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.

Prediction of Heat Transfer in a Rotating Cavity With a Radial Outflow

1991 ◽  
Vol 113 (1) ◽  
pp. 115-122 ◽  
Author(s):  
C. L. Ong ◽  
J. M. Owen
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Eddy Viscosity Model ◽  
Rotating Cavity ◽  
Wide Range ◽  
Turbine Disks ◽  
Radial Outflow ◽  
Cooling Air

Solutions of the differential boundary-layer equations, using the Keller-box scheme and the Cebeci-Smith eddy-viscosity model for turbulent flow, have been used to predict the Nusselt numbers on the disks of a heated rotating cavity with a radial outflow of cooling air. Computed Nusselt numbers were in satisfactory agreement with analytical solutions of the elliptic equations for laminar flow and with solutions of the integral equations for turbulent flow. For a wide range of flow rates, rotational speeds, and disk-temperature profiles, the computed Nusselt numbers were in mainly good agreement with measurements obtained from an air-cooled rotating cavity. It is concluded that the boundary-layer equations should provide solutions accurate enough for application to air-cooled gas turbine disks.

Prediction of Heat Transfer in a Rotating Cavity With a Radial Outflow

1989 ◽  
Author(s):  
C. L. Ong ◽  
J. M. Owen
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Eddy Viscosity Model ◽  
Box Scheme ◽  
Rotating Cavity ◽  
Wide Range ◽  
Radial Outflow ◽  
Cooling Air

Solutions of the differential boundary-layer equations, using the Keller-box scheme and the Cebeci-Smith eddy-viscosity model for turbulent flow, have been used to predict the Nusselt numbers on the discs of a heated rotating cavity with a radial outflow of cooling air. Computed Nusselt numbers were in satisfactory agreement with analytical solutions of the elliptic equations for laminar flow and with solutions of the integral equations for turbulent flow. For a wide range of flow rates, rotational speeds and disc-temperature profiles, the computed Nusselt numbers were in mainly good agreement with measurements obtained from an air-cooled rotating cavity. It is concluded that the boundary-layer equations should provide solutions accurate enough for application to air-cooled gas-turbine discs.

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.

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.

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.

Buoyancy effects on large-scale motions in convective atmospheric boundary layers: implications for modulation of near-wall processes

2018 ◽  
Vol 856 ◽  
pp. 135-168 ◽  
Author(s):  
S. T. Salesky ◽  
W. Anderson
Keyword(s):  
Boundary Layer ◽  
Velocity Field ◽  
Boundary Layers ◽  
Vertical Velocity ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Streamwise Velocity ◽  
Small Scale ◽  
Convective Conditions ◽  
Wide Range

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

Optimal energy growth in stably stratified turbulent Couette flow

2021 ◽  
Author(s):  
Grigory Zasko ◽  
Andrey Glazunov ◽  
Evgeny Mortikov ◽  
Yuri Nechepurenko ◽  
Pavel Perezhogin
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Couette Flow ◽  
Large Scale ◽  
Thin Layers ◽  
Plane Couette Flow ◽  
Turbulent Layer ◽  
Wide Range ◽  
The Mean ◽  
Optimal Disturbances

<p>In this report, we will try to explain the emergence of large-scale organized structures in stably stratified turbulent flows using optimal disturbances of the mean turbulent flow. These structures have been recently obtained in numerical simulations of turbulent stably stratified flows [1] (Ekman layer, LES) and [2] (plane Couette flow, DNS and LES) and indirectly confirmed by field measurements in the stable boundary layer of the atmosphere [1, 2]. In instantaneous temperature fields they manifest themselves as irregular inclined thin layers with large gradients (fronts), spaced from each other by distances comparable to the height of the entire turbulent layer, and separated by regions with weak stratification.</p><p>Optimal disturbances of a stably stratified turbulent plane Couette flow are investigated in a wide range of Reynolds and Richardson numbers. These disturbances were computed based on a simplified linearized system of equations in which turbulent Reynolds stresses and heat fluxes were approximated by isotropic viscosity and diffusion with coefficients obtained from DNS results. It was shown [3] that the spatial scales and configurations of the inclined structures extracted from DNS data coincide with the ones obtained from optimal disturbances of the mean turbulent flow.</p><p>Critical value of the stability parameter is found starting from which the optimal disturbances resemble inclined structures. The physical mechanisms that determine the evolution, energetics and spatial configuration of these optimal disturbances are discussed. The effects due to the presence of stable stratification are highlighted.</p><p>Numerical experiments with optimal disturbances were supported by the RSF (grant No. 17-71-20149). Direct numerical simulation of stratified turbulent Couette flow was supported by the RFBR (grant No. 20-05-00776).</p><p>References:</p><p>[1] P.P. Sullivan, J.C. Weil, E.G. Patton, H.J. Jonker, D.V. Mironov. Turbulent winds and temperature fronts in large-eddy simulations of the stable atmospheric boundary layer // J. Atmos. Sci., 2016, V. 73, P. 1815-1840.</p><p>[2] A.V. Glazunov, E.V. Mortikov, K.V. Barskov, E.V. Kadantsev, S.S. Zilitinkevich. Layered structure of stably stratified turbulent shear flows // Izv. Atmos. Ocean. Phys., 2019, V. 55, P. 312–323.</p><p>[3] G.V. Zasko, A.V. Glazunov, E.V. Mortikov, Yu.M. Nechepurenko. Large-scale structures in stratified turbulent Couette flow and optimal disturbances // Russ. J. Num. Anal. Math. Model., 2010, V. 35, P. 35–53.</p>

A Method for the Calculation of 3D Boundary Layers on Practical Wing Configurations

1981 ◽  
Vol 103 (1) ◽  
pp. 104-111 ◽  
Author(s):  
J. P. F. Lindhout ◽  
G. Moek ◽  
E. De Boer ◽  
B. Van Den Berg
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Eddy Viscosity ◽  
Separated Flow ◽  
Laminar Boundary Layers ◽  
Eddy Viscosity Model ◽  
Airplane Wing ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

This paper gives a description of a calculation method for 3D turbulent and laminar boundary layers on nondevelopable surfaces. A simple eddy viscosity model is incorporated in the method. Special attention is given to the organization of the computations to circumvent as much as possible stepsize limitations. The method is also able to proceed the computation around separated flow regions. The method has been applied to the laminar boundary layer flow over a flat plate with attached cylinder, and to a turbulent boundary layer flow over an airplane wing.

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.

Response of supersonic turbulent boundary layers to local and global mechanical distortions

2009 ◽  
Vol 630 ◽  
pp. 225-265 ◽  
Author(s):  
ISAAC W. EKOTO ◽  
RODNEY D. W. BOWERSOX ◽  
THOMAS BEUTNER ◽  
LARRY GOSS
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Flow Structure ◽  
Small Scale ◽  
Pressure Gradients ◽  
Local Surface ◽  
Turbulence Flow ◽  
Turbulent Flow Structure ◽  
The Mean

The response of the mean and turbulent flow structure of a supersonic high-Reynolds-number turbulent boundary layer flow subjected to local and global mechanical distortions was experimentally examined. Local disturbances were introduced via small-scale wall patterns, and global distortions were induced through streamline curvature-driven pressure gradients. Local surface topologies included k-type diamond and d-type square elements; a smooth wall was examined for comparison purposes. Three global distortions were studied with each of the three surface topologies. Measurements included planar contours of the mean and fluctuating velocity via particle image velocimetry, Pitot pressure profiles, pressure sensitive paint and Schlieren photography. The velocity data were acquired with sufficient resolution to characterize the mean and turbulent flow structure and to examine interactions between the local surface roughness distortions and the imposed pressure gradients on the turbulence production. A strong response to both the local and global distortions was observed with the diamond elements, where the effect of the elements extended into the outer regions of the boundary layer. It was shown that the primary cause for the observed response was the result of local shock and expansion waves modifying the turbulence structure and production. By contrast, the square elements showed a less pronounced response to local flow distortions as the waves were significantly weaker. However, the frictional losses were higher for the blunter square roughness elements. Detailed quantitative characterizations of the turbulence flow structure and the associated production mechanisms are described herein. These experiments demonstrate fundamental differences between supersonic and subsonic rough-wall flows, and the new understanding of the underlying mechanisms provides a scientific basis to systematically modify the mean and turbulence flow structure all the way across supersonic boundary layers.

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