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螺旋桨飞机滑流对全机气动特性影响的试验研究

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2024年4月14日发(作者:须艳丽)

螺旋桨飞机滑流对全机气动特性影响的试验研究

任庆祝;赵晓霞;刘毅;张鹏

【摘 要】为准确分析螺旋桨飞机有动力状态下的飞行性能和操纵品质,需要得到螺

旋桨动力系统,特别是滑流对全机气动特性的影响量.采用一种“小天平+主天平”

的多天平测量技术,可以分别测量得到螺旋桨的直接力和全机的气动力数据,进而得

到比较准确的纯滑流对全机气动特性的影响量.通过螺旋桨飞机的带动力测力风洞

试验研究表明:滑流会引起全机的升力系数、阻力系数,以及俯仰力矩系数相比无动

力状态有所增加,升力系数和阻力系数增量随迎角大致呈二次曲线规律递增,俯仰力

矩系数增量变化趋势与飞机所在迎角关系较大.滑流对横航向气动特性影响是降低

了全机横向力导数以及横、航向静稳定性,并可能引起零侧滑下的全机的不对称横、

航向力矩产生.

【期刊名称】《科学技术与工程》

【年(卷),期】2015(015)015

【总页数】4页(P214-217)

【关键词】滑流;气动特性;螺旋桨带动力风洞试验;多天平测量技术;桨盘系数

【作 者】任庆祝;赵晓霞;刘毅;张鹏

【作者单位】中航飞机研发中心1所,汉中723000;中航飞机研发中心1所,汉中

723000;中航飞机研发中心1所,汉中723000;中航飞机研发中心1所,汉中

723000

【正文语种】中 文

【中图分类】V211.7

凭借出色的燃油消耗率、低廉的使用成本、较高的维修性和可靠性,以及对动力选

择的多样化需求,涡轮螺旋桨发动机越来越广泛地被应用于航空飞行器中,如美军

V-22“鱼鹰”运输机、E-2C“鹰眼”预警机、空中客车A400M运输机,以及安

多诺夫AN-70运输机等。目前我国已服役的多款运输机及特种飞机均采用了螺旋

桨动力系统,滑流是螺旋桨动力飞机特有的一重要特征,研究滑流对飞机气动特性

的影响对于准确分析飞机的飞行性能和操纵品质具有十分重要的意义。

螺旋桨动力系统对飞机气动特性的影响主要有直接影响和间接影响两部分[1]。直

接影响是由螺旋桨动力系统产生的拉力、扭矩等直接力影响,也包含飞机有迎角

(或侧滑角)时气流斜吹螺旋桨后在桨盘平面内产生的螺旋桨径向力对全机气动特性

的影响[2];间接影响是由螺旋桨滑流引起的全机气动特性的变化,螺旋桨滑流对

全机的气动特性具有显著的影响[3—6]。

由于螺旋桨滑流的形成和发展过程比较复杂,且螺旋桨与飞机之间也存在一定的相

互干扰,不同机型、动力装置下的滑流影响差异也较大,难以做理论计算分析,目

前国内对螺旋桨滑流的研究主要以CFD数值模拟[7—10]和风洞试验为主[11,12]。

前者受计算模型和网格质量等影响,模拟难度较高。要得到满足工程设计使用要求

的滑流影响数据,必须进行螺旋桨飞机带动力风洞试验,常规的单天平的带动力风

洞试验得到的动力影响量数据里面含有螺旋桨直接力和滑流两部分影响量,本文采

用的基于“小天平+主天平”的多天平测量技术可以得到比较准确的纯滑流对全机

气动特性的影响量。

螺旋桨通过流经螺旋桨桨盘区域流管的动量产生推力,螺旋桨后方的流管即螺旋桨

滑流,飞机位于螺旋桨之后的并处于滑流之中的部件受滑流的影响表现为使部件前

方来流发生改变(速度大小、方向与滑流之外区域有很大不同)。以机翼部件为例,

如图2所示,机翼表面受滑流直接影响的区域比机翼上临近的其他区域承受更高

的动压,产生更大的升力。

与常规风洞试验方法不同的是,螺旋桨飞机带动力风洞试验不仅需要满足模型几何

相似等相似准则,还要根据飞机真实螺旋桨和发动机的工作特性,通过使螺旋桨试

验系统模型的拉力系数Tc、扭矩系数Qc、功率系数Cw以及螺旋桨的桨叶角Φ、

前进比λ、叶素迎角α等与真实螺旋桨发动机系统一致,同时试验马赫数M、雷

诺数Re、变形参数S等满足试验相似准则,来模拟真实螺旋桨滑流特性[13]。通

常只要拉力系数Tc、扭矩系数Qc、功率系数Cw三个气动力系数与真实动力系统

一致,即达到了动力模拟的目的。

本次试验在中国空气动力研究与发展中心低速所FL-12风洞完成,对模型螺旋桨

的驱动电机要求是尺寸小、功率大、调速方便、运转时间长。为保证驱动电机的安

全持续稳定工作还需设计电机内部水冷却管路甚至保护用的温度传感器等。另外,

为直接获得准确的各螺旋桨工作状态的气动力数据,还需设计小尺寸的测量天平与

螺旋桨驱动电机系统配装,这种由主天平和小天平分别负责测量全机和各螺旋桨气

动力数据的技术即为多天平测量技术。

某螺旋桨模型电机及全机带动力状态试验模型如图3所示,动力模拟的目标参数

曲线见图4。在各目标曲线特征点分别按试验任务安排进行带动力状态下的全机测

力风洞试验,得到不同拉力系数TC(或桨盘系数B)下各气动参数随迎角α(或侧滑

角β)的变化曲线,再减去相应状态无动力下的影响量,即得到螺旋桨动力系统带

来的气动影响量ΔRpow,再扣除螺旋桨直接力影响ΔRpde(该影响量可用螺旋桨

模型内置天平测量得到)即得到螺旋桨滑流对全机气动特性的影响量[14]。

某螺旋桨飞机滑流引起的升力系数增量ΔCL、阻力系数增量ΔCD、俯仰力矩系数

增量ΔCm以及不对称的偏航力矩系数增量ΔCn,β=0、滚转力矩系数增量ΔCl,

β=0随桨盘系数B和迎角α的变化如图5~图9所示,从图中可以看出;

1) 滑流引起的升力系数增量、阻力系数增量随桨盘系数B增加而增加,同一桨盘

系数B下该增量随迎角α大致呈二次曲线递增,直至失速;

2) 滑流引起的俯仰力矩系数增量与迎角α关系较大,其绝对值大小随桨盘系数的

增加而增加;

3) 由于各发动机螺旋桨桨叶旋转方向相同,滑流导致飞机在零侧滑角状态下,出

现了不对称的横向力矩Cn,β=0、Cl,β=0;

通过采用“小天平+主天平”的多天平带动力试验方法,得到了比较准确可靠的螺

旋桨滑流引起的全机各气动力、力矩特性的变化特性,为准确分析全机的气动特性、

飞行性能和操纵品质提供了更为坚实可靠的支撑。

【相关文献】

1 王勋年.低速风洞试验. 北京: 国防工业出版社, 2002: 157—164

Wang Xunnian. Low-speed wind tunnel test. Beijing: National Defense Industry Press,

2002: 157—164

2 欧阳绍修,赵晓霞,江宗辉,等. 螺旋桨径向力风洞试验方法研究.试验流体力学, 2012; 26(3): 91—94

Ouyang Shaoxiu, Zhao Xiaoxia, Jiang Zonghui,etal. The research on wind tunnel test

method of propeller’s radial force. Journal of Experiments in Fluid Mechanics, 2012;

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7 李尚斌,焦予秦.螺旋桨滑流的研究进展. 科学技术与工程, 2012;12(8):1867—1873

Li Shangbin, Jiao Yuqin. The investigate development of propeller sliptream’s effect.

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1103—1109

Xu Jianhua, Song Wenping, Han Zhonghua,etal. Aerodynamic performance research of

propellers based on CFD technology. Journal of Aerospace Power, 2010;25(5): 1103—1109

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2024年4月14日发(作者:须艳丽)

螺旋桨飞机滑流对全机气动特性影响的试验研究

任庆祝;赵晓霞;刘毅;张鹏

【摘 要】为准确分析螺旋桨飞机有动力状态下的飞行性能和操纵品质,需要得到螺

旋桨动力系统,特别是滑流对全机气动特性的影响量.采用一种“小天平+主天平”

的多天平测量技术,可以分别测量得到螺旋桨的直接力和全机的气动力数据,进而得

到比较准确的纯滑流对全机气动特性的影响量.通过螺旋桨飞机的带动力测力风洞

试验研究表明:滑流会引起全机的升力系数、阻力系数,以及俯仰力矩系数相比无动

力状态有所增加,升力系数和阻力系数增量随迎角大致呈二次曲线规律递增,俯仰力

矩系数增量变化趋势与飞机所在迎角关系较大.滑流对横航向气动特性影响是降低

了全机横向力导数以及横、航向静稳定性,并可能引起零侧滑下的全机的不对称横、

航向力矩产生.

【期刊名称】《科学技术与工程》

【年(卷),期】2015(015)015

【总页数】4页(P214-217)

【关键词】滑流;气动特性;螺旋桨带动力风洞试验;多天平测量技术;桨盘系数

【作 者】任庆祝;赵晓霞;刘毅;张鹏

【作者单位】中航飞机研发中心1所,汉中723000;中航飞机研发中心1所,汉中

723000;中航飞机研发中心1所,汉中723000;中航飞机研发中心1所,汉中

723000

【正文语种】中 文

【中图分类】V211.7

凭借出色的燃油消耗率、低廉的使用成本、较高的维修性和可靠性,以及对动力选

择的多样化需求,涡轮螺旋桨发动机越来越广泛地被应用于航空飞行器中,如美军

V-22“鱼鹰”运输机、E-2C“鹰眼”预警机、空中客车A400M运输机,以及安

多诺夫AN-70运输机等。目前我国已服役的多款运输机及特种飞机均采用了螺旋

桨动力系统,滑流是螺旋桨动力飞机特有的一重要特征,研究滑流对飞机气动特性

的影响对于准确分析飞机的飞行性能和操纵品质具有十分重要的意义。

螺旋桨动力系统对飞机气动特性的影响主要有直接影响和间接影响两部分[1]。直

接影响是由螺旋桨动力系统产生的拉力、扭矩等直接力影响,也包含飞机有迎角

(或侧滑角)时气流斜吹螺旋桨后在桨盘平面内产生的螺旋桨径向力对全机气动特性

的影响[2];间接影响是由螺旋桨滑流引起的全机气动特性的变化,螺旋桨滑流对

全机的气动特性具有显著的影响[3—6]。

由于螺旋桨滑流的形成和发展过程比较复杂,且螺旋桨与飞机之间也存在一定的相

互干扰,不同机型、动力装置下的滑流影响差异也较大,难以做理论计算分析,目

前国内对螺旋桨滑流的研究主要以CFD数值模拟[7—10]和风洞试验为主[11,12]。

前者受计算模型和网格质量等影响,模拟难度较高。要得到满足工程设计使用要求

的滑流影响数据,必须进行螺旋桨飞机带动力风洞试验,常规的单天平的带动力风

洞试验得到的动力影响量数据里面含有螺旋桨直接力和滑流两部分影响量,本文采

用的基于“小天平+主天平”的多天平测量技术可以得到比较准确的纯滑流对全机

气动特性的影响量。

螺旋桨通过流经螺旋桨桨盘区域流管的动量产生推力,螺旋桨后方的流管即螺旋桨

滑流,飞机位于螺旋桨之后的并处于滑流之中的部件受滑流的影响表现为使部件前

方来流发生改变(速度大小、方向与滑流之外区域有很大不同)。以机翼部件为例,

如图2所示,机翼表面受滑流直接影响的区域比机翼上临近的其他区域承受更高

的动压,产生更大的升力。

与常规风洞试验方法不同的是,螺旋桨飞机带动力风洞试验不仅需要满足模型几何

相似等相似准则,还要根据飞机真实螺旋桨和发动机的工作特性,通过使螺旋桨试

验系统模型的拉力系数Tc、扭矩系数Qc、功率系数Cw以及螺旋桨的桨叶角Φ、

前进比λ、叶素迎角α等与真实螺旋桨发动机系统一致,同时试验马赫数M、雷

诺数Re、变形参数S等满足试验相似准则,来模拟真实螺旋桨滑流特性[13]。通

常只要拉力系数Tc、扭矩系数Qc、功率系数Cw三个气动力系数与真实动力系统

一致,即达到了动力模拟的目的。

本次试验在中国空气动力研究与发展中心低速所FL-12风洞完成,对模型螺旋桨

的驱动电机要求是尺寸小、功率大、调速方便、运转时间长。为保证驱动电机的安

全持续稳定工作还需设计电机内部水冷却管路甚至保护用的温度传感器等。另外,

为直接获得准确的各螺旋桨工作状态的气动力数据,还需设计小尺寸的测量天平与

螺旋桨驱动电机系统配装,这种由主天平和小天平分别负责测量全机和各螺旋桨气

动力数据的技术即为多天平测量技术。

某螺旋桨模型电机及全机带动力状态试验模型如图3所示,动力模拟的目标参数

曲线见图4。在各目标曲线特征点分别按试验任务安排进行带动力状态下的全机测

力风洞试验,得到不同拉力系数TC(或桨盘系数B)下各气动参数随迎角α(或侧滑

角β)的变化曲线,再减去相应状态无动力下的影响量,即得到螺旋桨动力系统带

来的气动影响量ΔRpow,再扣除螺旋桨直接力影响ΔRpde(该影响量可用螺旋桨

模型内置天平测量得到)即得到螺旋桨滑流对全机气动特性的影响量[14]。

某螺旋桨飞机滑流引起的升力系数增量ΔCL、阻力系数增量ΔCD、俯仰力矩系数

增量ΔCm以及不对称的偏航力矩系数增量ΔCn,β=0、滚转力矩系数增量ΔCl,

β=0随桨盘系数B和迎角α的变化如图5~图9所示,从图中可以看出;

1) 滑流引起的升力系数增量、阻力系数增量随桨盘系数B增加而增加,同一桨盘

系数B下该增量随迎角α大致呈二次曲线递增,直至失速;

2) 滑流引起的俯仰力矩系数增量与迎角α关系较大,其绝对值大小随桨盘系数的

增加而增加;

3) 由于各发动机螺旋桨桨叶旋转方向相同,滑流导致飞机在零侧滑角状态下,出

现了不对称的横向力矩Cn,β=0、Cl,β=0;

通过采用“小天平+主天平”的多天平带动力试验方法,得到了比较准确可靠的螺

旋桨滑流引起的全机各气动力、力矩特性的变化特性,为准确分析全机的气动特性、

飞行性能和操纵品质提供了更为坚实可靠的支撑。

【相关文献】

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File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1723880881)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1723880881)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1724412091)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1724412091)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1726243838)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1726243838)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1726664172)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1726664172)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1726911134)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1726911134)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1727682249)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1727682249)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1728438012)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1728438012)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1730053205)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1730053205)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1730493678)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1730493678)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1730494441)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1730494441)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1095, humandate(1730731139)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(26))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
Error[2]: Trying to access array offset on value of type int, File: /www/wwwroot/www.usbmi.com/xiunophp/xiunophp.min.php, Line: 54
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 1096, humandate(1730731139)
File: /www/wwwroot/www.usbmi.com/tmp/model_thread.func.php, Line: 662, well_thread_format(array(27))
File: /www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm, Line: 249, well_thread_find_asc(array(20) , 20)
File: /www/wwwroot/www.usbmi.com/tmp/route_read.php, Line: 204, include(/www/wwwroot/www.usbmi.com/tmp/view_template_d8_htm_read.htm)
File: /www/wwwroot/www.usbmi.com/tmp/index.inc.php, Line: 129, include(/www/wwwroot/www.usbmi.com/tmp/route_read.php)
File: /www/wwwroot/www.usbmi.com/index.php, Line: 29, include(/www/wwwroot/www.usbmi.com/tmp/index.inc.php)
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