With the application of quantity risk analysis to the 18th subway line of Chengdu, China, FLACS code, as a computational fluid dynamics (CFD) tool, plays a key role. It embedded Q4, Q5,Q8 and Q9 as the models for equivalent fuel-air cloud volume.The benefit of the equivalent approaches is ease to get a representative distribution of explosion loads with minimum number of simulations.

In these models, the laminar burning velocity and volume expansion ratio are taken into account in the Q5 and Q9 methods, only the laminar burning velocity is taken into account in Q4, the volume expansion ratio is only taken into account in the Q8 method. Detailed information about them can be found in literature[1].

Q9, as the latest version, is widely used to assess the explosion loads as part of a risk or consequence analysis [2], and is described by Eq. (1) in FLACS:

where ER is equivalence ratio, (F/O is the ratio of fuel and oxygen); Vi is the ith control volume of the numerical grid inside the fuel-air region where the fuel-air is in the range of lower flammability limit (LFL) and the upper flammability limit(UFL), that is ERLFL≤ER≤ERUFL ; is volume expansion ratio at constant pressure in the ith control volume, its value depend on the ERi; is shown with Eq. (2):

(4)基于异常分离的概率成像能有效提高重力异常和重力梯度异常成像的分辨率，综合利用重力异常和重力梯度各分量结果能够提高地质解释的准确性。若实测资料没有重力梯度数据，可以应用理论公式把重力异常变换为导数函数，再进行重力异常和重力梯度综合解释与分析。

where SL is the laminar burning velocity.

In Eqs. (1) and (2), the volume expansion ratio and laminar burning velocity are the two key factors for representing the inhomogeneous fuel-air cloud as a homogeneous fuel-air cloud in Q9 model.

The factor, volume expansion ratio, employed in Q9 denotes that the part of ignitable heated fuel-air is expelled out of the control volume in explosion process because the Q9 can be got in the dispersion simulation stage prior to explosion simulation stage, thus, the donation of the expelled fuel-air to explosion load is ignored and its effect may be underestimated. However,in most realistic cases, the computing domain will not be completely filled with an ignitable fuel-air cloud, the deemed expelled fuel-air is still in the computing domain and also plays an important role in the explosion process, its donation on the explosion load cannot be neglected. It seems inappropriate that the volume expansion ratio is introduced into the equivalent approaching.

On the other hand, Q9 only employs SL with first order to describe the combustion process. Most of the realistic fuel-air explosion process, the fuel-air flow field turns into turbulent regime and the flame propagation is also in violent and turbulent status.

To give a more reasonable equivalent fuel-air cloud size, a turbulent burning velocity ST is proposed. Many models, such as Zimont correlation, Peters Correlation and Mueller correlation[3], describe ST as a function of SL and turbulence quantities. So, it is also reasonable to describe ST as the SL with a non-one order based on TNO (abbreviation for the Netherlands Organization) multi-energy method (ME).

Figure 1 shows the main features of an idealized explosion scenario, a ground-level hemispherical fuel-air cloud is ignited in the center, the flame front will then propagate symmetrically from the centre. the initial peak overpressure in the hemispherical fuel-air cloud zone is assumed as a constant P0 whereas the side-on overpressure and dynamic pressure will decay with distance outside of the fuel-air zone.

In the multi-energy method, an idealized fuel-air explosion scenario model is put forward, shown in Fig. 1. The explosion is based on a ground-level hemispherical fuel-air cloud which is filled with a fuel-air mixture at a stoichiometric concentration.

Fig. 1. Idealized fuel-air cloud explosion scenario model.

The peak overpressure calculations in the fuel-air cloud zone are given with the Eqs. (3) and (4). Equation (3) shows the 2 dimensional (2D) explosion expansion, and Eq. (4) shows 3 dimensional (3D) explosion expansion.

D typical diameter of the obstacles m

where Vgr is the obstructed cloud volume in an obstructed region.

Detailed descriptions of the multi-energy method and the calculation of other variables in Eqs.(3) and (4) are found in the literatures [4-11].

It is practicable to assess the peak overpressure of a fuel-air mixture with any concentration by the introduction of stoichiometric concentration. that is, a certain concentration fuelair mixture can be assumed as a kind of new pure flammable gas with a new SL1 when the flammable gas’s ER value equals 1.0, the new flammable gas is called pseudo-component gas in literature [6, 12]. As Eq.(3) or Eq.(4) indicate the different peak overpressure value between stoichiometric fuel-air cloud and the other concentration fuel-air cloud depends only on if the other variables remain unchanged (that means the same obstructed region, the same ignition location and the same ignition energy), notably, also indicates that turbulent burning plays a key role during an explosion.

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德城区建成区分阶段扩展特征见表3．由表3可见，扩张速度最快的是在2005—2010年的6年期间，城市建成区加速扩张，增加了29.24 km2，年均增长4.87 km2，扩展速度远高于20年平均增长水平．从扩展强度来看，强度最大的是在2005—2010年间．在2011—2017年这一阶段，扩展强度虽有所降低，但总体趋势是在持续扩张．数据结果总体表明，建成区面积持续扩展，德州市城市发展水平不断提高．

The new approach is trying to transform an inhomogeneous fuel-air cloud into a smaller stoichiometric fuel-air cloud where the explosion can generate similar peak overpressure as the inhomogeneous cloud.

The inhomogeneous fuel-air cloud gets the overpressure P0,and the stoichiometric fuel-air cloud gets the overpressure P1.Then, by setting P0=P1, the following Eq.(6) can be derived from the Eq. (3) or Eq. (4).

Thus, the following Eq. (9) can be derived by the use of the Eq. (5)

In the view of control volume (CV) from FLACS code, Eq. (12)can be shown as following:

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The whole computing domain, which is divided into many control volume using the gridding mechanism, is filled with the different concentration fuel-air cloud (concentration between LFL and UFL). Correspondingly, the homogenous stoichiometric fuel-air cloud volume Vstoi is expressed by the Eq. (13).

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The Eq. (13) is the proposed new equivalent cloud method.

A series of simulations are conducted to validate the new equivalent cloud method, For simplifying the representation of the inhomogeneous cloud, 1 m3 methane-air clouds with a certain ER value is employed. The obstacles include 61 m-length and 0.2 m-diameter pipes for the representation of blockage.The different ER values and the corresponding laminar burning velocities of methane-air mixtures are shown in Fig. 2, the data source is from the literature [1].

The obstacles and computing domain is shown in Fig. 3. As stated in Fig. 2, the laminar burning velocity curve for methaneair mixture is approximately symmetrical around the axis of ER value at 1.08, the laminar burning velocities where the ER values equals 0.7, 0.8, and 0.9 are selected for the validation simulations, the results from these ER values are the representative results for ER values at 1.37, 1.30 and 1.20 respectively because of the symmetry. When ER equals 1.08 or 1.10, the equivalent stoichiometric clouds volume is approximate same as the original gas clouds respectively, so, they are not selected any more.

Fig. 2. Laminar burning velocities vs. ER.

Fig. 3. Obstacles and computing domain.

For comprehensive analysis of the explosion load, three typical cases are taken into consideration, one is the methane-air explosion in open space with obstacles, the other one is the methane-air explosion in open space without obstacles, the last one is the methane-air cloud explosion is in an enclosed space with obstacles [13,14]. The simulating results are shown in Fig. 4.

There is a good agreement by the comparison of the explosion overpressure between equivalent clouds and the cloud which ER equals 0.9 for cases of the cloud explosions in open space. For other scenarios, it seems that there is a poor agreement, in fact, the low peak overpressures indicate the ignited non-stoichiometric clouds are not the explosion process but the combustion process.

For the cloud explosions in the enclosed space, there are good agreements for each ER value respectively. The cloud which ER equals 0.7 can generate the peak overpressure up to 6.561 barg, the corresponding equivalent stoichiometric cloud can generate up to 7.840 barg overpressure, The relative error is within 20%. The relative errors of the other two sets of scenarios are also within 20%.

In this paper, the fuel-air cloud resulting from an accidental discharge event is normally irregular in shape and varying in concentration. Performance of dispersion simulations using CFD-based tool FLACS can get an uneven and irregular cloud.For the performance of gas explosion study with FLACS, the equivalent stoichiometric fuel-air cloud concept is widely applied to get a representative distribution of explosion loads. The Q9 cloud model that is employed in FLACS is an equivalent fuelair cloud representation, in which the laminar burning velocity with first order SL and volume expansion ratio are taken into consideration. However, during an explosion in congested areas,the main part of the combustion involves turbulent flame propagation. Hence, to give a more reasonable equivalent fuelair size, the turbulent burning velocity must be taken into consideration. The paper presents a new equivalent cloud method using the turbulent burning velocity, which is described as a function of SL, deduced from the TNO multi-energy method. To validate the new equivalent cloud method, a series of simulations was conducted. There are good agreements by the comparison of the overpressures between equivalent clouds and the cloud with different ER values if explosion happened.

Fig. 4. Explosion of cloud with different ER values and the corresponding equivalent cloud. a ER=0.7 and the corresponding equivalent cloud in open space and obstacles. b ER=0.8 and the corresponding equivalent cloud in open space and obstacles. c ER=0.9 and the corresponding equivalent cloud in open space and obstacles. d ER=0.7 and the corresponding equivalent cloud in open space without obstacles. e ER=0.8 and the corresponding equivalent cloud in open space without obstacles. f ER=0.9 and the corresponding equivalent cloud in open space without obstacles. g ER=0.7 and the corresponding equivalent cloud in enclosed space and obstacles. h ER=0.8 and the corresponding equivalent cloud in enclosed space and obstacles. i ER=0.9 and the corresponding equivalent cloud in enclosed space and obstacles.

Nomenclature

where P0 is the peak overpressure; VBR is the volume blockage ratio of the obstructed region; Lp is the maximum flame path length; D is the typical diameter of the obstacles.

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(1)校本教师线上线下教学管理。本科高校会计学专业的教师根据《中级财务会计》课程的重要性质，根据最新会计准则和变化制定授课内容，并合理安排实践课程进度，录制实践内容的网课，制定学生的网上学习计划，实验室回答学生疑问。并在寒暑假期间，安排学生在企业财务工作环境中实践，与企业财务负责人交流沟通，及时反馈学生表现。

ER equivalence ratio -

VBR volume blockage ratio -

Lp flame path length m

高通滤波器的设计步骤很简单，如图1所示[4]。对于归一低通滤波器的设计采用插入损耗法(insertion loss method)，该方法采用网络综合技术设计出有完整的特定频率响应的滤波器。

P0 peak overpressure bar

SL laminar burning velocity m/s

古诗是小学语文阅读教学的重要内容之一，古诗对于小学生来说始终是较难理解的。因此在古诗教学中，教师应以诗人写作的背景资料作为切入点，有了背景的铺垫，学生就能比较自然、顺利地进入古诗的学习。例如六年级上册《春夜喜雨》一诗，杜甫在经历长时间的颠沛流离之后，辗转到天府之国——成都。饱经忧患的诗人度过长期颠沛流离的生活后，在亲朋好友的热心帮助下，建成了“杜甫草堂”，生活安定下来，写成了此诗。也凭借此诗表达了对人民疾苦的关心。教师以写作背景作为切入点来进行教学，帮助学生领悟诗情，体会诗人情感。

Ve volume expansion ratio -

Vgr obstructed cloud volume m3

Vi ith control volume m3

References

[1]A.S. Gexcon, FLACS v10.4 user’s manual, Bergen, 2015

[2]NORSOK Standard Z-013: Risk and emergency preparedness assessment, Norway, 2010

[3]ANSYS Inc., ANSYS CFX-Solver Theory Guide, Pennsylvania,2016

[4]C.J.H. van den Bosch, R.A.P.M. Weterings, Methods for the calculation of physical effects, TNO Prins Maurits Lab., Netherlands, 2005

[5]J.B.M.M. Eggen, GAME: development of guidance for the application of the multi-energy method, TNO Prins Maurits Lab.,Netherlands 1998

[6]DNV Software: UDM theory document, Norway, 2011

[7]W.P.M. Mercx, A.C. van den Berg, D. van Leeuwen, Application of correlations to quantify the source strength of vapour cloud explosions in realistic situations Final report for the project:"GAMES", TNO Prins Maurits Lab., Netherlands 1998

[8]DNV Software, Obstructed region explosion model (OREM)theory, Norway, 2010

[9]A.C. van den Berg, A.L. Mos, Research to improve guidance on separation distance for the multi-energy method (RIGOS), TNO Prins Maurits Lab., Netherlands 2005

[10]W. Zhang, D. Lu, J. Wang, Comparison of Vapor Cloud Explosion (VCE) Consequences Prediction Models, Industrial Safety and Environment Protection, 36 (2010) 48–52. (in Chinese)

[11]G. Fitzgerald, A Comparison of Simple Vapor Cloud Explosion Prediction Methodologies, Second Annual Symposium, Mary Kay O'Connor Process Safety Center "Beyond Regulatory Compliance: Making Safety Second Nature" Reed Arena, Texas A&M University, College Station, Texas, 2001

[12]Z. Wu, S. Hu, Y. Tan, Simplified Calculation of Maximum Blast Pressure of Poly-Ingredient Flammable Mixed Gases, Journal of Combustion Science and Technology 16 (2010) 118–122. (in Chinese)

[13]S. Tian, J. Liu, K. Gao, Experimental study on shock wave impulse and pressure rise rate of gas explosion in airtight pipeline,Journal of Safety Science and Technology, 11 (2015) 17–21. (in Chinese)

[14]E. Vyazmina, S. Jallais, Validation and recommendations for FLACS CFD and Engineering approaches to model hydrogen vented explosions Effects of concentration, obstruction vent area and ignition position, Hydrogen Energy, 2016