Compressible Flow Ejectors: Part I—Development of a Finite-Difference Flow Model

1974 ◽  
Vol 96 (3) ◽  
pp. 272-281 ◽  
Author(s):  
K. R. Hedges ◽  
P. G. Hill
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Initial Conditions ◽  
Length Distribution ◽  
Mixing Length ◽  
Jet Mixing ◽  
Free Jet ◽  
Finite Difference Approximations ◽  
Constant Diameter ◽  
Wide Range

A general method of calculating two-dimensional (plane and axisymmetric) mixing of a compressible jet in variable-area ducts has been developed. The method incorporates finite-difference approximations to the conservation equations, and is applicable to a wide range of Mach number, mass flow ratio, and initial conditions. The model was based on mixing length approximations deduced from boundary-layer and free-jet mixing for the upstream portion of the flow, and on a new mixing length distribution for the downstream zone which is entirely occupied by shear flow. The method has been tested and found satisfactory with existing data on boundary layer, constant-diameter duct entrance flow, constant-pressure jet mixing, and jet mixing in variable-area ducts. Part II of the paper describes tests of the method with new data from an experimental ejector study.

Heat and Mass Transfer in an Incompressible Turbulent Boundary Layer

1972 ◽  
Vol 94 (1) ◽  
pp. 23-28 ◽  
Author(s):  
E. Brundrett ◽  
W. B. Nicoll ◽  
A. B. Strong
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Plate ◽  
Mixing Length ◽  
Two Dimensional ◽  
Transfer Data ◽  
Incompressible Turbulent Boundary Layer ◽  
Wide Range ◽  
Incompressible Boundary

The van Driest damped mixing length has been extended to account for the effects of mass transfer through a porous plate into a turbulent, two-dimensional incompressible boundary layer. The present mixing length is continuous from the wall through to the inner-law region of the flow, and although empirical, has been shown to predict wall shear stress and heat transfer data for a wide range of blowing rates.

Equilibrium-Turbulent Boundary Layer Prediction for a Proposed Prandtl Mixing Length Distribution

1968 ◽  
Vol 10 (5) ◽  
pp. 426-433 ◽  
Author(s):  
F. C. Lockwood
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Length Distribution ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Mixing Length ◽  
Good Agreement

The momentum equation is solved numerically for a suggested ramp variation of the Prandtl mixing length across an equilibrium-turbulent boundary layer. The predictions of several important boundary-layer functions are compared with the equilibrium experimental data. Comparisons are also made with some recent universal recommendations for turbulent boundary layers since the equilibrium experimental data are limited. Good agreement is found between the predictions, the experimental data, and the recommendations.

scholarly journals Understanding isoprene photooxidation using observations and modeling over a subtropical forest in the southeastern US

2016 ◽  
Vol 16 (12) ◽  
pp. 7725-7741 ◽  
Author(s):  
Luping Su ◽  
Edward G. Patton ◽  
Jordi Vilà-Guerau de Arellano ◽  
Alex B. Guenther ◽  
Lisa Kaser ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Forest Canopy ◽  
Initial Conditions ◽  
Mixed Forest ◽  
Chemical Species ◽  
Early Morning ◽  
Convective Boundary ◽  
Southeastern Us ◽  
Wide Range ◽  
Boundary Layer Dynamics

Abstract. The emission, dispersion, and photochemistry of isoprene (C5H8) and related chemical species in the convective boundary layer (CBL) during sunlit daytime were studied over a mixed forest in the southeastern United States by combining ground-based and aircraft observations. Fluxes of isoprene and monoterpenes were quantified at the top of the forest canopy using a high-resolution proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS). Snapshot (∼  2 min sampling duration) vertical profiles of isoprene, methyl vinyl ketone (MVK) + methacrolein (MACR), and monoterpenes were collected from aircraft every hour in the CBL (100–1000 m). Both ground-based and airborne collected volatile organic compound (VOC) data are used to constrain the initial conditions of a mixed-layer chemistry model (MXLCH), which is applied to examine the chemical evolution of the O3–NOx–HOx–VOC system and how it is affected by boundary layer dynamics in the CBL. The chemical loss rate of isoprene (∼  1 h) is similar to the turbulent mixing timescale (0.1–0.5 h), which indicates that isoprene concentrations are equally dependent on both photooxidation and boundary layer dynamics. Analysis of a model-derived concentration budget suggests that diurnal evolution of isoprene inside the CBL is mainly controlled by surface emissions and chemical loss; the diurnal evolution of O3 is dominated by entrainment. The NO to HO2 ratio (NO : HO2) is used as an indicator of anthropogenic impact on the CBL chemical composition and spans a wide range (1–163). The fate of hydroxyl-substituted isoprene peroxyl radical (HOC5H8OO·; ISOPOO) is strongly affected by NO : HO2, shifting from NO-dominant to NO–HO2-balanced conditions from early morning to noontime. This chemical regime change is reflected in the diurnal evolution of isoprene hydroxynitrates (ISOPN) and isoprene hydroxy hydroperoxides (ISOPOOH).

scholarly journals A Non-Standard Finite Difference Scheme for Magneto-Hydro Dynamics Boundary Layer Flows of an Incompressible Fluid Past a Flat Plate

2021 ◽  
Vol 26 (1) ◽  
pp. 22
Author(s):  
Riccardo Fazio ◽  
Alessandra Jannelli
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Incompressible Fluid ◽  
Difference Scheme ◽  
Flat Plate ◽  
Finite Difference Scheme ◽  
Approximate Solutions ◽  
Numerical Results ◽  
Uniform Mesh ◽  
Wide Range

This paper deals with a non-standard implicit finite difference scheme that is defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. The proposed approach allows imposing the given boundary conditions at infinity exactly. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

scholarly journals Understanding isoprene photo-oxidation using observations and modelling over a subtropical forest in the Southeast US

2015 ◽  
Vol 15 (21) ◽  
pp. 31621-31663 ◽  
Author(s):  
L. Su ◽  
E. G. Patton ◽  
J. Vilà-Guerau de Arellano ◽  
A. B. Guenther ◽  
L. Kaser ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Forest Canopy ◽  
Initial Conditions ◽  
Mixing Time ◽  
Mixed Forest ◽  
Chemical Species ◽  
Convective Boundary ◽  
Photo Oxidation ◽  
Wide Range ◽  
Boundary Layer Dynamics

Abstract. The emission, dispersion and photochemistry of isoprene (C5H8) and related chemical species in the convective boundary layer (CBL) during sunlit daytime was studied over a mixed forest in the Southeast United States by combining ground-based and aircraft observations. Fluxes of isoprene and monoterpenes were quantified at the top of the forest canopy using a high resolution Proton Transfer Reaction Time of Flight Mass Spectrometer (PTR-TOF-MS). Snapshot (~ 2 min sampling duration) vertical profiles of isoprene, methyl vinyl ketone (MVK) + methacrolein (MACR), and monoterpenes were collected from aircraft every hour in the CBL (100–1000 m). Both ground-based and airborne collected volatile organic compound (VOC) data are used to constrain the initial conditions of a mixed layer chemistry model (MXLCH), which is applied to examine the chemical evolution of the O3-NOx-HOx-VOC system and how it is affected by boundary layer dynamics in the CBL. The chemical loss rate of isoprene (~ 1 h) is similar to the turbulent mixing time scale (0.1–0.5 h), which indicates that isoprene concentrations are equally dependent on both photo-oxidation and boundary layer dynamics. Analysis of a model-derived concentration budget suggests that diurnal evolution of isoprene inside the CBL is mainly controlled by surface emissions and chemical loss. The NO to HO2 ratio (NO : HO2) is used as an indicator of anthropogenic impact on the CBL chemical composition, and spans a wide range (1–163). The fate of hydroxyl-substituted isoprene peroxyl radical (HOC5H8OO·; ISOPOO) is strongly affected by NO : HO2, shifting from NO-dominant to NO-HO2-balanced condition from early morning to noontime. This chemical regime change is reflected in the diurnal evolution of isoprene hydroxynitrates (ISOPN) and isoprene hydroxy hydroperoxides (ISOPOOH).

Flow Separation and Reattachment in Confined Jet Mixing

1971 ◽  
Vol 93 (2) ◽  
pp. 192-198 ◽  
Author(s):  
John T. Exley ◽  
John A. Brighton
Keyword(s):  
Flow Separation ◽  
Velocity Ratio ◽  
Flow Measurements ◽  
Lower Velocity ◽  
Jet Mixing ◽  
Axisymmetric Jet ◽  
Constant Diameter ◽  
Wide Range ◽  
Secondary Velocity ◽  
Flow Separation And Reattachment

An experimental and theoretical investigation was conducted to study flow separation and reattachment for a confined axisymmetric jet. The fluid was air with an initially uniform velocity jet mixing with an initially uniform (but lower velocity) secondary flow. Both streams were at the same temperature and mixed in a constant-diameter duct. The location of the points of separation and reattachment and the line of zero velocity were determined by injecting smoke into the flow. Measurements were made over a wide range of diameter ratios (nozzle diameter to mixing tube diameter) and velocity ratios (jet velocity to secondary velocity at the inlet). The separation point was strongly affected by the velocity ratio—moving upstream with an increase in velocity ratio. Reattachment, however, was only slightly affected by velocity ratio. A single parameter, such as the Curtet number, was found to be inadequate in describing separation and reattachment over all diameter ratio and velocity ratio conditions.

Расчеты сверхзвукового пограничного слоя в полной и локально автомодельной постановках

2020 ◽  
Author(s):  
Y.N. Grigoryev ◽  
A.G. Gorobchuk ◽  
I.V. Ershov
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Initial Conditions ◽  
Plane Boundary ◽  
Transfer Coefficients ◽  
Vibrationally Excited ◽  
Limit Values ◽  
Various Boundary Conditions ◽  
Self Similar ◽  
Similar Solutions

The article considers the possibility of using locally self-similar solutions of a stationary boundary layer in linear stability problems. These solutions are compared with various boundary conditions for a vibrationally excited gas with finite-difference calculations of the corresponding flows. The initial system of equations for a plane boundary layer of a vibrationally excited gas was obtained from the complete equations of two-temperature relaxation aerodynamics. The relaxation of vibrational modes of gas molecules is described in the framework of the LandauTeller equation. Transfer coefficients depend on the static flow temperature. It is shown that in all considered cases the convergence of profiles of hydrodynamic variables to some limit values takes place for the longitudinal coordinate 8 . . . 15. In parallel, the same flows were calculated using the full formulation based on the finite-difference KrankNicholson type scheme. It is shown that for all considered boundary and initial conditions the limiting locally self-similar profiles coincide with the profiles calculated within the full formulation. The obtained result substantiates the use of locally self-similar solutions in problems of the linear theory of stability of boundary layer flows of vibrationally excited gas. Проведены расчеты течения в плоском пограничном слое сжимаемого колебательно возбужденного газа в локально автомодельной постановке для ряда характерных условий внешнего потока и теплообмена на границе. Показано, что во всех рассмотренных случаях имеет место сходимость профилей гидродинамических переменных к некоторым предельным значениям для продольной координаты x> 8 . . . 15. Параллельно те же течения рассчитывались в полной постановке на основе конечно-разностной схемы типа Кранка-Николсон. Показано, что для всех рассмотренных граничных и начальных условий предельные локально автомодельные профили совпадают с профилями, рассчитанными в полной постановке. Это позволяет обоснованно использовать легко рассчитываемые локально автомодельные профили в задачах линейной теории устойчивости.

Prediction of Transpired Turbulent Boundary Layers

1974 ◽  
Vol 96 (1) ◽  
pp. 89-94 ◽  
Author(s):  
R. H. Pletcher
Keyword(s):  
Compressible Flows ◽  
Length Distribution ◽  
Turbulent Boundary Layers ◽  
Mixing Length ◽  
Law Of The Wall ◽  
Damping Function ◽  
The Past ◽  
Wide Range ◽  
Layer Flow ◽  
New Formulation

A model for the mixing length distribution near the wall in turbulent boundary layer flow with transpiration is presented. The model is based on a new formulation of the exponential damping function originally suggested by Van Driest. The analysis used to evaluate the damping function employs the same set of assumptions successfully used by several investigators in the past to develop the law of the wall with blowing. This mixing length model is then used with the calculation method previously developed by the author to solve the governing conservation equations of mass, momentum, and energy in partial differential form. Predicted velocity profiles, skin friction coefficients, and Stanton numbers are compared with experimental results taken over a wide range of transpiration for both incompressible and compressible flows.

scholarly journals Sensitivity of quantitative precipitation forecasts to boundary layer parameterization: a flash flood case study in the Western Mediterranean

2005 ◽  
Vol 5 (4) ◽  
pp. 603-612 ◽  
Author(s):  
M. Zampieri ◽  
P. Malguzzi ◽  
A. Buzzi
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Flash Flood ◽  
Western Mediterranean ◽  
Precipitation Forecast ◽  
Convective System ◽  
Mixing Length ◽  
Hydrostatic Model ◽  
The Impact

Abstract. The "Montserrat-2000" severe flash flood event which occurred over Catalonia on 9 and 10 June 2000 is analyzed. Strong precipitation was generated by a mesoscale convective system associated with the development of a cyclone. The location of heavy precipitation depends on the position of the cyclone, which, in turn, is found to be very sensitive to various model characteristics and initial conditions. Numerical simulations of this case study using the hydrostatic BOLAM and the non-hydrostatic MOLOCH models are performed in order to test the effects of different formulations of the boundary layer parameterization: a modified version of the Louis (order 1) model and a custom version of the E-ℓ (order 1.5) model. Both of them require a diagnostic formulation of the mixing length, but the use of the turbulent kinetic energy equation in the E-ℓ model allows to represent turbulence history and non-locality effects and to formulate a more physically based mixing length. The impact of the two schemes is different in the two models. The hydrostatic model, run at 1/5 degree resolution, is less sensitive, but the quantitative precipitation forecast is in any case unsatisfactory in terms of localization and amount. Conversely, the non-hydrostatic model, run at 1/50 degree resolution, is capable of realistically simulate timing, position and amount of precipitation, with the apparently superior results obtained with the E-ℓ parameterization model.

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