RECEIVING WATER HYDRAULICS ASSIGNMENT 2

Transcription

1 RECEIVING WATER HYDRAULICS ASSIGNMENT 2 Desgn of wastewater dscharge from the cty of Göteborg. Example of a dffuser n a stratfed coastal sea Example of retenton tme calculatons Ths assgnment conssts of two parts. The frst part deals wth a proposed marne outfall arrangement for the wastewater dscharge from the cty of Göteborg nto the Skagerak coastal sea. Ths part s focused on the dffuser arrangement, the dluton of the jets n stratfed coastal water and the subsequent further dluton n the recevng water. The second part s more magnatve (no real counterpart), and the purpose s to use the concept of box models and retenton tmes for assessng concentratons of certan pollutants n a near-shore recevng water. Part 1 The proposed outfall s shown n a schematc manner n Fg 1. Bascally, a 2 km long man tunnel below the bottom of Skagerak, should brng the wastewater to the outlet area va a dffuser arrangement consstng of a long ppelne wth nozzles at equdstant locatons, see Fg 2. The desgn wastewater flow rate s 6 m 3 /s. The recevng water n the dffuser area s stratfed, and measurements of the densty characterstcs were performed durng two years n ths area. The resultng temporal and depth varatons of the densty are shown n Fg 3. The vertcal axs shows the depth measured from the water surface and the horzontal axs shows the tme. Fgure 3 conssts of lnes of constant densty devatons σ,.e. the real densty s gven by: ρ sea = 1 + σ kg/m 3 and s always larger than 1 kg/m 3 as the Skagerak s salne. The densty dstrbuton for a gven tme s obtaned by evaluatng the densty varaton along a vertcal lne for that specfc tme. Generally speakng, the densty always decreases n the upward drecton (stable condtons). Ths means, that a fresh water dscharge at a certan depth wll rse upwards due to buoyancy forces. However, most often the dscharge wll not reach the water surface, but wll fnd a neutral level, where the densty of the jet axs s equal to the densty of the recevng water at that level. From ths level the dscharge wll move horzontally and passvely wth the recevng water currents. The purpose of part 1 s to: - determne the length of the dffuser ppelne - determne the neutral densty level for dscharge n two dfferent cases,.e. occasons wth dfferent vertcal densty dstrbutons. The frst case should more or less correspond to a stuaton, where one could guess, that the wastewater wll rse a consderable dstance. The second case should be a stuaton, where the rse s small. - approxmately determne the vertcal thckness of the wastewater at the neutral level - approxmately determne the wdth of the wastewater plume 1 km downstream from the pont, where the wastewater reached the neutral level.

2 Jet calculaton n a stratfed water body As the recevng water body s stratfed, one has to resort to an approxmate step-wse calculaton of the jet behavour. Ths means, that the water s dvded nto a number of layers, each wth a vertcal thckness Δy j, and that one performs calculatons of the jet n one layer at a tme. The calculatons start at the nozzle level and contnue untl the jet has reached ts neutral level, see Fgure 4. A modfed Froude densmetrc number s defned for each layer: F = U y ρ = 1 Δy ρ ρ j ( r, j g d where y = vertcal dstance from the nozzle to the upper level of the specfc layer nr ρ = densty of the wastewater d = nozzle dameter U = ntal jet velocty If the layer thckness s constant,.e. y = Δy, one obtans: F = U ρ = 1 ( ρ ρ j r, j g d The dluton at the jet axs s then gven by: y y S f. 5 F d 44 = 54. m,. F ( ) d F. 38 y y S f. 5 F d 1 67 = 54. m,. F ( +. 66) d F The average densty, ρ n layer number n the recevng water s: r, ρr, ρr, + ρr, 1 =, = at the nozzle level, = 1 after the frst layer etc. 2 The densty ρ m, of the water at the jet axs s: ρ m, = ( ΔS m, ΔS 1) ρ S r, m, + ρ m, 1, m, ΔS m, = Sm, 1 m, = 1, ρm, = ρ S

3 The crteron for the neutral level s gven by: ρ r, ρ m, The vertcal thckness h of the wastewater at the neutral level after homogenzaton can be estmated through a contnuty consderaton: Q L = Urec h S = Urec h γ Sm, where Q = wastewater dscharge, L = dffuser length, U rec = water velocty n the recevng water at the neutral level, S = dluton of the jet after homogenzaton, S m, = dluton at the jet axs at the neutral level, γ = 2 = correcton factor for the homogenzaton process at the neutral level. Horzontal spreadng of the wastewater plume at the neutral level When the jet has reached the neutral level, a certan homogenzaton takes place, and after that the wastewater s transported horzontally n the downstream drecton due to the recevng water velocty at the neutral level. The spreadng n the vertcal drecton s very small due to the stratfcaton, whch strongly attenuates vertcal turbulence. However, horzontal spreadng takes place causng a wdenng of the wastewater plume. In order to approxmately evaluate ths wdenng an analogy wth the horzontal spreadng of a plume from a pont source s done, Fgure 5: B = 2 x 2 KH, Urec KH = B 2 (m / s) where B = wdth of the plume, x = dstance from the pont source, K H = horzontal dffuson coeffcent. Task 1. Determne the number of nozzles and the length of the dffuser on the bass of the followng data: Q = 6 m 3 /s, U and d accordng to the table below, ρ = 1 kg/m 3. In order to obtan a good dluton of the wastewater one should try to fulfll the followng condtons: a. a hgh jet velocty at the nozzles (U > 2 m/s) b. a small dameter of the nozzles (d, mn ~.1 m) c. dffuser locaton at a large water depth d. a farly large dstance l nozzle between consecutve nozzles, Fg 2: l max( 1 d and (. 1. 2) nozzle y neut When calculatng the length of the dffuser one could approxmately assume that the neutral level s located y neut = 2 m above the nozzles.

4 2. Each group should choose one set of data n the table below. On the bass of these data the followng parameters should be calculated: a. The neutral level for two densty stuatons n the recevng water. One stuaton should be characterzed by a small rse of the jet and the second one by a large rse of the jet. Choose the stuatons accordng to your own opnon b. The dluton, S m, at the jet axs at the neutral level for the two chosen cases c. The vertcal thckness of the wastewater at the neutral level after homogenzaton d. The wdth of the wastewater plume 1 km downstream of the locaton where the wastewater reaches the neutral level. Table: Data for each group Group nr Intal jet velocty Water depth Nozzle da- Recevng water U (m/s) of nozzles (m) meter d (m) velocty U rec (m/s) The calculatons should be performed wth a constant layer thckness Δy = 2 m. Part 2 As an alternatve to the marne outfall nto the open sea wth a long tunnel accordng to part 1 one has consdered to dscharge the wastewater after further treatment (6 m 3 /s) n a coastal recevng water. Ths near-shore recevng water could be consdered as beng farly enclosed, where the connecton to the open sea takes place through a number of strats. Moreover, a rver dscharges nto the enclosed recevng water, Fg 6. The area of the recevng water s A = 1 km 2 and the average depth D av = 3 m. The flow rate n the rver s farly constant and can be assumed to be Q = 5 m 3 /s. The water exchange n the recevng water s due to the rver dscharge as well as to flows through the strats, ntated by wnd and water level changes n the open sea. In order to assess the average flow rate E (m 3 /s) from the open sea to the recevng water (and vce versa for long tme averagng), a tracer experment s performed, whereby rhodamne (a soluton of an ntensely red compound, whch can be traced n very, very small concentratons) s mxed more or less nstantaneously and smultaneously at dfferent locatons n the recevng water. One assumes, that well-mxed and homogeneous condtons preval n the recevng water. The tracer concentraton s measured as a functon of tme provdng the followng data: Tme (days) Tracer conc c s 1 9 (kg/kg H 2 O) 1.2 (c s, ) 2.94

5 Determne the water exchange E (m 3 /s) between the open sea and the recevng water on the bass of the tracer measurements. The avklngnngshastghet of the tracer s d = 1-7 s -1. There s no tracer n the rver water or n the open sea 2. Assume that the wastewater contans.5 mg P/l and that the rver water contans.5 mg P/l. What wll the steady-state concentraton of phosphorus (P) be n the recevng water, f there s no degradaton of phosphorus? What wll the steady-state concentraton of phosphorus be, f t s degraded by the rate of 1 % per month?. The concentraton of phosphorus n the open sea s neglected 3. What wll the steady-stated concentraton of phosphorus be n the recevng water, f the concentraton of phosphorus n the rver water s reduced 1 tmes? Perform the calculaton wth and wthout degradaton. Fg 1. Proposed wastewater tunnel nto the Skagerak wth a dffuser at the end

6 Fg 2. Close-up of the dffuser and two of the nozzles

7 Fg 3. Densty devatons from ρ H2O = 1 kg/m3 for the recevng water n the area of the proposed outlet of the Göteborg marne outfall

8 Fg 4. The wastewater jet rses to the neutral level Fg 5. Horzontal dscharge pattern from a pont source. Notce that the two lnes from the source to the wdth B should be curved

9 Fg 6. Wastewater dscharge arrangement for part 2,.e. nto a near-shore coastal recevng water