Critical flow based mass flow verifier

• US 7,474,968 B2
• Filed: 06/30/2006
• Issued: 01/06/2009
• Est. Priority Date: 03/25/2005
• Status: Active Grant

• Current Assignee: MKS Instruments Incorporated
• Original Assignee: MKS Instruments Incorporated
• Inventors: Smith, Daniel, Shajii, Ali, Zarkar, Kaveh, Ding, Junhua
• Primary Examiner(s): Lau; Tung S
• Assistant Examiner(s): Kundu; Sujoy K
• Application Number:
  US11/479,092
• Publication Number:
  US 20060283254A1
• Time in Patent Office: 921 Days
• Field of Search: 702/45, 702/100, 73/13.5, 73/13.6, 73/11.6, 732/042.2, 738/665
• US Class Current: 702/45
• CPC Class Codes: G01F 25/15 specially adapted for gas meters G01F25/11 - G01F25/14, G01F25/17 take precedence
• CPC Class Codes: G01F 25/17 using calibrated reservoirs

Abstract

A flow verifier for verifying measurement by a fluid delivery device under test (DUT) includes a chamber configured to receive a flow of the fluid from the DUT, at least one temperature sensor to provide gas temperature in the chamber, at least one pressure transducer to provide gas pressure in the chamber, and a critical flow nozzle located upstream of the chamber along a flow path of the fluid from the DUT to the chamber. The critical flow nozzle and the flow verification process are configured to maintain the flow rate of the fluid through the nozzle at the critical flow condition such that the flow rate through the nozzle is substantially constant and substantially insensitive to any variation in pressure within the chamber downstream of the nozzle. Therefore, the varying chamber pressure during the flow verification period has substantially no impact on the downstream pressure of the DUT, and the external volume between the flow verifier and the DUT is substantially irrelevant to the flow verification calculation.

Claims

1. A flow verifier for verifying measurement by a fluid delivery device, the flow verifier comprising:

a chamber configured to receive a flow of the fluid from the device;

a pressure sensor configured to measure pressure of the fluid within the chamber;

a temperature sensor configured to measure temperature of the fluid within the chamber; and

a critical flow nozzle located upstream of the chamber along a flow path of the fluid from the device to the chamber;

wherein the critical flow nozzle is configured to maintain, during a critical flow time period t_cf, flow rate of the fluid through the nozzle substantially constant and substantially insensitive to variation in pressure within the chamber;

wherein the critical flow nozzle is configured to allow the fluid flowing through the nozzle to satisfy a critical flow condition during the critical flow time period t_cf, and wherein the critical flow condition is given mathematically by;

$\frac{P_d}{P_u}\le <br><br>a_{\mathrm{pc}}={\left(\frac{2}{\mathrm{\gamma <br><br>}+1}\right)}^{\frac{\mathrm{\gamma <br><br>}}{\mathrm{\gamma <br><br>}-1}},$

where

P_d is pressure of the fluid within the chamber and downstream of the critical flow nozzle, P_u is pressure of the fluid upstream of the critical flow nozzle, γ

is given by γ

=C_p/C_v and is a ratio of specific heats C_p and C_v of the fluid, where C_p is heat capacity of the fluid at constant pressure, and

C_v is heat capacity of the fluid at constant volume, and α

_pc is critical pressure ratio representing the maximum allowable ratio between P_d and P_u for which flow of the fluid across the nozzle will remain substantially constant and substantially insensitive to any variation in pressure within the chamber.

2. The flow verifier of claim 1, further comprising an upstream valve configured to shut on and off flow of the fluid from the device into an inlet of the chamber, and a downstream valve configured to shut on and off flow of the fluid from an outlet of the chamber.

3. The flow verifier of claim 2, further comprising:

a controller configured to control the downstream and upstream valves and the pressure and temperature sensors, the controller further configured to measure a rate of rise in pressure of the fluid within the chamber after the downstream valve is closed, and using the measured rate of rise to calculate the flow rate of the fluid from the device into the chamber, thereby verifying measurement by the fluid delivery device.

4. The flow verifier of claim 3, wherein the pressure sensor and the temperature sensor are configured to make measurements within the critical time period t_c, so that the flow verification process is substantially independent of the varying chamber pressure and the external volume between the verifier and the DUT.

5. The flow verifier of claim 2, wherein the critical flow time period t_cf is defined between a point in time when the downstream valve is shut, to a point in time when a ratio between P_d and P_u exceeds the critical pressure ratio limit, α

_p0, as given by;

$t_c=\frac{V<br><br>\left(a_{\mathrm{pc}}-a_{p<br><br><br><br>0}\right)}{C^{\mathrm{\prime <br><br>}}<br><br>{\mathrm{Af}}_g<br><br>\left(M,\mathrm{\gamma <br><br>},T\right)},$

where

V_c is chamber volume,

a_p0 is initial pressure ratio between the upstream and the downstream of the nozzle at t=0,

C′

is discharge coefficient for the nozzle,

A is cross-sectional area of the nozzle throat,

f_g(M,γ

, T)

$f_g<br><br>\left(M,\mathrm{\gamma <br><br>},T\right)={\left(\frac{\mathrm{RT}}{M}<br><br>\frac{2<br><br>\mathrm{\gamma <br><br>}}{\mathrm{\gamma <br><br>}+1}\right)}^{1/2}<br><br>{\left(\frac{2}{\mathrm{\gamma <br><br>}+1}\right)}^{1/\left(\mathrm{\gamma <br><br>}-1\right)}$

where

M is the molecular weight of the fluid,

R is the universal gas constant,

T is the gas temperature, and

γ

is a ratio of specific heats C_p and C_v of the fluid, C_p being the gas heat capacity at constant pressure, and C_v being the gas heat capacity at constant volume.

6. The flow verifier of claim 1, wherein flow rate of the fluid during the critical flow period t_cf is given by:

$Q=C^{\mathrm{\prime <br><br>}}<br><br>{{\mathrm{AP}}_{\mathrm{\mu <br><br>}}<br><br>\left(\frac{\mathrm{RT}}{M}<br><br>\frac{2<br><br>\mathrm{\gamma <br><br>}}{\mathrm{\gamma <br><br>}+1}\right)}^{1/2}<br><br>{\left(\frac{2}{\mathrm{\gamma <br><br>}+1}\right)}^{1/\left(\mathrm{\gamma <br><br>}-1\right)},$

where T is a temperature of the fluid;

A is a cross-sectional area of nozzle orifice, C′

is a discharge coefficient, M is a molecular weight of the fluid, R is a universal gas law constant, and

P_d, P_u, and γ

are defined as in claim 1.

7. The flow verifier of claim 3, wherein the controller is configured to verify the measurement of the fluid delivery device by:

a) opening the upstream valve and the downstream valve;

b) providing a flow set point for the device;

c) waiting until pressure within the chamber reaches a steady state and stabilizes;

d) start to record the chamber gas pressure and the chamber gas temperature for flow calculation;

e) shut the downstream valve, so that the pressure within the chamber rises;

f) wait for a period less than the critical flow period t_cf for flow verification;

g) open the downstream valve within a critical time period as measured from when the downstream valve was shut; and

h) compute the flow rate of the fluid into the chamber using;

$Q_{\mathrm{in}}=\frac{k_0·<br><br>T_{\mathrm{stp}}·<br><br>V_c}{P_{\mathrm{stp}}}<br><br>\frac{d<br><br>}{d<br><br>t}<br><br>\left(\frac{P}{T}\right)$

where V_c is the chamber volume,

T_stp is about 273.15K,

P_stp is about 1.01325e5 P_a,

K₀ is about 6×

10⁷ in SCCM units and 6×

10⁴ in SLM units

P is the chamber pressure measured by the pressure sensor/transducter

T is the gas temperature measured by the temperature sensor.

8. The flow verifier of claim 7 wherein the critical nozzle separates the chamber volume of the ROR verifier from external plumbing to the DUT, so that the external volume information is irrelevant to the flow rate calculation of the ROR mass flow verifier, and no setup calibration is needed to determine the external volume between the flow verifier and the DUT.

9. The flow verifier of claim 8, wherein the flow verifier is operable in a continuous-pulse-semi-real time (CPSR) operation mode in which the controller causes the pressure and temperature measurements to be made by the pressure sensor and the temperature sensor during each of a plurality of verification time periods, each verification time period starting when the downstream valve is shut, and ending when the downstream valve is opened before the critical flow period t_cf lapses from the time the downstream valve was shut, such that the flow across the nozzle is always at the critical flow condition and the varying chamber pressure has substantially no impact on the flow rate and the downstream pressure of the DUT.

10. The flow verifier of claim 9, wherein the flow rate computed by the controller is an averaged flow rate for multiple runs in the CPSR mode, so that a variance in the computed flow rate caused by measurement noise in the pressure sensor and temperature sensor is minimized.

11. The flow verifier of claim 1, wherein the critical flow nozzle is configured so as to restrict flow of the fluid through the nozzle to a critical flow.

12. A method of verifying measurement of a flow delivery device, comprising:

placing a critical flow nozzle along the flow path of the fluid between the mass flow verifier and the DUT to maintain flow of the fluid so that during a critical flow time period, flow of the fluid across the nozzle and pressure of the fluid upstream of the nozzle of the remains substantially constant and substantially insensitive to the rise of the pressure within the chamber;

causing the fluid to flow from the device into a chamber along a flow path, while an inlet and an outlet valve of the chamber is kept open;

allowing a flow rate of the fluid into the chamber and a pressure of the fluid within the chamber to reach a steady state;

closing a valve downstream of the chamber so that pressure of the fluid begins to rise within the chamber; and

making measurements of fluid pressure and fluid temperature within the critical flow time period to measure a rate of rise of pressure of the fluid within the chamber and using the measured rate of rise of pressure to compute the flow rate of the fluid along with the measurements of fluid temperature;

wherein the critical flow nozzle is configured to restrict flow of the fluid across the nozzle so that a critical flow condition is satisfied during the critical flow time period, and wherein the critical flow condition is given mathematically by;

$\frac{P_d}{P_u}\le <br><br>a_{\mathrm{pc}}={\left(\frac{2}{\mathrm{\gamma <br><br>}+1}\right)}^{\frac{\mathrm{\gamma <br><br>}}{\mathrm{\gamma <br><br>}-1}},$

where

P_d is pressure of the fluid within the chamber and downstream of the critical flow nozzle,

P_u is pressure of the fluid upstream of the critical flow nozzle,

γ

is given by γ

=C_p/C_v and is a ratio of specific heats C_p and C_v of the fluid, where C_p is heat capacity of the fluid at constant pressure, and C_v is heat capacity of the fluid at constant volume, and

α

_pc is a critical flow parameter representing maximum allowable ratio between P_d and P_u for which flow of the fluid across the nozzle will remain substantially constant and substantially insensitive to any variation in pressure within the chamber.

13. The method of claim 12, wherein the flow rate of the fluid is computed using:

$Q_{\mathrm{in}}=\frac{k_0·<br><br>T_{\mathrm{stp}}·<br><br>V_c}{P_{\mathrm{stp}}}<br><br>\frac{d<br><br>}{d<br><br>t}<br><br>\left(\frac{P}{T}\right)$

where P and T are measured by the pressure sensor and the temperature sensor during the verification period which is within the critical flow period such that the varying chamber pressure has not impact on the downstream pressure of the DUT.

14. The method of claim 13,

wherein the pressure and temperature measurements are made during each of a plurality of verification time periods, each verification time period starting when the downstream valve is shut, and ending when the downstream valve is opened before the critical flow time period t_cf lapses from the time the downstream valve was shut;

and

wherein the computed flow rate is an averaged flow rate during multiple runs in the CPSR mode so that measured noise is minimized.