CN107992655A

CN107992655A - The quick Virtual Numerical Experiments method of deflector type combustion chamber aeroperformance

Info

Publication number: CN107992655A
Application number: CN201711175310.7A
Authority: CN
Inventors: 王维明; 于锦峰; 邵伏永; 王大磊; 王春雪
Original assignee: Beijing Power Machinery Institute
Current assignee: Beijing Power Machinery Institute
Priority date: 2017-11-22
Filing date: 2017-11-22
Publication date: 2018-05-04

Abstract

The present invention relates to a kind of quick Virtual Numerical Experiments method of deflector type combustion chamber aeroperformance, it is related to small turbine engine experimental technique field.The present invention is by establishing a small turbine engine deflector type combustion chamber one-dimensional aerodynamic model quickly, simplified, applicable, solves the problems, such as combustion chamber aerodynamic model to be used in Virtual Numerical Experiments, and then form the method for the quick Virtual Numerical Experiments of small turbine engine deflector type combustion chamber aeroperformance, realize and quickly carry out combustion chamber aeroperformance experiment on a computer platform, obtain the purpose of its aeroperformance.This method computing is quick, under conditions of model empirical tests, can partly substitute the actual loading test of deflector type combustion chamber, so as to reduce the experimentation cost of combustion chamber, shortens the lead time, improves the development efficiency of combustion chamber.

Description

The quick Virtual Numerical Experiments method of deflector type combustion chamber aeroperformance

Technical field

The present invention relates to small turbine engine experimental technique field, and in particular to a kind of deflector type combustion chamber aeroperformance Quick Virtual Numerical Experiments method.

Background technology

Obtaining turbine engine combustion chamber aeroperformance mainly has two methods：A kind of is the reality using combustor test platform Thing experiment directly obtains aeroperformance；Another kind is to obtain aeroperformance using CFD technology of numerical simulation.Due to the latter's theory Limitation, such as without test data verification and correction model, limited by practical.Therefore, actual loading test is still the master used at present Want method.

Due to using the Virtual Numerical Experiments method of technology of numerical simulation, expense, the cost of development can be saved, shortening is ground In the cycle processed, improve development efficiency, avoid developing risk.So start to rise with CFD emulation technologies in eighties of last century the eighties For means, carry out the numerical analysis of turbogenerator aeroperformance and the research calculated, occur various self-editing or commercial CFD software, such as FLUENT, CFX and NUMECA etc..But what these software tools were calculated typically as general aerodynamic analysis What solver provided, it is not appropriate for as dedicated aeroperformance Virtual Numerical Experiments system, and use also inconvenience With it is convenient.

U.S. NASA develops NPSS systems, incorporates the aerothermodynamic of aero-turbine complete machine, component and system Various dimensions and the software and achievement in research of Multi-Scale Calculation analysis, establish virtual " the numerical value test run of aero-turbine Engine components, or even complete machine can be carried out Virtual Numerical Experiments, obtain the performance of engine or setting for verification engine by platform " Meter.Although China has also carried out similar ATPD plans, due to weak foundation, there is larger gap with foreign technology level, Not yet set up the tool software and environment of system, the also pole imperfection such as basic database and model library, Virtual Numerical Experiments skill Application of the art in small turbine engine experiment is not yet really carried out, and therefore, develops the critical component of small turbine engine The Virtual Numerical Experiments technology of (such as combustion chamber) is very necessary and urgent.External Virtual Numerical Experiments experience have shown that：Virtual examination The actual loading test amount that can significantly save is tested, development cost is reduced, reduces developing risk.

The content of the invention

(1) technical problems to be solved

The technical problem to be solved in the present invention is：A kind of deflector type suitable for small turbine engine how is designed to burn The quick Virtual Numerical Experiments method of room aeroperformance.

(2) technical solution

In order to solve the above technical problem, the present invention provides a kind of quick virtual number of deflector type combustion chamber aeroperformance It is worth test method, comprises the following steps：

Step 1, the subregion for carrying out combustion chamber one-dimensional aerodynamic model and calculating section are chosen；

Step 2. inputs the geometric parameter and primary condition of combustion chamber one-dimensional aerodynamic model, including：Combustion chamber inlet air Flow, inlet air stagnation pressure, inlet air total temperature, fuel flow, outlet total temperature and combustion efficiency of combustion chamber；

The geometric parameter and primary condition for the combustion chamber one-dimensional aerodynamic model that step 3. is inputted based on step 2, calculate baffling Formula combustion chamber inlet condition and Performance Parameters, including：

(a) calculating (formula (1)-(3)) of combustion chamber inlet air flow velocity coeffficient and speed；

(b) calculating (formula (4)) of the total excess air coefficient in combustion chamber；

(c) volume rate of combustion calculates (formula (5))；

(d) the total flow resistance coefficient in combustion chamber calculates (formula (6)) and total pressure recovery coefficient estimation (formula (11))；

The geometric parameter and primary condition for the combustion chamber one-dimensional aerodynamic model that step 4. is inputted based on step 2, deflector type combustion Burn the distribution (formula (12)-(13)) of room burner inner liner air mass flow；

The geometric parameter and primary condition for the combustion chamber one-dimensional aerodynamic model that step 5. is inputted based on step 2, deflector type combustion Process parameter in the flame tube head of room is burnt to calculate, including：

(a) in flame tube head total temperature calculating (formula (14))；

(b) in flame tube head static pressure calculating (formula (15))；

(c) in flame tube head static temperature (formula (19)), current density (formula (16)) and stagnation pressure calculating ((formula (20))；

(d) excess air coefficient (formula (13)) in the i-th section, air velocity (formula (17)), speed system in flame tube head The calculating of number (formula (18)) and effluxvelocity (formula (21))；

The geometric parameter and primary condition for the combustion chamber one-dimensional aerodynamic model that step 6. is inputted based on step 2, deflector type combustion Process parameter calculates after burning room flame tube head, including：

(a) air mass flow (formula (22)) of the i-th section wall air admission hole, superposition air mass flow (formula behind head (23)), excess air coefficient (formula (25)) and effluxvelocity (formula (26))；

(b) total temperature (formula (14)) in the i-th section, static temperature (formula (19)) and current density (formula (28)) behind head；

(c) stagnation pressure (formula (20)) in the i-th section behind head, static pressure (formula (16)), air velocity (formula (17)) and The calculating of velocity coeffficient (formula (18)), the calculating (formula (29)) of combustor total pressure recovery coefficient；

Step 7. judges whether that the flow in first calculating section after the last flow for calculating section and head behind head reaches Balance has been arrived, if uneven, has turned to step 4, modification air mass flow distribution, does cycle calculations, otherwise terminate.

Preferably, in step 1, the characteristics of flowing according to deflector type combustion chamber flame drum interior air-flow, by the one-dimensional gas in combustion chamber Movable model is divided into three computational domains：Head of combustion chamber region, combustion chamber central region and combustor exit region.

Preferably, in step 1, according to burner inner liner position of opening, combustion chamber one-dimensional aerodynamic model partition is calculated for n and is cut Face, each region select to calculate section number according to hole number of rows, and the n-th section is the outlet of combustion chamber.And take burner inner liner each along journey Center streamline of the line at section ring cavity height midpoint as burner inner liner.

(3) beneficial effect

The present invention is one-dimensional by establishing a small turbine engine deflector type combustion chamber quickly, simplified, applicable Aerodynamic model, solves the problems, such as combustion chamber aerodynamic model to be used in Virtual Numerical Experiments, and then forms for small-sized whirlpool The method of the quick Virtual Numerical Experiments of turbine deflector type combustion chamber aeroperformance, realize on a computer platform quickly into The aeroperformance experiment of row combustion chamber, obtains the purpose of its aeroperformance.This method computing is quick, in the condition of model empirical tests Under, it can partly substitute the actual loading test of deflector type combustion chamber, so as to reduce the experimentation cost of combustion chamber, shorten the lead time, Improve the development efficiency of combustion chamber.

Brief description of the drawings

Fig. 1 is the one-dimensional aerodynamic model schematic diagram in the deflector type combustion chamber of the embodiment of the present invention.

Embodiment

To make the purpose of the present invention, content and advantage clearer, with reference to the accompanying drawings and examples, to the present invention's Embodiment is described in further detail.

The quick Virtual Numerical Experiments method of the small turbine engine deflector type combustion chamber aeroperformance of the present invention includes Following steps：

Step 1. combustion chamber one-dimensional aerodynamic model division and calculating section are chosen.

Step 2. inputs combustion chamber model geometric parameter and primary condition, including：Combustion chamber intake air flow, import are empty Gas stagnation pressure, inlet air total temperature, fuel flow, outlet total temperature, combustion efficiency of combustion chamber etc..

Step 3. calculates deflector type combustion chamber inlet condition and Performance Parameters, including：

(c) volume rate of combustion calculates (formula (5))；

(d) the total flow resistance coefficient in combustion chamber calculates (formula (6)) and total pressure recovery coefficient estimation (formula (11)).

The distribution (formula (12)-(13)) of step 4. deflector type combustion chamber flame drum air mass flow.

Process parameter calculates in step 5. deflector type combustion chamber flame drum head, including：

(a) in flame tube head total temperature calculating (formula (14))；

(b) in flame tube head static pressure calculating (formula (15))；

(d) excess air coefficient (formula (13)) in the i-th section, air velocity (formula (17)), speed system in flame tube head The calculating of number (formula (18)) and effluxvelocity (formula (21)).

Process parameter calculates behind step 6. deflector type combustion chamber flame drum head, including：

(c) stagnation pressure (formula (20)) in the i-th section behind head, static pressure (formula (16)), air velocity (formula (17)) and The calculating of velocity coeffficient (formula (18)), the calculating (formula (29)) of combustor total pressure recovery coefficient.

Step 7. calculate convergence judge, if behind head finally calculate section flow and head after first calculating section Flow reached balanceIf uneven, step 4 is turned to, modification air mass flow distribution, does cycle calculations, otherwise, under continuing One step；

Step 8. the results show and analysis；

Step 9. terminates.

An embodiment of the present invention provides the aerodynamic model that the deflector type combustion chamber of the simplification shown in a Fig. 1 is one-dimensional, passes through The verification of test data, while be aided with the examination of three-dimensional CFD result of calculations, it was demonstrated that the validity of model.

Deflector type combustion chamber employs centrifugal fuel injection wheel loop configuration, has very compared with traditional single flow toroidal combustion chamber Big difference.The center streamline of straight-flow combustor burner inner liner is generally parallel with the axis of engine, it calculates section and hair The axis of motivation is vertical, and the burner inner liner of the deflector type combustion chamber of centrifugal fuel injection wheel is baffling structure, into the air-flow of burner inner liner Initially along Radial Flow, it is calculated, and section is parallel with engine axis, and then as turning back for air-flow, calculating section gradually turns It is changed into vertical with engine axis.

Therefore, in step 1, the characteristics of flowing according to deflector type combustion chamber flame drum interior air-flow, three meters are reduced to Calculate domain：Head of combustion chamber region (the A areas of Fig. 1), combustion chamber central region (the B areas of Fig. 1) and the combustor exit region (C of Fig. 1 Area)；Computation model can be divided into, each region selects suitable according to hole number of rows by n calculating section according to burner inner liner position of opening When calculating section number.N=12 in Fig. 1, wherein 1-5 sections are the head of burner inner liner, and 6-11 sections are in burner inner liner Portion, the 12nd section are the outlet of combustion chamber.Take burner inner liner along the line at each section ring cavity height midpoint of journey as in burner inner liner Heart streamline.

According to deflector type chamber structure size, the main geometric parameters for obtaining its one-dimensional aerodynamic model (Fig. 1), bag are calculated Include：The burner inner liner actual internal area in 12 calculating sections, combustion chamber inlet -duct area, import extended area, combustion chamber maximum cross-section Product, outer wall ring cavity sectional area, inner wall ring cavity sectional area and inside and outside ring cavity total sectional area etc..

In order to which main problem is quickly calculated and considered, following main assumption is done to model：

● air-flow flowing is stable state, i.e., each section flow parameter is permanent；

● burning indoor air flow flowing is unitary, and state parameter is uniform in the circumferential direction；

● for air-flow for that can not press stream, air-flow stagnation pressure in ring cavity passage is constant.

The calculating of deflector type combustion chamber one-dimensional aerodynamic model, calculates combustion chamber inlet condition and overall performance ginseng first Number, then carries out just sub-distribution to the air mass flow of burner inner liner by flow resistance method, iterates finally by one-dimensional flow theoretical method Calculate burner inner liner along journey aerothermo-parameters, until meeting the condition of convergence, the final aeroperformance for obtaining combustion chamber.

Formula involved in step 3 to step 6 is as follows：

(2) deflector type combustion chamber inlet condition and Performance Parameters calculate

(a) combustion chamber inlet air flow velocity coeffficient λ₃With speed V₃

Air intlet velocity coeffficient λ₃With speed V₃It is obtained by the following formula：

In formula, q (λ₃) it is flow function, R is gas constant, and k is specific heat ratio,For combustion chamber import stagnation pressure,For Combustion chamber import total temperature, m_aFor combustion chamber intake air flow, combustion chamber inlet -duct area A₃。

(b) the total excess air coefficient α in combustion chamber_Σ

Total excess air coefficient α_ΣCalculated by following formula：

In formula, m_fFor combustion chamber fuel flow, L₀For every kilogram of fuel oil theoretical combustion air.

(c) volume rate of combustion Q_VC

Volumetric heat intensity Q_VCFor：

In formula, L_cFor chamber length,For combustion efficiency of combustion chamber, A_MSectional area, H are referred to for combustion chamber_uFor aviation coal Oily calorific value.

(d) the total flow resistance coefficient φ in combustion chamber_MWith total pressure recovery coefficient σ_C

The total flow resistance coefficient φ in combustion chamber_MFor：

φ_M=φ_g+φ_fM+φ_Mh (6)

In formula, φ_gEnlargement loss for air-flow by diffuser, φ_fMFor total stream of each section wall air admission hole of burner inner liner Hinder coefficient, φ_MhFor the thermal resistance loss in burner inner liner.

The enlargement loss φ that air-flow passes through diffuser_gIt can be calculated by following formula：

Wherein, A_gIt is defined before other parameters for diffuser intake extended area.

Total flow resistance coefficient φ of each section wall air admission hole of burner inner liner_fMFor：

In formula, φ_MiFor the local flow resistance coefficient of the i-th section of burner inner liner wall air admission hole, calculated by following formula：

Wherein, μ_iFor the i-th discharge coefficient for discharging into stomata, A_iFor i-th gross area for discharging into stomata, A_fiGas is discharged into for i-th Burner inner liner circulation area at hole.

Thermal resistance loss φ in burner inner liner_MhIt can be calculated as follows：

In formula,For combustor exit total temperature,Ratio, A are heated for combustion chamber_fhFor flame tube head, last cuts The burner inner liner circulation area in face (the 5th section in this model).

The combustor total pressure recovery coefficient σ of estimation_cIt is given by：

Each parameter has been defined above in formula.

(3) the first sub-distribution of deflector type combustion chamber flame drum air mass flow

The relation with local flow resistance coefficient is distributed according to burner inner liner local flow, the i-th section of burner inner liner wall air admission hole Air inlet percentage K_iIt can be calculated by following formula：

Corresponding to the excess air coefficient α in each section_i, then calculated by following formula：

In formula,--- the overlaying flow percentage in the-the i-th section.

(4) process parameter calculates in deflector type combustion chamber flame drum head

(a) total temperature in flame tube head

According to energy-balance equation, the total temperature in the i-th section in burner inner linerIt can be calculated by following formula：

η_i(H_u-D_h)=α_iL₀(I_i-I₃)+H_i-H₀ (14)

In formula, I₃For combustion chamber import total temperatureUnder air unit heat content, D_hLost for thermal dissociation, I_iTo calculate section Total temperatureUnder air unit heat content, η_iTo calculate the efficiency of combustion in section, H₀On the basis of constant-temperature combustion enthalpy at temperature (15 DEG C) Difference, H_iTo calculate section total temperatureUnder constant-temperature combustion enthalpy difference.I in formula_i、H_iAll it isFunction, therefore, in known temperature Under the conditions of degree, I_i、H_iIt can be found, therefore can be obtained by iterative method by enthalpy tableFor last section (model of head In the 5th section) total temperature.

(b) static pressure P in flame tube head_fh

Static pressure P in flame tube head_fhCalculated by following formula：

In formula, N_hFor flame tube head section number,For the overlaying flow percentage in each section of flame tube head,For the air admission hole effective area of the superposition in each section of flame tube head,For the ring cavity stagnation pressure of flame tube head, can use

(c) static temperature T in flame tube head_fh, current density ρ_hAnd stagnation pressure

First with the total temperature in flame tube headAs T_fhInitial value, then flame tube head interior air-flow density p_hFor：

It can obtain the air velocity V in last section of flame tube head by following continuity equation_h:

Then, the air velocity coefficient lambda in last section of flame tube head is obtained by following formula_h:

Finally, static temperature T in flame tube head is obtained by following formula_fhValue：

T_fhValue returns formula (16) as approximation generation, above-mentioned calculating is repeated, until front and rear T twice_fhThe absolute error of value≤ Untill 0.1.The stagnation pressure in flame tube head can be obtained by following formula again

(d) in flame tube head the i-th section excess air coefficient α_hi, air velocity V_hi, velocity coeffficient λ_hiAnd effluxvelocity V_jhi

With the burner inner liner circulation area at the overlaying flow and respective cross-section in head Nei Ge sections, and by formula (13), formula (17) and formula (18) can obtain the α in the i-th section respectively_hi、V_hiAnd λ_hi.The effluxvelocity V in the i-th section in head_jhiCan be by following formula Calculate

Wherein, ρ₃For combustion chamber inlet air flow density, K_hiFor the flow percentage in the i-th section of flame tube head, μ_hiA_hiFor The perforate effective area of the air admission hole in the i-th section of flame tube head.

(5) process parameter calculates behind deflector type combustion chamber flame drum head

(a) behind head the i-th section wall air admission hole air mass flow m_ai, overlaying flow Σ m_ai, excess air coefficient α_iAnd jet stream Speed V_ji

The air mass flow m of i-th section wall air admission hole after flame tube head_aiIt can be calculated by following formula：

In formula, ρ_aniFor the ring cavity gas density in the i-th section, ρ can use_ani≈ρ_M。P_f(i-1)Cut for (i-1) in burner inner liner The static pressure in face,For the ring cavity stagnation pressure in the i-th section, can use

The superposition air mass flow Σ m in the i-th section behind head_aiFor：

Σm_ai=m_ah+ΣK_im_a (23)

In formula, m_ahFor the head air mass flow of burner inner liner, Σ K_iFor the superposition air mass flow percentage in the i-th section.

The superposition gas flow Σ m in the i-th section behind head_giFor：

Σm_gi=m_f+Σm_ai (24)

The excess air coefficient α in the i-th section behind head_iFor：

The effluxvelocity V of i-th section wall air admission hole behind head_jiFor：

(b) behind head the i-th section total temperatureStatic temperature T_fiAnd current density ρ_fi

According to the excess air coefficient α in the i-th section after flame tube head_i, iterated to calculate, can be obtained i-th behind head by formula (14) The total temperature in section

(i-1) section is taken in burner inner liner, as control volume, to ignore the influence of friction loss to the gas between i sections, control The body equation of momentum processed is：

In formula, V_fi、V_f(i-1)For in burner inner liner i-th and the combustion gas speed in (i-1) section, P_fi、P_f(i-1)For in burner inner liner I and the static pressure in (i-1) section, A_fi、A_f(i-1)For in burner inner liner i-th and the circulation area in (i-1) section, Σ m_gi、Σm_g(i-1)For In burner inner liner i-th and (i-1) section superposition gas flow, β is efflux angle.By P_fi=ρ_fiRT_fiWithSubstitution formula (27), can obtain：

Above formula is solved on ρ_fiQuadratic equation with one unknown, obtain combustion gas density p_fiValue, then by formula (17), (18) and (19) Obtain static temperature T_fiValue.By T_fiValue repeats above calculating process as approximation, until front and rear T twice_fiThe absolute error of approximation Untill≤0.01.Finally obtain the total temperature in the i-th section in burner inner liner behind headStatic temperature T_fiAnd current density ρ_fi。

(c) behind head the i-th section stagnation pressureStatic pressure P_fi, air velocity V_fiAnd velocity coeffficient λ_fi

Behind head in burner inner liner the i-th section static pressure P_fiIt can be calculated by equation of state (16), air velocity V_fiCan be by formula (17) calculate, velocity coeffficient λ_fiIt can be calculated by formula (18), stagnation pressureIt can be calculated by formula (20).After obtaining, the stagnation pressure of combustion chamber Recovery coefficient σ_cThen calculated by following formula：

In formula,For the stagnation pressure in burner inner liner outlet (the 12nd section in model).

Using the test data of combustion chamber (Fig. 1) in kind to deflector type combustion chamber one-dimensional aerodynamic computational methods of the invention And its aerodynamic model is verified, in computational accuracy, the outlet of deflector type combustion chamber one-dimensional aerodynamic model be averaged total temperature with Relative error maximum of the relative error, outlet total pressure recovery coefficient that test data compares compared with test data is no more than 1%.On the time is calculated, it can complete once to calculate in a few minutes.

The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, without departing from the technical principles of the invention, some improvement and deformation can also be made, these are improved and deformation Also it should be regarded as protection scope of the present invention.

Claims

1. the quick Virtual Numerical Experiments method of a kind of deflector type combustion chamber aeroperformance, it is characterised in that comprise the following steps：

Step 2. inputs the geometric parameter and primary condition of combustion chamber one-dimensional aerodynamic model, including：Combustion chamber intake air flow, Inlet air stagnation pressure, inlet air total temperature, fuel flow, outlet total temperature and combustion efficiency of combustion chamber；

The geometric parameter and primary condition for the combustion chamber one-dimensional aerodynamic model that step 3. is inputted based on step 2, calculate deflector type combustion Room inlet condition and Performance Parameters are burnt, including：

(c) volume rate of combustion calculates (formula (5))；

The geometric parameter and primary condition for the combustion chamber one-dimensional aerodynamic model that step 4. is inputted based on step 2, deflector type combustion chamber The distribution (formula (12)-(13)) of burner inner liner air mass flow；

The geometric parameter and primary condition for the combustion chamber one-dimensional aerodynamic model that step 5. is inputted based on step 2, deflector type combustion chamber Process parameter calculates in flame tube head, including：

(a) in flame tube head total temperature calculating (formula (14))；

(b) in flame tube head static pressure calculating (formula (15))；

(d) excess air coefficient (formula (13)) in the i-th section, air velocity (formula (17)), velocity coeffficient are (public in flame tube head Formula (18)) and effluxvelocity (formula (21)) calculating；

The geometric parameter and primary condition for the combustion chamber one-dimensional aerodynamic model that step 6. is inputted based on step 2, deflector type combustion chamber Process parameter calculates after flame tube head, including：

(a) air mass flow (formula (22)) of the i-th section wall air admission hole behind head, superposition air mass flow (formula (23)), remaining Gas coefficient (formula (25)) and effluxvelocity (formula (26))；

(c) stagnation pressure (formula (20)) in the i-th section, static pressure (formula (16)), air velocity (formula (17)) and speed behind head The calculating of coefficient (formula (18)), the calculating (formula (29)) of combustor total pressure recovery coefficient；

Step 7. judges whether that the flow in first calculating section after the last flow for calculating section and head behind head reaches Balance, if uneven, turns to step 4, modification air mass flow distribution, does cycle calculations, otherwise terminate.

2. the method as described in claim 1, it is characterised in that in step 1, according to deflector type combustion chamber flame drum interior air-flow stream The characteristics of dynamic, combustion chamber one-dimensional aerodynamic model is divided into three computational domains：Head of combustion chamber region, combustion chamber central region and combustion Burn room exit region.

3. method as claimed in claim 2, it is characterised in that in step 1, according to burner inner liner position of opening, by combustion chamber one Dimension aerodynamic model is divided into n calculating section, and each region selects to calculate section number according to hole number of rows, and the n-th section is burning The outlet of room.And take center streamline of the burner inner liner along the line at each section ring cavity height midpoint of journey as burner inner liner.

4. method as claimed in claim 3, it is characterised in that in step 3, burnt using following formula (1)-(3) The calculating of room inlet air flow velocity coeffficient and speed；

The calculating of the total excess air coefficient in combustion chamber is carried out using following formula (4)；

Volume rate of combustion calculating is carried out using following formula (5)；

The total flow resistance coefficient in combustion chamber is carried out using following formula (6) to calculate, and total pressure recovery is carried out using following formula (11) Coefficient estimate；

In step 4, the distribution of deflector type combustion chamber flame drum air mass flow is carried out using following formula (12)-(13)；

Step 5. carries out the calculating of total temperature in flame tube head using following formula (14)；Carried out using following formula (15) The calculating of static pressure in flame tube head；Utilize following formula (19)) calculating of static temperature in flame tube head is carried out, utilization is following Formula (16) carry out the calculating of current density, utilize following formula (20) to carry out the calculating of stagnation pressure；Utilize following formula (13) calculating of the excess air coefficient in the i-th section in flame tube head is carried out, air velocity is carried out using following formula (17) Calculate, the calculating of velocity coeffficient carried out using following formula (18), utilizes following formula (21)) carry out the meter of effluxvelocity Calculate；

The air mass flow that step 6. carries out the i-th section wall air admission hole behind head using following formula (22) calculates, utilize with Under formula (23) be overlapped the calculating of air mass flow, utilize following formula (25) to carry out the calculating of excess air coefficient, utilize Following formula (26) carries out the calculating of effluxvelocity；Utilize the total temperature in the i-th section behind following formula (14) progress head Calculate, the calculating of static temperature is carried out using following formula (19), the calculating of current density is carried out using following formula (28)；Profit The calculating of the stagnation pressure in the i-th section after carrying out head with following formula (20), the meter of static pressure is carried out using following formula (16) Calculate, the calculating of air velocity is carried out using following formula (17), velocity coeffficient calculating, profit are carried out using following formula (18) The calculating of combustor total pressure recovery coefficient is carried out with following formula (29)：

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In formula, combustion air inlet velocity coefficient is λ₃, speed V₃, q (λ₃) be flow function, R is gas constant, k be than Heat capacity ratio,For combustion chamber import stagnation pressure,For combustion chamber import total temperature, m_aFor combustion chamber intake air flow, combustion chamber into Open area is A₃；

The total excess air coefficient α in combustion chamber_ΣFor：

<mrow> <msub> <mi>&alpha;</mi> <mi>&Sigma;</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>m</mi> <mi>a</mi> </msub> <mrow> <msub> <mi>m</mi> <mi>f</mi> </msub> <msub> <mi>L</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

In formula, m_fFor combustion chamber fuel flow, L₀For every kilogram of fuel oil theoretical combustion air；

Volume rate of combustion Q_VCFor：

In formula, L_cFor chamber length, η_GFor combustion efficiency of combustion chamber, A_MSectional area, H are referred to for combustion chamber_uFor aviation kerosine heat Value；

The total flow resistance coefficient φ in combustion chamber_MFor：

φ_M=φ_g+φ_fM+φ_Mh (6)

In formula, φ_gEnlargement loss for air-flow by diffuser, φ_fMFor total flow resistance system of each section wall air admission hole of burner inner liner Number, φ_MhFor the thermal resistance loss in burner inner liner；

<mrow> <msub> <mi>&phi;</mi> <mi>g</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <msub> <mi>A</mi> <mn>3</mn> </msub> <msub> <mi>A</mi> <mi>g</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>A</mi> <mi>M</mi> </msub> <msub> <mi>A</mi> <mn>3</mn> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

Wherein, A_gFor diffuser intake extended area；

<mrow> <msub> <mi>&phi;</mi> <mrow> <mi>f</mi> <mi>M</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mrow> <mo>&lsqb;</mo> <mi>&Sigma;</mi> <msup> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>&phi;</mi> <mrow> <mi>M</mi> <mi>i</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>0.5</mn> </msup> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </msup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

In formula, φ_MiFor the local flow resistance coefficient of the i-th section of burner inner liner wall air admission hole

<mrow> <msub> <mi>&phi;</mi> <mrow> <mi>M</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mrow> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <msub> <mi>A</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>A</mi> <mi>M</mi> </msub> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>

Wherein, μ_iFor the i-th discharge coefficient for discharging into stomata, A_iFor i-th gross area for discharging into stomata, A_fiFor i-th row's air inlet position Burner inner liner circulation area；

Thermal resistance loss φ in burner inner liner_MhFor：

<mrow> <msub> <mi>&phi;</mi> <mrow> <mi>M</mi> <mi>h</mi> </mrow> </msub> <mo>=</mo> <mn>0.52</mn> <mrow> <mo>(</mo> <mfrac> <msubsup> <mi>T</mi> <mn>4</mn> <mo>*</mo> </msubsup> <msubsup> <mi>T</mi> <mn>3</mn> <mo>*</mo> </msubsup> </mfrac> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>A</mi> <mi>M</mi> </msub> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>h</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

In formula,For combustor exit total temperature,Ratio, A are heated for combustion chamber_fhFor last section of flame tube head Burner inner liner circulation area；

Combustor total pressure recovery coefficient σ_cFor：

<mrow> <msub> <mi>&sigma;</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mi>k</mi> <mn>2</mn> </mfrac> <msub> <mi>&phi;</mi> <mi>M</mi> </msub> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>A</mi> <mn>3</mn> </msub> <msub> <mi>A</mi> <mi>M</mi> </msub> </mfrac> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>

According to the distribution of burner inner liner local flow and the relation of local flow resistance coefficient, the air inlet of the i-th section of burner inner liner wall air admission hole Percentage K_iFor：

Corresponding to the excess air coefficient α in each section_iFor：

<mrow> <msub> <mi>&alpha;</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>m</mi> <mi>a</mi> </msub> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mn>1</mn> <mi>i</mi> </munderover> <msub> <mi>K</mi> <mi>i</mi> </msub> </mrow> <mrow> <msub> <mi>m</mi> <mi>f</mi> </msub> <msub> <mi>L</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>

In formula,For the overlaying flow percentage in the i-th section；

According to energy-balance equation, the total temperature in the i-th section in burner inner linerFor：

η_i(H_u-D_h)=α_iL₀(I_i-I₃)+H_i-H₀(14)

In formula, I₃For combustion chamber import total temperatureUnder air unit heat content, D_hLost for thermal dissociation, I_iTo calculate section total temperatureUnder air unit heat content, η_iTo calculate the efficiency of combustion in section, H₀For the constant-temperature combustion enthalpy difference under preset reference temperature, H_i To calculate section total temperatureUnder constant-temperature combustion enthalpy difference, the I in formula_i、H_iAll it isFunction, therefore, in known temperature strip Under part, I_i、H_iFound, therefore can be obtained by iterative method by enthalpy tableFor the total temperature in last section of head；

Static pressure P in flame tube head_fhFor：

<mrow> <msub> <mi>P</mi> <mrow> <mi>f</mi> <mi>h</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>P</mi> <mrow> <mi>a</mi> <mi>n</mi> </mrow> <mo>*</mo> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mi>a</mi> </msub> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mn>1</mn> <msub> <mi>N</mi> <mi>h</mi> </msub> </munderover> <msub> <mi>K</mi> <mi>i</mi> </msub> </mrow> <mrow> <munderover> <mo>&Sigma;</mo> <mn>1</mn> <msub> <mi>N</mi> <mi>h</mi> </msub> </munderover> <msub> <mi>&mu;</mi> <mi>i</mi> </msub> <msub> <mi>A</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>&rho;</mi> <mi>M</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

In formula, N_hFor flame tube head section number,For the overlaying flow percentage in each section of flame tube head, For the air admission hole effective area of the superposition in each section of flame tube head,For the ring cavity stagnation pressure of flame tube head, take

The air velocity V in last section of flame tube head is obtained by following continuity equation_h:

<mrow> <msub> <mi>V</mi> <mi>h</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mn>1</mn> <msub> <mi>N</mi> <mi>h</mi> </msub> </munderover> <msub> <mi>K</mi> <mi>i</mi> </msub> <msub> <mi>m</mi> <mi>a</mi> </msub> <mo>+</mo> <msub> <mi>m</mi> <mi>f</mi> </msub> </mrow> <mrow> <msub> <mi>&rho;</mi> <mi>h</mi> </msub> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>h</mi> </mrow> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>&lambda;</mi> <mi>h</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>V</mi> <mi>h</mi> </msub> <msqrt> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>k</mi> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <msubsup> <mi>RT</mi> <mrow> <mi>f</mi> <mi>h</mi> </mrow> <mo>*</mo> </msubsup> </mrow> </msqrt> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>T</mi> <mrow> <mi>f</mi> <mi>h</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>T</mi> <mrow> <mi>f</mi> <mi>h</mi> </mrow> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <msubsup> <mi>&lambda;</mi> <mi>h</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>

T_fhValue returns formula (16) as approximation generation, above-mentioned calculating is repeated, until front and rear T twice_fhThe absolute error of value is less than pre- If being worth, then the stagnation pressure in flame tube head is obtained by following formula

With the burner inner liner circulation area at the overlaying flow and respective cross-section in head Nei Ge sections, and by formula (13), formula (17) and Formula (18) obtains the excess air coefficient α in the i-th section respectively_hi, air velocity V_hiWith velocity coeffficient λ_hi, the jet stream in the i-th section in head Speed V_jhiCalculated by following formula：

Wherein, ρ₃For combustion chamber inlet air flow density, K_hiFor the flow percentage in the i-th section of flame tube head, μ_hiA_hiFor flame The perforate effective area of the air admission hole in cylinder the i-th section of head；

The air mass flow of the i-th section wall air admission hole is m behind head_ai, overlaying flow be Σ m_ai, excess air coefficient α_iAnd jet velocity Spend for V_ji；

The air mass flow m of i-th section wall air admission hole after flame tube head_aiFor：

In formula, ρ_aniFor the ring cavity gas density in the i-th section, ρ is taken_ani≈ρ_M；P_f(i-1)For in burner inner liner (i-1) section it is quiet Pressure,For the ring cavity stagnation pressure in the i-th section, take

The superposition air mass flow Σ m in the i-th section behind head_aiFor：

Σm_ai=m_ah+ΣK_im_a (23)

In formula, m_ahFor the head air mass flow of burner inner liner, Σ K_iFor the superposition air mass flow percentage in the i-th section；

The superposition gas flow Σ m in the i-th section behind head_giFor：

Σm_gi=m_f+Σm_ai (24)

The excess air coefficient α in the i-th section behind head_iFor：

<mrow> <msub> <mi>&alpha;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&Sigma;m</mi> <mrow> <mi>a</mi> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>m</mi> <mi>f</mi> </msub> <msub> <mi>L</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow>

According to the excess air coefficient α in the i-th section after flame tube head_i, iterated to calculate by formula (14), obtain the total of the i-th section behind head Temperature

(i-1) section is taken in burner inner liner to be as control volume, the control volume equation of momentum to the gas between i sections：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <mo>&Sigma;</mo> <msub> <mi>m</mi> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <msub> <mi>V</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <mn>0.5</mn> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>m</mi> <mrow> <mi>a</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mi>cos</mi> <mi>&beta;</mi> <mo>=</mo> <msub> <mi>P</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mo>&Sigma;</mo> <msub> <mi>m</mi> <mrow> <mi>g</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>27</mn> <mo>)</mo> </mrow> </mrow>

In formula, V_fi、V_f(i-1)For in burner inner liner i-th and the combustion gas speed in (i-1) section, P_fi、P_f(i-1)For the i-th He in burner inner liner (i-1) static pressure in section, A_fi、A_f(i-1)For in burner inner liner i-th and the circulation area in (i-1) section, Σ m_gi、Σm_g(i-1)For fire In flame cylinder i-th and (i-1) section superposition gas flow, β is efflux angle；By P_fi=ρ_fiRT_fiWithSubstitution formula (27), obtain：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>RT</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mfrac> <mrow> <mo>&lsqb;</mo> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </mfrac> <msubsup> <mi>&rho;</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mfrac> <mrow> <mo>&lsqb;</mo> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> <mo>&rsqb;</mo> </mrow> <mn>2</mn> </mfrac> <mo>+</mo> <mo>&Sigma;</mo> <msub> <mi>m</mi> <mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <msub> <mi>V</mi> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </msub> <mo>+</mo> <msub> <mi>m</mi> <mrow> <mi>a</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> <mi>cos</mi> <mi>&beta;</mi> <mo>)</mo> </mrow> <msub> <mi>&rho;</mi> <mrow> <mi>j</mi> <mi>i</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mo>&Sigma;</mo> <msub> <mi>m</mi> <mrow> <mi>g</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msub> <mi>A</mi> <mrow> <mi>f</mi> <mi>i</mi> </mrow> </msub> </mfrac> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow>

Above formula is solved on ρ_fiQuadratic equation with one unknown, obtain combustion gas density p_fiValue, then obtained by formula (17), (18) and (19) quiet Warm T_fiValue, by T_fiValue repeats above calculating process as approximation, until front and rear T twice_fiThe absolute error of approximation is less than pre- If value, the total temperature in the i-th section in burner inner liner behind head is finally obtainedStatic temperature T_fiAnd current density ρ_fi；

Behind head in burner inner liner the i-th section static pressure P_fiCalculated by equation of state (16), air velocity V_fiCalculated by formula (17), Velocity coeffficient λ_fiCalculated by formula (18), stagnation pressureCalculated by formula (20)；After obtaining, the total pressure recovery coefficient σ of combustion chamber_cThen Calculated by following formula：

<mrow> <msub> <mi>&sigma;</mi> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <msubsup> <mi>P</mi> <mrow> <mi>f</mi> <mn>12</mn> </mrow> <mo>*</mo> </msubsup> <msubsup> <mi>P</mi> <mn>3</mn> <mo>*</mo> </msubsup> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> </mrow>

In formula,For the stagnation pressure of burner inner liner outlet.

5. method as claimed in claim 4, it is characterised in that the preset reference temperature is 15 DEG C.

6. method as claimed in claim 4, it is characterised in that the preset value of the absolute error is 1%.