Turbulent Velocity Fluctuations Research Articles

On a numerical model for extracting TKE dissipation rate from very high frequency (VHF) radar spectral width

The standard model (e.g., Hocking in Earth Planets Space 51:525–541, 1999), varepsilon = c_{0} sigma^{2} N, (where sigma is the radar spectral width assumed to be equal to vertical turbulence velocity fluctuation sqrt {overline{{w^{2} }} }, N is the buoyancy frequency, and c0 is a constant), derived from Weinstock (J Atmos Sci 35:1022–1027, 1978; J Atmos Sci 38:880–883, 1981) formulation, has been used extensively for estimating the turbulence kinetic energy (TKE) dissipation rate varepsilon under stable stratification from VHF radar Doppler spectral width sigma. The Weinstock model can be derived by simply integrating the TKE spectrum in the wavenumber space from the buoyancy wavenumber k_{text{B}} = frac{N}{sigma } to infty. However, it ignores the radar volume dimensions and hence its spatial weighting characteristics. Labitt (Some basic relations concerning the radar measurements of air turbulence, MIT Lincoln Laboratory, ATC Working Paper NO 46WP-5001, 1979) and White et al. (J Atmos Ocean Technol 16:1967–1972, 1999) formulations do take into account the radar spatial weighting characteristics, but assume that the wavenumber range in the integration of TKE spectrum extends from 0 to infty. The White et al. model accounts for wind speed effects, whereas the other two do not. More importantly, all three formulations make the assumption that k−5/3 spectral shape of TKE spectrum extends across the entire wavenumber range of integration. It is traditional to use Weinstock formulation for k_{text{B}}^{ - 1} < 2a,2b (where a and b are radar volume dimensions in the horizontal and vertical directions) and White et al. formulation (without wind advection) for k_{text{B}}^{ - 1} > 2a,2b. However, there is no need to invoke these asymptotic limits. We present here a numerical model, which is valid for all values of buoyancy wavenumber k_{text{B}} and transitions from varepsilon simsigma^{2} behavior at lower values of sigma in accordance with Weinstock’s model, to varepsilon simsigma^{3} at higher values of sigma, in agreement with Chen (J Atmos Sci 31:2222–2225, 1974) and Bertin et al. (Radio Sci 32:791–804, 1997). It can also account for the effects of wind speed, as well the beam width and altitude. Following Hocking (J Atmos Terr Phys 48:655–670, 1986, Earth Planets Space 51:525–541, 1999), the model also takes into account contributions of velocity fluctuations beyond the inertial subrange. The model has universal applicability and can also be applied to convective turbulence in the atmospheric column. It can also be used to explore the parameter space and hence the influence of various parameters and assumptions on the extracted varepsilon values. In this note, we demonstrate the utility of the numerical model and make available a MATLAB code of the model for potential use by the radar community. The model results are also compared against in situ turbulence measurements using an unmanned aerial vehicle (UAV) flown in the vicinity of the MU radar in Shigaraki, Japan, during the ShUREX 2016 campaign.

Buoyancy-induced effects on large-scale motions in differentially heated vertical channel flows studied in direct numerical simulations

Direct numerical simulations of turbulent convection in a differentially heated vertical channel flow with Prandtl number Pr=0.71 are conducted with a fourth-order accurate finite volume method for a bulk Reynolds number Reb=4328 and three Grashof numbers Gr ∈ {0, 6.4 · 105, 9.5 · 105}. The discussion of instantaneous flow field snapshots, first- and second-order moments, budget equations, power density spectra and quadrant analyses shows that the turbulent velocity fluctuations are attenuated in the aiding flow and enhanced in the opposing flow. In contrast, temperature fluctuations are attenuated in the opposing flow and enhanced in the aiding flow. The analyses further reveal that the low-momentum flow structures in the aiding flow are warmer than the high-momentum flow structures and vice versa in the opposing flow. Due to their different temperatures, buoyancy accelerates and decelerates the flow structures differently, which leads to reduced and increased pressure and shear fluctuations in the aiding and opposing flow. Thus, the redistribution of turbulent velocity fluctuations is lower in the aiding flow and higher in the opposing flow. The Reynolds shear stresses are consequently decreased in the former and increased in the latter, influencing the production of streamwise velocity fluctuations accordingly. In summary, the discussed physical mechanisms underline the indirect effect of buoyancy on the turbulent velocity fluctuations.

Mixing Coefficient in Stably Stratified Flows

AbstractTurbulent mixing in the interior of the oceans is not as well understood as mixing in the oceanic boundary layers. Mixing in the generally stably stratified interior is primarily, although not exclusively, due to intermittent shear instabilities. Part of the energy extracted by the Reynolds stresses acting on the mean shear is expended in increasing the potential energy of the fluid column through a buoyancy flux, while most of it is dissipated. The mixing coefficient χm, the ratio of the buoyancy flux to the dissipation rate of turbulence kinetic energy ε, is an important parameter, since knowledge of χm enables turbulent diffusivities to be inferred. Theory indicates that χm must be a function of the gradient Richardson number. Yet, oceanic studies suggest that a value of around 0.2 for χm gives turbulent diffusivities that are in good agreement with those inferred from tracer studies. Studies by scientists working with atmospheric radars tend to reinforce these findings but are seldom referenced in oceanographic literature. The goal of this paper is to bring together oceanographic, atmospheric, and laboratory observations related to χm and to report on the values deduced from in situ data collected in the lower troposphere by unmanned aerial vehicles, equipped with turbulence sensors and flown in the vicinity of the Middle and Upper Atmosphere (MU) radar in Japan. These observations are consistent with past studies in the oceans, in that a value of around 0.16 for χm yields good agreement between ε derived from turbulent temperature fluctuations using this value and ε obtained directly from turbulence velocity fluctuations.

Spectral Characteristics of Turbulent Velocity Fluctuations at Different Reynolds Numbers

Different approaches to the theoretical description of the energy characteristics of turbulence are considered on a wide wavenumber range including both the inertial and the dissipation intervals. The description is based on the hypothesis on the locality of intermodal interactions and the cascade mechanism of energy transfer over the wavenumber spectrum. The concept of the Markovian nature of the transfer makes it possible to use the methods of renormalization group and to derive a renorm group equation supplementing the conventionally used dimensional considerations and the energy balance equation. Within the framework of a model that does not contain unphysical singularities of the type of the inverse spectral flux formulas for the spectral characteristics are obtained beyond the turbulence generation region at different Reynolds numbers determined by the turbulent energy pumping parameters on the small wavenumber range modeled by an external random force.

Mechanism of turbulence generation in the logarithmic region of the boundary layer affected by the adverse pressure gradient

The sequence of turbulent energy production, diffusion and dissipation processes in the region of the boundary layer of y/δ≈0.45 under conditions of streamwise adverse pressure gradient has been described for the first time using the Smoke Image Velocimetry (SIV) technique with a good spatial and temporal measurement scale commensurate with the linear and temporal scales of the Kolmogorov vortex dissipation. Considerable increase in the third-order moments of the turbulent velocity fluctuations and their spatial gradient describing the turbulent diffusion energy transport in the region of y/δ≈0.45 has been observed.

Large Eddy Simulation of Turbulent Attached Cavitating Flows around Different Twisted Hydrofoils

In this paper, the turbulent attached cavitating flows around two different twisted hydrofoils, named as NACA0009 and Clark-y, are studied numerically, with emphasis on cavity shedding dynamic behavior and the turbulence flow structures. The computational method of large eddy simulation (LES) coupled with a homogeneous cavitation model is applied and assessed by previous experimental data. It was found that the predicted results were in good agreement with that of the experiment. The unsteady cavity morphology of the two hydrofoils undergoes a similar quasi-periodic process, but has different shedding dynamic behavior. The scale of the U-type shedding structures forming on the suction surface of NACA0009 is larger than that of Clark-y. This phenomenon is also present in the iso-surface distributions of Q-criterion. Otherwise, the time-averaged cavity morphology is dramatically different for the two hydrofoils, and it is found that the attached location of the cavity is closely related to the hydrofoil geometry. The time fluctuation of the lift force coefficients is affected significantly by the cavity shedding dynamics. Compared with NACA0009, the lift force of Clark-y shows more fluctuation, due to its complicated shedding behavior. Further analysis of the turbulent structure indicates that the more violent shedding behaviors can induce higher levels of turbulence velocity fluctuations.

Interface methods for grey-area mitigation in turbulence-resolving hybrid RANS-LES

A grey area mitigation method is proposed for hybrid RANS-LES modeling. The proposed methodology is evaluated using a hybrid RANS-LES method based on a Low-Reynolds-Number k−ω model applied to channel flow, boundary layer flow and a spatially developing mixing layer flow. Emphasis is put on the use of commutation terms at the RANS-LES interfaces in the transport equations for the turbulent kinetic energy, the specific dissipation rate and the momentum equation in order to rapidly reduce the turbulent viscosity across a RANS-to-LES interface and to stimulate the development of resolved turbulent fluctuations. The proposed methodologies are applied at both wall-normal (and inlet) and wall-parallel RANS-LES interfaces.The proposed methodology gives a rapid reduction of the turbulent viscosity at the wall-normal RANS-LES interface from its RANS level to its LES level. Moreover, the proposed methodology contributes to a substantially more rapid establishment of the turbulence-resolving LES flow downstream of the wall-normal RANS-LES interface than if no grey-area mitigation method is applied. However, the proposed methodology has a weaker effect at wall-parallel RANS-LES interfaces, due to a stronger entrainment of LES contents into the near-wall RANS region, than at the wall-normal RANS-LES interfaces.Good agreement with experimental data is obtained with the proposed interface method for the evaluated flow cases. The most obvious grey area mitigation effect is given in the simulated mixing layer flow. Turbulent velocity fluctuations are efficiently established with the commutation term in the momentum equation at the RANS-LES interface in this flow as well as a rapid reduction of the turbulent viscosity due to the commutation terms in the k and ω equations, which gives an almost negligible delay in the development of the resolved turbulence.

Horizontal Dispersion of Buoyant Materials in the Ocean Surface Boundary Layer

ABSTRACTThe horizontal dispersion of materials with a constant rising speed under the exclusive influence of ocean surface boundary layer (OSBL) flows is investigated using both three-dimensional turbulence-resolving Lagrangian particle trajectories and the classical theory of dispersion in bounded shear currents generalized for buoyant materials. Dispersion in the OSBL is caused by the vertical shear of mean horizontal currents and by the turbulent velocity fluctuations. It reaches a diffusive regime when the equilibrium vertical material distribution is established. Diffusivity from the classical shear dispersion theory agrees reasonably well with that diagnosed using three-dimensional particle trajectories. For weakly buoyant materials that can be mixed into the boundary layer, shear dispersion dominates turbulent dispersion. For strongly buoyant materials that stay at the ocean surface, shear dispersion is negligible compared to turbulent dispersion. The effective horizontal diffusivity due to shear dispersion is controlled by multiple factors, including wind speed, wave conditions, vertical diffusivity, mixed layer depth, latitude, and buoyant rising speed. With all other meteorological and hydrographic conditions being equal, the effective horizontal diffusivity is larger in wind-driven Ekman flows than in wave-driven Ekman–Stokes flows for weakly buoyant materials and is smaller in Ekman flows than in Ekman–Stokes flows for strongly buoyant materials. The effective horizontal diffusivity is further reduced when enhanced mixing by breaking waves is included. Dispersion by OSBL flows is weaker than that by submesoscale currents at a scale larger than 100 m. The analytic framework will improve subgrid-scale modeling in realistic particle trajectory models using currents from operational ocean models.

Secondary motion in turbulent pipe flow with three-dimensional roughness

The occurrence of secondary flows is investigated for three-dimensional sinusoidal roughness where the wavelength and height of the roughness elements are systematically altered. The flow spanned from the transitionally rough regime up to the fully rough regime and the solidity of the roughness ranged from a wavy, sparse roughness to a dense roughness. Analysing the time-averaged velocity, secondary flows are observed in all of the cases, reflected in the coherent stress profile which is dominant in the vicinity of the roughness elements. The roughness sublayer, defined as the region where the coherent stress is non-zero, scales with the roughness wavelength when the roughness is geometrically scaled (proportional increase in both roughness height and wavelength) and when the wavelength increases at fixed roughness height. Premultiplied energy spectra of the streamwise velocity turbulent fluctuations show that energy is reorganised from the largest streamwise wavelengths to the shorter streamwise wavelengths. The peaks in the premultiplied spectra at the streamwise and spanwise wavelengths are correlated with the roughness wavelength in the fully rough regime. Current simulations show that the spanwise scale of roughness determines the occurrence of large-scale secondary flows.

The Critical Role of the Boundary Layer Thickness for the Initiation of Aeolian Sediment Transport

Here, we propose a conceptual framework of Aeolian sediment transport initiation that includes the role of turbulence. Upon increasing the wind shear stress τ above a threshold value τ t ′ , particles resting at the bed surface begin to rock in their pockets because the largest turbulent fluctuations of the instantaneous wind velocity above its mean value u ¯ induce fluid torques that exceed resisting torques. Upon a slight further increase of τ , rocking turns into a rolling regime (i.e., rolling threshold τ t ≃ τ t ′ ) provided that the ratio between the integral time scale T i ∝ δ / u ¯ (where δ is the boundary layer thickness) and the time T e ∝ d / [ ( 1 − 1 / s ) g ] required for entrainment (where d is the particle diameter and s the particle–air–density ratio) is sufficiently large. Rolling then evolves into mean-wind-sustained saltation transport provided that the mean wind is able to compensate energy losses from particle-bed rebounds. However, when T i / T e is too small, the threshold ratio scales as τ t / τ t ′ ∝ T e / T i ∝ s d 2 / δ 2 , consistent with experiments. Because δ / d controls T i / T e and the relative amplitude of turbulent wind velocity fluctuations, we qualitatively predict that Aeolian sediment transport in natural atmospheres can be initiated under weaker (potentially much weaker) winds than in wind tunnels, consistent with indirect observational evidence on Earth and Mars.

Heat Transfer Modulation by Inertial Particles in Particle-Laden Turbulent Channel Flow

We study the effects of particle-turbulence interactions on heat transfer in a particle-laden turbulent channel flow using an Eulerian–Lagrangian simulation approach, with direct numerical simulation (DNS) for turbulence and Lagrangian tracking for particles. A two-way coupling model is employed in which the momentum and energy exchange between the discrete particles and the continuous fluid phase is fully taken into account. Our study focuses on the modulations of the temperature field and heat transfer process by inertial particles with different particle momentum Stokes numbers (St), which in a combination of the particle-to-fluid specific heat ratio and the Prandtl number results in different particle heat Stokes numbers. It is found that as St increases, while the turbulent heat flux decreases due to the suppression of wall-normal turbulence velocity fluctuation, the particle feedback heat flux increases significantly and results in an increase in the total heat flux. The particle thermal feedback effect is illustrated using the instantaneous structures and statistics of the flow and temperature fields. The mechanisms of heat transfer modulation by inertial particles are investigated in detail. The budget of turbulent heat flux is examined. Moreover, by taking advantage of the ability of numerical simulation to address different momentum and heat processes separately, we investigate in detail the two processes of particles affecting heat transfer for the first time, namely the direct effect of particle thermal feedback to the fluid (i.e., heat feedback) and the indirect effect of the modulation of turbulent velocity field induced by the particles (i.e., momentum feedback). It is found that the contribution of heat transfer from turbulent convection is reduced by both heat and momentum feedback due to the decrease of the turbulent heat flux. The contribution of heat transfer from particle transport effects is barely influenced by the momentum feedback, even if St is large and is mainly affected by the heat feedback. Our results indicate that both heat and momentum feedback are important when the particle inertia is large, suggesting that both feedback processes need to be taken into account in computation and modeling.

Investigation of the effect of cavitation passive control on the dynamics of unsteady cloud cavitation

• We present a method to control various destructive effects of cloud cavitation such as vibration and high-pressure peaks. • Unsteady cloud cavitating flow around a hydrofoil was predicted using Partially-averaged Navier–Stokes (PANS) method. • Addition of the PANS Model in the OpenFOAM package. • Combination of the PANS method with Schnerr–Sauer cavitation model for obtaining the most accurate results. • Using a proper cavitation control a significant reduction in high wall-pressure peaks and vibration has been achieved. We present an efficient method to control the evolution of unsteady cloud cavitation around the CAV2003 benchmark hydrofoil using passive cavitation controllers so called cavitation-bubble generators (CGs). Cavitation control may be used in many engineering applications, particularly in the marine and turbo machinery field. We first simulated the unsteady cavitating flow around the hydrofoil without CGs using a Partially-averaged Navier–Stokes (PANS) method, and validated the acquired results against experimental data. We coupled the turbulence model with a mass transfer model and successfully implemented it in the open source toolbox OpenFOAM. Next, we studied the effect of different CGs on the qualitative parameters, such as the cavitation structure and the cavity shape. We varied size and location of the CGs to find the proper control of the cloud cavitation. We also analyzed in detail the effect of CGs on various destructive mechanisms of cavitation, such as highly unsteady cloud cavitation, turbulent velocity fluctuations , wall-pressure peaks, and degrading hydrodynamic performances . Our results revealed that CGs can substantially reduce instantaneous high-pressure pulsations on the hydrofoil surface. We observed that the cyclic behavior of unsteady cloud cavitation was suppressed, and the hydrodynamic efficiency of the hydrofoil was increased. The local boundary layer on the hydrofoil surface was altered, and the turbulent velocity fluctuation was reduced significantly, confirming that the vortex structures on the suction side and the wake region of the hydrofoil were changed remarkably.

Finite-sized rigid spheres in turbulent Taylor–Couette flow: effect on the overall drag

We report on the modification of drag by neutrally buoyant spherical finite-sized particles in highly turbulent Taylor–Couette (TC) flow. These particles are used to disentangle the effects of size, deformability and volume fraction on the drag, and are contrasted to the drag in bubbly TC flow. From global torque measurements, we find that rigid spheres hardly decrease or increase the torque needed to drive the system. The size of the particles under investigation has a marginal effect on the drag, with smaller diameter particles showing only slightly lower drag. Increase of the particle volume fraction shows a net drag increase. However, this increase is much smaller than can be explained by the increase in apparent viscosity due to the particles. The increase in drag for increasing particle volume fraction is corroborated by performing laser Doppler anemometry, where we find that the turbulent velocity fluctuations also increase with increasing volume fraction. In contrast to rigid spheres, for bubbles, the effective drag reduction also increases with increasing Reynolds number. Bubbles are also much more effective in reducing the overall drag.

How much does turbulence change the pebble isolation mass for planet formation?

Context. When a planet becomes massive enough, it gradually carves a partial gap around its orbit in the protoplanetary disk. A pressure maximum can be formed outside the gap where solids that are loosely coupled to the gas, typically in the pebble size range, can be trapped. The minimum planet mass for building such a trap, which is called the pebble isolation mass (PIM), is important for two reasons: it marks the end of planetary growth by pebble accretion, and the trapped dust forms a ring that may be observed with millimetre observations. Aims. We study the effect of disk turbulence on the PIM and find its dependence on the gas turbulent viscosity, aspect ratio, and particles Stokes number. Methods. By means of 2D gas hydrodynamical simulations, we found the minimum planet mass to form a radial pressure maximum beyond the orbit of the planet, which is the necessary condition to trap pebbles. We then carried out 2D gas plus dust hydrodynamical simulations to examine how dust turbulent diffusion impacts particles trapping at the pressure maximum. We finally provide a semi-analytical calculation of the PIM based on comparing the radial drift velocity of solids and the root mean square turbulent velocity fluctuations around the pressure maximum. Results. From our results of gas simulations, we provide an expression for the PIM vs. disk aspect ratio and turbulent viscosity. Our gas plus dust simulations show that the effective PIM can be nearly an order of magnitude larger in high-viscosity disks because turbulence diffuse particles out of the pressure maximum. This is quantified by our semi-analytical calculation, which gives an explicit dependence of the PIM with Stokes number of particles. Conclusions. Disk turbulence can significantly alter the PIM, depending on the level of turbulence in regions of planet formation.

Calculation of Higher-Order Moments in the Atmospheric Boundary Layer

The results of analyzing a number of models to calculate the statistical fourth-order moments of turbulent fluctuations of vertical velocity and temperature, which describe diffusion processes in equations for triple correlations in RANS models, are presented. Correct calculation of higher-order moments allows adequate description of the impact of large-scale vortex structures on the vertical flow of turbulence energy, as well as the impact of chemical reactions (in the case of reactive impurities) and/or phase transitions (moisture condensation and evaporation) in the atmospheric boundary layer.Results of calculations with the use of the quasi-normality hypothesis, a number of empirical formulas. and algebraic models for fourth-order cumulants are comparedwith in situ measurements in the convective boundary layer of the atmosphere. It is shown that the secondorder- closure models, which are much more efficient in numerical implementation than the thirdorder models, predict the behavior of the higher-order moments not worse than the latter.

Mechanistic prediction of post dryout heat transfer and rewetting

Abstract Post dryout heat transfer and rewetting are important processes determining the level and the time duration of high temperature phase and the integrity of the fuel cladding. In spite of extensive studies in the past decades, reliable prediction methods are still missing due to the complexity of processes involved, which consist mainly of interaction between solid wall, main gas flow and droplets. In the present study, a phenomenological model is proposed considering the three individual heat transfer processes between the three parts. Main new features of the present model compared to the models available in the open literature are the mechanistic modeling of (a) droplet concentration and droplet size, (b) turbulent fluctuation velocity of droplets and its critical value, (c) evaporation rate of droplets arriving the wall. Comparison of the new model with selected experimental data shows at least qualitatively good agreement. The experimental behavior of wall temperature can be well explained. According to the new model the Leidenfrost effect results in the hysteresis behavior of wall temperature.

Basal melting driven by turbulent thermal convection

Melting and, conversely, solidification processes in the presence of convection are key to many geophysical problems. An essential question related to these phenomena concerns the estimation of the (time-evolving) melting rate, which is tightly connected to the turbulent convective dynamics in the bulk of the melt fluid and the heat transfer at the liquid-solid interface. In this work, we consider a convective-melting model, constructed as a generalization of the Rayleigh-B\'enard system, accounting for the basal melting of a solid. As the change of phase proceeds, a fluid layer grows at the heated bottom of the system and eventually reaches a turbulent convection state. By means of extensive Lattice-Boltzmann numerical simulations employing an enthalpy formulation of the governing equations, we explore the model dynamics in two and three-dimensional configurations. The focus of the analysis is on the scaling of global quantities like the heat flux and the kinetic energy with the Rayleigh number, as well as on the interface morphology and the effects of space dimensionality. Independently of dimensionality, we find that the convective-melting system behavior shares strong resemblances with that of the Rayleigh-B\'enard one, and that the heat flux is only weakly enhanced with respect to that case. Such similarities are understood, at least to some extent, considering the resulting slow motion of the melting front (with respect to the turbulent fluid velocity fluctuations) and its generally little roughness (compared to the height of the fluid layer). Varying the Stefan number, accounting for the thermodynamical properties of the material, also seems to have only a mild effect, which implies the possibility to extrapolate results in numerically delicate low-Stefan setups from more convenient high-Stefan ones.

Droplets behavior of subcooled dispersed phase under nucleate boiling of continuous phase of liquid emulsion

The paper considers the influence of the dispersed phase of the emulsion upon the nature of heat and mass transfer in systems of immiscible liquids. In particular, is studied the interfacial interaction and breakage of subcooled drops of the dispersed phase during bubble boiling of the continuous phase of the emulsion. They predetermine the complex nature of the joint behavior of hydrodynamic and thermal processes. It is known that the controlled conditions for dispersion of emulsions in MQCL method under the minimum amount of cooling lubrication be able to improve the quality of metal processing by 10–18% (Maruda et al., 2017). Phase changes liquid generate in it a special kind of pulsation motion: «hot» turbulence of the superheated continuous phase. She is generated by process formation of nuclei and growth of steam bubbles accompanying by the pressure pulsations. Thus heat energy is converted into mechanical energy of the perturbed by the movement of vapor bubbles in evaporating liquid. The formula for the evaluating perturbations of the continuous phase of the emulsion under the influence of vapor bubbles is proposed. The behavior of these fluctuations depends on the frequency of the viable vapor phase nuclei formation related to the heat flow density. The dependence, obtained by Labuntsov (2000) for boiling homogeneous liquid, is used as a characteristic of the thermal velocity.Taking into account the character of the boiling of the continuous phase of emulsion, the generalization of the Kolmogorov-Hinze model has been performed for breakage drops in isothermal flow of emulsion under the influence of turbulent fluctuations of velocity. A correlation model of “thermal” breakup is proposed, which is complementary to the physical representations of the breakup for subcooled drops during the liquid emulsion boiling. Using dimensionless criteria was justified the form of the correlation for the maximum stable droplet size and thermal velocity fluctuations. This makes it possible to relate mechanisms hydrodynamic and thermal processes at use of usual computer tools used in practice for engineering calculations. The correlation for the maximum stable droplet size and thermal velocity fluctuations was developed in a dimensionless form. The results of the model studies were evaluated using the experimental data on the breakup of drops of oil in coolant “oil-water” (Januszkiewicz et al., 2004). They were obtained under conditions of creeping flow in a narrow channel, eliminating the creation of ordinary hydrodynamic turbulence. A good agreement with experimental data indicates that the present model would be promising for the extension of model representations about the breakup of droplets in complex processes of heat and mass transfer in liquid emulsions.

Modelling of the transition of a turbulent shock-flame complex to detonation using the linear eddy model

In the current study, the influence of turbulent mixing and local reaction rates on the transition to detonation of a turbulent shock-flame complex was investigated using a state-of-the-art large eddy simulation (LES) strategy. Specifically, detonation attenuation by a porous medium, and the subsequent re-initiation for methane–oxygen, a moderately unstable mixture, was considered. The purpose of the investigation was to validate the numerical strategy with previous experimental observations, and to determine what specific roles turbulent mixing and shock compression have on flame acceleration during the final stages of deflagration to detonation transition (DDT). The modelling procedure adopted was a grid-within-a-grid approach: The compressible linear eddy model for large eddy simulation (CLEM-LES). It was found that average turbulent velocity fluctuations greater than the laminar flame speed by an order of magnitude were required in order to maintain wave velocities above the Chapman–Jouguet (CJ)-deflagration velocity threshold, a precursor requirement for detonation re-initiation to occur. It was also found that sufficient turbulent burning on the flame surface was required in order to drive pressure waves to sufficiently strengthen the leading shock wave, locally, in order to trigger auto-ignition hot spots in the wave front. These local explosion events, which were found to burn out through turbulent surface reactions, drive transverse pressure waves outward. Upon subsequent shock reflections or interactions of the transverse waves, new local explosion events occurred, which further strengthened the adjacent leading shock wave above the CJ-detonation speed. Eventually, through this process, the wave sustained the CJ-detonation speed, on average, through the cyclic mechanism of local explosion events followed by turbulent surface reactions. Finally, combustion of the flame acceleration process was found to lie within the thin-reaction zones regime.

A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers.

The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, 'a fully developed passive scalar' refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the 'HRAP formalism' is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence: , where the instantaneous streamwise velocity fluctuation at a generic wall-normal location z is modelled as a sum of additive contributions from wall-attached eddies (a i ) and the number of addends is N z ~ log(δ/z). The HRAP model admits generalized logarithmic scalings including 〈ϕ 2〉~log(δ/z), 〈ϕ(x)ϕ(x+r x )〉 ~ log(δ/r x ), 〈(ϕ(x) - ϕ(x+r x ))2〉 ~ log(r x /z), where ϕ is the streamwise velocity fluctuation, δ is an outer length scale, r x is the two-point displacement in the streamwise direction and 〈·〉 denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for ϕ being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.