High Temperature and High Pressure Experiment and Modification of Phosphogypsum

ZHOU Dengfeng; SHAN Shuangming; YANG Ruidong; LUO Chaokun; NI Xinran; WANG Longbo

doi:10.11858/gywlxb.20200656

Volume 35 Issue 3

Jun 2021

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Article Contents

Abstract

References

Chinese Journal of High Pressure Physics > 2021 > 35(3): 031101.

XU Weizheng, WU Weiguo. Comparisons of Different Precision WENO Schemes for Simulating Blast Load of Gas Cloud Explosion inside a Cabin[J]. Chinese Journal of High Pressure Physics, 2018, 32(4): 042302. doi: 10.11858/gywlxb.20170689

Citation:

ZHOU Dengfeng, SHAN Shuangming, YANG Ruidong, LUO Chaokun, NI Xinran, WANG Longbo. High Temperature and High Pressure Experiment and Modification of Phosphogypsum[J]. Chinese Journal of High Pressure Physics, 2021, 35(3): 031101. doi: 10.11858/gywlxb.20200656

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High Temperature and High Pressure Experiment and Modification of Phosphogypsum

doi: 10.11858/gywlxb.20200656

ZHOU Dengfeng^{1, 2
,},
SHAN Shuangming³,
YANG Ruidong^{1, 2,*
,
,},
LUO Chaokun^{1, 2},
NI Xinran^{1, 2},
WANG Longbo^{1, 2}

1.
School of Resources and Environmental Engineering, Guizhou University, Guiyang 550025, Guizhou, China
2.
Key Laboratory of Karst Geological Resources and Environment, Ministry of Education, Guizhou University, Guiyang 550025, Guizhou, China
3.
Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550002, Guizhou, China

Received Date: 13 Dec 2020
Rev Recd Date: 25 Jan 2021

Abstract

Abstract

In this paper, the effects of high temperature and high pressure on single system and composite system of phosphogypsum were studied. By controlling the experimental conditions of high temperature and high pressure, the crystal morphology and mineral composition of different phosphogypsum systems at 300 ℃ and 300 MPa were studied. The phase and morphology of the synthesized samples were analyzed by X-ray diffraction (XRD) and scanning electron microscopy (SEM). XRD characterization results show that the mineral types and contents of different phosphogypsum systems were changed significantly under high temperature and high pressure. The specific performance is as follows: after high temperature and high pressure test, the SiO₂ content of phosphogypsum-quicklime composite system is lower than the detection limit; after high temperature and high pressure test, the mineral of phosphogypsum-diatomite composite system is completely transformed from dihydrate gypsum to anhydrous gypsum. SEM characterization results show that: in single phosphogypsum system, phosphogypsum-quicklime composite system, phosphogypsum-silica fume composite system and phosphogypsum-cement composite system, phosphogypsum crystals can spontaneously grow and crystallize in the reactor under high temperature and high pressure, with regular morphology and uniform dispersion. Most of the crystals are tetragonal, with smooth surface and agglomeration. The results show that the morphology of calcium sulfate whiskers is regular and uniform, the average diameter is 2.61 μm, and the average aspect ratio is about 8.
- phosphogypsum,
- high temperature and high pressure,
- admixture,
- calcium sulfate whisker,
- aspect ratio

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可燃性气云爆炸是石化工业灾害预防等领域研究的焦点。开敞空间中气云爆炸后将形成强度较大的带有负压区的空气冲击波，对工作人员和周边结构设施造成较大的损害。近年来学者们针对可燃气云、云雾爆炸进行了相应的数值、实验研究^[1-4]。这些研究中可燃气云、云雾被等效地简化为一团均匀高压气体，且主要采用低阶精度数值方法进行模拟；而针对舱室内部可燃气云爆炸的研究较少。

高精度激波捕捉格式对含激波流场的数值模拟具有重要意义，不但可以降低网格的规模，而且能较好地分辨流场中复杂的波系结构。Liu等^[5]于1994年首次提出加权本质无振荡(Weighted Essentially Non-Oscillatory，WENO)格式。之后，Jiang和Shu^[6]通过引入新的光滑因子，提出三阶WENO格式和五阶WENO格式，并扩展了其应用^[7-8]。Balsara等^[9]将WENO格式推广到更高阶形式，给出七、九、十一阶WENO格式。本研究在参考上述文献的基础上，采用三、五、七、九阶WENO格式，基于FORTRAN平台自主开发了高精度舱室内部气云爆炸三维数值计算程序，研究WENO格式精度对舱室内部气云爆炸载荷的影响规律。

1. 控制方程

可燃气云简化为均匀高压气体，采用三维可压缩欧拉方程描述爆炸流场，其具体形式如下

$\frac{{\partial \mathit{\boldsymbol{U}}}}{{\partial t}} + \frac{{\partial \mathit{\boldsymbol{E}}}}{{\partial x}} + \frac{{\partial \mathit{\boldsymbol{F}}}}{{\partial y}} + \frac{{\partial \mathit{\boldsymbol{G}}}}{{\partial z}} = 0$

(1)

其中

$\mathit{\boldsymbol{U}} = \left[ \begin{array}{l} \rho \\ \rho u\\ \rho v\\ \rho w\\ E \end{array} \right],\;\;\;\;\mathit{\boldsymbol{E}} = \left[ \begin{array}{l} \rho u\\ \rho {u^2} + p\\ \rho uv\\ \rho uw\\ u\left( {E + p} \right) \end{array} \right],\;\;\;\;\mathit{\boldsymbol{F}} = \left[ \begin{array}{l} \rho v\\ \rho vu\\ \rho {v^2} + p\\ \rho vw\\ v\left( {E + p} \right) \end{array} \right], \\ \mathit{\boldsymbol{G}} = \left[ \begin{array}{l} \rho w\\ \rho wu\\ \rho wv\\ \rho {w^2} + p\\ w\left( {E + p} \right) \end{array} \right]$

(2)

$E = \rho e + \frac{1}{2}\rho {u^2} + \frac{1}{2}\rho {v^2} + \frac{1}{2}\rho {w^2}$

(3)

$p = \left( {\gamma - 1} \right)\rho e$

(4)

式中: ρ是密度；u、v、w是x、y、z方向上的速度分量；p为流体压力；E是单位体积流体的总能量；e是比内能；γ表示气体绝热指数，取为1.4。对于多维欧拉方程的计算，采用Strang维数分裂法，将欧拉方程分解为x、y、z 3个方向求解。

2. 数值方法

程序中采用三阶、五阶、七阶、九阶WENO有限差分格式对欧拉方程进行数值离散和求解，下面给出不同精度WENO格式的离散过程。

2.1 三阶WENO格式

三阶WENO格式(WENO-JS3)的数值离散和推导过程如下。单元面中心x_i+1/2处数值通量f_i+1/2的两种重构方式分别为^[6]

$\left\{ \begin{array}{l} f_{i + 1/2}^0 = - \frac{1}{2}{f_{i - 1}} + \frac{3}{2}{f_i}\\ f_{i + 1/2}^1 = \frac{1}{2}{f_i} + \frac{1}{2}{f_{i + 1}} \end{array} \right.$

(5)

利用上述两种模板的凸组合计算数值通量f_i+1/2，即

${f_{i + 1/2}} = {\omega _0}f_{i + 1/2}^0 + {\omega _1}f_{i + 1/2}^1$

(6)

对于含激波间断流场，(6)式中的ω_k根据下式求得

${\omega _k} = {\alpha _k}/\sum\limits_{s = 0}^1 {{\alpha _s}} ,{\alpha _k} = \frac{{{d_k}}}{{{{\left( {\varepsilon + {\beta _k}} \right)}^2}}},\;\;\;\;k = 0,1$

(7)

式中：d_k表示WENO格式的线性权值，对于三阶WENO格式，其值为d₀=1/3，d₁=2/3。为避免分母为零，取ε=1.0×10^-6。光滑因子β_k(k=0, 1)的表达式如下^[6]

$\left\{ \begin{array}{l} {\beta _0} = {\left( {{f_i} - {f_{i - 1}}} \right)^2}\\ {\beta _1} = {\left( {{f_{i + 1}} - {f_i}} \right)^2} \end{array} \right.$

(8)

2.2 五阶WENO格式

五阶WENO格式(WENO-JS5)的数值离散和推导过程如下。单元面中心x_i+1/2处数值通量f_i+1/2的3种重构方式分别为^[6]

$\left\{ \begin{array}{l} f_{i + 1/2}^0 = \frac{1}{3}{f_{i - 2}} - \frac{7}{6}{f_{i - 1}} + \frac{{11}}{6}{f_i}\\ f_{i + 1/2}^1 = - \frac{1}{6}{f_{i - 1}} + \frac{5}{6}{f_i} + \frac{1}{3}{f_{i + 1}}\\ f_{i + 1/2}^2 = \frac{1}{3}{f_i} + \frac{5}{6}{f_{i + 1}} - \frac{1}{6}{f_{i + 2}} \end{array} \right.$

(9)

利用上述3种模板的凸组合计算数值通量f_i+1/2，即

${f_{i + 1/2}} = {\omega _0}f_{i + 1/2}^0 + {\omega _1}f_{i + 1/2}^1 + {\omega _2}f_{i + 1/2}^1$

(10)

对于含激波间断流场，(10)式中的ω_k根据下式求得

${\omega _k} = {\alpha _k}/\sum\limits_{s = 0}^2 {{\alpha _s}} ,{\alpha _k} = \frac{{{d_k}}}{{{{\left( {\varepsilon + {\beta _k}} \right)}^2}}},\;\;\;\;k = 0,1,2$

(11)

对于五阶WENO格式，d₀= $\frac{1}{{10}}$ ，d₁= $\frac{3}{{5}}$ ，d₂= $\frac{3}{{10}}$ 。光滑因子β_k(k=0, 1, 2)的表达式如下

$\left\{ \begin{array}{l} {\beta _0} = \frac{{13}}{{12}}{\left( {{f_{i - 2}} - 2{f_{i - 1}} + {f_i}} \right)^2} + \frac{1}{4}{\left( {{f_{i - 2}} - 4{f_{i - 1}} + 3{f_i}} \right)^2}\\ {\beta _1} = \frac{{13}}{{12}}{\left( {{f_{i - 1}} - 2{f_i} + {f_{i + 1}}} \right)^2} + \frac{1}{4}{\left( {{f_{i - 1}} - {f_{i + 1}}} \right)^2}\\ {\beta _2} = \frac{{13}}{{12}}{\left( {{f_i} - 2{f_{i + 1}} + {f_{i + 2}}} \right)^2} + \frac{1}{4}{\left( {3{f_i} - 4{f_{i + 1}} + {f_{i + 2}}} \right)^2} \end{array} \right.$

(12)

2.3 七阶WENO格式

七阶WENO格式(WENO-JS7)的数值离散和推导过程如下。单元面中心x_i+1/2处数值通量f_i+1/2的4种重构方式分别为^[9]

$\left\{ \begin{array}{l} f_{i + 1/2}^0 = - \frac{1}{4}{f_{i - 3}} + \frac{{13}}{{12}}{f_{i - 2}} - \frac{{23}}{{12}}{f_{i - 1}} + \frac{{25}}{{12}}{f_i}\\ f_{i + 1/2}^1 = \frac{1}{{12}}{f_{i - 2}} - \frac{5}{{12}}{f_{i - 1}} + \frac{{13}}{{12}}{f_i} + \frac{1}{4}{f_{i + 1}}\\ f_{i + 1/2}^2 = - \frac{1}{{12}}{f_{i - 1}} + \frac{7}{{12}}{f_i} + \frac{7}{{12}}{f_{i + 1}} - \frac{1}{{12}}{f_{i + 2}}\\ f_{i + 1/2}^3 = \frac{1}{4}{f_i} + \frac{{13}}{{12}}{f_{i + 1}} - \frac{5}{{12}}{f_{i + 2}} + \frac{1}{{12}}{f_{i + 3}} \end{array} \right.$

(13)

利用上述4种模板的凸组合计算数值通量f_i+1/2，即

${f_{i + 1/2}} = {\omega _0}f_{i + 1/2}^0 + {\omega _1}f_{i + 1/2}^1 + {\omega _2}f_{i + 1/2}^2 + {\omega _3}f_{i + 1/2}^3$

(14)

对于含激波间断流场，(14)式中的 ω_k 根据下式求得

${\omega _k} = {\alpha _k}/\sum\limits_{s = 0}^3 {{\alpha _s}} ,{\alpha _k} = \frac{{{d_k}}}{{{{\left( {\varepsilon + {\beta _k}} \right)}^2}}},\;\;\;\;k = 0,1,2,3$

(15)

对于七阶WENO格式，d₀= $\frac{1}{{35}}$ ，d₁= $\frac{12}{{35}}$ ，d₂= $\frac{18}{{35}}$ ，d₃= $\frac{4}{{35}}$ 。光滑因子β_k(k=0, 1, 2, 3)的表达式如下^[9]

$\left\{ \begin{array}{l} {\beta _0} = {f_{i - 3}}\left( {547{f_{i - 3}} - 3882{f_{i - 2}} + 4642{f_{i - 1}} - 1854{f_i}} \right) + \\ \;\;\;\;\;\;\;{f_{i - 2}}\left( {7043{f_{i - 2}} - 17246{f_{i - 1}} + 7042{f_i}} \right) + \\ {f_{i - 1}}\left( {11003{f_{i - 1}} - 9402{f_i}} \right) + 2107f_i^2\\ {\beta _1} = {f_{i - 2}}\left( {267{f_{i - 2}} - 1642{f_{i - 1}} + 1602{f_i} - 494{f_{i + 1}}} \right) + \\ \;\;\;\;\;\;\;{f_{i - 1}}\left( {2843{f_{i - 1}} - 5966{f_i} + 1922{f_{i + 1}}} \right) + \\ {f_i}\left( {3443{f_i} - 2522{f_{i + 1}}} \right) + 547f_{i + 1}^2\\ {\beta _2} = {f_{i - 1}}\left( {547{f_{i - 1}} - 2522{f_i} + 1922{f_{i + 1}} - 494{f_{i + 2}}} \right) + \\ \;\;\;\;\;\;\;{f_i}\left( {3443{f_i} - 5966{f_{i + 1}} + 1602{f_{i + 2}}} \right) + \\ {f_{i + 1}}\left( {2843{f_{i + 1}} - 1642{f_{i + 2}}} \right) + 267f_{i + 2}^2\\ {\beta _3} = {f_i}\left( {2107{f_i} - 9402{f_{i + 1}} + 7042{f_{i + 2}} - 1854{f_{i + 3}}} \right) + \\ \;\;\;\;\;\;{f_{i + 1}}\left( {11003{f_{i + 1}} - 17246{f_{i + 2}} + 4642{f_{i + 3}}} \right) + \\ {f_{i + 2}}\left( {7043{f_{i + 2}} - 3882{f_{i + 3}}} \right) + 547f_{i + 3}^2 \end{array} \right.$

(16)

2.4 九阶WENO格式

九阶WENO格式(WENO-JS9)的数值离散和推导过程如下。单元面中心x_i+1/2处数值通量f_i+1/2的5种重构方式分别为^[9]

$\left\{ \begin{array}{l} f_{i + 1/2}^0 = \frac{1}{5}{f_{i - 4}} - \frac{{21}}{{20}}{f_{i - 3}} + \frac{{137}}{{60}}{f_{i - 2}} - \frac{{163}}{{60}}{f_{i - 1}} + \frac{{137}}{{60}}{f_i}\\ f_{i + 1/2}^1 = - \frac{1}{{20}}{f_{i - 3}} + \frac{{17}}{{60}}{f_{i - 2}} - \frac{{43}}{{60}}{f_{i - 1}} + \frac{{77}}{{60}}{f_i} + \frac{1}{5}{f_{i + 1}}\\ f_{i + 1/2}^2 = \frac{1}{{30}}{f_{i - 2}} - \frac{{13}}{{60}}{f_{i - 1}} + \frac{{47}}{{60}}{f_i} + \frac{9}{{20}}{f_{i + 1}} - \frac{1}{{20}}{f_{i + 2}}\\ f_{i + 1/2}^3 = - \frac{1}{{20}}{f_{i - 1}} + \frac{9}{{20}}{f_i} + \frac{{47}}{{60}}{f_{i + 1}} - \frac{{13}}{{60}}{f_{i + 2}} + \frac{1}{{30}}{f_{i + 3}}\\ f_{i + 1/2}^4 = \frac{1}{5}{f_i} + \frac{{77}}{{60}}{f_{i + 1}} - \frac{{43}}{{60}}{f_{i + 2}} + \frac{{17}}{{60}}{f_{i + 3}} - \frac{1}{{20}}{f_{i + 4}} \end{array} \right.$

(17)

利用上述5种模板的凸组合计算数值通量f_i+1/2，即

${f_{i + 1/2}} = {\omega _0}f_{i + 1/2}^0 + {\omega _1}f_{i + 1/2}^1 + {\omega _2}f_{i + 1/2}^2 + {\omega _3}f_{i + 1/2}^3 + {\omega _4}f_{i + 1/2}^4$

(18)

对于含激波间断流场，(18)式中的ω_k根据下式求得

${\omega _k} = {\alpha _k}/\sum\limits_{s = 0}^3 {{\alpha _s}} ,\;\;\;{\alpha _k} = \frac{{{d_k}}}{{{{\left( {\varepsilon + {\beta _k}} \right)}^2}}},\;\;\;k = 0,1,2,3,4$

(19)

对于九阶WENO格式，d₀= $\frac{1}{{126}}$ ，d₁= $\frac{10}{{63}}$ ，d₂= $\frac{10}{{21}}$ ，d₃= $\frac{20}{{63}}$ ，d₄= $\frac{5}{{126}}$ 。光滑因子β_k(k=0, 1, 2, 3, 4)的表达式如下^[9]

$\left\{ \begin{array}{l} {\beta _0} = {f_{i - 4}}\left( {22658{f_{i - 4}} - 208501{f_{i - 3}} + 364863{f_{i - 2}} - 288007{f_{i - 1}} + 86329{f_i}} \right) + \\ \;\;\;\;\;\;\;{f_{i - 3}}\left( {482963{f_{i - 3}} - 1704396{f_{i - 2}} + 1358458{f_{i - 1}} - 411487{f_i}} \right) + \\ \;\;\;\;\;\;\;{f_{i - 2}}\left( {1521393{f_{i - 2}} - 2462076{f_{i - 1}} + 758823{f_i}} \right) + \\ \;\;\;\;\;\;\;{f_{i - 1}}\left( {1020563{f_{i - 1}} - 649501{f_i}} \right) + 107918f_i^2\\ {\beta _1} = {f_{i - 3}}\left( {6908{f_{i - 3}} - 60871{f_{i - 2}} + 99213{f_{i - 1}} - 70237{f_i} + 18079{f_{i + 1}}} \right) + \\ \;\;\;\;\;\;\;{f_{i - 2}}\left( {138563{f_{i - 2}} - 464976{f_{i - 1}} + 337018{f_i} - 88297{f_{i + 1}}} \right) + \\ \;\;\;\;\;\;\;{f_{i - 1}}\left( {406293{f_{i - 1}} - 611976{f_i} + 165153{f_{i + 1}}} \right) + \\ \;\;\;\;\;\;\;{f_i}\left( {242723{f_i} - 140251{f_{i + 1}}} \right) + 22658f_{i + 1}^2\\ {\beta _2} = {f_{i - 2}}\left( {6908{f_{i - 2}} - 51001{f_{i - 1}} + 67923{f_i} - 38947{f_{i + 1}} + 8209{f_{i + 2}}} \right) + \\ \;\;\;\;\;\;\;{f_{i - 1}}\left( {104963{f_{i - 1}} - 299076{f_i} + 179098{f_{i + 1}} - 38947{f_{i + 2}}} \right) + \\ \;\;\;\;\;\;\;{f_i}\left( {231153{f_i} - 299076{f_{i + 1}} + 67923{f_{i + 2}}} \right) + \\ \;\;\;\;\;\;\;{f_{i + 1}}\left( {104963{f_{i + 1}} - 51001{f_{i + 2}}} \right) + 6908f_{i + 2}^2\\ {\beta _3} = {f_{i - 1}}\left( {22658{f_{i - 1}} - 140251{f_i} + 165153{f_{i + 1}} - 88297{f_{i + 2}} + 18079{f_{i + 3}}} \right) + \\ \;\;\;\;\;\;\;{f_i}\left( {242723{f_i} - 611976{f_{i + 1}} + 337018{f_{i + 2}} - 70237{f_{i + 3}}} \right) + \\ \;\;\;\;\;\;\;{f_{i + 1}}\left( {406293{f_{i + 1}} - 464976{f_{i + 2}} + 99213{f_{i + 3}}} \right) + \\ \;\;\;\;\;\;\;{f_{i + 2}}\left( {138563{f_{i + 2}} - 60871{f_{i + 3}}} \right) + 6908f_{i + 3}^2\\ {\beta _4} = {f_i}\left( {107918{f_i} - 649501{f_{i + 1}} + 758823{f_{i + 2}} - 411487{f_{i + 3}} + 86329{f_{i + 4}}} \right) + \\ \;\;\;\;\;\;\;{f_{i + 1}}\left( {1020563{f_{i + 1}} - 2462076{f_{i + 2}} + 1358458{f_{i + 3}} - 288007{f_{i + 4}}} \right) + \\ \;\;\;\;\;\;\;{f_{i + 2}}\left( {1521393{f_{i + 2}} - 1704396{f_{i + 3}} + 364863{f_{i + 4}}} \right) + \\ \;\;\;\;\;\;\;{f_{i + 3}}\left( {482963{f_{i + 3}} - 208501{f_{i + 4}}} \right) + 22658f_{i + 4}^2 \end{array} \right.$

(20)

2.5 时间项数值离散

欧拉方程时间项采用三阶TVD-RK(Total Variation Diminishing Runge-Kutta)法进行数值离散，具体离散格式如下^[10]

$\left\{ \begin{array}{l} {\varphi ^{\left( 1 \right)}} = {\varphi ^n} + \Delta tL\left( {{\varphi ^n}} \right)\\ {\varphi ^{\left( 2 \right)}} = \frac{3}{4}{\varphi ^n} + \frac{1}{4}{\varphi ^{\left( 1 \right)}} + \frac{1}{4}\Delta tL\left( {{\varphi ^{\left( 1 \right)}}} \right)\\ {\varphi ^{\left( {n + 1} \right)}} = \frac{1}{3}{\varphi ^n} + \frac{1}{3}{\varphi ^{\left( 2 \right)}} + \frac{2}{3}\Delta tL\left( {{\varphi ^{\left( 2 \right)}}} \right) \end{array} \right.$

(21)

式中：φⁿ表示n时刻的守恒通量，φ⁽¹⁾、φ⁽²⁾为中间变量，Δt为时间步长，L为运算算子。

3. 经典算例

为了初步考察上述格式(WENO-JS3、WENO-JS5、WENO-JS7、WENO-JS9)的计算性能并验证所开发程序的可靠性，选取两个经典一维黎曼算例进行计算。

3.1 Sod激波管

该算例初始条件如(22)式所示^[11]，网格数为400，计算结束时间为0.18。图 1为计算结束时刻的密度曲线及其局部放大图。

${\left( {\rho ,u,p} \right)^{\rm{T}}} = \left\{ \begin{array}{l} {\left( {1,0,1} \right)^{\rm{T}}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;0 \le x < 0.5\\ {\left( {0.125,0,0.100} \right)^{\rm{T}}}\;\;\;\;\;\;\;\;\;0.5 \le x \le 1.0 \end{array} \right.$

(22)

图 1 Sod激波管算例密度曲线及其局部放大图

Figure 1. Density curve and its partially enlarged details for Sod shock tube

下载: 全尺寸图片幻灯片

3.2 激波与熵波相互作用

该算例初始条件如(23)式所示，网格数为400，计算结束时间为1.8。图 2为计算结束时刻的密度曲线及其局部放大图。

${\left( {\rho ,u,p} \right)^{\rm{T}}} = \left\{ \begin{array}{l} {\left( {3.857143,2.629369,10.333330} \right)^{\rm{T}}}\;\;\;\;\;\;\;\;\; - 5 \le x < - 4\\ {\left( {1 + 0.2\sin 5x,0.1} \right)^{\rm{T}}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; - 4 \le x \le 5 \end{array} \right.$

(23)

图 2 激波与熵波相互作用算例密度曲线及其局部放大图

Figure 2. Density curve and its partially enlarged details for shock-entropy wave interaction

下载: 全尺寸图片幻灯片

3.3 小结

根据图 1和图 2的计算结果，评估各格式的计算性能发现：WENO-JS9格式的计算性能最优，WENO-JS7、WENO-JS5格式次之，WENO-JS3格式的计算性能最低。即高精度WENO格式对含激波间断流场具有更低的耗散特性和更高的分辨率。

4. 舱室内气云爆炸载荷计算

为了考察不同精度WENO格式对舱室内部气云爆炸载荷的影响规律，采用所开发的三维程序开展封闭舱室和泄压舱室内爆炸载荷数值计算。

4.1 初始条件设置

舱室尺寸为800 mm×800 mm×800 mm，泄压舱室壁面上开有一个边长为160 mm的正方形泄压口。壁面上设置两个测点，分别编号为No.1、No.2，对爆炸超压时间历程进行输出，如图 3所示。

图 3 封闭舱室和泄压舱室及其测点分布(单位：mm)

Figure 3. Closed cabin and venting cabin and their gauging points (Unit:mm)

下载: 全尺寸图片幻灯片

半径为200 mm的球体气云位于舱室中间，气云参数为^[12-13]：密度1.99 kg/m³，压力1.38 MPa。周围空气参数为：密度1.225 kg/m³，压力0.1 MPa。计算初始条件见图 4(a)。考虑计算时间及精度的要求，经多次数值试验，网格数为40×40×40(见图 4(b))。壁面边界条件设置为反射边界，泄压口处边界条件设置为透射边界条件^[14]。

图 4 爆炸初场及网格分布

Figure 4. Initial condition and mesh distribution

下载: 全尺寸图片幻灯片

4.2 舱室内爆炸载荷特性

图 5给出了舱室内部气云爆炸壁面测点No.1和No.2处的超压时间历程曲线。由图 5可知：封闭舱室内爆炸载荷主要包含多峰值、强度逐渐衰弱的冲击波和持续时间较长、峰值保持稳定的准静态超压，泄压舱室内爆炸载荷主要包含多峰值、强度逐渐衰弱的冲击波和持续时间较长、呈指数衰减规律的准静态超压。

图 5 舱室内爆炸超压时间历程曲线

Figure 5. Overpressure histories of all the gauging points inside the cabin

下载: 全尺寸图片幻灯片

根据测点No.1和No.2的对比可知，测点的位置对爆炸前期的爆炸波超压峰值有较大的影响，而对形成的准静态超压时间历程几乎没有影响，说明舱室内部爆炸形成的准静态超压时间历程在空间上是近似均匀的。

4.3 封闭舱室内爆炸载荷比较

选取壁面典型测点No.1对爆炸载荷进行输出，探讨不同精度WENO格式对封闭舱室内气云爆炸载荷的影响规律。

通过对比图 6(a)~图 6(d)发现，高精度WENO格式能分辨出更精细的爆炸载荷特征，即高精度WENO格式具有更低的耗散特性和更高的分辨率。根据图 7可知，高精度WENO格式对于激波间断具有更低的耗散特性，给出更陡峭的激波峰值。然而，不同精度WENO格式对最终形成的准静态超压峰值影响较小，如图 7(a)中的绿色粗实线所示。

图 6 不同精度WENO格式下封闭舱室内气云爆炸测点No.1处的超压时间历程曲线

Figure 6. Overpressure histories at gauging point No.1 for different schemes in closed cabin

下载: 全尺寸图片幻灯片

图 7 不同精度WENO格式下封闭舱室内气云爆炸测点No.1处的超压比较及其局部放大图

Figure 7. Comparison of overpressure at gauging point No.1 for different schemes in closed cabin and its partially enlarged details

下载: 全尺寸图片幻灯片

4.4 泄压舱室内爆炸载荷比较

选取壁面典型测点No.1对爆炸载荷进行输出，探讨不同精度WENO格式对泄压舱室内爆炸载荷的影响规律。

通过对比图 8(a)~图 8(d)发现，高精度WENO格式能分辨出更精细的爆炸载荷特征，即高精度WENO格式具有更低的耗散特性和更高的分辨率。根据图 9可知，高精度WENO格式对于激波间断具有更低的耗散特性，给出更陡峭的激波峰值。然而，不同精度WENO格式对逐渐形成的、呈现指数衰减规律的准静态超压影响较小，如图 9(a)中的绿色粗实线所示。

图 8 不同精度WENO格式下泄压舱室内气云爆炸测点No.1处的超压时间历程曲线

Figure 8. Overpressure histories at gauging point No.1 for different schemes in venting cabin

下载: 全尺寸图片幻灯片

图 9 不同精度WENO格式下泄压舱室内气云爆炸测点No.1处的超压比较及其局部放大图

Figure 9. Comparison of overpressure at gauging point No.1 for different schemes in venting cabin and its partially enlarged details

下载: 全尺寸图片幻灯片

5. 结论

基于自主开发的高精度舱室内部气云爆炸三维数值计算程序研究了WENO格式精度对舱室内部气云爆炸载荷的影响规律，主要得到以下结论。

(1) 高精度WENO格式对含激波间断流场具有更低的耗散特性和更高的分辨率。

(2) 舱室内部气云爆炸载荷主要包含多峰值的瞬态冲击波和持续时间较长的准静态超压；封闭舱室内爆炸形成峰值保持不变的准静态超压，泄压舱室内爆炸形成呈指数衰减的准静态超压。

(3) WENO格式精度对舱室内爆炸冲击波载荷影响较大，高精度WENO格式给出更陡峭的激波峰值，而对舱室内爆炸准静态超压载荷的影响较小。

References(28)

References

[1]	ATTAR L A, AL-OUDAT M, KANAKRI S, et al. Radiological impacts of phosphogypsum [J]. Journal of Environmental Management, 2011, 92(9): 2151–2158. doi: 10.1016/j.jenvman.2011.03.041
[2]	夏海建. 磷石膏渣场池水循环利用过程中防堵塞技术研究[D]. 武汉: 武汉工程大学, 2015. XIA H J. The study on the technology of preventing blockage in recirculating water systems of phosphogypsum stacking [D]. Wuhan: Wuhan Institute of Technology, 2015.
[3]	王河, 吴维兴, 赵谊, 等. 磷石膏防渗渣场污水控制关键技术研究 [J]. 磷肥与复肥, 2019, 34(12): 36–39. doi: 10.3969/j.issn.1007-6220.2019.12.014 WANG H, WU W X, ZHAO Y, et al. Research on key technology of sewage control in anti-seepage field for phosphogypsum [J]. Phosphate and Compound Fertilizer, 2019, 34(12): 36–39. doi: 10.3969/j.issn.1007-6220.2019.12.014
[4]	TIAN T, YAN Y, HU Z H, et al. Utilization of original phosphogypsum for the preparation of foam concrete [J]. Construction and Building Materials, 2016, 115: 143–152. doi: 10.1016/j.conbuildmat.2016.04.028
[5]	MACÍAS F, CÁNOVAS C R, CRUZ-HERNÁNDEZ P, et al. An anomalous metal-rich phosphogypsum: characterization and classification according to international regulations [J]. Journal of Hazardous Materials, 2017, 331: 99–108. doi: 10.1016/j.jhazmat.2017.02.015
[6]	刘骥, 唐小春, 韦显文, 等. 浅谈磷石膏对水泥性能的影响 [J]. 企业科技与发展, 2020(9): 82–83. doi: 10.3969/j.issn.1674-0688.2020.09.035 LIU J, TANG X C, WEI X W, et al. Influence of phosphogypsum on cement properties [J]. Sci-Tech and Development of Enterprise, 2020(9): 82–83. doi: 10.3969/j.issn.1674-0688.2020.09.035
[7]	付强强, 沈彦辉, 陈宏坤, 等. 磷石膏综合利用现状及建议 [J]. 磷肥与复肥, 2020, 35(8): 44–46. doi: 10.3969/j.issn.1007-6220.2020.08.014 FU Q Q, SHEN Y H, CHEN H K, et al. Present situation and suggestions of comprehensive utilization of phosphogypsum [J]. Phosphate and Compound Fertilizer, 2020, 35(8): 44–46. doi: 10.3969/j.issn.1007-6220.2020.08.014
[8]	PAPASTEFANOU C, STOULOS S, IOANNIDOU A, et al. The application of phosphogypsum in agriculture and the radiological impact [J]. Journal of Environmental Radioactivity, 2006, 89(2): 188–198. doi: 10.1016/j.jenvrad.2006.05.005
[9]	张富存, 吴洪生, 周晓冬, 等. 磷石膏资源化利用对玉米生长影响 [J]. 西南农业学报, 2012, 25(2): 566–570. doi: 10.3969/j.issn.1001-4829.2012.02.043 ZHANG F C, WU H S, ZHOU X D, et al. Effect of recycling and reuse of phosphogypsum on corn growth [J]. Southwest China Journal of Agricultural Sciences, 2012, 25(2): 566–570. doi: 10.3969/j.issn.1001-4829.2012.02.043
[10]	李季, 吴洪生, 高志球, 等. 磷石膏对麦田CO₂排放和小麦产量的影响及其经济环境效益分析 [J]. 环境科学, 2015, 36(8): 3099–3105. doi: 10.13227/j.hjkx.2015.08.051 LI J, WU H S, GAO Z Q, et al. Impact of phosphogypsum wastes on the wheat growth and CO₂ emissions and evanuation of economic-environmental benefit [J]. Environmental Science, 2015, 36(8): 3099–3105. doi: 10.13227/j.hjkx.2015.08.051
[11]	SHEN W G, GAN G J, DONG R, et al. Utilization of solidified phosphogypsum as Portland cement retarder [J]. Journal of Material Cycles and Waste Management, 2012, 14(3): 228–233. doi: 10.1007/s10163-012-0065-x
[12]	贾兴文, 吴洲, 马英. 磷石膏建材资源化利用现状 [J]. 材料导报, 2013, 27(23): 139–141, 146. JIA X W, WU Z, MA Y. Present status of phosphogypsum utilization in building materials [J]. Materials Review, 2013, 27(23): 139–141, 146.
[13]	谭明洋, 张西兴, 相利学, 等. 磷石膏作水泥缓凝剂的研究进展 [J]. 无机盐工业, 2016, 48(7): 4–6. TAN M Y, ZHANG X X, XIANG L X, et al. Research progress of phosphorus gypsum as cement retarder [J]. Inorganic Chemicals Industry, 2016, 48(7): 4–6.
[14]	谢占金, 石文建, 金翠霞, 等. 晶种及晶型助长剂对磷石膏制备硫酸钙晶须的影响 [J]. 环境工程学报, 2012, 6(4): 1348–1352. XIE Z J, SHI W J, JIN C X, et al. Effect of crystal seed and crystal promoter on the preparation of calcium sulphate whiskers using phosphogypsum [J]. Chinese Journal of Environmental Engineering, 2012, 6(4): 1348–1352.
[15]	杨荣华, 宋锡高. 磷石膏的净化处理及制备硫酸钙晶须的研究 [J]. 无机盐工业, 2012, 44(4): 31–34. doi: 10.3969/j.issn.1006-4990.2012.04.011 YANG R H, SONG X G. Research on purification of phosphogypsum and preparation of calcium sulfate whisker [J]. Inorganic Chemicals Industry, 2012, 44(4): 31–34. doi: 10.3969/j.issn.1006-4990.2012.04.011
[16]	SHENG Z M, ZHOU J, SHU Z, et al. Calcium sulfate whisker reinforced non-fired ceramic tiles prepared from phosphogypsum [J]. Boletín de la Sociedad Española de Cerámicay Vidrio, 2018, 57(2): 73–78. doi: 10.1016/j.bsecv.2017.09.005
[17]	TAYIBI H, CHOURA M, LÓPEZ F A, et al. Environmental impact and management of phosphogypsum [J]. Journal of Environmental Management, 2009, 90(8): 2377–2386. doi: 10.1016/j.jenvman.2009.03.007
[18]	王慧媛, 郑海飞. 高温高压实验及原位测量技术 [J]. 地学前缘, 2009, 16(1): 17–26. doi: 10.3321/j.issn:1005-2321.2009.01.004 WANG H Y, ZHENG H F. High pressure-temperature experiment and in-situ measurement technology [J]. Earth Science Frontiers, 2009, 16(1): 17–26. doi: 10.3321/j.issn:1005-2321.2009.01.004
[19]	MCMILLAN P F. New materials from high-pressure experiments [J]. Nature Materials, 2002, 1(1): 19–25. doi: 10.1038/nmat716
[20]	余光, 柯龙华, 叶友章. 高温高压制备微晶纤维素新工艺的研究 [J]. 福建林业科技, 2010, 37(4): 58–61. doi: 10.3969/j.issn.1002-7351.2010.04.012 YU G, KE L H, YE Y Z. Study on the new process of microcrystalline cellulose in high temperature and pressure [J]. Journal of Fujian Forestry Science and Technology, 2010, 37(4): 58–61. doi: 10.3969/j.issn.1002-7351.2010.04.012
[21]	陶强, 王欣, 崔田, 等. 钼-硼化合物的高温高压制备及硬度特性探索[C]//第十四届全国物理力学学术会议缩编文集. 绵阳: 中国力学学会, 2016. TAO Q, WANG X, CUI T, et al. Preparation of molybdenum boron compounds at high temperature and high pressure and exploration of their hardness characteristics [C]//Abstracts of the 14th National Conference on Physical Mechanics. Mianyang: Chinese Society of Mechanics, 2016.
[22]	侯领, 沈维霞, 房超, 等. 高导热金刚石/铝复合材料的高温高压制备 [J]. 高压物理学报, 2020, 34(5): 053101. doi: 10.11858/gywlxb.20200514 HOU L, SHEN W X, FANG C, et al. High thermal conductivity of diamond/Al composites via high pressure and high temperature sintering [J]. Chinese Journal of High Pressure Physics, 2020, 34(5): 053101. doi: 10.11858/gywlxb.20200514
[23]	贾晓鹏. 类天然金刚石的高温高压合成研究 [J]. 原子与分子物理学报, 2020, 37(6): 909–915. doi: 10.19855/j.1000-0364.2020.064001 JIA X P. Study on the synthesis of “natural” diamond at high temperature and high pressure [J]. Journal of Atomic and Molecular Physics, 2020, 37(6): 909–915. doi: 10.19855/j.1000-0364.2020.064001
[24]	刘江, 杨红艳, 石文建, 等. 磷石膏水热法合成硫酸钙晶须 [J]. 化工环保, 2014, 34(2): 141–144. doi: 10.3969/j.issn.1006-1878.2014.02.011 LIU J, YANG H Y, SHI W J, et al. Synthesis of calcium sulphate whisker from phosphogypsum by hydrothermal method [J]. Environmental Protection of Chemical Industry, 2014, 34(2): 141–144. doi: 10.3969/j.issn.1006-1878.2014.02.011
[25]	李箫, 王莹, 万惠文, 等. 磷石膏制建筑石膏的试验研究 [J]. 武汉理工大学学报, 2015, 37(12): 40–46. LI X, WANG Y, WAN H W, et al. Experimental study on the gypsum preparation by the phosphogypsum [J]. Journal of Wuhan University of Technology, 2015, 37(12): 40–46.
[26]	熊春杨, 吕淑珍, 牛云辉, 等. 四川某地磷石膏制备建筑石膏及其性能研究 [J]. 非金属矿, 2020, 43(3): 33–36. doi: 10.3969/j.issn.1000-8098.2020.03.009 XIONG C Y, LÜ S Z, NIU Y H, et al. Preparation of building gypsum from phosphogypsum in Sichuan and its properties [J]. Non-Metallic Mines, 2020, 43(3): 33–36. doi: 10.3969/j.issn.1000-8098.2020.03.009
[27]	耿乾, 孙红娟, 彭同江, 等. 焙烧与生石灰改性对磷石膏中可溶磷含量的影响 [J]. 矿产保护与利用, 2019, 39(4): 9–13, 82. doi: 10.13779/j.cnki.issn1001-0076.2019.04.002 GENG Q, SUN H J, PENG T J, et al. Effect of roasting and quicklime modification on soluble phosphorus content in phosphogypsum [J]. Conservation and Utilization of Mineral Resources, 2019, 39(4): 9–13, 82. doi: 10.13779/j.cnki.issn1001-0076.2019.04.002
[28]	万惠文, 王银, 戴鹏, 等. 磷石膏/矿粉复合过硫胶凝材料的制备研究 [J]. 武汉理工大学学报, 2014, 36(3): 23–27. WAN H W, WANG Y, DAI P, et al. Study of phosphogysum/slag compound persulfate cementitious material [J]. Journal of Wuhan University of Technology, 2014, 36(3): 23–27.

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[20]	XU Ying-Fan, HUANG Xin-Ming, CHEN Hong, WANG Wen-Kui. Crystallization of Pd40Ni40P20 Bulk Metallic Glass under High Pressure[J]. Chinese Journal of High Pressure Physics, 1991, 5(1): 13-19 . doi: 10.11858/gywlxb.1991.01.003

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沈阳化工大学材料科学与工程学院沈阳 110142

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