测风求阻法解算矿井复杂通风网路外文文献翻译

Method of branch ariflow for calculatinga complicated mine ventilation networksLIU ZE gong（刘泽功）（University of Science and Technology of China, Hefei 230026, China）Abstract The solutions widely used at present for calculating complicated mine ventilation networks taken are ones in which resistance of the branches and characteristic parameters of the fans are as basic values. A new input data. But it is timE and-energy-consuming to obtain the branch resistance solution is developed in this paper in which the branch resistance values are obtained through measuring and evaluating the airflow of the whole ventilation network. Theoretical analysis is made of the establishment of a linear equation series with branch resistance as unknown numbers, an equation series for which one, and only one, result of solutions exists. This solution is programmed in C language and passed on a personal computer. The programmed solotion programmed proves of practical use, as demonstrated by specific examples. Being different from other solutions, the method takes the branch airflow and fan working points as basic input data, and the present solution is of greater advantage for calculating ventilation networks of mines in operationKeywords air resistance, measurements, calculation, computersIntroductionAt present the key problem of calculating complicated ventilation network methods widely used is that until the resistance value of n items of branches of the network graph G=（V,E） （V is the set of joint points, |V|=m，E is the set of the sides, |E|=n）are available （except the fixed airflow volume branohes），the accurate solutions can be obtained. Due to the difficulties of getting the precise values of tens, hundreds or even thousands of branches of a large scale network, this paper suggests a new method based on the data of branch airflow and fan working point, that is airflow measuring method. And the corresponding solution program is also given. 1 Basic law and basic principle1.1 Basic law（1） Airflow resistance lawAccording to mine ventilation, the roadway airflow resistance law isWhere, h is pressure loss along the roadway, Pa; R is resistance of branch, kg/ m7; Q is volume flow rate, m3/s.（2） Joining point airflow volume balance law The following equation underlies any joint point of a networkWhere, i is serial numbers of the networks joint points（i=1, 2, 3,m）; j is serial numbers of the networks branches （j=1, 2, 3,n）; Qj is volume flow rate in branch j , m3/s; aij is airflow direction function of branch j connecting with joint point i,airflow of branch j flows into joining point ibranch j doesnt connect with joining point iairflow of branch j flows from joining point i（3） Mesh airflow presure banlance law Where,i is serial number of meshes （i=1,2,3,n-m+1）;j is serial numbers of mesh branches （j=1,2,3,n）; HFi is airflow resistance value of branch j, kg/m7; Qij is volume airflow rate in branch j, m3/s; bij is airflow direction function of branch j of mesh i,airflow direction of branch j of mesh i identify with meshbranch j doesnt belong to mesh iairflow direction of branch j of mesh i doestt identify with mesh1.2 Basic principle Take the directive net graph as Go=（Vo, Eo） （|Vo|=m, | E0|=n ） as basic network and known volume airflow rate Qi（0） （i=1, 2, 3,n） as basic data, the independent circuits can be selected and the linear equations with branch resistance as variables can be obtained equation （3） According to graph theory, the number of independent circuits of a directive net graph is r0 （r0=n-m+1）1.2 .So only graph G0 can t build n independent circuit equations. But an operating mine often adjust its ventilation system, sometimes not affecting mine functioning, the ventilation system can be adjusted manually fo solving the ventilation network. Take G0 as the basic network graph,after first airflow adjustment, G0 can be changed into G1=（V1，E1） （|V1|=m1，|E1|=n1），the branch airflow volumes are Qi（1） （ i=1, 2,3,n1） respectively, the number of independent circuit equations is r1 （ r1 =n1-m1+ 1），after second airflow adjustment, the network is G2=（V2，E2） （|Vk|=m2, | E2|=n2），branch airflow values are Qi（2） （i= 1, 2, 3,nk），the number of independent circuit equations is r2 （ r2= n2-m2+ 1）,after k times of adjustment, the network is Gk=（Vk,Ek） （|Vk|=mk., |Ek|=nk），branch airflow volumes are Qik （i=1, 2, 3,n2），the number of circuit equations is rk （rk=nk-mk+ 1）. For basic network graph Go , among r1, r2,rk circuit equations have r1，r2,.,rk corresponding circuit equations with adjustable branches, hence equations should be cut off from r （ r=r1+r2+ r3+.+ rk.） before building branch resistance circuit equations. And k should guarantee r-rn.In general, after 13 times of airflow adjustment of G0, the number of the built independent circuit equations can exceed n.2 The establishment of mathematics model2.1 Predefinition（1）The branch between two identical joining points in G0, G1,Gk indicates the same branch, i.e. its branch airflow resistance value is constant; （2） Apply network solution to basic ventilation network graph Go; （3）T he joining point set Vs（s = 0, 1, 2,k） of G0, G1,Gk are the same, i.e. the joining points serial numbers of every ventilation network graph should be identical despite the adjustment of ventilation system;（4） The corresponding branch serial numbers of the same points of every ventilation network graph should be identical.2.2 The establishment of branch airflow resistance linear equationsWhere, bij（s） is airflow direction function of branch j of circuit i in network Gs ; Qij（s） is volume airflow rate in branch j of circuit i in network Gs , Pa ;Hni（s） is resistance of branch j of network Gs，kg/ m7; Hfi（s） is fan working pressure of circuit i of network Qs, Pa; HNi（s） is natural pressure of circuit i of netwok Gs, Pa.Make Cij（s）=bij（s） Qij2（s），Hi（s）= HFi（s）+ HNi（s）, while（Cij（0）,Cij（2） ,Cij（3）, Cij（s） ,.,Cij（k） const;（Hi（0）, Hi（1） ,Hi（2） ,Hi（k） ） const. Equation（4） belong to the system of homogeneous linear equadons, then equation（4） can be described as following:According to predefinition, the branch airflow resistance are all contained in equations（5） for solving basic network graph Go. Therefore, if any of solution Ri （i=1, 2, 3,n） of equations （5） is zero or doesn t exit, the whole solution then proves to ineffective. For equations（5），there are n independent variabler, r-r circuit equations and r-rn，so it is obvious that the only solution can be obtained by sclecting n linear irrelevant circuit equations for（5）.2.3 Discussion of soleness of equation（5） solution（1） Simplification of equations（5） From ventilation network theory, we know that pressure resources HFi , HNi cant exit in all n-m+1 selected independent circuits of ventilation network Go, so the other equations without pressure resources are asWhere, s is serial numbers of network graphs（,s=0, 1, 2, 3, k）; i is the number i independent circuit of Gs.Equation（6） affect equation（5） efficiently in solving. Again from graph theory, for the directive joining graph Gs=（ Vs, Es ） the rank of basic circuit matrix is （ns-ms+1）. When s=0, the equations with the same branches and the same structure as equation（6） appears no more than one time. So when s=0, 1,2,k, the number of equations involved in equation（7）is no more than k+1. By simplifying equation （6），it can be described asWhere, （ Rj1, Rj2 ,RjL ） （R1 , R2 ,RS）As for equation（7），when its cefficient matrix rank R （A） is smaller than the number of the independent variables, equation（7） can only retain R （A） number of linear irrelevant equations and rid of others. When R（A） equals the number of the independent variables, there should be（Rj1, Rj2 ,RjL）=0. W bile in fact, （Rj1, Rj2 , RjS,RjL ） coexist in G0, G1, G2, Gk and cant be zero. Thus only R （ A）=1 number of linear irrelevant equations can be kept. （2） Discussion of soleness of branch linear equations solutionAfter removal of equations like 0 in equation（5），the number of the equations should be assumed to be bigger than the number of independent variables for equation（5） possibly still contain linear relevant equations. By further analysis of coefficient matrix rank and selecting n number of linear irrelevant cuit equations from equation（5），new equations are born:where, C=（Cij（s）nn is coefficient matrix ; R=（R1 , R2, Rn ）T is the resistance vector of branch to be solved; H=（H1, H2 ,Hs）T is the column vector of circuit airflow pressure. Explanation about building equations（8）The n number of elements of unknow n vector of equations CR=H correspond to n number of branch Resistances of basic network G0 and G0 can only create r0 （r0=n-m+1） number of independent circuit equations. Building n number of independent circuit equations requires airflow adjustment of basic network G0. After first alteration of some branch value, G0 can be changed into G0 and its net airflow volumes have to be reallocated. For the independent circuit equations after net airflow adjustment, if come circuit equations have resistance altered branch, then it cant join equation（8）.Due to the difference of airflow resistance of altered branch before or after adjusting, the altered branches putting in equation（8） means variables adding. So before next airflow adjustment, if possible, the airflow resistance of first adjusted branches should be restored to its original status to reduce the number of adjusted branches. Under permission of on the spot conditions, the adduced branches should be chosen in the branches which have better effect on net airflow volume distribution and this also become a factor causing equations（8） non-strangeness.During establishing equation（8），some similar and linear relevant rows of equations coefficient matrix should be avoided, otherwise liable to produce error or no solution. As demonstrated by Fig. 1, the complicated subsystems consist of many branches. Supposing in the beginning, the volume airflow rate of branch a, b, c are Qa0，Qb0 , Qc0; after first airflow adjustment of branch a, b, c，their volumes airflow rate are Qa1，Qb1 , Qc1; restore branch a to its former value and adjust airflow in branch b, the volume airflow rate of a, b, c are Qa2，Qb2 , Qc2. if Qc1 is very close to Qc2, the circuit coefficient matrix of the equations in those two adjustments are linear relevant very similarly. So to avoid this, we should adjust the branches whick can affect network volume greatly.Fig.1 Complicatde subsystemAirflow volume balance of the ventilation networkThe network airflow volume and fan working parameters by surveying of ventilation reports are influenced by some factors such as instruments precision, surveying technology and airflow flowing, so the on thespot airflow volume values cant well satisfy equations（2）.Thus the spot-surveying data cant act as the basic data to build equation（8） and should be redistributed at first.Assuming the spot-surveying airflow vector of the network is （ q1, q2, q3, qn）T the revised airflow of branches is Q=（Q1，Q2,., Qn）T and its solution method can refer to reference 3, 4. T hen the redistributed Q isWhere , Q=（Q1, Q2, Q3, Qn）T, m3/s.4 ConclusionsFor basic network graph G0 （referring to Fig.2（a） ），after tow times of airflow adjustments it can be changed into Fig.2（b） and 2 （c）.The branch airflow resistance and fan working parameters of every network figure Gs=（0, 1, 2） is known, at first we solve the network by D. Scott-F. Hinsley method and its results involving branch airflow volume and fan working points can act as the basic data for measuring airflow method. By comparison, we can see their solutions are cost the same and it manifest that airflow method is an effective way.Fig.2 Ventilation networks（2） Theoretically, proper airflow adjustment methods and accurate rneasuring data can ensure comparably results. But it should avoid some similar linear relevant vectors in built equations coefficient matrix or cause great error.（3） The differences between measuring airflow method and others are embodied in the original parametern, i.e. the measuring airflow method utilizes branch airflow volume and fan working points as its basic data, and these can be easily measured and obtained in ventilation reports. The key point of this method is to estahlish branch linear equations CR=H of basic network Go, and thus requires proper airflow volume adjustment of Go. On account of no permission of circuit equations containing adjusted branches in the equations, the smaller the number of adjusted branches the better. And the times of adjusting times. s is relative to the network structure, some measures as increasing resistance and decreasing resistance method can be taken when adjusting airflow resistance of branches.测风求阻法解算矿井复杂通风网路刘泽功（中国科技大学，合肥，230026，中国）目前广泛应用的解算矿井复杂通风网璐方法是以风网的各分支风阻值和扇风机工作特性参数作为解算基础数据，而获得风网各分支的风阻值是费时费力的。为此，本文提出了通过测算风网风量求分支风阻的方法解算矿井复杂通风网路。从理论上分析了以分支风阻为未知数的线性方程组建立过程及方程组解存在的唯一性。用BASIC语言编写了测风求阻法解算复杂通风网路的计算机程厅，并在超群386微机上通过。通过具体实例说明程序的实用性。该解算方法与其它解算方法不同的是本法以风网的风量和扇风机工况点作为解算网路的基础数据，对生产矿井的通风网路解算更能显示其优越性。主题词：通风阻力；风量；计算；电子计算机；风阻概 述对矿井复杂通风网络的解算，国内外的学者已进行了大量的研究，提出了不同的解算方法。经过多年的应用发现，目前较广泛使用的解算复杂通风网路方法的关键问题之一是对通风网路图G=（V，E） （V是节点的集合、V=E是边的集合、E=n）中的n条分支的风阻值R（固定风最分支除外）都必须确知，才能获得正确的解算结果。对于大型矿井通风网路中的分支少者几十条，多者几百条乃至上千条。要想确切地知道这些分支的风阻值，可靠的办法是进行阻力测定，这种处理方法虽然原理简单，但是，实施这种方法费时、费力，数据处理繁琐。因此，在对一个大型矿井通风网路解算之前，要做很多的准备工作和对网路图做必要的简化，才能保证解算结果的正确性。然而，生产矿井通风系统图中大部分巷道内的风量都要经常进行测量。所以，分支风量和风机工况点的获得是非常简单、方便的。既便是部分巷道内的通过风量没有经过测量或者无法进行测量，可以利用节点风量平衡定律或补测很容易获得。由于风量是指导通风管理必不可少的数据，因此，通风系统每进行一次调整，其大部分巷道内通过风量必须实测。鉴于生产矿井的风量数据十分丰富这一有利条件，本文提出了一种用分支风量和扇风机工况点作为基础数据解算矿井复杂通风网路的新方法测风求阻法。并编写了用计算机解算网路的解算程序。 1 基本定律与基本原理1.1基本定律1.1.1巷道通风阻力定律：在矿井通风学中，巷道的通风阻力定律为: 式中 h巷道通风阻力，Pa; R巷道风阻，kg/m7; Q巷道风量，m3/s。1.1.2 节点风量平衡定律：对于网路图中任一节点，都有下式成立:式中 i网路图的节点编号（i = 1, 2, 3,，m）; j网路图的分支编号（j = 1, 2, 3,，n）; Qij第j条分支风, m3/s； aij表示与第i号节点相连接的第j条分支的风向函数。第j条分支风流流入节点i第j条分支不与节点i相连第j条分支风流流出节点i1.1.3网孔风压平衡定律对网路图中任一闭合回璐，各种压力的代数和为零：式中 i回路编号（1=1, 2, 3, ，n-m+1）; j网路图的分支编号（j =1, 2, 3, ，n）; HFi第i回路中风机工作风压，Pa; HNi第i回路的自然风压，Pa; Rj分支j的风阻值，kg/m7 Qij通过分支j的风量，m3/s； b ij表示第i条回路中第j条分支的风向函数。回路i中第j条分支风向与回路方向一致第j条分支不属子回路i回路i中第j条分支风向与回路方向相反1.2基本原理 以通风网路的有向连通图G0=（V0, E0/|V0|=m，|E0|=n）作为基础网路图，把各分支的已知风量Qi（0） = （1, 2, 3,，n）作为基础数据，圈划独立回路，然后根据（3）式建立以分支风阻为未知数的线性方程组。由图论理论可知，对于有向连通图G0的独立回路个数为r0（ =n-m+1）12。因此，仅由图G0不能建立起n个独立回路方程。但是，生产矿井经常对通风系统进行调整，有时为了解算通风网路，在不影响生产的情况下，也可以而且必需人为地对通风系统进行调整。以G0作为基本网路图，通风系统进行第一次调整时，则G0变为G1=（V1,E1/|V1|=m1,|E1|=n1 ），此时各分支风量变为Qi（1） （i=1, 2, 3,., n1），独立回路方程个数r1 （=n1-m1+1）；作第二次调风时，网路变为G2=（V2,E2/|V2|=m2, |E2|=n2），分支风量为Qi （2） （i=1, 2, 3, ,nk），独立回路方程数为r2 （=n2-m2+1）; 。进行第k次调风时则网路图为Gk= （ Vk, Ek|Vk|=mk ,|Ek|=nk ），分支风量为Qik（i=1, 2, 3, ，nk ），回路个数为rk （=nk-mk+1）。对于基本网路图G0 r1，r2 ，.， rk回路方程中，对应有 r1, r2,，rk个回路方程含有被调阻分支，则在建立分支风阻回路方程组时，应首先将r （=r1+r2+r3+十rk）个方程从r（=r1+r2+r3+十rk）中剔除。对k的取值原则是保证r-rn。一般情况下，只要对网路图G0进行13次调风，建立起来的独立回路方程数就会超过未知数个数n。2数学模型的建立2.1 约定 通风网路图G0, G1,Gk相同两节点间分支表示同一条分支，即保证两节点间分支风阻值R不变， 对基本通风网路图Go实施网路解算;G0, G1,Gk 的节点集合Vs （s = 0, 1, 2,k）均相同，即无论通风系统如何调整，必须保证各通风网路图的节点编号完全一致; 各通风网路图相同两节点对应分支的编号要一致。2.2分支风阻线性方程组的建立根据（3）式，由图G0, C1, G2,GK圈划的独立回路建立的方程组如下:式中 bij（s）表示通风网路图Gs第i回路中，第j条分支的风向函数; Qij（s）表示通风网路图Gs第i个回路中，第j条分支的风量,Hni（s）通风网路图Gs第j条分支的风阻，Kg/m7 ；Hfi（s）网路图Gs第i个回路中风机的工作压力，Pa;HNi（s）网路图G s第i个回路中自然风压，Pa 。令Cij（s）=bij（s） Qij2（s），Hi（s）= HFi（s）+ HNi（s） 则（4）式变为：根据约定，对基本网路图G0进行解算，G0图中分支风阻完全包含在方程组（5）中。因此，从方程组（5）中求得的Ri（ i=1, 2, 3,n）中的任意一个若为零值或者不存在，则表明整个解无效。方程组（5）中含有n个未知数，r-r个回路方程，且r-rn，显然，只要从方程组（5）中取出n个线性无关的回路方程，即可获得唯一解。2.3方程组（5）解存在的唯一性讨论2.3.1方程组（5）的简化由通风网络理论可知通风网路图G0圈划的n-m+1个独立回路不可能所有回路内都含有压源H Fi，HNi，那么部分不含压源的回路方程的形式为:式中 s网路图编号（s=0,1, 2, 3, ，k ）; i表示图Gs的第i个独立回路。方程组（6）对（5）式的求解影响较明显。根据图论理论，对于有向连通图Gs=（Vs,Es/|Vs|=ms,|Es|=ns ）基本回路矩阵的秩为（ns-ms+1）。当s=0时，回路中所含分支相同且与（6）式同结构的方程最多会出现一次。所以，当s = 0, 1, 2,，k时，方程组（6）所含方程个数最多为k+1个。把（6 ） 式进行简化，则可用下列矩阵形式表示:式中（ Rj1, Rj2 ,RjL ） （R1 , R2 ,RS）对于方程组（7），当系数矩阵的秩R（A）小于未知数时，（7）式只保留R（A）个线性无关的方程，其余方程应剔除。当R（A）等于未知数个数时，则必有（Rj1, Rj2 ,RjL）=0事实上，（Rj1, Rj2 ,RjL）同时存在于G0, G1, G2, Gk中，则不能为0。因此，只保留R（A）-1个线性无关的方程，其余一个应剔除。2.2.3分支线性方程组解存在的唯一性讨论 方程组（5）中剔除了部分0型方程后，其内仍可能含有线性相关的方程，此时，还要保证剔除部分方程后的（5）式所含有的方程数大于未知数的个数。通过对方程组（5）的系数矩阵求秩分析，进一步从（5）式中找出n个线性无关的回路方程，形成一个新的方程组，即式中C=（Cij（s）nn 是系数矩阵；R=（R1 , R2, Rn ）T为分支风阻列向量，是待求未知数，H=（H1, H2 ,Hs）T 是回路风压列向量。2.4对建立方程组（8）的说明方程组CR=H中的未知向量R所含的n个元素与基本网路G0中的n个分支风阻是对应的。因此，仅由G0则只能建立r0=（n-m+1）个独立回路方程。为建立n个独立回路方程，必须对基本风网G0进行调风。当第一次改变某分支风阻值时，则G0变为G1,其风网的风量就要重新分配。对风网调风后形成的独立回路方程，当某一回路方程含有被调阻分支时，就不能放入（8）式中。由于调风前后，被调阻分支风阻值不同，如将含有被调阻分支放入（8）式，则又增加了一个未知数（未知风阻）。在需要进行下一次调风之前，若有可能，尽量把第一次调阻分支风阻恢复到原来状态，以减少被调分支数。被凋分支的确定，在现场条件允许下，应在对风网风量分配影响较大的分支内调节。这也是影响方程组（8）系数矩阵非奇的一个因素。关于调风次数确定的原则是保证方程组（8）系数矩阵C非奇。对于复杂通风网路的调风次数是由计算机根据系数矩.阵C是否非奇来确定的。在建立方程组（8）时，要避免所建立的方程组系数矩阵中的某些行非常近似的线性相关。否则其解算结果误差会很大，甚至无解。如图1所示，图中复杂子系统是由许多分支组成的复杂子风网。假设初始状态下，分支啊a,b, c的风量为Qa0，Qb0 , Qc0 ;在a分支内进行第一次调风，则分支a，b，c风量改变为Qa1，Qb1 , Qc1;将a分支风阻恢复到原来的风阻值，在b分支内进行二次调风，则分支a, b, c风量变为Qa2，Qb2 , Qc2。若Qc1和Q c2非常接近；即Qc1Q c2，则在这两次调风中，除了a,b分支风量变化外，其余所有分支风量也几乎不变。因此，由这两次调风建立起来的回路方程其系数是非常近似的线性相关。为了避免这种情况的出现，尽可能在对风网风量分配影响较大的分支内进行调节。 图13风网的风量平衡 由实测或由通风报表获得的风网风量和扇风机工作参数因受测量仪器精度、测试技术及风流动态等因素的影响，实测风量值不可能完全满足（2）式。因此，实测获得的数据还不能直接作为建立方程组（8）的基础数据，应首先对风网的实测风里进行平衡。设风网的实测风量向量为q=（ q1, q2, q3, qn）T，则分支风量修正量为Q=（Q1，Q2,., Qn）T，其求算方法见文献3、4。则平衡后的风量Q为：式中Q=（Q1, Q2, Q3, Qn）T, m3/s4结论 基本网路图G0见图2（a），对G0进行两次调风后的风网图分别为图2 （b），图2 （c）。通过分支气流抵抗和每个通风网络Gs=（0, 1, 2）的风扇运作的参量，以斯考德恒斯雷法解算结果中的分支风量和风机工况点作为测风求阻法解算网路的基础参数。用斯考德恒斯雷法解算的风量、风机工况点作为测风求阻法解算网路的基础数据，解算出的分支风阻和阻力与斯考德恒斯雷法解算网路所用的原始数据分支风阻及其娜算求得的分支阻力几乎完全相同。从而说明测风求阻法是解算复杂矿并通风网路的有效方法。图2（2）上述对测风求阻法解算复杂通风网路的可行性进行了理论分析。从理论上讲，只要调风方法适当，实测数据准确，测风求阻法解算通风网路的结果也是比较准确的。在应用此方法时，要避免所建立的方程组系数矩阵中的某些行非常近似的线性相关，否则其解算的结果误差会很大。（3）测风求阻法与其它解算方法解算通风网路的不伺点主要表现在原始参数不同，即测风求阻法把风网各分支风量和风机工况点作为解算通风网路的基础数据，这些数据可以很容易测得或从通风报表中获得。测风求阻法解算通风网路的关键是对基本网路图G0建立分支线性方程组CR=H。为建立此方程组，必须对基本网路图G0进行风量调节。因方程组不得含有被调阻分支存在的回路方程，所以，调风时被调阻分支越少越好。调风次数s与风网的结构有关。实施调风方采时，被调阻分支可采用增阻、减阻等调节措施。