Channel design. riprap-lined channels

Transcription

1 Chael desig Vegetatio ad cobbles are used to cotrol erosio, dissipate eergy ad provide a evirometally sustaiable way to desig differet size chaels riprap-lied chaels

2 Smooth chaels i circular coduits: PVC pipes use the frictio factor for smooth pipes log(re f ) 0.8 f if we use 4RU Re ad we derive f from uiform flow equatio K 2/3 A V R S R Q VA P γ R S V if we e solve for the 2 fv 8g S V 4R2g f K (8g) 8g f f R RS 1/ 6 velocity f RS C RS 2 A8 RgS 2 Q where: ote the velocity scale V ~ (g d S) 1/2 d is the circular coduit diameter Q* d Re* 2 Q ( gds) d( gds) d y

3 Gravity sewer desig (hydrodyamically rough) desig goal 1 : work as ope chael flow (ot as pipe uder pressure) to avoid formatio of air pockets ad pulsatig flow desig depth y max /d =0.8 at max discharge Q circular cross sectio of diameter d We ca derive a expressio for d: AR 2/3 Q 2 K d / 8/3 d 1/ 8/ S d 1.56 where 1.56=1/0.3 S Q K d 8/3 3/8 by usig this figure, we impose the flow to behave as a ope chael flow with circular cross sectio

4 desig goal 2: trasport particles i order to avoid deposit formatio (self cleasig) V Refied model defie S R obtai the slope S c V c K K u g *c a critical stress R 2/3 R c c R 1/ circular cross sectio of diameter d c c, R use substitute ito Maig V u *c c 1/ 6 Vc g R V 1/ 6 Ku*cd d dimesioless form c* K R 2/3 S empirical suggestio V > 0.6m/s desig goal 1+2 d, R, S are desig parameters give Q (users), (material) V c is a costrait (V> V c ) ote d= pipe diameter where: A partially full area, A f = full area=d 2 /4

5 riprap chaels desig goal: avoid the mobility of the cobbles/ stoes the roughess effect must be related to the size of the rocks, specifically: 0.04 d 1/6 d 50 max 0c 4 dimesioally bad formulatio : must remember that this is valid oly if the media diameter d 50 is expressed i [feet] ad 0c i [lbs/ft 2 ] 50 Problem: how about side baks ad bed??? bed: max = 1.5 RS sidewalls: max = 1.2 RS

6 icliatio of the baks, depeds o the agle of repose which depeds o the type of stoes 2 1 desig procedure: 1)defie a size based o bed/bak stability, 2)estimate the iduced roughess, uiform flow depth, shear stress 3)compare with critical shear stress ad iterate desig criterio critical (d s ) < max bed: max = 1.5 RS sidewalls: max = 1.2 RS Remember that alog the side walls gravity act i favor of stoe mobility. If I have 0 crit (at the bottom) w crit (at the sidewall) TRACTIVE FORCE RATIO BB 17bis-18, iduced roughess (maig) size depedet d K 8g R / d 50 1/ 6 1/ log R / d 50 calculate y 0 (uiform flow)estimate ad w, safe max, verify that max < crit at the bottom ad at the sidewalls (the slope agle eters through geometry A, P)

7 Grass lied chaels Deisig procedure: attempt a vegetatio, estimate flow resistace parameter, calculate the uiform flow depth, the stress ad verify it does ot exceed deig values 1) choose a vegetatio class AE (based o resistace ad stiffess) 2) calculate the stiffess as MEI (#stems per uit area*elasticity modulus*momet of iertia of the stem cross sectioal area) 3) estimate the roughess height K of the deflected stems (h s is the stem height with o flow) 4) attempt a depth value y try, calculate R K h s ( MEI / 0) 0.14 h 5) estimate the roughess coefficiet =f(mei, K, R, tables o the vegetatio types) 6) use the uiform flow maig formula to calculate y 0 compare y try with y 0 ad iterate 7) calculate the shear stress = RS 8) verify < admissible shear stress for the chose vegetatio type if ot ok, reiterate o the vegetatio type k 1/6 s / K R / k 8g( a blog R / k

8 Caopy similarity law Ghisalberti ad Nepf 2009 occurrig 1) i vegetated rivers, 2) durig floods 3) i atmospheric flows over crops ad forests 4) aroud coral reef uder ocea currets I caopy flows, the wake from the sigle roughess elemet (stem, tree log,...) merges with the other wakes geeratig a class of specific turbulet flows.

9 Why we talk about caopy similarity? because all the terrai types we cosidered at the begiig display mixig layer characteristics

10 mea velocity profile above a caopy With the displacemet i height d, we shift up the 0 of the mea velocity accoutig for the mea mometum that is absorbed withi the caopy. ukows(3): z 0, u *, d Multiple regressio results i at best ±25% error (Bradley Fiiga 1983) d compesate for the curvature of the mea velocity ear the caopy top

11 Jackso (1981) itroduced the drag partitioig cocept: how much drag is related to the sigle roughess elemet as compared to the typical rough wall surface 0.7 is quite a good value... d has a dyamic sigificace. Whatever the origi of z, the displacemet height d adjusts the referece level for the velocity profile to the height at which the mea surface shear appears to act. Shiu Yeug Hui ad Athoy Crockfor

12 How about roughess z 0? Aerodyamic drag model based o caopy characteristics (whe depth>>h) z sparse caopies dese caopies U(z) Raupach 1992 U h D D is a roughess desity or frotal area per uit groud: for cyliders: D*h/ s 2 = Dh/A dimesioless where is the umber of cyliders per uit area A=1, s is the spacig s h h h is the cylider ad caopy height, z 0 is the aerodyamic roughess legth U(z)=u*/k l(z/z 0 ) (with u* the shear or frictioal velocity)

13 caopy geometry log law parameterizatio FAI =frotal area idex i this case we have uiformly vertical roughess elemets: A f (frotal area), A g (groud area) Low sparse caopy High dese caopy (limited shear peetratio u * / U h peak i z 0 idicates the worst caopy (or best, depedig o the goal) ~0.7h

14 Shallow flow over submerged caopies: Ghisalberti ad Nepf 2009 U h (whe depth ~ h) shear layer thickess of the caopy The key scales are: U h mea velocity at the caopy height a frotal area per uit volume of the rods =D (ote that = ah) Mixig layer regime: C d ah > 0.1, where C d is the drag coefficiet of the sigle roughess elemet deceleratio withi the caopy

15 Raupach Fiiga Bruet 1996 U h ~L s L s =U(h)/dU(h)/dh ~ expasio of the shear layer