Minimum Jet Velocity for Unbounded Domain Fluidization as a New Dredging Methods

Transcription

1 Article Minimum Jet Velocity or Unbounded Domain Fluidization as a New Dredging Methods Muhammad Arsyad Thaha,a, Radianta Triatmadja,b,*, Nur Yuwono, and Nizam Department o Ciil Engineering, Hasanuddin Uniersity, Makassar, Indonesia Department o Ciil and Enironmental Engineering, Gadjah Mada Uniersity, Yogyakarta, Indonesia a arsyad999@gmail.com, b radiantatoo@yahoo.com (Corresponding author) Abstract. Unlike or the bounded domain, the minimum luidization elocity o the unbounded luidization domain has not been well deeloped. The aimed o the research is to ormulate the minimum jet (holes) elocity ( oc) theoretically and experimentally as the criteria or unbounded domain luidization. Physical experiments were conducted or bounded and unbounded luidizations o 0 cm to 45 cm thickness o sand bed. The bounded luidization was carried out using a transparent ertical tube, whilst the unbounded luidization was conducted on a transparent box. The luidization discharge and pressure were measured. Empirical equations on jet holes elocity based on the experiment was deeloped. It was ound that oc depends on the required supericial elocity at the surace o sediment deposit ( c) and low rate loose actor () due to unbounded domain conditions. The c is greater than the minimum luidization elocity in bounded domain ( m). The conseratie alues o elocity conersion actor (k s) were ound to be approximately.0. Keywords: Bounded domain, unbounded domain, required surace elocity, and minimum jet elocity. ENGINEERING JOURNAL Volume Issue 5 Receied 9 December 07 Accepted 9 June 08 Published 30 September 08 Online at DOI:0.486/ej

2 DOI:0.486/ej Introduction In the last three decades, the study and application o luidization technology hae been deeloped especially in coastal and rier engineering ields. Fluidization method has shown satisactory perormance and was considered worthy as an alternatie method or waterway maintenance dredging. Studies and research on this method hae been done using experimental, analytical and numerical models by Weisman et al. (98, 988, 994) in [], [], & [3]; Lennon et al. (990, 995) in [4] & [5]; Research ranges rom predicting o incipient luidization, luidization discharge, jet orientation, diameter and jet holes distance and ormed trench dimensions. The method has also been applied by a local consulting irm to maintain channel depth in the port o Ana Maria, Florida (986) and by the US Army Corps o Engineers or additional system o sand by passing project in Oceanside Caliornia (99), as presented by Collins et al. (99) and Bisher & West (993) in [6]. Law [7] determined the pore pressure on the sediment bottom to start luidization. Mechanism o bed luidization using ariation o elocities and requencies o wae riction hae been studied by Mehta, Williams and Feng [8]. Three dimensional numerical model conducted by Lennon and Weisman (995) in [5] has completed the earlier study to measure the loss o the high pressure shat by a layer o sediment. Response o luidized sediments by a waterall has been reiewed by Foda, DeNeale and Huang [9]. In Indonesia, research on luidization method or channel maintenance has been done since 000 started by Hadisantosa and Harnaeni ollowed by Prasojo, Sidabutar and Simanjuntak (00). The studies included channel ormation mechanism; eriication jet orientation and eectieness o the luidization mechanism on the muddy sand. Triatmadja [0] & [] has elaborated the sediment bed luidization method and concluded that it was prospectie as an alternatie method or rier mouth and waterway maintenance. Thaha et al. (00 up to 006) conducted a more comprehensie experimental studies among which hae eriied the design parameters and identiied that clogging is the main problems in the operational o luidizer system [], comparison o required head between ertical and horizontal jet directions [3]; eriication o initial pressure required or unbounded domain luidization [4]; trench ormation perormance with 3D experiments [5]; The prospects o its application to Indonesian ield conditions [6]; deepening the understanding o luidization phenomena between theory and laboratory experiments [7]. Mechanisms o unbounded domain luidization process hae been obsered in detailed and ormulated through the deelopment o the ortex in the sediment bed by a pressurized lows [8]. Releant study hae been undertaken by Yongxin He et al. [9]. The mechanism or the caity eolution aboe the ertical jet was ound that the stages were no caity, a stable caity, an unstable caity propagating upward, and ull luidization. An analytical model was deeloped to predict the critical low rate or ull luidization. Other study regarding an example design application o the luidizer system at Panoang Rier o Bantaeng, Indonesia has been disseminated in International Conerence [0]. The luidization method is a technique in which water is injected through jet holes o buried pipes into granular medium (typically sand) causing the grains to lit up and separate. As the sediment aboe the pipes is ully luidized, surace low may remoe the lited grains downstream. Jet elocity plays an important role in determining the high pressure and discharge required to achiee luidization conditions. The role o the jet stream, has een been deeloped by Ploypailin Romphophak et.al [] to dispose o water turbidity. Fluidization technique in the coastal engineering area is a relatiely new method or naigable waterway maintenance. Since the problem o luidization along a waterway channel is three dimensional and the luidized area is an unbounded domain, the requirement o minimal jet elocity that is capable o creating ull bed luidization should be well understood. This paper presents the critical jet elocity as a criteria or unbounded luidization domain.. Criteria or Unbounded Fluidization Domain According to Lennon, G.P., Chang, T. and Weisman, R.N. [] and Weisman and Lennon [], the required minimum discharge through a jet hole to luidize sediment bed o thickness d b, is Q oc, where Q oc is a unction o pressure dierence between inside and outside o the luidizer pipe and can be written as ollows. Q oc Po Cd Ah g () ENGINEERING JOURNAL Volume Issue 5, ISSN (

3 DOI:0.486/ej C d is low coeicient, A h = area o jet holes, g is graitational acceleration and is speciic weight. Equation () can be soled when either Q oc or P o that initiates luidization is known. In order to determine the alue o Q oc or P o, the minimum elocity required or luidization ( c) near the sediment surace should be ulilled. Hence, this required elocity ( c) should be deined. The best approach to deine c is based on m in one dimensional luidization as suggested by Allen [], Snabre and Mills [3] and Goldman [4]. The minimum elocity or luidization was deeloped by Richardson-Zaki (954) in []; [3] & [4] as explained in the ollowing. The theoretical process o one dimensional luidization (bounded domain) such presented in Fig. is required to explain how to determine the m. The low elocity through a ertical cylinder o sand was gradually increased. The relation between the supericial elocity () and the pressure dierence under the sand material (P o) or (h) showed that the increase o dierential pressure (h) is proportional to the supericial elocity () until it reached a critical state o luidization (h e). Hence, Darcy Law is still applicable at this stage. Piezomete r h Le/L Sediment expands Q out h Superisial elocity () h Sediment bed L Q in he Dierensial Head( h) 0 he constant Minimum luidisasi elocity ( m) Superisial elocity () D Fig.. Relationship between supericial elocity and pressure drop (h or P o). Richardson-Zaki correlation was deeloped based on the relation between single sediment all elocity and bulk sediment all elocity as presented in Eq. (Richardson, 97 in [6]). o m C () with is all elocity or bulk sediment; o is all elocity or single particle o sediment; C is sediment concentration in normal condition. Based on the equilibrium o orces acting on the sediment in the water, the minimum luidization elocity ( m) as the upward orce to lit the bed grains should be equal to the grains all elocity (). Lapidus and Elgin (957), C.C. Harris (959) and Anderson (96) in [3] stated in dierent way that the luidization mechanism is equal to the sedimentation mechanism in the opposite direction. At initial condition o luidization, C is replaced by C and m is an empirical actor that depend on grain Reynold number. Triatmadja et al [] urther elaborated m using sediment porosity at initial luidization ( ) to replace ( - C ), and hence Eq. () can be written as Eq. (3). m o m (3) The ( ) m parameter is a actor that represents riction between particles within the lock o sediment which has to be urther determined. The next substantial discussion is how to relate the m or c at the surace o sediment deposit to the jet hole elocity ( oc) at the luidizer pipe, where the oc is an important ariable or Q oc. There are two approaches that can be used to determine the relationship between m or c to oc. First, m may be considered as the aerage elocity on the cross-section o imaginary tube o luidized sand bed. This ENGINEERING JOURNAL Volume Issue 5, ISSN ( 3

4 DOI:0.486/ej approach requires obseration o the tube diameter and the rate o the missing low rate outside through the wall o the imaginary tube. Secondly, the correlation o the m with a minimum jet elocity ( oc) is ormulated through experiment. 3. Minimum Jet Velocity & Pressure Requirement at the Hole Based on the law o continuity, the low across the stream tube (imaginary tube) domain can be used to ormulate the relationship between the minimum supericial elocity ( c) at the sediment surace and the minimum jet elocity ( oc) at the jet holes (see Fig. ). When oc is known, both the required pressure and low rate at the jet holes (h oc and Q oc) can be determined. Figure presents low through an imaginary tube rom point () to point () in an unlimited domain condition. In this condition, some amount o water low out through the imaginary tube wall (represented by arrows to the right and let). The amount o low rate through imaginary wall can be accommodated using ariable Q' and thereore the continuity equation can be expressed as Eq. (4). A = A + Q (4) where, Q' is a loss low rate through imaginary tube wall. By using a low rate loss actor ψ, the lost low rate can be written as Q' = ψ ( A ). Equation (4) can then be written as Eq. (5). (- ψ) A = A (5) A in the aboe equation is the cross sectional area at point in Fig.. Equation (6) may be written based on Eq. (5). h b o /g h k h o h e D s Velocity distribution at the surace o sediment bed ( c is aerage elocity in D s ) h h z z o d 50, s, Fluidizer Pipe Jet hole with dia. D Fig.. Schematic o unbounded domain ertical jet luidization [4]. 4 ENGINEERING JOURNAL Volume Issue 5, ISSN (

5 DOI:0.486/ej A D (6) ( ) A ( ) D The supericial elocity at point ( ) should be a minimum required elocity ( c) and is a minimum required jet hole elocity or namely minimum jet elocity ( oc) at point. The c may dier rom m in the bounded domain luidization (in the real tubes where no low rate loss), and thereore, urther supericial elocity near the surace as the D luidization criteria will be used c. D is equal to the luidized zone diameter (D s) which is assumed to be a unction o d b (the thickness o the sediment bed) or D s = (d b). Thus Eq. (6) can be written as: oc c D ( ) D s (7) where D s is approximately 0.3d b by Widiyanto [5], D is diameter o the hole. The right hand side o Eq. (7) is the low rate lost actor through the imaginary tube wall. The relationship between c and m, is assumed to be linear in which, k (8) c s m where k s is elocity conersion actor. The m can be rewritten rom Eq. (3) such that: 0,5 m 4( s ) gd m 3 (9) CD where is the minimum required porosity, m is an empirical actor as a unction o grain shape and Reynolds number (Re = od 50/). Subtitution o Eq. (8) and Eq. (9) into the minimum required jet hole discharge or luidization (Q oc) leads to Eq. (0). Q oc C d A h ks m Ds ( ) D (0) with C d is discharge coeicient that was ound to be 0.79 by Weisman dan Lennon [3]; A h is the hole cross section area. 4. Experimental Procedures One and two dimensional (D & D) experiments or sand bed luidization such as indicated in Fig. 3 and Fig. 4 hae been conducted at The Hydraulic Laboratory o Gadjah Mada Uniersity, Indonesia. Three types o sand were used as the sediment bed o D experiments, ranging rom coarse sand (d 50 = 0.56 mm; s =.973 N/m 3 and o = 0.05 m/s); medium sand (d 50 = 0.8 mm; s =.935 N/m 3 ; and o = m/s) to ine sand (d 50 = 0.7 mm; s = N/m 3 ; and o = 0.0 m/s). While D experiments were conducted using medium sand (d 50 = 0.344; d =.643; = and o = ) as the sediment bed. Vertical transparent tube o 5 cm in diameter that illed with arious thickness o sand bed. Low to high low rate o water were injected at the bottom o the ertical tube to test the luidization. The gradient hydraulics (h/l) and elongation o sediment cylinder (L e) were measured (see Fig. 3), while supericial elocity () was calculated based on Darcy ormula. The unbounded domain or D experiment were perormed using a transparent box o 0 cm x 80 cm x 50 cm, equipped with a water low circulation system (Fig. 4). Water was pump rom a storage tank to a ENGINEERING JOURNAL Volume Issue 5, ISSN ( 5

6 DOI:0.486/ej luidizer pipe that was placed under the sediment deposit o thickness d b. The excess water rom the box oerlowed throu gh a ertical pipe and return to the storage tank. In order to luidize the sand beds, it requires a certain pressure (head) in the luidizer pipe. By gradually increasing the low discharges in the system, the luidization process can be obsered and recorded. The pressure in the luidizer pipe was indicated by a manometer, while the pressure distribution within the sediment deposits were measured using pressure gauges and were directly recorded by a computer. Fig. 3. Bounded domain (D), reproduced rom [7]. Fig. 4. Unbounded domain (D) luidization, reproduced rom [8]. 5. Results and Discussion 5.. Minimum Fluidization Velocity ( m) A new approach to determine the minimum luidization elocity ( m) using minimum required porosity parameter ( ) hae been introduced in Eq. (3) and Eq. (9). Direct measurement o in the experiments is ery diicult, and thereore, it was approximated based on a theoretical approach. The Carman- Kozeny equation relates hydraulic conductiity (K) to the porosity o a sediment bed as in Eq. (). K 3 g 5 ( ) d 6 () 6 ENGINEERING JOURNAL Volume Issue 5, ISSN (

7 DOI:0.486/ej where is dynamic iscocity, is the porosity o grains and d is the mean diameter o sediment grain. In order to ormulate, the minimum hydraulic conductiity in the initial luidization (K ) shall be analyzed. The Darcy s Law is suitable or deining K based on the obsered both the initial elocity and hydraulic gradient in the initial condition o luidization since at tha coditions the low is still laminar and hence: dh m K () L In which, dh/l is to be obsered at initial luidization and m is calculated. Bear (97) stated that dh/l is approximately equal to in []. Wen and Yu (966) in [] suggested that the alue o m is approximately /0 times o o or large size o particles and /00 times o o or small size o particles. With these in mind and by using Eq. () and Eq. (), it is possible to write Eq. (3). K K C With R e d R e (3) where, is m/ o ranging rom 0.0 to 0. or ine to coarse sediment respectiely, while C is a coeicient that ollows Eq. (4). C dh dl 40 ( ) r 3 CD (4) Figure 5 shows the experimental results using medium sand (between ine and coarse sand) compared with Eq. (3). K/K y = 8.88x R² = Re Experimental Data Experimental Data Theoretical Eq (3) or ine to coarse sand Fig. 5. K /K as a unction o Re between theoretical approach and experimental data. Figure 5 indicates that the theoretical approach was within the range o the experimental data. The empirical equation can be simpliied and written as Eq. (5). K 8.8 (5) K Re From Fig. 5, both Eq. (3) and Eq. (5) shows that R e has a strong inluence on K /K. The cure indicates that the smaller is R e the greater is K /K. Critical porosity ( ) may be urther deined in term o K /K rom the experimental data in Fig. 6 and Eq. (6). ENGINEERING JOURNAL Volume Issue 5, ISSN ( 7

8 Required Minimum Critical Porosity Porosity () () DOI:0.486/ej Porositas kritis ( ) = 0.403(K /K ) 0.08 R = K /K Fig. 6. The relationship K /K with. K 0.40 K 0. (6) Figure 6 shows a strong relationship between K /K with, where increases with the increasing K /K or iner sediment grain size. This result is in agreement with the relationship K according to Carman- Kozeny. Based on the experiment, the alue o m is calculated and illustrated as a unction o R e in Eq. (7) and is compared to the alue o m o the Richardson-Zaki correlation in Fig. 7. m Fig. 7. Relationship o Re with m. m = R e R = Korelasi Richardson-Zaki Penelitian ini R e = o.d 50 / 0. e m 5.85R (7) Figure 7 shows that m reduces as R e increases. This means that iner grain size produces higher m. The empirical relationship o m and R e can be written as in Eq. (7), with R e = o.d 50/in the range o to 30. Based on Fig. 7, the relation o R e to m was generally closed to the Richardson-Zaki cure. Furthermore, the m can be computed using Eq. (9). The required ariables are deined using Eq. (5), Eq. (6) and Eq. (7). The results are compared with the preious studies in Fig ENGINEERING JOURNAL Volume Issue 5, ISSN (

9 Minimum jet elocity, oc (m/s) DOI:0.486/ej Figure 8 indicates that the alue o the present m is similar to preious researches by Richardson-Zaki, Daidson-Harrison and Yu Wen. m Vm (m/dtk) (m/s) Daidson and Harrison (963) Wen dan Yu (966) Zaki-Richardson (97) Equation Penelitian () (9) ini (004) Experimental Data eksperimen Data Experimental Data R e = o.d 50 / Fig. 8. The comparison o the m alue o preious results. 5.. Formulation o the Minimum Required Jet Velocity ( oc) Minimum jet elocity ( oc) and holes discharge (Q oc) can be calculated based on Eq. (7) and Eq. (0). Both equations require ariable k s which has not been known theoretically. Hence k s was deined based on experimental data using Eq. (0). In this case, was equal to 0.4 [] and D s was taken as 0.3d b (Widiyanto, [5]) whilst m was calculated based on Eq. (9). By arying k s, the alue o oc or Q oc can be ound. The results o the simulated alue o oc or Q oc are gien in Fig. 9 or k s equal to.0,.0 and.4 together with the measured data Experimental data Equation 7 (ks = & psi = 0.4) Equation 7 (ks = & psi = 0.4) Equation 7 (ks =.4 & psi = 0.4) D s =(d b ) 5 0 Q oc D d b Thickness o sediment bed, d b (m) Fig. 9. Relationship d b- oc in experimental and theoretical or k s = ; k s = & k s =.4 in = 0.4. Figure 9 suggests that a alue o k s equal to produces oc that is much lower than the experimental results, while k s equal to.4 produces oc higher than the experimental results. The best it is achieed when k s equals.0. The inding k s gies an understanding that the achieement o luidized conditions in ENGINEERING JOURNAL Volume Issue 5, ISSN ( 9

10 DOI:0.486/ej unbounded domain is require times o minimum supericial elocity ( c) compared to the elocity requirement or bounded domain or cylindrical tube luidization ( m). This is because about 40% o the low rate is lost in the horizontal direction o the media. The implication is that it requires greater discharge and pressure (head) than in cylindrical tube luidization. Based on the inding alue o k s as described aboe, the jet elocity ( oc) can be ormulated as in Eq. (8). oc m 0.34 d D b (8) with oc is the minimum single jet elocity; m is the minimum luidization elocity o Eq. (3); d b is the thickness o sediment; D is the diameter o jet hole. The equation 6. Conclusions Equation o the jet hole critical elocity ( oc) has been established. The oc depends on the required surace critical elocity ( c) and low rate loose actor () due to unbounded domain conditions. As expected, the critical elocity or unlimited domains ( c) is greater than the minimum ludization elocity or limited luidization domains ( m). The conseratie alues o k s were ound to be approximately.0. These indings can be used to acilitate luidizer system design as an alternatie dredging method or the purpose o maintaining the rier channel, rier mouth and other waterways in coastal enironment. Reerences [] R. N. Weisman and A. G. Collins, Maintaining tidal inlet channels by luidization, J. Waterway, Port Coast. And Oc. Di., ol. 08, no. 4, 98. [] R. N. Weisman, G. P. Lennon, and E. W. Roberts, Experiment on luidization in unbounded domains, Journal o Waterway, Port, Coastal, and Ocean Engineering, ol. 4, no. 5, May 988. [3] R. N. Weisman and G. P. Lennon, Design o luidizer system or coastal enironment, Journal o Waterway, Port, Coastal, and Ocean Engineering, ol. 0, no. 5, Sep.-Oct [4] G. P. Lennon, T. Chang, and R. N. Weisman, Predicting incipient luidization o ine sands in unbounded domains, Journal o Hydraulic Engineering, ol. 6, no., 990. [5] G. P. Lennon and R. N. Weisman, Head requirement or incipient luidization o ine sands in unbounded domains, Journal o Hydraulic Engineering, ol., no., pp , 995. [6] US Army Engineer, Waterways Experiment Station, Fluidizer system design or channel maintenance and sand bypassing, Dredging Research Technical Notes, Vicksburg, 99. [7] A. W. K. Law, Incipient luidization o ine sands in deep seabed, Journal o Hydraulic Engineering, ol., no. 9, pp , 995. [8] A. J. Mehta, D. J. A. Williams, P.R. Williams, and J. Feng, Tracking dynamical changes in mud bed due to waes, Journal o Hydraulic Engineering, ol., no. 6, pp , 995. [9] M. A. Foda, D. F. Hill, P. L. DeNeale, and C. M. Huang, Fluidization response o sediment bed to rapidly alling water surace, Journal o Water Way, Port, Coastal and Ocean Engineering, ol. 3, no. 5, pp. 6-65, 997. [0] R. Triatmadja, Basic luidization as an alternatie method or maintenance o rier mouth and naigation waterway, in Proceedings o National Seminar on Coastal Engineering, 00, PAU-IT UGM, Yogyakarta, pp [] R. Triatmadja and A. Thaha, Require head or loose-ine material luidizer system, in Proceedings o the th Asian Congress o Fluid Mechanics, 008, Daejeon, Korea. [] A. Thaha, N. Yuwono, and R. Triatmadja, Fluidization technology or maintenance o waterway, (in Indonesian), in Proceeding o Indonesian National Seminar Theory and Application o Ocean Technology, 004, Institut Teknologi Sepuluh Nopember (ITS), Surabaya. [3] A. Thaha, N. Yuwono, R. Triatmadja, and N. Nizam, Hydraulic design o ertical jet luidization or waterway maintenance dredging, (in Indonesian), in Proceeding o Annual Meeting o Indonesian Hydraulics Engineer Association (PIT HATHI), 005, Yogyakarta. 0 ENGINEERING JOURNAL Volume Issue 5, ISSN (

11 DOI:0.486/ej [4] A. Thaha, N. Yuwono, R. Triatmadja, and N. Nizam, Hydraulic study o initial luidization on unlimited domains, (in Indonesian) Journal o Ciil Engineering Forum, 006. [5] A. Thaha, N. Yuwono, R. Triatmadja, and N Nizam, The perormance o trench ormation in 3D experimental o luidization system, (in Indonesian), in National Seminar on Water Resources Engineering, 006, Itenas, Bandung. [6] A. Thaha and R. Triatmadja, Prospect o luidization technology application or watershed maintenance in Indonesia, (in Indonesian), in Proceeding o the Annual Scientiic Meeting (PIT) HATHI XXIV, 007, Makassar. [7] A. Thaha, Fluidization phenomenon or waterway maintenance engineering Basic concepts and laboratory eriication, (in Indonesian), Journal o Ciil Engineering Research, 007. [8] A. Thaha, R. Triatmadja, and I. Dwipuspita, The hydraulic behaior o ertical jet sediment bed luidization rom the ortex growth point o iew, International Journal o Hydraulic Engineering (IJHE), ol., no. 5, pp. 85-9, 03. Aailable: [9] Y. He, D. Z. Zhu, T. Zhang, Y. Shao, and T. Yu, Experimental obserations on the initiation o sand-bed erosion by an upward water jet, Journal o Hydraulic Engineering (ASCE Library), ol. 43, no. 7, 07. [0] A. Thaha, N. Yuwono, and R. Triatmadja, Fluidizer system design or maintenance dredging: A case study on the riers mouth surrounding Bantaeng Coastline, Indonesia, in Proceedings o The 8th International Symposium on Lowland Technology, International Association o Lowland Technology (IALT), Nusa Dua, Bali, 0. [] P. Romphophak, K. Wongwailikhit, N. Chawaloesphonsiya, P. Samornkraisorakit, and P. Painmanakul, Study o low pattern in jet clariier or remoal o turbidity by residence time distribution approach, Engineering Journal, ol. 0, no., pp. 7-7, 06. [] J. R. L. Allen, Sedimentary structures, their character and physical basis, in Deelopments in Sedimentology, ol. I and II. Amsterdam-Oxord-New York-Tokyo: Elseier, 984. [3] P. Snabre and P. Mills, Settling and luidization o non Brownian hard spheres in a iscous liquid, The European Physical Journal Eng., ol., pp. 05-4, 000. [4] D. I. Goldman, Pattern ormation and luidization in ibrated granular layers, and grain dynamics and jamming in a water luidized bed, Doctor o Philosophy dissertation, Uniersity o Texas, Austin, 00. [5] W. Widiyanto, Required head and discharge or single jet ertical luidization in the large scale experiment, Master o Engineering thesis, Gadjah Mada Uniersity, Yogyakarta, 004. ENGINEERING JOURNAL Volume Issue 5, ISSN (