scholarly journals Three-Dimensional Separations in Axial Compressors

2005 ◽  
Vol 127 (2) ◽  
pp. 331-339 ◽  
Author(s):  
Semiu A. Gbadebo ◽  
Nicholas A. Cumpsty ◽  
Tom P. Hynes
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Compressor Blades ◽  
Navier Stokes Equations ◽  
Axial Compressors ◽  
Computational Fluid Dynamics Cfd ◽  
Limiting Streamlines

Flow separations in the corner regions of blade passages are common. The separations are three dimensional and have quite different properties from the two-dimensional separations that are considered in elementary courses of fluid mechanics. In particular, the consequences for the flow may be less severe than the two-dimensional separation. This paper describes the nature of three-dimensional (3D) separation and addresses the way in which topological rules, based on a linear treatment of the Navier-Stokes equations, can predict properties of the limiting streamlines, including the singularities which form. The paper shows measurements of the flow field in a linear cascade of compressor blades and compares these to the results of 3D computational fluid dynamics (CFD). For corners without tip clearance, the presence of three-dimensional separation appears to be universal, and the challenge for the designer is to limit the loss and blockage produced. The CFD appears capable of predicting this.

scholarly journals Three-Dimensional Separations in Axial Compressors

2004 ◽  
Author(s):  
Semiu A. Gbadebo ◽  
Nicholas A. Cumpsty ◽  
Tom P. Hynes
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Compressor Blades ◽  
Navier Stokes Equations ◽  
Linear Cascade ◽  
Axial Compressors ◽  
Limiting Streamlines

Flow separations in the corner regions of blade passages are common. The separations are three dimensional and have quite different properties from the two-dimensional separations that are considered in elementary courses of fluid mechanics. In particular the consequences for the flow may be less severe than the two-dimensional separation. This paper describes the nature of three-dimensional separation and addresses the way in which topological rules, based on a linear treatment of the Navier-Stokes equations, can predict properties of the limiting streamlines, including the singularities which form. The paper shows measurements of the flow field in a linear cascade of compressor blades and compares these with the results of 3D CFD. For corners without tip clearance, the presence of three-dimensional separation appears to be universal and the challenge for the designer is to limit the loss and blockage produced. The CFD appears capable of predicting this.

Numerical Investigation of the Effect of Balancing-Hole on the Axial Force of a Partial Emission Pump

2014 ◽  
Author(s):  
Zhang Lisheng ◽  
Jiang Jin ◽  
Xiao Zhihuai ◽  
Li Yanhui
Keyword(s):  
Axial Force ◽  
Stokes Equations ◽  
Dominant Role ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Design Parameters ◽  
Navier Stokes Equations ◽  
Computational Fluid Dynamics Cfd ◽  
The Cost

In this paper numerical simulations were conducted to analyze the effects of design parameters and distribution of balancing-hole on the axial-force of a partial emission pump. The studied pump is a single stage pump with a Barske style impeller. Based on the original impeller, we designed 7 pumps with different balancing-hole diameters and the partial emission pump equipped with different impellers were simulated employing the commercial computational fluid dynamics (CFD) software Fluent 12.1 to solve the Navier-Stokes equations for three-dimensional steady flow. A sensitivity analysis of the numerical model was performed with the purpose of balancing the contradiction of numerical accuracy and the cost of calculation. The results showed that, with increasing of the capacity, the axial force varies little. The diameter of the inner balancing-hole plays a dominant role of reducing axial-force of partial emission pump, the axial-force decreases with increasing of inner balancing-hole diameter on the whole range of operation, the axial-force of impeller without inner balancing-hole is approximately 3 times larger than that of impeller with inner balancing-hole. While the diameter of outer balancing-hole has a reverse effects compared with that of inner balancing-hole. With increasing of outer balancing-hole, the axial force increases accordingly.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

Effect of Blade Numbers on Pressure Drop of Axial Cyclone Separators by CFD

2011 ◽  
Vol 55-57 ◽  
pp. 343-347 ◽  
Author(s):  
Yi Gang Luan ◽  
Hai Ou Sun
Keyword(s):  
Pressure Drop ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Three Dimensional Model ◽  
Navier Stokes Equations ◽  
Pressure Drops ◽  
Computational Fluid Dynamics Cfd ◽  
Cfd Method ◽  
Resistance Performance

In this article, computational fluid dynamics(CFD) method is used to predict the effect of blade numbers on the pressure drop of axial cyclone separators. A three-dimensional model is built to acquire the resistance of axial cyclone separators with different blade numbers. The flow field inside cyclone separators is calculated using 3D Reynolds-averaged Navier-Stokes equations. And turbulence model is used to simulate the Reynold stress. Also pressure drop of cyclone separators with different blade numbers is expressed as a function of different inlet velocities. At the same inlet velocity with increasing the blade numbers, pressure drops of cyclones reduce greatly. And changing the blade number of cyclone separator is an effective method to improve its resistance performance.

Three-dimensional impulsive vortex formation from slender orifices

2011 ◽  
Vol 666 ◽  
pp. 506-520 ◽  
Author(s):  
F. DOMENICHINI
Keyword(s):  
Stokes Equations ◽  
Intermediate Phase ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Vortex Ring Formation ◽  
Long Time ◽  
Definition Of

The vortex formation behind an orifice is a widely investigated phenomenon, which has been recently studied in several problems of biological relevance. In the case of a circular opening, several works in the literature have shown the existence of a limiting process for vortex ring formation that leads to the concept of critical formation time. In the different geometric arrangement of a planar flow, which corresponds to an opening with straight edges, it has been recently outlined that such a concept does not apply. This discrepancy opens the question about the presence of limiting conditions when apertures with irregular shape are considered. In this paper, the three-dimensional vortex formation due to the impulsively started flow through slender openings is studied with the numerical solution of the Navier–Stokes equations, at values of the Reynolds number that allow the comparison with previous two-dimensional findings. The analysis of the three-dimensional results reveals the two-dimensional nature of the early vortex formation phase. During an intermediate phase, the flow evolution appears to be driven by the local curvature of the orifice edge, and the time scale of the phenomena exhibits a surprisingly good agreement with those found in axisymmetric problems with the same curvature. The long-time evolution shows the complete development of the three-dimensional vorticity dynamics, which does not allow the definition of further unifying concepts.

Three-Dimensional Analysis of Turbine Rotor Flow Including Tip Clearance

1993 ◽  
Author(s):  
R. Heider ◽  
J. M. Duboue ◽  
B. Petot ◽  
G. Billonnet ◽  
V. Couaillier ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Turbine Rotor ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbine Rotor Blade ◽  
Calculation Results ◽  
Rotor Flow

A 3D Navier-Stokes investigation of a high pressure turbine rotor blade including tip clearance effects is presented. The 3D Navier-Stokes code developed at ONERA solves the three-dimensional unsteady set of mass-averaged Navier-Stokes equations by the finite volume technique. A one step Lax-Wendroff type scheme is used in a rotating frame of reference. An implicit residual smoothing technique has been implemented, which accelerates the convergence towards the steady state. A mixing length model adapted to 3D configurations is used. The turbine rotor flow is calculated at transonic operating conditions. The tip clearance effect is taken into account. The gap region is discretized using more than 55,000 points within a multi-domain approach. The solution accounts for the relative motion of the blade and casing surfaces. The total mesh is composed of five sub-domains and counts 710,000 discretization points. The effect of the tip clearance on the main flow is demonstrated. The calculation results are compared to a 3D inviscid calculation, without tip clearance.

Solution of three-dimensional incompressible flow problems

1977 ◽  
Vol 82 (2) ◽  
pp. 309-319 ◽  
Author(s):  
S. M. Richardson ◽  
A. R. H. Cornish
Keyword(s):  
Stream Function ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Vector Potentials

A method for solving quite general three-dimensional incompressible flow problems, in particular those described by the Navier–Stokes equations, is presented. The essence of the method is the expression of the velocity in terms of scalar and vector potentials, which are the three-dimensional generalizations of the two-dimensional stream function, and which ensure that the equation of continuity is satisfied automatically. Although the method is not new, a correct but simple and unambiguous procedure for using it has not been presented before.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

Numerical study of ribbon-induced transition in Blasius flow

1987 ◽  
Vol 178 ◽  
pp. 345-365 ◽  
Author(s):  
Philippe R. Spalart ◽  
Kyung-Soo Yang
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Random Disturbances ◽  
Rapid Amplification ◽  
Dimensional Wave

The early three-dimensional stages of transition in the Blasius boundary layer are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and low-amplitude three-dimensional random disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wavenumber increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. The agreement with experimental and theoretical results is discussed.

Numerical investigation of the interaction of the Klebanoff-mode with a Tollmien–Schlichting wave

2002 ◽  
Vol 450 ◽  
pp. 1-33 ◽  
Author(s):  
HERMANN F. FASEL
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Free Stream Turbulence ◽  
Turbulent Transition ◽  
Tollmien Schlichting

Direct numerical simulations (DNS) of the Navier–Stokes equations are used to investigate the role of the Klebanoff-mode in laminar–turbulent transition in a flatplate boundary layer. To model the effects of free-stream turbulence, volume forces are used to generate low-frequency streamwise vortices outside the boundary layer. A suction/blowing slot at the wall is used to generate a two-dimensional Tollmien–Schlichting (TS) wave inside the boundary layer. The characteristics of the fluctuations inside the boundary layer agree very well with those measured in experiments. It is shown how the interaction of the Klebanoff-mode with the two-dimensional TS-wave leads to the formation of three-dimensional TS-wavepackets. When the disturbance amplitudes reach a critical level, a fundamental resonance-type secondary instability causes the breakdown of the TS-wavepackets into turbulent spots.

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