Parametric Study of the Discharge Coefficient on Critical Sonic Nozzles ISO-9300 With Turbulent Boundary Layer

2002 ◽  
Author(s):  
F. Sa´nchez Silva ◽  
J. A. Cruz Maya ◽  
A. Go´mez Mercado ◽  
G. Tolentino Eslava
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Analytical Model ◽  
Parametric Study ◽  
Discharge Coefficient ◽  
Numerical Data ◽  
Starting Point ◽  
Two Dimensional Flow ◽  
Viscous Stresses ◽  
Good Agreement

A parametric study on determining discharge coefficient in ISO 9300 [1] toroidal sonic nozzles have been developed. The focus of this paper is to obtain the an analytical model for the calculus of this discharge coefficient on turbulent boundary layer conditions for gases at Pr = 0.7. The problem is divided in two sections: one in which the viscous stresses are taking in to account at boundary layer zone, based on turbulent boundary layer theory and taking as starting point the work carried out by Stratford [2]. Then, curvature of flow field is studied at the nucleus of the nozzle, obtaining discharge coefficient values using numerical simulation for a two-dimensional flow. The results have a good agreement with correlations of ISO-9300 [1], experimental and numerical data of Wu-Yan [3] and the analytical model from Stratford [2].

scholarly journals CHARAGERIZATION OF THE DISCHARGE COEFFICIENT OF A SONIC VENTURI NOZZLE

2005 ◽  
Vol 3 (02) ◽  
Author(s):  
A. Cruz-Mava ◽  
F. Sánchez-Sllva ◽  
P. Qulnto-Dlez ◽  
M. Toledo-Velázquez
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Discharge Coefficient ◽  
Reynolds Numbers ◽  
Thermal Boundary Condition ◽  
Korea Research Institute ◽  
Critical Flow Regime ◽  
Venturi Nozzle ◽  
Viscous Stresses ◽  
Better Than

This paper identifles and determines the main parameters used to calculate the dlscharge coefficlent of a toroidal Venturl nozzle accordlng to the ISO Standard 9300, operating at the critical flow regime (sonlc). Thls study was conducted to investigate the effeds of the viscous stresses In the turbulent boundary layer, the wall thermal boundary condition, and the flow fleld curvature at the nucleus of the nozzle on the dlscharge coefflclent by means of a theoretical and numerlcal approach. Characterlzation of the dlscharge coefflclent in the Venturi sonlc nozzle was performed consldering the viscous and multidlmenslonal effects of the flujd flow as uncoupled phenomenon. As a result. each non-ideal mechanism can be  analyzed independently from the Inftuence of the other mechanlsm. We present a numerlcal procedure to characterlze the dlscharge coefflclent In the invlscld reglon of the ftow, by uslng the numerical simulation of the inviscld maln ftow by means of the commerclal CFD code. In the region of the vlscous stresses, the charaderlzation of thls coefflclent is based on the analytlcal theory of the turbulent boundary layer. Thls charaderization allowed obtalning a correlation of the dlscharge coefflclent that was valldated by dlred comparlson between the experimental correlations of the dlscharge coefflclent In turbulent boundary layer proposed by ISO-9300 and the Korea Research Institute of Standards and Sclence (KRISS). Thls valldation was carried out for throat Reynolds numbers from 1.4 to 2.6x10'. The agreement of the theoretical and measured dlscharge coefflclents by these correlations was better than  0.2%.

The response of a turbulent boundary layer to lateral divergence

1979 ◽  
Vol 94 (2) ◽  
pp. 243-268 ◽  
Author(s):  
A. J. Smits ◽  
J. A. Eaton ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Structural Parameters ◽  
Axial Flow ◽  
Turbulence Structure ◽  
Two Dimensional ◽  
Transition Section ◽  
Two Dimensional Flow ◽  
Made In

Measurements have been made in the flow over an axisymmetric cylinder-flare body, in which the boundary layer developed in axial flow over a circular cylinder before diverging over a conical flare. The lateral divergence, and the concave curvature in the transition section between the cylinder and the flare, both tend to destabilize the turbulence. Well downstream of the transition section, the changes in turbulence structure are still significant and can be attributed to lateral divergence alone. The results confirm that lateral divergence alters the structural parameters in much the same way as longitudinal curvature, and can be allowed for by similar empirical formulae. The interaction between curvature and divergence effects in the transition section leads to qualitative differences between the behaviour of the present flow, in which the turbulence intensity is increased everywhere, and the results of Smits, Young & Bradshaw (1979) for a two-dimensional flow with the same curvature but no divergence, in which an unexpected collapse of the turbulence occurred downstream of the curved region.

scholarly journals Metric for attractor overlap

2019 ◽  
Vol 874 ◽  
pp. 720-755 ◽  
Author(s):  
Rishabh Ishar ◽  
Eurika Kaiser ◽  
Marek Morzyński ◽  
Daniel Fernex ◽  
Richard Semaan ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Particle Image Velocimetry Data ◽  
Open Loop ◽  
Operating Conditions ◽  
Wall Turbulence ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Starting Point

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e. ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshot-to-snapshot ensembles of two attractors. A reduced-order analysis for big data and many attractors is enabled by coarse graining the snapshots into representative clusters with corresponding centroids and population probabilities. For a large number of attractors, MAO is augmented by proximity maps for the snapshots, the centroids and the attractors, giving scientifically interpretable visual access to the closeness of the states. The coherent structures belonging to the overlap and disjoint states between these attractors are distilled by a few representative centroids. We employ MAO for two quite different actuated flow configurations: a two-dimensional wake with vortices in a narrow frequency range and three-dimensional wall turbulence with a broadband spectrum. In the first application, seven control laws are applied to the fluidic pinball, i.e. the two-dimensional flow around three circular cylinders whose centres form an equilateral triangle pointing in the upstream direction. These seven operating conditions comprise unforced shedding, boat tailing, base bleed, high- and low-frequency forcing as well as two opposing Magnus effects. In the second example, MAO is applied to three-dimensional simulation data from an open-loop drag reduction study of a turbulent boundary layer. The actuation mechanisms of 38 spanwise travelling transversal surface waves are investigated. MAO compares and classifies these actuated flows in agreement with physical intuition. For instance, the first feature coordinate of the attractor proximity map correlates with drag for the fluidic pinball and for the turbulent boundary layer. MAO has a large spectrum of potential applications ranging from a quantitative comparison between numerical simulations and experimental particle-image velocimetry data to the analysis of simulations representing a myriad of different operating conditions.

Numerical simulation of crossing-shock-wave/turbulent-boundary-layer interaction using a two-equation model of turbulence

2000 ◽  
Vol 409 ◽  
pp. 121-147 ◽  
Author(s):  
D. KNIGHT ◽  
M. GNEDIN ◽  
R. BECHT ◽  
A. ZHELTOVODOV
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Equation Model ◽  
Adiabatic Wall ◽  
Layer Interaction ◽  
Boundary Layer Interaction ◽  
Good Agreement

A crossing-shock-wave/turbulent-boundary-layer interaction is investigated using the k–ε turbulence model with a new low-Reynolds-number model based on the approach of Saffman (1970) and Speziale et al. (1990). The crossing shocks are generated by two wedge-shaped fins with wedge angles α1 and α2 attached normal to a flat plate on which an equilibrium supersonic turbulent boundary layer has developed. Two configurations, corresponding to the experiments of Zheltovodov et al. (1994, 1998a, b), are considered. The free-stream Mach number is 3.9, and the fin angles are (α1, α2) = (7°, 7°) and (7°, 11°). The computed surface pressure displays very good agreement with experiment. The computed surface skin friction lines are in close agreement with experiment for the initial separation, and are in qualitative agreement within the crossing shock interaction region. The computed heat transfer is in good agreement with experiment for the (α1, α2) = (7°, 7°) configuration. For the (α1, α2) = (7°, 11°) configuration, the heat transfer is significantly overpredicted within the three-dimensional interaction. The adiabatic wall temperature is accurately predicted for both configurations.

scholarly journals Analytical model of the time developing turbulent boundary layer

JETP Letters ◽  
2007 ◽  
Vol 86 (2) ◽  
pp. 102-107 ◽  
Author(s):  
V. S. L’vov ◽  
A. Pomyalov ◽  
A. Ferrante ◽  
S. Elghobashi
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Analytical Model

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.

The effects of surface topography on momentum and mass transfer in a turbulent boundary layer

1981 ◽  
Vol 108 ◽  
pp. 423-442 ◽  
Author(s):  
R. A. Dawkins ◽  
D. R. Davies
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Turbulent Boundary Layer ◽  
Theoretical Calculations ◽  
Eddy Diffusivity ◽  
Open Circuit ◽  
Applied Theory ◽  
Mean Velocity ◽  
Method Of Calculation ◽  
Good Agreement

An approximate, conveniently applied theory with corresponding experimental data is presented concerning the changes in momentum and mass transfer produced by a ridge of small slopes in a flat-surface quasi-stationary turbulent boundary layer. A first-order mean velocity perturbation solution is found to be in good agreement with measured velocities on the up-slope side of a two-dimensional ridge, of length 20 cm and height 1 cm, fixed on the floor of the working section of an open-circuit wind tunnel. A vapour-transfer eddy-diffusivity distribution is then calculated for the inner boundary-layer region and solutions of the consequent vapour-transfer equation give the variation of rate of evaporation from surfaces of varying lengths placed at different positions on the up-slope region of the ridge. Corresponding measurements are found to be in good agreement with the theoretical calculations, and show that, even over small slopes (of 1 in 10), the evaporation rate varied with position by 25% from maximum to minimum. This method of calculation is extended to examine the effect of surface curvature on diffusion of gas from an upstream line source in a turbulent boundary layer over the ridge; experimental and theoretical concentration profiles compare extremely well over the leading slope.

Turbulent Boundary Layer Heat Transfer on Curved Surfaces

1979 ◽  
Vol 101 (3) ◽  
pp. 521-525 ◽  
Author(s):  
R. E. Mayle ◽  
M. F. Blair ◽  
F. C. Kopper
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Convex Surface ◽  
Concave Surface ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Streamline Curvature ◽  
Turbulent Shear Stress ◽  
Two Dimensional Flow

Heat transfer measurements for a turbulent boundary layer on a convex and concave, constant-temperature surface are presented. The heat transferred on the convex surface was found to be less than that for a flat surface, while the heat transferred to the boundary layer on the concave surface was greater. It was also found that the heat transferred on the convex surface could be determined by using an existing two-dimensional finite difference boundary layer program modified to take into account the effect of streamline curvature on the turbulent shear stress and heat flux, but that the heat transferred on the concave surface could not be calculated. The latter result is attributed to the transition from a two-dimensional flow to one which contained streamwise, Taylor-Go¨rtler type vortices.

scholarly journals Large Eddy Simulation of Microbubble Drag Reduction in Fully Developed Turbulent Boundary Layers

2020 ◽  
Vol 8 (7) ◽  
pp. 524
Author(s):  
Tongsheng Wang ◽  
Tiezhi Sun ◽  
Cong Wang ◽  
Chang Xu ◽  
Yingjie Wei
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Eddy Simulation ◽  
Drag Reduction ◽  
High Speed ◽  
Streamwise Velocity ◽  
Burst Frequency ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Good Agreement

Microbubble drag reduction has good application prospects. It operates by injecting a large number of bubbles with tiny diameters into a turbulent boundary layer. However, its mechanism is not yet fully understood. In this paper, the mechanisms of microbubble drag reduction in a fully developed turbulent boundary layer over a flat-plate is investigated using a two-way coupled Euler-Lagrange approach based on large eddy simulation. The results show good agreement with theoretical values in the velocity distribution and the distribution of fluctuation intensities. As the results show, the presence of bubbles reduces the frequency of bursts associated with the sweep events from 637.8 Hz to 611.2 Hz, indicating that the sweep events, namely the impacting of high-speed fluids on the wall surface, are suppressed and the streamwise velocity near the wall is decreased, hence reducing the velocity gradient at the wall and consequently lessening the skin friction. The suppression on burst frequency also, with the fluid fluctuation reduced in degree, decreases the intensity of vortices near the wall, leading to reduced production of turbulent kinetic energy.

scholarly journals THE DYNAMICS OF OSCILLATING SHEETFLOW

1986 ◽  
Vol 1 (20) ◽  
pp. 71 ◽  
Author(s):  
W.T. Bakker ◽  
W.G.M. Van Kesteren
Keyword(s):  
Boundary Layer ◽  
Numerical Model ◽  
Turbulent Boundary Layer ◽  
Analytical Model ◽  
Darcy Law ◽  
Elastic Response ◽  
Sheet Flow ◽  
Grain Interaction ◽  
Spherical Grains ◽  
Intrusion Depth

Two mathematical models for the simulation of the dynamics of sheetflow are presented, an analytical and a numerical one. In the analytical model the theory of Bagnold (1954) is implemented: a constant ratio between shear stress and normal stresses is assumed. In the numerical model the motion of each layer of grains is considered separately; each layer exists of a rigid rectangular structure of spherical grains. Grain- grain interaction between the successive layers occurs in two ways: on one hand viscous interaction forces, comparable with squeezing forces in lubrication problems and on the other hand direct contact with elastic response when the distance between the grains becomes less than .01 of the grain diameter. When the relative motion of adjacent layers results into compression or dilatation, a resistant force analogous to the Darcy law is assumed.The numerical model has been combined with the turbulent boundary layer model of Bakker and v. Kesteren (1984). Results of computations are compared with measurements of Bagnold (1954) and Horikawa et al (1982). The analytical model predicted the concentration in the sheet flow layer and the intrusion depth rather well, where the numerical model gave reasonable results with respect to the velocity pattern above the sheetflow layer. It is concluded, that up to now the more sophisticated assumptions of the numerical model do not lead as yet to higher accuracy with respect to the intrusion depth of the sheet flow, probably because the separation between sheet flow and the turbulent boundary layer above has been assumed too smooth.

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