Flow Between Contra-Rotating Discs

1993 ◽  
Author(s):  
Xiaopeng Gan ◽  
Muhsin Kilic ◽  
J. Michael Owen
Keyword(s):  
Turbulent Flow ◽  
Shear Layer ◽  
Boundary Layers ◽  
Turbulence Model ◽  
Reynolds Numbers ◽  
The Core ◽  
Rotating Discs ◽  
Wide Range ◽  
Type Flow ◽  
Radial Outflow

The paper describes a combined experimental and computational study of laminar and turbulent flow between contra-rotating discs. Laminar computations produce Batchelor-type flow: radial outflow occurs in boundary layers on the discs and inflow is confined to a thin shear layer in the mid-plane; between the boundary layers and the shear layer, two contra-rotating cores of fluid are formed. Turbulent computations (using a low-Reynolds-number k-ε turbulence model) and LDA measurements provide no evidence for Batchelor-type flow, even for rotational Reynolds numbers as low as 2.2 × 104. Whilst separate boundary layers are formed on the discs, radial inflow occurs in a single interior core that extends between the two boundary layers; in the core, rotational effects are weak. Although the flow in the core was always found to be turbulent, the flow in the boundary layers could remain laminar for rotational Reynolds numbers up to 1.2 × 105. For the case of a superposed outflow, there is a source region in which the radial component of velocity is everywhere positive; radially outward of this region, the flow is similar to that described above. Although the turbulence model exhibited premature transition from laminar to turbulent flow in the boundary layers, agreement between the computed and measured radial and tangential components of velocity was mainly good over a wide range of nondimensional flow rates and rotational Reynolds numbers.

Flow Between Contrarotating Disks

1995 ◽  
Vol 117 (2) ◽  
pp. 298-305 ◽  
Author(s):  
X. Gan ◽  
M. Kilic ◽  
J. M. Owen
Keyword(s):  
Turbulent Flow ◽  
Shear Layer ◽  
Boundary Layers ◽  
Turbulence Model ◽  
Computational Study ◽  
Reynolds Numbers ◽  
The Core ◽  
Wide Range ◽  
Type Flow ◽  
Radial Outflow

The paper describes a combined experimental and computational study of laminar and turbulent flow between contrarotating disks. Laminar computations produce Batchelor-type flow: Radial outflow occurs in boundary layers on the disks and inflow is confined to a thin shear layer in the midplane; between the boundary layers and the shear layer, two contrarotating cores of fluid are formed. Turbulent computations (using a low-Reynolds-number k–ε turbulence model) and LDA measurements provide no evidence for Batchelor-type flow, even for rotational Reynolds numbers as low as 2.2 × 104. While separate boundary layers are formed on the disks, radial inflow occurs in a single interior core that extends between the two boundary layers; in the core, rotational effects are weak. Although the flow in the core was always found to be turbulent, the flow in the boundary layers could remain laminar for rotational Reynolds numbers up to 1.2 × 105. For the case of a superposed outflow, there is a source region in which the radial component of velocity is everywhere positive; radially outward of this region, the flow is similar to that described above. Although the turbulence model exhibited premature transition from laminar to turbulent flow in the boundary layers, agreement between the computed and measured radial and tangential components of velocity was mainly good over a wide range of nondimensional flow rates and rotational Reynolds numbers.

scholarly journals Flow in a Rotating Cavity With a Peripheral Inlet and Outlet of Cooling Air

1996 ◽  
Author(s):  
Xiaopeng Gan ◽  
Iraj Mirzaee ◽  
J. Michael Owen ◽  
D. Andrew S. Rees ◽  
Michael Wilson
Keyword(s):  
Boundary Layers ◽  
Turbulence Model ◽  
Laser Doppler Anemometry ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Recirculation Region ◽  
Rotating Disc ◽  
The Core ◽  
Radial Outflow ◽  
Cooling Air

In some engines, corotating gas–turbine discs are cooled by air introduced at the periphery of the system. The air enters through holes in a stationary peripheral casing and leaves through the rim seals between the casing and the discs. This paper describes a combined computational and experimental study of such a system for a range of flowrates and for rotational Reynolds numbers of up to Reϕ = 1.5 × 106. Computations are made using an axisymmetric elliptic solver, incorporating the Launder–Sharma low–Reynolds–number k–ε turbulence model, and velocity measurements are obtained using laser–Doppler anemometry. The stationary peripheral casing creates a recirculation region: there is radial outflow in boundary layers on the discs and inflow in the core between the boundary layers. The radial extent of the recirculation region increases as the flow rate increases and as the rotational speed decreases. In the core, the radial and tangential components of velocity, Vr and Vϕ, are invariant in the axial direction, and the measured values of Vϕ conform to a Rankine–vortex flow. The agreement between the computed and measured velocities is not as good as that found for other rotating–disc systems, and deficiencies in the turbulence model are believed to be responsible.

Turbulent Flow Between Two Discs Contra-Rotating at Differential Speeds

1994 ◽  
Author(s):  
Muhsin Kilic ◽  
Xiaopeng Gan ◽  
J. Michael Owen
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Axial Flow ◽  
Radial Component ◽  
Velocity Measurements ◽  
Rotating Discs ◽  
Type Flow ◽  
Radial Outflow

This paper describes a combined computational and experimental study of the turbulent flow between two contra-rotating discs for −1 ≤ Γ ≤ 0 and Reφ ≃ 1.2 × 106, where Γ is the ratio of the speed of the slower disc to that of the faster one and Reφ is the rotational Reynolds number. The computations were conducted using an axisymmetric elliptic multigrid solver and a low-Reynolds-number k-ε turbulence model. Velocity measurements were made using LDA at nondimensional radius ratios of 0.6 ≤ x ≤ 0.85. For Γ = 0, the rotor-stator case, Batchelor-type flow occurs: there is radial outflow and inflow in boundary layers on the rotor and stator, respectively, between which is an inviscid rotating core of fluid where the radial component of velocity is zero and there is an axial flow from stator to rotor. For Γ = −1, anti-symmetrical contra-rotating discs, Stewartson-type flow occurs with radial outflow in boundary layers on both discs and inflow in the viscid nonrotating core. At intermediate values of Γ, two cells separated by a streamline that stagnates on the slower disc are formed: Batchelor-type flow and Stewartson-type flow occur radially outward and inward, respectively, of the stagnation streamline. Agreement between the computed and measured velocities is mainly very good, and no evidence was found of nonaxisymmetric or unsteady flow.

Turbulent Flow Between Two Disks Contrarotating at Different Speeds

1996 ◽  
Vol 118 (2) ◽  
pp. 408-413 ◽  
Author(s):  
M. Kilic ◽  
X. Gan ◽  
J. M. Owen
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Unsteady Flow ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Axial Flow ◽  
Radial Component ◽  
Velocity Measurements ◽  
Type Flow ◽  
Radial Outflow

This paper describes a combined computational and experimental study of the turbulent flow between two contrarotating disks for −1 ≤ Γ ≤ 0 and Reφ ≈ 1.2 × 106, where Γ is the ratio of the speed of the slower disk to that of the faster one and Reφ is the rotational Reynolds number. The computations were conducted using an axisymmetric elliptic multigrid solver and a low-Reynolds-number k–ε turbulence model. Velocity measurements were made using LDA at nondimensional radius ratios of 0.6 ≤ x ≤ 0.85. For Γ = 0, the rotor–stator case, Batchelor-type flow occurs: There is radial outflow and inflow in boundary layers on the rotor and stator, respectively, between which is an inviscid rotating core of fluid where the radial component of velocity is zero and there is an axial flow from stator to rotor. For Γ = −1, antisymmetric contrarotating disks, Stewartson-type flow occurs with radial outflow in boundary layers on both disks and inflow in the viscid nonrotating core. At intermediate values of Γ, two cells separated by a streamline that stagnates on the slower disk are formed: Batchelor-type flow and Stewartson-type flow occur radially outward and inward, respectively, of the stagnation streamline. Agreement between the computed and measured velocities is mainly very good, and no evidence was found of nonaxisymmetric or unsteady flow.

Numerical Prediction of Turbulent Flow in Rotating Cavities

1988 ◽  
Vol 110 (2) ◽  
pp. 202-211 ◽  
Author(s):  
A. P. Morse
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Predictive Accuracy ◽  
Turbulent Transport ◽  
Reynolds Numbers ◽  
Spreading Rate ◽  
Flow Conditions ◽  
Wide Range ◽  
Ekman Layers ◽  
Radial Outflow

Predictions of the isothermal, incompressible flow in the cavity formed between two corotating plane disks and a peripheral shroud have been obtained using an elliptic calculation procedure and a low turbulence Reynolds number k–ε model for the estimation of turbulent transport. Both radial inflow and outflow are investigated for a wide range of flow conditions involving rotational Reynolds numbers up to ∼106. Although predictive accuracy is generally good, the computed flow in the Ekman layers for radial outflow often displays a retarded spreading rate and a tendency to laminarize under conditions that are known from experiment to produce turbulent flow.

Computation of Flow Between Two Discs Rotating at Different Speeds

2002 ◽  
Author(s):  
Muhsin Kilic ◽  
J. Michael Owen
Keyword(s):  
Boundary Layers ◽  
Gas Turbines ◽  
Reynolds Numbers ◽  
Internal Cooling ◽  
Measured Velocity ◽  
Rotating Discs ◽  
Layer Flow ◽  
Radial Outflow ◽  
Cooling Air ◽  
Good Agreement

Discs rotating at different speeds are found in the internal cooling-air systems of most gas turbines. Defining Γ as the ratio of the rotational speed of the slower disc to that of the faster one then Γ = −1, 0 and +1 represents the three important cases of contra-rotating discs, rotor-stator systems and co-rotating discs, respectively. A finite-volume, axisymmetric, elliptic, multigrid solver, employing a low-Reynolds-number k-ε turbulence model, is used for the fluid-dynamics computations in these systems. The complete Γ region, −1 ≤ Γ ≤ +1, is considered for rotational Reynolds numbers of up to Reφ = 1.25 × 106, and the effect of a radial outflow of cooling air is also included for nondimensional flow rates of up to Cw = 9720. As Γ → −1, Stewartson-flow occurs with radial outflow in boundary layers on both discs and between which is a core of nonrotating fluid. For Γ ≈ 0, Batchelor-flow occurs, with radial outflow in the boundary layer on the faster disc, inflow on the slower one, and between which is a core of rotating fluid. As Γ → +1, Ekman-layer flow dominates with nonentraining boundary layers on both discs and a rotating core between. Where available, measured velocity distributions are in good agreement with the computed values.

Boundary-Layer Flows in Rotating Cavities

1989 ◽  
Vol 111 (3) ◽  
pp. 341-348 ◽  
Author(s):  
C. L. Ong ◽  
J. M. Owen
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Reverse Flow ◽  
Source Region ◽  
Linear Equations ◽  
Inviscid Fluid ◽  
Eddy Viscosity Model ◽  
Wide Range ◽  
Radial Outflow

A rotating cylindrical cavity with a radial outflow of fluid provides a simple model of the flow between two corotating air-cooled gas-turbine disks. The flow structure comprises a source region near the axis of rotation, boundary layers on each disk, a sink layer on the peripheral shroud, and an interior core of rotating inviscid fluid between the boundary layers. In the source region, the boundary layers entrain fluid; outside this region, nonentraining Ekman-type layers are formed on the disks. In this paper, the differential boundary-layer equations are solved to predict the velocity distribution inside the entraining and nonentraining boundary layers and in the inviscid core. The equations are discretized using the Keller-box scheme, and the Cebeci–Smith eddy-viscosity model is used for the turbulent-flow case. Special problems associated with reverse flow in the nonentraining Ekman-type layers are successfully overcome. Solutions are obtained, for both laminar and turbulent flow, for the “linear equations” (where nonlinear inertial terms are neglected) and for the full nonlinear equations. These solutions are compared with earlier LDA measurements of the radial and tangential components of velocity made inside a rotating cavity with a radial outflow of air. Good agreement between the computations and the experimental data is achieved for a wide range of flow rates and rotational speeds.

scholarly journals Sound propagation in a lined nozzle with shear and bias flows

2018 ◽  
Vol 18 (1) ◽  
pp. 3-48
Author(s):  
LMBC Campos ◽  
C Legendre
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Boundary Layers ◽  
Lower Boundary ◽  
Cross Flow ◽  
Core Flow ◽  
The Core ◽  
Wide Range ◽  
Bias Flow ◽  
Number Formula

In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an “acoustic triple deck” consisting of third-order non-sinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 × 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acoustic-shear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number [Formula: see text] relative to the mean flow Mach number [Formula: see text] can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a–c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i–iv) of the problem.

Computation of Heat Transfer in Rotating Cavities Using a Two-Equation Model of Turbulence

1990 ◽  
Author(s):  
A. P. Morse ◽  
C. L. Ong
Keyword(s):  
Heat Transfer ◽  
Turbulence Model ◽  
Radial Direction ◽  
Reynolds Numbers ◽  
Systematic Errors ◽  
Equation Model ◽  
Sufficient Accuracy ◽  
Nusselt Numbers ◽  
Radial Outflow ◽  
Cooling Air

The paper presents finite-difference predictions for the convective heat transfer in symmetrically-heated rotating cavities subjected to a radial outflow of cooling air. An elliptic calculation procedure has been used, with the turbulent fluxes estimated by means of a low Reynolds number k-ε model and the familiar ‘turbulence Prandtl number’ concept. The predictions extend to rotational Reynolds numbers of 3.7 × 106 and encompass cases where the disc temperatures may be increasing, constant or decreasing in the radial direction. It is found that the turbulence model leads to predictions of the local and average Nusselt numbers for both discs which are generally within ± 10% of the values from published experimental data, although there appear to be larger systematic errors for the upstream disc than for the downstream disc. It is concluded that the calculations are of sufficient accuracy for engineering design purposes, but that improvements could be brought about by further optimization of the turbulence model.

Hot-wire spatial resolution issues in wall-bounded turbulence

2009 ◽  
Vol 635 ◽  
pp. 103-136 ◽  
Author(s):  
N. HUTCHINS ◽  
T. B. NICKELS ◽  
I. MARUSIC ◽  
M. S. CHONG
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Spatial Resolution ◽  
Reynolds Numbers ◽  
Energy Spectra ◽  
Small Scale ◽  
Wire Length ◽  
Hot Wire ◽  
Wide Range ◽  
Near Wall

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

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