pRTA (Probe Recovery Temperature Anemometry)

Volume 1 ◽

10.1115/ht-fed2004-56806 ◽

2004 ◽

Cited By ~ 1

Author(s):

Masahiro Ishibashi

Keyword(s):

Prandtl Number ◽

Flow Velocity ◽

Contact Point ◽

Recovery Factor ◽

Angle Of Incidence ◽

Square Root ◽

Critical Nozzle ◽

Axis Of Symmetry ◽

Thermocouple Wire ◽

Recovery Temperature

It is shown that the recovery temperature measured by a thin thermocouple wire inserted in airflow does not depend on the angle of incidence of the flow onto the wire and agrees very well with the theoretical value assuming the recovery factor of the square root of the Prandtl number. This fact allows RTA (Recovery Temperature Anemometry) employing a sensor of various structures; pRTA (probe RTA) is one of the examples where the thermocouple wire is bent at its contact point forming the probe apex. The paper demonstrates that pRTA measures the same flow velocity distributions in a critical nozzle as those by sRTA (streamwise RTA) where a thermocouple wire is settled parallel to the axis of symmetry of the nozzle.

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Compressibility Effects on the Extended Crocco Relation and the Thermal Recovery Factor in Laminar Boundary Layer Flow

Journal of Fluids Engineering ◽

10.1115/1.1637626 ◽

2004 ◽

Vol 126 (1) ◽

pp. 32-41 ◽

Cited By ~ 8

Author(s):

B. W. van Oudheusden

Keyword(s):

Boundary Layer ◽

Prandtl Number ◽

Pressure Gradient ◽

Boundary Layer Flow ◽

Numerical Solutions ◽

Thermal Recovery ◽

Recovery Factor ◽

Perturbation Approach ◽

Layer Flow ◽

Compressibility Effects

The relation between velocity and enthalpy in steady boundary layer flow is known as the Crocco relation. It describes that for an adiabatic wall the total enthalpy remains constant throughout the boundary layer, when the Prandtl number (Pr) is one, irrespective of pressure gradient and compressibility. A generalization of the Crocco relation for Pr near one is obtained from a perturbation approach. In the case of constant-property flow an analytic expression is found, representing a first-order extension of the standard Crocco relation and confirming the asymptotic validity of the square-root dependence of the recovery factor on Prandtl number. The particular subject of the present study is the effect of compressibility on the extended Crocco relation and, hence, on the thermal recovery in laminar flows. A perturbation analysis for constant Pr reveals two additional mechanisms of compressibility effects in the extended Crocco relation, which are related to the viscosity law and to the pressure gradient. Numerical solutions for (quasi-)self-similar as well as non-similar boundary layers are presented to evaluate these effects quantitatively.

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Initial Stage of Natural Convection Over a Hot Aerosol Sphere

Journal of Fluids Engineering ◽

10.1115/1.2734195 ◽

2006 ◽

Vol 129 (6) ◽

pp. 695-701

Author(s):

Elaad Mograbi ◽

Ezra Bar-Ziv

Keyword(s):

Prandtl Number ◽

Linear Process ◽

Navier Stokes ◽

Transient Temperature ◽

Square Root ◽

Analytical Treatment ◽

Initial Development ◽

Initial Flow ◽

Linear Solution ◽

Initial Stage

Background: Analytical study is presented on the transient problem of buoyancy-induced motion due to the presence of a hot aerosol sphere in unbounded quiescent fluid. Method of Approach: Because the initial flow field is identically zero, the initial stage of the process is governed by viscous and buoyancy forces alone where the convective inertial terms in the momentum and energy balances are negligible, i.e., the initial development of the field is a linear process. The previous statement is examined by analyzing the scales of the various terms in the Navier-Stokes and energy equations. This scale analysis gives qualitative limitations on the validity of the linear approximation. A formal integral solution is obtained for arbitrary Prandtl number and for transient temperature field. Results: We consider, in detail, the idealized case of vanishing Prandtl number for which the thermal field is developed much faster than momentum. In this case, analytical treatment is feasible and explicit expressions for the field variables and the drag acting on the particle are derived. Detailed quantitative analysis of the spatial and temporal validity of the solution is also presented. Conclusions: The linear solution is valid throughout space for t<10 diffusion times. For t>10, an island in space appears in which inertial effects become dominant. The transient process is characterized by two different time scales: for short times, the development of the field is linear, while for small distances from the sphere and finite times, it is proportional to the square root of time. The resultant drag force acting on the sphere is proportional to the square root of time throughout the process.

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On “how to start a fire”, or transverse forced-convection, hyperbaric laser chemical vapor deposition of fibers and textiles

Textile Research Journal ◽

10.1177/0040517514527373 ◽

2014 ◽

Vol 84 (18) ◽

pp. 1976-1986

Author(s):

James L Maxwell ◽

Nicholas Webb ◽

Douglas Bradshaw ◽

Marcie R Black ◽

Karlene Maskaly ◽

...

Keyword(s):

Chemical Vapor Deposition ◽

Critical Temperature ◽

Flow Velocity ◽

Flow Rate ◽

Growth Rates ◽

Vapor Deposition ◽

Chemical Vapor ◽

Forced Flow ◽

Square Root ◽

Laser Chemical Vapor Deposition

This work explores the transverse forced flow of precursor gases during hyperbaric pressure laser chemical vapor deposition (HP-LCVD). Axial and mass growth rates of carbon fibers are measured experimentally, and a numerical model is developed that provides fiber growth rates in both the mass-transport-limited (MTL) and kinetically limited (KL) regimes. It is found that the fiber’s transport-limited rate increases as the square root of the flow velocity, while simultaneously, the temperature drops with the inverse square root of the flow velocity. Growth is enhanced by forced flow so long as the reaction zone remains within the MTL regime; upon reaching a critical temperature and flow rate, however, fibers enter the KL regime, and the growth rate declines with rising flow rate. Molecular properties of the precursors employed and gas concentrations ultimately determine the range of the MTL and the locations of the critical temperature and flow rate. The growth rates of fibers can indeed be enhanced by transverse forced convection—to at least three times the zero-flow steady-state rate, provided an MTL regime exists. Complex three-dimensional structures may be grown from these fibers in a freeform manner, and the more rapidly such microstructures can be fabricated, the more practical HP-LCVD becomes for industrial use, including the fabrication of novel textiles.

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Quasi-Non Intrusive Measurement of the Transonic Flow Field in an Axi-Symmetric Critical Nozzle Based on Recovery Temperature Measurement Using a Thin Thermocouple

Transactions of the Society of Instrument and Control Engineers ◽

10.9746/sicetr1965.37.609 ◽

2001 ◽

Vol 37 (7) ◽

pp. 609-617

Author(s):

Masahiro ISHIBASHI ◽

Masaki TAKAMOTO

Keyword(s):

Flow Field ◽

Temperature Measurement ◽

Transonic Flow ◽

Critical Nozzle ◽

Recovery Temperature

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Relationship between the recovery factor and the viscous dissipation in a confined, impinging, circular jet of high-Prandtl number liquid

International Journal of Heat and Fluid Flow ◽

10.1016/s0142-727x(97)00049-0 ◽

1997 ◽

Vol 18 (6) ◽

pp. 585-590 ◽

Cited By ~ 12

Author(s):

De-Yu Li ◽

Zeng-Yuan Guo ◽

Chong-Fang Ma

Keyword(s):

Prandtl Number ◽

Viscous Dissipation ◽

Recovery Factor ◽

High Prandtl Number

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Influence of Margin Geometry on Failure of Brittle Coatings on Compliant Substrates: Relevance to Failure of Dental Crowns

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.334-335.573 ◽

2007 ◽

Vol 334-335 ◽

pp. 573-576 ◽

Cited By ~ 1

Author(s):

Tarek Qasim ◽

Anne Whitton ◽

Chris Ford ◽

Mark Bush ◽

Xiao Zhi Hu

Keyword(s):

Crack Initiation ◽

Contact Area ◽

Contact Point ◽

Layer Model ◽

Indentation Force ◽

Compliant Substrates ◽

Dental Crowns ◽

Layer Structures ◽

Large Contact Area ◽

Axis Of Symmetry

This paper explores the so-called “margin failures” observed in loaded curved bi-layer structures. Hemispherical bi-layer model test specimens consisting of glass shells with varying margin geometry filled with epoxy resin, simulating brittle crowns on tooth dentine, are loaded with compliant indenters along the (convex) axis of symmetry. Using this unique setup, the influence of margin geometry on margin failure is examined. Nearly all previous studies have utilised hard spherical indenters of various radii, and examined crack initiation and evolution at the contact point. However, the modes of fracture observed in this traditional contact problem, surface cone cracking or flexure-induced radial cracking initiate close to or inside the (small) contact area, and thus not explain the margin failures commonly observed by dentists. Crack growth at the margins distant from the contact zone cannot be generated under indentation using hard spherical indenters. The use of a compliant (soft) indenter distributes the indentation force over a large contact area, generating a compressive zone underneath the contact, and effectively inhibiting the modes of fracture typically observed using hard indenters (radial and cone cracking). Consequently, significant tensile stresses at the support margin become dominant, and the focus shifts to fracture initiating at the support margins. In this study, cylindrical indenters composed of PTFE Teflon, with a modulus several orders of magnitude lower than the indented materials, are used to examine margin fracture in brittle crown like structures. The specific focus is the effect of margin geometry – Chamfered; Round; Shoulder margins are examined, and their influences on crack initiation and damage evolution are reported.

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The recovery factor in a supersonic flow of gas with a low Prandtl number

High Temperature ◽

10.1007/s10740-006-0029-8 ◽

2006 ◽

Vol 44 (2) ◽

pp. 234-242 ◽

Cited By ~ 13

Author(s):

A. I. Leontiev ◽

V. G. Lushchik ◽

A. E. Yakubenko

Keyword(s):

Supersonic Flow ◽

Prandtl Number ◽

Recovery Factor

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A generalized Reynolds analogy for compressible wall-bounded turbulent flows

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.620 ◽

2013 ◽

Vol 739 ◽

pp. 392-420 ◽

Cited By ~ 37

Author(s):

You-Sheng Zhang ◽

Wei-Tao Bi ◽

Fazle Hussain ◽

Zhen-Su She

Keyword(s):

Mach Number ◽

Prandtl Number ◽

Boundary Layers ◽

Turbulent Flows ◽

Wall Temperature ◽

Velocity Fields ◽

Recovery Factor ◽

Mean Velocity ◽

Reynolds Analogy ◽

The Mean

AbstractA generalized Reynolds analogy (GRA) is proposed for compressible wall-bounded turbulent flows (CWTFs) and validated by direct numerical simulations. By introducing a general recovery factor, a similarity between the Reynolds-averaged momentum and energy equations is established for the canonical CWTFs (i.e. pipes, channels, and flat-plate boundary layers that meet the quasi-one-dimensional flow approximation), independent of Prandtl number, wall temperature, Mach number, Reynolds number, and pressure gradient. This similarity and the relationships between temperature and velocity fields constitute the GRA. The GRA relationship between the mean temperature and the mean velocity takes the same quadratic form as Walz’s equation, with the adiabatic recovery factor replaced by the general recovery factor, and extends the validity of the latter to diabatic compressible turbulent boundary layers and channel/pipe flows. It also derives Duan & Martín’s (J. Fluid Mech., vol. 684, 2011, pp. 25–59) empirical relation for flows at different physical conditions (wall temperature, Mach number, enthalpy condition, surface catalysis, etc.). Several key parameters besides the general recovery factor emerge in the GRA. An effective turbulent Prandtl number is shown to be the reason for the parabolic profile of mean temperature versus mean velocity, and it approximates unity in the fully turbulent region. A dimensionless wall temperature, that we call the diabatic parameter, characterizes the wall-temperature effects in diabatic flows. The GRA also extends the analysis to the fluctuation fields. It recovers the modified strong Reynolds analogy proposed by Huang, Coleman & Bradshaw (J. Fluid Mech., vol. 305, 1995, pp. 185–218) and explains the variation of the temperature–velocity correlation coefficient with wall temperature. Thus, the GRA unveils a generalized similarity principle behind the complex nonlinear coupling between the thermal and velocity fields of CWTFs.

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STUDIES ON SEISMIC WAVES: I. REFLECTION AND REFRACTION OF PLANE WAVES

Geophysics ◽

10.1190/1.1437210 ◽

1946 ◽

Vol 11 (1) ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

C. Y. Fu

Keyword(s):

Rayleigh Waves ◽

Seismic Waves ◽

Plane Waves ◽

The Body ◽

Body Waves ◽

Angle Of Incidence ◽

Apparent Velocity ◽

Square Root ◽

Absolute Value ◽

Reflection And Refraction

By taking the apparent velocity along the boundary as the parameter instead of the angle of incidence, the equations for the different wave amplitudes may be put in more symmetrical forms. In this way, it is more convenient to discuss both the body waves and the Rayleigh waves at the same time. A difficulty in the plotting of the square root of the wave intensity against the angles is also discussed. When the reflection or refraction coefficient is not real, the meaning of the intensity, as obtained by squaring the absolute value of the latter quantity, needs clarification.

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