RANS simulations of neutral atmospheric boundary layer flow over complex terrain with comparisons to field measurements

Micro‐scale Reynolds‐averaged Navier‐Stokes (RANS) simulations of the neutral atmospheric boundary layer (ABL) over complex terrain and a comparison of the results with conditionally averaged met‐tower data are presented. A robust conditional sampling procedure for the meteorological tower (met‐tower) data to identify near‐neutral conditions based on a criterion for the turbulence intensity is developed. The conditionally averaged wind data on 14 met‐towers are used for the model validation. The ABL flow simulations are conducted over complex terrain which includes a prominent hill using the OpenFOAM‐based simulator for on/offshore wind farm applications (SOWFA) with the k?? and the SST k?ω turbulence models. The discretization of the production term in the transport equation for the turbulent kinetic energy (TKE) is modified to greatly reduce the commonly observed nonphysical near surface TKE peak. The driving inflow is generated through an iterative approach using a precursor method to reproduce the measured wind statistics at the reference tower. Both of the RANS models are able to capture the flow behavior windward of the hill. The SST k?ω model predicts more intense flow separation than the k?? model downstream of the steepest sections of the hill. The wind statistics predicted at the location of the met‐towers by both of the RANS models are fairly consistent. Overall, the comparisons of the direction, mean, and standard deviation of the wind between the simulations and the tower data show reasonable agreement except for the differences of the mean wind speeds at four met‐towers located closer to the main ridge of the hill in a region of strong terrain variations.     

Performance of two equation turbulence models for prediction of flow and heat transfer over a wall mounted cube

This paper deals with the CFD predictions of the three dimensional incompressible flow over a wall mounted cubic obstacle placed in fully developed turbulent flow along with the heat transfer calculations. Reynolds number considered in this study is 1870 based on cube height, h and bulk velocity U_b. Our main objective is to find out the appropriate two equation turbulence model for the complex flow structure which involves recirculation, separation and reattachment. We have used standard k–ε, low-Reynolds number k–ε, non-linear k–ε model, standard k–ω and improved k–ω models to solve the closure problem. The non-linear k–ε model and improved k–ω models along with standard models are validated with bench mark problem – flow through a backward facing step (BFS). Results showed that the improved k–ω model is giving overall better predictions of the flow field especially recirculation zone, mean streamwise velocity, and turbulent characteristics when compared to those by standard eddy viscosity models. The non-linear k–ε model is giving better prediction when compared to standard k–ε and low Reynolds number k–ε models. The complex vortex structure around the cube causes large variation in the local convective heat transfer coefficient. The maximum of the heat transfer coefficient occurred in the proximity of the reattachment points and the minimum is found at the recirculation zone.     

Numerical simulations of non-premixed turbulent combustion of CH4–H2 mixtures using the PDF approach

The present work is devoted to the study of non-premixed turbulent combustion with the PDF approach using three turbulence models: k-? model, modified k-? model and RSM model. A detailed kinetic mechanism is used in the numerical simulations. The three turbulence models are compared and evaluated with the experimental data and the numerical results of the literature. The evaluation concludes that the modified k-? is the most appropriate for simulating this kind of flame. A study of the effect of hydrogen addition on methane combustion is performed. Hydrogen addition causes the elevation of combustion temperature, the decreasing of CO and CO₂ mass fractions but leads to the increase of NO mass fraction.     

CFD simulation for turbulent mixing with the stochastic approach

A computational fluid‐dynamic simulation for a turbulent nonuniform combustion is established using a stochastic approach. At each point in a turbulent flow field, the variations of species mass fraction and temperature are statistically described by the joint‐probability density function (pdf), and the velocity variation is expressed using the conventional k–? turbulent model. The transport equation of this joint pdf of mass fraction and temperature is calculated by a finite‐difference method in convection and turbulent diffusion and by the Curl collision‐redispersion model in molecular mixing. This method is applied to simulate the process of scalar dispersion in a uniform isotropic turbulent flow. The results show that the profile of an averaged scalar is quite similar to those calculated using conventional transport equations. Furthermore, a reasonable degree of reproduction is achieved for the pdfs of the scalar at each point in the flow field. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 503–511, 2001     

Numerical investigation of turbulent natural convection in an inclined square cavity with a hot wavy wall

The turbulent natural convection of air flow in a confined cavity with two differentially heated side walls is investigated numerically up to Rayleigh number of 10¹². The objective of the present work is to study the effect of the inclination angle and the amplitude of the undulation on turbulent heat transfer. The low-Reynolds-number k–ε, k–ω, k–ω–SST RANS models and a coarse DNS are used and compared to the experimental benchmark data of Ampofo and Karayiannis [F. Ampofo, T.G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 (2003) 3551–3572]. The k–ω–SST model is then used for the following test-cases as it gives the closest results to experimental data and coarse DNS for this case. The mean flow quantities and temperature field show good agreement with coarse DNS and measurements, but there are some slight discrepancies in the prediction of the turbulent statistics. Also, the numerical results of the heat flux at the hot wall are over predicted. The strong influence of the undulation of the cavity and its orientation is well shown. The trend of the local heat transfer is wavy with different frequencies for each undulation. The turbulence causes an increase in the convective heat transfer on the wavy wall surface compared to the square cavity for high Rayleigh numbers. A correlation of the mean Nusselt number function of the Rayleigh number is also proposed for the range of Rayleigh numbers of 10⁹–10¹².     

Calibrated models for simulation of stratified hot water heat stores

Hot water heat stores (HWHS) are generally used to overcome the diurnal or seasonal mismatch in the availability and demand of thermal energy. To enhance the system efficiency, good thermal stratification of the HWHS is required. In order to simulate different flow processes in stratified HWHS the effects of stratification on the turbulence are to be considered. Benchmark experiments have been conducted on turbulent flows into a continuously stratified HWHS. Based on these benchmark experiments, different two‐equation turbulence transport models namely the RNG (ReNormalizable Group) and the realizable k–ε turbulence models have been calibrated. The major improvement is provided to the ε‐equation by introducing the effects of the buoyancy field on the turbulence dissipation rate. It is achieved by calibrating the coefficient of the dissipation term (C_ε2 in the RNG and C₂ in the realizable k–ε model) based on the benchmark experiments. A re‐definition of the turbulent Prandtl number (Pr_t) incorporating the effects of stratification on turbulent thermal diffusivity improved the calibration further. The calibrated computational fluid dynamic models are found to predict the charging, discharging and storing processes of typical HWHS with good accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

An improved k‐ ϵ model applied to a wind turbine wake in atmospheric turbulence

An improved k‐ ? turbulence model is developed and applied to a single wind turbine wake in a neutral atmospheric boundary layer using a Reynolds averaged Navier–Stokes solver. The proposed model includes a flow‐dependent C_μ that is sensitive to high velocity gradients, e.g., at the edge of a wind turbine wake. The modified k‐ ? model is compared with the original k‐ ? eddy viscosity model, Large‐Eddy Simulations and field measurements using eight test cases. The comparison shows that the velocity wake deficits, predicted by the proposed model are much closer to the ones calculated by the Large‐Eddy Simulation and those observed in the measurements, than predicted by the original k‐ ? model. Copyright © 2014 John Wiley & Sons, Ltd.     

The k‐ϵ‐fP model applied to wind farms

The recently developed k‐?‐f_P eddy‐viscosity model is applied to one on‐shore and two off‐shore wind farms. The results are compared with power measurements and results of the standard k‐? eddy‐viscosity model. In addition, the wind direction uncertainty of the measurements is used to correct the model results with a Gaussian filter. The standard k‐? eddy‐viscosity model underpredicts the power deficit of the first downstream wind turbines, whereas the k‐?‐f_P eddy‐viscosity model shows a good agreement with the measurements. However, the difference in the power deficit predicted by the turbulence models becomes smaller for wind turbines that are located further downstream. Moreover, the difference between the capability of the turbulence models to estimate the wind farm efficiency reduces with increasing wind farm size and wind turbine spacing. Copyright © 2014 John Wiley & Sons, Ltd.     

Prediction of convection from a finned cylinder in cross flow using direct simulation,turbulence modeling,and correlation-based methods

Direct numerical simulation (DNS), two shear-stress transport (SST) turbulence models, and three k-ε models are used to predict mixed convection associated with air in cross flow over an isothermal, finned cylinder. The DNS predictions reveal complex time-variation in the flow field. Convection heat transfer coefficients predicted by the SST models are in good agreement with those generated by DNS, whereas the k-ε models do not accurately predict heat fluxes. Correlation-based predictions of heat transfer coefficients are, in general, in poor agreement with the DNS and SST predictions. The impact of various geometrical modifications on convection coefficients is also presented.     

Simulation of airflow in one- and two-room enclosures containing a fire source

In this study, the airflow in a room that contains a heat source is simulated numerically. The flow is considered turbulent and buoyant. The results of the mathematical model are validated with available experimental data at specific locations in the domain. A simple geometry is adopted, consisting of a room with a door that plays the role of both inlet–outlet for the fluid (air). At the centre of the room a methane burner is placed to serve as a heat source. The problem is simulated using two turbulence models, the well-known standard k–ε model and the RNG k–ε model, both modified to account for buoyancy effects on turbulence. The burner is considered as a volumetric heat source. It is concluded that the fire plume development as well as the distributions of velocity and temperature are reasonably well predicted. Following this conclusion, both models are also applied to a different, more complex geometry that consisted of two rooms communicating via a door, while the heat source was placed in the first room. Unfortunately, there are no experimental data to compare with for this case, but the results appear plausible. Finally, important design factors, such as mass flow rates and neutral-plane heights, are calculated utilizing the CFD results, and are compared with those obtained by well-known empirical correlations. It is concluded that the bi-directional flow existing through the burning-room vent is similarly predicted by both turbulence models; the RNG k–ε model leading to higher, and more accurate predictions of temperature variations within the hot upper layer, at least for the single-room case.     

Validation of a methodology for thermal stratification analysis in sodium‐cooled fast reactors

Thermal stratification phenomena usually occur in the upper plenum after a scram of sodium‐cooled fast reactors, which should be closed concerned in the fields of structural integrity assessment and residual heat removal capacity. A 2‐dimensional analysis program under cylindrical coordinate was developed for predicting the in‐vessel thermal hydraulics. Non‐orthogonal block‐structured grids were generated to resolve the problems with complex structures. A second‐order discrete scheme based on midpoint rule was applied to the spatial discretization of convection and diffusion terms. Two sets of experiments characterized by distinct shapes of their apparatuses were used for the validation, mainly from the viewpoints of vertical temperature distribution and rising behaviors of the stratification interface. Results show that RANS‐type turbulent models make the significant impacts on different flow regimes. In the calculation of a scaled model with plenty of stagnant sodium in the upper region, the realizable k ? ε model (RKE) considering the mean deformation rate gives better outcomes than the standard k ? ε model (SKE). For the plant‐type upper plenum with considerable flow rate along the entire height, buoyancy modeling is the crucial issue to follow the upward movement of the interface and the relaxation process of the temperature gradient. In this case, employment of the turbulent Prandtl number reflecting the damping effect by incorporating the local Richardson number well reproduced the experimental results.     

SIMULATION OF TURBULENT FLOW IN IRREGULAR GEOMETRIES USING A CONTROL-VOLUME FINITE-ELEMENT METHOD

A modified error indicator and a locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh are developed to study the supersonic turbulent flow over a backward-facing step. In the Cartesian coordinate system, the unsteady Favre-averaged Navier-Stokes equations with a low-Reynolds-number k –ε turbulence model are solved. The modified error indicator, in which the unified magnitude of substantial derivative of pressure and unified magnitude of substantial derivative of vorticity magnitude are incorporated, is applied to treat the new node spacing of mesh remeshing. To assess the present approach, the transsonic turbulent flow around an NACA 0012 airfoil is performed. According to the high-resolution result on the adaptive mesh, the structure of the back-step corner vortex, expansion wave, and oblique shock wave are distinctly captured.     

Autoignition of turbulent hydrogen jet in a coflow of heated air

Autoignition of hydrogen, leading to flame development under turbulent flow conditions is numerically investigated including a detailed chemical mechanism. The chosen configuration consists of a turbulent jet of hydrogen diluted with nitrogen which is issued into a coflow of heated air. Numerical simulations are performed with the Conditional Moment Closure model, to capture the transient evolution of the flow. Turbulence closure is achieved using the k–? model. Simulations revealed that the injected hydrogen mixes with coflowing air, autoignites and a stable diffusion flame is established. Sometimes, flashback of the ignited mixture is observed, whereby the flame travels upstream and stabilizes. It is found that the constants assumed in various modeling terms can severely influence the degree of mixing. Hence, certain modifications to these constants are suggested, and improved predictions are obtained. The sensitivity of autoignition length to the coflow temperature is investigated. The predicted autoignition lengths show a reasonable agreement with the experimental data and LES results.     

Simulation of Swirling Turbulent Heat Transfer in a Vortex Heat Exchanger

ABSTRACT

This article presents a numerical simulation of swirling turbulent flow and heat transfer in a novel vortex heat exchanger. A new algebraic Reynolds stress/heat flux model (ASM/AFM) is applied to the simulation. The computation is performed under different air flow rates for both swirling and nonswirling flows. The calculated mean heat transfer coefficients on both inner and outer walls of the annular duct are compared with the measured data. They are generally improved over the results predicted by the new ASM/k–? model. The effects of swirl on enhancing heat transfer in the annular duct are illustrated. The heat transfer performance of the vortex heat exchanger under different air flow rates is obtained.     

Calculation of wall heat transfer in pipeexpansion turbulent flows

A new modified low-Reynolds-number k-ε turbulence [Chang, Hsieh and Chen (CHC)] model, which possesses the proper near-wall limiting behaviors and is free of the singular defect occurring near the reattachment point when applied to separated flows, is examined for use in wall heat transfer problems in flow with pipe expansion geometry. Another eight low-Reynolds-number k-ε models, found in open literature, are also examined in this study. Attention is specifically focused on the flow region surrounding the reattachment point. Comparative results show that only the CHC model and the model developed by Abe et al. [Abe, Kondoh and Nagano (AKN model)] can yield satisfactory distributions of the Nusselt number along the wall. However, the CHC model adopted the same model constants as conventionally used for the standard k-ε model. Thus, the CHC model is more universal than the AKN model.     

Experimental study on friction factor and numerical simulation on flow and heat transfer in an alternating elliptical axis tube

This paper focuses on the experimental study on friction factor and the numerical simulation on the periodic fully developed fluid flow and heat transfer in an alternating elliptical axis tube (AEAT). The experimental results show that in the laminar flow regime fRe = 84.7, and the transition from laminar to turbulent flow occurs at an earlier Reynolds number about 1000. The predicted cycle average Nusselt numbers from the standard k–ε model and RNG k–ε model are quite close to each other, which are appreciably higher than that of elliptic tube and round tube. Heat transfer performance comparisons are made under identical pumping power constraint, showing the obvious superiority of AEAT over a round tubes. In addition, the complicated multi-longitudinal vortex structure of the flow is detected in detail from the numerical simulation results, which improves the synergy between velocity field and temperature gradient in a large extent, hence, greatly enhancing the convective heat transfer.     

A study on the prediction of aerofoil trailing‐edge noise for wind‐turbine applications

This paper presents a comparative study between the so‐called BPM and TNO models for the prediction of aerofoil trailing‐edge noise with particular emphasis on wind‐turbine applications (the BPM model is named after Brooks, Pope and Marcolini who first proposed the model, and the TNO model is named after the TNO institute of Applied Physics where it was first proposed). In this work, two enhanced versions of the BPM model are proposed, and their performances are compared against two recent anisotropic TNO models that require more detailed boundary‐layer information than the BPM‐based models. The two current enhanced models are denoted as BPMM‐PVII and BPMM‐BLkω, where the former uses a panel method with viscous‐inviscid interaction implemented (PVII) for boundary‐layer calculations, the latter estimates the boundary‐layer (BL) properties using a two‐dimensional k‐ω turbulence model (kω), and BPMM stands for BPM‐Modified. By comparing the predicted sound spectra with existing measurement data for seven different aerofoils tested in the current study, it is shown that the BPMM‐PVII model exhibits superior results to those by the other models for most cases despite the simplicity without considering anisotropy. The BPMM‐PVII model is then combined with Prandtl's nonlinear lifting‐line theory to calculate and investigate three‐dimensional rotor noise characteristics of an NREL UAE Phase‐VI wind turbine (NREL UAE stand for the National Renewable Energy Laboratory Unsteady Aerodynamic Experiment). It is demonstrated that the current approach may provide an efficient solution for the prediction of rotor aerodynamics and noise facilitating industrial design and development for low‐noise wind turbines. Copyright © 2016 John Wiley & Sons, Ltd.     

A phenomenological model for the prediction of soot formation in diesel spray combustion

A phenomenological soot model coupled with complex chemistry mechanism for the prediction of soot formation in diesel spray combustion is presented. The prototype of the model is one proposed by Leung and Lindstedt in which soot formation is treated by four global stages: particle nucleation, surface growth, surface oxidation, and particle coagulation, each of which is represented by only a few reaction steps. In the present study, the model is modified according to recent literature data. The formation of soot particles is linked with gas-phase chemistry via diacetylene and naphthalene, which are presumed to be indicative species of particle inception/nucleation. The soot surface growth is described using Frenklach et al.'s active site model, and the oxidation mechanism includes both Nagle and Strickland-Constable's O₂ oxidation and Neoh et al.'s OH oxidation models. The soot model integrated with the gas-phase kinetics is then applied in multidimensional spray simulations. The KIVA3 code that is widely used in diesel combustion studies is modified and employed for the simulations. The turbulent flow is predicted using the compressible k-ε model, and the turbulence-chemistry interaction handled by a partially stirred reactor model. The IDEA experimental data for n-heptane sprays in diesel-like conditions (800 K and 50 bar) are used for evaluation of the model. Some reaction rate constants are adjusted to achieve better agreement with the measurements. Further, sensitivity studies have been carried out and the effects of some parameters that affect the predictions are discussed. The results indicate that the model, if applied together with other models that properly describe sprays and turbulent flow, can be used for qualitative and even quantitative prediction of soot formation in diesel combustion.     

Calibration of a spinner anemometer for yaw misalignment measurements

The spinner anemometer is an instrument for yaw misalignment measurements without the drawbacks of instruments mounted on the nacelle top. The spinner anemometer uses a non‐linear conversion algorithm that converts the measured wind speeds by three sonic sensors on the spinner to horizontal wind speed, yaw misalignment and flow inclination angle. The conversion algorithm utilizes two constants that are specific to the spinner and blade root design and to the mounting positions of the sonic sensors on the spinner. One constant, k₂, mainly affects the measurement of flow angles, while the other constant, k₁, mainly affects the measurement of wind speed. The ratio between the two constants, k_α=k₂/k₁, however, only affects the measurement of flow angles. The calibration of k_α is thus a basic calibration of the spinner anemometer. Theoretical background for the non‐linear calibration is derived from the generic spinner anemometer conversion algorithm. Five different methods were evaluated for calibration of a spinner anemometer on a 500 kW wind turbine. The first three methods used rotor yaw direction as reference angular, while the wind turbine, was yawed in and out of the wind. The fourth method used a hub height met‐mast wind vane as reference. The fifth method used computational fluid dynamics simulations. Method 1 utilizing yawing of the wind turbine in and out of the wind in stopped condition was the preferred method for calibration of k_α. The uncertainty of the yaw misalignment calibration was found to be 10%, giving an uncertainty of 1° at a yaw misalignment of 10°. © 2014 The Authors. Wind Energy published by John Wiley & Sons, Ltd.     

Modifications to Reynolds-averaged Navier–Stokes turbulence models for the wind flow over buildings

The standard k–ε turbulence model is well known to perform poorly in the stagnation regions in front of buildings where it over-predicts the turbulent kinetic energy, k. It is less well known that this error is compounded by an excess decay of the turbulence over and behind a building so that k is eventually under-estimated in the building wake. A new formulation of the eddy viscosity in the standard k–ε turbulence model was developed and compared with previous modifications designed for stagnation regions. The new formulation provides more accurate values of k and it showed similar results for streamwise mean velocity predicted by the shear stress transport turbulence model. A blend between the new model and the standard eddy viscosity model provides the best overall prediction of the mean velocities and turbulence.