Department of Fluid Mechanics

Transcription

1 Budaesti Uniersity of Technology and Economics Deartment of Fluid Mechanics Pre-measurement class I. Comiled by: László Nagy 07. sring Deartment administrator of measurements: Dr. Csaba Horáth Deartment of Fluid Mechanics H- Bertalan Lajos u AE building

2 General information Deartment webage: Student information age: (test scores, reort and resentation uload etc.) Subject webage: Laboratory webage (materials, control tools):

3 Méréselőkészítő Munkaédelmi oktatás

4 General information Timetable: st session: Measurement deices, measurement methods. Introduction to the measurement facilities, measurement uncertainty nd session: A measurement, B measurement 3 rd session: Makeu measurements 4 th session: A+B measurement resentations (Details can be found in the syllabus)

5 General information Measurement grous: 4 students measurement leaders for each measurement (A and B), the other assist the measurement (attendance is obligatory!) The measurement leaders reare one reort and one resentation for the gien measurement (same number of oints will be gien for both students) For each measurement a subtask is assigned. The members of the grous and the subtasks can be found on the webage Examle: Tomasics S. and Nootni G. did their measurement in section B (nd measurement). They did measurement 5 with subtask E.

6 Prearing for the laboratory measurements In rearing for the laboratory measurements, all members of the measurement grou must read the syllabus and understand the measurement which is to be made. A hand written outline of the measurement needs to be reared by the lab leader. This outline should contain the following: The measurement grou s information (names, netun codes), leaing a sace for checking attendance Sace where the measurement suerisor can sign each age. A list of the instruments which will be used during the measurement, leaing room for the serial numbers, which will be documented during the measurement Tables for documenting the measured and calculated alues, including atmosheric conditions (e.g. atmosheric ressure and temerature, etc.) The equations which are necessary in order to comlete the measurement and the associated calculations, leaing room for erification calculations. Millimeter aer needs to be brought to the laboratory measurements

7 During the laboratory measurement At the beginning of the laboratory the hand written outline will be checked by the instructor suerising the measurement, and questions will be asked in order to determine whether the grou is reared for the measurement. If the grou is unreared, they will be sent away The measurements need to be comleted during the allotted time. The digital manometer needs to be calibrated during the laboratory measurement, with the hel of the Betz micro manometer. During the measurement, deartment ersonnel suerising the measurements will assign a task to each grou, by which some alues measured during the laboratory measurement will be drawn on the millimeter aer, in order to check the correctness of the measurement and the understanding of the measured results. If the task can not be comleted in a satisfactory manner, the measurements must be reeated.

8 After the laboratory measurement A measurement reort must be roduced from the measured data Laboratory calculations must be checked utilizing the deartments online ealuation tools. Use of the control tools is mandatory. The control tools only ealuate whether the equations were alied roerly. If the calculations were deemed inalid, they must be reeated. There is no limit as to the number of attemts which can be made, but the attemts are logged, and can be taken into account when giing grades. (fair use olicy) In reious semesters each measurement had students who were able to comlete the calculations correctly uon their first attemt. Once the calculations are correct, a code is roided to the student. This code must be included on the laboratory reort coer. The number of attemts, and the calculation error [%], as comared to the exected calculated alue, will be taken into consideration when grades are assigned.

9 After the laboratory measurement Examle: It is not mandatory to fill out the grey cells.. If the rogram deems the calculations incorrect, then it might be useful to fill out these cells, in order to hel one find the source of the error.

10 After the laboratory measurement After the calculations are acceted, the reorts must be submitted through the oseidon network. Reorts must be submitted by midnight of the second Sunday following the measurements. Consultations: The faculty members grading the reorts will roide one consultation oortunity er week for each measurement (one hour er measurement er week) they are grading. Consultation timetables can be found on the deartment website. The measurement grous can also come to the laboratory to consult with the suerisors oerseeing the gien measurements during the last 5 minutes of any regular measurement session.

11 Requirements regarding the laboratory reorts I. The coer of the laboratory reort must be downloaded from the website. The lab reort can only be 8 ages long lus the required reort coer and mandatory annex The reort should contain the following: Code (roing that the calculations are right) on the coer Short descrition of the measurement, data of the measurement deice The subtask Equations The measured and calculated data in tables Uncertainty calculations Necessary diagrams with uncertainty (error bars) Interretation of the measurement results Bibliograhy

12 [m/s] Requirements regarding the laboratory reorts II. The calculations and tables used for making the diagrams (Excel) need to be submitted together with the reort The diagrams need to be oint diagrams (scatter lot, XY lot). The use of line diagrams is UNACCEPTABLE! (in this case the distances on the X axis will not be roortional) [m/s] Velocity along the axis of the jet [m/s] Distance [mm] Unaccetable (and ugly) (the alues along the X axis are only considered as names or titles) Accetable (the alues along the X axis are considered as numbers)

13 The uncertainty is not marked Requirements regarding the laboratory reorts III. UNACCEPTABLE AND UGLY DIAGRAM The cure does not need to be colored. Why is a grey backgroun d used? The tye of diagram used is unaccetabl e Unnecessary use of sace. This makes the diagram small. Since there is only one set of data, it is een more so unnecessary. The use of a frame is unnecessary

14 Requirements regarding the laboratory reorts IV. AN ACCEPTABLE DIAGRAM Frame:.5- t, main diisions: 0.5 t. Named axis and [units] M3. mérési jegyzőköny 3 Diagram title (not always necessary, since one can also make use of the descrition of the diagram below it) Letters should be of legible size Measurement uncertainty (Error bars) The axis starts from 0. (Do not use autoscale, unless it is necessary for correctly isualizing the 3. ábra. A ladiffúzor hatásfoka a két mért konfigurációban a résméret függényében. Points are connected using straight lines (we are not interolating between the oints, but rather connecting those oints which belong together. This is not Minimum number of contrasting colors Logical key The diagram is not miniature, but rather uses all the sace roided

15 Requirements regarding the laboratory reorts V. The reort should be logical and nice Justified form Equations are created with the equation editor and not coied in as a icture Diagrams are uniform Hand made figures should be aoided (use: hotos, CAD softwares ) EXCEL: use scatter lot, XY lot. The file extension of the reort should be PDF A mandatory annex to the 8 ages needs to contain the following: A scanned coy of the hand written notes which were signed uon comletion of the laboratory measurement, and which contain all the tables of all the data which was recorded. The uloaded zi file must contain an excel file in which the calculations were made and the df of the laboratory reort. The name of the file should be in the following form: Lastname_netun_lastname_netun_Mx_deadline.zi Examle: Tomasics_ABC3_Nootni_DEF456_M5E_0606.zi

16 After the laboratory measurement ALL LABORATORY REPORTS NEED TO BE ORIGINAL AND MADE BY THE LAB GROUP! ANY MEASUREMENT LEADERS SUBMITTING WORK WHICH WAS NOT SOLELY PRODUCED BY THE GROUP, WITHOUT CITING THE APPROPRIATE SOURCE, WILL BE REPORTED TO THE DEAN S OFFICE AND THE ETHICS COMMITTEE IN ACCORDANCE WITH THE RULES OF THE TVSz. The reorts are ealuated within working days, and a message is sent to the student through the oseidon network informing the student whether the reort was acceted or not. A reort can be resubmitted once for a better grade. The submission needs to made by the following Sunday at midnight. If the reort is unaccetable, there is one oortunity to resubmit the reort by the following Sunday at midnight, howeer in this case you can only receie the 50% of the maximal oints. The reort is acceted if the receied oints reach the 40% of the maximal oints An acceted reort is a criterion of the resentation Please note that in some cases the reorts need to be submitted earlier in

17 Presentation An examle of a tyical resentation, can be downloaded from the webage. 8 minutes er resentation The measurement needs to be summarized. The ersonal measurement assignment needs to be resented and exlained. The measurement stand and the used equiment needs to be resented. Measurement uncertainty calculations need to be resented. The ealuation of the results needs to be resented. The results need to be shown The conclusions and results need to be summarized. Try to make it unique and interesting!

18 Late submission and make u Sanctions for late submission -0% er day If the delay is more than a week than an extra fee will be charged At the lastest, the reort must be submitted by Friday at :00 on the 4th week! (this is a ery seere delay) Make u for the measurement mid-term: A redefined time eriod, outside of the normal schedule is roided in the TAD Second make u: oral exam ( The student needs to aly for this. We will not search for those who failed) Make u of the resentation: On the make u week (5th week) Extra fee is charged

19 Checklist At the measurement: In rearing for the measurement (hand written measurement lan): assignment, netun code, name, documentation, ersonal assignment, mm aer, signature. CHECK The laboratory instructor checks your rearedness with or questions CHECK Record atmosheric conditions ( 0, T 0 ) before and after the laboratory CHECK Calibrate to the Betz micro manometer CHECK You can ask questions from any of the laboratory instructors at the laboratory session, but it is adised to ask from the one leading your measurement Check the list of sulies in your measurement box. The box will be oened and closed by the laboratory instructor. The laboratory instructor will roide manometers, and will relace those which need to be charged. Do not connect digital manometers to chargers! Consultation Consultations can be made with the aroriate instructor during consultation hours. (rior to the measurements (!) you can also turn to the fluid mechanics student grou) Calculation results need to be checked Once calculations are correct and the reort is comlete, submit the reort: (df+xls) file name = Lastname_netun_lastname_netun_Mx_deadline.zi

20 Determining the uncertainty of the results (error calculation) I. - Absolute error (measurement uncertainty): the region within which the measurement data is located. - Notation if the measured data is X: - The correct secification of the measurement data in this case: - Relatie error: - In case of a calculated quantitity (R) the error roagates, and the following equation is used: - In case of multie, indeendently measured ariables : X X X X X X X X R R X R R n i i i i n X X X R R X X X R R,...,,

21 Determining the uncertainty of the results (error calculation) II. Examle: Velocity measurement uncertainty Dynamic ressure measured using a Pitot-static (Prandtl) tube: d =486.Pa Atmosheric conditions exerienced in the lab: 0 =00hPa ; T= C (93K); Secific gas constant of air R=87 J/kg/K = f T,,Δ,const 0 d. alues = Quantities haing uncertainties (X i ): -The measurement uncertainty of the atmosheric ressure comes from the error arising when reading the scale: 0 =00Pa - The measurement uncertainty of the atmosheric temerature in the lab: T=K - The ressure measurement uncertainty arising when making a measurement using a Pitot-static (Prandtl) robe and a EMB-0XY digital manometer: i )=Pa = ρ 0 air Δ Δ d RT d = R T ρ air 0 m kg = 8.55 ρ air =. 3 s m

22 Determining the uncertainty of the results (error calculation) III. Examle: Velocity measurement uncertainty Tyical calculation of absolute error: n = i i i X R δx δr = d 3 0 Δ = ; X = X = T; X R = n i i i X X, T, d )) Pa s m T R Pa s m T R K s m T R T d d d d ,,, RT d 0

23 Determining the uncertainty of the results (error calculation) IV. Examle: Velocity measurement uncertainty The absolute uncertainty of the elocity measurement: δ = δt R Δ δ = = T + δ R T Δ d 0 d 0 d 0 0 m s m s Based on which: 3 + δ Δ R T Δ The number of significant digits! Max. significant digits should be roided. d The relatie uncertainty of the elocity measurement: δ = % The result of the elocity measurement: = 8.55 ± 0.08 m s

24 Budaesti Uniersity of Technology and Economics Deartment of Fluid Mechanics Pre-measurement class II. Comiled by: László Nagy 07. sring Deartment administrator of measurements: Dr. Csaba Horáth Deartment of Fluid Mechanics H- Bertalan Lajos u AE building

25 Summary of the measurement rocess Successful measurement midterm exam Download and read the measurement syllabus Hand made measurement lan Measurement (rearation, measurement lan, millimeter aer are necessary) Preare measurement reort and excel file at home Check if your calculations were correct If the calculations are correct, uload the reort and the excel (the deadline is midnight of the second Sunday following the measurement) Correct the reort according to the comments Preare a resentation (if the reort was acceted) Uload the resentation Present

26 Measuring ressure differences (measuring Δ) Proides the basis of many measurements (e.g. elocity, olume flow rate) For a fluid medium, ressure differences can be measured between two oints It is often measured with regard to a reference alue (atmosheric ressure, static ressure in a duct) Measurement instruments U tube manometer Betz manometer Inclined micro manometer Bent tube micro manometer EMB-00 digital handheld manometer

27 Measuring Δ / U tube manometer I. Pie flow Butterfly ale Aerage of the ressure measured on the ressure tas around the erimeter The manometers balance equation: + ρ f = = L R g H = + ρ f g ρ ρ g Δh m f H H Δh+ ρ g Δh m > g Notice that Can be simlified if f << m (e.g. if the measured fluid is air and the measurement fluid is water) = ρm g Δh Δ f ( H ) f L R

28 Measuring Δ / U tube manometer II. The manometers balance equation: gh m Density of the measuring fluid m (aroximately) f kg ρ Hg 3600 m 3 ρ water 000 kg m 3 mercury water f ρ Alcohol = 830 kg m 3 alcohol Density of the measured fluid: f (For examle air) ρ air 0 kg = =.9 m 3 R T 0 - atmosheric ressure [Pa] ~0 5 Pa R - secific gas constant for air 87[J/kg/K] T - atmosheric temerature [K] ~93K=0 C

29 Measuring Δ / U tube manometer III. Examle: the reading: The accuracy ~mm: The absolute error: How to write the correct alue with the absolute error(!) The relatie error: Disadantages: Reading error (need to make two measurements) Accuracy~mm For a small ressure difference, the relatie error is large Adantages: Reliable Does not require sericing δ(δh)= ± mm δ Δh Δh h 0mm h 0mm mm mm = 0mm = 0.= 0%

30 Measuring Δ / uside down U tube micro manometer The manometer s balance equation = ρ ρ g h water air Since in most cases uside down U tube manometers are used to measure liquid (e.g. water) filled lines, the measurement fluid is usually air, and the density ratio is therefore (./000). - a (density of air) can be neglected. The adantage of this measuring deice is that when it is used for liquid filled systems, air can be used instead of mercury in order to imroe the accuracy of the relatie error of the readings! w a

31 Measuring Δ / Betz micro manometer The relatie error is reduced by otical means, imroing the accuracy. Accuracy ~0,mm: The absolute error is: Δh = 0mm ± 0.mm The relatie error: δ Δh Δh 0.mm = 0mm = 0.0= %

32 Measuring Δ / inclined micro manometer The manometers balance equation = ρm g Δh Δh = L sinα Accuracy: L~±mm, Relatí error in the case of =30 δl L = δl Δh sinα = mm 0mm sin30 = 0.05= 5% The relatie error is a function of the inclination angle - f() - It is characterized by a changing relatie error.

33 Measuring Δ / bent tube micro manometer Is characterized by a constant relatie error and a nonlinear scale

34 Measuring Δ / bent tube micro manometer Is characterized by a constant relatie error and a nonlinear scale 009. taasz

35 Measuring Δ / EMB-00 digital manometer List of buttons to be used during the measurements On/Off Green button Factory reset 0 followed by the STR Nr Changing the channel CH I/II Setting 0 Pa 0 Pa Aeraging time(/3/5s) Fast/Slow (F/M/S) Measurement range: Measurement error: 50Pa Pa

36 Measuring Δ / EMB-00 digital manometer Calibration of the EMB-00 digital manometer (obligatory!): - The digital manometer is comared to a more accurate instrument: the Betz micro manometer - A regression line will be used for the calibration - This can be done by a linear trend line in Excel. The alues measured with the digital manometer should be on the horizontal axis, an the alues measured with the Betz should be on the ertical axis. Both should be in Pa dimension. - The accurate measurement alues can be determined from the alues measured with the digital manometer using the regression line.

37 Measuring Δ / EMB-00 digital manometer Calibration of the EMB-00 digital manometer: EXAMPLE Atmosheric data: t 0 [ C] 5 T 0 [K] 98.5 ρ w [kg/m 3 ] 997. g [N/kg] 9.8 Measured and calculated alues: dig [Pa] Betz [w.c.mm] Betz [Pa] The diagram:

38 Measuring Δ / Pressure ta When measuring ressures we need the streamlines to be arallel and straight In this case the ressure is not changing erendicularly to the streamlines (The normal comonent of the Euler equation) a) Correct b) c) Incorrect Méréselőkészítő 38.

39 Velocity measurement deices Pitot tube/robe Pitot-static (Prandtl) tube/ robe Theoretical background: Simle form of the Bernoulli equation for lossless flow: If U =U and =0: U U

40 Velocity measurement / Pitot tube/robe Pitot, Henri (695-77), French engineer. Determining the dynamic ressure: d = t st t st the ressure measured in the stoed fluid (total ressure) the ressure acting on a surface which is arallel to the flow (static ressure) ρ f d = Determining the elocity: = ρ f d

41 Velocity measurement / Pitot-static (Prandtl) tube/robe Prandtl, Ludwig on ( ), German fluid mechanics researcher t

42 Measuring olume flow rate Definition of olume flow rate: the olume of fluid which asses through a gien surface er unit time. Usually it is the basis of accounting or system control It is denoted by : q, its dimension is: olume / unit time (e.g..: m 3 /s) Measurement method based on elocity measurements in multile oints Non-circular cross-sections Circular cross-sections 0 oint method 6 oint method Pie flow meters based on flow contraction Venturi flow meter (horizontal/inclined axis) Through flow orifice (contraction ratio, iteration) Inlet orifice Inlet bell mouth

43 Volume flow rate / based on elocity measurements I. Non-circular cross-sections q Assumtions: ΔA = A = ΔA da = ΔA i = n i= A n m,i ΔA i q = ΔA i n i= m,i = A n n i= m,i = A q q.. q 3 q

44 Calculating an aerage elocity from multile elocity measurements Very imortant: the square root of the aerages the aerage of the square roots(!) Examle: Measuring the dynamic ressure in multile oints and calculating the elocity from it i = ρ f Δ i = ρ f Δ ny ny ny ny 3 4 ny 4 Correct Incorrect

45 Volume flow rate / based on elocity measurements II. Circular cross-sections, 0 oint (6 oint) method The elocity rofile is assumed to be a nd order arabola Steady flow conditions Based on Pitot-static (Prandtl) tube measurements of the dynamic ressure This is a standardized rocedure, and the measurement oint are gien in the standard (MSZ 853/): S i /D= 0.06, 0.08, 0.46, 0.6, 0.34, 0.658, 0.774, 0.854, 0.98, 0.974

46 Volume flow rate / based on elocity measurements III. Circular cross-sections, 0 oint (6 oint) method q = A Assumtions: + A = A =... = A 0 The adantage of this method, as comared to methods based on flow contraction, is that the flow is not disturbed greatly, and therefore the oeration oint of the system is not altered, and it is easy to execute the measurements. The disadantage is that the error can be much larger with this method. For long measurements it is also hard to kee the flow conditions constant. (0 oints x.5 minutes = 5 minutes)

47 Volume flow rate / flow contraction methods Venturi ie m ny h H A A Bernoulli equation (=const., U=const., no losses): s m = q A= cont = q 3. A = A = q f f ρ + = ρ d d ρ Δ = d d ρ Δh g ρ ρ = f f f m If comressibility is negligible (=constant):

48 Volume flow rate / flow contraction methods Through flow orifice Standard orifice - ressure difference or q = α ε d π 4 or ρ = d/d Cross-section ratio d [m] Diameter of the smallest cross-section D [m] Diameter of the ie ustream of the orifice Re D = D/ Reynolds number s basic equation [m/s] The aerage elocity in the ie of diameter D [m /s] kinematic iscosity [Pa] The ressure measured ustream of the orifice [Pa] The ressure measured downstream of the orifice Exansion number (()~ since for air, the change in ressure is small) Contraction ratio, =(,Re) (When used according to the standard) Heat caacity ratio or Isentroic exansion factor = / Pressure ratio or

49 Volume flow rate / flow contraction methods Inlet orifice (not standard) Not a standard contraction ressure difference q = α ε d π 4 or ρ or α = 0.6 q = k d π 4 or ρ or

50 Comarison of olume flow rate measurement methods

51 Information on the measurement midterm 4 tasks: Unit conersion Theoretical question calculation tasks Acceted from 50% Examle tests are aailable on the webage

52 Thank you for your attention! Méréselőkészítő 5.