ITTC - Recommended Procedures and Guidelines

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1 Page of 9 able of Contents UCERAIY AALYSIS - EXAMPLE FOR WAERJE PROPULSIO ES PURPOSE OF PROCEDURE EXAMPLE FOR WAERJE PROPULSIO ES est Desgn Measurement Systems and Procedure Uncertanty Analyss Jet thrust from nozzle Flow Rate Change n Momentum Flux Effectve Jet System Power REFERECES... 7 Updated / Edted by 26 th IC Specalst Commttee for Hgh-Speed Craft Approved Date 4/ Date 9/ 26 th IC

2 Page 2 of 9. PURPOSE OF PROCEDURE he purpose of the procedure s to provde an example for the uncertanty analyss of a model propulson test wth waterjets, followng the IC procedures -- Rev, Uncertanty Analyss n EFD, Uncertanty Assessment Methodology and --2 Rev, Uncertanty Analyss n EFD, Gudelnes for owng an ests. 2. EXAMPLE FOR WAERJE PROPULSIO ES hs procedure provdes an example showng an uncertanty assessment for the results from a model propulson test wth waterjets. he bas and precson lmts and total uncertantes for sngle and multple runs have been estmated for the flow rate Q J, the change n momentum flux M x and effectve jet system power P JSE. A further uncertanty analyss on delvered power P D and the total nteracton effect ncludng the thrust deducton factor ( t), has not been wored out here. hese uncertantes can be determned after an uncertanty analyss of the waterjet system tests and the bare hull resstance test has been conducted (see Fg. ). Furthermore, extrapolaton to full scale has not been consdered n ths example. Although t mght lead to sgnfcant sources of error and uncertanty, t s not essental for the present purpose of demonstratng the methodology. When performng an uncertanty analyss for a real case, the detals need to be adapted accordng to the equpment used and procedures followed n each respectve faclty. 2. est Desgn here are essentally two roads that lead to a predcton of the power-speed relaton P U. D ( ) he shortest road leads va the measured effectve jet system power P JSE from the propulson test and the nternal jet system effcency η JS from the waterjet system tests: P JSE P D = () ηjs he second road gves a more complete revew of all powerng parameters. It ncludes apart from the delvered power P D -predcton also a full predcton of all jet-hull nteracton terms. he power predcton s then based on a predcton of the resstance or effectve power P E and the overall effcency η D. he delvered power can thus be obtaned from: P E P D = (2) ηd he frst route should theoretcally lead to the smallest uncertanty, as the addtonal un-

3 Page 3 of 9 certanty of the bare hull resstance s not ncluded n the power predcton, whereas t does enter n the uncertanty for the second route (through the thrust deducton fracton t). 2.2 Measurement Systems and Procedure Fgure shows a bloc dagram for the waterjet propulson test, ncludng the ndvdual measurement systems, measurement of ndvdual varables, data reducton and expermental results. o enhance the process of dentfyng and estmatng the elementary bas lmts for each measurement system, four categores of error sources are dstngushed: calbraton data acquston data reducton conceptual bas Expermental Error Sources tow force waterjet geometry velocty dstrb. ntae snage speed flow rate press. dff. temperature, densty Indvdual measurement systems F D D, w A uxa ( yz, ) z6 U p, ρ Measurement of ndvdual varables Q = J A ρc M = c U x x m J m6 ρ A Aρ P 2 ( ) 2 JSE = 2 ce C p U gz6 cm6 2ρA Data reducton equatons Q, M, P η, η, η J x JSE I mi ei Expermental results waterjet system test hull resstance test ηjs = ηductηp R BH PD, n ( t ), η D Fgure Bloc dagram for the waterjet propulson test. he bas lmts of the nput parameters are subsequently reduced nto the bas lmts for the results by usng the data reducton equatons of Fgure. he precson lmts for model scale are estmated by an end-to-end method for multple tests (M) and a sngle run (S).

4 Page 4 of 9 he measured value of ± U uncertanty nterval about the X s the band wthn whch the expermenter s 95 per cent confdent the true value of the varable les. he 95% confdence uncertanty s gven by: U = B + P (3) 2 2 Instead of usng the dmensonal senstvty, t s often more convenent to use a nondmensonal senstvty θ, relatng the nondmensonal error n the result b R to the nondmensonal error n the source parameter b : ( θ b ) 2 R = b = (4) where the non-dmensonal bas error s defned by: b S = (5) X and the non-dmensonal senstvty by: R X θ = (6) X R A smlar result s found for the nondmensonal precson error p. he advantage of normalzng the error contrbutons n ths fashon s that all error contrbutons and senstvtes can be compared mmedately for ther relevance n the fnal result. he elemental bas lmts ( ) B must be estmated for each varable X usng the best nformaton one has avalable at the tme. Manufacturers specfcatons, analytcal estmates and prevous experence have typcally provded the bass for most of the estmates. Estmates for the bas errors here have been largely based on the results from the standardzaton tests. Addtonal conceptual bas errors resulted from not measurng drectly the varable n the data reducton equaton. An example of such an error s the error that results from assumng that the vena contracta n the jet concdes wth the nozzle dscharge openng (staton 6 nstead of staton 7 s used for the determnaton of momentum and energy fluxes). he precson lmt n the pressure dfference over the transducer has been determned, from whch the flow rate and momentum and energy fluxes are derved. hs lmt has been determned wth an end to end method, where all the precson errors for speed, pressure transducers, mpeller revolutons and temperature / densty are ncluded. Regardless as to whether the precson lmt s to be determned for sngle or multple runs, the standard devaton must be determned from multple tests n order to nclude random errors. If t s not possble to perform repeated tests, the expermenter must estmate a value for the error usng the best nformaton avalable at that tme. he error has then become a bas error. he precson lmt for multple tests s calculated accordng to: P ( M ) K. SDev = (7) M where M = number of runs for whch the precson lmt s to be establshed, S Dev s the sample standard devaton establshed by multple runs and the so called coverage factor K depends on the dstrbuton of the error. For a Gaussan dstrbuton of the error and a large

5 Page 5 of 9 sample, ths K factor equals approx. 2 (see also IC procedure -- Uncertanty assessment methodology ). he precson error for a sngle run can be calculated from: ( S ) K.SDev P = (8) Defntons Symbol Value (unt) Gravty g 9.8 m/s 2 Densty, model basn ρ g/m 3 Knematc vscosty ν.39-6 m 2 /s Water temperature (test average) 5. deg able 2 Constants for Athena model tests 2.3 Uncertanty Analyss hs secton presents the results of the uncertanty analyss for jet thrust from the nozzle, flow rate Q J, change n momentum flux M x (or net thrust) and effectve jet system power P JSE. he uncertanty analyss s conducted for the Athena at a speed of 25 n. he results are vald for model scale. Extrapolaton and converson of effectve jet system power to delvered power to the pump mpeller are not ncluded here. In able and able 2, the prncpal partculars of the model and the constants used n the example are presented. Defntons Symbol Value (unt) Length model L PP m Dsplacement Vol model.428 m 3 o. of waterjets 2 ozzle dameter.846 m D w Waterjet ntae wdth.25 m able Athena model partculars 2.3. Jet thrust from nozzle able 3 presents the uncertanty results for the best estmate of the jet thrust as determned from the propulson tests. As ths thrust cannot be measured drectly, t s determned from a Dfferental Pressure transducer that s calbrated durng a bollard pull test. An mportant assumpton that s made here s that the relaton between jet thrust from the nozzle and pressure readng s the same durng calbraton n bollard pull condton and durng the propulson tests. A conceptual bas error n the rato jetx / jetx cal s ntroduced to account for the uncertanty about the equalty of ths relaton n both tests. he best estmate for the jet thrust s consequently gven by: = J xcal (9) J xcal where the calbrated jet thrust s obtaned from: J xcal = a + adp () and a denotes the calbraton coeffcents. on-dmensonal senstvty, precson error and bas error for each varable are presented, and the 95% confdence uncertanty

6 Page 6 of 9 nterval URSS@95% s calculated analogc to eq. (3). Fgure 2 shows that the dfferental pressure transducer and the error n the assumpton that the jet thrust calbraton durng bollard pull can be used durng propulson tests are the domnant error sources. he total uncertanty URSS() n jet thrust s estmated to be approx..5% for the Athena at a speed of 25 n.. percentage contrbuton Fgure 2 Relatve mportance of errors n jetthrust over sources. Wth the uncertanty n, the uncertanty n flow rate, thrust and power can subsequently be determned Flow Rate. Applyng the bollard pull thrust for calbraton of the flow rate, ths flow rate s gven by: Q a a A n J = () ρcm6 Dp Error source jetx/jetxcal percentage contrbuton Fgure 3 Relatve mportance of errors n flow rate over sources. Fgure 3 shows that the domnant error sources for the flow rate are the jet thrust and the momentum velocty coeffcent for the velocty feld at the nozzle dscharge (staton 6) Change n Momentum Flux. he change of momentum flux over the waterjet control volume s a best estmate for the net thrust net. hs change n momentum flux s obtaned from: M jetx An rho cm6 thetan Error source c U ρa n x = m (2) he results of the uncertanty analyss are presented n able 5. he dstrbuton of errors over the dstnct sources s presented n Fgure 4. It s shown here that the domnant error sources are agan n the jet thrust estmate and also n the momentum velocty coeffcent n the capture area at Staton A. able 4 presents the uncertanty analyss for the flow rate.

7 Page 7 of 9 percentage contrbuton jetx [] cm [-] Um [m/s] rho [g/m3] An [m2] thetan [deg] Error source Fgure 4 Relatve mportance of errors n change n momentum flux over sources. percentage contrbuton jetx [] An [m2] rho [g/m3] cm6 [-] thetan [deg] Error source ce [-] U [m/s] g [m/s2] z6 [m ] Fgure 5 Relatve mportance of errors n effectve jet system power Effectve Jet System Power. he effectve jet system power PJSE can be computed drectly from the derved jet thrust, as gven by eq. (3). he results of the uncertanty analyss for the effectve jet system power PJSE are presented n able 6. he dstrbuton of errors over the dstnct sources s presented n Fgure 5. It s shown here that the domnant errors are caused by the jet thrust estmate and the nozzle area A n. P An ρ cm6 2ρAn 2 2 ( ) C p U gz JSE = 6 (3) 3. REFERECES IC, 25, Report of Specalst Commttee on Valdaton of Waterjet est Procedures, Proceedngs of the 24 th IC. Van erwsga,.j.c., 996, Waterjet-Hull Interacton, PhD hess, Delft Unversty of echnology, Aprl 996, ISB

8 Page 8 of 9 Error source Mean value on dmensonal senstvty Precson error θ ' s [%] b [%] Bas error ( Kθ s ) 2 + ( θ b ) 2 Comments a mean value from IC-tests, error estmate (Van erwsga, 996) a p 4.37E / cal....2 error estmate (Van erwsga, 996) otals.2.49 URSS@95%.57 = = (Kθ s ) 2 + (θ b ) 2 able 3 Uncertanty analyss of jet thrust J predcton from propulson test Error source Mean value on dmensonal senstvty ' Precson error θ s [%] b [%] Bas error ( Kθ s ) + ( θ b ) 2 2 Comments From able 3 A n Ρ c m θ otals..3 URSS@95%.32 = (Kθ s ) 2 + (θ b ) 2 able 4 Uncertanty analyss of flow rate predcton =

9 Page 9 of 9 Error source Mean value on dmensonal senstvty Precson error θ ' s [%] b [%] Bas error ( Kθ s ) 2 + ( θ b ) 2 Comments [] From able 3 c m [-] U [m/s] ρ [g/m 3 ] E-2. A n [m 2 ] θ [deg] VR.7 otals URSS@95% 3.45 = (Kθ s ) 2 + (θ b ) 2 able 5 Uncertanty analyss of change of momentum flux predcton = Error source Mean value on dmensonal senstvty Precson error Bas error ( Kθ s ) + ( θ b ) 2 2 Comments θ s [%] b [%] [] From able 3 A n [m 2 ] ρ [g/m 3 ]...82E-2. c m6 [-].98. θ [ ] c e [-] U [m/s] g [m/s 2 ] z 6 [m].7.. otals URSS@95% 3.62 = (Kθ s ) 2 + (θ b ) 2 = able 6 Uncertanty analyss of effectve jet system power P JS