应用数学和力学

2016 Vol. 37, No. 12

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WU Chui-jie, LIAO Shi-jun, LU Xi-yun

2016, 37(12): 1-1.

Abstract(1064) PDF(517)

Abstract:
On September 16-20, 2016, the top-level exchange of research results in computational fluid dynamics studies in Asia, i.e. the 11th Asian Computational Fluid Dynamics Conference (ACFD11) was held at Dalian University of Technology, Dalian, China. Based on ACFD11, Applied Mathematics and Mechanics invited Prof. Wu Chui-jie from Dalian University of Technology, Prof. Liao Shi-jun from Shanghai Jiao Tong University and Prof. Lu Xi-yun from University of Science and Technology of China as guest editors to compile this Special Issue of ACFD11 on Engineering Computational Fluid Dynamics. The issue carries the latest research results, to help exchange innovative ideas and share theoretical and applied frontiers of computation in fluid and heat transfer sciences.

Investigation of Flow Development and Noise Generation of Free and Chevron Jets

RAN Ling-ke, YANG Hai-hua, ZHANG Xing-chen, WAN Zhen-hua, SUN De-jun

2016, 37(12): 1255-1271. doi: 10.21656/1000-0887.370507

Abstract(1054) PDF(735)

Abstract:
Large eddy simulation (LES) is performed to study high subsonic round and chevron jets with a diameterbased Reynolds number Re=10⁵.2 different chevron jet flows are considered, which are with 6 lobes and 4 lobes respectively.The simulation results are checked by comparing mean axial velocity profiles and overall sound pressure levels (OASPLs) of the round jet with the existent experimental and LES results, and they are in good agreement with each other. Then the properties of chevron jets are compared with those of round jets. The chevron jets show higher radial expansion rate in the nearnozzle region and shorter potential core lengths. The OASPLs of the chevron jets decrease as high as 4 dB at the shallow angles compared with the round jets and without apparent noise increment at the sideline. 3 azimuthal modes,m=0,1,2of the farfield pressure fluctuations from both the round and chevron jets are investigated. All cases show similar OASPL distribution profiles vs. the polar angles for each azimuthal mode. But, apparent noise increment is found at high polar angles in the zeroth and first azimuthal modes for the chevron jet with 4 lobes when compared with the round jet. By performing proper orthogonal decomposition (POD), the most energetic coherent structures at specified coupled azimuthal wavenumbers are extracted. The wavepacket features associated with coherent structures of round and chevron jets are analyzed in detail to explain changes of noise properties in the far fields.

Detached-Eddy Simulation of Flow Past Tandem Cylinders

ZHAO Wei-wen, WAN De-cheng

2016, 37(12): 1272-1281. doi: 10.21656/1000-0887.370546

Abstract(1453) PDF(640)

Abstract:
In this paper, 2 detached-eddy simulation (DES) approaches, namely SST-DES and SST-DDES are implemented, integrated in to the naoe-FOAM-SJTU solver which is developed based on the open source platform OpenFOAM. Flow past 2 cylinders in tandem arrangement is selected as the benchmark case for the validation of the SST-DES and SST-DDES approaches. The experiment was previously conducted in 2 different wind tunnels at the NASA Langley Research Center. Time-averaged flow fields and some quantities of computational results are compared with experiments. In addition, the 3D instantaneous flow structures are also given and discussed. It is shown that the current implementation of SST-DES and SST-DDES is able to resolve some characteristics for massively separated complex turbulent flows.

Comparative Numerical Studies of Flow Past a Cylinder at Reynolds Number 3 900

JIN Yao, CAI Jin-sheng, LIAO Fei

2016, 37(12): 1282-1295. doi: 10.21656/1000-0887.370512

Abstract(1577) PDF(1107)

Abstract:
The flow past a cylinder at a Reynolds number of 3 900 is addressed with the delayed DES (DDES) and constrained large-eddy simulation (CLES). The experiments and numerical simulations in this case have been extensively analyzed in previous researches. It is commonly recognized that the flow structures and recirculation length are closely related to the dispersion and dissipation properties of the scheme. Under such consideration, an optimized scheme is chosen and validated for several typical flows with multi-scale structures and strong shocks. Then, the DDES and CLES are performed to obtain pressure distribution, mean velocity profiles and the turbulence statistics in the near wake. By comparing the results from calculations with the experimental data, it is found that the averaged quantities from the CLES agree slightly better with the experimental data than those from the DDES. In the instantaneous flow field, complicated structures are captured by both the DDES and the CLES. A significant difference between them is that small-scale motions can be observed in the near-wall region for the CLES. Lastly, though the CLES predicts the mean statistics slightly better, the implementation of the CLES is much more complex than that of the DDES.

D Compressible Lattice Boltzmann Model and Its Appliaction to Low Mach Number Turbulent Flow

KUNISHIMA Yuichi, KAJISHIMA Takeo

2016, 37(12): 1296-1307. doi: 10.21656/1000-0887.370556

Abstract(1231) PDF(774)

Abstract:
We intend to improve the finite-difference lattice Boltzmann method (FDLBM) for the use of direct numerical simulation of aerodynamic sound.Using a feature of the LB-based solver, the constant advection velocity in the kinetic equation enables easy implementation of higher-order upwind difference schemes, resulting in high resolutions for sound waves as well as turbulent flow. We release a new particle model which recovers the compressible Navier-Stokes system with flexible specific heat ratio in the 3D space. In addition, we introduce a heat flux modification, which enables us to set Prandtl number freely under the Bhatnagar-Gross-Krook(BGK) collision operator. Our new method performs well in validation problems of weak acoustic waves in a shock tube, and laminar Taylor-Couette flow with a temperature gradient. We conduct a 3D simulation of flow around the NACA0012 aerofoil. The Reynolds number, Mach number and angle of attack are 2×10⁵, 8.75×10^－2 and 9° respectively. Our results are in good agreement with the experimental data about the position of the separation bubble near the leading edge and the Mach number dependence of the surface pressure fluctuation intensity.

Application of Sound Source Models to the Heated Subsonic Jet

ZHANG Xing-chen, YANG Hai-hua, WAN Zhen-hua, SUN De-jun

2016, 37(12): 1308-1323. doi: 10.21656/1000-0887.370526

Abstract(621) PDF(742)

Abstract:
The noise generation mechanisms associated with instability waves in the heated subsonic transitional jet are studied, which are compared with its cold counterpart. The spatial evolution of instability waves is obtained by solving linear parabolized stability equations (LPSE) based on the time-averaged flow field of the large eddy simulation (LES). Then, the linear and nonlinear models for jet noise are built based on the LPSE solutions, coupled with the acoustic analogy. The LPSE results show that heating increases the spatial-growth rate and leads to earlier saturation. For high-frequency components, the sound pressure levels (SPL) are raised by heating as shown in the linear model. In general, compared with that for the cold jet, the gap of SPL between the linear model and the LES is reduced for the heated jet, which indicates that the linear mechanism plays a more important role in the hot jet. For a cold subsonic jet, previous studies have shown that the nonlinear model is able to raise acoustic efficiency. Here, it is found that the gap of SPL between the nonlinear model and the LES could be further decreased in the hot jet, and the thermodynamic sound source terms play a bigger role.

On the Splitting Methods of Inviscid Fluxes for Implementing High-Order Weighted Compact Nonlinear Schemes

TU Guo-hua, CHEN Jian-qiang, MAO Mei-liang, ZHAO Xiao-hui, LIU Hua-yong

2016, 37(12): 1324-1344. doi: 10.21656/1000-0887.370518

Abstract(1497) PDF(677)

Abstract:
There is increasing popularity in using high-order weighted compact nonlinear schemes(WCNS) for complex flow simulations. The WCNS can be used in combination with many inviscid flux splitting methods. However, it is still uncertain which flux splitting is most suitable for the WCNS because most of the methods are devised on the basis of low-order discretization methods. It is also not very clear what will happen when these splitting methods are mounted directly in high-order accurate schemes. In order to provide some guide for selecting inviscid fluxes in the computation of surface heat transfer, the dissipations of the fluxes are studied. Every inviscid flux can be expressed as a summation of a central part and a dissipation part. All the fluxes have an identical central part which is very simple. However, different fluxes have different dissipation parts which are more or less complicated. The analysis on the source of flux dissipation shows that the dissipation is nearly proportional to flux jumps on grid interfaces. Numerical experiments show that high-order schemes usually produce far less flux jumps than low-order schemes in smooth regions, and logically the flux dissipations are quite lower. 3 canonical flows including hypersonic shock wave/boundary layer interactions(SWBLI) are simulated to show the influence of inviscid fluxes on heat transfer computing. Finally, a suggestion is given for selecting inviscid fluxes based on the dissipations and shock instabilities of van Leer’s flux splitting, the Steger-Warming(SW) flux splitting, the kinetic flux vector splitting (KFVS), Roe’s flux splitting, the AUSM(advection upwind splitting method)-type flux splitting and the HLL-type flux splitting.

Investigations of Self-Propulsion in Waves of Fully Appended ONR Tumblehome Model

WANG Jian-hua, WAN De-cheng

2016, 37(12): 1345-1358. doi: 10.21656/1000-0887.370525

Abstract(2269) PDF(598)

Abstract:
In the present work, the CFD-based method coupled with the dynamic overset grid technique is applied to investigate the hydrodynamic performance of the fully appended ONR tumblehome ship model under self-propulsion condition in head waves. All the computations are carried out by our in-house CFD solver naoe-FOAM-SJTU and the overset grid module is used to update the ship motions with rotating propellers while a self-developed 3D wave tank module is applied to generate desired wave environment. The ship model is advancing at its model point obtained with previous CFD results in calm water and the simulation is according to the benchmark case from the Tokyo 2015 CFD Workshop in ship hydrodynamics. The predicted results, i.e. ship motions and instantaneous advancing speeds are presented and compared with the available experimental data. Propulsion coefficients, K_T and K_Q, as well as detailed information of the flow field are also given to explain the hydrodynamic performance during the self-propulsion in waves. Good agreements are achieved which indicate that the present approach is applicable for the direct simulation of self-propulsion in waves.

An MPS-FEM Coupled Method for the Comparative Study of Liquid Sloshing Flows Interacting With Rigid and Elastic Baffles

ZHANG You-lin, CHEN Xiang, WAN De-cheng

2016, 37(12): 1359-1377. doi: 10.21656/1000-0887.370514

Abstract(1331) PDF(594)

Abstract:
Fluid-structure interaction (FSI) problems caused by fluid impact loads are commonly existent in naval architectures and ocean engineering fields. For instance, the impact loads due to non-linear fluid motion in a liquid sloshing tank potentially affect the structural safety of cargo tanks or vessels. The challenges of numerical study on FSI problems involve not only multidisciplinary features, but also accurate description of non-linear free surface. A fully Lagrangian particle-based method , the moving particle semi-implicit and nite element coupled method (MPS-FEM), is developed to numerically study the FSI problems. Taking into account the advantage of the Lagrangian method for large deformations of both fluid and solid boundaries, the MPS method is used to simulate the fluid field while the finite element method(FEM) to calculate the structure field. Besides, the partitioning strategy is employed to couple the MPS and FEM modules. To validate accuracy of the proposed algorithm, a benchmark case is numerically investigated. Both the patterns of free surface and the deflections of the elastic structures are in good agreement with the experimental data. Then, the present FSI solver is applied to the comparative study of the mitigating effects of rigid baffles and elastic baffles on the sloshing motions and impact loads.

Numerical Study on Coupling Effects of FPSO Ship Motion and LNG Tank Sloshing in Low-Filling Conditions

ZHUANG Yuan, WAN De-cheng

2016, 37(12): 1378-1393. doi: 10.21656/1000-0887.370516

Abstract(1254) PDF(533)

Abstract:
In this paper, numerical simulations of FPSO ship motion coupled with LNG tank sloshing with low-filling ratios are conducted. The fully coupled problem is addressed with our own unsteady RANS solver: naoe-FOAM-SJTU developed based on the open source tool libraries of OpenFOAM. The internal tank sloshing and external wave flow are solved simultaneously. The FPSO model includes 2 LNG tanks. For the ship 3-DOFs are released in the regular beam waves. The filling ratios of the 2 tanks are 20%~20%, lower than the external free surface. This kind of low-filling condition reduces ship roll motion significantly, and produces complex free surface shapes in tanks. 4 different incident wave frequencies are considered in the simulation in comparison with the existing experimental data. The comparison shows that the numerical results are in good agreement with the experimental data, proving the reliability of the proposed method. The filling conditions with large wave amplitudes are studied further, and due to the coupling effect, violent sloshing occurs in tanks and impulsive pressure forms on bulkhead.

Study on the Nozzle Jet in Arc Spraying

TAMAKI Ryoji, YAMAKAWA Masashi

2016, 37(12): 1394-1402. doi: 10.21656/1000-0887.370554

Abstract(1019) PDF(553)

Abstract:
The jet plume formed immediately adjacent to the nozzle of an arc spray gun has a significant effect on the properties of the resultant coating. This study applied the computational fluid dynamics (CFD) and the Schlieren photography to elucidate the properties of jet plumes. The Schlieren images examined revealed that the properties and widths of the plume depend on the direction of material wires for thermal coating. Through the CFD approach, we observed the formation of shock waves immediately after the nozzle aperture and damping of the shock waves in the downstream plume.

Statistical Error Analysis of the DSMC Method Considering Time Correlations Between Samples

LI Jin, GENG Xiang-ren, CHEN Jian-qiang, JIANG Ding-wu

2016, 37(12): 1403-1409. doi: 10.21656/1000-0887.370533

Abstract(846) PDF(472)

Abstract:
The DSMC method has evolved into a most powerful numerical tool for rarefied gas flow in the past half century. The problems related to accuracy have got much attention in DSMC professions. There are 2 types of errors in the DSMC method. One is termed “statistical error”, and the other is “numerical error”. In the DSMC method, the macroscopic properties are obtained with the sample average of the microscopic information. The simulation results are therefore inherently statistical and statistical errors due to finite sampling need to be fully quantified. Statistical error plays an important role in the DSMC method. However, it has not been well understood as yet. Most of the investigations are based upon the assumption that the successive sample results are independent. It is still not clear how many sampling steps are required to get accurate results. Obviously the time correlations make the theoretical analysis of the statistical error more difficult, which has seldom been taken into accounted in the previous researches. With the autocorrelation function and the modified central limit theorem in the statistics, the time correlations between samples can be quantified. The statistical error of the DSMC method was studied based on the benchmark problem of the Couette flow, in view of the time correlations between samples. Quantitative results show that the time correlations affect the statistical error greatly. The time correlations tend to increase the variance of sampled values of random variables, and it takes almost 100 sample steps for the autocorrelation function to decay to 0.