Low Reynolds Number Turbulence Research Articles

Formation of spanwise vorticity in oblique turbulent bands of transitional plane Couette flow, part 2: Modelling and stability analysis

This article presents a modelling of the formation of spanwise vorticity in the turbulent streaks of the oblique bands and spots of transitional plane Couette flow. A functional model is designed to mimic the coherent flow in the streaks. The control parameters of the model are extracted from Direct Numerical Simulations (DNS) statistical data. A Reynolds stress is proposed to study the effect on the instability of this additional force maintaining the baseflow. Local (quasi-parallel) temporal stability analysis is performed on that model to investigate the linear development of the spanwise vorticity. Results show that average profiles, even if they have an inflection, are stable: the shear layers inside the velocity streaks are responsible for the vorticity formation. Emphasis is put on the convective or absolute nature of the instability, depending on the location in the band. This shows that a transition from a convective to an absolute instability occurs in the zone in between fully turbulent and laminar flow. The group velocity of the most unstable modes compares well to the advection velocity of spanwise vorticity measured in DNS. This investigation is completed by the global (non-parallel) stability analysis of a typical band case. Eventually, the possible cycles of sustainment of localised low Reynolds number turbulence of shear flows are discussed in the light of these results.

Asymmetric turbulent boundary layers along long thin circular cylinders at low-Re

Notable deviations of the asymmetric turbulent boundary layer (TBL) statistics from their axisymmetric counterpart along long thin circular cylinders are vitally important to the naval and oceanographic jurisdictions. Although the available experimental evidence backs their concern, the realm of parametric variability (both geometric and kinematic) is extremely limited to draw solid conclusions. We know that only small misalignments which quantify less than one degree of incidence between the freestream and the straight cylinder axis can substantially alter the boundary layer thicknesses, mean axial velocity, and Reynolds stresses. But the statistical database is plainly inadequate to justify modifying the design tools that were founded solely for axisymmetric flow conditions. Herein, we begin rectifying this drawback by numerical means. The investigation centers on low turbulent Reynolds numbers (500 ≤ Rea ≤ 2500) and small angles-of-incidence (0° < α < 9°) to validate and complement the lions-share of the present database (Rea = aUo/ν, where a, Uo, and ν are the cylinder radius, freestream velocity, and kinematic viscosity, respectively). In particular, we numerically resolved the statistical responses of the TBL, mean axial velocity, Reynolds stresses, and skin friction under angles-of-incidence up to the earliest signs of Strouhal-type shedding. Clearly, the first prominent response was the thinning and thickening of the TBL along the respective windward and leeward sides to only a minor misalignment. Tilting the straight cylinder to slightly higher yaw angles transformed the TBL to a transitional boundary layer along the windward side for all simulated Reynolds numbers. For yaw angles α > 2°, all turbulent statistics of the asymmetric boundary layer were measurably dissimilar to those of the axisymmetric state.

Computational Study of Effect of Increasing Heat Flux on Convective Heat Transfer in Sub Channels of Carbon Dioxide Flow at Pressure above Critical Value

This paper is focused on flow simulation in the sub channel of fuel rod assembly using code ANSYS Fluent 14, which is commercial computational fluid dynamics (CFD) code. Computational simulations are reported on convective heat transfer to carbon dioxide at a pressure of 7.59MPa. Pressure which is used in this simulation are just above the thermodynamic critical pressure value of CO2. These have been carried out using a variable property, elliptic computational formulation incorporating low Reynolds number turbulence models ofk–ε. Firstly, the simulations were compared with the effect of increasing heat flux on heat transfer coefficient. It has been found that the effect of buoyancy on turbulence production and heat transfer in fluids at supercritical pressure can be very significant even under conditions of relatively low buoyancy parameter based on bulk properties. It is clear that new heat transfer correlations are needed to account for such effects on heat transfer to supercritical pressure fluids as they come to be used more and more in new energy systems applications such as, advanced water-cooled nuclear reactors, high pressure water oxidation plant for waste processing.

Unsteady-RANS simulation of conjugate heat transfer in a cavity with a vertical semitransparent wall

A numerical study of the unsteady conjugate heat transfer for a square cavity with a semitransparent (glass) wall is presented. The cases with or without solar control film on the semitransparent wall were studied from 8:00 to 18:00h. This wall interacts with the environment through the incident solar radiation and the outdoor air temperature, which were considered changing over the time. URANS (Unsteady Reynolds Averaged Navier–Stokes) model together with the model of Low-Reynolds number turbulence k–w were solved using the finite volume method. The results show flow patterns from multicellular to unicellular in different times for each case as result of the temperature in the semitransparent wall. Moreover, at approximately 9:00am, the solar control film increased the air temperature inside the cavity up to 10°C compared to the air temperature when the solar control film is not used. The cavity with solar control film has a lower period of time with a multicellular flow than the cavity without film. When the solar control film is used, the average heat flux due to convection and radiation represents 45% and 55%, respectively of the interior heat flux (qint). On the contrary, when the solar control film is not used, the heat flux due to radiation represents 70%.

Investigation on the relative performance of various low-Reynolds number turbulence models for buoyancy-driven flow in a tall cavity

The present study deals with the numerical investigation of turbulent buoyancy driven flow in a differentially heated rectangular cavity with adiabatic horizontal walls. The aspect ratio of cavity is 5 and the Rayleigh number based on the cavity height is 4.56 × 1010. The computations have been carried out using the finite volume method on a staggered grid and SIMPLEC algorithm for pressure–velocity coupling. The low-Reynolds number \(k-\epsilon\) model proposed by Yang and Shih (YS), low-Reynolds number \(k-\omega\) model proposed by Wilcox, and \(k-\omega\) shear stress transport (SST) model of Menter have been applied for turbulence closure. The performance comparison of different models have been carried out using the experimental, LES and various RANS results available in the literature. The computation of turbulent natural convection flow is numerically challenging due to complex flow involving laminar, transition and turbulent regions, coupling of velocity with the energy equation, and some other problems reported in literature e.g. grid dependency of solution, numerical stability problem, etc. The flux Richardson number is calculated to get an estimate of relative importance of buoyancy and shear force in different regions of flow. The shearing and swirling zones have been identified in the entire flow domain using the \(\lambda _{2}\) criterion. Based on the comparison of mean flow, heat transfer and turbulence characteristics with the available results, it has been found that YS model performs better. The better performance obtained from YS model may be due to peculiarity of model that takes into account the Kolmogorov time scale near the wall and the conventional time scale \((k/\epsilon )\) away from the wall.

A methodology for including wall roughness effects in k-ɛ low-Reynolds turbulence models - Part I and Part II: Part I. Basis of the methodology

A model accounting for wall roughness effects in k-ɛ low-Reynolds turbulence models is described in the present paper. In particular, the introduction in the transport equations of k and ɛ of additional source terms related to roughness, based on simple assumptions and dimensional relationships, is proposed. An objective of the present paper, in addition to obtaining more realistic predictions of wall friction, is the application of the proposed model to the study of heat transfer to supercritical fluids.A first validation of the model is reported. The model shows the capability of predicting, at least qualitatively, some of the most important trends observed when dealing with rough pipes in very different flow conditions. Qualitative comparisons with some DNS data available in literature are also performed. Further analyses provided promising results concerning the ability of the model in reproducing the trend of friction factor when varying the flow conditions, though improvements are necessary for achieving better quantitative accuracy.First applications of the model in simulating heat transfer to supercritical fluids are also described, showing the capability of the model to affect the predictions of these heat transfer phenomena, in particular in the vicinity of the pseudo-critical conditions. A more extended application of the model to relevant deteriorated heat transfer conditions will clarify the usefulness of this modelling methodology in improving predictions of these difficult phenomena. Whatever the possible success in this particular application that motivated its development, this approach suggests a general methodology for accounting for wall roughness effects in low-Reynolds number turbulence models.

Modelling the Flow in a Transonic Diffuser with One Reynolds-Stress and Two Eddy-Viscosity Models

Turbulence modeling combined with the mass averaged Navier-Stokes equations and detailed comparisons with experimental data are presented for a transonic flow in a converging diverging diffuser for two different inlet Mach numbers. Three low-Reynolds number turbulence models, which do not use the concept of the wall distance and wall normal vector calculation are adopted: a linear eddy-viscosity model, a cubic non-linear eddy-viscosity model and a non-linear Reynolds-stress model. The compressibility effects due to the mean density variations are incorporated in a subsonic pressure-based flow solver through minor modifications to the pressure velocity-coupling algorithm and by introducing the dilatation-dissipation of turbulence to the equations of the turbulent models. Grid dependency studies were conducted and detailed velocity and pressure coefficient distributions are presented in comparison with available experimental data providing also information for the boundary layer development on the diffuser walls in the region downstream the shock wave. The final results are very promising concerning the capability of the turbulence models to capture the compressibility effects in transonic flows when they are incorporated with appropriate modifications in a pressure-based flow solver.

Numerical Simulation of Airliner Cabin Environment based on Various Inlet Angles

The study of airflow transport in airliner cabins is extremely important in creating a comfortable environment. The air temperature field and velocity field in the airliner cabin have significant influence on the health of pilots and passengers. In this study, heat transfer based on numerical study was carried out to investigate the effects of natural convection and air distribution with different angles. The average Reynolds equation and low Reynolds number turbulence model were used to simulate the airflow in the cabin. The convective term of convection diffusion equation was implemented with higher-order accurate schemes. Mathematical statistics was adopted to process the final data. Results showed that the effect of the natural convection could be negligible. Additional studies presented that air temperature field and flow field were largely affected by various inlet angles. A set of optimum matching inlet vane angles that could create a comfortable environment was determined.

Structure Analysis of a Low Reynolds Number Turbulent Submerged Jet Interacting With a Free Surface

In this study, the spatial structures of a submerged turbulent jet interacting with a free surface were investigated experimentally. The jet axis was located at three different depths (H/D = 2, H/D = 4 and H/D = 6) beneath the free surface and the Reynolds number was fixed as 3480. Laser-induced fluorescence technique was used for qualitative visualization and the time-resolved particle image velocimetry technique was used for the quantitative measurements. The dynamics of the flow structures were examined further using the proper orthogonal decomposition analysis technique. The results revealed that the dynamic characteristics of large-scale turbulent motions were significantly different with the submerged depths. In case of H/D = 2, the dominant spatial structures displayed a surface vibration induced reverse flow along the boundary, and its subsequent deflection changed the flow structures in the horizontal center plane. The violent free surface vibration caused an unsteady up-and-down motion of the flow structures and had a “squeeze effect” on the flow structures. In case of H/D = 4, the upwelling motion of some vortices in the jet and their subsequently downward entrainment motion significantly changed the dominant spatial structures both in the vertical and horizontal central planes. When the jet was fully attached to the free surface, the vortical structures underwent a merging and restructuring process due to the vertical confinement of the free surface. In case of H/D = 6, the dominant spatial structures both in the vertical and horizontal central planes showed an approximately symmetric pattern, indicating that the dominant structures were not changed by the free surface. After attached to the free surface, the jet did not undergo a merging and restructuring process as shown in case of H/D = 4.

Reverse flow region associated to a heat transfer in a turbulent wall jet

A numerical study is performed in order to investigate the effects of the inlet flow structure on the flow and heat transfer characteristics in the reattachment zone downstream a backward facing step. Indeed, two inlet flow configurations are considered; a turbulent wall jet (WJ) which presents a particular structure with two sources of turbulence production (one is due to the shear flow related to the inner layer with small scale eddies and another one corresponds to the free shear jet flow with entrainment of large turbulence scales) and a standard channel flow (CF). The numerical approach is based on two-scale energy-flux model coupled with a full Reynolds stress closure valid at low turbulence Reynolds numbers. To calculate the turbulent heat-flux vector, we considered two models: a Single Gradient Diffusion Hypothesis (SGDH) and a Generalized Gradient Diffusion Hypothesis under a fixed heat flux boundary condition. Numerical predictions for the CF configuration are compared with experimental data of Vogel and Eaton (1985). So the present study would contribute emphasizing the role of the large eddies in the outer flow on the convective heat transfer in the recirculation zone.

Turbulent heat transfer in a counterflow moving porous bed using a two-energy equation model

This work investigates the influence of physical properties on heat transfer in a turbulent counterflow in a moving bed using the High and Low Reynolds number turbulence models, in which the working fluid flows in opposite direction to that of the steady movement of the permeable rigid medium. Transport equations for flow and heat transfer in a moving bed equipment are applied and discretized using the control-volume method. The system of algebraic equations obtained is relaxed via the SIMPLE algorithm. The effects of Reynolds number, solid-to-fluid velocity ratio, permeability, porosity, ratio of solid-to-fluid thermal capacity and ratio of solid-to-fluid thermal conductivity on heat transport are investigated. Results indicate that motion of solid material, contrary to the direction of the fluid, enhances heat transfer between phases. The same effect was observed for smaller Darcy number and porosity, as well as for higher solid-to-fluid thermal capacity and thermal conductivity ratios. When the intrinsic fluid velocity increases there is a greater conversion of mechanical kinetic energy into turbulence, increasing the final levels of the turbulent kinetic energy for both High and Low Reynolds number models.

Multidisciplinary simulation of a regeneratively cooled thrust chamber of liquid rocket engine: Turbulent combustion and nozzle flow

The present study proposed a unified framework to simulate multi-physical processes which are crucial for trade-off design of liquid rocket thrust chambers among propulsive performance, regenerative cooling, and pressure budget. As the first part, a turbulent combustion model based on the flamelet approach was developed to effectively incorporate detailed chemistry of high hydrocarbon fuel, turbulent mixing, enthalpy loss, and pressure variations within the nonadiabatic nozzle flow. In order to correctly capture the convective heat transfer and viscous friction in the turbulent boundary layer at the chamber wall, an advanced low-Reynolds number turbulence model is adopted in an axisymmetric compressible RANS solver, which is interactively coupled with a cooling analysis module for the conjugate heat transfer and hydraulics through the regenerative cooling channels. The present method has been applied to an actual regeneratively cooled thrust chamber and compared with measurement of hot-firing tests in terms of specific impulse, characteristic velocity, and thrust coefficient. Based on the numerical results, the effects of additional fuel cooling injection and wall friction on the propulsive parameters are discussed.

A comparative study of turbulence models in a transient channel flow

The performance of a number of low-Reynolds number turbulence models is evaluated against direct numerical simulations (DNS). All models are applied to an unsteady flow comprising a ramp-type excursion of flow rate inside a closed channel. The flow rate is increased linearly with time from an initial Reynolds number of 9308 (based on hydraulic diameter and bulk velocity) to a final Reynolds number of 29,650. The acceleration rate is varied to cover low, intermediate and high accelerations. It is shown that among the models investigated, the k–ε models of Launder and Sharma (1974) and Chang et al. (1995) [28] and the γ–Reθ transition model of Langtry and Menter (2009) [38] capture well the key flow features of these unsteady turbulent flows. For the cases of low and intermediate acceleration rates, these three models yield predictions of wall shear stress that agree well with the corresponding DNS data. For the case of high acceleration, the γ–Reθ model of Langtry and Menter (2009) [38] and the k–ε model of Launder and Sharma (1974) yield reasonable predictions of wall shear stress.

Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

Imbalance wall functions with density and material property variation effects applied to engine heat transfer computational fluid dynamics simulations

Heat transfer is a significant factor affecting internal combustion engine efficiency, emissions and performance. This study concentrates on model development for convective heat transfer and near-wall turbulent flow. The solution of complete fluid dynamics equations within the very thin-wall boundary layers is, and will be in the near future, very impractical in engineering scale flows with any present day method. An advanced numerical near-wall treatment method within the Reynolds averaged Navier–Stokes framework has been developed. The method solves simplified boundary layer equations for enthalpy, momentum, turbulent kinetic energy and dissipation in wall adjacent cells on cellwise high-resolution subgrids, adaptive to local conditions. The boundary layer equations include temperature gradient–induced density/multicomponent material property variations and complete imbalance contributions, for example, convection, transients, pressure gradient and external sources, in compact forms. The resulting numerical wall functions are valid with near-wall grid resolution ranging from the viscous sublayer to the fully turbulent region, thus avoiding the conflicting near wall resolution requirements of common low–Reynolds and high–Reynolds number turbulence models. The advanced near wall treatment method, comprising the numerical imbalance wall functions and accordingly modified low–Reynolds number turbulence model, is implemented in STAR-CD 4.12, extensively utilized in engine simulations. The near wall treatment method is validated against available measurements and direct numerical simulation data of strongly heated pipe flow. Performance of the near-wall treatment method in engine conjugate heat transfer simulations is also demonstrated. Local and average effects of variable properties and imbalance contributions on piston surface heat transfer, friction and turbulent sources are elaborated and contrasted to the standard high–Reynolds number near-wall treatment.

Integration of thermophysiological body model in CFD

Abstract A two-node mathematical model of the human thermophysiological system has been integrated into a Computational Fluid Dynamic (CFD) simulation of the airflow in a room. Temperature inputs from the CFD are used by the model to evaluate the dry and latent heat flux from the body surface and output them as boundary conditions. This is an iterative process and convergence is ensured by under-relaxation of the latent heat flux. The model also considers the dry and latent heat resistance of clothing. Numerical predictions of the body heat loss and airflow are compared against physical measurements in a climate chamber. Good agreement was observed when using the low Reynolds number turbulence model. The integrated simulation performs well under wide set of conditions, predicting body core and skin temperature, blood flow, skin wittedness, as well as the transfer of heat and moisture released by the body into the room.

Characterization of non-isothermal flows typical of built environments in a laboratory scale model. Part II – Numerical predictions with CFD

CFD predictions of built environment flows require turbulence modelling. RANS-based turbulence models (standard and RNG k–ε) have been widely used due to their ability to capture the main features of the time-averaged variables of such flows without demanding unaffordable computer requirements. Herein, the experimental results presented in Part I are used to validate numerical predictions of non-isothermal flows performed with the standard, the RNG with turbulent viscosity formulation and, for the first time, the RNG with differential effective viscosity formulation k–ε models. Two office geometries are simulated for mixing and displacement ventilation strategies. For mixing the RNG k–ε model with the differential effective viscosity provides the most accurate results for both U and V velocity components, temperature, turbulence intensity and PPD comfort index. However, the W velocity component and the DR comfort index are better predicted by the high-Reynolds number models. For displacement there is not a remarkable improvement in results of the velocity, temperature, turbulence intensity and comfort indexes generated by the RNG k–ε with the differential effective viscosity calculation, when compared with those obtained with the turbulent viscosity formulation. Both models yield much more accurate results for temperature and velocity than those given by the standard k–ε model. In opposition, the former yields the best results for the DR comfort index. From the analysis of the turbulence intensity profiles for both ventilation strategies it is possible to infer the need to improve the buoyancy model when using low-Reynolds number turbulence models.

Performance and implementation of the Launder–Sharma low-Reynolds number turbulence model

The Launder–Sharma model (Lett. Heat Mass Transfer 1, 1974, 131–138) is one of the earliest and most-widely used low-Reynolds number (LRN) models and has been shown to be in good agreement with experimental and DNS data for a range of turbulent flow problems, performing better than many other LRN k–ε models. However, some recent studies including those using commercial CFD solvers report the model to behave otherwise. In the present study, the LS model has been implemented in FLUENT using user-defined functions (UDFs), and its performance in predicting steady and unsteady turbulent flows has been tested and found to agree closely with those reported in the literature using ‘in-house’ CFD codes. However, this FLUENT-UDF LS model performs very differently from the in-built FLUENT LS model. The former agrees well with experimental and DNS data, whereas the latter does not. In addition, the UDF is used to demonstrate that the model predictions are very sensitive to the interpretation of the model formulation. Consequently, it is concluded that whereas the LS model is not sensitive to numerical method or method of coding, it is sensitive to changes in the interpretation of the formulation of the model.

Comparison of two low-Reynolds number turbulence models for fluid flow study of wall bounded jets

A comparative study of flow field and turbulence characteristics of a turbulent offset jet has been done. The computational results obtained from low-Reynolds number k–ϵ models proposed by Launder and Sharma, and Yang and Shih are compared with that of the standard k–ϵ model. The existence of Moffatt vortices (secondary recirculation region) have been identified near the corner of the wall for low-Reynolds number modeling. A velocity similarity profile has been observed as expected due to the resemblance of an offset jet with that of the wall jet flow in the wall jet region. The linear law of the wall (u+=y+) has been found to be valid up to y+≈3.0 in the wall jet region which agrees with the experimental results. The integral constant of momentum flux is higher for lower offset ratio due to a smaller recirculation region. The distribution of pressure field, Reynolds shear stress, budget of turbulent kinetic energy in the recirculation region and the jet characteristic parameters such as variation of the jet half-width (Y0.5) along the streamwise direction and decay of the maximum streamwise velocity are discussed in detail.

2E1 低レイノルズ数乱流域における再付着流れ場の能動制御(流体工学2)

2E1 低レイノルズ数乱流域における再付着流れ場の能動制御(流体工学2)