Turbulent Kinetic Energy Spectrum Research Articles

Direct measurement of the inertial-convective subrange above ocean surface waves

The −5/3 power law over the inertial subrange of the turbulence kinetic energy spectrum is one of the most well-known concepts in fluid physics. Obukhov and Corrsin extended the original hypothesis to a passive tracer, leading to the concept of an inertial-convective subrange. These postulates have been empirically validated in the atmospheric turbulence over land but have not been comprehensively studied in the marine air flow. During a recent oceanic campaign, the platform FLIP was deployed with an array of sensors to measure the perturbation wind velocity, temperature, and water vapor. Using these data, a previous study found that Kolmogorov's hypothesized −5/3 was not universally valid over the ocean. Here, we continue that work to analyze the spectrum of temperature and water vapor to empirically evaluate the theoretical extension by Obukhov-Corrsin. For temperature, the observed spectra were too noisy for thorough analysis; our conjecture for the source of noise and its implications for near-surface observations of atmospheric turbulence are discussed. For water vapor, we found strong agreement with the previous analysis of the kinetic energy spectrum. These findings corroborate (1) the theoretical notion of the scalar energy dissipation subrange driven by the inertial motions in the marine boundary layer and (2) evidence for non-Kolmogorov turbulence in the high Reynolds flow immediately above ocean waves. Our analysis shows a strong relationship with distance from the wavy surface; using linear extrapolation, we find that divergence from −5/3 persists in the lowest 25 m of the atmosphere.

Inertial range scaling of inhomogeneous turbulence

We investigate how inhomogeneity influences the $k^{-5/3}$ inertial range scaling of turbulent kinetic energy spectra (with $k$ the wavenumber). For weak statistical inhomogeneity, the energy spectrum can be described as an equilibrium spectrum plus a perturbation. Theoretical arguments suggest that this latter contribution scales as $k^{-7/3}$ . This prediction is assessed using direct numerical simulations of three-dimensional Kolmogorov flow.

Can IR Images of the Water Surface Be Used to Quantify the Energy Spectrum and the Turbulent Kinetic Energy Dissipation Rate?

Near-surface oceanic turbulence plays an important role in the exchange of mass, momentum, and energy between the atmosphere and the ocean. The climate modifying the air-sea CO2 transfer rate varies linearly with the surface turbulent kinetic energy dissipation rate to the 1/4 power in a range of systems with different types of forcing, such as coastal oceans, river estuaries, large tidal freshwater rivers, and oceans. In the first part of this paper, we present a numerical study of the near-surface turbulent kinetic energy spectra deduced from a direct numerical simulation (DNS) compared to turbulent kinetic energy spectra deduced from idealized infrared (IR) images. The DNS temperature fields served as a surrogate for IR images from which we have calculated the underlying kinetic energy spectra. Despite the near-surface flow region being highly anisotropic, we demonstrated that modeled isotropic and homogeneous turbulence spectra can serve as an approximation to observed near-surface spectra within the inertial and dissipation ranges. The second part of this paper validates our numerical observations in a laboratory experiment. In this experiment, we compared the turbulent kinetic energy spectra near the surface, as measured using a submerged shear sensor with the spectra derived from infrared images collected from above the surface. The energy dissipation measured by the shear sensor was found to be within 20% of the dissipation value derived from the IR images. Numerically and experimentally, we have demonstrated that IR-based and remote measurement techniques of the aquatic near surface offer a potentially accurate and non-invasive way to measure near-surface turbulence, which is needed by the community to improve models of oceanic air-sea heat, momentum, and gas fluxes.

Euler-Euler LES of bubble column bubbly flows by considering sub-grid scale turbulent dispersion effect on modulating bubble transport

It has now been recognised and generally accepted that turbulent dispersion may be modelled using the time average of the fluctuating part of the interphase momentum, employing the drag the Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. As the turbulent eddies in the surrounding of bubbles interact strongly with the bubbles in bubbly flow, the bubble trajectories and bubble oscillation take place accordingly as the consequence of continuous deformation of the bubble surfaces. When using large eddy simulation for modelling bubbly flow, the sub-grid scale (SGS) filtered velocity fluctuations of liquid phase can be interpreted as many small eddies that may act on the surface of bubbles, consequently giving rise to bubble shape variations and the dispersion of bubbles. This study employs Euler/Euler large-eddy simulation (LES) modelling to demonstrate that the turbulent dispersion force model can be used to effectively indicate the influence of turbulent eddies on bubble dynamics, in particular the bubble cluster oscillations, which leads to remarkable improvements in the prediction of bubble lateral dispersion behaviour. The use of spatial filtering to model the SGS bubble dispersion is proposed with a modification on SGS eddy viscosity to reflect turbulent dispersion due to bubble induced turbulence. The results of the time-averaged LES modelled bubble velocities and bubble volume fraction profiles are in good agreement with the experimental data while the turbulent kinetic energy spectrum obtained at different locations on the centreline of the bubble column still exhibits the conventional −5/3 scaling for shear induced turbulence and a −3 scaling for bubble induced turbulence.

Statistical characterization of a shock interacting with an inclined gas column

We present a statistical characterization of the interaction between a planar shock and a finite-diameter, cylindrical column of dense gas based on three-dimensional, large-eddy simulation results. In the simulation, the column of gas is initially inclined at an angle $\alpha _0$ with respect to the shock plane. Effects of the initial column angle on the mixing characteristics are examined at Mach number 2.0 for column incline angles $1^\circ$ , $5^\circ$ , $10^\circ$ and $30^\circ$ . Mean velocity profiles show that the column angle affects the gas velocity components in the vertical plane, but not in the spanwise direction. The gas undergoes higher initial upward acceleration at larger initial column incline angles. With time, the gas motion tends to become one-dimensional in the streamwise direction. Initially, velocity fluctuations are most intense within the interior of the column, but concentrate near the column leading edge over time. At high wavenumbers $\kappa$ , the turbulent kinetic energy spectra follow a power-law scaling of $\kappa ^{-1}$ . The structure functions of the mass fraction do not clearly demonstrate power-law scaling except at early times for $\alpha _0=30^\circ$ , manifesting overall trends very similar to those observed in earlier experiments. Probability distributions of the mass fraction show independence of the mean and the standard deviation of the mixed gas on $\alpha _0$ . The column angle was also found to have little effect on the mixing efficiency characterized by the molecular mixedness. Velocity components in the streamwise and transverse directions tend towards a bimodal distribution for larger $\alpha _{0}$ .

Large Eddy Simulation of Bubble Column Bubbly Flow Considering Subgrid‐Scale Turbulent Diffusion Effects and Bubble Oscillation

AbstractThrough Euler/Euler large eddy simulation (LES) modeling, it is demonstrated that turbulent dispersion of bubbles can effectively indicate the impact of turbulent eddies on the bubble dynamics, i.e., the bubble oscillation behavior. This finding builds on previous work using the Euler/Lagrange LES modeling approach and leads to a significant improvement in predicting bubble lateral dispersion. Spatially filtered terms were proposed for the subgrid‐scale (SGS) turbulent dispersion and added mass stress force models, with a modification made to the SGS eddy viscosity to reflect bubble turbulent dispersion and oscillations. The proposed model substantially improves the prediction of bubble volume fraction distribution, bubble and liquid phase velocity profiles, the turbulent kinetic energy spectrum, and mass transfer.

Energetics of buoyancy-generated turbulent flows with active scalar: pure buoyant plume

A framework for the budget of Reynolds stress, temperature and density variations, turbulent mass flux and turbulent heat flux is presented for buoyancy-generated turbulent flows with a focus on turbulent plumes. The dynamical interactions between the turbulence generated from the velocity and thermodynamic fluctuations in thermal and heated gas plumes is studied. A large-eddy simulation tool has been used to simulate heavier and lighter than air plumes released from a circular heated source for high Reynolds number (Re). The budget equations are developed using a Favre-averaging approach. Both heated air plumes and heated gas plumes, namely, heated ${\rm SO}_2$ and heated ${\rm CH}_4$ plumes, are included in the study. The study focuses on addressing key questions – does the turbulence kinetic energy (TKE) spectrum follow the classical inertial $-5/3$ spectrum or is there a $-3$ buoyancy regime with a different scaling law? Fundamental pathways for generation of turbulence through velocity fluctuations, and temperature and density fluctuations are discussed. Analysis of the TKE and scalar variance budget equations has demonstrated that multiple mechanisms dominate the transport of Reynolds stresses, and in particular that correlations between the density and the velocity dominates the turbulence production mechanisms. Entrainment is connected to the turbulent transport and pressure-dilation processes.

Evaluation of Turbulence and Dispersion in Multiscale Atmospheric Simulations over Complex Urban Terrain during the Joint Urban 2003 Field Campaign

Abstract This paper evaluates the representation of turbulence and its effect on transport and dispersion within multiscale and microscale-only simulations in an urban environment. These simulations, run using the Weather Research and Forecasting Model with the addition of an immersed boundary method, predict transport and mixing during a controlled tracer release from the Joint Urban 2003 field campaign in Oklahoma City, Oklahoma. This work extends the results of a recent study through analysis of turbulence kinetic energy and turbulence spectra and their role in accurately simulating wind speed, direction, and tracer concentration. The significance and role of surface heat fluxes and use of the cell perturbation method in the numerical simulation setup are also examined. Our previous study detailed the model development necessary for our multiscale simulations, examined model skill at predicting wind speeds and tracer concentrations, and demonstrated that dynamic downscaling from mesoscale to microscale through a sequence of nested simulations can improve predictions of transport and dispersion relative to a microscale-only simulation forced by idealized meteorology. Here, predictions are compared with observations to assess qualitative agreement and statistical model skill at predicting wind speed, wind direction, tracer concentration, and turbulent kinetic energy at locations throughout the city. We also investigate the scale distribution of turbulence and the associated impact on model skill, particularly for predictions of transport and dispersion. Our results show that downscaled large-scale turbulence, which is unique to the multiscale simulations, significantly improves predictions of tracer concentrations in this complex urban environment. Significance Statement Simulations of atmospheric transport and mixing in urban environments have many applications, including pollution modeling for urban planning or informing emergency response following a hazardous release. These applications include phenomena with spatial scales spanning from millimeters to kilometers. Most simulations resolve flow only within the urban area of interest, omitting larger scales of turbulence and regional influences. This study examines a method that resolves both the small and large-scale flow features. We evaluate simulation accuracy by comparing predictions with observations from an experiment involving the release of a tracer gas in Oklahoma City, Oklahoma, with emphasis on correctly modeling turbulent fluctuations. Our results demonstrate the importance of resolving large-scale flow features when predicting transport and dispersion in urban environments.

DNS analysis of turbulence modulation by lean premixed prevaporized spray flames in a model combustor

Turbulence modulation by lean premixed prevaporized (LPP) spray flames, which involve droplet motion, evaporation and gaseous reaction, is complicated and essential to organizing clean and efficient combustion. Direct numerical simulations of LPP combustion in a model swirling combustor under high pressure of 20 bar are performed. The gaseous flow is solved in the low-Mach-number limit, and the droplets are tracked as two-way coupled Lagrangian particles. The corrected infinite thermal conductivity model is adopted to describe droplet evaporation, and a reduced two-step kerosene/air chemistry mechanism is used to present combustion. Four cases, i.e., a non-reacting gaseous flow, a non-reacting spray flow and two reacting spray flows with different droplet sizes, are conducted to cover key features of LPP flame on turbulence modulation. The results show that the spray combustion significantly depresses the mean axial velocity on the centerline in the upstream, indicating an enhancement of the inner recirculation zone. The influence of droplets on the mean and fluctuating velocities is generally negligible except on the azimuthal modulation, while combustion can increase the velocities, which is more evident in downstream due to the pressure effect. In reacting cases, the turbulent kinetic energy (TKE) spectra in the shear layers reduce at high wavenumbers, reflecting the combustion-induced dissipation at small scales (below the laminar flame thickness scale). Besides, droplet evaporation can introduce energy at small scales while this modulation is balanced by combustion. Moreover, TKE budget analysis indicates that spray combustion mainly depresses the TKE and redistributes mean shear along the radial direction. Heat release increases the local fluid viscosity, depresses local turbulent transport, and increases viscous dissipation. Finally, the vortex stretching analysis shows that LPP combustion enhances the alignment with the intermediate strain rate component.

A spectral inspection for turbulence amplification in oblique shock wave/turbulent boundary layer interaction

Turbulence amplification and the large-scale coherent structures in shock wave/turbulent boundary layer interaction flows have been studied at length in previous research, while the direct association between these two flow features is still lacking. In the present study, the transport equation of turbulent kinetic energy spectra is derived and utilized to analyse the scale-by-scale energy budget across the interaction zone, enabling us to reveal the association between the genesis of the large-scale motions and the turbulence amplification. For the presently considered flow with incipient shock-induced separation, we identified in turbulent kinetic energy spectra distribution that the most energetic motions are converted from the near-wall small-scale motions to large-scale motions consisting of velocity streaks and cross-stream circulations as they go through the interaction zone. The amplification of streamwise velocity fluctuation is triggered first, resulting in the emergence of large-scale velocity streaks, which is attributed to the adverse pressure gradient, as indicated by the spectra of the production term. The energy carried by large-scale velocity streaks is transferred to other velocity components by the pressure-strain term, producing large-scale cross-stream circulations. When large-scale motions are convected downstream, their energy is transferred via turbulent cascade to smaller scales and dissipated by viscosity. The spanwise uniform fluctuations, reminiscent of the unsteadiness of the separation bubble, are contributed primarily by the inter-scale energy transfer from the finite spanwise scale motions.

A novel laser Doppler anemometer (LDA) for high-accuracy turbulence measurements

High accuracy and dynamic range have been some of the most prominent challenges when it comes to fine-scale turbulence measurements. The current commercial LDA processors, which perform the signal processing of Doppler bursts directly using hardware components, are essentially black boxes and in particular are renown for suffering from practical limitations that reduce the measurement reliability and accuracy. A transparently functioning novel LDA, utilizing advanced technologies and up-to-date hardware and software has therefore been developed to enhance the measurement quality and the dynamic range. In addition, the self-developed software comes with a highly flexible functionality for the signal processing and data interpretation. The LDA setup and the combined forward/side scattering optical alignment (to minimize the effective measuring volume) are described first, followed by a description of the signal processing aspects. The round turbulent jet has been used as the test bed since it presents a wide range of degree of difficulty for the LDA processor (accuracy, dynamic range etc.) across the different radial distances and downstream development. The data are diagnosed for dynamic range in residence and interarrival times, and compared to a typical hardware driven processor. The radial profiles of measured mean streamwise velocity and variance agree well with previous studies of the round jet. The spatial turbulent kinetic energy spectra in the fully developed region perfectly match the expected (and in this region well established) -5/3 power law even for the largest measured distances from the centerline (where shear and turbulence intensity are significant).

How small-scale flow structures affect the heat transport in sheared thermal convection

We investigate the counter-intuitive initial decrease and subsequent increase in the Nusselt number $Nu$ with increasing wall Reynolds number $Re_w$ in the sheared Rayleigh–Bénard (RB) system by studying the energy spectra of convective flux and turbulent kinetic energy for Rayleigh number $Ra = 10^{7}$ , Prandtl number $Pr=1.0$ and inverse Richardson numbers $0 \leq 1/Ri \leq 10$ . These energy spectra show two distinct high-energy regions corresponding to the large-scale superstructures in the bulk and small-scale structures in the boundary layer (BL) regions. A greater separation between these scales at the thermal BL height correlates to a higher $Nu$ and indicates that the BLs are more turbulent. The minimum $Nu$ , which occurs at $1/Ri=1.0$ , is accompanied by the smallest separation between the large- and small-scale structures at the thermal BL height. At $1/Ri=1.0$ , we also observe the lowest value of turbulent kinetic energy normalized with the square of friction velocity within the thermal BL. Additionally, we find that the domain size has a limited effect on the heat and momentum transfer in the sheared RB system as long as the domain can accommodate the small-scale convective structures at the thermal BL height, signifying that capturing the large-scale superstructures is not essential to obtain converged values of $Nu$ and shear Reynolds number $Re_{\tau }$ . When the domain is smaller than these small-scale convective structures, the overall heat and momentum transfer reduces drastically.

Experiments on turbulence from colliding ice floes

Increased knowledge about energy dissipation processes around colliding ice floes is important for improved understanding of atmosphere-ice-ocean energy transfer, wave propagation through sea ice, and the polar climates. The aim of this study is to obtain such information by investigating colliding ice floe dynamics in a large-scale experiment and directly measuring and quantifying the turbulent kinetic energy (TKE). The field work was carried out at Van Mijen Fjord on Svalbard, where a 3 × 4 m ice floe was sawed out in the fast ice. Ice floe collisions and relative water–ice motion were generated by pulling the ice floe back and forth in an oscillatory manner in a 4 × 6 m pool, using two electrical winches. Ice floe motion was measured with a range meter and accelerometers, and the water turbulence was measured acoustically with Doppler velocimeters and optically with a remotely operated vehicle and bubbles as tracers. Turbulent kinetic energy spectra were found to contain an inertial subrange where energy was cascading at a rate proportional to the −5/3 power law. The TKE dissipation rate was found to decrease exponentially with depth. The total TKE dissipation rate was estimated by assuming that turbulence was induced over an area corresponding to the surface of the floe. The results suggest that approximately 37% and 8% of the input power from the winches were dissipated in turbulence and absorbed in the collisions, respectively, which experimentally confirms that energy dissipation by induced turbulent water motion is an important mechanism for colliding ice floe fields.

Euler/Euler large eddy simulation of bubbly flow in bubble columns under CO2 chemisorption conditions

It has been generally recognised that the turbulent dispersion force plays an important role in interphase momentum transfer. However, the effect of the added mass stress on the momentum and mass transfer in bubble column bubbly flow has not been addressed appropriately. As the turbulent eddies in the surroundings of bubbles interact strongly with the rising bubbles in bubble column bubbly flow, such interactions will bring out the change of interfacial areas between the bubbles and carrier fluid, consequently leading to changes in the interfacial mass transfer. When employing large eddy simulation for modelling bubbly flow coupled with the chemisorption process, the SGS filtered velocity fluctuations of liquid phase can be interpreted as the turbulent eddies that continuously hit the surfaces of bubbles, causing bubble deformation and the variation of bubble interfacial areas, which give rise to the turbulent dispersion and added mass stress forces. The present study will demonstrate through Euler/Euler large-eddy simulations (LES) modelling that by considering the turbulent dispersion force (SGS-TDF) and added mass stress (SGS-AMS), the bubble dynamics and mass transfer under the chemisorption conditions can be better indicated, which leads to remarkable improvements in the prediction of bubble lateral dispersion and the interfacial mass transfer. The turbulent dispersion and added mass stress related to the spatially filtering were proposed with a modification on SGS eddy viscosity to reflect turbulent dispersion due to bubble-induced turbulence. A comprehensive assessment of the effects of these additional filtered stress terms on the time-averaged velocity and bubble volume fraction profiles, flow patterns, mass transfer and the pH variation during CO2 chemisorption and the turbulent kinetic energy and species concentration spectra was conducted.

On the Mechanism Responsible for Extreme Turbulence Intensity Generation in the Hi-Pilot Burner

In this study, we apply particle image velocimetry (PIV), hot-wire anemometry (HWA), and large-eddy simulation (LES) to identify and characterize a key mechanism by which high-intensity turbulence measured in the “Hi-Pilot” burner is generated. Large-scale oscillation of the high-velocity jet core about its own mean axial centerline is identified as a dominant feature of the turbulent flow field produced by this piloted Bunsen burner. This oscillation is linked to unsteady flow separation along the expanding section of the reactant nozzle and appears stochastic in nature. It occurs over a range of frequencies (100–300 Hz) well below where the turbulent kinetic energy (TKE) spectrum begins to follow a – 5/3 power law and results in a flow with significant scale separation in the TKE spectrum. Although scale separation and intermittency are not unusual in turbulent flows, this insight should inform analysis and interpretation of previous, and future studies of this unique test case.

Multiscale Analysis of Anisotropy of Reynolds Stresses, Subgrid Stresses and Dissipation in Statistically Planar Turbulent Premixed Flames

The characterisation of small-scale turbulence has been an active area of research for decades and this includes, particularly, the analysis of small-scale isotropy, as postulated by Kolmogorov. In particular, the question if the dissipation tensor is isotropic or not, and how it is related to the anisotropy of the Reynolds stresses is of particular interest for modelling purposes. While this subject has been extensively studied in the context of isothermal flows, the situation is more complicated in turbulent reacting flows because of heat release. Furthermore, the landscape of Computational Fluid Dynamics is characterised by a multitude of methods ranging from Reynolds-averaged to Large Eddy Simulation techniques, and they address different ranges of scales of the turbulence kinetic energy spectrum. Therefore, a multiscale analysis of the anisotropies of Reynolds stress, dissipation and sub-grid scale tensor has been performed by using a DNS database of statistically planar turbulent premixed flames. Results show that the coupling between dissipation tensor and Reynolds stress tensor is weaker compared to isothermal turbulent boundary layer flows. In particular, for low and moderate turbulence intensities, heat release induces pronounced anisotropies which affect not only fluctuation strengths but also the characteristic size of structures associated with different velocity components.

Investigation of Aerator Flow Pressure Fluctuation Using Detached Eddy Simulation with VOF Method

The detached eddy simulation model and volume of fluid (VOF) method were combined to simulate the pressure fluctuations in the downstream region of an aerator in a spillway tunnel, which often lead to hydraulic structure failure. The predictions were compared to experimental data to validate the model. Satisfactory agreement was obtained between the simulation and experimental results. The root mean square and fluctuation coefficient exhibited single-peak distribution, with the maximum values attained in the impact zone. The ranges of fluctuations of the pressure coefficient in the impact and stable zones were 3.31%–7.08% and 0.96%–3.15%, respectively. The probability density distribution obeyed a normal distribution law and presented a positive skew. The pressure fluctuation characteristics were primarily controlled by large-scale coherent eddies. The flow in the downstream region was a typical low-frequency fluctuation flow. The turbulent kinetic energy spectrum of the flow was congruent with Kolmogorov’s –5/3 law. Our method is convenient for engineers to analyze pressure fluctuation characteristics and propose the shape of a hydraulic structure with superior hydraulic characteristics.

Large Eddy Simulation of Leakage Flow in a Stepped Labyrinth Seal

Large eddy simulation (LES) and Reynolds averaged Navier-Stokes simulation (RANS) of leakage flow in straight-through and stepped labyrinth seals were performed in order to compare their performances in sealing the secondary flow passage of the gas turbine based on the respective discharge coefficients. The results indicate a 17.8% higher leakage prevention performance for the stepped seal relative to that of the straight seal. Further, while the LES predicts an ~7% reduction in the discharge coefficient due to shaft rotation, this effect is underestimated by the RANS. Moreover, the LES correctly predicts a laminarized flow pattern in the clearance, whereas the RANS overestimates the turbulence kinetic energy. In addition, a turbulence kinetic energy spectrum analysis was performed based on the vorticity at selected points in order to identify the flow structure that has a dominant influence on the oscillation of the discharge coefficient. This analysis also enabled identification of the changes in the flow structure due to shaft rotation.

Reformulation and improvement of a universal subgrid eddy viscosity model based on the multiscale framework

A universal multiscale Smagorinsky model (UMSM) is established for the large eddy simulation (LES) of wall-bounded turbulent flows by reformulating a universal subgrid eddy viscosity model presented by Gu et al. (Europhysics Letter 94(3):34003,2011). The UMSM is adapted to the LES of wall-bounded turbulent flows by integrating the “small-all” form of the multiscale Smagorinsky model with the dynamic subgrid characteristic length, controlled by subgrid-scale (SGS) motions. The dynamic subgrid characteristic length is determined by the characteristic wave number, which is calculated from a new energy-weighted-mean method when the SGS turbulent kinetic energy and the dissipation wave number are known. The dissipation wave number is derived from the SGS turbulent kinetic energy spectrum equation and the total dissipation rate spectrum equation. The UMSM is used to simulate the fully developed channel flow and the turbulent flow past a square cylinder. The dynamic subgrid characteristic length, as a counterpart of Germano’s procedure, evaluates the rapidly fluctuating small-scale behavior and spatial variations of turbulent characteristics. The results for fully developed channel flow show that the errors in the streamwise velocity and the velocity fluctuations change slowly. The flat nature of the UMSM error across different multiscale Smagorinsky coefficients (Cs’) indicates that the model is relatively insensitive to the value of Cs′. Additionally, the UMSM is less sensitive to grid resolution since more details of turbulence fluctuations are captured on the same grid-points compared to the RVBMM (Journal of Computational Physics, 234:79-107,2013) and DSM (Journal of Fluid Mechanics 319:353-385,1996). Overall, the proposed model and the DSM exhibit similar behavior, and both LES formulations provide good agreement with reference data from direct numerical simulations. However, the UMSM is more computationally efficient, being 17% faster than the dynamic Smagorinsky model.

Wake instabilities of a pre-swirl stator pump-jet propulsor

The wake of a pump-jet propulsor (PJP) with a pre-swirl stator is investigated using stress-blended eddy simulations. The flow field is analyzed in detail through a systematic comparison of the wake morphology under different loading conditions, allowing the destabilization process and the mechanism of wake instabilities to be inspected. To further examine the evolution of the vortices, as well as their interaction and destabilization, the pressure fluctuations and spectra of turbulent kinetic energy are considered. The mean loads are in good agreement with experimental results. The PJP flow field has a complex vortical system, the evolution of which determines the wake instabilities. The tip clearance leakage vortex first exhibits short-wave instabilities, and the destabilization process then accelerates under the effects of duct shed vortices, which promote the generation of secondary vortices. The secondary vortices further enhance the destabilization process and lead to chaotic evolution. The stator blade root vortices are strongly affected by the rotor blade root vortices, causing an exchange of vorticity that depends on the relative intensity of the two sets of root vortices. The instability of the hub vortices is apparently related to the upstream vortices. The correlation between the tip clearance leakage vortices and the instability of hub vortices is very weak.