Two-equation turbulence modeling of an oscillatory boundary layer under steep pressure gradient

2010 ◽  
Vol 37 (4) ◽  
pp. 648-656 ◽  
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Detailed Comparison ◽  
Stream Velocity ◽  
Oscillatory Boundary Layer

A total of seven versions of two-equation turbulence models (four versions of low Reynolds number k–ε model, one k–ω model and two versions of k–ε / k–ω blended models) are tested against the direct numerical simulation (DNS) data of a one-dimensional oscillatory boundary layer with flat crested free-stream velocity that results from a steep pressure gradient. A detailed comparison has been made for cross-stream velocity, turbulent kinetic energy (TKE), Reynolds stress, and ratio of Reynolds stress and turbulent kinetic energy. It is observed that the newer versions of k–ε model perform very well in predicting the velocity, turbulent kinetic energy, and Reynolds stress. The k–ω model and blended models underestimate the peak value of turbulent kinetic energy that may be explained by the Reynolds stress to TKE ratio in the logarithmic zone. The maximum bottom shear stress is well predicted by the k–ε model proposed by Sana et al. and the original k–ω model.

Use of k−ε−γ Model to Predict Intermittency in Turbulent Boundary-Layers

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Rate Of Dissipation ◽  
Dissipation Equation ◽  
Averaged Model

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]

scholarly journals The rough favourable pressure gradient turbulent boundary layer

2009 ◽  
Vol 641 ◽  
pp. 129-155 ◽  
Author(s):  
RAÚL BAYOÁN CAL ◽  
BRIAN BRZEK ◽  
T. GUNNAR JOHANSSON ◽  
LUCIANO CASTILLO
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Rough Surface ◽  
Reynolds Stress ◽  
Friction Velocity ◽  
Free Stream ◽  
Stream Velocity ◽  
The Mean ◽  
Stress Profiles

Laser Doppler anemometry measurements of the mean velocity and Reynolds stresses are carried out for a rough-surface favourable pressure gradient turbulent boundary layer. The experimental data is compared with smooth favourable pressure gradient and rough zero-pressure gradient data. The velocity and Reynolds stress profiles are normalized using various scalings such as the friction velocity and free stream velocity. In the velocity profiles, the effects of roughness are removed when using the friction velocity. The effects of pressure gradient are not absorbed. When using the free stream velocity, the scaling is more effective absorbing the pressure gradient effects. However, the effects of roughness are almost removed, while the effects of pressure gradient are still observed on the outer flow, when the mean deficit velocity profiles are normalized by the U∞ δ∗/δ scaling. Furthermore, when scaled with U2∞, the 〈u2〉 component of the Reynolds stress augments due to the rough surface despite the imposed favourable pressure gradient; when using the friction velocity scaling u∗2, it is dampened. It becomes ‘flatter’ in the inner region mainly due to the rough surface, which destroys the coherent structures of the flow and promotes isotropy. Similarly, the pressure gradient imposed on the flow decreases the magnitude of the Reynolds stress profiles especially on the 〈v2〉 and -〈uv〉 components for the u∗2 or U∞2 scaling. These effects are reflected in the boundary layer parameter δ∗/δ, which increase due to roughness, but decrease due to the favourable pressure gradient. Additionally, the pressure parameter Λ found not to be in equilibrium, describes the development of the turbulent boundary layer, with no influence of the roughness linked to this parameter. These measurements are the first with an extensive number of downstream locations (11). This makes it possible to compute the required x-dependence for the production term and the wall shear stress from the full integrated boundary layer equation. The finding indicates that the skin friction coefficient depends on the favourable pressure gradient condition and surface roughness.

Measurements and Predictions of a Highly Turbulent Flowfield in a Turbine Vane Passage

2000 ◽  
Vol 122 (4) ◽  
pp. 666-676 ◽  
Author(s):  
R. W. Radomsky ◽  
K. A. Thole
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Gas Turbine ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Complex Geometry ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Stress Model ◽  
Mean Flow

As highly turbulent flow passes through downstream airfoil passages in a gas turbine engine, it is subjected to a complex geometry designed to accelerate and turn the flow. This acceleration and streamline curvature subject the turbulent flow to high mean flow strains. This paper presents both experimental measurements and computational predictions for highly turbulent flow as it progresses through a passage of a gas turbine stator vane. Three-component velocity fields at the vane midspan were measured for inlet turbulence levels of 0.6%, 10%, and 19.5%. The turbulent kinetic energy increased through the passage by 130% for the 10% inlet turbulence and, because the dissipation rate was higher for the 19.5% inlet turbulence, the turbulent kinetic energy increased by only 31%. With a mean flow acceleration of five through the passage, the exiting local turbulence levels were 3% and 6% for the respective 10% and 19.5% inlet turbulence levels. Computational RANS predictions were compared with the measurements using four different turbulence models including the k-ε, Renormalization Group (RNG) k-ε, realizable k-ε, and Reynolds stress model. The results indicate that the predictions using the Reynolds stress model most closely agreed with the measurements as compared with the other turbulence models with better agreement for the 10% case than the 19.5% case. [S0098-2202(00)00804-X]

Dynamics of a low Reynolds number turbulent boundary layer

2000 ◽  
Vol 404 ◽  
pp. 87-115 ◽  
Author(s):  
JUAN M. CHACIN ◽  
BRIAN J. CANTWELL
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Velocity Gradient ◽  
Rapid Change ◽  
Joint Probability ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor

The generation of Reynolds stress, turbulent kinetic energy and dissipation in the turbulent boundary layer simulation of Spalart (1988) is studied using the invariants of the velocity gradient tensor. This technique enables the study of the whole range of scales in the flow using a single unified approach. In addition, it also provides a rational basis for relating the flow structure in physical space to an appropriate statistical measure in the space of invariants. The general characteristics of the turbulent motion are analysed using a combination of computer-based visualization of flow variables together with joint probability distributions of the invariants. The quantities studied are of direct interest in the development of turbulence models. The cubic discriminant of the velocity gradient tensor provides a useful marker for distinguishing regions of active and passive turbulence. It is found that the strongest Reynolds-stress and turbulent-kinetic-energy generating events occur where the discriminant has a rapid change of sign. Finally, the time evolution of the invariants is studied by computing along particle paths in a Lagrangian frame of reference. It is found that the invariants tend to evolve toward two distinct asymptotes in the plane of invariants. Several simplified models for the evolution of the velocity gradient tensor are described. These models compare well with several of the important features observed in the Lagrangian computation. The picture of the turbulent boundary layer which emerges is consistent with the ideas of Townsend (1956) and with the physical picture of turbulent structure set forth by Theodorsen (1955).

Near-wall measurements in a three-dimensional turbulent boundary layer

1997 ◽  
Vol 350 ◽  
pp. 189-208 ◽  
Author(s):  
DEBORA A. COMPTON ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Three Dimensional ◽  
Mean Flow ◽  
The Mean ◽  
Near Wall

An experiment was performed to measure near-wall velocity and Reynolds stress profiles in a pressure-driven three-dimensional turbulent boundary layer. An initially two-dimensional boundary layer (Reθ≈4000) was exposed to a strong spanwise pressure gradient. At the furthest downstream measurement locations there was also a fairly strong favourable streamwise pressure gradient.Measurements were made using a specially designed near-wall laser-Doppler anemometer (LDA), in addition to conventional methods. The LDA used short focal length optics, a mirror probe suspended in the flow, and side-scatter collection to achieve a measuring volume 35 μm in diameter and approximately 65 μm long.The data presented include mean velocity measurements and Reynolds stresses, all extending well below y+=10, at several profile locations. Terms of the turbulent kinetic energy transport equation are presented at two profile locations. The mean flow is nearly collateral (i.e. W is proportional to U) at the wall. Turbulent kinetic energy is mildly suppressed in the near-wall region and the shear stress components are strongly affected by three-dimensionality. As a result, the ratio of shear stress to turbulent kinetic energy is suppressed throughout most of the boundary layer. The angles of stress and strain are misaligned, except very near the wall (around y+=10) where the angles nearly coincide with the mean flow angle. Three-dimensionality appears to mildly reduce the production of turbulent kinetic energy.

scholarly journals Spatiotemporal Dynamics of the Kinetic Energy in the Atmospheric Boundary Layer from Minisodar Measurements

Atmosphere ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 421
Author(s):  
Alexander Potekaev ◽  
Liudmila Shamanaeva ◽  
Valentina Kulagina
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Atmospheric Boundary Layer ◽  
Turbulent Kinetic Energy ◽  
Time Of Day ◽  
Linear Increase ◽  
Spatiotemporal Dynamics ◽  
Intermediate Layers ◽  
Subsequent Decrease ◽  
Stable Atmospheric Boundary Layer

Spatiotemporal dynamics of the atmospheric kinetic energy and its components caused by the ordered and turbulent motions of air masses are estimated from minisodar measurements of three velocity vector components and their variances within the lowest 5–200 m layer of the atmosphere, with a particular emphasis on the turbulent kinetic energy. The layered structure of the total atmospheric kinetic energy has been established. From the diurnal hourly dynamics of the altitude profiles of the turbulent kinetic energy (TKE) retrieved from minisodar data, four layers are established by the character of the altitude TKE dependence, namely, the near-ground layer, the surface layer, the layer with a linear TKE increase, and the transitive layer above. In the first layer, the most significant changes of the TKE were observed in the evening hours. In the second layer, no significant changes in the TKE values were observed. A linear increase in the TKE values with altitude was observed in the third layer. In the fourth layer, the TKE slightly increased with altitude and exhibited variations during the entire observation period. The altitudes of the upper boundaries of these layers depended on the time of day. The MKE values were much less than the corresponding TKE values, they did not exceed 50 m2/s2. From two to four MKE layers were distinguished based on the character of its altitude dependence. The two-layer structures were observed in the evening and at night (under conditions of the stable atmospheric boundary layer). In the morning and daytime, the four-layer MKE structures with intermediate layers of linear increase and subsequent decrease in the MKE values were observed. Our estimates demonstrated that the TKE contribution to the total atmospheric kinetic energy considerably (by a factor of 2.5–3) exceeded the corresponding MKE contribution.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

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