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Six two-equation turbulence models, comprising three versions from the k - epsilon group and the same number of k - omega model versions, have been tested against the direct numerical simulation (DNS) data for a boundary layer under slowly varying 1D oscillatory flow. A detailed comparison has been made for mean velocity, turbulent kinetic energy,...
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... the predictions for turbulent kinetic energy presented in Fig. 3, the differences are obvious. It can be observed that JL and the three k models underestimate the peak value of k, especially at t30, 150, and 180°; however, far from the wall all these models perform well except WL. The models under consideration can predict the generation of turbulent kinetic energy near the wall very well during the ...
Citations
... This fact motivated Menter (1994) to propose a blended k- model in which near the wall k- and far from the wall k- model is employed. Sana and Shuy (2002) reviewed some k- model versions for oscillatory boundary layers on a smooth bed and Sana et al. (2009) tested the blended k- model versions on a rough bed. ...
Prediction of the sediment transport in streams requires an accurate estimation of bed shear stress (for bed load) and eddy viscosity (for suspended load). In general, shallow water models employ empirical relationships to estimate the bottom shear stress. However, with the advancement of computing systems, the utilization of advanced turbulence models is getting common. In this paper, a number of model versions are reviewed based on their predictive abilities against the well-known bottom boundary layer properties in open channels and computational economy. Qualitative and quantitative comparisons have been made to infer that the choice of model versions should be based on the field application. For example, the bottom shear stress is very well predicted by the k-? model whereas the cross-stream velocity profile and turbulent kinetic energy are predicted more efficiently by k-? model versions. This study may be useful for researchers and practicing engineers in selecting a suitable two-equation model for calculating various bottom boundary layer properties.
... However, using two-equation models for simulating wave boundary layers started in late 70s and became more popular in 90s. Since then, various types of wave boundary layers have been analyzed using two-equation models [3][4][5][6][7][8]. ...
Different turbulence models of variable complexity
based on the user’s requirements are used to analyze
turbulence boundary layers. The governing (Navier-
Stokes) equation is a nonlinear, time-dependent, 3D
partial differential equation. The actual
solutions of this equation are few and only applicable to
laminar flow. At high Reynolds numbers, which is the case
for most of the practical applications, the laminar flow
undergoes instabilities, generally referred as turbulence.
Since these instabilities generate three-dimensional
features, no satisfactory 2D approximations for turbulent
phenomena are available. In addition, turbulence being
random process in time, the deterministic approach is not
fully applicable. The turbulent flows contain small
fluctuations, which can be resolved by choosing very fine
grids and time steps, such that a direct simulation is not
feasible for high Reynolds numbers.
Using Reynolds Averaged Navier-Stokes (RANS)
models, the computational costs are significantly reduced,
however, it requires closure assumptions for the higher
moments. Large Eddy Simulation (LES) aims to reduce the
dependence on the turbulence model by simulating the
major portion of the flow without any models, resolving by
the grid. Only the scales smaller than the resolution of the
grid are simulated by a model. Such a computational
strategy makes LES approach computationally more
demanding than RANS. It is estimated that RANS models
have a computing time of about 5% of the LES whereas,
LES has a computing time of about 10% of DNS [1].
Owing to the computational economy and reasonable
accuracy of RANS models, various practical flow
phenomena have been simulated using different types of
models. In this paper, a brief review of some of the
applications of two-equation turbulence models in different
types of wave boundary layers is presented. Such a review
may be helpful in selecting an appropriate turbulence
model for relevant field applications.
... Rodi(1984) has reviewed several turbulence models and their applications in steady flow fields. Sana and Tanaka(2000) and Sana and Shuy (2002) have reviewed some popular versions of two-equation models by virtue of their applicability to the oscillatory boundary layers. Davies and Gerritsen(1994) have compared some three-dimensional tidal hydrodynamic models for the Irish Sea. ...
Various places along the coast of Al-Batinah region in Sultanate of Oman are undergoing severe erosion. There are several theories to explain this phenomenon but none of them has been fully studied using the measured data or numerical modeling. The authors have undertaken a research project to study this phenomenon using field measurements as well as numerical modeling. The measured data not only will be a valuable source of information on the coastal profiles in the study area, it will serve as an input to the numerical model as well. The numerical model, once implemented in the study area and calibrated using field data, will be used to predict the coastal erosion in future. This will help the decision makers in the planning and management of the coastal zone in Al-Batinah.
At this stage the development of the conceptual model of the study area is underway. This paper, therefore, describes brief literature review, methodology, an outline of the numerical model and its setup to be used in the present study.
... For sinusoidal oscillatory boundary layers two-equation turbulence models have been utilized by a number of researchers. For practical purposes, two equation models have been very successful in predicting the mean and fluctuating parameters of oscillatory boundary layers on smooth bottoms (Sana and Tanaka, [14], Sana and Shuy, [13]) and rough boundaries (Sajjadi and Waywell, [10] [1] to study the boundary layer properties under irregular waves and current. In the present study, the experiments have been conducted under irregular oscillatory motion on a rough bottom. ...
... Patel and Yoon [9] compared the results of k- model proposed by Wilcox [19] and a two-layer k- model for turbulence under separated flow and found the former model performing much better than the latter one. Blended models proposed by Menter have been used for an oscillatory wave boundary layer and good agreement has been found with DNS data (Sana and Shuy, [13]). ...
A numerical study has been conducted to investigate the properties of irregular wave boundary layers on a rough bottom. The original version of k- model and two versions of blended k-/k- models have been used to predict the boundary layer properties for the existing experimental data. It was found that the model could reproduce the shear stress variation in time quite successfully but the magnitude could not be predicted adequately. This discrepancy may partly be due to the estimation of the shear stress from the velocity data by log-law.
... Although this type of model was initially developed for steady boundary layers, its utilization for analyzing oscillatory boundary layers is commonplace. Sana and Tanaka (et al. 2000) and Sana and Shuy (et al. 2002) have provided brief reviews of the studies carried out in the past on the application of two equation models to oscillatory boundary layers. The low Reynolds number k-ε model was originally developed by Jones and Launder (et al. 1972). ...
... The variation of wave friction factor with the r values shows that by increasing the r value beyond 1.04 (refining the grid further) does not significantly improve the calculation the friction factor (Fig. 4). The friction factor is defined here as: The YS model shows closer agreement with the DNS data for wave friction factor as shown earlier by Sana and Shuy(et al. 2002). ...
The effect of grid spacing in two versions of low Reynolds number k-ε model is studied using the DNS data of one-dimensional sinusoidal oscillatory boundary layer. A detailed comparison has been made for cross-stream velocities, turbulent kinetic energy (T.K.E.), bottom shear stress, friction factor and phase difference. It is observed that in order to predict the boundary layer properties with reasonable accuracy, the first grid point should be placed well within the viscous sub layer. For the present DNS data the limiting value of the distance to the first grid point from the wall is expressed in terms of Stokes layer thickness. The results of the present study may be useful for the practicing engineers and researchers for choosing appropriate grid spacing for low Reynolds number k-ε models.
... Moreover, Tanaka et al. (1998) has studied the properties of asymmetric oscillatory boundary layers on the smooth bottom and comparison has been made with k-ε model prediction. Sana and Shuy (2002) have applied various types of two-equation turbulence models for sinusoidal oscillatory boundary layers on smooth bed and a detailed quantitative comparison by virtue of the error prediction has been made. Recently, Foti and Scandura (2004) have modified the low Reynolds number k-ε model in order to describe a turbulent flow over both smooth and rough beds. ...
Non-linearity in wave motion is one of the factors causing net sediment transport under oscillatory waves. Thus, there is a high necessity to incorporate wave non-linearity in an estimation of bottom shear stress. In the present paper, turbulent boundary layer characteristics for asymmetric waves according to the non-linearity effect is examined through both experimental and the baseline (BSL) k-ω turbulence model. Moreover, a new calculation method of bottom shear stress based on incorporating acceleration and velocity terms is used to examine both the experimental and the BSL k-ω turbulence model results. Experiments of turbulent boundary layer flow for cnoidal waves were conducted in an oscillating wind tunnel over rough bed. Laser Doppler Velocimeter (LDV) was used to measure flow velocity distribution for three cases with different non-linearity index, N i , namely N i =0.67, 0.60 and 0.58.
... Applications of various turbulence models of twoequation, consisting of three versions of the k-ε group, the Wilcox's k-ω [2], the BSL (baseline) k-ω [3] and the SST (shear stress transport) k-ω model [3] have been carried out by [4] on the DNS and experimental data for the smooth beds oscillatory boundary layer for sinusoidal. Instead, quantitative and detailed comparisons based on the prediction results have been done for selecting the best turbulence model. ...
Turbulent structures in the bottom boundary layer beneath the wave motion have an important role in the nearshore sediment transport modeling and its analyses. Cnoidal waves can be used as a representative of asymmetry waves in the ocean. This paper is aimed to observe the structure of turbulent boundary layer under cnoidal waves as a representative of asymmetry waves in which the effect of asymmetric is actualized along wave cycle related with the wave asymmetric parameter, Ni. The turbulent boundary layer characteristics beneath cnoidal waves motion (i.e. mean velocity and turbulent intensity) are given in the results of experimental results and turbulent numerical models (i.e. the k-ε, the k-ω, the BSL k-ω and the SST k-ω model). Turbulent properties prediction of cnoidal waves from each turbulence model is compared among them and that of experimental results. A laser Doppler velocimeter (LDV) is used to measure the profiles of velocity distribution in the tunnel of oscillating wind over rough bed beneath cnoidal waves motion. From the comparison of the average velocity distribution between all the models of turbulence and the results of experimental for the cases of cnoidal waves in general, it has been obtained that the model of BSL k-ω is superior to predict which is followed by the model of k-ε, the model of k-ω and the model of SST k-ω.
... Whereas, the experimental data does not show such behavior near the bed. The boundary layer thickness is also overestimated by the model, a phenomenon shown by the BSL model in sinusoidal wave boundary layer layers as well (Sana and Shuy, 2002) Bottom shear stress calculated from laminar theory and BSL version of k-ω model shows significant differenc e because of transitional behavior of the wave BL. This difference conforms to the prediction of the veloc ity profile where the model showed turbulent behavio r around the crest of the free-stream velocity. ...
A number of studies on bottom boundary layers under sinusoidal and cnoidal waves were carried out in the past owing to the role of bottom shear stress on coastal sediment movement. In recent years, the bottom boundary layers under long waves have attracted considerable attention due to the occurrence of huge tsunamis and corresponding sediment movement. In the present study two-equation turbulent models proposed by Menter(1994) have been applied to a bottom boundary layer under solitary waves. A comparison has been made for cross-stream velocity profile and other turbulence properties in x-direction.
... Sana and Tanaka (2000) used five different versions of the − k ε model to simulate an oscillatory boundary layer over a smooth wall and compared their results with the results of the DNS by Spalart and Baldwin (1989). Later, Sana and Shuy (2002) extended the analysis by Sana and Tanaka (2000) by considering other two-equation turbulence models (the original − k ω model of Wilcox (1988), the two-layer − k ω model and the shear stress transport model proposed by Menter (1994)). Sana and Tanaka (2010) compared the results of the different turbulence models with the results of DNS by Spalart and Baldwin (1989), hence they considered a smooth bottom only. ...
We investigate the turbulent oscillatory flow generated by propagating surface waves close to the sea bottom focusing our attention on moderate values of the Reynolds number Rδ of the bottom boundary layer. For such moderate values of Rδ, turbulent fluctuations appear only during parts of the oscillation cycle and the flow recovers a laminar-like behaviour in the remaining parts. Different roughness sizes are considered and both the smooth and the rough flow regimes are analysed. The aim of the present investigation is to test the performance of different two-equation turbulence models to compute the flow field over both smooth and rough walls and for moderate values of the Reynolds number. The considered models are the e−ω model by Saffman and Wilcox (1974), two k−ω models (Wilcox (1988) and a model derived from Wilcox (1992)), a low-Reynolds number k−ε model (Foti and Scandura, 2004) and the model by Menter et al. (2003). To evaluate the performance of the models, the numerical predictions of the bottom shear stress are compared both with experimental measurements and with results of direct numerical simulations (DNS). All the models are found to provide fair results for high values of Rδ and for a smooth wall. For moderate values of Rδ, when turbulence is observed only during parts of the oscillating cycle, only one of the low-Reynolds number k−ω models is able to describe the rapid growth of the wall shear stress due to turbulence appearance. On the other hand, if a rough wall is considered, the performance of the models greatly depends on the size of the roughness.
... Moreover, Tanaka et al. (1998) has studied the properties of asymmetric oscillatory boundary layers on the smooth bottom and comparison has been made with k-ε model prediction. Sana and Shuy (2002) have applied various types of two-equation turbulence models for sinusoidal oscillatory boundary layers on smooth bed and a detailed quantitative comparison by virtue of the error prediction has been made. Recently, Foti and Scandura (2004) have modified the low Reynolds number k-ε model in order to describe a turbulent flow over both smooth and rough beds. ...
