Understanding Transition to Turbulence: Reynolds' Experiment
School
The University of Western Australia**We aren't endorsed by this school
Course
ENSC 3003
Subject
Mechanical Engineering
Date
Dec 10, 2024
Pages
19
Uploaded by DeanCaribou4462
ENSC 3003 Lab1: Transition to turbulence GENG2003 - ENSC3003 – 2023 Fluid Mechanics Laboratory 1 Transition to Turbulence – Reynolds’ Experiment INTRODUCTION This experiment is based on the experiments reported in the original 1883 paper by Osborne Reynolds (Philosophical Transactions of the Royal Society of London, v174, pp 935-982, 1883). A Dye stream is injected into a pipe flow to enable you to visually identify the transition from laminar to turbulent flow. Through manometry, you will be measure the head loss between two points in the pipe, and use it to determine the pipe friction factor in laminar and turbulent flow and plot it as a function of the Reynolds number. BACKGROUND1. Experimental Apparatus Specifications: Pipe internal diameter, Dp= 10.10 mm Test section length, L= 1 m Discharge cylinder diameter, Dc= 90 mm SG (kerosene) = 0.78 Figure 1. Experimental setup 'h 1 H Discharge cylinder Water reservoir 2 Kerosene/Water manometer • Dye reservoir • W K *PlotfrichorfactorasafunctionoftheReynold'snumber.headlossI↓todeterminePipefrictiousfactorP+P-PrDPr9D-PrePrkewsenesyFPswater
ENSC 3003 Lab1: Transition to turbulence 2. Pipe flow The flow through a circular pipe is characterised by the average velocity, ܷഥ, the pipe diameter, Dp, the absolute viscosity of the fluid, µ, the density of the fluid,U, and the pipe wall roughness length scale, H. When a fluid flows through a pipe, energy is lost due to friction at the pipe walls. The head loss due to friction ('HD) over a length of pipe is determined as follows. For a uniform part of the test section, we can say οܪ=݂(ܮ,ܦ,ܷഥ,݃,ߩ,ߤ,߳)Arranging the variables into dimensionless groups results in οܪܷഥଶ2݃Τ=݂ ቆߩܷഥܦߤԢܮܦԢܷഥଶ݃ܦԢߝܦቇThe first dimensionless group on the RHS is known as the Reynolds number (Re), and describes the relationship between inertial and viscous forces in a fluid. The third dimensionless group on the RHS is known as the Froude number, and describes the relationship between inertial and gravity forces in a fluid. The head loss due to friction in a straight pipe of uniform diameter is given by the Darcy-Weisbach equation: οܪ=݂ܮܷഥଶ2݃ܦHere, fDis the Darcy friction factor, which is a function of (i) Reynolds number and (ii) the relative roughness, H/D. The dependence of fDon Reynolds number and H/Dis shown in the Moody chartat the end of these instructions. The “lowest” line on the Moody chart is for smooth pipes. One of the most interesting features of pipe flow (and one of Reynolds discoveries) is that the friction factor is dependent on whether the flow is laminar (smooth) or turbulent (chaotic). For small values of Re, the flow is laminar and viscosity is important in determining the head loss due to friction, and wall roughness has no effect (for laminar flow, fD= 64/Re). With increasing Reynolds Number, the flow initially becomes turbulent, and as Reynolds number continues to increase the viscosity has a decreasing influence - until eventually the flow becomes fully turbulent, and the friction factor becomes independent of Reynolds number (being solely dependent on relative roughness). In a fully turbulent flow the roughness determines the form of the velocity profile near the wall, and in turn the shear stresses and turbulence generation that determine head loss. Numerical analyses exist for the transition to turbulence in an infinitely long pipe. The results from these analyses show that the basic velocity profile of laminar flow is potentially unstable at all Reynolds numbers. However, the action of viscosity is capable of damping out any tendency for the flow to become unstable (and thus turbulent) at Reynolds numbers below a critical value of approximately2000. A laboratory investigation will differ from an infinitely long pipe in that it has an entrance and an exit. Depending on the exact configuration of these pipe ends, they may -headlossReynold'smakingthemdimensionlessnumberusingthecharacteristicpropertiesFroudenumberForlaminarflowviscosityplaysaroleinthefrictionfactorbutrelativeroughnessdoesn't
ENSC 3003 Lab1: Transition to turbulence introduce disturbances that trigger turbulence and so lead to a lower critical Reynolds number. Friction diminishes the amount of mechanical energy in the flow. Mechanical energy in a fluid flow can take 3 forms: gravitational potential energy (PE), kinetic energy (KE) and pressure. The pipe in our experiment is horizontal, so there is no change in PE. Conservation of mass tells us that the KE cannot change along a pipe of constant diameter. So, the friction energy loss between points 1 and 2 ܧ݃Τalong a straight horizontal pipe manifests solely as a loss in pressure energy, and is evident as a pressure head loss οܪ. That is: ܧ݃ؠ οܪ=ܲଵߩ݃െܲଶߩ݃3. Experimental Procedure Experimental ProcedureThe procedure for the experiment is as follows (note – for students completing the laboratory online, the procedure below was followed in creating the video): 1. Note the discharge control valve, discharge cylinder, the manometer, and the dye release mechanism. Before the experiment starts, the zero flow rate level differential in the manometer must be checked – and should be zero. At the end of the experiment, it should be confirmed that the level differential returns to zero when the discharge control valve was closed. If it does not, the manometer should be checked to determine whether an air bubble or blockage was disrupting the system – if there is a bubble or blockage, the level differentials recorded cannot be trusted. 2. The constant head reservoir should be filled (if it is not already filled), and the operation of the cistern control valve operation checked. The water supply to the reservoir is maintained throughout the experiment, with the cistern valve operating to ensure a constant water level. 3. Flow rate is measured by closing the valve at the bottom of the Discharge Cylinder, and recording the time taken for the level to rise between set levels. After each measurement, the valve at the bottom of the discharge cylinder should be opened to empty the discharge cylinder. 4. The flow rate in the pipe is set by adjusting the Discharge Control Valve. 5. For each flow rate the following measurements are to be taken: (i) Record the levels on the right and left hand side of the kerosene/water manometer. For those watching the video, note that the camera angle was not perfect – so there may appear to be discrepancies between the levels reported and the images on the video. Once each flow rate is set, allow the flow rate to evolve for at least two minutes to ensure that a steady state is achieved. Failure to do so could result in significant error in the measured head loss in the tube. leadtoalowercritical↑Reynold<2000
ENSC 3003 Lab1: Transition to turbulence (ii) The volume flow rate through the tube is measured by determining the rate of change of water height ('hDC/'t) in the discharge cylinder. You must record the discharge cylinder start and finish levels used and the time 't taken for the water surface to travel between those levels. (iii) Record your observations of the thin stream of dye in the table below. 6. The experiment is to be repeated for 8 different flow rates, remembering that the aim of the experiment is to study the transition from laminar to turbulent flow. The data points should be taken at flow rates covering Reynolds numbers ranging from about 200 to 15,000 (the maximum Reynolds number that can be achieved with this equipment). For the final flow rate, three repeated data points are to be taken to illustrate the variability of the data. Record your measurements and observations in the table below. Data Point 1 2 3 4 5 Cylinder hDC1(cm) Cylinder hDC2(cm) 't (s) Manometer Right hMR(cm) Manometer Left hML(cm) Observation Laminar Transition Turbulent Data Point 6 7 8 9 10 Cylinder hDC1(cm) Cylinder hDC2(cm) 't (s) Manometer Right hMR(cm) Manometer Left hML(cm) Observation Laminar Transition Turbulent
998810191918182064.0521.0916.2114.T111.49296100102.5108.5878479.57771101010101020202020209.047.005.925.855.74118135.5153.5153.5153.561.543.524.52.524-5
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ReynoldsnumberRe=PULListhecharacteristiclength=DpM=1000x0.01010xUp0.001=10100xUp->Up-Idea-lides(D)At-⊥DynamicHedLossAHD=monometerleft-monometerrightDareyfrictionfactorgravityisthegravityofearth+9.81m)S2BHD=foAHD2gDp=foLi/Chumr-hma)+(2+9.81)+(001010)1x(79·4038x/Wdca-hole,Attm2-Wmr0.002495623635141Indec-hal
ENSC 3003 Lab1: Transition to turbulence Report For your report, you are required to provide (note – the items below represent everything that you are expected to provide in the report); xA cover sheet, identifying the experiment, your name and student number, and the date and time of your laboratory session. Note – this is not the University “cover sheet” – that is not requiredxA table showing the raw experimental results (on the first page following the cover sheet). This must include all the data recorded in the table above, but should be reproduced professionally in a word/excel table (rather than a stapled-in hand-written sheet from lab handout). xOn a new page, a table showing the calculated values for each data point oVolume Flow Rate Q (m3/s) oAverage Velocity in the tube ܷഥ(m/s) oReynolds Number oDynamic Head Loss 'HD(in m of water) oDarcy Friction Factor fDxStarting on the next page, answers to the following questions; Q1. Derive the equation that relates the average velocity in the tube (ܷഥ) to the rate of change of height in the discharge cylinder ('hDC/'t). Q2. Given that the specific gravity of kerosene is 0.78, derive an expression relating the pressure head loss ('HD) between points 1 and 2 to the two-fluid manometer reading (the difference between interface levels 'hM). Q3. Calculate the Reynolds number and Darcy friction factor for each run. Plot your results on the Moody chart (provided below) and use them to obtain an estimate for the roughness of the tube (H). Describe the method used to estimate the roughness and state the confidence intervals for the estimate. Include the Moody chart with the plotted points in your report. Do your results make sense? If not, what are the possible causes? Q4. For the repeated run, you should have 3 sets of results for exactly the same experimental conditions. Use this data (and appropriate statistical measures, such as confidence limits) to estimate the uncertainty in your quoted Re and fDvalues. In this experiment, what are the largest sources of this uncertainty? Q5. Discuss the relationship between the visual dye indicator observations and your estimated Reynolds numbers. What do your results suggest is the bounding range for the critical Reynolds number for flow in this tube? I210different3values&5->50values·-~usureuncertainlyinmotedRedlimits)Confidenctovalues
Properanswering1.VolumeFlowRatepipe=pcylinder=cUsingconservationofmassrivi=ioutmpipe=mcylinderPUpAp=PUcAc->assumingthatdensityisconstantaswaterisincompressibleUpAp=UcAUpAp=Uc#De↓Q2.Averagevelocityinthepipe#=UDAp=#Dp2Ap#=UcDCDp2=UcXDo>Uc=Idea-ludeDPAt#=Add-Wdc(
ReynoldsnumberRe=Pw=1000hMm3Re=PwupDpMw=0.001Mu#=Ap=en1. (E)DpMuL=characteristiclength=Dp=PwUcDeeMwD21p=pu1Idoa-holeIDe"MwAtDpHeadLossH(m)=(vmr-wes
DarcyFrichowfactor(fd)#Hp2gDp=fD-2↓UpfD=2DHDX9xDpL=Im2x([p)2046516197)faz-DAC-
2.AHD=AromSgu=0.78hmkensene1w=10001in3Sk=0.78xlewaterW=780APoP,m3P,-OrgAm+engghm=PP.-Pa=PwgDrm-IngAhm=gNhom(ew-(a)AHD=-OgAHD(pg)=garm(pw-Pk)-(e)=-On)g)-constantinstant
ENSC 3003 Lab1: Transition to turbulence The report is to be submitted in a single pdf file (< 10 MB) to LMS before 17:00 on Friday, April 28th. The late and presentation penalties prescribed in the unit outline will apply. Presentation will also be a factor in the marking scheme for the reports. AcknowledgementsThis lab procedure document has been developed from the original procedure developed by the School of Environmental Systems Engineering, as provided by Dr Marco Ghisalberti.
ENSC 3003 Lab1: Transition to turbulence Moody Chart – From “Fluid Mechanics and Hydraulics, 3rdedition, Schaum’s Outlines, 1995200O
TheoryConservationofmassmeasuringQMout=MoutGm=PAYNBxUp=DaxUseIup=( xDcDa0.01010Up=U0.09⊥79.40398000196059Re=Upe=heRe=DM=0.001PasMp=1000=(10100)ID=inmetresUsevelocityofpipetocalculateReynoldsnumbertoknowwhichregime
Errorfromreadingthecollculation->AhErrorfromestimatingflowregimeBubbleinthepipeDensity↓occosityassumptiontobeconstantiswrong