CN102519832B - Method for determining CMF (constant mass flow) pressure drop by adopting CFO (critical flow orifice) device - Google Patents

Abstract

The invention relates to the cigarette draw resistance (or pressure drop) measuring field, and especially relates to a method for determining the CMF pressure drop by adopting a CFO device and a method for establishing a model for the CMF pressure drop determination. According to the invention, the method for determining the CMF pressure drop by adopting the CFO device and the method for establishing the model for the CMF pressure drop determination are disclosed, theoretical models of a CFO draw resistance measure method and the CMF draw resistance measure method are detailedly introduced and analyzed, and a case that a derived formula is closer to a table transition relation than a formula in an ISO6565 table is obtained by comparing the formula which is used for the transition between the CFO method and the CMF method and is obtained by deriving through the theoretical models with the formula in the ISO6565 table.

Description

Adopt the CFO device to measure the method for CMF pressure drop

Technical field

The present invention relates to the fields of measurement of Cigarette Draw Resistance (or pressure drop), relate in particular to employing CFO device and measure the method for CMF pressure drop and the method for building up of this model.

Background technology

The instrument of two types is arranged at present for the measurement of resistance to suction (or pressure drop), the apparatus describing of two kinds of vacuumizings is as follows: the first type is called critical hole plate current amount (CFO), and the device of a constant volume flow is arranged.This instrument keeps a constant volumetric flow rate and does not consider the air pressure size at the output terminal of tester all the time, and along with the tester pressure drop increases, input end's flow velocity will reduce.Like this, mass velocity reduces along with the increase of tester pressure drop.

The second type is called constant-quality flow (CMF), keeps the air of a constant-quality flow velocity by the device of all testers.The pressure of this instrument energy auto-compensation tester output terminal changes and keeps a constant mass velocity, and result remains unchanged at input end's volume flow rate.Same tester always is greater than the flow velocity by CFO by the flow velocity of CMF, thereby the pressure drop reading of CMF instrument is greater than the pressure drop reading of CFO instrument.But the CMF instrument can't be realized in actual measurement.

Critical hole plate current amount CFO (CriticalFlowOrifice) is one of standard component of resistance absorbing instrument.In the appendix D of ISO6565 " tobacco and tobacco product---resistance to suction falls in Cigarette Draw Resistance and filter---standard conditions and measurement ", explanation CFO is a kind of flow apparatus that keeps constant volume at the specimen end, and its mass rate reduces with the increase of tester resistance to suction; And CMF is a kind of flow apparatus that keeps constant-quality at the specimen entrance point, therefore same sample CMF device and CFO device record resistance to suction difference, wherein for same sample, the CMF device is larger than the resistance to suction measurement result of CFO device, and this resistance to suction difference increases and significantly increase along with the resistance to suction of sample, and it is as follows to have provided conversion relation between the two:

$P_{\mathrm{CMF}}=P_{\mathrm{CFO}}\frac{P_a}{P_a-P_{\mathrm{CFO}}}---\left(1\right)$

$P_{\mathrm{CFO}}=P_{\mathrm{CMF}}\frac{P_a}{P_a+P_{\mathrm{CMF}}}---\left(2\right)$

Above-mentioned reduction formula is only an experimental formula, there is no theoretical foundation.

Summary of the invention

An object of the present invention is to provide the method that adopts the CFO device to measure the CMF pressure drop, second purpose of the present invention is to provide the method for building up of the conversion model between the resistance to suction voltage drop value that CFO device and CMF device record.Conversion model in measuring method of the present invention has the advantages that more approach the form transformational relation than ISO6565 formula.

In order to realize first above-mentioned purpose, the present invention has adopted following technical scheme:

Adopt the CFO device to measure the method for CMF pressure drop, it is characterized in that the method comprises the following steps:

A) adopt the CFO device to record the pressure drop P that the CFO device records _cFO;

B) then by following method, calculate the pressure drop P that the CMF device records _cMF:

$P_{\mathrm{CMF}}=P_a-\sqrt{P_a^2-P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}};$

Above-mentioned P _cMFthe pressure drop recorded for the CMF device; P _cFOthe pressure drop recorded for the CFO device; P _afor atmospheric pressure.

In order to realize second above-mentioned purpose, the present invention has adopted following technical scheme:

The method for building up of the conversion model between the resistance to suction voltage drop value that CFO device and CMF device record, the method comprises the following steps:

The pressure at assumes samples two ends is respectively P _inand P _out, volumetric flow rate is respectively Q _inand Q _out, P for actual measurement _inwith atmospheric pressure, equate, i.e. P _in=P _a, P _afor atmospheric pressure

By the Ideal-Gas Equation

PV＝nRT (3)

Two ends at sample have

P _aQ _in＝P _outQ _out＝(P _a-P)Q _out (4)

In formula, P is sample pressure reduction;

$\frac{\∂\left(\mathrm{PQ}\right)}{\∂z}=P\frac{\∂Q}{\∂z}+Q\frac{\∂P}{\∂z}=0---\left(5\right)$

The length that in formula, z is sample;

(5) are changed and have

$\frac{\∂Q}{\∂z}=\frac{Q}{P}\frac{\∂P}{\∂z}---\left(6\right)$

Mobile pressure discharge relation per sample, suppose that resistance to suction is directly proportional to flow,

P＝KLQ (7)

In formula, L is sample length, and K is coefficient, by

$\frac{P}{L}=-\frac{\∂P}{\∂z}---\left(8\right)$

Therefore have

$\frac{\∂P}{\∂z}=-\mathrm{KQ}---\left(9\right)$

In formula, negative sign means that pressure reduces along with sample length is increased in;

(9) substitution (6) is had

$\frac{\∂Q}{\∂z}=K\frac{Q^2}{P}=K\frac{Q^3}{\mathrm{QP}}---\left(10\right)$

(10) formula integration is had

$\left(\mathrm{PQ}\right)\underset{Q_{\mathrm{in}}}{\overset{Q_{\mathrm{out}}}{\∫}}\frac{1}{Q^3}\mathrm{dQ}=K\underset{0}{\overset{L}{\∫}}\mathrm{dz}---\left(11\right)$

In formula, (PQ) can be to be constant because (PQ) does as a whole in the outside of integration type, shown in (4);

(11) distortion is had:

$\mathrm{PQ}(\frac{1}{2Q_{\mathrm{in}}^2}-\frac{1}{2Q_{\mathrm{out}}^2})=\mathrm{KL}---\left(12\right)$

By

PQ＝P _aQ _in＝P _outQ _out (13)

(13) substitution (12) is had:

$\frac{P_a}{Q_{\mathrm{in}}}-\frac{P_{\mathrm{out}}}{Q_{\mathrm{out}}}=2\mathrm{KL}---\left(14\right)$

To after (4) substitution (14) conversion, have:

$P=\mathrm{KL}\frac{2Q_{\mathrm{in}}{Q}_{\mathrm{out}}}{Q_{\mathrm{in}}+Q_{\mathrm{out}}}---\left(15\right)$

CMF be constant mass rate by sample, because the density of sample input is the density of air, at the entrance point of sample, keep constant volumetric flow rate; And being end at sample, CFO keeps constant volumetric flow rate; Known this volumetric flow rate of the definition of resistance to suction is 17.5ml/s;

(15) formula is applied to these two kinds of methods to be had:

$P_{\mathrm{CMF}}=\mathrm{KL}\frac{2{Q_{\mathrm{in}}}^{\′}{Q_{\mathrm{out}}}^{\′}}{{Q_{\mathrm{in}}}^{\′}+{Q_{\mathrm{out}}}^{\′}}---\left(16\right)$

$P_{\mathrm{CFO}}=\mathrm{KL}\frac{2Q_{\mathrm{in}}{Q}_{\mathrm{out}}}{Q_{\mathrm{in}}+Q_{\mathrm{out}}}---\left(17\right)$

For same sample KL, equate;

Q ' in two kinds of measuring methods _in=Q _out, will after (16) and (17) conversion, have:

$P_{\mathrm{CMF}}(2P_a-P_{\mathrm{CMF}})=P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}---\left(18\right)$

P wherein _afor known number, suppose to know respectively P _cFOand P _cMFthe time, can apply the quadratic equation radical formula and obtain P _cMFand P _cFO; For P _cMFuse P _cFOmean, have

$P_{\mathrm{CMF}}^2-2P_a{P}_{\mathrm{CMF}}+P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}---\left(19\right)$

$P_{\mathrm{CMF}}=P_a\±\sqrt{P_a^2-P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}}---\left(20\right)$

Equally, for P _cFOuse P _cMFmean, have

$P_{\mathrm{CFO}}^2=[P_{\mathrm{CMF}}(2-\frac{P_{\mathrm{CMF}}}{P_a})+2P_a]P_{\mathrm{CFO}}+P_{\mathrm{CMF}}(2P_a-P_{\mathrm{CMF}})=0---\left(21\right)$

$P_{\mathrm{CFO}}=P_{\mathrm{CMF}}(1-\frac{P_{\mathrm{CMF}}}{2P_a})+P_a\±\sqrt{P_{\mathrm{CMF}}^2{(1-\frac{P_{\mathrm{CMF}}}{2P_a})}^2+P_a^2}---\left(22\right)$

Formula (20) and (22) are P _cMFand P _cFOthe expression formula mutually transformed; Consider real process, in aspiration procedure, pressure is less than P _a, can select reasonably value from formula (20) and (22), obtain

$P_{\mathrm{CMF}}=P_a-\sqrt{P_a^2-P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}}---\left(23\right)$

$P_{\mathrm{CFO}}=P_{\mathrm{CMF}}(1-\frac{P_{\mathrm{CMF}}}{2P_a})+P_a-\sqrt{P_{\mathrm{CMF}}^2{(1-\frac{P_{\mathrm{CMF}}}{2P_a})}^2+P_a^2}---\left(24\right).$

The present invention is by above-mentioned technical scheme, introduce in detail the theoretical model of having analyzed CFO measurement resistance to suction method and CMF measurement resistance to suction method, and by the CFO of theoretical model inference and the formula of the conversion between the CMF method, and with formula and form in ISO6565, compare, the formula of derivation more approaches the form transformational relation than ISO6565 formula.

Embodiment

The method for building up of conversion model between the resistance to suction voltage drop value that CFO device and CMF device record, the method comprises the following steps:

The pressure at assumes samples (cigarette and filter stick) two ends is respectively P _inand P _out, volumetric flow rate is respectively Q _inand Q _out, P for actual measurement _inwith atmospheric pressure, equate, i.e. P _in=P _a(P _afor atmospheric pressure).

By the Ideal-Gas Equation

PV＝nRT (3)

Two ends at sample have

P _aQ _in＝P _outQ _out＝(P _a-P)Q _out (4)

In formula, P is sample pressure reduction (resistance to suction).

$\frac{\∂\left(\mathrm{PQ}\right)}{\∂z}=P\frac{\∂Q}{\∂z}+Q\frac{\∂P}{\∂z}=0---\left(5\right)$

The length that in formula, z is sample.

(5) are changed and have

$\frac{\∂Q}{\∂z}=\frac{Q}{P}\frac{\∂P}{\∂z}---\left(6\right)$

Mobile pressure discharge relation per sample, can suppose that resistance to suction is directly proportional to flow,

P＝KLQ (7)

In formula, L is sample length, and K is coefficient (constant), by

$\frac{P}{L}=-\frac{\∂P}{\∂z}---\left(8\right)$

Therefore have

$\frac{\∂P}{\∂z}=-\mathrm{KQ}---\left(9\right)$

In formula, negative sign means that pressure reduces along with sample length is increased in.

(9) substitution (6) is had

$\frac{\∂Q}{\∂z}=K\frac{Q^2}{P}=K\frac{Q^3}{\mathrm{QP}}---\left(10\right)$

(10) formula integration is had

$\left(\mathrm{PQ}\right)\underset{Q_{\mathrm{in}}}{\overset{Q_{\mathrm{out}}}{\∫}}\frac{1}{Q^3}\mathrm{dQ}=K\underset{0}{\overset{L}{\∫}}\mathrm{dz}---\left(11\right)$

In formula, (PQ) can be to be constant because (PQ) does as a whole in the outside of integration type, shown in (4).

(11) distortion is had:

$\mathrm{PQ}(\frac{1}{2Q_{\mathrm{in}}^2}-\frac{1}{2Q_{\mathrm{out}}^2})=\mathrm{KL}---\left(12\right)$

By

PQ＝P _aQ _in＝P _outQ _out (13)

(13) substitution (12) is had:

$\frac{P_a}{Q_{\mathrm{in}}}-\frac{P_{\mathrm{out}}}{Q_{\mathrm{out}}}=2\mathrm{KL}---\left(14\right)$

To after (4) substitution (14) conversion, have:

$P=\mathrm{KL}\frac{2Q_{\mathrm{in}}{Q}_{\mathrm{out}}}{Q_{\mathrm{in}}+Q_{\mathrm{out}}}---\left(15\right)$

CMF be constant mass rate by sample, because the density of sample input is the density of air, at the entrance point of sample, keep constant volumetric flow rate; And being end at sample, CFO keeps constant volumetric flow rate.Known this volumetric flow rate of the definition of resistance to suction is 17.5ml/s.

(15) formula is applied to these two kinds of methods to be had:

$P_{\mathrm{CMF}}=\mathrm{KL}\frac{2{Q_{\mathrm{in}}}^{\′}{Q_{\mathrm{out}}}^{\′}}{{Q_{\mathrm{in}}}^{\′}+{Q_{\mathrm{out}}}^{\′}}---\left(16\right)$

$P_{\mathrm{CFO}}=\mathrm{KL}\frac{2Q_{\mathrm{in}}{Q}_{\mathrm{out}}}{Q_{\mathrm{in}}+Q_{\mathrm{out}}}---\left(17\right)$

For same sample KL, equate.

Q ' in two kinds of measuring methods _in=Q _out, will after (16) and (17) conversion, have:

$P_{\mathrm{CMF}}(2P_a-P_{\mathrm{CMF}})=P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}---\left(18\right)$

P wherein _afor known number, suppose to know respectively P _cFOand P _cMFthe time, can apply the quadratic equation radical formula and obtain P _cMFFand P _cFO.For P _cMFuse P _cFOmean, have

$P_{\mathrm{CMF}}^2-2P_a{P}_{\mathrm{CMF}}+P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}---\left(19\right)$

$P_{\mathrm{CMF}}=P_a\±\sqrt{P_a^2-P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}}---\left(20\right)$

Equally, for P _cFOuse P _cMFmean, have

$P_{\mathrm{CFO}}^2=[P_{\mathrm{CMF}}(2-\frac{P_{\mathrm{CMF}}}{P_a})+2P_a]P_{\mathrm{CFO}}+P_{\mathrm{CMF}}(2P_a-P_{\mathrm{CMF}})=0---\left(21\right)$

$P_{\mathrm{CFO}}=P_{\mathrm{CMF}}(1-\frac{P_{\mathrm{CMF}}}{2P_a})+P_a\±\sqrt{P_{\mathrm{CMF}}^2{(1-\frac{P_{\mathrm{CMF}}}{2P_a})}^2+P_a^2}---\left(22\right)$

Formula (20) and (22) are P _cMFand P _cFOthe expression formula mutually transformed.Consider real process, in aspiration procedure, pressure is less than P _a, can select reasonably value from formula (20) and (22), obtain

$P_{\mathrm{CMF}}=P_a-\sqrt{P_a^2-P_a{P}_{\mathrm{CFO}}\frac{2P_a-P_{\mathrm{CFO}}}{P_a-P_{\mathrm{CFO}}}}---\left(23\right)$

$P_{\mathrm{CFO}}=P_{\mathrm{CMF}}(1-\frac{P_{\mathrm{CMF}}}{2P_a})+P_a-\sqrt{P_{\mathrm{CMF}}^2{(1-\frac{P_{\mathrm{CMF}}}{2P_a})}^2+P_a^2}---\left(24\right)$

Table 1 and table 2 are comparisons of formula (23) and (24) and ISO6565 formula appendix D.

Table 1CFO and CMF transformational relation

Although provide reduction formula and form between CFO and CMF in ISO6565, the derivation of formula do not had to the theoretical procedure explanation.The present invention introduces the theoretical model of having analyzed CFO measurement resistance to suction method and CMF measurement resistance to suction method in detail, and by the CFO of theoretical model inference and the formula of the conversion between the CMF method, and with formula and form in ISO6565, compare, the formula of derivation more approaches the form transformational relation than ISO6565 formula.

Claims (1)

1. adopt the CFO device to measure the method for CMF pressure drop, it is characterized in that the method comprises the following steps:

1) adopt the CFO device to record the pressure drop P that the CFO device records _cFO ;

2) then by following method, calculate the pressure drop P that the CMF device records _cMF :

；

Above-mentioned P _cMF the pressure drop recorded for the CMF device; P _cFO the pressure drop recorded for the CFO device; p _afor atmospheric pressure.