order of a few hundred times the discharge width.

Part II: Steady aerofoil-spoiler characteristics

1987 ◽  
Vol 91 (908) ◽  
pp. 359-366
Keyword(s):  
Separated Flow ◽  
Experimental Results ◽  
Surface Singularity ◽  
Separation Region ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Singularity Method ◽  
Total Head ◽  
Low Speeds ◽  
Theoretical Results

Summary A surface singularity method has been formulated to predict two-dimensional spoiler characteristics at low speeds. Vorticity singularities are placed on the aerofoil surface, on the spoiler surface, on the upper separation streamline from the spoiler tip and on the lower separation streamline from the aerofoil trailing edge. The separation region is closed downstream by two discrete vortices. The flow inside the separation region is assumed to have uniform total head. The downstream extent of the separated wake is an empirical input. The flows both external and internal to the separated regions are solved. Theoretical results have been obtained for a range of spoiler-aerofoil configurations which compare reasonably with experimental results. The model is deficient in that it predicts a higher compression ahead of the spoiler than obtained in practice. Furthermore, there is a minimum spoiler angle below which a solution is not possible; it is thought that this feature is related to the physical observation that at small spoiler angles, the separated flow from the spoiler reattaches on the aerofoil upper surface ahead of the trailing edge.

An Investigation of the Predicting Capabilities of a Variable Flow Stress Machining Theory

2001 ◽  
Author(s):  
P. Mathew
Keyword(s):  
Flow Stress ◽  
Material Flow ◽  
Three Dimensional ◽  
Experimental Results ◽  
Two Dimensional ◽  
Variable Flow ◽  
Comparative Results ◽  
Intermittent Cutting ◽  
Theoretical Results ◽  
Modelling Approach

Abstract The Oxley Machining Theory, which has been developed over the last 40 years, is presented in this paper. The capability of the model is described with its initial two-dimensional machining approach followed by the extension to the generalised model for three-dimensional machining. The theoretical results from the model are compared with the experimental results to determine the model capability. A brief description of the work associated with the effect of strain hardening at the interface is presented and comparative results are shown. A further extension of the model to intermittent cutting process of reaming is also presented and a comparison with the experimental results indicates the model developed is quite capable of predicting cutting forces for reaming. In explaining the results obtain, the assumptions made are explained and the inputs required. The limitations of the modelling approach are presented. It is pointed out that the Oxley model is a versatile model as long as proper description of the material flow stress properties is presented.

scholarly journals Double Hopf Bifurcation in Microbubble Oscillators with Delay Coupling

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jinbin Wang ◽  
Rui Zhang ◽  
Lifenq Ma
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Two Dimensional ◽  
Main Attention ◽  
Dimensional Parameter ◽  
Center Manifold Reduction ◽  
Double Hopf Bifurcation ◽  
Physical Phenomena ◽  
Manifold Reduction ◽  
Theoretical Results

Using center manifold reduction methodswe investigate the double Hopf bifurcation in the dynamics of microbubble with delay couplingwith main attention focused on nonresonant double Hopf bifurcation. We obtain the normal form of the system in the vicinity of the double Hopf point and classify the bifurcations in a two-dimensional parameter space near the critical point. Some numerical simulations support the applicability of the theoretical results. In particularwe give the explanation for some physical phenomena of the system using the obtained mathematical results.

A free-streamline solution for stratified flow into a line sink

1965 ◽  
Vol 21 (3) ◽  
pp. 535-543 ◽  
Author(s):  
Timothy W. Kao
Keyword(s):  
Froude Number ◽  
Inverse Method ◽  
Separated Flows ◽  
Two Dimensional ◽  
Mathematical Solution ◽  
Velocity Discontinuity ◽  
Natural Processes ◽  
A Value ◽  
Line Sink ◽  
Two Dimensional Flow

An analysis is made of the two-dimensional flow under gravity of an inviscid non-diffusive stratified fluid into a line sink, involving a velocity discontinuity in the flow field. The fluid above the discontinuity is stagnant and hence is not drawn into the sink. At sufficiently low values of the modified Froude number, this is the only physically possible mode of flow, and is the cause of flow separation in many industrial and natural processes. A proper mathematical solution for flows with a stagnant zone has so far been lacking. This paper presents such a solution, after posing the problem as one involving a free-streamline, which is the line of velocity discontinuity. The solution to be given here is obtained by an inverse method. It is also found herein that the modified Froude number has a value of 0·345 for all separated flows of the kind in question.

Bioheat Transfer in a Branching Countercurrent Network During Hyperthermia

1989 ◽  
Vol 111 (4) ◽  
pp. 263-270 ◽  
Author(s):  
C. K. Charny ◽  
R. L. Levin
Keyword(s):  
Muscle Blood Flow ◽  
Equation Model ◽  
Bioheat Transfer ◽  
Tissue Temperature ◽  
Transfer Model ◽  
Temperature Profiles ◽  
The Mean ◽  
Pennes Model ◽  
Theoretical Results ◽  
Two Parameter

A bioheat transfer model which computes the spatial variations in the arteriole, venule, and muscle temperatures in a human extremity under both resting and hyperthermic conditions is presented. This model uses the two-parameter model first proposed by Baish et al. [2] to account for the heat exchange between tissue and the paired arterioles and venules that comprise the microcirculation. Thermoregulation of the muscle blood flow during hyperthermia is also incorporated into the model. Results show that even when the paired arteriole and venule are assumed to have equal radii, the mean temperature under both steady and transient conditions is not equal to the mean of the arteriole and venule blood temperatures. Tissue temperature profiles during hyperthermia computed with the three-equation model presented in this study are similar in shape and magnitude to those predicted by the traditional one-equation Pennes bioheat transfer model [1]. This is due primarily to the influence of thermoregulatory mechanism in the heated muscle. The unexpected agreement is significant given the inherent relative simplicity of the traditional Pennes model. An “experimental” thermal conductivity is presented to relate the theoretical results to experimental procedures that are widely used to estimate the enhancement of conductivity by perfusion.

Theoretical Modelling of Free Falling Wedges Entering the Water Surface: Part I — Wedge Motions

2013 ◽  
Author(s):  
Jingbo Wang
Keyword(s):  
Numerical Simulations ◽  
Froude Number ◽  
Penetration Depth ◽  
Water Surface ◽  
Theoretical Models ◽  
Theoretical Modelling ◽  
Rapid Variation ◽  
Drag Coefficients ◽  
Free Falling ◽  
Theoretical Results

As the first of two companion papers, theoretical models are proposed to describe the motions of free falling wedges vertically entering the water surface at Froude numbers: 1 ≤ Fn < 9 (Here, the Froude number is defined as Fn=V0/gc0). The time evolutions of the penetration depth, the velocity and the acceleration are analyzed and expressed explicitly The maximum and average accelerations are predicted. The drag (slamming) coefficients are extensively studied. It is found that for the light wedge the transient drag coefficients have slow variation in the first half stage and rapid variation in the last half stage, and for the heavy wedge the transient drag coefficients vary slowly during the whole stage and can be treated as constant. The theoretical results are compared with numerical simulations by nonlinear BEM (Wang & Faltinsen (2010, 2013)), and good agreements are obtained.

scholarly journals Restoration of superconductivity in high magnetic fields in UTe2

2020 ◽  
Vol 34 (32) ◽  
pp. 2030007
Author(s):  
Andrei G. Lebed
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Superconducting State ◽  
Critical Magnetic Field ◽  
High Magnetic Fields ◽  
Two Dimensional ◽  
Upper Critical Magnetic Field ◽  
Reentrant Superconductivity ◽  
Theoretical Results ◽  
General Method

It was theoretically predicted more than 20 years ago [A. G. Lebed and K. Yamaji, Phys. Rev. Lett. 80, 2697 (1998)], that a triplet quasi-two-dimensional (Q2D) superconductor could restore its superconducting state in parallel magnetic fields, which are higher than its upper critical magnetic field, [Formula: see text]. It is very likely that, recently, such phenomenon has been experimentally discovered in the Q2D superconductor UTe2 by Nicholas Butch, Sheng Ran, and their colleagues and has been confirmed by Japanese–French team. We review our previous theoretical results using such a general method that it describes the reentrant superconductivity in the abovementioned compound and will hopefully describes the similar phenomena, which can be discovered in other Q2D superconductors.

Simultaneously enhanced discharge energy density and efficiency in nanocomposite film capacitors utilizing two-dimensional NaNbO3@Al2O3 platelets

Nanoscale ◽  
2019 ◽  
Vol 11 (21) ◽  
pp. 10546-10554 ◽  
Author(s):  
Zhongbin Pan ◽  
Qiling Ding ◽  
Lingmin Yao ◽  
Shuangwu Huang ◽  
Shuang Xing ◽  
...  
Keyword(s):  
Energy Density ◽  
Nanocomposite Film ◽  
Nanocomposite Films ◽  
Two Dimensional ◽  
Discharge Energy ◽  
High Discharge ◽  
Discharge Efficiency ◽  
Discharge Energy Density

Nanocomposite films loaded with small 2D NaNbO3@Al2O3 platelets exhibit a high discharge energy density of 14.59 J cm−3 and simultaneously an outstanding discharge efficiency of 70.1%.

scholarly journals On the Thermal Regime of an Arctic Valley Glacier: A Study of White Glacier, Axel Heiberg Island, N.W.T., Canada

1987 ◽  
Vol 33 (114) ◽  
pp. 200-211 ◽  
Author(s):  
Heinz Blatter
Keyword(s):  
Climatic Conditions ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Temperature Minimum ◽  
Climatic Warming ◽  
Simple Scheme ◽  
Glacier Surface ◽  
Temperature Distributions ◽  
Valley Glacier ◽  
Simple Numerical Model

AbstractFrom 1974 to 1981, a total of 32 bore holes was drilled on White Glacier and vertical ice-temperature profiles measured. The data obtained allowed the construction of three longitudinal and four transverse profiles of the two-dimensional temperature distributions. Thus, an extensive layer of temperate or near-temperate ice was discovered close to the bedrock in the lowest part of the glacier tongue. It was also found that the temperature distribution cannot be in a steady state, since there is a temperature minimum 100–150 m below the glacier surface in the accumulation area. A simple numerical model calculation shows that this minimum can be mostly explained by the general climatic warming since 1880. The 10 m temperatures show diffuse relations to climatic conditions and balance zones. A simple scheme for extrapolating “surface temperatures” is discussed.

Design and control of a two-dimensional telerobotic system with a haptic interface

2003 ◽  
Vol 217 (3) ◽  
pp. 169-185
Author(s):  
M-G Her ◽  
M Karkoub ◽  
K-S Hsu
Keyword(s):  
Haptic Interface ◽  
Two Dimensional ◽  
Direct Drive ◽  
Closed Loop System ◽  
Human Arm ◽  
Control Scheme ◽  
Reaction Forces ◽  
And Control ◽  
Theoretical Results ◽  
Good Agreement

A model for a ‘master-slave’ two-dimensional telerobotic dynamic system with a haptic interface device is derived. The telerobotic system consists of a ‘master’ robot, which is a direct-drive robot operated by a human arm, and a ‘slave’ robot, which is an x-y type pallet located at a remote site. When the active handle of the master is moved along an arbitrary trajectory, the remote slave duplicates the motion in a constrained or unconstrained environment. The behaviour of the environment is felt by the operator through the active handle of the master. This is achieved by feeding back the disturbance and reaction forces from the environment and the loads to the active handle. Consequently, the operator gets a feel of the task being performed without being physically at the location of the task. A control scheme is devised for the telerobotic system to establish smooth communication between the master and slave robots. This control scheme integrates the dynamics of the human arm, actuators and the environment in the closed-loop system. It was shown that the experimental and the theoretical results are in good agreement and that the design controller is robust to constrained/unconstrained environments.

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