Reasons to Build a Hydraulic Model

Transcription

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2 Reasons to Build a Hydaulic Model Detemine dischage coefficient fo lage flow measuement stuctue (spillway o wei) Develop effective method fo enegy dissipation at outlet of hydaulic stuctue Development of economic & efficient hydaulic stuctue (spillway)

3 Pupose fo Rive Models Patten of flood wave though ive Effect of atificial stuctues on sedimentation and hydaulic effects upsteam and downsteam

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5 Model vs. Pototype Hydaulic Model Use pinciples of similitude to coelate model and pototype behavio Pinciple on which hydaulic model studies ae based compises the theoy of hydaulic similitude Desied that the physical behavio of model simulate that of the pototype Dimensional analysis basic elationship of the physical quantities involved in the dynamic behavios of wate flow in a hydaulic stuctue

6 Pinciples of Similitude Physical behavio of the model should simulate in a know manne the behavio of the pototype Can use data fom the model can be used to pedict esponse of the pototype Pinciples of similitude coelate model to pototype behavio Thee basic types of similitude 1. Geometic similaity 2. Kinematic similaity 3. Dynamic similaity Foces dominate hydaulics fo models equie Dynamic Similaity

7 Pinciples of Similitude Geometic Similaity all homologous dimensions on model and pototype ae equal Kinematic Similaity all homologous velocities and acceleations ae equal between model and pototype Dynamic Similaity all homologous foces the same between model and pototype

8 Geometic Similaity Implies similaity of fom Fixed atio (scale) fo all lengths in the pototype and model Quantities of geometic similaity ae: Length (L) Aea (L 2 ) Volume (L 3 ) Scale Ratio = L P / L M = L R

9 Geometic Similaity Aea A A P M = L L 2 P 2 M = L 2 Volume Vol Vol 3 P 3 M = L L 3 P 3 M = L 3

10 Kinematic Similaity Implies similaity of motion Involves time scale and length Time atio (T )fo homologous paticles to tavel homologous distance in model and pototype Time T m = T P T Velocity V V P M = L T L T P P M M = L T

11 Kinematic Similaity Acceleation a a P M = L T L T P 2 P M 2 M = L T 2 Dischage Q Q P M = L T L T 3 P P 3 M M = L T 3

12 Dynamic Similaity Implies similaity of foces in motion Foce atio (F )fo homologous foces in model and pototype is constant Foce F = F F P M Dynamic Similaity equies and implies kinematic similaity and geometic similaity Must evaluate foces of (1) inetia, (2) pessue, (3) gavity, (4) viscosity, (5) suface tension, (6) elasticity

13 Dynamic Similaity Foce is mass time acceleation and mass is density time volume: Wok 4 2 = = = M M M P P P M M p p T L a Vol a Vol a M a M F ρ ρ ρ M M P P M P L F L F L F W W = =

14 Dynamic Similaity Tue dynamic similitude equies that all five types of foces be the same between the model and pototype ( FI ) ( FP ) ( FG ) ( FV ) ( FT ) ( F ) P P P P P E P F = = = = = = ( FI ) ( FP ) ( FG ) ( FV ) ( FT ) ( FE ) M M M Hydaulic models ae not capable of simulating all the foces simultaneously In pactice model designed to study the effect of only a few dominant foces Flow in most hydaulic stuctues fo example detemined by the effect of gavity M M P

15 Hydaulic Phenomenon Govened by Gavity Foude Law When inetia and gavity ae consideed to be the only dominant foces of fluid motion then Foude Numbe of the pototype and model must be the same V N F = = gl inetia gavity foce foce Also is velocity divided by celeity of gavity wave Applicable to model studies of most hydaulic stuctues including weis, spillways, gates, chutes, stilling basins, locks, tansitions, and othes

16 Foude Law Ratios Foude Numbe atio ( ) N F = 2 V g L Usually g = 1 if both subject to same gavitational field and same fluid is used so that V = L

17 Foude Law Ratios Dischage Q = A V = L 5/2 Pessue P = γ L = L if same fluids Foce F = γ (Volume) = L 3 Enegy E = F L = L 4 Powe P = E T = L 5/2 Momentum M = m V =ρ (Volume) L 1/2 = L 7/2 Time T = L / V = L 1/2

18 HYDRAULIC SIMILITUDE Hydaulic Phenomenon Govened by Viscosity Reynolds Numbe Law Fully enclosed flow (ie. pipe) gavity and suface tension have no effect Viscosity alone will contol velocity and pessue fom fiction with inelastic flow Reynolds Numbe (N R ) must be equal in model and pototype N = R inetia viscous foce foce N R = ρlv µ

19 Hydaulic Phenomenon Govened by Viscosity Reynolds Numbe Law Impotant application of Reynolds Law is study of dag foces on immesed objects (ie. ships) Difficulties ae encounteed with Reynolds Law model studies if the numbe is high Velocity atio is invesely popotional to the length atio, model velocities have to be high Requies a wind tunnel with ai as fluid

20 Reynolds Law Ratios Velocity V = ν /L = 1/ L if same fluids Dischage Q = A V = L 2 ν /L = ν L = L Pessue P = 1/ L 2 if same fluids Foce F = 1.0 Enegy E = F L = L Powe P = E T = 1/ L Momentum M = m V =ρ (Volume) ν /L =µ L 2 Time T = L / V = ν L 2 = L 2

21 Model Studies With Both Gavity and Viscous Foces Example of this case Open Channel on mild slopes Suface vessels moving though wate Shallow wate waves in open channels Both Foude numbe and Reynolds numbe N F = N R ρ L V µ = ( ) 1/ 2 g V L

22 Model Studies With Both Gavity and Viscous Foces Simplifies to ν = L 3/ 2 Almost impossible to meet equiement since special model fluid with kinematic viscosity atio Fo example a 1:10 scale model equies model fluid with kinmeatic viscosity 30 times less than wate Solution fo ship esistance, the model is based on Reynolds law and opeates in towing tank by Foude Law

23 Open Channel Models Fixed Bed Fixed Bed Study is distinguished fom Moveable Bed Study Channel models ae concened with velocity and slope pattens so effect of bed oughness is vey impotant Empiical hydaulic elation Manning equation used fo similaity between model and pototype V = V V p m = R ( y / L ) 2 / 3 1/ 2 2 / 3 1/ 2 S R n = n

24 Open Channel Models Fixed Bed Fo the condition of an undistoted model then S =1 and R = L so: 2/ 3 L V = n Since V = L 1/2 then n = L 1/6 Howeve, model velocity will be so small (o model oughness lage) as to make accuate measuement difficult Solution is to use a distoted model

25 Open Channel Models Distoted Model Distoted model whee the vetical scale and hoizontal scale atios do not have same value Choose smalle vetical scale atio o X > Y Means model Slope geate than pototype Case 1 Roughness values known fo model and pototype then the distotion calculated fom: 2 y S = = L n R y 4 / 3

26 Open Channel Models Distoted Model Case 2 Distotion atio is fixed based on space consideations then model oughness calculated fom: Means model oughness must be adjusted by tial and eo until equied flowate obtained / / / / / L R L R S n = = 2 3 / V V V L V y L A V Q = = = =

27 Model Design Geneal Model equied when established design pocedues and available technical infomation fails to povide solution to hydaulic poblems Hydaulic poblems should be thooughly examined Define the accuacy of esults fom model Fist and most impotant step is to select scale Fo maximum similaity model should be lage as possible Lage model impoves accuacy of measuements and esults Difficulty in opeation and costs

28 Open Channel Model Scale Selection Channel model scales typically ange fom 1:15 to 1:70 Scale depends on the following Type of poblem Relative oughness between model and pototype Size of pototype Scale atios of 1:15 to 1:30 fo supecitical wave pattens and outlet woks having gates o valves Same scale used fo sectional models of dop stuctues, spillways

29 Open Channel Model Scale Selection Canal stuctues, such as chutes and dops have scales atios 1:3 to 1:20 Smalle atios 1:30 to 1:70 ae used fo geneal model studies of long channels Rive model scale atios 1:100 to 1:1000 Vetical scale fo distoted ive models atios 1:20 to 1:100

30 Open Channel Model Scale Selection Flow measuements may contol scale selection Most models of channel ae geneally built to give depths of flow about 0.5 feet Channel widths of 1 to 2 feet Common scales used the Los Angeles ACOE Distict Hydaulic Laboatoy ae 1:25 to 1:40

31 CHANNEL MODELS

32 CHANNEL MODELS

33 CHANNEL MODELS

34 CHANNEL MODELS

35 CHANNEL MODELS

36 CHANNEL MODELS

37 CHANNEL MODELS

38 CHANNEL MODELS

39 CHANNEL MODELS

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41 Model Study Centeed on I 405 Culvet System Physical Model Study Reach = 1000 ft

42 100 y Q = 5330 cfs Upsteam of Confluences 100 y Q = 5910 cfs Downsteam of Confluences

43 Limitations of Compute Modeling Unequal lengths, slopes & geometies of the C05 culvets Assumption of unifom flow distibution acoss channel section

44 Edinge A Limitations of Compute Modeling Confluence Angles of C05 culvets and tibutay channels Seconday cuents, tubulence, and votex action esulting fom non unifom flow pattens Newland B C05 Tiple Box C05 Ellipticals Edinge B

45 Physical Model Objectives 1. Evaluate Channel Pefomance at Design Dischage Establish 100 y wate suface pofiles fo C05 & C05S01 2. Detemine Maximum Channel Capacity Test diffeent flow combinations in main channel and tibutaies 3. Impove Channel Capacity Test vaious modifications to educe enegy loss

46 Physical Model Design 3D CAD Model channel designed using as builts and poposed impovement dawings fo Newland & Edinge facilities

47 15:1 Scale Selection Diven by Poject Budget Measuement accuacy (allowable eo) small scaled eo can become lage pototype eo Channel oughness (mateial selection) Scaled mannings oughness value fo concete = Available Waehouse Space

48 Hydaulic Popeties of 15:1 Scale Model Model hydaulics influenced by inetial and gavitational foces Scale to pototype elationships, hydaulic similitude, based on Foude Numbe Law

49 Hydaulic Model Stuctue Model Channel elevated on adjustable platfom Stoage esevoi below povides conveyance and submegence ove pump intakes Head tank dissipates flow enegy befoe enteing channel

50 Pump System designed fo Max Efficiency and Flexibility Hoizontal Pump Dimensions: 15 Hosepowe, 3 Phase 1200 gpm at 15 of Head Weight = 156 lbs Height, A = Min Submegence, B = 30 Dischage Diamete, D = 6 NPT Pump Length, E = Pump Width, F = 16

51 Model Fabication Model channel consists of ¾ plywood einfoced with a 2x4 fame and 45 kickes. Platfom stuctue made up of a ¾ plywood deck ove 2x8 16 o.c. 4x8 s span between posts & scew jacks to suppot the platfom

52 Model Channel was Watepoofed using a lot of Silicone and a Multi coat Watepoof Paint

53 Low Flow Channels Upsteam and Downsteam of I 405 Culvets wee Fomed with Concete

54 Model Channel Fabicated to a Toleance of ft Scew Jacks placed along both sides of flume allow fo vetical adjustment Final adjustments made with the help of a suveyo using a total station

55 Dual Function Stoage Resevoi Povides equied submegence depth fo pumps to opeate Convey flow fom tail box to pumps Captues leakage fom model channel Watepoofed using seam welded PVC line

56 Head Tanks Designed to Hold 8 ft Stuctual 2x lumbe used to fom ibs Lined with 1 plywood and coated with watepoof paint Hanging baffles dissipate flow enegy fom pumps of Wate

57 Scaled Culvet Geomety Pesents a Scaled dimensions of elliptical culvet ae 5.13 x 8.07 Fabicated using CNC technology to ceate foam molds Fibeglass fomed aound molds to coect dimensions Unique Challenge

58 CNC Technology allowed fo fabication of unique culvet geomety Complex tansitions fom ectangula to elliptical in a cuved alignment occu at entance and exit of each C05 elliptical culvet

59 Pump & Piping System Includes Multiple Valves fo Fine Tuning Flow Rate

60 Adjustable (Tail) Gate Povides Downsteam Bounday Contol

61 Model vs Pototype Compaison Upsteam of I 405

62 Model vs Pototype Compaison Downsteam of I 405

63 Model vs Pototype Compaison Newland Channel

64 Model Calibation Suface Roughness Initial tests will be conducted to veify channel oughness values Point gages will be used to measue flow depth to the neaest 0.1 mm ( )

65 Model Calibation Flow Mete Readings Shap cested weis will be used to calibate the Ultasonic flow mete eadings V notch wei will be used fo flows up to 1,000 gpm Rectangula wei used fo flows up to 3,000 gpm

66 Expeiments will be Classified Accoding to Fixed Paametes 1. Downsteam wate suface elevation estimated by WSPG model of entie C05 channel 2. Constant Flow Rate into main channel (C05) and tibutay channels (C05S01 and C05S05) Flow Combinations to be Tested: 100-y EV Retun Inteval EGGWC Upsteam Newland Bifucation Pototype Dischages (cfs) Newland Channel Edinge Channel EGGWC Downsteam C05 C05S01 A C05S01 B C05S05 C05 Case Case Model Dischages in gpm and (cfs) Case (6.12) (0.28) 73.1 (0.16) 99.9 (0.22) 3044 (6.78) Case (5.11) (0.78) (0.45) (0.44) 3044 (6.78)

67 Additional Tests will Evaluate Options fo Impoving Channel Pefomance Adjustments to size and angle of Newland Channel confluence Splitte walls, pie noses o othe ways to educe enegy loss

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