Near-wall Model Research Articles

Near-wall LES closure based on one-dimensional turbulence modeling

A novel near-wall LES closure model is developed based on a revised form of the one-dimensional turbulence (ODT) model of Kerstein and is tested by performing LES calculations of turbulent channel flow at Reynolds numbers based on friction velocity ranging from 395 to 10,000. In contrast to previous models, which invoke Reynolds averaging, near-wall velocity fluctuations and turbulent transport are simulated down to the smallest scales, and can be compared directly to DNS data. Thus, the approach provides more than just a boundary condition. Rather, it is itself a complete (although simplified) model for the wall-normal profiles of velocity within the near-wall region. LES/ODT coupling is bi-directional and occurs both through the direct calculation of the subgrid turbulent stress by temporally and spatially filtering the ODT-resolved momentum fluxes (up-scale coupling), and through the LES-resolved pressure and velocities impacting the ODT behavior (down-scale coupling). The formulation involves finely resolved ODT lines that are embedded within each wall-adjacent LES cell – denoted the inner region. LES cells that are within approximately one LES filter width of the inner region belong to an overlap region where both ODT and LES modeling is active. All other cells are treated using a standard LES approach. Although more expensive than simpler models, the cost of the model relative to the LES portion of the simulation scales favorably with problem size, leading to computationally affordable simulations even at relatively high Reynolds numbers.

Development of a nonlinear near-wall turbulence model for turbulent flow and heat transfer

A new nonlinear near-wall turbulence model is developed on the basis of realizability constraints to predict turbulent flow and heat transfer in strongly nonequilibrium flows. The linear k– ε– f μ model of Park and Sung (Fluid Dyn. Res., 20 (1997) 97) is extended to a nonlinear formulation. The stress–strain relationship is derived from the Cayley–Hamilton theorem in a homogeneous flow. The ratio of production to dissipation ( P k/ ε) is employed to solve an algebraic equation of the strain dependent coefficients. A near-wall treatment is dealt with by reproducing the model coefficients from a modified strain variable. An improved explicit heat flux model is proposed with the aid of Cayley–Hamilton theorem, which includes the quadratic effects of flow deformations. The near-wall asymptotic behavior is incorporated by modifying the f λ function. Emphasis is placed on the model performance on the truncated strain terms. The model performance is shown to be generally satisfactory.

Analysis and Application of Chorochronic Periodicity in Turbomachinery Rotor/Stator Interaction Computations

A methodology for predicting the three-dimensional unsteady aerodynamics of the interaction between two turbomachinery blade rows that are in relative angular motion with one another is described. In this case, the kinematics of the blades introduce a chorochronic (space‐time) periodicity. This periodicity is analyzed in detail, and a mathematically straightforward methodology, based on Fourier series in µ (azimuth) and t (time), is presented for treating the interface between the two rows. These results are implemented in a computational method solving the three-dimensional Favre ‐Reynolds-averaged Navier ‐Stokes equations, with a near-wall wall-normalfree Reynolds-stress model. Only one blade passage per blade row is discretized. At the pitchwise boundaries, phase-lagged periodicity is applied using Fourier series in time. Both the pitchwise boundaries time harmonics and the interface chorochronic tµ harmonics are updated using a low-storage moving-averages technique. Computational results are presented and compared with measurements for a 1 1 -stage turbine, where the two stators have the same number of blades enabling the use of chorochronic periodicity. Sample results are also presented for a transonic inlet guide vane/rotor interaction, illustrating the ability of the interface treatment to handle shock waves.

Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional Two-Equation Turbulence Models

The paper presents recent trends in modeling jets in crossflow with relevance to film cooling of turbine blades. The aim is to compare two classes of turbulence models with respect to their predictive performance in reproducing near-wall flow physics and heat transfer. The study focuses on anisotropic eddy-viscosity/diffusivity models and explicit algebraic stress models, up to cubic fragments of strain and vorticity tensors. The first class of models are direct numerical simulation (DNS) based two-layer approaches transcending the conventional k−ε model by means of a nonisotropic representation of the turbulent transport coefficients; this is employed in connection with a near-wall one-equation model resolving the semi-viscous sublayer. The aspects of this new strategy are based on known channel-flow and boundary layer DNS statistics. The other class of models are quadratic and cubic explicit algebraic stress formulations rigorously derived from second-moment closures. The stress-strain relations are solved in the context of a two-layer strategy resolving the near-wall region by means of a nonlinear one-equation model; the outer core flow is treated by use of the two-equation model. The models are tested for the film cooling of a flat plate by a row of streamwise injected jets. Comparison of the calculated and measured wall-temperature distributions shows that only the anisotropic eddy-viscosity/diffusivity model can correctly predict the spanwise spreading of the temperature field and reduce the strength of the secondary vortices. The wall-cooling effectiveness was found to essentially depend on these two particular flow features. The non-linear algebraic stress models were of a mixed quality in film-cooling calculations.

Near-Wall Modeling of Turbulent Convective Heat Transport in Film Cooling of Turbine Blades With the Aid of Direct Numerical Simulation Data

The paper presents novel developments in the DNS-based, turbulence modeling strategy of Lakehal et al. developed for calculating jets in crossflow. The particular features of the model include: 1) dynamic coupling of the high-Re k−ε with a one-equation model resolving the near-wall viscosity-affected layer; 2) inclusion of the anisotropy of turbulent transport coefficients for all transport equations; 3) near-wall variation of the turbulent Prandtl number as a function of the local Reynolds number. Most of the important aspects of the proposed model are based on known DNS statistics of channel and boundary layer flows. The model is validated against experiments for the case of film cooling of a flat plate, where coolant air is injected from a row of streamwise inclined jets. Excellent results were obtained for this configuration as compared to earlier numerical investigations reported in the open literature. The model is then extended to calculate film cooling of a symmetrical turbine blade by a row of laterally injected jets for various blowing rates. Comparison of the calculated and measured wall-temperature distributions show that only with this anisotropy eddy-viscosity/diffusivity model can the spanwise spreading of the temperature field be well predicted and the strength of the secondary vortices reduced. Furthermore, results of additional calculations show that combining the anisotropy eddy viscosity model with the DNS-based relation for turbulent Prandtl number promotes the eddy diffusivity of heat vis-a`-vis that of momentum further, leading to an enhanced spanwise spreading of the jet. The performance of this new approach improves with increasing blowing rate.

Computation of Ship Viscous Flow at Full Scale Reynolds Number

The present study concerns simulation of ship viscous flow at full-scale Reynolds number. The main objectives are two folds: (1) development of Reynolds-averaged Navier-Stokes equation method applicable to full-scale flow simulation; and (2) investigation on appropriate physical model for full-scale Reynolds number in conjunction with consideration of near-wall flow model including surface roughness effects. In particular, the validity and advantage of two-point wall-function approach have been investigated and the extension was made for inclusion of surface roughness effects on flow and resistance; and currently, evaluation for roughness effects on flat plate flow has been completed. The present numerical method for full-scale flow simulation is based on extension of method developed by the present author, such that, in association with standard k-e model, two near-wall models can be employed, i.e., two-layer method and two-point wall-function method; where the latter has been shown more suitable in practical design use.

An experimental and numerical investigation of turbulent catalytically stabilized channel flow combustion of hydrogen/air mixtures over platinum

The turbulent catalytically stabilized combustion (CST) of fuel-lean hydrogen/air mixtures over platinum was investigated experimentally and numerically in channel-flow configurations. Experiments were performed in an optically accessible catalytic channel reactor, established by two Pt-coated ceramic plates 300 mm long and placed 7 mm apart, with incoming Reynolds numbers of 15,000 and 30,000. Planar laserinduced fluorescence of the OH radical was used to monitor the onset of homogeneous (gas-phase) ignition, one-dimensional (across the 7 mm transverse direction) Raman measurements of major species and temperature assessed the turbulent scalar transport, laser doppler velocimetry yielded the inlet velocity and turbulence, and thermocouples embedded beneath the catalyst provided the surface temperature distribution. Computations were carried out with a two-dimensional elliptic fluid mechanical code that included elementary heterogeneous and homogeneous chemical reaction schemes. Three different low-Reynolds number near-wall turbulence models were examined, in conjunction with a thermochemistry model that included a presumed-shape (Gaussian) probability density function approach for the gaseous reactions and a laminar-like closure for catalytic reactions. Comparisons between predictions and measurements have shown that key CST issues, such as catalytic fuel conversion and onset of homogeneous ignition, are strongly dependent on the particular turbulence model. Moreover, the discrepancies between predictions and measurements were ascribed to the capacity of the various turbulence models to capture the strong flow laminarization induced by the heat transfer from the hot catalytic surfaces. A turbulence model that yields good agreement with the measurements is presented as particularly suited for CST. Experiments and predictions have shown that a continuous increase of the turbulent transport led to incomplete combustion through the gaseous reaction zone with subsequent catalytic conversion of the leaked fuel and, finally, to extinction of the gaseous flame.

New-wall modeling for complex flows using the large eddy simulation technique in curvilinear coordinates

This investigation presents modifications and improvements to the dynamic subgrid scale model and introduces a new-wall model. These modifications are implemented in the large eddy simulation technique in curvilinear coordinates. They are then validated and tested in three-dimensional complex geometries. The large eddy simulation method captures many scales of turbulence up to the grid size. A closure model is used to simulate subgrid turbulence. The Smagorinsky and dynamic subgrid models are presented and tested. The dynamic model overcomes many of the deficiencies of the Smagorinsky subgrid scale model. Spatial and temporal low-pass filters have been introduced in the dynamic subgrid scale model for numerical stability. Several near-wall models are considered for the large eddy simulation technique. A local averaging technique lends these models to be applicable in complex geometry situations. A new model is introduced which overcomes planar averaging near the wall and captures ejection and sweep effects. These models have been implemented in a large eddy simulation computer program. Results are validated and tested in a lid driven cavity flow at Reynolds number of 10 000. A single tube in a channel is simulated to show the applicability of the models to complex geometries with attachment and separation as well as end-wall effects. The shedding effect was captured and turbulence statistical characteristics were acceptable.

A two-layer turbulence model for simulating indoor airflow: Part I. Model development

Energy efficient buildings should provide a thermally comfortable and healthy indoor environment. Most indoor airflows involve combined forced and natural convection (mixed convection). In order to simulate the flows accurately and efficiently, this paper proposes a two-layer turbulence model for predicting forced, natural and mixed convection. The model combines a near-wall one-equation model [J. Fluid Eng. 115 (1993) 196] and a near-wall natural convection model [Int. J. Heat Mass Transfer 41 (1998) 3161] with the aid of direct numerical simulation (DNS) data [Int. J. Heat Fluid Flow 18 (1997) 88].

Analyses of heat transfer in stationary and rotating ribbed blade cooling passages using computational fluid dynamics.

Computational fluid dynamics (CFD) predictions of the flow patterns and heat transfer in simplified ribbed-wall turbine blade cooling passages were performed for representative stationary and rotating conditions. Analyses have been performed with different mesh densities and using different turbulence models to assess the sensitivity of predictions to these variables. Computed local heat transfer results are compared to measurements available in the literature to assess their accuracy. The results generally agree well with experiment, although the peak values of the heat transfer coefficients were under-predicted in the first leg of the channel. Some sensitivity to mesh density was seen, while the choice of near-wall turbulence model appeared to have little effect.

DNS of Turbulent Heat Transfer in Channel Flow With Heat Conduction in the Solid Wall

The Direct Numerical Simulation (DNS) of the fully developed velocity and temperature fields in the two-dimensional turbulent channel flow coupled with the unsteady conduction in the heated walls was carried out. Simulations were performed at constant friction Reynolds number 150 and Prandtl numbers between 0.71 and 7 considering the fluid temperature as a passive scalar. The obtained statistical quantities like root-mean-square temperature fluctuations and turbulent heat fluxes were verified with existing DNS studies obtained with ideal thermal boundary conditions. Results of the present study were compared to the findings of Polyakov (1974), who made a similar study with linearization of the fluid equations in the viscous sublayer that allowed analytical approach and results of Kasagi et al. (1989), who performed similar calculation with deterministic near-wall turbulence model and numerical approach. The present DNS results pointed to the main weakness of the previous studies, which underestimated the values of the wall temperature fluctuations for the limiting cases of the ideal-isoflux boundary conditions. With the results of the present DNS it can be decided, which behavior has to be expected in a real fluid-solid system and which one of the limiting boundary conditions is valid for calculation, or whether more expensive conjugate heat transfer calculation is required.

Numerical study of turbulent diesel flow in a pipe with sudden expansion

Three two-equation models and a second-moment closure are implemented in the case of turbulent diesel flow in a pipe with sudden expansion. The chosen two-equation closures are: the standard k– ε, the RNG k– ε and the two-scale k– ε models. The performance of the models is investigated with regard to the non-equilibrium parameter η and the mean strain of the flow, S. Velocity and turbulence kinetic energy predictions of the different models are compared among themselves and with experimental data and are interpreted on the basis of the aforementioned quantities. The effect of more accurate near-wall modeling to the two-equation models is also investigated. The results of the study demonstrate the superiority of the second-moment closure in predicting the flow characteristics over the entire domain. From the two-equation models the RNG derived k– ε model also gave very good predictions, especially when non-equilibrium wall-functions were implemented. As far as η and S are concerned, only the closures with greater physical consistency, such as the two-scale k– ε model, give satisfactory results.

Improved Prediction of Turbomachinery Flows Using Near-Wall Reynolds-Stress Model

In this paper an assessment of the improvement in the prediction of complex turbomachinery flows using a new near-wall Reynolds-stress model is attempted. The turbulence closure used is a near-wall low-turbulence-Reynolds-number Reynolds-stress model, that is independent of the distance-from-the-wall and of the normal-to-the-wall direction. The model takes into account the Coriolis redistribution effect on the Reynolds-stresses. The five mean flow equations and the seven turbulence model equations are solved using an implicit coupled OΔx3 upwind-biased solver. Results are compared with experimental data for three turbomachinery configurations: the NTUA high subsonic annular cascade, the NASA_37 rotor, and the RWTH 1 1/2 stage turbine. A detailed analysis of the flowfield is given. It is seen that the new model that takes into account the Reynolds-stress anisotropy substantially improves the agreement with experimental data, particularily for flows with large separation, while being only 30 percent more expensive than the k−ε model (thanks to an efficient implicit implementation). It is believed that further work on advanced turbulence models will substantially enhance the predictive capability of complex turbulent flows in turbomachinery.

Computation of Flow and Heat Transfer in Two-Pass Channels With 60 deg Ribs

Numerical predictions of three-dimensional flow and heat transfer are presented for a two-pass square channel with and without 60 deg angled parallel ribs. Square sectioned ribs were employed along one side surface. The rib height-to-hydraulic diameter ratio e/Dh is 0.125 and the rib pitch-to-height ratio (P/e) is 10. The computation results were compared with the experimental data of Ekkad and Han [1] at a Reynolds number (Re) of 30,000. A multi-block numerical method was used with a chimera domain decomposition technique. The finite analytic method solved the Reynolds-Averaged Navier Stokes equation in conjunction with a near-wall second-order Reynolds stress (second-moment) closure model, and a two-layer k-ε isotropic eddy viscosity model. Comparing the second-moment and two-layer calculations with the experimental data clearly demonstrated that the angled rib turbulators and the 180 deg sharp turn of the channel produced strong non-isotropic turbulence and heat fluxes, which significantly affected the flow fields and heat transfer coefficients. The near-wall second-moment closure model provides an improved heat transfer prediction in comparison with the k-ε model.

A near-wall two-equation heat transfer model for wall turbulent flows

A proposed near-wall t 2 –ε t two-equation model for turbulent heat transport reproduces the correct near-wall behavior of temperature under various wall thermal boundary conditions. In this model, a mixing timescale is introduced to model the production term of ε t equation, and a more convenient boundary condition for ε t under the uniform wall heat flux is suggested. The present model is tested through application to turbulent heat transfer for channel flow. Predicted results are compared with direct numerical simulation (DNS) data. The near-wall t 2 –ε t two-equation model predicts reasonably well the distributions of the time-mean temperature, normal turbulent heat flux, temperature variance, dissipation rate and their near-wall budgets.

Development of a near-wall turbulence model and application to jet impingement heat transfer

A near-wall turbulence model was developed and applied to heat and fluid flows for an impinging jet flow. The k–ε–fμ model was modified for predictions in strongly strained turbulent flows. To derive a realizable eddy viscosity, the fμ2 function was newly formulated. The near-wall effect and the anisotropic production were reflected in the ε-equation. The model performance was validated by the relevant experimental data. The predicted results were compared with those by the k–ε model and by the k–ε–v2 model. The application to jet impingement heat transfer revealed that the present numerical predictions of wall heat transfer show good agreement with the experimental data in the stagnation region. The influence of the Reynolds number on the stagnation Nusselt number was investigated. The model performance was shown to be generally satisfactory.

Development of a Nonlinear Near-Wall Model for Turbulent Flow and Heat Transfer

A new nonlinear near-wall turbulence model is developed to predict turbulent flow and heat transfer in strongly nonequilibrium flows. The k--f/, model of Park and Sung(1)/ is extended to a nonlinear formulation. The stress-strain relationship is the thrid-order in the mean velocity gradients. The strain dependent coefficients are obatined from the realizability constraints and the singular behavior at large strains. An improved explicit heat flux model is proposed with the aid of Cayley-Hamilton theorem. This new model includes the quadratic effects of flow deformations. The near-wall asymptotic behavior is incorporated by modifying the fλ/ function. The model performance is shown to be satisfactory.

Computational modelling of flow around a circular cylinder in sub-critical flow regime with various turbulence models

The numerical simulation of transitional flow around a two-dimensional stationary circular cylinder is presented using two groups of turbulence models in a sub-critical flow regime. In the first group, enhanced two-equation turbulence models based on the eddy viscosity concept are used. They include the non-linear k–e model with extended models, such as renormalization group (RNG) and the anisotropic model. In the second group, flow simulation is carried out using the large eddy simulation (LES) method, which is based on a standard sub-grid scale (SGS) model with a near-wall approach. This near-wall model, without using the ‘law of wall’, is achieved in a finite element code. The numerical results extracted from these simulations are compared with each other and with the experimental data in order to determine the relative performance of these turbulence models and to find the best model for the flow of interest. Although most of the LES simulations have been previously carried out using finite volume methods, results from using the present model show that the finite element method (FEM) can also be used with confidence. Copyright © 2001 John Wiley & Sons, Ltd.

Isothermal and heated turbulent upflow in a vertical annular channel – Part II. Numerical simulations

Numerical simulations of isothermal and heated turbulent upflow of a liquid in a vertical concentric annular channel with its inner wall heated were carried out. Near-wall two-equation turbulence models were used to close the Reynolds-averaged momentum and thermal energy equations. In addition, a near-wall explicit turbulent heat flux model was incorporated. The results reported include mean and turbulence quantities. Comparison with our measurements reported in Part I of this two-part paper is presented. The Reynolds number at the channel inlet ranged from 22 800 to 46 400, and the range of Gr/ Re 2 at the measurement plane was 0.009–0.078. Buoyancy effects which influenced the velocity and thermal fields were observed in the simulation results as they were in the measurements.

Three-Dimensional Mean Velocity Analysis of a 30 Degree Bend Flow

The 3D velocity profiles of the 30° bend flow of Flack and Johnston have been analyzed in terms of the existing 3D turbulent boundary layer theories. Various cross-flow and near-wall similarity models were tested. Coles's cross-flow model described the velocity profiles satisfactorily. The wall function matched the data well, and the experimentally determined wake functions collapsed into a narrow band, which was however different from the originally suggested wake function. A new form of wake function has been proposed. Among the near-wall models, Hornung and Joubert's and Prahlad's models matched the data very well and excellent near-wall similarity from the wall to the boundary layer edge was achieved. This is rather unexpected in a 3D turbulent boundary layer flow with large skewing. The excellent performance of these two near-wall models could not be attributed to any particular reason.