Turbulent Kinetic Energy Distribution Research Articles

CFD Modelling of a Stepped Spillway with Various Step Layouts

A traditional stepped spillway is prone to cavitation risks. To improve its hydraulic behaviors, distorted step faces and pool weirs are devised. By numerical modelling, comparative studies are conducted to look into the flow features. The pressures on step surfaces of the unconventional layouts exhibit 3D distributions. Pool weirs are essential in increasing both the min. and max. pressure loads. Pressures on the downstream bed show a unique pattern for V- and inverted V-shaped models, with the extreme pressures at the sidewalls for the former and at the central plane for the latter. Symmetrical secondary flows are formed in V- and inverted V-shaped cases with different patterns. Distributions of turbulent kinetic energy suggest differences in flow motions in all cases. Furthermore, the relative energy loss of flat setups is ∼5.4% lower than that of the pooled ones with the same step face angle; inverting the face angle does not give rise to noticeable change. The results provide reference for relevant projects.

Direct numerical simulation of turbulent heat transfer in a wall-normal rotating channel flow

Investigations into the characteristics of turbulent heat transfer and coherent flow structures in a plane-channel subjected to wall-normal system rotation are conducted using direct numerical simulation (DNS). In order to investigate the influence of system rotation on the temperature field, a wide range of rotation numbers are tested, with the flow pattern transitioning from being fully turbulent to being quasilaminar, and eventually, fully laminar. In response to the Coriolis force, secondary flows appear as large vortical structures, which interact intensely with the wall shear layers and have a significant impact on the distribution of turbulence kinetic energy (TKE), turbulence scalar energy (TSE), temperature statistics, and turbulent heat fluxes. The characteristic length scales of turbulence structures responsible for the transport of TSE are the largest at the quasilaminar state, which demands a very large computational domain in order to capture the two-dimensional spectra of temperature fluctuations. The effects of the Coriolis force on the turbulent transport processes of the temperature variance and turbulent heat fluxes are thoroughly examined in terms of their respective budget balances.

Three-dimensional simulations of turbulent mixing in spherical implosions

High-resolution large-eddy simulations of turbulent mixing at the inner surface of a dense shell which undergoes forced compression by a spherically imploding shock wave are presented. Perturbations on the inner surface grow as a result of Richtmyer-Meshkov and Rayleigh-Taylor instabilities and effects related to geometric convergence and compressibility. Three different cases with different initial surface perturbations, one broadband and two narrowband, are considered. The perturbation power spectrum is related to the mode number via Pℓ ∝ ℓn, where the case with broadband perturbations has n = −2, and modes in the range ℓ = 6–200. The narrowband perturbations have n = 0 and modes in the range ℓ = 50–100 and ℓ = 100–200. The simulations are carried out in spherical coordinates using the PLUTO hydrodynamics code. Results on the mix layer width, molecular mix, and turbulent kinetic energy distribution are presented, demonstrating clearly the impact of the amplitude and spectral form of the initial perturbation on the evolution of integral properties. A recently developed model predicting the growth of single mode perturbations in spherical implosions including shock waves is extended to predict mix layer amplitudes for broadband and narrowband cases, along with a model proposed by Mikaelian [“Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells,” Phys. Rev. A 42, 3400–3420 (1990)]. The resultant layer amplitude predictions from the new model are in good agreement with the numerical results while the longest wavelengths are not yet saturated, while Mikaelian’s model agrees well where the initial modes are saturated.

Dynamic hazard evaluation of explosion severity for premixed hydrogen–air mixtures in a spherical pressure vessel

To evaluate dynamic explosion severity levels of premixed hydrogen–air mixtures, pressure sensors were used to test explosion pressure in a spherical pressure vessel (inner diameter: 0.34 m). ANSYS Fluent 19.0 three-dimensional software was used to simulate the explosion process. The results revealed that when the hydrogen volume fraction was 30 vol%, the explosion pressure and pressure rise rate reached maximum values at 1.0 atm. As the initial pressure increased, the explosion pressure, and pressure rise rate increased gradually. At initial pressures of 1.0, 1.2, 1.5, and 2.0 atm, the peak pressure levels were 0.85, 0.87, 0.92, and 0.99 MPa and the pressure rise rates were approximately 198, 241, 302, and 558 MPa/s, respectively. The initial pressure exerted greater effects on the pressure rise rate than did the explosion pressure. The simulation results were consistent with the experimental findings. Moreover, the simulation yielded multi-dimensional transient explosion parameters—such as turbulent kinetic energy distribution—that are difficult to obtain in experiments. The findings pertaining to the physical experiments, numerous simulations, and influence of initial pressure on the explosion reaction mechanism of premixed hydrogen–air mixtures were discussed.

Effects analysis on diesel soot continuous regeneration performance of a rotary microwave-assisted regeneration diesel particulate filter

In order to investigate effects of various factors on continuous regeneration performance of a rotary microwave-assisted regeneration diesel particulate filter (MRDPF), a regeneration mathematical model and a field synergy model of the rotary MRDPF are developed, and turbulent kinetic energy distribution and pressure distribution of the rotary MRDPF based on three different turbulence models are analyzed. The results indicate that the RNG k-ε model is more suitable for simulation of the rotary MRDPF and appropriate increment of filter unit number, oxygen content and exhaust gas temperature can result in the regeneration performance improvement of the rotary MRDPF. Inlet flow velocity of exhaust gas can change synergy degree between the velocity field and the temperature field and high synergy area is mainly concentrated in the upper and central parts of the filter unit. Moreover, field synergy degree and regeneration efficiency of the filter unit are both better when the flow velocity reaches 0.3 m/s during regeneration phase, where regeneration optimized area ratio and maximum regeneration efficiency are 0.51 and 91%, respectively. This work provides great reference values for optimizing the continuous regeneration performance of the rotary MRDPF.

Energetics of blood flow in Fontan circulation under VAD support

The need to simulate the normal operating conditions of the human body is the key factor in every study and engineering process of bioelectronic devices designed for implantation. The Fontan procedure is an example of such aprocess aimed to support the human body function. It is a standard treatment method for patients with a functionally univentricular heart. However, it has significant drawbacks such as overload of the only functional heart ventricle that often leads to the necessity of the heart transplantation. In this study, we analyze the total cavopulmonary connection (TCPC) influence on the blood with and without connected auxiliary blood circulation pump. We investigate four different types of TCPC configurations, analyze blood pressure and different flow rate, study the turbulent kinetic energy distribution, and evaluate hydraulic and power losses for various cases. Finally, we calculate volumetric scalar shear stresses distribution and demonstrate the high potential of TCPC configuration with connected rotary pump as a tool for the load redistribution in the functional heart ventricle. This work is particularly relevant for improving existing TCPCs' quality that can extend the life of Fontan patients. Moreover, it also applies to the reduction of morbidity and mortality of the patients waiting for the heart transplantation.

Effect of vegetation patches on flow structures and the estimation of friction factor

ABSTRACT In rivers, irrigation canals, and drainage channels vegetation patches often appear over the bed. Flow over vegetation patches is in non-developed region which significantly influences the flow structures, thus affecting the estimation of friction factor. In the present study, the experiments were conducted in a laboratory flume to investigate the interaction of vegetation patches with turbulent flow structures evolving area over small patches. Different roughness coefficients were applied in the presence of vegetation patches, and velocity distributions, Reynolds stress distributions, and Turbulent Kinetic Energy (TKE) distributions were analyzed because they play an important role in the estimation of friction factor. Results showed that Reynolds stress and TKE at the trailing edge of vegetation patches increased due to the vertical circulation downstream of each patch. However, the vertical circulation, Reynolds stress, and TKE decreased in the flow over three patches in comparison to the flow over two patches. Results also indicated that the geometric features of a vegetation patch played an important role in the friction factor in open channels with vegetation patches on the bed.

Experimental and numerical investigation of flow characteristics in an open rectangular cavity

ABSTRACT Turbulent flow over open cavity has been investigated experimentally in water channel using Acoustic Doppler Velocimetry (ADV) and numerically using FLUENT. The mean velocity and turbulent kinetic energy distribution of the flow over cavity having an aspect ratio, l/d = 2 (where l and d is the length and depth of the cavity) obtained from FLUENT are validated by experimental results. Effects of different Reynolds numbers and aspect ratios of the cavity (i.e. l/d = 1, 2 and 4) on the flow are reported. The results show that there exists a critical Reynolds number at which the trend of variation of physical variables breaks in response to the change in Reynolds numbers. Recirculating zone inside the cavity for l/d = 1, interacts with downstream cavity flow whereas, for l/d = 2 and 4, the mass exchange between the cavity and upstream flow is noticed. As the aspect ratio is increased, the upstream flow becomes more attached and the instability near the trailing edge increases.

Assessment of advanced RANS models ability to predict a turbulent swept liquid metal flow over a wire in a channel

This paper presents the assessment of different Reynolds-averaged Navier-Stokes (RANS) based turbulence models against the direct numerical simulation (DNS) reference data of turbulent swept flow over a wire in a channel which is topologically equivalent to a wire-wrapped sub-channel assembly in the liquid metal reactor. Computational grids were generated to archive the low y+ wall treatment approach condition. All the candidate turbulence models were compared to the DNS results both qualitatively and quantitatively under three different crossflow conditions. RANS based CFD results were compared to time-averaged DNS results regarding the flow structure, turbulent kinetic energy, and wall shear stress at each particular location defined by a flow structure along the cross-flow direction. Computation times were measured between each model with appropriate solution convergence strategy. In terms of the flow structure, two-equation and four-equation models were found to over-predict the size of the primary recirculation bubble. The seven-equation model is also over-predicting the recirculation zone as a result of the inclusion of SSG formulations for the pressure-strain term, but this model is clearly outperforming the other models' predictions in terms of local velocity profiles, turbulent kinetic energy distributions, and the shear stress alignments within reasonable computation time.

Measurements of turbulence sources in a swirl-supported diesel engine

The combustion efficiency and pollutant formation in swirl-supported diesel engines strongly depend on the in-cylinder turbulent flows. But the physical mechanism of turbulence generation remains inadequately understood. To identify the sources of turbulence at various spatial locations and to understand the relationship between the flow structures and turbulence production, planar particle image velocimetry experiments are performed in this study to characterize the evolution of turbulent flow in a motored optical diesel engine with a compression ratio of 13:1 and a swirl ratio of 1.5. The temporal and spatial distributions of turbulent kinetic energy ( k) and the turbulence sources are correlated. An extremely high k generated by the intake jet during the intake process was observed, and it remains only 1.6%–3.3% during the later compression stroke. Near the cylinder center, k changes significantly with the crank angle and the higher k was always observed near the swirl center. The production via shear stresses correlates with k well. In other regions, k almost keeps unchanged with the crank angle because of the rigid-body-like swirl flow, which results in a negligible net production by flow deformation. In addition, in the middle region, the evolution of radial angular momentum gradient matches with the k evolution reasonably well, which indicates that k may depend on the transport by the squish flow although the underlying physics deserves further exploration.

Experimental and numerical analysis of the spray characteristics of biodiesel–ethanol fuel blends

The effects of adding ethanol on the macroscopic and microscopic spray characteristics of biodiesel were investigated by experimental and numerical methods. The spray tip penetration (STP) was recorded with a high-speed camera system, while the statistical size distribution of atomized droplets and the Sauter mean diameter (SMD) were obtained using a Malvern laser particle size analyzer. The spray calculation models were established with Fluent software, and the calculation results were validated by the experimental results. Then the numerical simulation of the spray characteristics for diesel, biodiesel, and biodiesel–ethanol fuel blends were conducted. The results showed that the farther the distance is from the nozzle exit, the lower the concentration and the velocity of atomized droplets. The concentration and the velocity of atomized droplets gradually decrease along the radial direction, extending from the center to the periphery. The turbulent kinetic energy (TKE) at the front and rear of the spray is relatively lower, while the TKE is higher in the middle of the spray, and turbulent vortices appear on both sides of the axial spray center. In addition, the spray characteristics of the different fuels revealed that compared to diesel, the STP and SMD of biodiesel increase by 33.59% and 33.08% on average, respectively. The maximum concentration of biodiesel is higher than that of diesel, and the concentration distribution is more concentrated. The droplet velocity and TKE of biodiesel respectively decrease by 7.38% and 14.49% in comparison to diesel. When ethanol was added to biodiesel by a volume percentage of 30%, the STP and SMD of biodiesel–ethanol fuel blends reduce by 22.05% and 20.88%, respectively. The concentration distribution, the velocity distribution, and the TKE distribution of the fuel blends are similar to that of diesel. This indicates that adding 30% ethanol to biodiesel can effectively improve its spray quality.

A direct numerical investigation of two-way interactions in a particle-laden turbulent channel flow

Understanding the two-way interactions between finite-size solid particles and a wall-bounded turbulent flow is crucial in a variety of natural and engineering applications. Previous experimental measurements and particle-resolved direct numerical simulations revealed some interesting phenomena related to particle distribution and turbulence modulation, but their in-depth analyses are largely missing. In this study, turbulent channel flows laden with neutrally buoyant finite-size spherical particles are simulated using the lattice Boltzmann method. Two particle sizes are considered, with diameters equal to 14.45 and 28.9 wall units. To understand the roles played by the particle rotation, two additional simulations with the same particle sizes but no particle rotation are also presented for comparison. Particles of both sizes are found to form clusters. Under the Stokes lubrication corrections, small particles are found to have a stronger preference to form clusters, and their clusters orientate more in the streamwise direction. As a result, small particles reduce the mean flow velocity less than large particles. Particles are also found to result in a more homogeneous distribution of turbulent kinetic energy (TKE) in the wall-normal direction, as well as a more isotropic distribution of TKE among different spatial directions. To understand these turbulence modulation phenomena, we analyse in detail the total and component-wise volume-averaged budget equations of TKE with the simulation data. This budget analysis reveals several mechanisms through which the particles modulate local and global TKE in the particle-laden turbulent channel flow.

Large Eddy Simulation of Flow over Wavy Cylinders with Different Twisted Angles at a Subcritical Reynolds Number

The deformation of the cylinder has been proved to greatly reduce the fluctuation of lift and the vortex-induced vibration. In this article, a new form of deformation mode for the smooth cylinder is proposed in order to reduce the vortex-induced vibrations, which can be applied to marine risers and submarine pipelines to ensure the working performance and safety of offshore platforms. Large eddy simulation (LES) is adopted to simulate the turbulent flow over wavy cylinders with three different twisted angles at a subcritical Reynolds number Re = 28,712. Comparing with the results of smooth cylinder, the maximum drag and lift reduction of wavy cylinder A3 with α = 40° can reach 17% and 84%, respectively, and the corresponding vortex formation length increases significantly, while the turbulence intensity decreases relatively. Meanwhile, the circumferential minimum pressure coefficient is greater than that of the smooth cylinder, which also provides a greater drag reduction for the cylinder. The surface separation line, turbulent kinetic energy distribution, and wake vortex structure indicate that the elongation of separated shear layer and wake shedding position is larger than that of the smooth cylinder, and the vorticity value in the near wake region decreases. A periodic vortex structure is generated along the spanwise direction, and a weaker and more stable Karman vortex street is reformed at a further downstream position, which ultimately leads to the reduction of drag and fluctuating lift of the wavy cylinder.

Maximum Entropy Method for Solving the Turbulent Channel Flow Problem.

There are two components in this work that allow for solutions of the turbulent channel flow problem: One is the Galilean-transformed Navier-Stokes equation which gives a theoretical expression for the Reynolds stress (u′v′); and the second the maximum entropy principle which provides the spatial distribution of turbulent kinetic energy. The first concept transforms the momentum balance for a control volume moving at the local mean velocity, breaking the momentum exchange down to its basic components, u′v′, u′2, pressure and viscous forces. The Reynolds stress gradient budget confirms this alternative interpretation of the turbulence momentum balance, as validated with DNS data. The second concept of maximum entropy principle states that turbulent kinetic energy in fully-developed flows will distribute itself until the maximum entropy is attained while conforming to the physical constraints. By equating the maximum entropy state with maximum allowable (viscous) dissipation at a given Reynolds number, along with other constraints, we arrive at function forms (inner and outer) for the turbulent kinetic energy. This allows us to compute the Reynolds stress, then integrate it to obtain the velocity profiles in channel flows. The results agree well with direct numerical simulation (DNS) data at Reτ = 400 and 1000.

Optical Measurement Method of Particle Suspension in Stirred Vessels

AbstractSuspending particles in liquids is an important and versatile case for industrial stirring processes. By using advanced optical, non‐invasive measurement techniques like particle image velocimetry (PIV), it is possible to gain deep insights into the involved fluid dynamics without affecting the flow. However, for suspensions, the application of PIV is not trivial since both, suspended and tracer particles are present and need to be discerned during experiments. The here presented method development solves this problem and thus leads to a better insight into turbulent kinetic energy distribution, which can be utilized for process optimization through improved stirred vessel design.

LES investigation of the influence of cavitation on flow patterns in a confined tip-leakage flow

In the present paper, Large Eddy Simulations combined with the Zwart-Gerber-Belamri cavitation model are conducted to study the flow characteristics in a tip-leakage flow. A reasonable agreement is obtained between the numerical and experimental data. With the numerical results, the influence of cavitation in a tip-leakage flow on the gross features of tip-leakage vortex (TLV) and tip-separation vortex (TSV), the behavior of tip-leakage jet, the time-averaged vorticity field and turbulent kinetic energy (TKE) distributions are discussed in detailed. Our results demonstrate that more complex induced vortexes are observed in the non-cavitation case when compared with the cavitation case. Moreover, the results indicate that cavitation promotes the fusion of TLV and TSV. The narrower passageway in the gap when cavitation occurs increases the strength of tip-leakage jet, which leaves significant influence on local vorticity and turbulent kinetic energy. Cavitation trends to suppress the production of spanwise and pitchwise vorticity and promotes the TKE production. Further analysis shows that the spanwise and pitchwise flow patterns are mainly responsible for the TKE production. The fluctuations of v and w velocity and the corresponding spanwise and pitchwise velocity gradient components need to be controlled if a decrease in the viscous losses is desired.

Experimental and numerical studies on the closed and vented explosion behaviors of premixed methane-hydrogen/air mixtures

The explosion overpressure behaviors of premixed methane-hydrogen/air mixtures in a duct were evaluated by a pressure sensor, while the flame propagation behaviors in the duct and the vented explosion region were captured by a high-speed schlieren camera and a high-speed video camera, respectively. It indicated that the flame front with various concentrations had different development processes. Meanwhile, the velocity of flame front experienced three acceleration processes and explosion overpressure went up three times accordingly. The ratio of the second overpressure peak to the first one increased with the rising methane-hydrogen concentration, which signified that the second explosion severity with higher concentration of methane-hydrogen in the vented explosion region was more drastic than that with lower concentration. In addition, the simulation was applied to reveal the explosion mechanism of premixed methane-hydrogen/air mixtures. The numerical results revealed that the flame shape and pressure dynamic varying processes were corresponding to the experimental results. Besides, the numerical results also yielded several explosion parameters which were difficult to be obtained in the experiments, such as the flame temperature distribution, explosion overpressure distribution, gas-flow velocity distribution, and gas turbulent kinetic energy distribution, whose coupling effect played an important role in the explosion venting.

Turbulent Kinetic Energy in Bolt Fishway

The paper presents an analysis the spatial distribution of turbulent kinetic energy (TKE) for bolt fishways, including the impact of additional spillway slots and fixed channel development. The research was done for two models, each containing a different arrangement of slots. The presented results of research for bolt fishways were obtained as an effect of laboratory tests. The measurements were done for three components of instant flow velocity magnitude (speed). Analysis of the results was done for a 3D flow structure using Matlab software. In the case of bolt fishways, significant differences were noted for the method of velocity and TKE distribution, in reference to research comprising channels with biological development. It was stated that a reason for this is the flexible development of the channel. The occurrence of extreme TKE values in the chamber (pool) is strictly associated with the characteristics of interaction zones between various flow structures. It was also stated that the lower the parapet of the slot’s spillway shelf is in the fishway’s partition, the higher TKE could be expected just downstream of the section. These establishments may be important for the designing process in the case of fish passes of various types of construction.

Turbulent Kinetic Energy Distribution of Nutrient Solution Flow in NFT Hydroponic Systems Using Computational Fluid Dynamics

Hydroponics is crucial for providing feasible and economical alternatives when soils are not available for conventional farming. Scholars have raised questions regarding the ideal nutrient solution flow rate to increase the weight and height of hydroponic crops. This paper presents the turbulent kinetic energy distribution of the nutrient solution flow in a nutrient film technique (NFT) hydroponic system using the computational fluid dynamics (CFD) method. Its main objective is to determine the dynamics of nutrient solution flow. To conduct this study, a virtual NFT hydroponic system was modeled. To determine the turbulent kinetic energy distribution in the virtual NFT hydroponic system, we conducted a CFD analysis with different pipe diameters (3.5, 9.5, and 15.5 mm) and flow rates (0.75, 1.5, 3, and 6 L min−1). The simulation results indicate that different pipe diameters and flow rates in NFT hydroponic systems vary the turbulent kinetic energy distribution of nutrient solution flow around plastic mesh pots.

Assembling a bubble-induced turbulence model incorporating physical understanding from DNS

Bubble-induced turbulence (BIT) is a two-phase flow phenomenon characterized by complex interfacial interactions that fundamentally alter the resulting liquid turbulent kinetic energy distribution, budgets, and scales. Incorporating this complexity into a BIT model remains a formidable challenge, as existing two-equation BIT closures struggle with accurately predicting the turbulent kinetic energy and mean flow profiles. The present work assembles a BIT model that incorporates additional physical understanding into its formulation by leveraging insights garnered from experiments, DNS, and previous assessment. The model comprises new turbulent viscosity and time-scale formulations, in addition to optimized values for the modulation parameter, dissipation coefficient, and newly proposed turbulent viscosity multiplier. Improved model performance is demonstrated through simulation of air/water experimental cases and direct comparison with existing closures, which includes qualitative inspection of individual sets as well as quantitative assessment of the turbulent kinetic energy error distribution. Future work delving into momentum closure development, new experimental campaigns, and DNS parametric studies is motivated and linked to BIT model improvements.