Local Flow Structure Research Articles

Enhancing ignition stability in an annular combustor using a pre-chamber ignition system

The traditional method using spark electrode ignition in annular combustors lacks safety due to its long ignition delay and deficiencies in reliability and repeatability. The present work investigates the ignition characteristics of a premixed annular combustor using pre-chamber combustion (PCC) as an ignition source. The ignition process of the annular combustor is studied experimentally with PCC and is compared to the one with the traditional spark electrode ignition under the same equivalence ratio and bulk velocities. The ignition process is recorded using a high-speed camera. The two-dimensional time-resolved Mie scattering technique is employed to determine the flame front position in the annular combustor. It was found that the jet issued from PCC generates hot radicals associated with strong turbulence, exhibiting distributed ignition sites along the jet trajectory inside the annular combustor. Introducing PCC to the annular combustor increases the ignition probability and burning rate, as well as reduces the light-round time by about 24 % compared to the spark electrode at a thermal power of 18.6 kW. Moreover, the experimental results indicate that flame propagation in the annular combustor is significantly influenced by the PCC operating parameters. In contrast, combustion within the PCC is less affected by the local flow structure in the annular combustor, making the PCC a favourable solution for various operating conditions. Additionally, a slightly rich mixture in the PCC increases the burning rate, whereas a very rich mixture decreases the burning rate.

Experimental and numerical study of improving flow and heat transfer in a serpentine cooling channel with topology-optimized TPMS porous structures

Serpentine cooling channels have been employed in various industrial applications to control the heat loads in the system by increasing heat transfer while lowering the total pressure loss. As additive manufacturing (AM) enables the fabrication of complex structures, more sophisticated cooling models have been proposed to improve the thermal performance of the serpentine channel. This work designs a high-performance serpentine cooling channel based on topology optimization and triply periodic minimal surface (TPMS). The transient liquid crystal thermography (TLC) is used to reveal the endwall heat transfer characteristics of the optimized serpentine channel infilled with the Diamond TPMS topology within the Reynolds number of 10,000–40,000. The overall and local flow structures are revealed by numerical simulation, and the results are compared with the baseline serpentine channel. The experimental results show that at the Reynolds number of 10,000, the topology-optimized model with the Diamond structure shows a higher wetted-area averaged Nusselt number in the second pass by 70.7 % while reducing the total pressure loss by 19.2 %, compared to the smooth channel. Within the studied Reynolds numbers, the heat transfer enhancement in the second pass is 2.30–2.39 times relative to a smooth channel. The numerical results show that the topology-optimized model significantly improves the thermal performance by up to 82.7 % compared to the baseline because the flow recirculation and the regions of low heat transfer are eliminated. The optimized channel also mitigates the negative effect of the Dean's vortices while keeping high turbulence and improving flow and heat transfer uniformity.

Data-driven modal analysis of turbulent momentum exchange and heat transfer in composite porous fluid systems

This paper investigates the dynamics governing turbulent momentum exchange and heat transfer between pore flow within porous media and the turbulent flow passing over it. Employing high-fidelity pore-scale large eddy simulation, our investigation explores the fundamental mechanisms driving these phenomena. Modal analysis based on snapshot proper orthogonal decomposition (POD) is employed to quantify the modes of interaction between porous and non-porous regions, providing a comprehensive understanding of the underlying processes. Spatial and temporal modes reveal the existence of localized flow structures at the pore scale, contributing to time-varying patterns of information exchange. At the commencement of the porous block, the mean flow (Mode = 0) from the porous to non-porous region is the dominant mechanism in momentum exchange and heat transfer. This mode facilitates convective heat transfer from the porous to the non-porous region through upward and forward flow movements, showcasing positive flow leakage. In addition to the mean flow, the turbulent flux inherent in alternate POD modes (Mode ≠ 0) plays a substantial role in information propagation, influencing diverse directions. Spatial modes, complemented by statistical analysis, uncover a significant likelihood of observing negative vertical velocity values in the wake of the porous ligaments at the porous-fluid interface, indicative of negative flow leakage. This negative flow leakage precisely corresponds to the local penetration of fluid from the non-porous region into the porous region. Furthermore, our study reveals that information exchange via turbulence fluctuations manifests through complex outward and inward interactions in regions characterized by substantial positive flow leakage. Notably, these regions exhibit a distinct tendency for high-momentum streamwise-oriented flow to migrate outward from the porous region into the non-porous region (outward interactions). Conversely, inward interactions arise in these regions when the instantaneous magnitude of positive flow leakage is smaller than the mean value of positive flow leakage, emphasizing the pulsating nature of positive flow leakage. Finally, the distribution of the Nusselt number highlights that more than 60% of total heat transfer occurs within the initial one-third of the porous block length. Significantly, a notable portion of the porous ligaments experiences insufficient cooling due to positive flow leakage, underlining the critical implications of these findings for the understanding of turbulent momentum exchange and heat transfer in a composite porous-fluid system.

New similarity laws reduced from local Mach factors in longitudinal–transverse force theory

The rapid advancement in aeronautics has led to the emergence of intricate dynamic processes and structures, such as vortices, shock waves, flow separation, and turbulence, resulting from the flow around airfoils. Acquiring a profound understanding of these local structures and unraveling the physical mechanisms underlying flow phenomena represents an essential and challenging issue in the field of flight science. In this research, the longitudinal–transverse force theory (L–T force theory), as proposed by previous researchers, is employed to quantitatively assess contributions of local flow structures to aerodynamic forces. Specifically, the research encompasses an analysis of steady and viscous compressible flow over the Royal Aircraft Establishment (RAE)-2822 airfoil, with free-stream Mach number (M∞) ranging from 0.1 to 2.0. We comprehensively estimate longitudinal forces (L-force) and transverse forces (T-force), along with effects of compressibility on aerodynamic forces. Furthermore, recognizing the necessity for high-precision algorithms in the computation of L–T force theory, this investigation utilizes a sixth-order accuracy algorithm for spatial discretization and differencing. Our analysis reveals that the influence of compressibility and the contributions of L-forces to aerodynamic forces become increasingly significant in high M∞ regimes as shearing processes weaken. Additionally, a new similarity law is established to characterize aerodynamic forces acting on the RAE-2822 airfoil based on a novel moderating factor, ζmo, reduced from local Mach factors in the L–T force theory. This coefficient, ζmo, elucidates the degree to which transverse processes are modulated by longitudinal processes. Various angles of attack α and airfoils have also been analyzed, including National Advisory Committee for Aeronautics (NACA)0012 and NACA0006, by introducing a parameter denoted as κ to further validate the universality of the new similarity laws. The results demonstrate a high degree of accuracy in fitting the aerodynamic coefficients.

Experimental investigation on local flow structures of upward cap-bubbly flows in a vertical large-size square channel

Gas–liquid two-phase flows are typical in engineering systems involving heat and mass transfers. The cross-sectional geometries and sizes of these flow channels vary, exerting a notable impact on the thermofluid behavior. To develop thermofluid models, it is imperative to obtain local measurements of two-phase flows and gain insights into their characteristics from these measurements. Numerous experimental studies have investigated the local flow characteristics in circular pipes and rectangular channels; however, few studies on square channels have been conducted, particularly for flow regimes beyond bubbly flows, such as cap-bubbly flows. Given the importance of two-phase flows in large square channels for advanced nuclear reactors, such as the economic simplified boiling water reactor (ESBWR), we experimented with upward cap-bubbly flows in a large square channel. Detailed cross-sectional distributions of the void fractions, axial gas velocities, and interfacial area concentrations for two bubble-size groups were obtained at three axial locations using local measurements of a four-sensor optical probe. Based on the database, the cap-bubbly flow characteristics were understood, including flow development in a large square channel. In addition, the existing drift-flux correlations for large circular pipes predicted the measured void fraction with an accuracy of approximately ± 10 %, whereas the existing interfacial area concentration correlations reasonably correlated with the measured interfacial area concentration with an accuracy of approximately ± 30 %. Furthermore, the database was used to calculate the covariances of the void fractions. The correlations for large circular pipes significantly underestimated the void fraction covariance of the larger bubble group, probably because of the peculiar void fraction distribution of the group in a large square channel. The other covariances were well predicted.

CFD analysis of coolant mixing in VVER-1000/V320 reactor pressure vessel

This study presents a code-to-code and model-to-model comparison of coolant mixing in the VVER-1000/V320 Kozloduy Unit 6 nuclear power plant using Computational Fluid Dynamics (CFD). Four different CFD codes were used to simulate coolant mixing in the reactor vessel, namely ANSYS Fluent, ANSYS CFX, TrioCFD, and STAR-CCM+. Two different approaches were used to model the upper plenum, while a single simplified model was used for the reactor pressure vessel. The simulations were performed for VVER-1000 coolant transient benchmark (V1000CT-2) mixing exercise. The results were compared between the different CFD codes and models to assess the accuracy and consistency of the simulations with the available experimental data. Overall, the results showed good agreement between the different CFD codes and models, with minor differences observed in some cases. The simplified models were found to be sufficient for predicting the overall coolant mixing patterns observed in the reactor vessel, provided additional insights into the local flow structures and mixing characteristics. This study demonstrates the applicability and reliability of CFD simulations for coolant mixing analysis in VVER-1000/V320 nuclear power plants.

Turbulence and Pollutant Statistics around a High-Rise Building with and without Overhangs

Wind flow around an isolated building is highly turbulent. Facade appurtenances can further increase the complexity of the flow, which strongly affects the gas dispersion around the building. This study investigated the turbulence and pollutant statistics around a high-rise building with large-eddy simulations and determined the influence of overhangs on the local wind flow and dispersion. Large-scale periodic vortex motion was detected. The results indicated that both the oncoming flow and the flow around the building followed a standard Gaussian distribution, whereas the occurrence frequencies of pollutant concentrations were far from Gaussian for pollutants discharged from both the rooftop and the ground behind the building. Near the pollutant sources, the positive concentration fluctuations occurred more frequently; occasionally, positive and negative fluctuations occurred equally. For the majority of areas far from the source, negative fluctuations were more common, but the maximum positive fluctuations were much larger. Overhangs changed the local flow structures near the building facade. Both the maximum concentration fluctuation and the maximum occurrence frequency decreased in the region between overhangs because turbulence was restricted.

Characteristics of local flow structure with different particle properties in a gas-solid diameter-varying fluidized bed

The effects of particle property on gas-solid flow in the diameter-varying riser are experimentally examined using the optical fiber probe in this research. Local flow features are obtained by signal analysis method under the operating conditions of 3–7 m/s and 8–63 kg/m2s. The results show that solid holdup distribution of glass beads is wider than that of catalyst particle particles in the wall region but is narrow in the center region. Solid holdup fluctuations tend to decrease with the increase of particle density under low-concentration conditions but increase at high-concentration conditions. The results from power spectrum density (PSD) show that the increase in particle density strengthens the periodic flow features in the enlarged section. The motion intensity decreases at the particle level but increases at the cluster level for high-density particles. Additionally, as particle density rises, the solid concentration discrepancies between the straight section and the enlarged section widen. In contrast to the upper straight section, the effects of particle density on gas-solid flow are minimal in the enlarged section.

On the spurious effects in Lamb-vector-based force decomposition methods

Recent methods based on Lamb vector integration allow for a far-field formulation and decomposition of the whole aerodynamic force, with identification of local flow structures associated with the force generation. Different exact Lamb-vector-based force formulations were proposed in the past and the decomposition of total drag into lift-induced and parasite contributions was subject of very recent studies. However, inconsistencies were also reported, raising questions on the physical role of a non-zero induced drag found in two-dimensional flows. Moreover, the effect of the arbitrary pole (appearing in Lamb-vector-based formulas) on the numerical accuracy of such methods was never investigated. Additionally, the separation of parasite drag into viscous and wave drag contributions by Lamb vector field analysis is still questioned. In this paper, the accuracy of different force formulas and of the drag decomposition in lift-induced and parasite contributions is first analyzed, for steady flows. Two-dimensional numerical solutions around RAE2822 and NACA0012 airfoils are considered, the latter in both inviscid and viscous flows (at low and high Reynolds number), to analyze consistency between lift-induced/parasite drag definitions and the drag generated in isentropic flow conditions (reversible drag) or due to entropy production (irreversible drag). A spurious induced drag contribution (related to the streamwise momentum perturbation) is identified, resulting in negative induced drag values in two-dimensional flows. The effect of a shift in the pole location is also analysed, with reference to its impact on the total force and on drag decomposition accuracy, then a new approach to parasite drag breakdown into physical constituents (viscous and wave contributions) is proposed and results are compared against predictions obtained using consolidated thermodynamic-based methods and against available results from recent literature.

Swaying motions of submerged flexible vegetation

Submerged vegetation plays a subtle role in exchanging the fluid mass and energy in the vegetated flow zone, where the swaying motions of flexible plants are the important source of turbulent kinetic energy production. Flume experiments were conducted to study the modes, characteristics and factors of swaying of individual submerged flexible plants. A modified plant model in a new form, representing the highly flexible vegetation with clustered leaves, was employed. A ‘rigid-like’ synchronous swaying mode and a ‘whip-like’ asynchronous flapping mode are found to appear alternately for the individual plants. The interaction between these modes depends on the resulting local flow structure affected by the plants. Compared with a plant in isolation with the same flow Reynolds number, the swaying motions of a plant within the vegetation patch are less frequent but more prone to the synchronous mode. The eigen frequency of the motions increases linearly with an increase in flow Reynolds number in the range of 2 × 104–5 × 104, but the normalised amplitude reaches a saturation at a high flow Reynolds number. Moreover, the in-line and spanwise motions have a 2 : 1 frequency ratio for an ‘8’ shaped trajectory on the horizontal plane and a 1 : 1 ratio for a ‘0’ shaped circular trajectory, or a combination of both.

Visualization of local two-phase flow structure in a packed bed of spheres

A two-phase flow structure in porous media is essential to clarify the debris cooling characteristics during a severe accident in nuclear power plants. In previous experimental studies, a packed bed of spheres has been used instead of the porous debris bed. Many models to predict the flow and heat transfer characteristics in the packed bed have been proposed based on the experimental data in the sphere-packed bed. However, those models have not considered the local flow structure, which should be studied to enhance the prediction accuracy. In this study, the local flow structure of the air-water two-phase flow in the unit model of the sphere-packed bed was measured by neutron computed tomography. The distribution of the gas phase was reconstructed by acquired images. From these results, the breakup and coalescence of the bubbles in the packed bed were evaluated.

THE COASTAL MACRO-VORTICES DYNAMICS: A CASE STUDY IN HONG KONG WATERS

Coastal circulations are basic information when considering sediment transport and water quality in the oceanic environment, particularly the macro-vortices dynamics which greatly affected the mass transfer and extended the residence time (Hasegawa et al., 2009). Large-scale macro-vortices could be formed in the lee or around natural obstacles such as islands and headlands during the interaction between geographical features and coastal circulations induced by tides and winds. Pearl River is the second largest river in China considering discharge, delivering 3.26 × 1011 m3 freshwater every year into the South China Sea (SCS) through eight outlets (Wu et al., 2016). Hong Kong (HK) is located downstream of the Pearl River Estuary (PRE), acting as a bridge between the PRE and the SCS, as shown in Figure 1. HK possesses more than 200 islands as well as narrow channels and complex coastlines, which have a great impact on shaping local flow structures. In addition, prevailing southwest winds blow during the summer, while stronger northeast winds gust during the winter. Embracing tides from the SCS and river discharge from the PRE, HK waters is an energetic and interesting area and worth a detailed investigation.

Feature importance in neural networks as a means of interpretation for data-driven turbulence models

This work aims at making the prediction process of neural network-based turbulence models more transparent. Due to its black-box ingredients, the model’s predictions cannot be anticipated. Therefore, this paper is concerned with the quantification of each feature’s importance for the prediction of trained and fixed NNs, which is one possible type of explanation for opaque models. Two conceptually different attribution methods, namely permutation feature importance and DeepSHAP, are chosen in order to assess global, regional and local feature importance. The neuralSST turbulence model, which serves as an example, will be investigated in greater detail. While the global importance scores provide a quick and reliable way to detect irrelevant features and may thus be used for feature selection, only the (semi-)local analysis provides meaningful and trustworthy interpretations of the model. In fact, the local importance scores suggest that hypotheses with a common high-level influence on the turbulence model, e.g. adjusting the net production of turbulent kinetic energy or the Reynolds stress anisotropy, are similarly affected by local mean flow structures such as attached boundary layers, free shear layers or recirculation zones.

Experimental Analysis of the Three Dimensional Flow in a Wells Turbine Rotor

An experimental investigation of the local flow field in a Wells turbine has been conducted, in order to produce a detailed analysis of the aerodynamic characteristics of the rotor and support the search for optimized solutions. The measurements were conducted with a hot-wire anemometer (HWA) probe, reconstructing the local three-dimensional flow field both upstream and downstream of a small-scale Wells turbine. The multi-rotation technique has been applied to measure the three velocity components of the flow field for a fixed operating condition. The results of the investigation show the local flow structures along a blade pitch, highlighting the location and radial extension of the vortices which interact with the clean flow, thus degrading the turbine’s overall performance. Some peculiarities of this turbine have also been shown, and need to be considered in order to propose modified solutions to improve its performance.

Eulerian-Eulerian Modeling of the Features of Mean and Fluctuational Flow Structure and Dispersed Phase Motion in Axisymmetric Round Two-Phase Jets

The features of the local mean and fluctuational flow structure, carrier phase turbulence and the propagation of the dispersed phase in the bubbly and droplet-laden isothermal round polydispersed jets were numerically simulated. The dynamics of the polydispersed phase is predicted using the Eulerian–Eulerian two-fluid approach. Turbulence of the carrier phase is described using the second-moment closure while taking into account the presence of the dispersed phase. The numerical analysis was performed in a wide range of variation of dispersed phase diameter at the inlet and particle-to-fluid density ratio (from gas flow laden with water droplets to carrier fluid flow laden with gas bubbles). An increase in the concentration of air bubbles and their size leads to jet expansion (as compared to a single-phase jet up to 40%), which indicates an increase in the intensity of the process of turbulent mixing with the surrounding space. However, this makes the gas-droplet jet narrower (up to 15%) and with a longer range in comparison with a single-phase flow. The addition of finely dispersed liquid droplets to an air jet suppresses gas phase turbulence (up to 15%). In a bubbly jet, it is found that small bubbles (Stk < 0.1) accumulate near the jet axis in the initial cross-sections, while concentration of the large ones (Stk > 0.2) along the jet axis decreases rapidly. In the gas-droplet jet, the effect of dispersed phase accumulation is also observed in the initial cross-section, and then its concentration decreases gradually along the jet axis. For gas bubbles (Stk < 0.1), small turbulence attenuation (up to 6%) is shown.

A new type of weighted compact nonlinear scheme with minimum dispersion and adaptive dissipation for compressible flows

A new type of weighted compact nonlinear scheme (WCNS) with state-of-the-art spectral properties is developed based on an adaptive, nonlinear optimization strategy that considers the diversity of flow structures and the influence of nonlinearity. The optimization is realized by simultaneously adjusting the free parameters (η and ξ) and the nonlinear weighting function (C) at each local region. In this way, minimum dispersion and adaptive dissipation can be achieved for the scheme. The optimization contains two steps: (1) η is optimized to obtain minimum dispersion; (2) ξ and C are optimized depending on the local flow structure to obtain adaptive dissipation. Following these steps, a 6-point WCNS with excellent spectral properties is achieved. The optimized WCNS is then extended to multi-species flows by incorporating the double-flux algorithm. Numerical results of benchmark test cases show that the present WCNS exhibits better resolution and stronger robustness than recently-developed high-resolution schemes.

Effects of Fuel Lewis Number on Wall Heat Transfer During Oblique Flame-Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

The influence of fuel Lewis number {mathrm{Le}}_{F} on the statistical behaviour of wall heat flux and flame quenching distance has been analysed using direct numerical simulation (DNS) data for the turbulent V-shaped flame-wall interaction in a channel flow configuration corresponding to a friction velocity-based Reynolds number of 110 for fuel Lewis number, {mathrm{Le}}_{F}, ranging from 0.6 to 1.4. It has been found that the maximum wall heat flux magnitude in turbulent V-shaped flame-wall interaction increases with decreasing {mathrm{Le}}_{F} but just the opposite trend was observed for 2D laminar V-shaped flame-wall interaction and 1D laminar head-on quenching cases. This behaviour has been explained in terms of the correlation of temperature and fuel reaction rate magnitude with local flame surface curvature for turbulent flames due to the thermo-diffusive effects induced by the non-unity Lewis number. The wall heat flux magnitude and wall shear stress magnitude are found to be negatively correlated for all cases considered here. Moreover, their mean variations in the streamwise direction are qualitatively different irrespective of {mathrm{Le}}_{F}, although the magnitudes of wall heat flux and wall shear stress increase with decreasing {mathrm{Le}}_{F}. Furthermore, the flame alignment relative to the wall also affects the wall heat flux and it has been found that local occurrences of head-on quenching can lead to higher magnitudes of wall heat flux magnitude. It has been found that {mathrm{Le}}_{F} also affects the evolution of the flame quenching distance in the streamwise direction with the progress of flame quenching for different flame normal orientations with respect to the wall. This analysis shows that the effects of fuel Lewis number on flame orientation, correlations of reaction rate and temperature with local flame curvature and coherent flow structures within the turbulent boundary layer ultimately affect the wall heat transfer and flame quenching distance. Thus, the thermo-diffusive effects arising from the non-unity Lewis number need to be taken into account for accurate modelling of wall heat transfer during flame-wall interaction in turbulent boundary layers.

Vortex-induced sound prediction of slat noise from time-resolved particle image velocimetry data

A data-driven method for predicting the vortex-induced sound from time-resolved velocimetry data is presented and applied to the sound generated by flow passing through the slat in a multi-element high-lift airfoil. The time-dependent velocity fields in the slat-cove region of the 30P30N multi-element airfoil are obtained from time-resolved particle image velocimetry measurements, and a low-order reconstruction is achieved by using the rank-one vbnm modes from spectral proper orthogonal decomposition. The pressure force and associated dipole sound are then computed via the application of the force and acoustic partitioning methods (Seo et al. in Phys Fluids 34(5):053607, 2002) which involve volume integrals of the product of the second invariant of the velocity gradient tensor and geometry-dependent influence fields. The method enables estimation of the dipole sound generated by local flow structures, and the results are shown to be consistent with theory of vortex sound. Comparison with the measured sound data suggests that while the shear layer modes are responsible for the tonal noise, the interactions between the shear layer modes and other parts of the wing also generate a substantial level of flow noise.

Influence of Inlet Boundary Conditions on the Prediction of Flow Field and Hemolysis in Blood Pumps Using Large-Eddy Simulation

Inlet boundary conditions (BC) are one of the uncertainties which may influence the prediction of flow field and hemolysis in blood pumps. This study investigated the influence of inlet BC, including the length of inlet pipe, type of inlet BC (mass flow rate or experimental velocity profile) and turbulent intensity (no perturbation, 5%, 10%, 20%) on the prediction of flow field and hemolysis of a benchmark centrifugal blood pump (the FDA blood pump) and a commercial axial blood pump (Heartmate II), using large-eddy simulation. The results show that the influence of boundary conditions on integral pump performance metrics, including pressure head and hemolysis, is negligible. The influence on local flow structures, such as velocity distributions, mainly existed in the inlet. For the centrifugal FDA blood pump, the influence of type of inlet BC and inlet position on velocity distributions can also be observed at the diffuser. Overall, the effects of position of inlet and type of inlet BC need to be considered if local flow structures are the focus, while the influence of turbulent intensity is negligible and need not be accounted for during numerical simulations of blood pumps.

An investigation on the wake flow of a generic ship using IDDES: The effect of computational parameters

The study of the ship airwake is critical as it explores the effect of unsteady wake flow on helicopter operations. This paper studied the near-wake flow topology of a generic ship at Re = 8 × 104 to assess the capability of a hybrid RANS/LES (Reynolds-averaged Navier–Stokes/large-eddy simulation) approach, known as IDDES (improved delayed detached-eddy simulation). The impact of computational parameters, including the mesh grid, residual level, time-step size, momentum discretization scheme and transient formulation, on the wake flow was investigated. The numerical results were validated by using the previous experimental data and LES results. The results show that except of the mesh resolution all other computational parameters varied in the current study do not have significant effect on the global drag forces, but showing large differences on the prediction of the local wake flow structures. This point has not been evidently reported in the previous work. The finer grid resolution is sufficient to produce an accurate qualitative and quantitative prediction of the flow structures, while using a poor grid resolution (coarse mesh) leads to inaccurate prediction of the flow topology. The recommended parameters for the time-step size (7.5 × 10−5s) and residual level (1 × 10−4) provide sufficient accuracy of wake predictions, showing good agreement with reference studies. For the convective term of the momentum equation in IDDES, the bounded central differencing scheme is proposed for its discretization, while the bounded second-order implicit is proposed to be adopted as the transient formulation.