A Three-Dimensional Axisymmetric Calculation Procedure for Turbulent Flows in a Radial Vaneless Diffuser

1986 ◽  
Vol 108 (1) ◽  
pp. 118-124 ◽  
Author(s):  
L. F. Schumann
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Vaneless Diffuser ◽  
Fully Developed Flow ◽  
The Core ◽  
Continuity Equations ◽  
Tangential Momentum ◽  
Axisymmetric Duct

An analytical model is proposed to calculate the three-dimensional axisymmetric turbulent flowfield in a radial vaneless diffuser. The model assumes that the radial and tangential boundary layer profiles can be approximated by power-law profiles. Then, using the integrated radial and tangential momentum and continuity equations for the boundary layer and corresponding inviscid equations for the core flow, there result six ordinary differential equations in six unknowns which can easily be solved using a Runge-Kutta technique. A model is also proposed for fully developed flow. The results using this technique have been compared with the results from a three-dimensional viscous, axisymmetric duct code and with experimental data and good quantitative agreement was obtained.

On vortex boundary layers

1985 ◽  
Vol 400 (1819) ◽  
pp. 253-261 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Outer Flow ◽  
The Core ◽  
Dimensional Boundary ◽  
Radial Pressure Gradient ◽  
Potential Vortex ◽  
Vortex Axis

Flow visualization is used to study the flow that results when a potential vortex rotates normal to a stationary horizontal disc. Viscosity is seen to remove the singularity on the vortex axis and lead to the development of a three-dimensional boundary layer. The flow remains laminar below a Reynolds number, Re , of about 10 4 , where Re is based on radius and velocity at the disc edge. With further increases in Re the boundary layer becomes turbulent but relaminarizes as it is advected radially inwards by the highly favourable radial pressure gradient associated with the outer flow. The radius of the zone of relaminarized fluid decreases with increasing Re . Close to the axis the flow effuses vertically to form the core of the vortex which, for Re < 10 4 , is observed to undergo a massive disruption, either of the axisymmetric or helical form. The sense of the helix was observed on some occasions to be with that of the outer flow and on others to be opposite that of the outer flow.

Does Balance Dynamics Well Capture the Secondary Circulation and Spinup of a Simulated Hurricane?

2021 ◽  
Vol 78 (1) ◽  
pp. 75-95
Author(s):  
Michael T. Montgomery ◽  
John Persing
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Three Dimensional ◽  
Realistic Model ◽  
Secondary Circulation ◽  
Balance Model ◽  
Tangential Momentum ◽  
Physics Model ◽  
Balanced Dynamics

AbstractThis study investigates a claim made by Heng et al. in an article published in 2017 and intimated soon after in their article published in 2018 that axisymmetric “balanced dynamics can well capture the secondary circulation in the full-physics model” during hurricane spinup. Using output from a new, convection-permitting, three-dimensional numerical simulation of an intensifying hurricane, azimuthally averaged forcings of tangential momentum and heat are diagnosed to force an axisymmetric Eliassen balance model under strict balance conditions. The balance solutions are found, inter alia, to poorly represent the peak inflow velocity in the boundary layer and present a layer of relatively deep inflow extending well above the boundary layer in the high-wind-speed region of the vortex. Such a deep inflow layer, a hallmark of the classical spinup mechanism for tropical cyclones comprising the radial convergence of absolute angular momentum above the boundary layer, is not found in the numerical simulation during the period of peak intensification. These deficiencies are traced to the inability of the balance model to represent the nonlinear boundary layer spinup mechanism. These results are contrasted with a pseudobalance Eliassen formulation that improves the solution in some respects while sacrificing strict thermal wind balance. Overall, the quantitative results refute the Heng et al. claim and implicate the general necessity of the nonlinear boundary layer spinup mechanism to explain the spinup of a hurricane in realistic model configurations and in reality.

Development and assessment of computer methods for three-dimensional turbulent boundary layers

1999 ◽  
Vol 103 (1024) ◽  
pp. 287-297
Author(s):  
J. Wu ◽  
U. R. Müller
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Theoretical Data ◽  
Field Method ◽  
Curvilinear Coordinates ◽  
Integral Boundary ◽  
Boundary Layer Equations ◽  
Computer Methods

Abstract This paper describes the development of a finite difference method that solves the boundary-layer equations for three-dimensional compressible turbulent flows. The most prominent achievements are the employment of a Newton technique for the simultaneous solution of all governing equations, an option to choose an algebraic or a k-ε eddy-viscosity turbulence model, and the flexible use of curvilinear coordinates. The method is validated by comparisons with a number of experimental and theoretical data sets of three-dimensional, compressible and incompressible, steady and unsteady boundary layers. In parallel, the performance of a three-dimensional compressible industrial integral boundary-layer technique is evaluated by comparisons with experimental test cases and with the results of the field method.

scholarly journals Efficient investigation on fully developed flow in a mildly curved 180° open-channel

2014 ◽  
Vol 16 (6) ◽  
pp. 1250-1264 ◽  
Author(s):  
Yuchuan Bai ◽  
Xiaolong Song ◽  
Shuxian Gao
Keyword(s):  
Secondary Flow ◽  
Flow Pattern ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Engineering Application ◽  
Experimental Investigations ◽  
Shear Stresses ◽  
Fully Developed Flow ◽  
Wall Shear ◽  
Volume Method

Turbulent flow in meandering open channels is one of the most complicated and unpredictable turbulent flows as the interaction of various forces, such as pressure gradient, centrifugal force, and wall shear stresses severely affect the flow pattern. In order to improve significance in engineering application, understanding the overall flow characteristic is the focus. This paper presents the results of numerical and experimental investigations of flow in a 180° mild bend, which is close to criticality with curvature ratio R/B = 3. Considering the characteristic of various models, three-dimensional (3D) re-normalization group (RNG) k–ε model was adopted to simulate the flow efficiently. Governing equations of the flow were solved with a finite-volume method. The pressure-based coupled algorithm was used to compute the pressure. The flow velocities were measured experimentally with Micro acoustic Doppler velocimeter. Good agreement between the numerical results and measurements indicated that RNG k–ε model can successfully predict this flow phenomenon. The flow pattern in this bend is influenced widely by the secondary flow. The variations of velocity components, streamlines, secondary flow, and wall shear stresses are analysed in the study. Some newly discovered phenomenon in this special state are worth noting.

Three-dimensional viscous wakes

1962 ◽  
Vol 14 (2) ◽  
pp. 233-240 ◽  
Author(s):  
Martin H. Steiger ◽  
Martin H. Bloom
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Axial Symmetry ◽  
Constant Velocity ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Axial Velocity Distribution ◽  
Fluid Properties ◽  
Laminar And Turbulent Flows

The velocity fields of three-dimensional viscous wakes are examined with the use of the boundary-layer approximations, Oseen's linearization of the convective terms, and the assumption of constant fluid properties. Transform methods yield solutions for general types of initial conditions. As an illustration, the axial velocity distribution of a wake whose initial isovels (lines of constant velocity) are of elliptic shape and their decay to axial symmetry are demonstrated. Both laminar and turbulent flows are considered.

The Unsteady Boundary Layer in a Shock Tube

1976 ◽  
Vol 190 (1) ◽  
pp. 287-296 ◽  
Author(s):  
B. E. L. Deckker ◽  
M. E. Weekes
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Rectangular Duct ◽  
Unsteady Boundary Layer ◽  
High Quality ◽  
Schlieren System ◽  
Theoretical Predictions ◽  
Laminar And Turbulent Flows

SYNOPSIS The unsteady boundary layer behind a moving shock wave in a rectangular duct 7.62 cm wide × 5.08 cm high has been studied using a high quality schlieren system. Growth of the boundary layer has been compared with the results of calculations for laminar and turbulent flows. The experimental results indicate that three dimensional effects are present which cause, in some cases, very early transition from laminar to turbulent flow. Agreement with theory is satisfactory only in the case of the weakest shock wave examined although the trends in growth rates generally conform to theoretical predictions.

The resonant-triad nonlinear interaction in boundary-layer transition

1987 ◽  
Vol 179 ◽  
pp. 227-252 ◽  
Author(s):  
F. T. Smith ◽  
P. A. Stewart
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Finite Amplitude ◽  
Boundary Layer Transition ◽  
Transition To Turbulence ◽  
Layer Transition ◽  
Structured Analysis

Recent controlled experiments by Kachanov & Levchenko (1984) and others indicate that, during some slower kinds of transition to turbulence in boundary layers, three-dimensionality can come into play initially as a resonant-triad phenomenon, depending on the disturbance sizes present. The triad interaction, suggested theoretically in the boundary-layer context by Craik (1971) and others, is studied in the present work by means of multi-structured analysis for high characteristic Reynolds numbers. A finite-amplitude/relatively high-frequency approach leads rationally to the nonlinear triad equations, solutions for which are then obtained analytically and computationally in certain central cases of interest (temporal and spatial). The solutions have a rather chaotic spiky appearance as continual energy exchange develops between the two- and three-dimensional nonlinear modes, whose large-scale response seems governed by inviscid dynamics but subject to important, continual ‘rejuvenation’ from small- (fast-) scale viscous action in-between. The three-dimensional growth rate is thereby increased, but not the two-dimensional. Subsequently the disturbed flow enters a higher-amplitude regime similar to that studied in some related papers by the authors and co-workers. Comparisons with the experiments are very supportive of the theory (in the small and in the large), yielding both qualitative and quantitative agreement.

Departures from Axisymmetric Balance Dynamics during Secondary Eyewall Formation

2014 ◽  
Vol 71 (10) ◽  
pp. 3723-3738 ◽  
Author(s):  
Sergio F. Abarca ◽  
Michael T. Montgomery
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclone ◽  
Three Dimensional ◽  
Balance Model ◽  
Wind Maximum ◽  
Secondary Eyewall Formation ◽  
Tangential Wind ◽  
Eyewall Replacement Cycle ◽  
Tangential Momentum ◽  
Balance Dynamics

Abstract Departures from axisymmetric balance dynamics are quantified during a case of secondary eyewall formation. The case occurred in a three-dimensional mesoscale convection-permitting numerical simulation of a tropical cyclone, integrated from an initial weak mesoscale vortex in an idealized quiescent environment. The simulation exhibits a canonical eyewall replacement cycle. Departures from balance dynamics are quantified by comparing the azimuthally averaged secondary circulation and corresponding tangential wind tendencies of the mesoscale integration with those diagnosed as the axisymmetric balanced response of a vortex subject to diabatic and tangential momentum forcing. Balance dynamics is defined here, following the tropical cyclone literature, as those processes that maintain a vortex in axisymmetric thermal wind balance. The dynamical and thermodynamical fields needed to characterize the background vortex for the Sawyer–Eliassen inversion are obtained by azimuthally averaging the relevant quantities in the mesoscale integration and by computing their corresponding balanced fields. Substantial differences between azimuthal averages and their homologous balance-derived fields are found in the boundary layer. These differences illustrate the inappropriateness of the balance assumption in this region of the vortex (where the secondary eyewall tangential wind maximum emerges). Although the balance model does broadly capture the sense of the forced transverse (overturning) circulation, the balance model is shown to significantly underestimate the inflow in the boundary layer. This difference translates to unexpected qualitative differences in the tangential wind tendency. The main finding is that balance dynamics does not capture the tangential wind spinup during the simulated secondary eyewall formation event.

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