CN106503363A - A kind of transient state unstable airflow computational methods of roadway containing high concentration gas - Google Patents

Abstract

Patent of the present invention discloses a kind of transient state unstable airflow computational methods of roadway containing high concentration gas, its computation model is made up of gas dispersion equation and roadway ventilation network equation, gas dispersion equation carries out finite difference using Crank Nicholson methods, obtains roadway point gas density using chasing method；Roadway ventilation network equation solves the air quantity (wind speed) of roadway branch using runge kutta method；Couple solution is carried out to two equations on this basis；Computation model of the present invention considers impact of the high concentration gas to roadway unstable airflow, it is achieved that the distinguished and admirable quantitative Analysis of the branch of roadway containing high concentration gas transient state.

Description

A kind of transient state unstable airflow computational methods of roadway containing high concentration gas

Technical field

The present invention relates to a kind of roadway transient state unstable airflow computational methods, more particularly to a kind of calculating is containing high concentration gas The method of roadway transient state unstable airflow.

Background technology

The high concentration gas stability distinguished and admirable to roadway produces certain impact；By taking coal and gas prominent as an example, work as protrusion After generation, high concentration gas accumulate in roadway, cause roadway wind current control, or even induce sending out for the secondary disasters such as gas explosion Raw.Forefathers have carried out more in-depth study to fire period roadway transient state unstable airflow, and main consideration is acted in fire heating air pressure Under, the distinguished and admirable infestation regularity of roadway.Zhou Yan, Wang Shengshen are respectively adopted static analysis method（Cloth Drake method）With dynamic-analysis method pair The critical condition of Parallel Airway During Mine Five in Ascensional Ventilation wind current control has carried out relative analyses；Zhang Xingkai, Wang Zhencai etc. are according to mine The distinguished and admirable flow performance of the combustion law and ventilating network of fire period, analyzes the distinguished and admirable transient of During Mine Fire Period Draught principle, establishes mine fire MATHEMATICAL MODEL OF COMBUSTION and distinguished and admirable unsteady flow equation group, and gives calculation method, with When by work out computer software achieve the simulation to mine fire combustion process and its distinguished and admirable change procedure.Gas air-flow exists Migration in roadway is transient state, and its impact distinguished and admirable to roadway branch is also dynamic.Chinese scholars are to containing highly concentrated at present Degree gas roadway transient state unstable airflow Journal of Sex Research is less, a kind of reliable computational methods of proposition of still needing.Result of study is anti-to mine Calamity rescue, catastrophe are divulged information and effectively prevent secondary disaster accident to be respectively provided with important theoretical and realistic meaning.

Particular content

A kind of in view of deficiency of existing computational methods, the invention provides transient state unstable airflow of roadway containing high concentration gas Computational methods, the method consideration high concentration gas impact distinguished and admirable to roadway branch transient state, can be realized using the computational methods Any roadway branch of ventilation network is solved in air quantity Changing Pattern not in the same time.

For solving above-mentioned technical problem, patent of the present invention is adopted the following technical scheme that：Its computation model is by gas dispersion side Journey

With roadway ventilation network equation

Constitute, wherein formula（1）Middle u_iFor the wind speed of roadway branch i, x_iIt is the space length along roadway branch i, t is the time, c_iFor The mash gas concentration of roadway branch i, E_xFor gas dispersion coefficient, formula（2）Middle q_k(k=1,2 ..., it is b) branch's air quantity, R_iFor Branch's i windages,For the ventilation blower blast of branch i,For the gas blast of branch i, c_jiFor circuit matrix, c_ikFor loop square Battle array c_jiTransposed matrix, wherein gas dispersion equation（1）Method for solving is that had initially with Crank-Nicholson methods Limit difference, then obtains roadway point gas density using chasing method, while roadway ventilation network equation（2）Method for solving is to adopt Runge-Kutta method solves the air quantity of roadway branch（Wind speed）, need to equation in solution procedure（1）And equation（2）Carry out coupling to ask Solution.

Described gas dispersion coefficient E_x, it is characterised in that gas dispersion coefficientWherein r is pipe half Footpath, α are coefficient of frictional resistance, and u is roadway branch airflow velocity.

Described branch's air quantity, it is characterised in that branch air quantity q_k(k=1,2 ..., b) it is parameter to be asked, and the time Function, i.e., required value is b unknown function, and b is the number of independent loop in ventilation network；q_kIt is that judge roadway is distinguished and admirable steady Qualitatively index, q_k=0 represents distinguished and admirable stagnation, q_k＜ 0 represents wind current control, q_k＞ 0 represents that wind direction keeps constant.

Described ventilation blower blast, it is characterised in that fan pressurea₀, a₁..., a_nFor curve Fitting coefficient；Given three or three blast with fan, air quantity data, solve fitting coefficient by method of least square.

Described gas blastCharacterized in that, For the average density of branch i, For t_nThe gas density of j-th spatial mesh size of moment branch, For t_nThe mash gas concentration of j-th spatial mesh size of moment branch, ρ_mAnd ρ_aThe density of respectively methane and air, h is space Step-length, L_iFor the length of roadway branch i, spatial mesh size numbers of the N (i) for branch i, z_iAnd z (0)_i(L_i) it is respectively the beginning of branch i End point absolute altitude.

Described gas dispersion equation（1）Method for solving, it is characterised in that entered using Crank-Nicholson methods Row finite difference, obtains tri-diagonal system, and distinguished and admirable flowing in ventilating system is one-dimensional incompressible flow, each in ventilation network Last spatial mesh size of tunnel is equal in the gas density of gas density moment back length with certain moment, and gas is released Mix with distinguished and admirable after putting immediately, and tunnel intersection each distinguished and admirable in gas be mutually mixed immediately, using chasing method solve three pairs Angle equation group, obtains roadway point gas density.

The method for solving of roadway ventilation network equation (2), it is characterised in that order Each variable is expressed as matrix form is：A=[a_jk], C= [c_ji], K=[k_ii], C^T=[c_ik], D=(D₁,D₂,…D_b)^T, q=[q₁,q₂,…,q_k]^T(k=1,2 ..., b), wherein k_ii= K_i, and A=CKC^T, formula（2）Being expressed as matrix form isFrom improved Euler's formula（Runge-Kutta method）Solve The air quantity of each roadway branch, on this basis, according to the basal area of roadway branch, draws the wind speed of roadway branch.

Need to equation in described solution procedure（1）And equation（2）Carry out couple solution, it is characterised in that to described Formula（1）And formula（2）Carry out couple solution, t₀The value of moment each parameter is, it is known that first solve formula（1）t₁Moment gas density, then will The value for solving substitutes into formula（2）Solve t₁Moment air quantity, the air quantity for obtaining substitute into formula（1）Solve t₂The gas density at moment, successively class Push away concentration distribution and the air force that each time step tunnel is obtained.

Description of the drawings

Fig. 1 is the transient state unstable airflow computational methods overall schematic of roadway containing high concentration gas of the present invention；

Specific embodiment

The embodiment of the present invention will be described in further detail below；Due to for any roadway branch, gas density Dispersion Equation is：Due to formula（1）Middle u and E_xNot constant, but the function of time, the model is Nonlinear partial differential equation, its analytic solutions are difficult to calculate, so numerical value of the present invention using the method calculating above formula of finite difference Solution；In the differential equation, replace partial derivative with difference coefficient, obtain corresponding difference equation, differential side is obtained by solving difference equation The approximation of journey solution.Before difference is carried out, each tunnel is temporally divided difference gridding with locus first.Assume tunnel Length is L, divides N sections interval along air flow in laneway direction, then every section of siding-to-siding block length h=L/N, x_jIt is that j-th spatial mesh size is saved away from beginning The distance of point, is expressed as jh；Time same time step τ demarcation interval will be pressed simultaneously, then t_nThe corresponding time at moment is n τ, adopts Use Crank-Nicholson difference schemes.For in roadway, gas density Dispersion Equation presses Crank-Nicholson form difference For

Abbreviation can be obtained：Wherein：

Gas dispersion model above is set up On the basis of single tunnel, and any one mine ventilation system all has multi-mine roadway perhaps, distinguished and admirable in each associated tunnel In migration process, branch has the continuous transmission of matter in front and back.It is thus desirable to setting up the network association of the gas density of each branch Model.For this purpose, assuming：1）In ventilating system, distinguished and admirable flowing is one-dimensional incompressible flow；2）In ventilation network, each tunnel is last One spatial mesh size is equal in the gas density of gas density moment back length with certain moment；3）Stand after gas release Mix with distinguished and admirable, and tunnel intersection each distinguished and admirable in gas be mutually mixed immediately.If according to above-mentioned it is assumed that ventilation network is total Branch's number is m, and the spatial mesh size number of i-th branch's division is N（i）, then in ventilation network, the gas density of any branch i can be pressed Following formula is calculated, i.e.,

In formula, i=1,2 ..., m；J=1,2 ..., N (i) -1.The arbitrarily gas density boundary condition of branch i is

In formula：Represent t_n+1The gas density of last spatial mesh size of moment branch i；Represent t_nMoment, branch i fell The gas density of second spatial mesh size of number；And Q_i' represent t respectively_n+1Moment, the unit bodies that branch i is flowed into by contiguous branch Product gas amount and unit volume air quantity.Obviously boundary condition will be obtained（5）, it is necessary to first solveAnd Q_i'.For this purpose, definition MatrixThe distinguished and admirable relation of branch i and branch k in ventilation network is represented, and

When, remember δ=1, represent the distinguished and admirable inflow branch i of branch k；When, remember δ=0, represent branch k's Distinguished and admirable outflow branch i or branch k and branch i is unconnected.Then have

In formula,Represent t_n+1The air quantity of moment branch k.By formula（6）And formula（7）Substitution formula（5）, obtain

As the present invention does not consider the changes of section in same tunnel, so for same tunnel its wind speed u and dispersion coefficient E_x Do not change with locus, be only the function of time.So A [x can be made_j]=a, B [x_j]=b, C [x_j]=c, D [x_j] =d_j, and

In formulaT is represented respectively_nThe airflow velocity and dispersion coefficient of moment branch i.For branch i, if t_nThe wind at moment SpeedAnd dispersion coefficient, it is known that a, b, c can be calculated then with reference to spatial mesh size and time step, while according to each in the branch The gas density of spatial mesh size, it can be deduced that d_j(2≤j≤N-1), and the gas density boundary condition according to branch i, can obtain Arrive t_n+1Gas density x of two step-lengths in the first end in moment tunnel₁And x_N, the data of 2≤j in tunnel≤N-1 spatial mesh sizes are substituted into Formula（3）And launch

Equation group is tri-diagonal system, can be solved with chasing method, so as to obtain t_n+1The each space steps of moment branch i Long gas density.Roadway ventilation network equation expression formula is：

Formula（2）Middle R_iFor branch's i windages,For the ventilation blower blast of branch i, can be obtained by fan performance curve Equation for Calculating Arrive；For the gas density in the gas blast of branch i, with roadway branch, the high difference correlation in tunnel.It is time and wind The function of amount, air quantity q_k(k=1,2 ..., b) it is parameter to be asked, and the function of time, i.e., required value is b unknown letter Number.Formula（2）Complex, it is difficult to directly which to be solved, it is therefore desirable to which is converted according to correlation values solution, this Invention uses improved Euler's formula（Runge-Kutta method）Method.Order

For convenience of solving, each variable is expressed as matrix form is：A=[a_jk], C=[c_ji], K=[k_ii], C^T=[c_ik], D= (D₁,D₂,…D_b)^T, q=[q₁,q₂,…,q_k]^T(k=1,2 ..., b), wherein k_ii=K_i, and A=CKC^T.So formula（2）It is expressed as Matrix form is

I.e.

By formula（11）The b independent differential equation can be listed, equation can be solved.Using finite difference calculus, from improved Euler Formula（Runge-Kutta method）Solve above formula and can reach enough precision.According to finite difference theory, first the time the same time will be pressed Step-length τ demarcation interval, then t_nThe corresponding time at moment is n τ.As the above analysis, formula（11）Actually air quantity is inclined Lead with regard to time and the function of primary branch air quantity, so q' can be expressed as_k=f_k(t,q₁,q₂,…,q_b) (k=1,2 ..., b), Then according to improved Euler's formulaCan obtain

f_k(t,q₁,q₂,…,q_b) (k=1,2 ..., expression formula b) should be with regard to time and the letter of each primary branch air quantity Number, so above formula correctly will be solved, needs its dependent variable to be converted into regard to time and the function of each primary branch air quantity.According to Derivation above, also includes each branch's fan pressure in the expression formulaWith gas blastTwo variables.The blast of blower fan can To be obtained by fan performance curve Equation for Calculating, what air pressure characteristics curve reflected is the relation of the blast with air quantity of ventilation blower. Following fitting of a polynomial generally can use：h_F=a₀+a₁q+a₂q²+a₃q³+...+a_nqⁿ, a in formula₀, a₁..., a_nFor curve matching system Number, q are blower fan place branch air quantity.The degree of polynomial of curve requires determination according to computational accuracy, gets 2 herein.I.e. h_F=a₀+a₁q+a₂q².In order to be fitted the active section of characteristic curve of fan, three point (q on its active section are given₁,h₁),(q₂, h₂),(q₃,h₃), substitute into above formula, you can obtain the linear equation containing three unknown numbers.Solve this Simultaneous Equations and can be obtained by wind Every fitting coefficient in pressure characteristic curve equation.

So for any branch i, if known blower fan place branch air quantity Q_i, then branch's fan pressureCan be expressed as：

Additionally, gas blast to be solvedThe average density of each branch's gas should first be calculatedI.e.

Due to the mixed gas that the gas is methane and air, so

In formula, M_iFor the air gross mass of branch i, kg；V_iFor the total air amount of branch i, m³；A_iFor the sectional area of branch i, m²；H is spatial mesh size, m；For t_nThe gas density of j-th spatial mesh size of moment branch, kg/m³；For t_nMoment branch's jth The gas density of individual spatial mesh size（Volume fraction）；ρ_mFor methane density, kg/m³；ρ_aFor atmospheric density, kg/m³.In formula (1) Speed u is calculated by air quantity q, and is solving formula using improved Euler's method（2）Formula is used during air quantity q again（1）In Concentration c, so the present invention is by formula (1) and formula（2）Carry out couple solution.t₀The value of moment each parameter is, it is known that first solve formula（1）t₁ Then the value for solving is substituted into formula by moment gas density（2）Solve t₁Moment air quantity, the air quantity for obtaining substitute into formula（1）Solve t₂When The gas density at quarter, the like i.e. be obtained each time step tunnel concentration distribution and air force.

Claims (8)

1. a kind of transient state unstable airflow computational methods of roadway containing high concentration gas, its computation model is by gas dispersion equation

$\frac{\∂c_i}{\∂t}+u_i\frac{\∂c_i}{\∂x_i}=E_x\frac{{\∂}^2{c}_i}{\∂x_i^2}---\left(1\right)$

With roadway ventilation network equation

$\underset{i=1}{\overset{m}{\Σ}}\[c_{ji}{K}_i\left(\underset{k=1}{\overset{b}{\Σ}}{c}_{ik}\frac{{\mathrm{dq}}_k}{dt}\right)\]=\underset{i=1}{\overset{m}{\Σ}}{c}_{ji}\left(h_{F_i}+h_{M_i}-R_i\left|\underset{k=1}{\overset{b}{\Σ}}{c}_{ik}{q}_k\right|\underset{k=1}{\overset{b}{\Σ}}{c}_{ik}{q}_k\right)---\left(2\right)$

Constitute, wherein u in formula (1)_iFor the wind speed of roadway branch i, x_iIt is the space length along roadway branch i, t is the time, c_iFor The mash gas concentration of roadway branch i, E_xFor gas dispersion coefficient, in formula (2)For branch's air quantity, R_iFor branch I windages,For the ventilation blower blast of branch i,For the gas blast of branch i, c_jiFor circuit matrix, c_ikFor circuit matrix c_ji Transposed matrix, wherein gas dispersion equation (1) method for solving is to carry out finite difference initially with Crank-Nicholson methods Point, then roadway point gas density is obtained using chasing method, while roadway ventilation network equation (2) method for solving is using dragon Ge-Ku Tafa solve the air quantity (wind speed) of roadway branch, need to carry out couple solution to equation (1) and equation (2) in solution procedure.

2. one kind roadway containing high concentration gas transient state unstable airflow computational methods according to claim 1, its feature exist In：Described gas dispersion coefficientWherein r is pipe radius, and α is coefficient of frictional resistance, and u is roadway branch Wind speed.

3. one kind roadway containing high concentration gas transient state unstable airflow computational methods according to claim 1, its feature exist In：Described branch air quantity q_k(k=1,2 ..., b) it is parameter to be asked, and the function of time, i.e., required value is that b is individual unknown Function, b are the number of independent loop in ventilation network；q_kBe pass judgment on roadway unstable airflow index, q_k=0 represents distinguished and admirable stopping Stagnant, q_k＜ 0 represents wind current control, q_k＞ 0 represents that wind direction keeps constant.

4. one kind roadway containing high concentration gas transient state unstable airflow computational methods according to claim 1, its feature exist In：Described ventilation blower blasta₀, a₁..., a_nFor curve matching coefficient；Given three or three with The blast of fan, air quantity data, solve fitting coefficient by method of least square.

5. one kind roadway containing high concentration gas transient state unstable airflow computational methods according to claim 1, its feature exist In：Described gas blast For the average density of branch i, For t_nMoment point The gas density of j-th spatial mesh size is propped up, For t_nJ-th sky of moment branch Between step-length mash gas concentration, ρ_mAnd ρ_aThe density of respectively methane and air, h is spatial mesh size, L_iFor roadway branch i's Length, spatial mesh size numbers of the N (i) for branch i, z_iAnd z (0)_i(L_i) it is respectively the whole story node absolute altitude of branch i.

6. one kind roadway containing high concentration gas transient state unstable airflow computational methods according to claim 1, its feature exist In：The method for solving of gas dispersion equation (1) carries out finite difference using Crank-Nicholson methods, obtains three pairs Angle equation group, distinguished and admirable flowing in ventilating system is one-dimensional incompressible flow, and last is empty for ventilation network Zhong Ge roadways branch Between step-length equal in the gas density of gas density moment back length with certain moment, gas release after immediately with distinguished and admirable Mixing, and tunnel intersection each distinguished and admirable in gas be mutually mixed immediately, using chasing method solve tri-diagonal system, obtain well Lane branch gas density.

7. one kind roadway containing high concentration gas transient state unstable airflow computational methods according to claim 1, its feature exist In：The method for solving formula (2) of described roadway ventilation network equation (2), order Each variable is expressed as matrix form is：A=[a_jk], C= [c_ji], K=[k_ii], C^T=[c_ik], D=(D₁,D₂,…D_b)^T, q=[q₁,q₂,…,q_k]^T(k=1,2 ..., b), wherein k_ii= K_i, and A=CKC^T, formula (2) is expressed as matrix form and isSolved from improved Euler's formula (Runge-Kutta method) The air quantity of each roadway branch, on this basis, according to the basal area of roadway branch, draws the wind speed of roadway branch.

8. one kind roadway containing high concentration gas transient state unstable airflow computational methods according to claim 1, its feature exist In：Need to carry out couple solution, t to equation (1) and equation (2) in described solution procedure₀The value of moment each parameter is, it is known that first ask Solution formula (1) t₁Then the value for solving is substituted into formula (2) and solves t by moment gas density₁Moment air quantity, the air quantity for obtaining substitute into formula (1) t is solved₂The gas density at moment, the like i.e. be obtained each time step tunnel concentration distribution and air force.