Local Turbulent Reynolds Number Research Articles

Soot Modeling in Large Eddy Simulation of Turbulent Buoyant Flames Using the Laminar Smoke Point and the Eddy Dissipation Concept

ABSTRACT The paper presents a comprehensive set of Large Eddy Simulations (LES) of turbulent diffusion buoyant flames with a focus on soot modeling. Combustion modeling is based on the Eddy Dissipation Model (EDM) with an infinitely fast chemistry approach. Soot formation and oxidation are modeled with finite-rate chemistry based on the Laminar Smoke Point (LSP) concept. A turbulence-soot interaction model is proposed based on the Eddy Dissipation Concept (EDC) to close the chemical sink/source term for soot. A novel aspect of the modeling is the hybrid EDC formulation, where the mean chemical source term is a weighted average of a laminar term and a turbulent term, based on the local turbulent Reynolds number. The correct limiting behavior in the laminar regime is demonstrated for a laminar ethylene flame. Improvements in soot predictions near the fuel injection are obtained for a 13.7 cm-diameter turbulent ethylene flame and a 30 cm-diameter heptane flame. Additionally, the influence of the combustion model on soot predictions is carefully examined, especially with respect to the mixing time scale formulation and the related influence of the cell size (used as filter width in LES). A proposed dynamic model allows obtaining improved results even in under-resolved simulations and mitigating mesh sensitivity for soot predictions.

A case study of multi-structure turbulence: Uniformly sheared flow distorted by a grid

The fine and large–scale structures of spatially developing uniformly sheared flow (USF) and USF distorted by a square–mesh grid were examined experimentally using one– and two–point, two–component hot–wire anemometry. In agreement with previous findings, it was confirmed that USF has a far downstream region, where the dissipation parameter Cε is approximately constant, and an intermediate region, where it scales with the local turbulent Reynolds number as Cɛ∝Reλ−0.6. The insertion of a grid across the USF resulted in the creation of multi-structure turbulence (a flow in which at least two kinds of dominant eddies exist and contribute significantly to the local averages at the energy-containing level) and a permanent reduction of the kinetic energy and the integral length scales of the turbulence. Near the grid the dissipation parameter scaled as Cɛ∝Reλ−1, as in decaying grid turbulence, despite the opposite evolution rates of Reλ in the two flows. The turbulence fine structure within this multi–structure region was unaffected significantly by the grid, whereas the large–scale anisotropy was markedly changed. Second–order structure functions, normalised by Kolmogorov scales, collapsed in the viscous sub–range , whereas within the inertial sub–range the effects of grid insertion were measurable.

Dissipation scaling in constant-pressure turbulent boundary layers

Using results from previous direct numerical simulations and experiments in the outer region of spatially evolving turbulent boundary layers, we compute the streamwise evolution and the wall-normal variation of the dissipation parameter CE, namely, the turbulent kinetic energy dissipation rate, normalized by appropriate powers of the local turbulent kinetic energy and integral length scale. For Reθ3 10000 (Reθ is a Reynolds number on the freestream velocity and the local momentum thickness), CE is essentially constant in the streamwise direction, but varies by up to 50% in the wall-normal direction. For Reθ<10000, CE is additionally found to vary in the streamwise direction and is inversely proportional to the local turbulence Reynolds number Reλ.

Energy dissipation scaling in uniformly sheared turbulence.

The rate of turbulent kinetic energy dissipation in spatially developing, uniformly sheared turbulence is examined experimentally. In the far-downstream fully developed region of the flow, we confirm that the dissipation parameter C(ɛ) is constant. More importantly, however, we find two upstream regions where this parameter could be scaled with the local turbulent Reynolds number as C(ɛ)=ARe(λ)(α); the exponents in these two regions are, respectively, α=-0.6 and 0.5. The observed changes in scaling laws are explained by consideration of structural changes in the turbulence.

A rule of minimal energy dissipation in modeling of channel flow turbulence

ABSTRACTA model of turbulence is proposed to solve Reynolds equations for fully developed flow in a wall-bounded straight channel. We show that for the channel flow the Reynolds number can be defined as a ratio of flow kinetic energy to the work of friction/dissipation forces. Then, we introduce a turbulent Reynolds number as a balance between energy losses due to the momentum exchange by turbulent vortices traveling from lowto high-velocity areas and wall friction. The main idea of the model is expressed in the following phenomenological law: The minimal energy dissipation rule requires that a local deformation of the axial velocity profile can and, in the presence of finite-size instabilities, should generate turbulence with such intensity that it keeps the local turbulent Reynolds number below the critical value. Thus, the only empirical parameter in the model is the critical Reynolds number.The model is applied to several basic channel flows such as the fully developed flow in a circular tube, in an infinite plane channel, and in an annulus. The application of the minimal energy dissipation rule requires an additional integral equation, and this can be considered as an integral-equation algebraic model of turbulence.

Effect of fuel composition and differential diffusion on flame stabilization in reacting syngas jets in turbulent cross-flow

Three-dimensional direct numerical simulation results of a transverse syngas fuel jet in turbulent cross-flow of air are analyzed to study the influence of varying volume fractions of CO relative to H2 in the fuel composition on the near field flame stabilization. The mean flame stabilizes at a similar location for CO-lean and CO-rich cases despite the trend suggested by their laminar flame speed, which is higher for the CO-lean condition. To identify local mixtures having favorable mixture conditions for flame stabilization, explosive zones are defined using a chemical explosive mode timescale. The explosive zones related to flame stabilization are located in relatively low velocity regions. The explosive zones are characterized by excess hydrogen transported solely by differential diffusion, in the absence of intense turbulent mixing or scalar dissipation rate. The conditional averages show that differential diffusion is negatively correlated with turbulent mixing. Moreover, the local turbulent Reynolds number is insufficient to estimate the magnitude of the differential diffusion effect. Alternatively, the Karlovitz number provides a better indicator of the importance of differential diffusion. A comparison of the variations of differential diffusion, turbulent mixing, heat release rate and probability of encountering explosive zones demonstrates that differential diffusion predominantly plays an important role for mixture preparation and initiation of chemical reactions, closely followed by intense chemical reactions sustained by sufficient downstream turbulent mixing. The mechanism by which differential diffusion contributes to mixture preparation is investigated using the Takeno Flame Index. The mean Flame Index, based on the combined fuel species, shows that the overall extent of premixing is not intense in the upstream regions. However, the Flame Index computed based on individual contribution of H2 or CO species reveals that hydrogen contributes significantly to premixing, particularly in explosive zones in the upstream leeward region, i.e. at the preferred flame stabilization location. Therefore, a small amount of H2 diffuses much faster than CO, creating relatively homogeneous mixture pockets depending on the competition with turbulent mixing. These pockets, together with high H2 reactivity, contribute to stabilizing the flame at a consistent location regardless of the CO concentration in the fuel for the present range of DNS conditions.

Dissipation in Turbulent Flows

This article reviews evidence concerning the cornerstone dissipation scaling of turbulence theory: [Formula: see text], with Cϵ=const., ϵ the dissipation rate of turbulent kinetic energy [Formula: see text], and [Formula: see text] an integral length scale characterizing the energy-containing turbulent eddies. This scaling is intimately linked to the Richardson-Kolmogorov equilibrium cascade. Accumulating evidence shows that a significant nonequilibrium region exists in various turbulent flows in which the energy spectrum has Kolmogorov's −5/3 wave-number scaling over a wide wave-number range, yet Cϵ∼RemI/RenL, with m≈1≈n, ReI a global/inlet Reynolds number, and ReL a local turbulence Reynolds number.

Development of a gas phase combustion model suitable for low and high turbulence conditions

A novel hybrid gas phase combustion model suitable for low as well as high turbulent combustion conditions is proposed. In particular, in the region above the fuel bed of small-scale biomass combustion plants, gas phase mixing is highly influenced by laminar and low turbulence zones. Here, the eddy break-up combustion models are not valid because they were originally developed for highly turbulent flows. Therefore, a CFD gas phase reaction model applicable over the whole Reynolds range from laminar to turbulent flows is developed. It is a hybrid Eddy Dissipation Concept/finite rate kinetics model which calculates the effective reaction rate from laminar finite rate kinetics and the turbulent reaction rate and weights them depending on the local turbulent Reynolds number of the flow. To validate the proposed model, comparisons are made with experimental data for a series of jet flames covering laminar, transitional, and turbulent flow conditions. The simulation results show that the prediction of flame can be improved with the proposed hybrid combustion model.

Key Factors in Determining the Magnitude of Vorticity in Turbulent Plane Wakes

We examine the effects of local turbulence Reynolds number Rλ and inflow conditions on the magnitude of vorticity in plane turbulent wakes. Measurements of the spanwise component (ω3) of the fluctuating vorticity vector ω = ω1i + ω2j + ω3k (here the subscripts 1, 2 and 3 denote the streamwise, lateral and spanwise directions, respectively) are made in turbulent wakes of a screen and a circular cylinder. Lateral distributions of ω3* (normalized) in general depend on both Rλ and inflow conditions. In the developing region, as the downstream distance x1 increases, ω3* increases significantly in the screen wake but decreases slightly in the cylinder wake. Far downstream in the self-preserving region, ω3* increases linearly with Rλ while it no longer varies with x1 and depends weakly on the influence of inflow conditions. Our analysis suggests that these findings from the measurement of ω3* should apply for the magnitude of ω.

Investigation of Energy Loss Mechanisms in Cyclone Separators

Based on the transient Navier-Stokes equation of an incompressible Newtonian fluid, a vorticity form of the mean mechanical energy equation is derived which is suitable for strongly swirling flow or vortex flow, and reveals the mechanism of mean mechanical energy losses in cyclone separators. Results show that the mean mechanical energy losses in cyclone separators are mainly caused by mean viscous dissipation, turbulent diffusion, and turbulent energy production in a steady turbulent flow. Order-of-magnitude analysis indicates that the rate of local turbulent energy production and mean viscous dissipation is related to the local turbulent Reynolds number at each point in cyclone separators. A large local turbulent Reynolds number designates the turbulent energy production as the primary contributor to mean mechanical energy losses, whereas in the case of a small turbulent Reynolds number the order-of-magnitude quotient between the two quantities decreases, indicating the increased significance of the mean viscous dissipation contribution to mean mechanical energy losses. A combination of theoretical analysis and LDV experimental results indicates the mean viscous dissipation is larger in the quasi-forced vortex region and the boundary layer than in other regions of cyclone separators. The energy losses are mainly caused by turbulent energy production in a majority of the regions (except in the laminar sublayer very close to the wall), especially the largest energy losses in the central quasi-forced vortex region. Hence, decreasing turbulence is an effective approach for drag reduction in cyclone separators.

Numerical Prediction of Secondary Flows in Complex Areas Using Concept of Local Turbulent Reynolds Number

A new model of turbulence is proposed for the estimation of Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. The main idea of a Multi-Scale Viscosity (MSV) model can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of the local turbulent Reynolds number below some critical one. Therefore, in MSV, the only empirical parameter is the critical Reynolds number. Multi-scale viscosity has been verified on the pipe flow and applied to simulation of turbulence-driven secondary flow in elementary cell of the infinitive hexagonal rod array. Since MSV can predict turbulent viscosity anisotropy in directions normal and parallel to the wall, it is capable to calculate secondary flows in the cross-section of the rod bundle. Calculations have shown that maximal intensity of secondary flow is about 1% of the mean axial velocity for the low-Re flows (Re=8, 170), while for higher Reynolds number (Re=160, 100) the intensity of secondary flow is as negligible as 0.2%.

Numerical Prediction of Secondary Flows in Complex Areas Using Concept of Local Turbulent Reynolds Number

A new model of turbulence is proposed for the estimation of Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. The main idea of a Multi-Scale Viscosity (MSV) model can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of the local turbulent Reynolds number below some critical one. Therefore, in MSV, the only empirical parameter is the critical Reynolds number. Multi-scale viscosity has been verified on the pipe flow and applied to simulation of turbulence-driven secondary flow in elementary cell of the infinitive hexagonal rod array. Since MSV can predict turbulent viscosity anisotropy in directions normal and parallel to the wall, it is capable to calculate secondary flows in the cross-section of the rod bundle. Calculations have shown that maximal intensity of secondary flow is about 1% of the mean axial velocity for the low-Re flows (Re=8, 170), while for higher Reynolds number (Re=160, 100) the intensity of secondary flow is as negligible as 0.2%.

Two-equation turbulence modelling of a transitional separation bubble

Calculations of the Reynolds averaged equations using two different turbulence models have been compared with direct numerical simulation of a transitional separation bubble. Three methods of transition modelling were investigated. The first had no transition adjustment, the second involved fixing the transition point at the location observed in the simulation and the third was a direct transformation of a method proposed by Wilcox [1] which involved sensitising the eddy viscosity and transport equations to the local turbulent Reynolds number. The models captured the general features of the flow but were unable to show the recovery behaviour of the flow behind the bubble. Reasons for the failure are discussed using apriori analysis of terms in the model equations.

ASSESSMENT OF TURBULENCE MODELS FOR NATURAL CONVECTION IN AN ENCLOSURE

Abstract Two available low-Reynolds-number k-σ turbulence models have been used to predict turbulent natural convection within a differentially heated enclosure for the purpose of assessing their relative merits. In one model, fixed numerical values are employed for the model coefficients; in the other model, the coefficients vary with the value of the local turbulence Reynolds number. The numerical results from both models are compared to published experimental data. In general, the variable coefficient model predicts lower turbulence levels than the fixed coefficient model. Both models predict measured velocity profiles adequately, but overall, the predictions of the variable coefficient model are superior. The average Nusselt numbers are predicted more accurately by the variable coefficient model than by the fixed coefficient model.

Anisotropy of the dissipation tensor in a turbulent boundary layer

The second and third invariants of the Reynolds stress anisotropy tensor and the Reynolds stress dissipation rate anisotropy tensor have been evaluated from direct numerical simulation data for a boundary layer. The departure from isotropy increases in both inner and outer regions of the layer as the momentum thickness Reynolds number Rθ decreases. The relationship between the two anisotropy tensors has been examined in some detail. A linear relation, with a constant of proportionality depending on the local turbulence Reynolds number, is well supported by the outer region data for three values of Rθ.

Particle drag in a dilute turbulent two-phase suspension flow

The drag between phases plays an important role in the study of a turbulent two-phase suspension flow and its physical understanding will greatly promote progress in theoretical treatments of a whole range of important industrial and technical problems involving such a flow. The conventional practice of using the results of measurements based on a single particle in a laminar stream for the case of a turbulent flow of a dilute suspension is questioned. An analysis of the results of local measurements of upward turbulent flows of a solid particle-air two-phase suspension leads to the determination of the realistic particle drag coefficient over a wide range of flow conditions. It is established that the particle drag can be described by the simple Stokes law, based on an apparent turbulent viscosity of the fluid for the particles in the suspension flow. A correlation is provided for this apparent turbulent viscosity in terms of the particle size and concentration in the suspension, the local flow turbulence Reynolds number and the particle-to-fluid density ratio.

Lift-off Heights and Visible Lengths of Vertical Turbulent Jet Diffusion Flames in Still Air

Abstract The lift-off heights and visible-flame lengths of jet diffusion flames in still air have been determined for hydrogen, propane, methane and ethylene. The flame lift-off height varies linearly with the jet exit velocity and is independent of the burner diameter for a given gas. The results support the assumption that if the burner exit flow is choked the burner can be approximated by an equivalent convergent-divergent nozzle at whose exit the flow has expanded to ambient pressure. The data for different gases can be collapsed onto a single curve if they are plotted in terms of the appropriate non-dimensional groupings. These results and previous results for blow-out stability suggest that diffusion flames blow out when the base is lifted to between 0.65 and 0.75 times the height at which stoichiometric concentration is reached at the jet axis. It can be deduced from the experimental results that, at the base of the flame. the ratio of turbulent burning velocity to laminar burning velocity varies as the square root of the local turbulence Reynolds number based on the integral length scale. The predicted correlation for the turbulent burning velocity agrees well with the experimental data presented in the literature. The flame length results for different gases and burner diameters can be collapsed onto a single curve if plotted in terms of the non-dimensional groupings suggested by Becker and Liang (Combust. Flame. 32, p. 115, 1978). The results near the forced convection limit are in line with the theoretical work presented by Becker and Liang but disagree with their final recommendation. Away from the forced convection limit, the flame length correlation is similar to that proposed by Becker and Liang.

An approach to the theoretical description of turbulent jet diffusion flames—Part I: Combustion model and calculation

The microscopic structure of the reaction zone in turbulent diffusion flames may be considered to be composed of numerous flame sheets, each of which behaves like a laminar diffusion flame. Wohlenberg [1] has proposed a combustion model for turbulent diffusion flames with the basic premise being that a large part of the macroscopic effects of turbulence on the reaction rate are accounted for by the increase in reaction interface extension due to the turbulence. Starting from this model, the authors proposed a model by attaching importance to the stretching of the reaction interface and the molecular diffusion of reactants, and introduced an equation giving the local reaction rate for turbulent diffusion flames. A function B involved in this equation expresses the effect of turbulence upon the reaction rate and is correlated with the local turbulent Reynolds number. The equation of local reaction rate was used as a source term of the conservation equations on turbulent diffusion flames. Using the GEMIX 4 program developed for boundary layers by Patankar and Spalding [2], numerical calculations were conducted on two coaxial jet diffusion flames of hydrogen and propane. A reasonably good agreement was found with the experimental results, e.g., flame shape, temperature distribution and coexistence of reactants.

Chemical Reaction in a Turbulent Flow Field with Uniform Velocity Gradient

A simplified statistical theory is developed which describes the chemically reacting, turbulent shear flows in a tractable manner. This theory, which is based on the concept of the generalized Brownian motion, instead of Navier-Stokes equation, is completely self-containing provided that the molecular Schmidt number is of order one and that the local turbulence Reynolds number is sufficiently large. The latter requirement restricts the theory to the flow region outside of the laminar sublayers. The homologous flow and concentration fields are first analyzed for the chemically frozen case. From the analyses, the relationships between the mean velocity and concentration gradients, and the Reynolds stress, turbulence energy, turbulent transport of chemical species, and the mean square fluctuation of the species concentration are established. Comparison of the present results with the available experimental data is made, which shows a satisfactory agreement. The nonequilibrium chemical reaction is then analyzed and is found to create an inhomogeneity in the concentration field which, among other things, causes the mean square fluctuation to vary nonuniformly with respect to the Damkohler number and the flow region.