Theoretical and Computational Fluid Dynamics
Journal Prestige (SJR): 0.47 Citation Impact (citeScore): 1 Number of Followers: 22 Hybrid journal (It can contain Open Access articles) ISSN (Print) 14322250  ISSN (Online) 09354964 Published by SpringerVerlag [2468 journals] 
 Wavy ground effects on the stability of cylinder wakes

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Abstract: The stability of the flow past a circular cylinder in the presence of a wavy ground is investigated numerically in this paper. The wavy ground consists of two complete waves with a wavelength of 4D and an amplitude of 0.5D, where D is the cylinder diameter. The vertical distance between the cylinder and the ground is varied, and four different cases are considered. The stability analysis shows that the critical Reynolds number increases for cases close to the ground when compared to the flow past a cylinder away from the ground. The maximum critical Reynolds number is obtained when the cylinder is located in front of the waves. The wavy ground adds layers of clockwise (negative) vorticity due to flow separation from the wave peak, to the oscillating Kármán vortex. This negative vorticity from the wave peak also cancels part of the positive (counterclockwise) vorticity shed from the bottom half of the cylinder. In addition, the negative vorticity from the wave peak strengthens the clockwise (negative) vorticity shed from the top half of the cylinder. These interactions combined with the ground effect skewed the flow away from the ground. The base flow is skewed upward for all the nearground cases. However, this skew is larger when the cylinder is located over the wavy ground. The vortex shedding frequency is also altered due to the presence of the waves. The main eigenmode found for plain flow past a cylinder appears to become suppressed for cases closer to the ground. Limited particle image velocimetry experiments are reported which corroborate the finding from the stability analysis. Graphical abstract
PubDate: 20240221

 Simulation of the unsteady vortical flow of freely falling plates

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Abstract: An inviscid vortex shedding model is numerically extended to simulate falling flat plates. The body and vortices separated from the edge of the body are described by vortex sheets. The vortex shedding model has computational limitations when the angle of incidence is small and the free vortex sheet approaches the body closely. These problems are overcome by using numerical procedures such as a method for a nearsingular integral and the suppression of vortex shedding at the plate edge. The model is applied to a falling plate of flow regimes of various Froude numbers. For \(\text {Fr}=0.5\) , the plate develops largescale sidetoside oscillations. In the case of \(\text {Fr}=1\) , the plate motion is a combination of sidetoside oscillations and tumbling and is identified as a chaotic type. For \(\text {Fr}=1.5\) , the plate develops to autorotating motion. Comparisons with previous experimental results show good agreement for the falling pattern. The dependence of change in the vortex structure on the Froude number and its relation with the plate motion is also examined. Graphical abstract
PubDate: 20240214

 Linear stability analysis of surface waves of liquid jet injected in
transverse gas flow with different angles
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Abstract: A theoretical and experimental study was conducted to investigate the effect of injection angle on surface waves. Linear stability theory was utilized to obtain the analytical relation. In the experimental study, highspeed photography and shadowgraph techniques were used. Image processing codes were developed to extract information from photos. The results obtained from the theoretical relation were validated with the experimental results at different injection angles. In addition, at the injection angle of 90 \({^\circ }\) , the theoretical results were evaluated with the experimental results of other researchers. This evaluation showed that the theory results were in good agreement with the experimental data. The proper orthogonal decomposition (POD) and the power spectra density (PSD) analysis were also used to investigate the effect of the injection angle on the flow structures. The results obtained from the linear stability were used to determine the maximum waves’ growth rate, and a relation was presented for the breakup length of the liquid jet at different injection angles. The breakup length results were compared with theory and published experimental data. The presented relation is more consistent with experimental data than other theories due to considering the nature of waves. The results showed that the instability of the liquid jet is influenced by three forces: inertial, surface tension, and aerodynamic. Therefore, Rayleigh–Taylor, Kelvin–Helmholtz, Rayleigh–Plateau, and azimuthal instabilities occur in the process. Decreasing the injection angle changes the nature of waves and shifts from Rayleigh–Taylor to Kelvin–Helmholtz. That reduces the wavelength and increases the growth rate of the waves. Axial waves have a significant impact on the physics of the waves and influence parameters. If axial waves are not formed, the growth rate of the waves is independent of the injection angle. An increase in the gas Weber number causes a change in the type of dominant waves and a greater instability of the liquid jet. In contrast, an increase in the liquid Weber number causes an enhancement in the resistance of the liquid jet against the transverse flow without changing the type of the dominant waves. Decreasing the density ratio reduces the effect of Rayleigh–Taylor waves and strengthens the Kelvin–Helmholtz waves. It causes two trends to be observed for the growth rate of waves at low spray angles, while one trend occurs at high spray angles. Graphical abstract
PubDate: 20240212

 Fluid flow past a freely moving body in a straight or distorted channel

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Abstract: The focus here is on a thin solid body passing through a channel flow and interacting with the flow. Unsteady twodimensional interactive properties from modelling, analysis and computation are presented along with comparisons. These include the effects of a finite dilation or constriction, as the body travels through, and the effects of a continuing expansion of the vessel. Finitetime clashing of the body with the channel walls is investigated as well as the means to avoid clashing. Sustained oscillations are found to be possible. Wake properties behind the body are obtained, and broad agreement in trends between fullsystem and reducedsystem responses is found for increased body mass. Graphical abstract
PubDate: 20240125

 Free surface wave interaction with a submerged body using a DtN boundary
condition
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Abstract: Recently, Rim (Ocean Engng 239:711, 2021; J Ocean Engng Mar Energy 9:4151, 2023 ) suggested an exact DtN artificial boundary condition to study the threedimensional wave diffraction by stationary bodies. This paper is concerned with threedimensional linear interaction between a submerged oscillating body with arbitrary shape and the regular water wave with finite depth. An exact DirichlettoNeumann (DtN) boundary condition on a virtual cylindrical surface is derived, where the virtual surface is chosen so as to enclose the body and extract an interior subdomain with finite volume from the horizontally unbounded water domain. The DtN boundary condition is then applied to solve the interaction between the body and the linear wave in the interior subdomain by using boundary integral equation. Based on verification of the present model for a submerged vertical cylinder, the model is extended to the case of a submerged chamfer box with fillet radius in order to study 6DoF oscillatory motion of the body under the free surface wave. Graphical abstract
PubDate: 20240119

 Theory and simulation of shock waves freely propagating through monoatomic
nonBoltzmann gas
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Abstract: The effect of nonBoltzmann energy distributions on the free propagation of shock waves through a monoatomic gas is investigated via theory and simulation. First, the nonBoltzmann heat capacity ratio \(\gamma \) , as a key property for describing shock waves, is derived from first principles via microcanonical integration. Second, atomistic molecular dynamics simulations resembling a shock tube setup are used to test the theory. The presented theory provides heat capacity ratios ranging from the wellknown \(\gamma = 5/3\) for Boltzmann energydistributed gas to \(\gamma \rightarrow 1\) for delta energydistributed gas. The molecular dynamics simulations of Boltzmann and nonBoltzmann driven gases suggest that the shock wave propagates about 9% slower through the nonBoltzmann driven gas, while the contact wave appears to be about 4% faster if it trails nonBoltzmann driven gas. The observed slowdown of the shock wave through applying a nonBoltzmann energy distribution was found to be consistent with the classical shock wave equations when applying the nonBoltzmann heat capacity ratio. These fundamental findings provide insights into the behavior of nonBoltzmann gases and might help to improve the understanding of gas dynamical phenomena. Graphical abstract
PubDate: 20240118

 An adjointbased methodology for calculating manufacturing tolerances for
natural laminar flow airfoils susceptible to smooth surface waviness
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Abstract: An adjointbased method is presented for determining manufacturing tolerances for aerodynamic surfaces with natural laminar flow subjected to wavy excrescences. The growth of convective unstable disturbances is computed by solving Euler, boundary layer, and parabolized stability equations. The gradient of the kinetic energy of disturbances in the boundary layer (E) with respect to surface grid points is calculated by solving adjoints of the governing equations. The accuracy of approximations of \(\Delta E\) , using gradients obtained from adjoint, is investigated for several waviness heights. It is also shown how secondorder derivatives increase the accuracy of approximations of \(\Delta E\) when surface deformations are large. Then, for specific flight conditions, using the steepest ascent and the sequential least squares programming methodologies, the waviness profile with minimum \(L2\) norm that causes a specific increase in the maximum value of N factor, \(\Delta N\) , is found. Finally, numerical tests are performed using the NLF(2)0415 airfoil to specify tolerance levels for \(\Delta {N}\) up to 2.0 for different flight conditions. Most simulations are carried out for a Mach number and angle of attack equal to 0.5 and \(1.25^{\circ }\) , respectively, and with Reynolds numbers between \(9\times 10^6\) and \(15\times 10^6\) and for waviness profiles with different ranges of wavelengths. Finally, some additional studies are presented for different angles of attack and Mach numbers to show their effects on the computed tolerances. Graphic abstract
PubDate: 20231228

 Stability of supersonic boundary layer over an unswept wing with a
parabolic airfoil
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Abstract: Under the lownoise Mach 3 flight conditions for a supersonic passenger aircraft having unswept wings with a thin parabolic airfoil, laminarturbulent transition is due to amplification of the first mode. Stability of a local selfsimilar boundary layer over such a wing is investigated both using the \(e^{N}\) method in the framework of linear stability theory and direct numerical simulation (DNS). It is found that the instability amplitude should reach a maximum over the entire spectral range above the profiles of 2.5% and thicker. The locus of maximum appears at the trailing edge and moves to the leading edge as the profile becomes thicker, while the maximum amplitude decreases. The theoretical findings are supported by DNS of the linear wave packets propagating in the boundary layer. Significance of these results to the design of laminar supersonic wings is discussed. Graphical abstract
PubDate: 20231228

 Inviscid modeling of unsteady morphing airfoils using a discretevortex
method
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Abstract: A loworder physicsbased model to simulate the unsteady flow response to airfoils undergoing largeamplitude variations of the camber is presented in this paper. Potentialflow theory adapted for unsteady airfoils and numerical methods using discretevortex elements are combined to obtain rapid predictions of flow behavior and force evolution. To elude the inherent restriction of thinairfoil theory to small flow disturbances, a timevarying chord line is proposed in this work over which to satisfy the appropriate boundary condition, enabling large deformations of the camber line to be modeled. Computational fluid dynamics simulations are performed to assess the accuracy of the loworder model for a wide range of dynamic trailingedge flap deflections. By allowing the chord line to rotate with trailingedge deflections, aerodynamic loads predictions are greatly enhanced as compared to the classical approach where the chord line is fixed. This is especially evident for largeamplitude deformations. Graphical abstract
PubDate: 20231207

 Investigation of Stokes flow in a grooved channel using the spectral
method
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Abstract: Pressuredriven Newtonian fluid flow between grooved and flat surfaces is analysed with noslip boundary conditions at walls. The effect of corrugation on the fluid flow is investigated using the meshfree spectral method. The primary aim of the present work is to develop an asymptotic/semianalytical theory for confined transverse flows to bridge the gap between the limits of thin and thick channels. The secondary aim is to calculate permeability with reference to the effect of wall corrugation (roughness) without the restriction of pattern amplitude. We performed mathematical modelling and evaluated the analytical solution for hydraulic permeability with respect to the flat channel. The Pad \(\acute{e}\) approximate is employed to improve the solution accuracy of an asymptotic model. The results elucidate that permeability always follows a decreasing trend with increasing pattern amplitude using the spectral approach at the longwave and shortwave limits. The prediction of the spectral model is more accurate than the asymptoticbased model by Stroock et al. (Anal Chem 74(20):5306, 2002) and Pad \(\acute{e}\) approximate, regardless of the grooved depth and wavelength of the channel. The finiteelementbased numerical simulation is also used to understand the usefulness of theoretical models. A very low computational time is required using the meshfree spectral model as compared to the numerical study. The agreement between the present model and the fully resolved numerical results is gratifying. Regarding numerical values, we calculated the relative error for different theoretical models such as an asymptotic model, Pad \(\acute{e}\) approximate, and a meshfree spectral model. The spectral model always predicts the maximum relative error as less than \(3 \%\) , regardless of the large pattern amplitude and wavelength. In addition, the results of the molecular dynamic (MD) simulations by Guo et al. (Phys Rev Fluids 1(7):074102, 2016) and the theoretical model by Wang (Phys Fluids 15(5):1121, 2003) are found to be quantitatively compatible with the predictions of effective slip length from the spectral model in the thick channel limit. Graphical abstract
PubDate: 20231101
DOI: 10.1007/s00162023006796

 GPU computing of yield stress fluid flows in narrow gaps

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Abstract: We present a Graphic Processing Units (GPU) implementation of nonNewtonian HeleShaw flow that models the displacement of HerschelBulkley fluids along narrow eccentric annuli. This flow is characteristic of many longthin flows that require extensive calculation due to an inherent nonlinearity in the constitutive law. A common method of dealing with such flows is via an augmented Lagrangian algorithm, which is often painfully slow. Here we show that such algorithms, although involving slow iterations, can often be accelerated via parallel implementation on GPUs. Indeed, such algorithms explicitly solve the nonlinear aspects only locally on each mesh cell (or node), which makes them ideal candidates for GPUs. Combined with other advances, the optimized GPU implementation takes \(\approx 2.5\%\) of the time of the original algorithm. Graphical abstract
PubDate: 20231019
DOI: 10.1007/s0016202300674x

 Application of the lattice Boltzmann method to the study of ultrasound
propagation and acoustic streaming in threedimensional cavities:
advantages and limitations
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Abstract: The paper presents a threedimensional numerical study of the acoustic streaming induced by the dissipation of ultrasounds during their propagation in the air. The waves are generated by a circular acoustic source positioned at the center of the left wall of a parallelepipedic cavity. The simulations are performed with the lattice Boltzmann method associated with the D3Q19 multiple relaxation time model. A validation of this model is first performed by comparing the numerical and analytical acoustic intensities along the central axis of the acoustic source. The main objective of this study is to use two different methods to calculate the acoustic streaming flow. The first method is the direct calculation of the mean velocity fields as the mean values of the instantaneous velocities. The second method is an indirect technique, which first calculates the acoustic streaming force and then injects this force into the numerical code to produce the streaming. A comparison between the results obtained by the two methods was carried out and a good agreement was found between them. These different investigations, rather new in threedimensional configurations, have allowed us to discuss the advantages and limitations of the lattice Boltzmann approach to simulate real situations of wave propagation and acoustic streaming. Graphical abstract
PubDate: 20231019
DOI: 10.1007/s00162023006769

 Inverted stochastic lattice BoltzmannLagrangian model for identifying
indoor particulate pollutant sources
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Abstract: This paper studies the inverted stochastic lattice BoltzmannLagrangian approach for identifying indoor particulate pollutant sources. The dynamics of the fluid (indoor air) as well as the transport of the particles in the Eulerian description are solved using the lattice Boltzmann method. The particles regard as rigid bodies, and the data interactions between lattice fluid and particle movement are implemented by calculating for interaction force and void fraction. Particlewall collision process is based on the softball model which describes the dynamic characteristics of particles in microscopic state. The results are shown that the particle forward and inverted drifting paths and its mechanisms are investigated clearly than previous methods. Indoor particulate pollutant sources can exactly identify with this approach. This research can offer theoretical relevance to the modeling of multiphase particle fluid. Graphical abstract
PubDate: 20231015
DOI: 10.1007/s0016202300675w

 Networktheoretic modeling of fluid–structure interactions

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Abstract: The coupling interactions between deformable structures and unsteady fluid flows occur across a wide range of spatial and temporal scales in many engineering applications. These fluid–structure interactions (FSI) pose significant challenges in accurately predicting flow physics. In the present work, two multilayer network approaches are proposed that characterize the interactions between the fluid and structural layers for an incompressible laminar flow over a twodimensional compliant flat plate at a 35 \(^{\circ }\) angle of attack. In the first approach, the network nodes are formed by wake vortices and bound vortexlets, and the edges of the network are defined by the induced velocity between these elements. In the second approach, coherent structures (fluid modes), contributing to the kinetic energy of the flow, and structural modes, contributing to the kinetic energy of the compliant structure, constitute the network nodes. The energy transfers between the modes are extracted using a perturbation approach. Furthermore, the network structure of the FSI system is simplified using the community detection algorithm in the vortical approach and by selecting dominant modes in the modal approach. Network measures are used to reveal the temporal behavior of the individual nodes within the simplified FSI system. Predictive models are then built using both datadriven and physicsbased methods. Overall, this work sets the foundation for networktheoretic reducedorder modeling of fluid–structure interactions, generalizable to other multiphysics systems. Graphical abstract
PubDate: 20231010
DOI: 10.1007/s0016202300673y

 Aerodynamic and aeroacoustic performance of a pitching foil with trailing
edge serrations at a high Reynolds number
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Abstract: The aerodynamic and aeroacoustic performance of a lowaspectratio ( \(\hbox {AR}=0.2\) ) pitching foil during dynamic stall are investigated numerically with focus on the effects of trailing edge serrations. A hybrid method coupling an immersed boundary method for incompressible flows with the Ffowcs Williams–Hawkings acoustic analogy is employed. Large eddy simulation and turbulent boundary layer equation wall model are also employed to capture the turbulent effects. A modified NACA0012 foil with a rectangular trailing edge flap attached to the trailing edge (baseline case) undergoing pitching motion is considered. Trailing edge serrations are applied to the trailing edge flap and their effects on the aerodynamic and aeroacoustic performance of the oscillating airfoil are considered by varying the wave amplitude ( \(2h^*= 0.05, 0.1\) , and 0.2) at a Reynolds number of 100,000 and a Mach number of 0.05. It is found that the reduction of the sound pressure level at the dimensionless frequency band \(St_{b}\in [1.25,4]\) can be over 4 dB with the presence of the trailing edge serrations ( \(2h^*=0.1\) ), while the aerodynamic performance and its fluctuations are not significantly altered except a reduction around 10% in the negative moment coefficient and it fluctuations. This is due to the reduction of the average spanwise coherence function and the average surface pressure with respect to that of the baseline case, suggesting the reduction of the spanwise coherence and the noise source may result in the noise reduction. Analysis of the topology of the near wake coherent structure for \(2h^*=0.1\) reveals that the alignment of the streamwiseoriented vortex with the serration edge may reduce the surface pressure fluctuation. Graphical abstract
PubDate: 20231009
DOI: 10.1007/s00162023006778

 Shock standoff distances over sharp wedges for thermally nonequilibrium
dissociating nitrogen flows
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Abstract: In this study, shock standoff distances for thermally and chemically nonequilibrium flows of nitrogen over wedges are computationally investigated via a hypersonic computational fluid dynamics solver, hyperReactingFoam by spanning a parameter space that consists of ranges of Mach number, 4–10, specific heat ratio, 1.40–1.61 and wedge angles, 60 \(^\circ \) –90 \(^\circ \) . Then, the space is reduced into the parameters of inverse density ratio across the shock and dimensionless wedge angle which will be used as variables for quadratic functions that represent shock standoff distances. Besides the functions of shock standoff distances, detached shock profiles of computationally modeled flows are represented by parabolic equations. The flows are observed to be chemically frozen for Mach number ranges of 4–5 regardless of the specific heat ratio value of the nitrogen mixture. Our results show that the shock standoff distance decreases as Mach number is increased from 4 to 7, if the wedge angle and freestream specific heat ratio are kept the same. On the other hand, if Mach number is increased beyond 7, the shock standoff distance starts to extend due to the dissociation of nitrogen molecules behind the shock wave. At Mach 10, nitrogen completely dissociates over 90 \(^\circ \) wedge for all specific heat ratios considered in the present study. Increased leading edge angle of the wedge or specific heat ratio of freestream yields longer shock standoff distance. Graphic abstract
PubDate: 20230729
DOI: 10.1007/s00162023006698

 Linear stability analysis of compressible pipe flow

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Abstract: The linear stability of a compressible flow in a pipe is examined using a modal analysis. A steady fully developed flow of a calorifically perfect gas, driven by a constant body acceleration, in a pipe of circular cross section is perturbed by smallamplitude normal modes and the temporal stability of the system is studied. In contrast to the incompressible pipe flow that is linearly stable for all modal perturbations, the compressible flow is unstable at finite Mach numbers due to modes that do not have a counterpart in the incompressible limit. We obtain these higher modes for a pipe flow through numerical solution of the stability equations. The higher modes are distinguished into an “odd” and an “even” family based on the variation of their wavespeeds with wavenumber. The classical theorems of stability are extended to cylindrical coordinates and are used to obtain the critical Mach numbers below which the higher modes are always stable. The critical Reynolds number is calculated as a function of Mach number for the even family of modes, which are the least stable at finite Mach numbers. The numerical solution of the stability equations in the high Reynolds number limit demonstrates that viscosity is essential for destabilizing the even family of modes. An asymptotic analysis is carried out at high Reynolds numbers to obtain the scalings, and solutions for the eigenvalues in the high Reynolds number limit for the lower and upper branches of the stability curve. Graphical abstract
PubDate: 20230724
DOI: 10.1007/s0016202300672z

 Interaction between depth variation and turbulent diffusion in
depthaveraged vorticity equations
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Abstract: Steady, depthaveraged, shallow water vorticity transport equations including advection, surface and bed shear stresses, and turbulent diffusion effects are written out in vorticityvelocity and stream function formalisms. The Boussinesq approximation is used to represent turbulent stresses in the effective stress tensor. We consider two different forms of the curl of the effective stress tensor: its complete form and the commonly used form neglecting the terms expressing interaction with variable water depth. After deriving the two equations in vorticityvelocity formalism, we recast the equations into stream function formalism, revealing all the internal effects associated with variable water depth. We examine the differences between the models through analytical solutions of the stream function equations for simple but realistic flows. The solutions are validated with CFD simulations. Graphical abstract
PubDate: 20230721
DOI: 10.1007/s0016202300665y

 Faster flicker of buoyant diffusion flames by weakly rotatory flows

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Abstract: Flickering buoyant diffusion methane flames in weakly rotatory flows were computationally and theoretically investigated. The prominent computational finding is that the flicker frequency nonlinearly increases with the nondimensional rotational intensity R (up to 0.24), which is proportional to the nondimensional circumferential circulation. This finding is consistent with the previous experimental observations that rotatory flows enhance flame flicker to a certain extent. Based on the vortexdynamical understanding of flickering flames that the flame flicker is caused by the periodic shedding of buoyancyinduced toroidal vortices, a scaling theory is formulated for flickering buoyant diffusion flames in weakly rotatory flows. The theory predicts that the increase of flicker frequency f obeys the scaling relation \(\left( ff_{0} \right) \propto R^{2}\) , which agrees very well with the present computational results. In physics, the external rotatory flow enhances the radial pressure gradient around the flame, and the significant baroclinic effect \(\mathrm {\nabla }p\times \mathrm {\nabla }\rho \) contributes an additional source for the growth of toroidal vortices so that their periodic shedding is faster. Graphical abstract
PubDate: 20230718
DOI: 10.1007/s00162023006710

 An Eulerian–Eulerian–Lagrangian modeling of twophase
combustion
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Abstract: In simulating twophase combustion, most Reynoldsaveraged Navier–Stokes (RANS) simulation and largeeddy simulation (LES) used Eulerian–Lagrangian (E–L) modeling (Eulerian treatment of gas phase and Lagrangian treatment of particles/droplets) which needs much more computational time than the Eulerian–Eulerian (E–E) or twofluid modeling. However, in the E–E modeling, the problem of how to reduce the computation time for polydispersed particles is encountered . To solve this problem, the present author proposed an Eulerian–Eulerian–Lagrangian (E–E–L) modeling of twophase combustion for both RANS modeling and LES. The E–E–L modeling is an Eulerian treatment of gas phase and a combined Eulerian–Lagrangian treatment of particles/droplets, in which the particle velocity and concentration are solved by Eulerian modeling, and particle temperature and mass change due to reaction are solved by Lagrangian modeling. In this paper, a review is given for an E–E–L modeling of coal combustion, its application in RANS simulation and its possible application in LES. For E–E–L LES, an energy equation model of twophase subgrid scale (SGS) stresses accounting for the interaction between twophase SGS stresses is suggested, and a secondorder moment SGS (SOMSGS) turbulencechemistry model is adopted to simulate gasphase reaction in twophase combustion. These SGS models were separately assessed by comparison with experiments. Graphic abstract
PubDate: 20230715
DOI: 10.1007/s0016202300666x
