H5 Gas meter calibration

Transcription

1 H5 Gas mete calibation Calibation: detemination of the elation between the hysical aamete to be detemined and the signal of a measuement device. Duing the calibation ocess the measuement equiment is comaed with an ethalon o anothe measuement device with a highe class of accuacy. The measuement setu Figue. Sketch of the measuement setu and the alied equiment The cylindical esevoi, denoted with H, of the calibation device has an oen to and is filled with oil. A second vessel (meteing tank) H which is tuned uside down, is immesed into the annulus shaed, oil filled sace of the esevoi H. The sace, bounded by the solid walls and the oil is filled with comessed ai. The ai is deliveed though ie C fom the comessed ai netwok of the laboatoy afte closing the valves Sz and Sz3 and oening Sz. The volume of the comessed ai elevates vessel H (Z ). The loweing of the meteing tank fom this osition to Z can be used to measue the volume flow of the ai. The moving vessel is ket vetically using a chain mechanism, and coaxially with the esevoi using a ail. The comessed ai will slightly incease the essue in the closed sace which makes the suface of the oil in the oute annulus section to elevate and to lowe in the inne one. Afte the meteing tank is elevated to the desied level, valve Sz can be closed to sto the ai flow. The eaation of the measuement aaatus is comleted with this last ste. The measuement ange of the scale on the side wall of the meteing tank is: 00 mm < z < 000 mm This means that the maximum elevation of the meteing tank, eached by the comessed ai flow, can be z000 mm. Duing the measuement the level may not descend unde z00 mm. Afte eaching the minimum level the vessel has to be efilled with ai.

2 At lowe ai consumtion moe oints can be measued in the ue egion of the scale. All oints should be measued with at least z 80 mm level-change, even the ones at low ai consumtion. Duing the measuement of a oint, valve Sz is in its closed osition while the valve Sz and/o the aallel valve Sz3 is oened to each the desied volume flow. Sz3 can be used when the fine setting of the consumtion is necessay. The goal of the esent measuement is to calibate a household gas mete. To calibate the device the volume flow is measued with the method of scaling. Duing the ocedue the level change of the meteing tank H ( z), and the duation of the level change τ is measued. The level can be detemined using the [mm]-scale mounted on the side of the meteing tank. The time duation is detemined using a sto-watch. With these the volume flow is: q α z τ () whee α [dm 3 /mm] vessel-constant, volume of a mm thick vessel section, z z - z [mm] measued level change, τ [s] time duation of the level change. In case of gases the volume flow is calculated unde nomal conditions. The hysical nomal conditions ae as follows: t n 0 C, meaning T n 73 K density of ai ρ gn.93 kg/m 3 b760 mmhg, meaning n 0.36 kpa The essue t inside the vessel filled with the comessed ai is measued using a U-tube manomete t ove ρ v g h ρ v g (h f - h a ). The measuing liquid in the manomete is wate with the density of ρ v. Knowing the vessel essue the density of the ai inside can be calculated. Assuming an ideal gas and homogeneous temeatue distibution /ρ constant. To detemine the essue at the inlet of the gas mete the essue ( G o G ) has to be measued using the built-in wate filled U-tube manomete level diffeence ( h G h Gf - h Ga, and h G h Gf - h Ga ).

3 Thee ae thee sto-watches available to measue the time: The fist one is to measue the time duation τ of the level change z of the vessel H. The second and thid ae to measue seaately the time of evolution (τ and τ ) of the two gas metes G and G. Thee ae seveal vaiables to be measued at the instant of the measuement stat (τ 0) of one oint in the calibation diagam: z the level of the vessel (at τ 0), h Gf ; h Ga the levels of the U-tube manomete at gas mete G, h Gf ; h Ga the levels of the U-tube manomete at gas mete G,,0 the cuent value of the gas amount shown by G (at τ 0),,0 the cuent value of the gas amount shown by G (at τ 0). To stat and sto the sto-watches the last dislay wheel of the gas metes is to be used as efeence. This value should be a whole numbe both at the stat and at the end of the measuement. The diffeence of the values shown by the gas metes at the stat and the end is the amount of gas V with dimension [dm 3 ]. Afte the measuement eiods (τ, τ, and τ ) the following values need to be ecoded again: z cuent level of the vessel (at τ),,τ the cuent value of the gas amount shown by G ( at τ ),,τ the cuent value of the gas amount shown by G ( at τ ). The meteing tank was calibated eviously. The line fit on the oints of the calibation diagam (V [m 3 ] - z [mm]) of the meteing tank gives the vessel constant α, which is the volume of a height unit. The value of this constant in the esent case is: 3 α 0.4 dm mm ± 0.5%. Knowing this allows the detemination of the volume flow of the gas by measuing the level change of the meteing tank and the essue t inside. The small amount of oil level change caused by the volume of the comessed ai in the vessel can be neglected duing the calculations. q dm3 t V ( z ) V z s τ ( ) ( ) α z z τ 0.4 dm3 z [ mm ] z mm. () mm τ s [ ] [ ] With this, assuming isothemal change of state the volume flow at the entance of the gas metes can be calculated as follows: q tg t qt, and (3) G q t tg qt (4) G 3

4 To calculate the volume flows, the absolute values of the essue have to be used. This means that knowing the measued athmosheic essue o the essues ae: t abs o + t ove ρ Hg g b + ρ v g h vessel essue, (5) G abs o + G ove ρ Hg gb + ρ v g h G absolute esssue at the inlet of G, (6) G abs o + G ove ρ Hg gb + ρ v g h G absolute esssue at the inlet of G (7) The volume flows measued by the gas metes can be calculated as: q G, τ,0, (8) τ and Measuement ocess q G, τ,0. (9) τ The size of the gou should not be ove 6 esons. Half of the gou calibates the gas mete G and the othe half G. To make the calibational diagams the measuement have to be eeated at least in 0 diffeent valve settings (Sz, and Sz3) and the measued values have to be witten in the table shown below. Half of the measuement oints ae to be measued at low gas consumtion and half of them at moe oen valve ositions. Data of a gas mete calibation: Ssz. τ,0,τ h Gf h Ga h G q G z z τ q tg [s] [dm 3 ] [dm 3 ] [mm] [mm] [mm] [dm 3 /s] [mm] [mm] [s] [dm 3 /s] Equat. (8) (,3,5,6).. 0. A diagam of the calibation have to be dawn using a millimete ae. Two cuves ae to be made: f ( q ), and q f ( q ) G tg G tg q The measuement oints ae to be noted by + signs. A line has to be fitted on the measued oints using Wald s method as descibed in the Aendix. Measuement eaations: -Daw the emty calibation diagam: daw and name the axes 4

5 -Make eady the ages of the measuement eot: goal of the measuement, sketch of the measuement setu, measuement ocess and fomulae to be used Abaham Wald s method to fit linea cuves Abaham Wald develoed a method whitch can take into consideation the measuement eo in both the indeendent and deendent vaiable of a linea function. In the following the mathematical theoem is stated and its alication is descibed. The oof can be found in the cited documents. (Ábahám Wald gaduated in the Piaist High school of Kolozsvá in 9, woked in the United States whee he founded the science of moden statistics.) Let thee be a linea elation between two vaiables y a o + a x (6.4) The measuement eo is esent in case of both vaiables and it has a Gaussian distibution and an exected value of zeo. x + δ δ ( 0,σ x ) y + ε ε ( 0,σ y ) Based on the measued oints { }, with Wald s method a undestoted aoximation can be made fo α 0 and α (see late): M (α o ) a o and M(α ) a. Whee M ( ) is the exected value The method oosed by Wald is simle and it can be easily memoized with the hel of Figue 6.6. Let us daw the measuement oints on a (, ) coodinate system. The vaiable ais have to be soted in an ascending ode based on the vaiable. Let us denote this new. set with {, },,

6 6 The soted set have to be divided into two subsets at an abitay index (fo details see below). The coodinates centes of mass of the two subsets have to be calculated seaately. The coodinates of S and S ae esectively:, & & & & + + Figue 6.6 Wald s method Let us calculate the sloe of the line going though both S and S : α (6. 5) Calculate coodinates the cente of mass of the whole oint set: Daw a line though this oint with the sloe calculated befoe (α ) yielding:

7 α o α (6. 6) The aoximation of the line becomes moe ecise if the two cente of mass get futhe fom each othe. That is why it is necessay to sot the oints in an ascending ode and to choose the to be the index in the middle. It can be also stated that if we know that the elation between two vaiables is linea then it is bette to measue this elation by measuing data at the two ends of the measuement ange to aoximate the sloe moe accuately by having the centes of mass fa fom each othe. Liteatue:. Halász Gábo Huba Antal: Mőszaki Méések. Mőegyetemi Kiadó, A. Wald: The Fitting of Staight Lines if both Vaiables ae Subect to Eo. Annalysis of Mathematical Statistics. Vol.. no

8 Photos The meteing tank H with the mechanisms ensue its vetical oientation 8

9 The meteing tank elevated by the comessed ai 9

10 The gas metes to be calibated, and to measue the gas consumtion 0

11 The scale to measue the level change of the meteing tank