A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Axisymmetric Inertial Oscillations in Transient Rotating Flows in a Cylinder

1997 ◽  
Vol 119 (2) ◽  
pp. 390-396
Author(s):  
Jae Won Kim ◽  
Jae Min Hyun
Keyword(s):  
Large Time ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Experimental Studies ◽  
Numerical Results ◽  
Navier Stokes ◽  
Inertial Oscillations ◽  
Time Duration ◽  
Navier Stokes Equations

A numerical study is made of axisymmetric inertial oscillations in a fluid-filled cylinder. The entire cylinder undergoes a spin-up process from rest with an impulsively started rotation rate Ω(t) = Ω0 + εω cos(ωt). Numerical solutions are obtained to the axisymmetric, time-dependent Navier-Stokes equations. Identification of the inertial oscillations is made by inspecting the evolution of the pressure difference between two pre-set points on the central axis, Cp. In the limit of large time, the inertial frequency thus determined is in close agreement with the results of the classical inviscid theory for solid-body rotation. As in previous experimental studies, the t* − (Ω0/ω) plots are constructed for inertial oscillations, where t* indicates the time duration until the maximum Cp is detected. These detailed numerical results are in broad agreement with the prior experimental data. Flow intensifications under the resonance conditions are illustrated based on the numerical results. Depictions are made of the increase in the amplitude of oscillating part of the total angular momentum under the resonance conditions. Also, the patterns of t* − (Ω0/ω) curves are displayed for different inertial frequency modes.

scholarly journals Leakage Effects in the Rotor Tip-Clearance Region of a Multistage Axial Compressor: Part 1 — Innovative Experiments

1998 ◽  
Author(s):  
P. C. Ivey ◽  
M. Swoboda
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Measurement Techniques ◽  
Axial Compressor ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tip Clearance Flow ◽  
Clearance Flow

This paper describes work conducted as part of an experimental and numerical study of leakage effects by numerous Research and Industrial partners. For clarity it is presented in two parts. Part 1 presents measurements of tip-clearance flow for a 3rd stage rotor embedded in a four stage low-speed research compressor. The measurements are innovative and comprise measurements in the rotor relative frame of reference and 3D Laser time-of-flight Anemometry. Both techniques are relevant for improved understanding of multistage compressor flow dynamics and consequently, validated multistage CFD simulations. In part 2 of this paper (see Politis et al 1997b) it is shown that downstream of the rotor passage the location and size of a tip-clearance vortex, identified from both independent measurement techniques in Part 1, is in good agreement with 3D solutions of the Navier-Stokes equations modelling this compressor. These 3D numerical solutions reveal the tip-clearance flow structure using a multiblock grid technique.

A Numerical Study of the Influence of Disc Geometry on the Flow and Heat Transfer in a Rotating Cavity

1990 ◽  
Author(s):  
B. L. Lapworth ◽  
J. W. Chew
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Model Calculations ◽  
Flow And Heat Transfer ◽  
Rotating Cavity ◽  
Radial Outflow

Numerical solutions of the Reynolds-averaged Navier-Stokes equations have been used to model the influence of cobs and a bolt cover on the flow and heat transfer in a rotating cavity with an imposed radial outflow of air. Axisymmetric turbulent flow is assumed using a mixing length turbulence model. Calculations for the non-plane discs are compared with plane disc calculations and also with the available experimental data. The calculated flow structures show good agreement with the experimentally observed trends. For the cobbed and plane discs, Nusselt numbers are calculated for a combination of flow rates and rotational speeds; these show some discrepancies with the experiments, although the calculations exhibit the more consistent trend. Further calculations indicate that differences in thermal boundary conditions have a greater influence on Nusselt number than differences in disc geometry. The influence of the bolt cover on the heat transfer has also been modelled, although comparative measurements are not available.

Oscillatory flow states in an enclosed cylinder with a rotating endwall

1999 ◽  
Vol 389 ◽  
pp. 101-118 ◽  
Author(s):  
J. L. STEVENS ◽  
J. M. LOPEZ ◽  
B. J. CANTWELL
Keyword(s):  
Oscillatory Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Modulation Frequency ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Multiple Time ◽  
Navier Stokes Equations ◽  
Flow States

A combined experimental and numerical investigation is presented of the multiple oscillatory states that exist in the flows produced in a completely filled, enclosed, circular cylinder driven by the constant rotation of one of its endwalls. The flow in a cylinder of height to radius ratio 2.5 is interrogated experimentally using flow visualization and digitized images to extract quantitative temporal information. Numerical solutions of the axisymmetric Navier–Stokes equations are used to study the same flow over a range of Reynolds numbers where the flow is observed to remain axisymmetric. Three oscillatory states have been identified, two of them are periodic and the third is quasi-periodic with a modulation frequency much smaller than the base frequency. The range of Reynolds numbers for which the quasi-periodic flow exists brackets the switch between the two periodic states. The results from the combined experimental and numerical study agree both qualitatively and quantitatively, providing unambiguous evidence of the existence and robustness of these multiple time-dependent states.

Nonlinear Triple-Deck Studies in Boundary-Layer Receptivity

1990 ◽  
Vol 43 (5S) ◽  
pp. S158-S166 ◽  
Author(s):  
R. J. Bodonyi
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Steady Flow ◽  
Strouhal Number ◽  
Spectral Methods ◽  
Numerical Solutions ◽  
Free Stream ◽  
Numerical Study ◽  
Surface Geometry ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry such as a hump or suction strip has been carried out using both finite difference and spectral methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by linearized disturbance equations. The numerical solutions illustrate the growth or decay of the TS waves generated by the interaction, depending on the value of a scaled Strouhal number.

Transonic aerofoils admitting anomalous behaviour of lift coefficient

2014 ◽  
Vol 118 (1202) ◽  
pp. 425-433 ◽  
Author(s):  
A. Kuzmin ◽  
A. Ryabinin
Keyword(s):  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Lift Coefficient ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Small Perturbations ◽  
Navier Stokes Equations ◽  
Adverse Conditions ◽  
Abrupt Changes

Abstract Transonic flow past a Boeing 737 Outboard aerofoil and Whitcomb one with a defected aileron is studied. The flow simulation is based on the system of Reynolds-averaged Navier-Stokes equations. The numerical study demonstrates the existence of free-stream conditions in which small perturbations produce abrupt changes of the lift coefficient. Also the simulation reveals adverse conditions in which aileron deflections have no influence on the lift.

Numerical prediction of incompressible separation bubbles

1975 ◽  
Vol 69 (4) ◽  
pp. 631-656 ◽  
Author(s):  
W. Roger Briley ◽  
Henry Mcdonald
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Free Stream Turbulence ◽  
Separation Bubbles

A method is presented for performing detailed computations of thin incompressible separation bubbles on smooth surfaces. The analysis consists of finite-difference solutions to the time-dependent boundary-layer or Navier-Stokes equations for the flow in the immediate vicinity of the bubble. The method employs the McDonald-Fish turbulence model, to predict the development of the time-mean flow field, as influenced by the free-stream turbulence level. It also employs a viscous-inviscid interaction model, which accounts for the elliptic interaction between the shear layer and inviscid free stream. The numerical method is based on an alternating-direction implicit scheme for the vorticity equation. It employs transformations, to allow the free-stream boundary to change in time with the shape of the computed shear layer, and to ensure an adequate resolution of the sublayer region. Numerical solutions are presented for transitional bubbles on an NACA 663-018 airfoil at zero angle of incidence with chordal Reynolds numbers of 2·0 × 106 and 1·7 × 106. These have a qualitative behaviour similar to that observed in numerous experiments; they are also in reasonable quantitative agreement with available experimental data. Little difference is found between steady solutions of the boundary-layer and Navier-Stokes equations for these flow conditions. Numerical studies based on mesh refinement suggest that the well-known singularity at separation, which is present in conventional solutions of the steady boundary-layer equations when the free-stream velocity is specified, is effectively removed when viscous-inviscid interaction is allowed to influence the imposed velocity distribution.

A Numerical Study of the Influence of Disk Geometry on the Flow and Heat Transfer in a Rotating Cavity

1992 ◽  
Vol 114 (1) ◽  
pp. 256-263 ◽  
Author(s):  
B. L. Lapworth ◽  
J. W. Chew
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Model Calculations ◽  
Flow And Heat Transfer ◽  
Rotating Cavity ◽  
Radial Outflow

Numerical solutions of the Reynolds-averaged Navier–Stokes equations have been used to model the influence of cobs and a bolt cover on the flow and heat transfer in a rotating cavity with an imposed radial outflow of air. Axisymmetric turbulent flow is assumed using a mixing length turbulence model. Calculations for the non-plane disks are compared with plane disk calculations and also with the available experimental data. The calculated flow structures show good agreement with the experimentally observed trends. For the cobbed and plane disks, Nusselt numbers are calculated for a combination of flow rates and rotational speeds; these show some discrepancies with the experiments, although the calculations exhibit the more consistent trend. Further calculations indicate that differences in thermal boundary conditions have a greater influence on Nusselt number than differences in disk geometry. The influence of the bolt cover on the heat transfer has also been modeled, although comparative measurements are not available.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

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