Processline/Flowmeasurement/Big report
COMPUTERCALCULATION OF THROATDEVICE FOR FLOWMEASUREMENT IN TUBES ACCORDING STANDARD ISO 5167-1 & 2 from 2003 Date: 2010-02-06 /Time: 00:00:31 Computerprogram; Processline.0911/Windows from MATEMATICA Tel: +46-(0)708-387910, e-mail: mail@matematica.se
skype; stefan.rudback copyright (c) 1995,2009 Stefan Rudbäck, Matematica, Sweden Calculation done by Matematica __________________INPUT______________________ ISO5167:2003 Differential pressure kPa 1.Orifice plate, Corner tappings Media: Saturated steam Static Pressure? (at + Pressure tapping)___________(kPa) 289 Material throat =Steel 5:1.4301:1.4401:1.4541:1.4550:1.4571:1.4580:1.4910:1.4919 1st order expansionfactor________________________(E-6/C) 17 2nd order______________________________________ (E-6/C2) 0,0038 Material tube =Steel 1:1.0037:1.0038:1.0254:1.0345:1.0425:1.0460:1.5415:1.7335 1st order expansionfactor________________________(E-6/C) 12,6 2nd order______________________________________ (E-6/C2) 0,0043
Interior tubediameter cold (=20 C)?_________________(mm) 392,8 Mean radius rk of unsharp inlet edge of orifice?____(mm) 0 Pipe roughness k?___________________________________(mm) 0,1 Maximal flow?____________________________________(ton/h) 35 Minimal flow?____________________________________(ton/h) 3,5 Throatdiameter d cold (20 C)?_______________________(mm) 201,04 Upstream fitting: 1. One(/two, separation>30D) 90 degrre Bend Pos.of fitting upstream (from upstream press.tapp.)?_(m) 10 Pos.of fitt.downstream (from downstream press.tapp.)?(m) 10
__________________OUTPUT_____________________ NOTE! CALCULATIONRESULT OUTSIDE STANDARDLIMITS DIFFPRESSURE TO BIG MAXLIMIT (kPa)= 72,250 MAIN RESULT Maximal Differential Pressure(not=P-loss)____(kPa)= 90,696
Table; Relation btw flow and differential pressure (at operating cond.= 132,27 C, 289 kPa) flow 3,5000 7,0000 10,500 14,000 17,500 21,000 24,500 28,000 31,500 35,000 dp 0,7420 2,9900 6,7874 12,208 19,364 28,419 39,613 53,297 70,019 90,696
MOUNTING IN TUBE Max eccentricity tube/throat 0% add. error____(mm)= 3,8099 Max eccentricity for 0.3% additional error____(mm)= 7,6197 Maximal angle tube/throat_________________________=1 DEGREE
CONFIGURATION OF dp-TRANSMITTER 1.Linear dp-transmitter (used for very good precision from >=50 to 100% flow) Adjust the transmitter for max signal 20 mA at maximal diff. pressure= 90,696 kPa Then calculate the flow with flowcalculation-method 1,2 or 3 below
2.Square-root dp-transm. (used for good precision from <50 to 100% flow)
2.1.Best precision at normal flow=67%*maxflow; Adjust the transmitter for max signal 20 mA by adjusted maxflow= 37,214 ton/h= 90,696 kPa
2.2.Best precision at maxflow; Adjust the transmitter for max signal 20 mA at 35,000 ton/h= 90,696 kPa
2.3.Best precision at all flows Adjust the transmitter for max signal 20 mA at 35,000 ton/h= 90,696 kPa Then improve the flowvalue in computer with adjustment functions fmat and fdens(/fdens_mat) according pos 3 & 4 below.
1 OR 2 dp-transmitters? 1.Average additional Uncertainty with 1 dp-cell (% of maximal flow)= 0,129 2.Average additional Uncertainty with 2 dp-cells (% of maximal flow)= 0,062 (If the Uncertainty of the dp-transmitters = 0.1% of span) 3. Optimal limit between small and big dp-transmitter (% av maximal dp)= 30,5 4. Optimal limit between small and big dp-transmitter (% av maximal flow)= 55,3 5. Configuration of small dp-transmitter; 20 mA= 27,704 kPa =(pos 2.1) 20,568 (2.2) 19,344 (2.3) 19,344 ton/h (If the Uncertainty of the dp-transmitters are equal (in % of span)
SOME FLOWCALCULATIONALGORITHMS WITH UNCERTAINTIES* *(at operating cond.= 132,27 C, 289 kPa) *(NOTE! Sqrt calculation of flow in dp-cell OR computer, NOT BOTH!) Average standard uncertainty btw. min- & maxflow__(%)= 0,6
1.Avg. standard unc. + calculation error in calculation algorithm 1; q_rot_normal= 3,90767*sqrt(dp) < 3,4 % Used for best Precision at Normal flow=67%*Maximal flow.
2.Avg. standard unc. + Calc. error in Calculation algorithm 2; q_rot_max= 3,67514*sqrt(dp) < 6,6 % Used for best Precision at Maximal flow.
3.Avg. standard unc. + Calculation error in calculation algorithm 3; q_pol_mat=q_rot_mat*fmat < 0,7 % where q_rot_mat= 3,67514*Sqrt(dp) where fmat(q_rot_mat)=(1-0,76840E-4*q_rot_mat**2*289,000/(P*1.00000))/0,90587*(1+0,65830E-2/q_rot_mat**(3/4))/1,00046 (Where ** = raised to) Used for best Precision at all flows
(* KODFABRIKEN;Generation of standardised code, IEC61131, ST, f ex ABB Industrial IT Copyright (c) 2009 Matematica, mail@matematica.se, +46-(0)708-387910 Scaling; 20 mA from dp-cell= 90.6958 kPa= 20 mA to control system 1.Calculation error<=0,0% av beräknat flödesvärde q_pol_mat_PT For;3,50000 <q_pol_mat_PT< 35,0000 289,000 <P< 289,000 T= 132,273533677539 2.Parameters dpcell real in kPa,=dp-signal from dp-transmitter, linear or sqrt-calculated dp_max real in 90.6958 kPa=20 mA dp_rot bool in 0 0=linear dp-cell/1=square root dp-cell q_pol_mat_PT real out ton/h,PT compensated & polynom calculated flowsignal,use this 3.Variables q_pol_mat real ton/h,polynom calculated flow,not to be used q_rot_mat real ton/h,sqrt-calculated flow, not to be used fmat real dp real kPa,=calculated dp = dpcell at linear dp-tarnsm. 4.Code *) dp:=dpcell; if dp_rot then dp:=dpcell*dpcell/dp_max/dp_max*dp_max; end_if; q_rot_mat:=3.67514*Sqrt(dp); fmat:=(1-0.76840E-4*expt(q_rot_mat,2)*289.000/(P*1.00000))/0.90587*(1+0.65830E-2/expt(q_rot_mat,0.75))/1.00046; q_pol_mat:=q_rot_mat*fmat; (*simple Pressure/temp-correction of density, advanced see Density calculations*) q_pol_mat_PT:=q_pol_mat*sqrt(P*1.00000/289.000*(273.15+132.274)/(273.15+T));
FLOWREPORT Adjusted maxflow for square root function_________= 37,214 Note: Used to minimize calculation error at normalflow=0.67*maxflow Pressureloss at maxflow (not=diff. pressure)_(kPa)= 65,431 Pressureloss at minflow (not=diff. pressure)_(kPa)= 0,5353 Power loss at maxflow_________________________(kW)= 398,96 Flow speed in tube (at maxfllow)_____________(m/s)= 50,169 Flowspeed in throat (at maxflow)_____________(m/s)= 214,12 Flowspeed in vena contracta (at maxflow)_____(m/s)>SOUNDLIMIT! (CRITICAL FLOW= 79,4 % of maxflow) Reynolds number (at maximal flow)_________________= 2,3489E6 Maxflowlimit of the standard________(% of maxflow)= 91,191 Minflowlimit of the standard________(% of maxflow)= 0,2129
PHYSICS REPORT Temperature____________________________________(C)= 132,27 Density____________________________________(kg/m3)= 1,5945 Dynamic viscosity________________________(Pas*E-6)= 13,397 Kappa (Isentropic expansioncoeff.)________________= 1,3145 Temperature correction factor of throatdiameter___= 1,0020 Temperature correction factor of tubesize_________= 1,0015
STANDARD REPORT Epsilon (at maxflow)______________________________= 0,9071 Alfa (=C*E) (at normalflow)_______________________= 0,6256 C (at normal flow)________________________________= 0,6037 Beta (d/D) at operating conditions________________= 0,5121 Area ratio (beta*beta) at operating conditions____= 0,2622
The following table shows shortest possible straight tube length between different disturbancies and the upstream pressure tapping of the throat device. The disturbancies are upstreams but not for the last table line, which shows the length between downstream pressure tapping and disturbance. Two lengths are specified, for 0% and 0.5% flowmeasurement error contribution. ADDITIONAL ERROR (Measured from upstream pressure tapping) 0% 0.5% DISTURBANCE STRAIGHT LENGTH (m) One(/two, separation>30D) 90 degrre Bend 16,5.......... 5,11 Two 90 degrees bends in the same plane (separation>10D) 11,8.......... 7,08 Two 90 degrees bends in the same plane (separation<10D) 16,5.......... 7,08 Two 90 degrees bends in different planes (separation>5D) 17,3.......... 7,08 Two 90 degrees bends in different planes (separation<5D) 37,4.......... 9,8 90 degree Tee with or without extension 11,4.......... 7,08 One(/Two 45 degree bends separated>2D) in the same plane 11,8.......... 7,08 Concentric reducer 2D/D over a length of= 1.5D - 3D 3,54.......... 1,97 Concentric expander 0.5D/D over a length of= 1D - 2D 10,2.......... 4,33 Full bore ball valve or gate valve fully open 5,51.......... 2,75 Globe valve fully open (ISO 5167:1991) 9,44.......... 4,72 Open large vessel 11,8 Abrupt symmetrical reduction 11,8.......... 5,90 Thermometer pocket < 3% of tube diameter 1,97.......... 1,18 Thermometer pocket >3% & <13% of tubediameter 7,87.......... 3,93 All fittings downstream* 2,75.......... 1,38 (*Measured from downstream pressure tapping) (Only 0.5% additional uncertainty upstreams OR downstreams, NOT BOTH!)
Error-/Uncertainty calculation
Standard/Flowcalculationmethod 1/2/3?___________________(S/1/2/3) S ERROR/UNCERTAINTYSOURCE SIZE IMPACT ON FLOWMEASUREUNCERTAINTY (%) Flow in % of maxflow_________________ 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0 90,0 100 mv Standard uncertainty 0,50 0,50 0,50 0,51 0,53 0,56 0,62 0,70 0,82 0,98 0,61 Flow calculation mathematical error 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 dp-transmitter % of maxdp 0,10 5,89 1,49 0,65 0,36 0,22 0,15 0,10 0,07 0,05 0,04 0,59 dp-transmitter % of act. dp 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Square root function in dp-transm.(Y/ J Control system A/D conversion % of sp 0,10 1,10 0,55 0,36 0,27 0,21 0,17 0,14 0,11 0,10 0,08 0,27 Control system A/D conversion % of ac 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Throat diameter (mm) 0,01 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Inlet edge radius (mm) 0,10 0,28 0,28 0,28 0,28 0,28 0,28 0,28 0,28 0,28 0,28 0,28 Tube diameter (mm) 1,00 -0,0 -0,0 -0,0 -0,0 -0,0 -0,0 -0,0 -0,0 -0,0 -0,0 0,04 Tube roughness (mm) 0,05 0,01 0,01 0,01 0,01 0,01 0,01 0,01 0,01 0,01 0,01 0,01 Density Table uncertainty (% of actua 1,00 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50 0,50 Density calculation error (% of actua 0,10 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 Viscosity (% of actual) 1,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Kappa (% of actual) 1,00 0,00 0,00 0,01 0,01 0,02 0,03 0,04 0,05 0,07 0,09 0,03 Media static pressure (% of actual) 0,10 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 0,05 Media static temp (C) 0,10 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Other ERRORS % actual Flow 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Other UNCERTAINTIES % actual Flow 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 0,00 Total uncertainty % of actual Flow___ 6,05 1,77 1,09 0,92 0,87 0,87 0,90 0,96 1,05 1,18 1,26
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