Condensation on Coherent Turbulent Jets: Part II—A Theoretical Study

1989 ◽  
Vol 111 (4) ◽  
pp. 1075-1082 ◽  
Author(s):  
S. Kim ◽  
A. F. Mills
Keyword(s):  
Ad Hoc ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Turbulent Transport ◽  
Turbulent Jets ◽  
Eddy Diffusivity ◽  
Liquid Jets ◽  
Laminar Jets ◽  
Boussinesq Hypothesis ◽  
Order Of Magnitude

Condensation on coherent turbulent liquid jets was investigated theoretically. The governing conservation equations were obtained using an order of magnitude analysis, and were solved numerically using a finite difference method. The Boussinesq hypothesis was invoked to model turbulent transport. Various eddy diffusivity models, of varying degrees of complexity, were evaluated through comparison with experimental data, and shortcomings noted. An ad hoc model, which allows for axial decay of turbulence by viscosity, and radial decay by both surface tension and viscosity, is shown to be in reasonable agreement with experiment. Numerical solutions were also obtained for laminar jets, and are essentially exact; these solutions are used to give some insight into the nature of the jet heat transfer problem.

Prediction of Local and Integral Turbulent Transport Properties for Liquid-Metal Heat Transfer in Equilateral Triangular Rod Arrays

1975 ◽  
Vol 97 (2) ◽  
pp. 238-243 ◽  
Author(s):  
H. Ramm ◽  
K. Johannsen
Keyword(s):  
Heat Transfer ◽  
Liquid Metal ◽  
Transport Properties ◽  
Turbulence Model ◽  
Transfer Problem ◽  
Turbulent Transport ◽  
Three Dimensional ◽  
Theoretical Method ◽  
Eddy Diffusivity ◽  
Thermal Mixing

A theoretical method based on a phenomenological turbulence model has been applied to evaluate turbulent transport properties for liquid-metal heat transfer in bare equilateral triangular rod bundles. Results obtained for local distributions of thermal eddy diffusivity in the various directions are presented in terms of correlations. From a subsequent solution of the three-dimensional heat transfer problem between two characteristic interior subchannels under conditions characteristic for tracer-type mixing experiments, integral thermal mixing coefficients and thermal length scales have been evaluated. Results demonstrate that the basic concept of subchannel analysis treating molecular conduction and turbulent transport independently of each other tends to underestimate intersubchannel transport. The uncertainties which are involved in principal assumptions of the turbulence-model as well as in the available empirical results are discussed in some detail.

The breakup of a turbulent liquid jet in a gaseous atmosphere

1973 ◽  
Vol 60 (4) ◽  
pp. 689-701 ◽  
Author(s):  
Ralph E. Phinney
Keyword(s):  
Turbulent Jets ◽  
Gaseous Atmosphere ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Electrical Method ◽  
Data Support ◽  
Laminar Jets

An electrical method of detecting and measuring the breakup of liquid jets is applied to the turbulent case. New data produced by this means, together with previous data, support the conjecture that the theory and understanding that were developed in connexion with the breakup of laminar jets can be used as a guide for turbulent jets as well.

Submerged jets in short cylindrical flow vessels

1966 ◽  
Vol 25 (2) ◽  
pp. 367-375 ◽  
Author(s):  
K. J. Mcnaughton ◽  
C. G. Sinclair
Keyword(s):  
Turbulent Jets ◽  
Reynolds Numbers ◽  
Uniform Flow ◽  
Geometric Parameters ◽  
Liquid Jets ◽  
Laminar Jets ◽  
Submerged Jets ◽  
Inlet Tube ◽  
Tracer Solution ◽  
Cylindrical Tanks

Liquid-into-liquid jets in short cylindrical vessels have been investigated under conditions of uniform flow by using an aqueous blue tracer solution in conjunction with tránsparent cylindrical tanks. The vessels had diameters D of 3, 6, 12 and 24in., length-to-diameter ratios L/D of 1, 2 and 3 and inlet diameters d between ¼ and 1 in. Reynolds numbers in the inlet tube, Rei, ranged between 100 and 28,000. Four main types of jet were observed: \[ \begin{array}{@{}l@{\qquad}l@{\quad}l@{}} & \hbox{dissipated-laminar jets} & (Re_i < 300\;\hbox{approx}.);\\ & \hbox{fully laminar jets} & (300 < Re_i < 1000\;\hbox{approx}.);\\ & \hbox{semi-turbulent jets} & (1000 < Re_i < 3000\;\hbox{approx}.);\\ \hbox{and} & \hbox{fully turbulent jets} & (Re_i > 3000). \end{array} \]The laminar length a of sub-turbulent jets was investigated and correlated with Rei and the geometric parameters by the equation \[ a/d = 9.97 \times 10^7 Re_i^{-2.46}(D/d)^{-0.48} (L/d)^{0.74}. \]

Assessment of AASHTO Load-Spreading Method for Buried Culverts and Proposed Improvement

2021 ◽  
pp. 036119812110215
Author(s):  
Michael G. Katona
Keyword(s):  
Ad Hoc ◽  
Soil Depth ◽  
Free Field ◽  
Peak Stress ◽  
Element Model ◽  
Surface Load ◽  
Accuracy Evaluation ◽  
Simple Modification ◽  
Homogeneous Half Space ◽  
Order Of Magnitude

AASHTO’s ad hoc method (AAM) for predicting free-field soil stress under a rectangular loading area is a simple and very useful tool for the analysis of buried culverts subject to vehicular wheel loads. AAM assumes the surface load spreads with soil depth into an ever-increasing rectangular area whose dimensions are controlled by a constant spread angle θ usually taken as 30°, denoted as AAM-30°. Both simplified and comprehensive culvert analysis procedures utilize AAM predictions for adjusting pressure distributions acting on the culvert periphery. Also, AAM-30° is routinely used to determine the two-wheel soil interaction depth, in which the combined effect of both axial wheels need to be considered. To date, a thorough accuracy analysis of AAM-30° has not been published in the open literature. This paper provides a unique and rigorous evaluation of AAM-30° using an exact solution from an elasticity-based model (EBM) of a homogeneous half-space with rectangular surface load. One key discovery is the depth parameter called y*, which is the soil depth at which AAM-30° peak-stress prediction exactly matches the exact EBM solution. Moreover, it is shown that y* may be determined by a simple, yet accurate formula that only depends on the square root of the load area. However, the investigation reveals that AAM-30° significantly underestimates peak stress in the shallow-depth zone 0 <  y < ½ y* by as much as 31.3% of the applied surface pressure. As this is a large nonconservative error it cannot be ignored. Accordingly, a very simple modification is introduced called AAM-θ*, in which θ* is a spread angle that linearly increases to 30° at soil depth ½ y* and thereafter θ* remains constant at 30°. An accuracy evaluation of AAM-θ* reveals an order of magnitude increase in accuracy in which the small residual error is conservative, not nonconservative. The paper concludes with discussions on applying AAM-θ* to the analysis of buried culverts when using either simple or finite element model solution procedures.

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

scholarly journals Investigating the Scale Adaptivity of a Size-Filtered Mass Flux Parameterization in the Gray Zone of Shallow Cumulus Convection

2018 ◽  
Vol 75 (4) ◽  
pp. 1195-1214 ◽  
Author(s):  
Maren Brast ◽  
Vera Schemann ◽  
Roel A. J. Neggers
Keyword(s):  
Mass Flux ◽  
Turbulent Transport ◽  
Eddy Diffusivity ◽  
Coarse Grained ◽  
Parameterization Scheme ◽  
Quasi Equilibrium ◽  
Gray Zone ◽  
Cumulus Clouds ◽  
Eddy Simulation ◽  
Shallow Cumulus

Abstract In this study, the scale adaptivity of a new parameterization scheme for shallow cumulus clouds in the gray zone is investigated. The eddy diffusivity/multiple mass flux [ED(MF)n] scheme is a bin-macrophysics scheme in which subgrid transport is formulated in terms of discretized size densities. While scale adaptivity in the ED component is achieved using a pragmatic blending approach, the MF component is filtered such that only the transport by plumes smaller than the grid size is maintained. For testing, ED(MF)n is implemented into a large-eddy simulation (LES) model, replacing the original subgrid scheme for turbulent transport. LES thus plays the role of a nonhydrostatic testing ground, which can be run at different resolutions to study the behavior of the parameterization scheme in the boundary layer gray zone. In this range, convective cumulus clouds are partially resolved. The authors find that for quasi-equilibrium marine subtropical conditions at high resolutions, the clouds and the turbulent transport are predominantly resolved by the LES. This partitioning changes toward coarser resolutions, with the representation of shallow cumulus clouds gradually becoming completely carried by the ED(MF)n. The way the partitioning changes with grid spacing matches the behavior diagnosed in coarse-grained LES fields, suggesting that some scale adaptivity is captured. Sensitivity studies show that the scale adaptivity of the ED closure is important and that the location of the gray zone is found to be moderately sensitive to some model constants.

scholarly journals The Seasonal Cycle of Upper-Ocean Mixing at 8°N in the Bay of Bengal

2020 ◽  
Vol 50 (2) ◽  
pp. 323-342 ◽  
Author(s):  
D. A. Cherian ◽  
E. L. Shroyer ◽  
H. W. Wijesekera ◽  
J. N. Moum
Keyword(s):  
Bay Of Bengal ◽  
Seasonal Cycle ◽  
Sea Water ◽  
Turbulent Transport ◽  
Low Frequency ◽  
Salt Flux ◽  
Strong Mixing ◽  
Northeast Monsoon ◽  
Order Of Magnitude ◽  
Episodic Mixing

AbstractWe describe the seasonal cycle of mixing in the top 30–100 m of the Bay of Bengal as observed by moored mixing meters (χpods) deployed along 8°N between 85.5° and 88.5°E in 2014 and 2015. All χpod observations were combined to form seasonal-mean vertical profiles of turbulence diffusivity KT in the top 100 m. The strongest turbulence is observed during the southwest and postmonsoon seasons, that is, between July and November. The northeast monsoon (December–February) is a period of similarly high mean KT but an order of magnitude lower median KT, a sign of energetic episodic mixing events forced by near-inertial shear events. The months of March and April, a period of weak wind forcing and low near-inertial shear amplitude, are characterized by near-molecular values of KT in the thermocline for weeks at a time. Strong mixing events coincide with the passage of surface-forced downward-propagating near-inertial waves and with the presence of enhanced low-frequency shear associated with the Summer Monsoon Current and other mesoscale features between July and October. This seasonal cycle of mixing is consequential. We find that monthly averaged turbulent transport of salt out of the salty Arabian Sea water between August and January is significant relative to local E − P. The magnitude of this salt flux is approximately that required to close model-based salt budgets for the upper Bay of Bengal.

Simultaneous Wall and Fluid Axial Conduction in Laminar Pipe-Flow Heat Transfer

1980 ◽  
Vol 102 (1) ◽  
pp. 58-63 ◽  
Author(s):  
M. Faghri ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Pipe Flow ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Upstream Region ◽  
Heated Region ◽  
Axial Conduction ◽  
Conductance Parameter ◽  
Flow Heat ◽  
Laminar Pipe Flow

Consideration is given to a laminar pipe flow in which the upstream portion of the wall is externally insulated while the downstream portion of the wall is uniformly heated. An analysis of the problem is performed whose special feature is the accounting of axial conduction in both the tube wall and in the fluid. This conjugate heat transfer problem is governed by two dimensionless groups—a wall conductance parameter and the Peclet number, the latter being assigned values from 5 to 50. From numerical solutions, it was found that axial conduction in the wall can carry substantial amounts of heat upstream into the non directly heated portion of the tube. This results in a preheating of both the wall and the fluid in the upstream region, with the zone of preheating extending back as far as twenty radii. The preheating effect is carried downstream with the fluid, raising temperatures all along the tube. The local Nusselt number exhibits fully developed values in the upstream (non directly heated) region as well as in the downstream (directly heated) region. Of the two effects, wall axial conduction can readily overwhelm fluid axial conduction.

Effects of Unsteady Free-Stream Velocity and Free-Stream Turbulence at a Stagnation Point

1983 ◽  
Vol 105 (1) ◽  
pp. 66-71 ◽  
Author(s):  
R. S. R. Gorla
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Free Stream ◽  
Eddy Diffusivity ◽  
Descent Method ◽  
Free Stream Velocity ◽  
Steepest Descent Method ◽  
Wall Friction ◽  
Stream Velocity ◽  
Free Stream Turbulence

An analysis is presented to investigate the combined effects of transient free-stream velocity and free-stream turbulence at a stagnation point on a cylinder situated in a crossflow. A model has been successfully formulated for the eddy diffusivity induced by the free-stream turbulence. The governing momentum equation has been integrated by the steepest descent method. Numerical solutions are provided for the unsteady wall shear stress function for specific free-stream transients. The results are correlated by a new turbulence parameter. It has been found that the wall friction increases with increasing free-stream turbulence intensity. In the case of flows involving unsteady free-stream velocity, the friction factor increases with increasing values of the reduced frequency of oscillations.

Three-Dimensional Laminar Natural Convection in a Vertical Air Slot With Hexagonal Honeycomb Core

1990 ◽  
Vol 112 (1) ◽  
pp. 130-136 ◽  
Author(s):  
Y. Asako ◽  
H. Nakamura ◽  
M. Faghri
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Side Wall ◽  
Temperature Fields ◽  
Honeycomb Core ◽  
Wall Boundary Conditions ◽  
Laminar Natural Convection

Numerical solutions are obtained for a three-dimensional natural convection heat transfer problem in a vertical air slot with a thin hexagonal honeycomb core. The air slot is assumed to be of such dimensions that the velocity and temperature fields repeat themselves in successive enclosures. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the complex cross section onto a rectangle, coupled with a calculation procedure for fully elliptic three-dimensional flows. The calculations are performed for the Rayleigh number in the range of 103 to 105, for a Prandtl number of 0.7, and for five values of the aspect ratio of the honeycomb enclosure. The average Nusselt number results for the case of a thin honeycomb core are compared with the previously obtained results for a thick honeycomb core with conduction and adiabatic side wall boundary conditions.

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