应用数学和力学

2023 Vol. 44, No. 9

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A Special Topic on Turbulent Combustion and Atomization
Solid Mechanics

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A Special Topic on Turbulent Combustion and Atomization

2023, 44(9): ⅰ-ⅰ.

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Abstract:

Application of Enthalpy Deficit Flamelet Model in Spray Combustion Simulation

HE Junyi, LI Feng, HU Qun, WANG Lipo

2023, 44(9): 1017-1030. doi: 10.21656/1000-0887.440064

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Abstract:
An OpenFOAM-based solver for spray combustion simulation with the large eddy simulation (LES) and the flamelet generated manifold (FGM) method, was developed. A simple reduction of the temperature was employed to account for the evaporative heat loss. The solver was firstly validated against the Sydney piloted ethanol spray flame benchmark EtF7. The predicted mean gas temperature and droplet statistics correspond well with the experimental data and have similar accuracy to the spray flamelet model. The turbulence-chemistry interaction modeling may have a larger influence on the simulation accuracy. Then a realistic gas turbine slinger combustor was simulated with 2 sets of operating conditions. The simulation results reveal different flame characteristics of the 2 working conditions. The predicted total pressure losses are close to the measured values.

Modelling Intermediate Species in Partially Premixed Turbulent Combustion Based on the LES-FGM Method

ZHANG Weijie, WANG Jinhua, HU Guangya, LI Deli, WANG Ziqi, HUANG Zuohua

2023, 44(9): 1031-1041. doi: 10.21656/1000-0887.440068

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Abstract:
The LES of partially premixed turbulent flame MRB in TU Darmstadt was conducted based on the flamelet-tabulated combustion model FGM, and effects of premixed and partially premixed tabulations on the modelling results were studied. The results show that, different methods of tabulation exhibit limited influences on the predictions of the flame structure, velocity, and major species, but using a partially premixed tabulation largely improves the reliability of modelling intermediate minor species CO and H₂. The underlying reason lies in a better inclusion of the fuel-air mixing effects through the partially premixed tabulation, which is built based on laminar counter-flow flames. Adding extra transport equations for the intermediate species improves the predictions of intermediate species, especially given a premixed tabulation adopted; meanwhile, the stretch effects in this turbulent flame are ignorable. The results are significant to guide the high-fidelity simulation of partially premixed turbulent flames based on the flamelet-tabulated combustion model.

Numerical Analysis of Flame Flashback and Instability in Cavity-Stabilized Supersonic Combustion

XIAO Yexin, JIN Tai

2023, 44(9): 1042-1053. doi: 10.21656/1000-0887.440103

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Abstract:
Aimed at the phenomenon of flame flashback and low-frequency combustion oscillation in the scramjet combustor with equal straight cross sections, 3D simulations were conducted, with the hybrid RANS/LES method (delayed detached-eddy simulation, DDES) for turbulence modeling and the partially stirred reactor (PaSR) for turbulence-reaction interactions. The obtained entire combustion oscillation period is consistent with the low-frequency combustion oscillation phenomenon observed in the experiment. The low-frequency combustion oscillation period can be divided into 3 stages: the cavity-holding flame, the flame flashback, and the flame blowout. By analysis of the reacting flow field in different stages of the low-frequency combustion oscillation cycle, the possible formation mechanism of low-frequency combustion oscillations was summarized. The results show that, there is no choking in the combustion chamber during the whole low-frequency combustion oscillation period. The pressure rise induced by shock interaction and the heat released by combustion are the key factors for the formation of low-frequency combustion oscillations in the combustion chamber.

Breakup and Atomization Characteristics of Liquid Jets in Strong Swirling Crossflow Based on the VOF-LPT Method

XIE Mingyun, PU Tianhao, LIU Hong, WU Shengqi

2023, 44(9): 1054-1069. doi: 10.21656/1000-0887.440110

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Abstract:
The liquid jet breakup and atomization interacting with a strong swirling crossflow is of significance in designing advanced aeroengines. The Eulerian-Lagrangian method was utilized to simulate the jet breakup and atomization processes. The volume of fluid (VOF) method was employed to track the gas-liquid interface topology evolution during the jet breakup, while the Lagrangian particle tracing (LPT) method was used to track the discrete droplets and obtain the information on far-field liquid dispersion. The crossflow was designed with different swirl numbers, ranging from 0 to 2.5. Momentum ratio q between the liquid jet and the air flow was set to 10, and the gas Weber number was 39. Under these conditions, both the column and shear breakups were observed. The results indicate that, the development of axial waves induced by the Kevin-Helmholtz (KH) instability was the main cause for column breakup. During the surface breakup, ligaments and small liquid jet branches were stripped from the liquid jet surface, primarily driven by azimuthal shear waves. The strong swirling airflow enhances the jet column breakup process, leading to a lower radial height for the breakup location and a shorter breakup time. However, as the swirl number increases, the radial height of the onset of breakup would increase, which suggests the swirl flow would delay the surface breakup of liquid jets. With the increase of the swirl number, the velocity component in the flow direction decreases, and the jet trajectory in the radial direction increases significantly. The deflection angle of the jet shows a linear relationship with the position of the flow direction, with larger air swirl numbers resulting in a steeper slope. Furthermore, as the swirl number increases, the Sauter mean diameter (SMD) of the entire spray field would decrease, and the liquid dispersion would increase.

Low-Order Predictions of Spatial Distributions of Conserved Scalars in Swirl Combustors Based on the Gaussian Plume Function

WU Ziheng, ZHANG Chi, ZHANG Shihong, WANG Bosen

2023, 44(9): 1070-1086. doi: 10.21656/1000-0887.440119

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Abstract:
The mixture fraction is a conserved scalar characterizing the fuel-air mixing. As a key reference scalar for turbulent combustion modelling, its spatial distribution is usually obtained through 3D numerical simulation, which are, however, time-consuming and costly for combustors with complex geometries. To overcome such low efficiency in the iterative designing process, a low-order model was developed based on the Gaussian plume function to compute the mixture fraction field in the swirl combustor to accelerate the evaluation of the fuel-air mixing strategy and the parameterized design process. Compared with the conventional formulation, the derived new Gaussian plume function includes the effects of convection and corrections due to swirl flows. A mirror image reflection model was further developed to simulate the wall-plume interactions, together with the relevant corrections to ensure mass conservation. This newly derived Gaussian plume model was applied to the low-older prediction of the mixture fraction field in a methane swirl combustor. Based on the database generated through 3D numerical simulations, the model parameters were optimized with the least square method first. The prediction accuracy under broad working conditions was demonstrated. This study not only provides a novel approach for quick predictions of mixture fractions in swirl combustors, but also sets an instance for further development and application of the Gaussian plume model.

Numerical Simulation Study of Spray Wall Impingement Combustion

QIN Wenjin, HAN Tianxiang, ZHANG Zhendong, SUN Yuedong

2023, 44(9): 1087-1096. doi: 10.21656/1000-0887.440077

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Abstract:
Fuel spray wall impingement is a common phenomenon in small high-pressure direct injection diesel engines. Fuel spray wall impingement influences the in-cylinder combustion process, and significantly impacts the engine's dynamics, fuel economy, and emissions. To better understand the combustion characteristics of fuel spray wall impingement, the numerical simulation was applied to calculate the process and explore this process. The results show that, during the 2-stage combustion process of spray wall impingement, the impingement promotes the radial development radius and the vortex height of the spray, enhances oil-gas mixing near the wall, and forms favorable conditions for low-temperature ignition near the wall. Low-temperature combustion reactions start in the near-wall region, where the mixture is relatively dilute, and then develop into the dense mixed gas area in the center of the impinging spray. As low-temperature oxidation combustion continues to release heat, the maximum temperature in the center of the impinging spray will gradually increase, and a large amount of CH₂O will accumulate. Meanwhile, the impinging spray can cause the formation of a more concentrated mixture in the center of the impinging spray, and low-temperature combustion would release less heat, resulting in the incomplete combustion of some carbon, and increasing the amount of soot generated. Additionally, as high-temperature combustion proceeds, the temperature will continue rising, and the impinging spray will draw more oxygen, generating a large amount of NO_x through oxidation reactions.

Solid Mechanics

Influences of Impact Points on the Penetration Depth of Reinforced Concrete

HUANG Chenglong, CHEN Yeqing, LI Shutao, ZHANG Sheng, WANG Zhenqing

2023, 44(9): 1097-1111. doi: 10.21656/1000-0887.440016

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Abstract:
In the research field of projectile penetration into reinforced concrete, the penetration depth discreteness generally exists in experiments and empirical formulas, and the difference of impact positions is one of the main reasons for this discreteness. To explore the penetration depth discreteness caused by the impact position difference and reveal its mechanism, the finite element models of 3 typical impact positions were established with reference to a published penetration test. The main reasons for the differences in the penetration processes of 3 typical impact positions were compared and analyzed. Based on the numerical calculation results, the expression characterizing the discreteness of penetration depth was summarized. The results show that, the penetration depth of the projectile impacting reinforced concrete is a range value. The expression was preliminarily verified. The main factors causing the penetration depth discreteness are the number of rebars hit by the projectile and the duration of contact with steel bars. This discreteness decreases with the ratio of the projectile diameter to the mesh size of rebars.

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints

LI Yihao, XU Dian, CHEN Yiming, AN Dongqi, LI Rui

2023, 44(9): 1112-1121. doi: 10.21656/1000-0887.440051

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Abstract:
Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells.

The Mindlin-Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects

LU Shuang, LI Dongbo, CHEN Jingbo, XI Bo

2023, 44(9): 1122-1133. doi: 10.21656/1000-0887.440017

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Abstract:
Based on the Hamiltonian variational principle, the 2D field equations and boundary conditions for flexoelectricity were derived, and the corresponding governing equations were obtained through substitution of the constitutive relation and geometric equations into the field equation. The in-plane tensile deformation, thickness-stretch deformation, symmetric thickness-shear deformation, and their coupled flexoelectric polarization of flexoelectric nanoplates caused by inhomogeneous temperature changes, were studied. The displacement fields and electric potential fields were solved with the double Fourier series method. The results demonstrate that, all fields are sensitive to the temperature load, which raises the prospect of controlling the mechanical and electrical behaviors of flexoelectric nanoplates by means of the temperature field. The effects of the thermal field and mechanical field on the displacement field were compared and examined. The work extends the Mindlin-Medick plate structure analysis theory in view of the flexoelectric and temperature effects, and provides a reference for the structural design of micro- and nano-scale devices.

Topology Optimization Design of Heat Convection Problems With Variable-Density Cells

WANG Qin, LIU Liyang, QIANG Bo, WEI Yanqiang

2023, 44(9): 1134-1144. doi: 10.21656/1000-0887.430383

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Abstract:
The method of designing cell structures with variable-density cells based on erode-dilate operators was applied to the optimization of thermal structures. A series of variable-density microstructures with the same topology definition but different volume fractions were obtained with erode-dilate operators. Then, the thermal conductivity of the variable-density cells was extracted and the equivalent thermal conductivity fitting curve was obtained. After this, the method of moving asymptotes was used to update macro design variables, and the variable-density microstructure was implanted into the macroscopic unit of the corresponding volume fraction to complete the assembly. Numerical examples were given to compare and analyze the thermal compliance, the mean temperature, the variance and other parameters of the temperature fields with different optimization methods. The results show that, variable-density cell structures have better heat dissipating performance than traditional single-scale cell structures and periodic cell structures.

Elastic Analysis of Anisotropic Rotating Sandwich Circular Ring With a Functionally Graded Transition Region

PENG Xulong, XIE Xiaopeng, HUANG Haiping, WEI Wenchao, TANG Xuesong

2023, 44(9): 1145-1156. doi: 10.21656/1000-0887.440003

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Abstract:
The elastic analysis of anisotropic rotating sandwich ring with a functionally graded transition region was carried out. Like the shell sandwich structure in nature, the ring is composed of 3 well-bonded regions, of which the inner and outer regions are made of homogeneous anisotropic materials, and the intermediate transition region is made of a material with arbitrary-gradient properties along the radial direction. Based on the boundary conditions and the continuity conditions at the interface, the 2nd Fredholm integral equation for the radial stress was obtained with the integral equation method, then the stress and displacement fields of the sandwich ring structure were obtained through numerical solution. The distributions of the stress and displacement fields in the sandwich ring structure were given. Different gradient changes encountered in engineering practice can be solved only through substitution of the corresponding function model. The effectiveness and accuracy of the integral equation method were verified through comparison of the numerical solutions with the exact ones for a special power function gradient variation form. The more general Voigt function model was adopted for the intermediate transition region, and the influences of the anisotropy degree, the gradient parameter, and the thickness on the stress and displacement fields were analyzed. The proposed Fredholm integral equation method provides a powerful tool for the optimal design of anisotropic functionally graded materials and sandwich ring structures. The numerical results make a theoretical guidance for the safety design of anisotropic functionally graded sandwich ring structures.