CN102539177A - Method for testing property of cooling tower - Google Patents

Abstract

The invention discloses a method for testing the property of a cooling tower. The method comprises the following testing steps of: I, based on a cooling property equation N'=A lambda<m>, establishing a new property equation mode being N<0>=A lambda<m>q<o>tl<p>(delta t/(t2-tau))a; II, selecting testing items, including heat radiation and disperse medium total coefficient of packing, inlet water temperature, atmospheric temperature, packing density and influence of an operation interval of the cooling tower to the cooling property; III, selecting an orthogonal test table L9(3<4>), and respectively testing steam-water ratio lambda, packing density q, tower-inlet water temperature t1 and tower-inlet wet bulb temperature tau1; and IV, analyzing to obtain the primary and secondary sequence of factors influencing the cooling property, and working out a new cooling property equation by adopting multiple regression. The method disclosed by the invention has the credibility being more than 95% weight respect to test of the property of the cooling tower, is low in error and greatly improved in design precision, and provides a more correct instructive method for designing the cooling tower reasonably.

Description

A kind of method of testing the cooling tower characteristic

Technical field

The invention belongs to the refrigerator technical field of measurement and test, be specifically related to a kind of method that adopts the characteristic of multiple regression analysis and orthogonal design test cooling tower.

Background technology

Along with commercial production is flourishing day by day, human society urbanization progress is constantly quickened, water requirement heightens, and causes the in short supply day by day of water resource, and especially industry water consumption such as electric power, iron and steel, petrochemical industry, weaving are huge.For example the power station cooling water inflow of gigawatt is approximately 35m ³/ s, crude oil water 20～40m ³/ ton oil, the about 500～1200m of ethene cooling water inflow ³/ ton ethene, the synthetic ammonia water is 600～1900m ³/ ton ammonia, the annual water consumption of certain petro-chemical corporation reaches 1,500,000,000 meters ³The consumption of whole world cooling circulating water is huge, wastes also very surprisingly, exists considerable saving potentiality; In industrial processes, singly be that used heat is brought cooling tower into through hot water, reuse after cooling can be saved the demand of the water resource about 95%, its adverse effect to environment of corresponding reduction.In the age of this " low carbon emission reduction ", cycling use of water is the energy-saving and emission-reduction effective way.The circulating water cooling tower use is wide, amount is big, is widely used in each industrial sector and air conditioner refrigerating covil construction.Therefore strengthen research and improvement to cooling characteristics, improve constantly cooling tower efficient, energy consumption, noise, the minimizing that reduces self waftd and dripped loss, reduces environmental pollution, has direct meaning.

Prior art has accumulated rich experience for the characteristic research of cooling tower; And the experimental formula that differs from one another has been proposed: the empirical equation that at first is nineteen twenty-five your (Merkel) utilization heat and mass transfer process of Mike; Having set up is the famous heating power calculating fundamental equation of expulsive force with the enthalpy difference; But there are bigger ambiguity in method for solving, especially its applicability of your equation of Mike, so that there is bigger error in practice result; Other Germania thinks that the evaporated water that you ignore by Mike and error that not very possibly cause very little of heat of taking away thereof reach 4～7%, introduce a correction factor K so should not ignore this; Bake and Ma Te (Baker&Mart) propose, and the hot water inflow temperature is significantly to the adverse effect of characteristic, introduce water temperature correction factor M for round-off error, and when the hot water temperature rose to 80 ℃, this scheme still can obtain satisfied result; There was the scholar to pass through thermodynamic property test afterwards, set up new expression formula N=(1.28-0.027q) the * λ of cooling characteristics and gas-water ratio filler ^0.37, this shows that cooling characteristics N is not only the single-valued function of steam-water ratio λ, spray density q is also influential to cooling characteristics.Individual other achievement in research and conclusion (of pressure testing) are beneficial to the objective intension that discloses cooling characteristics all sidedly, lay a good foundation for setting up the new expression formula of cooling characteristics, thereby are that the characteristic that designs, tests heat interchanger more exactly provides foundation.But in the actual motion and characteristic test of cooling tower, find that above-mentioned each expression formula exists to be suitable for interval narrow, defective that error is big, therefore be necessary cooling tower characteristic test and expression formula thereof are continued that research improves and perfect.

Summary of the invention

The technical issues that need to address of the present invention are; Overcome prior art deficiency, exploratory development cooling tower characteristic, analytical error produce reason, improve experiment condition testing program and data preparation method; It is less to set up an error; Can demonstrate fully the mathematical model of cooling characteristics, a kind of method of testing the cooling tower characteristic is provided, the theoretical foundation of directiveness more accurately is provided for improving the cooling tower performance.

One, cooling tower heating power calculates the foundation of fundamental equation and the approximation of existence thereof:

The empirical equation of nineteen twenty-five Mike's that utilization heat and mass transfer process; Having set up is the famous heating power calculating fundamental equation of expulsive force with the enthalpy difference; Make contribution for the cooling tower cooling theory is applied to engineering design, be still the foundation of the research of cooling tower industry, practice and standard so far.But in its derivation, done some necessary hypothesis and simplification, must also can cause certain error, made the heating power accounting equation become approximate equation, and the approximation of remote-effects cooling tower cooling characteristics, be summarized as follows:

1. transmission of heat by contact: heat transfer capacity dQ _α(t-θ) is directly proportional with temperature difference expulsive force

dQ＝α(t-θ)dV Kcal/m ³/h (1-1)

2. liquid surface evaporation: the poor (P of evaporation capacity dL and partial pressure _t" P _θ) be directly proportional

dL＝Kp(Pt”-P ₀)dV kg/m ³/h (1-2)

In the formula: Pt " be the saturated steam partial pressure of t for water temperature

P θ is the steam partial pressure under the soft air temperature θ

Matter coefficient k g/m looses on surface when Kp is corresponding with the partial pressure difference ²

Because Pt "=X _t"/(X _t+ 0.622) * P _B≈ X _t* 1.61P _B(1-1.61X _θ")

P _θ＝X _θ/(X _θ+0.622)*P _B≈X _θ*1.61P _B(1-1.61X _θ”)

Substitution (1-2):

dL＝1.61P _B*Kp{(Xt”-X _θ)-1.61 ²*P _B[(Xt”) ²-(X _θ) ²]}dV

Having ignored the trace in the bracket can be similar to:

dL＝1.61P _B*Kp(Xt”-X _θ)dV (1-3)

Other is Ka=1.61*P _B* K _P

Then dL=Ka (Xt "-X _θ) dV (1-4)

By evaporation institute energy delivered be:

dQ _k＝(r ₀+C _nt)*dL

＝Ka(X _t-X _θ)(r ₀+C _nt)dV (1-5)

In the formula: r ₀Be the latent heat of vaporization r of water at 0 ℃ ₀=595kCal/kg

Cn is the desirable Cn=0.47kCal/kg of the specific heat at constant pressure of water vapor ℃

3. total heat transfer capacity dQ

dQ＝dQ _α+dQ _k＝α*(t-θ)dV+Ka(X _t-X _θ)(r ₀+C _nt)dV

Because r ₀+ C _nT=r _t+ C _nt

dQ＝Ka*dV{α/Ka(t-θ)+r ₀Xt”-r ₀X _θ+C _nt(Xt”-X _θ)}

If Lewis (Lewis) is several α of being/(Cp*Ka)=1 reaches

I=C _p* θ+r ₀* X ₀And i "=C _p* t+r ₀* Xt "

Put in order:

dQ＝Ka(i”-i)dV+C _ntdL (1-6)

If dL=0 then

dQ＝Ka(i”-i)dV (1-7)

4. thermal balance equation:

L*dt＝Ka(i”-i)dV (1-8)

You calculate fundamental equation by heating power the famous Mike of variables separation

$\mathrm{KaV}/L={\&Integral;}_{t2}^{t1}\frac{\mathrm{dt}}{i\&prime;\&prime;-i}---(1-9)$

KaV/L is called cooling characteristics and uses N ' expression

is called the evaporation characteristic number and representes with N

When counting evaporated water dL ≠ 0, and Lewis number α/(Cp*Ka) ≠ 1 o'clock, the heating power accounting equation did more accurately

${\&Integral;}_{t2}^{t1}\frac{\mathrm{Ldt}}{(i\&prime;\&prime;-i)+(\mathrm{\&alpha;}/(\mathrm{Cp}*\mathrm{Ka})-1)\mathrm{Cp}(t-\mathrm{\&theta;})}+{\&Integral;}_{L2}^{L1}\frac{\mathrm{tdL}}{(i\&prime;\&prime;-i)+(\mathrm{\&alpha;}/(\mathrm{Cp}*\mathrm{Ka})-1)\mathrm{Cp}(t-\mathrm{\&theta;})}=\mathrm{KaV}/L---(1-10)$

You have made following hypothesis Mike in the theoretical derivation of its heating power calculating fundamental equation:

When (1) the air water contact and evaporating is cooled off, suppose that evaporated water dL is very little, can ignore (being dL=0) just obtains formula (1-8)

As when counting the heat that evaporated water takes away, the heat that air is taken away can increase, and its balance equation can be expressed as:

Gdi＝Ldt+ΔLt ₁ (1-11)

Transplant dt/di=L/G+t1/G* Δ t/t1

＝1/λ(1+t1/L*ΔL/Δt)

λ is a gas-water ratio in the formula

The t1 inflow temperature

The L quantity of circulating water

Δ L evaporated water

The Δ t temperature difference

In the early stage magazine of Japan " air-conditioning and health brief guide ",, wherein proved when temperature difference t is big the influence that Mike's that has omitted evaporated water about the cooling tower design; And the error ratio of equation is bigger; If t1=55 ℃, Δ t=20 ℃, the cooling number of trying to achieve big approximately 4%; Design the height that cooling tower will reduce cooling tower in view of the above, say it is dangerous from security standpoint.Except, can find to ignore evaporated water from equation (1-10) and simplify thermal balance equation again and also can cause 4～5% error, this point tends to out in the cold.

Heat and mass complexity of calculation in the tower is thought heat transfer coefficient and mass transfer coefficient Ka on the surface of contact, and the specific heat of heat of vaporization r0 and soft air all is constant, Mike you when setting up fundamental equation, introduced Lewis's coefficient relational expression:

α/Ka＝Cw≈1.05 [kJ/kg℃] (1-12)

Formula (1-11) shows: there are analogy relation in heat interchange and mass exchange, are similar to the specific heat Cw of soft air, and are approximately equal to 1.But heat exchange coefficient α and matter exchange coefficient Ka can only try to achieve through test, and many tests find that Different researchers obtains different results under the Different Boundary test condition:

α/β x ≈ 0.265～0.27 (Japan)

α/βx≈0.213～0.221 (Merkel)

α/β x ≈ 0.9 (institute of water section of the Chinese Academy of Sciences)

α/β x ≈ 0.357～1.03 (other Germanias)

The introducing of Lewis's scale-up factor also is one of reason of your equation approximation of Mike, and is less because of the numerical value of Lewis's scale-up factor own, is generally 0.8～1.3.The error that causes and little (being about 1.2%).But visible by equation (1-10): because set α/(Cp*Ka)=1, then in the sign of integration [α/(Cp*Ka)-1] Cp (t-θ) is zero, i.e. (t-θ) this influence has been left in the basket, and is when t-θ is big, very important to the influence of evaporation characteristic number N.You make hypothesis and it can also be seen that the evaporative cooling characteristic number is except that enthalpy difference i from Mike in a word "-i influence 4 factors in addition:

1. atmospheric pressure P _B

2. temperature θ

3. water temperature t1

4. relative humidity φ (test confirms that the relative humidity influence is less, can ignore)

You are made many errors of supposing that peace treaty causes surely in time of setting up fundamental equation to have proved Mike in " adopting temperature correction coefficient to eliminate the theoretical approximation of Merkel " (being translated from " Journal of Cooling Tower institute V&N1988 " by yellow tin Yue); Though some error wherein is not a simple superposition; Some factors are compensated to each other; But will be similar to equation (1-9) and more accurately equation (1-10) make comparisons; Difference differs greatly under the identical situation of temperature conditions, even 37.7 ℃ of differences of temperature surpass 10% usually.When water temperature is 83 ℃, when temperature was 26.6 ℃, difference was up to 20%.Understand the process that fundamental equation develops, analyze and produce reasons of error, can help our objective understanding cooling characteristics (N '), analyze and research and improve it.Cooling tower ordinary test method does not adopt orthogonal experiment design method at present, and shortcoming is to cannot analyse the factor of influence of cooling tower characteristic, and influences each factor importance of cooling tower characteristic.The cooling tower test data analyzer is to adopt least square method at present, and this analytical approach is applicable to the data processing of single factor of influence.

Two, cooling characteristics and influencing factors analysis thereof:

Cooling tower heating power calculates fundamental equation (1-9) left end and is referred to as cooling characteristics, characterizes the height of cooling tower cooling power, and domestic custom is called cooling number or heat interchange number, that is:

N’＝KaV/L (1-13)

Ka claims β xv again in the formula, characterizes the diffusing matter overall coefficient of heat radiation of packing, has represented the height of filler heat and mass ability, can only try to achieve through test.See the cooling characteristics of cooling tower from the funtcional relationship of equation: after water yield L and packing volume were confirmed, cooling characteristics was directly proportional with Ka, and emphasis is studied packing property Ka exactly when studying cooling characteristics.With reference to the criteria equation Nu=C*Pr in the thermal conduction study ^m* Re ⁿPattern has been set up the expression formula of Ka

Ka＝Bg ^mq ⁿ (1-14)

G in the formula---ventilation density

Q---spray density

B---test constant

M, n---the index that test is tried to achieve

Formula (1-14) substitution formula (1-13) is got

N’＝Bg ^mq ⁿ*F*H/(F*q)＝BHg ^mq ^n-1＝BH(g/q) ^m*q ^m+n-1 (1-15)

H packed height m in the formula

The net sectional area m2 of F filler

Setting m+n=1 makes A=BH that λ=g/q then has

N’＝Aλ ^m (1-16)

This formula is exactly present widely used cooling tower characteristic approximate expression, and this expression formula shows the just single-valued function of gas-water ratio λ of cooling characteristics N '.A large amount of in fact test findings prove that the cooling characteristics that the filler of same specification obtains is different under the different test parameters condition of identical testing equipment, error ratio is bigger; Sometimes differ nearly one times; So the research cooling characteristics is asked for the new expression formula of cooling characteristics, it is extremely urgent to improve precision.

Influence the factor of cooling characteristics N ' or Ka:

Find that in process of the test corresponding one group of cooling condition can be in the hope of a specific cooling characteristics, cooling characteristics is not only the single-valued function of gas-water ratio, and it is also relevant with factors such as atmospheric pressure, spray density, dry-bulb temperature, inflow temperatures.

(1) influence of inflow temperature t1:

Can influence the fact of cooling characteristics to numerous factors, calculate through the discriminant analysis of positive quadraturing design test method and show that inflow temperature t1 is tangible to the influence of cooling characteristics." evaporative cooling of recirculated water " by the other Germania of the Soviet Union of people such as Hu Lunzhen translation is referred to as hot water temperature's influence " hot water effect " and introduces correction factor M; Be called Mike's that correction factor; And point out to be increased to more than 40 ℃ when water temperature, you can produce Mike than mistake by equation.In addition, pretty one, the grand test findings in middle village of hand mound provides into the water temperature to the formula that influences of packing property in " cooling tower " (1 day November calendar year 2001 of Zhao Zhen state water conservancy and hydropower publishing house):

$\mathrm{\&beta;xv}=B*q^m*g^{n^{*}}{(t1/40)}^{-0.45}---(1-17)$

The fact that we adopt multiple-factor can influence cooling characteristics is carried out discriminant analysis through the positive quadraturing design test method, has also proved the existence of t1 influence.

(2) influence of atmospheric temperature (dry bulb and wet bulb):

N.W Kerry (Kelly), Ge Gangchang are male, the total heat radiation of the filler matter overall coefficient Ka value of loosing is thought in the pretty first-class people's of hand mound test; The influence that not changed by the atmosphere wet bulb; Reflect in this test air themperature θ, relative humidity φ, atmospheric pressure especially (t1-θ) influenced the calculated value of evaporation characteristic number; Nature can influence cooling characteristics, just influences less.

(3) influence of spray density:

Spray density is the function of packing property, i.e. Ka and q ⁿBe directly proportional, though summarized this factor in the characteristic equation of tower, it is with the embodied of gas-water ratio.The factor degassed water of from the lot of test data, finding to influence cooling characteristics is than outside the λ, and spray density also has certain influence.Did demonstration in " the enthalpy difference power that cooling tower heating power calculates is theoretical " (First Machinery Industry Department's the tenth designing institute's Li Ning a beautiful gem is write), m+n ≠ 1 (＞1), equation (1-15) becomes:

N＝A*λ ^mq ^m+n-1 (1-18)

This explanation N～λ relation is not simple straight line, and spray density is different, and family curve is also had any different.

(4) the cooling tower traffic coverage is to the influence of cooling characteristics:

The state of atmosphere is the environment at evaporative cooling process place; It with area, height above sea level, season, change round the clock and change; Turnover water temperature and corresponding wet-bulb temperature constitute the interval of cooling procedure; Coolant water temperature t2 is then closely related with atmospheric condition, and therefore different cooler environments can obtain different characteristic.Cooling characteristics curve according to test is set up has just limited its any application.

Existing characteristic equation N '=A λ ^mError analysis:

This equation shows that cooling number is the single-valued function of λ, and it is to carry out statistical study according to experimental data by least square method, Coefficient m of trying to achieve and A.Owing to ignored many factors that influences cooling number, caused error ratio to see for details more greatly like following table 1:

In the table:

Formula 1 (being existing computing formula): N '=A λ ^m

Coefficient N is in the table: N=1.06 λ ^0.4395

Formula 2 (being the formula of present technique scheme): ζ=(Δ t/ (t2-τ))

Coefficient N is in the table: N=8.25* λ ^0.62* q ^-0.165t ₁ ^-0.365* ζ ^0.236

Table 1 (1) filler A performance test is summary sheet (H=0.915m) as a result

Table 1 (2) filler A performance test is summary sheet (H=0.915m) as a result

75 groups of test sample data statistic analysis are learnt when the given level of signifiance (α=0.05), λ and N have correlativity (related coefficient is about 0.53～0.7) preferably.But standard deviation, the coefficient of variation all bigger (detailed calculated slightly).It is thus clear that empirical equation N '=A λ ^mIt is not optimal equation.

The objective of the invention is to be achieved through following technical proposals:

A kind of method of testing the cooling tower characteristic comprises the steps:

I. with existing cooling characteristics equation N '=A λ ^mBe the basis, the pattern of tentatively setting up new characteristic equation is N ⁰=A λ ^mq ^ot ₁ ^p(Δ t/ (t ₂-τ)) ^aIn the formula, λ is a steam-water ratio, and q is a spray density, kg/m ²H; t ₁Be inflow temperature, ℃; Δ t is the cold width of cloth, ℃; t ₂Be leaving water temperature, ℃; A is a coefficient, and m, o, p, a are index;

II. selected test event: the heat radiation of the packing matter overall coefficient Ka that looses, kg/m ³H; Inflow temperature t ₁, ℃; Atmospheric temperature (dry bulb and wet-bulb temperature); Spray density q, kg/m ²H; The cooling tower traffic coverage influences cooling characteristics, i.e. environmental efficiency coefficient η=Δ t/ (t ₂-τ);

The definition air-circulation features is counted N '=KaV/L, and in the formula, V is packing volume m ³, L is quantity of circulating water m ³/ s calculates fundamental equation according to your heating power of Mike,

The latter is called evaporation characteristic number N;

III. select positive quadraturing design test table L for use ₉(3 ⁴) (four factors, three levels), respectively to steam-water ratio λ, spray density q, advance tower water temperature t ₁, advance tower wet-bulb temperature τ ₁Test;

IV. analyzing to draw influences the factor of cooling characteristics primary and secondary and is followed successively by λ → q → t in proper order ₁→ η adopts multiple regression procedure to try to achieve the new equation of cooling characteristics.

Gather great number tested data through orthogonal test and know, after water yield L and packing volume V are definite, cooling characteristics N ⁰Diffusing matter overall coefficient Ka is directly proportional with the heat radiation of packing; The ratio of definition ventilation density and spray density is gas-water ratio λ; The measured value and spray density coefficient q, inflow temperature t1 and the environmental efficiency coefficient η that confirm steam-water ratio λ, atmospheric temperature (dry bulb and wet bulb) are directly related with the cooling tower cooling characteristics, and the correlation factor primary and secondary is followed successively by λ → q → t in proper order ₁→ η; The employing multiple regression procedure is tried to achieve new equation and is done

N ⁰＝A＊λ ^m＊q ⁿ＊t ₁ ^p＊η ^c；

In the formula

N ⁰---cooling characteristics;

λ---gas-water ratio;

Q---spray density, kg/m ²H;

T1---inflow temperature, ℃;

η---environmental efficiency coefficient, η=Δ t/ (t2-τ).

The confidence level of this expression formula is more than 95%, and error is little, and has improved design accuracy greatly.

The invention has the beneficial effects as follows:

The present invention has at first proved the approximation that the cooling tower characteristic exists; Adopt orthonormal design of experiments method and multiple regression procedure then; Try to achieve this model of new mathematics of test cooling tower characteristic, the present invention tests the confidence level of cooling tower characteristic more than 95%, and error is little; And having improved design accuracy greatly, the present invention provides guiding more accurately method for the appropriate design cooling tower.

Following content is selected from " orthogonal design " Peking University mathematics mechanical system probability statistics group and is compiled Beijing: Chemical Industry Press, 1976.

Orthogonal design method is introduced:

(1), in scientific experimentation, often run into test findings and receive influence of various factors, will make of the influence of each factor like this clear to test findings; Distinguish whose main whose time of factors; Understand fully the relation between them, if factor is a lot, and every kind of factor has multiple level again; What tested number can be very so is big, obviously can not each test all do.Can reduce test number (TN) significantly and can not reduce the method for testing confidence level is exactly orthogonal design.

(2), orthogonal design brief introduction

The result that test need to be investigated is called index, and those maybe be influential to test findings (being index), and has proposed in test the factor that clear and definite condition contrasts and be called the factor.Each actual conditions that each factor will contrast in test is called its each level.If have five factors in a problem, each factor all is two levels, so call five factorial experiments of two levels to it, brief note 2 ⁵The type test.

Carry out orthogonal test, at first need select one and the corresponding orthogonal table of experimental factor level, had the mathematician to make a lot of corresponding tables, as long as find need just passable.So-called orthogonal table, the ready-made testing program of a cover just through carefully calculating, when testing, matching each other with those several levels makes an experiment the test number (TN) after the overall test number of times of scheme is all considered much smaller than every kind of situation at every turn.Just have only 9 row such as 3 levels, 4 factor tables, much smaller than traveling through 81 times that test.

(3), the statistical study of orthogonal design

In multifactor contrast test, speak of the size of factor pair index influence, always be meant when this factor is in different horizontal the size of test findings difference.Therefore for two horizontal factor,, just say that the influence of this factor pair index is bigger if the mean value of two horizontal corresponding datas differs bigger.For the multilevel factor also is the same, if the difference between the data mean value is bigger under its each level, just says that the influence of this factor pair index is bigger; Otherwise,, just say that this factor pair index influence is less if these mean value difference are little.Therefore, the size of factor pair index influence be investigated, its multilevel degree of scatter of data mean value down can be seen.Generally speaking, these mean values distribute to such an extent that relatively disperse, and just we can say that its influence is bigger, and mean value is more concentrated, just we can say that its influence is smaller.

Generally with mean value of this group number as one " benchmark ", regard the difference of each number and mean value in the group as this number " departing from " to " benchmark ".All " departing from " gather, and have just depicted the degree of scatter of this group number.But,, so can not be easily when gathering them one add and get over, and want first square, and then add up because " departing from " always has and just having negatively.The quadratic sum of one group of number " departing from ", promptly the quadratic sum of the difference of one group of number and its mean value is called the deviation of this group number.The size that compares two groups of number degrees of scatter is as long as compared the size of their deviations.

Table 2 L ₉(3 ⁴) test result and analysis

The deviation of the average in the reckoner under three levels of factors A:

Get their average (average of total data just) (I earlier _A+ II _A+ III _A)/9=T/9 calculates the corresponding data mean value of each level and the deviation of this benchmark then as a benchmark:

I _A/3-T/9

II _A/3-T/9

III _A/3-T/9

As previously mentioned, these three quadratic sum (I that depart from _A/ 3-T/9) ²+ (II _A/ 3-T/9) ²+ (III _A/ 3-T/9) ²Be exactly the deviation between the data mean value under three levels of factors A, the deviation that in like manner can try to achieve data mean value under factor B, three levels of C is respectively:

(I _B/3-T/9) ²+(II _B/3-T/9) ²+(III _B/3-T/9) ²

(I _C/3-T/9) ²+(II _C/3-T/9) ²+(III _C/3-T/9) ²

Compare three deviations obtaining, deviation is big more, explains that then the influence of certain factor pair index that deviation is corresponding is big more.

Multiple regression analysis:

In production and scientific research, people often run into various variablees.These variablees connect each other, interdependence, that is to say the certain relation of outwardness between them.In order to understand the essence of things in depth, often need set up the relational expression between various variablees quantitatively, handle this type problem and will use multiple regression analysis.

Its analysis principle is following:

Consider k+1 amount

x ₁, x ₂..., x _kAnd y

Total N group trial value

x ₁₁，x ₂₁，......，x _k1；y ₁

x ₁₂，x ₂₂，......，x _k2；y ₂

x _1N，x _2N，......，x _kN；y _N

So-called multiple linear regression is looked for y and x exactly ₁, x ₂..., x _kBetween linear relation

y＝b ₀+b ₁x ₁+b ₂x ₂+...+b _kx _k

Ask the coefficient b in the formula (2-58) with least square method ₀, b ₁, b ₂..., b _kThat is to say, if:

${\hat{y}}_i=b_0+b_1{x}_{1i}+b_2{x}_{2i}+...+b_k{x}_{\mathrm{Ki}},$ I=1,2 ..., N so, will confirm b exactly ₀, b ₁, b ₂..., b _kSo that

$Q=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(y_i-{\hat{y}}_i)}^2=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(y_i-b_0-b_1{x}_{1i}-b_2{x}_{2i}-\&CenterDot;\&CenterDot;\&CenterDot;-b_k{x}_{\mathrm{ki}})}^2$

Reach minimum value.Can know these b through mathematical derivation _iShould satisfy system of equations

$\left\{\begin{array}{c}{l}_{11}{b}_1+l_{12}{b}_2+...+l_{1k}{b}_k=l_{01}\\ l_{21}{b}_1+l_{22}{b}_2+...+l_{2k}{b}_k=l_{02}\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\\ b_{k1}{b}_1+l_{k2}{b}_2+...+l_{\mathrm{kk}}{b}_k=l_{0k}\end{array}\right.$

And $b_0=\stackrel{\&OverBar;}{y}-\underset{p=1}{\overset{k}{\mathrm{\&Sigma;}}}{b}_p{\stackrel{\&OverBar;}{x}}_p$

Wherein:

$l_{00}=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(y_i-\stackrel{\&OverBar;}{y})}^2=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_i^2-\frac{1}{N}{\left(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_i\right)}^2$

$l_{01}=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(x_{1i}-{\stackrel{\&OverBar;}{x}}_1)(y_i-\stackrel{\&OverBar;}{y})$

$l_{02}=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(x_{2i}-{\stackrel{\&OverBar;}{x}}_2)(y_i-\stackrel{\&OverBar;}{y})$

$l_{0k}=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(x_{\mathrm{ki}}-{\stackrel{\&OverBar;}{x}}_k)(y_i-\stackrel{\&OverBar;}{y})$

$l_{\mathrm{pq}}=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(x_{\mathrm{pi}}-{\stackrel{\&OverBar;}{x}}_p)(x_{\mathrm{qi}}-{\stackrel{\&OverBar;}{x}}_q)$

(p，q＝1，2，......，k)

And ${\stackrel{\&OverBar;}{x}}_p=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_{\mathrm{Pi}}$ (p=1,2 ..., k)

$\stackrel{\&OverBar;}{y}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_i$

Total change quadratic sum l of y ₀₀Resolve into two parts:

l ₀₀＝U+Q

Wherein:

U is a regression sum of square, and computing formula is:

$U=\underset{p=1}{\overset{k}{\mathrm{\&Sigma;}}}{b}_p{l}_{0p}$

Q is a residual sum of square, and computing formula is:

$Q=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{(y_i-{\hat{y}}_i)}^2=l_{00}-U$

In order to check y and x ₁, x ₂..., x _kWhether tangible linear relationship is arranged, use F ratio

$F=\frac{U/k}{Q/(N-k-1)}$

With critical value F _a(k N-k-1) compares and gets final product.If F＞F _a, just can think y and x ₁, x ₂..., x _kBetween tangible linear relationship is arranged.In addition, also can use multiple correlation coefficient

$R=\sqrt{\frac{U}{l_{00}}}$

Check, if R is not less than corresponding to variable number k+1, the critical value of error degree of freedom N-k-1 just can be thought y and x ₁, x ₂..., x _kBetween tangible linear relationship is arranged.

Embodiment

Elaborate in the face of embodiments of the invention down: present embodiment has provided detailed embodiment and concrete operating process being to implement under the prerequisite with technical scheme of the present invention, but the protection domain of invention is not limited to following embodiment.

Testing procedure comprises:

I. with existing cooling characteristics equation N '=A λ ^mBe the basis, through analyzing and quoting as proof, the pattern of tentatively setting up new characteristic equation is N ⁰=A λ ^mq ^ot ₁ ^p(Δ t/ (t2-τ)) ^a

II. selected test event: the heat radiation of the packing matter overall coefficient Ka that looses; Inflow temperature t1; Atmospheric temperature (dry bulb and wet bulb); Spray density; The cooling tower traffic coverage influences cooling characteristics, i.e. environmental efficiency coefficient η=Δ t/ (t2-τ);

III. select orthogonal test table L for use ₉(3 ⁴) (four factors, three levels), respectively to steam-water ratio λ, spray density q, advance tower water temperature t ₁, advance tower wet-bulb temperature τ ₁Test; The gained data rows is as shown in table 1;

Analysis draws influences the factor of cooling characteristics primary and secondary order, adopts multiple regression to try to achieve new equation.

Table 3 orthogonal experiment test data

IV. analyzing to draw influences the factor of cooling characteristics primary and secondary and is followed successively by λ → q → t in proper order ₁→ τ,

The employing multiple regression is tried to achieve new equation and is done

N ⁰＝A＊λ ^m＊q ⁿ＊t ₁ ^p＊η ^c。

More than show and described ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should understand; The present invention is not restricted to the described embodiments; That describes in the foregoing description and the instructions just explains principle of the present invention; Under the prerequisite that does not break away from spirit and scope of the invention, the present invention also has various changes and modifications, and these variations and improvement all fall in the scope of the invention that requires protection.The present invention requires protection domain to be defined by appending claims and equivalent thereof.

Claims (2)

1. method of testing the cooling tower characteristic, testing procedure comprises:

I. with existing cooling characteristics equation N '=A λ ^mBe the basis, the pattern of tentatively setting up new characteristic equation is N ⁰=A λ ^mq ^ot ₁ ^p(Δ t/ (t ₂-τ)) ^aIn the formula, λ is a steam-water ratio, and q is a spray density, kg/m ²H; t ₁Be inflow temperature, ℃; Δ t is the cold width of cloth, ℃; t ₂Be leaving water temperature, ℃; A is a coefficient, and m, o, p, a are index;

II. selected test event: the heat radiation of the packing matter overall coefficient Ka that looses, kg/m ³H; Inflow temperature t ₁, ℃; Atmospheric temperature (dry bulb and wet-bulb temperature); Spray density q, kg/m ²H; The cooling tower traffic coverage influences cooling characteristics, i.e. environmental efficiency coefficient η=Δ t/ (t ₂-τ);

The definition air-circulation features is counted N '=KaV/L, and in the formula, V is packing volume m ³, L is quantity of circulating water m ³/ s calculates fundamental equation according to your heating power of Mike,

The latter is called evaporation characteristic number N;

III. select positive quadraturing design test table L for use ₉(3 ⁴) (four factors, three levels), respectively to steam-water ratio λ, spray density q, advance tower water temperature t ₁, advance tower wet-bulb temperature τ ₁Test;

IV. analyzing to draw influences the factor of cooling characteristics primary and secondary order, adopts multiple regression procedure to try to achieve the new equation of cooling characteristics.

2. the method for testing of cooling tower characteristic according to claim 1; It is characterized in that; The ratio of definition ventilation density and spray density is gas-water ratio λ; The measured value and spray density coefficient q, inflow temperature t1 and the environmental efficiency coefficient η that confirm steam-water ratio λ, atmospheric temperature (dry bulb and wet bulb) are directly related with the cooling tower cooling characteristics, and the correlation factor primary and secondary is followed successively by λ → q → t in proper order ₁→ η; The employing multiple regression is tried to achieve new equation and is done

N ⁰＝A＊λ ^m＊q ⁿ＊t ₁ ^p＊η ^c；

In the formula

N ⁰---cooling characteristics;

λ---gas-water ratio;

Q---spray density, kg/m ²H;

T1---inflow temperature, ℃;

η---environmental efficiency coefficient, η=Δ t/ (t2-τ).