Numerical Computation of Tip Vortex Flow Generated by a Marine Propeller

1999 ◽  
Vol 121 (3) ◽  
pp. 638-645 ◽  
Author(s):  
Chao-Tsung Hsiao ◽  
Laura L. Pauley
Keyword(s):  
Cross Section ◽  
Vortex Flow ◽  
Tip Vortex ◽  
Navier Stokes ◽  
Marine Propeller ◽  
Mean Velocity ◽  
Cavitation Inception ◽  
Section Design ◽  
The Mean ◽  
Propeller Performance

The uniform flow past a rotating marine propeller was studied using incompressible Reynolds-averaged Navier-Stokes computations with the Baldwin-Barth turbulence model. Extensive comparison with the experimental data was made to validate the numerical results. The general characteristics of the propeller flow were well predicted. The current numerical method, however, produced an overly diffusive and dissipative tip vortex core. Modification of the Baldwin-Barth model to better predict the Reynolds stress measurements also improved the prediction of the mean velocity field. A modified tip geometry was also tested to show that an appropriate cross section design can delay cavitation inception in the tip vortex without reducing the propeller performance.

Scaling of Tip Vortex Cavitation Inception Noise With a Bubble Dynamics Model Accounting for Nucleus Size Distribution

2003 ◽  
Author(s):  
Chao-Tsung Hsiao ◽  
Georges L. Chahine
Keyword(s):  
Size Distribution ◽  
Vortex Flow ◽  
Bubble Dynamics ◽  
Tip Vortex ◽  
Navier Stokes ◽  
Nucleus Size ◽  
Scaling Effects ◽  
Dynamics Model ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception

A Surface-Averaged Pressure (SAP) spherical bubble dynamics model accounting for a statistical nuclei size distribution was used to model the acoustic signals generated by cavitating bubbles near inception in a tip vortex flow. The flow field generated by finite-span elliptic hydrofoils is obtained by Reynolds-Averaged Navier-Stokes computations. An “acoustic” criterion which defines the cavitation inception by counting the number of acoustical signal peaks that exceed a certain level per unit time was applied to deduce the cavitation inception number for different scales. It was found that the larger scale results in more cavitation inception events per unite time because more nuclei are excited by the tip vortex at the larger scale. The nuclei size was seen to have an important effect on cavitation inception number with scaling effects due to nuclei increasing as nuclei sizes decreases.

Study of Tip Vortex Cavitation Inception Using Navier-Stokes Computation and Bubble Dynamics Model

1999 ◽  
Vol 121 (1) ◽  
pp. 198-204 ◽  
Author(s):  
Chao-Tsung Hsiao ◽  
Laura L. Pauley
Keyword(s):  
Vortex Core ◽  
Bubble Dynamics ◽  
Three Dimensional ◽  
Window Size ◽  
Tip Vortex ◽  
Navier Stokes ◽  
Cavitation Inception ◽  
Flow Effects ◽  
Bubble Sizes ◽  
Real Flow

The Rayleigh-Plesset bubble dynamics equation coupled with the bubble motion equation developed by Johnson and Hsieh was applied to study the real flow effects on the prediction of cavitation inception in tip vortex flows. A three-dimensional steady-state tip vortex flow obtained from a Reynolds-Averaged Navier-Stokes computation was used as a prescribed flow field through which the bubble was passively convected. A “window of opportunity” through which a candidate bubble must pass in order to be drawn into the tip-vortex core and cavitate was determined for different initial bubble sizes. It was found that bubbles with larger initial size can be entrained into the tip-vortex core from a larger window size and also had a higher cavitation inception number.

scholarly journals A Novel Simplification of the Reynolds-Chou-Navier-Stokes Turbulence Equations of Incompressible Flow

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Incompressible Flow ◽  
Velocity Fluctuation ◽  
Explicit Representation ◽  
Navier Stokes ◽  
Mean Velocity ◽  
The Mean ◽  
Turbulence Formulations

Based on author's previous work [Sun, B. The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed. Preprints 2018, 2018060461 (doi: 10.20944/preprints201806.0461.v1)], this paper proposed an explicit representation of velocity fluctuation and formulated the Reynolds stress tensor in terms of the mean velocity field. The proposed closed Reynolds Navier-Stokes turbulence formulations reveal that the mean vorticity is the key source of producing turbulence.

scholarly journals Numerical Investigation of Tip-Vortex Cavitation Noise of an Elliptic Wing Using Coupled Eulerian-Lagrangian Approaches

2020 ◽  
Vol 10 (17) ◽  
pp. 5897 ◽  
Author(s):  
Garam Ku ◽  
Cheolung Cheong ◽  
Hanshin Seol
Keyword(s):  
Flow Field ◽  
Numerical Method ◽  
Vortex Flow ◽  
Acoustic Pressure ◽  
Tip Vortex ◽  
Experimental Result ◽  
Cavitation Noise ◽  
Navier Stokes Equation ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception

In this study, a numerical methodology is developed to investigate the tip-vortex cavitation of NACA16-020 wings and their flow noise. The numerical method consists of a sequential one-way coupled application of Eulerian and Lagrangian approaches. First, the Eulerian method based on Reynolds-averaged Navier–Stokes equation is applied to predict the single-phase flow field around the wing, with particular emphasis on capturing high-resolution tip-vortex flow structures. Subsequently, the tip-vortex flow field is regenerated by applying the Scully vortex model. Secondly, the Lagrangian approach is applied to predict the tip-vortex cavitation inception and noise of the wing. The initial nuclei are distributed upstream of the wing. The subsequent time-varying size and position of each nucleus are traced by solving spherically symmetric bubble dynamics equations for the nuclei in combination with the flow field predicted from the Eulerian approach. The acoustic pressure at the observer position is computed by modelling each bubble as a point source. The numerical results of the acoustic pressure spectrum are best matched to the measured results when the nuclei number density of freshwater is used. Finally, the current numerical method is applied to the flows of various cavitation numbers. The results reveal that the cavitation inception determined by the predicted acoustic pressure spectrum well matched the experimental result.

Numerical Experiments for Flow Around a Ducted Tip Hydrofoil

2002 ◽  
Author(s):  
Hildur Ingvarsdo´ttir ◽  
Carl Ollivier-Gooch ◽  
Sheldon I. Green
Keyword(s):  
Turbulence Model ◽  
Vortex Core ◽  
Vortex Flow ◽  
Computational Study ◽  
Near Field ◽  
Vortex Formation ◽  
Tip Vortex ◽  
Navier Stokes ◽  
Computational Studies ◽  
Tip Vortices

The performance and cavitation characteristics of marine propellers and hydrofoils are strongly affected by tip vortex behavior. A number of previous computational studies have been done on tip vortices, both in aerodynamic and marine applications. The focus, however, has primarily been on validating methods for prediction and advancing the understanding of tip-vortex formation in general, rather than showing effects of tip modifications on tip vortices. Studies of the most relevance to the current work include computational studies by Dacles-Mariani et al. (1995) and Hsiao and Pauley (1998, 1999). Daeles-Mariani et al. carried out interactively a computational and experimental study of the wingtip vortex in the near field using a full Navier-Stokes simulation, accompanied with the Baldwin-Barth turbulence model. Although they showed improvement over numerical results obtained by previous researchers, the tip vortex strength was underpredicted. Hsiao and Pauley (1998) studied the steady-state tip vortex flow over a finite-span hydrofoil, also using the Baldwin-Barth turbulence model. They were able to achieve good agreement in pressure distribution and oil flow pattern with experimental data and accurately predict vertical and axial velocities of the tip vortex core within the near-field region. Far downstream, however, the computed flow field was overly diffused within the tip vortex core. Hsiao and Pauley (1999) also carried out a computational study of the tip vortex flow generated by a marine propeller. The general characteristics of the flow were well predicted but the vortex core was again overly diffused.

Numerical Simulations of Turbulent Flow Through a 90° Elbow

2019 ◽  
Author(s):  
Ravon Venters ◽  
Brian Helenbrook ◽  
Goodarz Ahmadi
Keyword(s):  
Turbulent Flow ◽  
Cross Section ◽  
Navier Stokes ◽  
Mean Square ◽  
Reynolds Stresses ◽  
Streamline Curvature ◽  
Secondary Motion ◽  
Flow Through ◽  
The Mean ◽  
Flow Transitions

Abstract Turbulent flow in an elbow has been numerically investigated. The flow was modeled using two approaches; Reynolds Averaged Navier-Stokes (RANS) and Direct Numerical Simulation (DNS) methods. The DNS allows for all the scales of turbulence to be evaluated, providing a detailed depiction of the flow. The RANS simulation, which is typically used in industry, evaluates time-averaged components of the flow. The numerical results are accompanied by experimental data, which was used to validate the two methods. Profiles of the mean and root-mean-square (RMS) fluctuating components were compared at various points along the midplane of the elbow. Upstream of the elbow, the predicted mean and RMS velocities from the RANS and DNS simulations compared well with the experiment, differing slightly near the walls. However, downstream of the elbow, the RANS deviated from the experiment and DNS, showing a longer region of flow re-circulation. This caused the mean and RMS velocities to significantly differ. Examining the cross-section flow field, secondary motion was clearly present. Upstream secondary motion of the first kind was observed which is caused by anisotropy of the reynolds stresses in the turbulent flow. Downstream of the bend, the flow transitions to secondary motion of the second kind which is caused by streamline curvature. Qualitatively, the RANS and DNS showed similar results upstream of the bend, however downstream, the magnitude of the secondary motion differed significantly.

Application of a Three-Dimensional Inverse Method to the Design of a Centrifugal Compressor Impeller

1998 ◽  
Author(s):  
Alain Demeulenaere ◽  
Olivier Léonard ◽  
René Van den Braembussche
Keyword(s):  
Centrifugal Compressor ◽  
Inverse Method ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Mean Velocity ◽  
Blade Shape ◽  
Compressor Impeller ◽  
Real Performance ◽  
The Mean

The use of a three-dimensional Euler inverse method for the design of a centrifugal impeller is demonstrated. Both the blade shape and the endwalls are iteratively designed. The meridional contour is modified in order to control the mean velocity level in the blade channel, while the blade shape is designed to achieve a prescribed loading distribution between the inlet and the outlet. The method salves the time dependent Euler equations in a numerical domain of which some boundaries (the blades or the endwalls) move and change shape during the transient part of the computation, until a prescribed pressure distribution is achieved on the blade surfaces. The method is applied to the design of a centrifugal compressor impeller, whose hub endwall and blade surfaces are modified by the inviscid inverse method. The real performance of both initial and modified geometries are compared through three-dimensional Navier-Stokes computations.

The effects of secondary flow on the laminar dispersion of an injected substance in a curved tube

1970 ◽  
Vol 315 (1520) ◽  
pp. 99-113 ◽  
Keyword(s):  
Secondary Flow ◽  
Cross Section ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Flux Ratio ◽  
Original Method ◽  
Asymptotic Solutions ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Mean Velocity

The numerical solution by McConalogue & Srivastava (1968) of Dean’s simplified Navier–Stokes equations for the laminar flow of an inviscid fluid through a tube of circular cross-section of radius a , coiled in a circular arc of radius L , and valid for k in the range (16.6, 77.1), where k = Re √( a / L ), Re the Reynolds number, is compared with experiment, correlated to the asymptotic solutions for k > 100, and extended to study the convective axial dis­persion of a substance injected into the tube. The variation of the calculated flux ratio agrees closely with White’s (1929) measurements of the inverse quantity over the same range, and the field patterns for the upper end of the range establish the validity of the two basic assumptions of the asymptotic solutions. The original method is extended to calculate the mean axial velocity of a typical particle of the fluid and to present the statis­tical distribution of mean velocity over the particles of a substance injected as a thin disk uniformly over the cross section of the tube. These distributions are used to display the varia­tion with k of the shape of indicator concentration-time curves. The expected effect of secondary flow, in producing a more uniform distribution of velocity over the fluid than in Poiseuille flow, is evident.

scholarly journals On the cooling and evaporative powers of the atmosphere, as determined by the kata-thermometer

1919 ◽  
Vol 90 (632) ◽  
pp. 438-447 ◽  
Keyword(s):  
Body Temperature ◽  
Skin Temperature ◽  
Cross Section ◽  
Cooling Power ◽  
Mean Velocity ◽  
Cross Section Area ◽  
Section Area ◽  
Order Of Magnitude ◽  
The Mean ◽  
A Current

In a paper published in ‘Phil. Trans.’ (B, vol. 207, 1916, pp. 183-220) by L. Hill, O. W. Griffiths, and M. Flack, there was detailed the theory and use of an instrument, the kata-thermometer, a large-bulbed alcohol thermometer, for determining the cooling power of the atmosphere on a surface at body temperature. A formula H/ θ = 0⋅27 + 0⋅36 √V, where H = heat lost in mille-calories per square centimetre per second, θ = (36⋅5— t )°C., where t = temperature of enclosure, and V = velocity of air current in metres per second, was obtained for the loss of heat of the dry kata-thermometer in a current of air; 36⋅5° C. was chosen as the skin temperature. This is a variable, and only reaches that figure in warm atmospheres. The constant 0⋅36 in the above formula was determined from experiments which were carried out with the apparatus then available in a tube of which the cross-section area was of the same order of magnitude as that of the kata. Therefore, in calculating the velocity of the air current i.e ., the mean velocity of the air striking the kata, the area of cross-section of the kata was subtracted from that of the tube.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

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