SCOUR AND DYNAMIC PRESSURE OF IMPINGING JETS WITH AND WITHOUT AERATION: AN ANNOTATED REVIEW

Transcription

1 SCOUR AND DYNAMIC PRESSURE OF IMPINGING JETS WITH AND WITHOUT AERATION: AN ANNOTATED REVIEW ZHIYONG DONG Faculty of Civil Engineering and Architecture, Zhejiang University of Technology, Hangzhou , Zhejiang Province, P. R. China, E-ail: PEILAN SU Faculty of Forestry, Shanxi Agricultural University, Taigu , P. R. China, E-ail: This paper deals ith scour and dynaic pressure of ipinging jets ith and ithout aeration in the plunge pool. At present, though e have over 30 epirical forulas of scour depth, there are considerable differences beteen calculated results fro these forulas and easured data. It is easily found that the axiu error is up to 400% and the iniu error is at least 30%. So it is iperative to further develop ore reasonable forula of scour depth due to ipinging jets. Many researchers have conducted experiental and theoretical studies on it. Soe researchers think ipinging jets ith air entrainent ould eaken scour capacity of the jet; hoever, the other researchers suggest ipinging jet ith air entrainent ould deepen the scour. In addition, this paper deals ith ipinging dynaic pressure on the plunge pool botto, including tie-averaged and fluctuation distribution of pressure, correlation and frequency-spectru properties of pressure fluctuation, effects of air entrainent on tie-averaged pressure and pressure fluctuation etc. 1 Introduction Flip bucket and free overfall jets are of the advantages of loer cost, siple structures and short construction period as ell as stronger adaptability to tail ater level, hich are ost used in hydraulic engineering and have becoe effective ays of energy dissipation for flood release structures ith high-head and large discharge per unit idth. A huge energy carried by the jets priarily dissipates in the process of turbulent diffusion in the plunge pool. So a great deal of attention to hether or not the ipinging jets ay result in severe erosion of river bed, instability and destruction of apron, and vibration of structures etc have been being paid. According to the investigated data, if e ould copare the over 30 calculation forulas available in the orld for the scour depth ith the odel and prototype data, e can find the axiu error is up high to 400%, and the iniu is even to 30%. The questions as entioned above give us food and thought: hether e have been poorly considering the other factors that stand for iportant

2 hydraulic characteristics of prototype except for the discrepancy in geological conditions. In fact, the high velocity jets issued fro flip buckets have entrained a large aount of air in the process of diffusion, and for high concentration air-ater to-phase flos. In addition, the ipinging jets also entrain air at the point of entry( Dong 1997). Scour of ipinging jet on rock base is related to scour capacity of jet and scour resistance of rock base, hich is coplicated. There are different points of vie on scour echanis of rock base. Most of researchers ould think scour of ipinging jet on rock base is originated fro pressure fluctuation ithin joints and cracks on rock base(hartung 和 Hausler 1973, Chen 1980). Dynaic Pressure of Ipinging Jet ith and ithout Aeration.1. Tie-averaged Pressure Diensionless tie-averaged pressure profile of to-diensional jet on the plunge pool botto indicates that either vertical jet or oblique jet, either jet ith aeration or jet ithout aeration, the experiental data points gather together, hich exhibits a good siilarity and can be expressed as Gaussian distribution(dong, Yang and Wu 1994): ( 0.5η ) p = exp (1) p here p and p denote tie-averaged pressure and axiu tie-averaged pressure, respectively; η = y b 1,in hich y is distance fro axiu tie-averaged pressure point, b1 is half-value idth,i.e., value of y at p = 0. 5p. The first author of this paper found on the basis of experiental results of ipinging jet ith and ithout aeration that ipinging jet ith aeration akes tie-averaged pressure ithin the ipingeent region on the plunge pool botto decrease as shon in Fig.1, hich results fro density decrease of aerated flo in the pool after ipinging jet entrained air. The sybol C in the Figure denotes air concentration. Xu and Yu(1983)investigated ipingeent dynaic pressure of plane ater jet on the pool botto under an oblique jet, and copared it ith plane gaseous ipinging jet(beltaos 1976). They obtained that tie-averaged pressure distributions beteen ater jet and gaseous jet are basically agreeable.

3 Tie-averaged pressure(c) C=0 C= Port Figure 1. Effect of ipinging jet ith aeration on tie-averaged pressure in the plunge pool 1.. Intensity of Pressure Fluctuation Diensionless, the root-ean-square values of pressure fluctuation shoed experiental points ith and ithout aeration gathered under various ipinging angles(dong, Yang and Wu 1994). Certain siilarity also exists ithin ipingeent region. Hoever, the data points located belo the rollers are scattered. Especially ith ipinging angle decrease, the points ithin the loer roller scattered ore. Within ipinging region, intensity of pressure fluctuation can be ritten as p 0.5 ( 0.84η ) p = exp () in hich p denotes pressure fluctuation,and p axiu pressure fluctuation. Relation beteen axiu fluctuation intensity of pressure and pool depth is shon in Fig.(Dong 1993). It follos fro the Figure that axiu fluctuation intensity of pressure increases ith pool depth because potential core converges and turbulent boundary layer spreads in the zone of flo establishent. Conversely, in the zone of established flo that is fully developed turbulent boundary layer, fluctuation intensity gradually decays ith pool depth. Pressure fluctuation on the botto of plunge pool results fro loer frequency large-scale vortices, and fluctuation energy as under loer frequency doain(10hz). There as no doinant frequency in the fluctuation energy, hich approached a hite-noise spectru(dong, Wu and Yang 1994). In addition, variation in axiu dynaic pressure, frequency-spectru correlation and transversion beteen point and area of pressure fluctuation ere in detail discussed (Dong 1997).

4 Maxiu pressure fluctuation Pool depth Figure. Relation beteen axiu fluctuation intensity of pressure and pool depth Soe researchers investigated effects of air entrainent on dynaic pressure on the pool botto ipinged by jets. Luo and Guo(199), Dong, Yang and Wu(1994) obtained that jet ith air entrainent ould ake tie-averaged pressure decrease and pressure fluctuation intensity increase Theoretical Analysis of Effects of Air Entrainent on Dynaic Pressure Dynaic pressure can be expressed as p = ρ V (3) If e express instantaneous value as a su of tie-averaged and fluctuation values, e have p p + p, p = p + p, ρ = ρ + ρ = ρ = ρ + ρ, ρ (1 C ) ρ, V = V + V in hich the subscripts and denote ater and air-ater ixture, respectively. For clear ater, dynaic pressure can be ritten as 1 1 p ( ) = ρ V = ρ V + V (4) After averaging Eq.(4), e have 1 p = ρ ( V + V ) (5) Dynaic pressure of air-ater ixture can be ritten as 1 1 p ( )( ) = ρ V = ρ + ρ V + V (6)

5 After averaging Eq.(6), e obtain 1 p = ( 1 C ) ρ ( V + V ) (7) Subtracting Eq(5) fro Eq.(7), e have 1 p p = Cρ ( V + V ) (8) Obviously, p < p (9) It follos fro Eq.(9) that jet ith air entrainent ould ake tie-averaged pressure decrease. Mechanis of pressure fluctuation has not copletely understood ell yet. To hypotheses are suggested, that is, velocity field effects and vortex transfer. The forer, based on the basic equation of pressure fluctuation(chou 1945), suggested pressure fluctuation at certain location in turbulent flo arose fro velocity fluctuation at the location, hich divided into to types of fluctuating sources of interaction beteen turbulence-shear and turbulence-turbulence. The latter suggested pressure fluctuation arose fro stochastic otion of vortex in turbulent flo. Also, ith the developent of coherent structures hypothesis, it is considered that vortex in shear layer of jet is characterized by topology. It is the results of vortex pairing that the jet entrains surrounding fluid and its cross-section spreads. Wall pressure fluctuation is ainly caused by lo frequency large-scale coherent structures. 3 Effects of Jet ith Air Entrainent on Plunge Pool Scour Since the earlier research of Schoklitch on jet scour, any forulas of scour depth have been developed so far. Zhu and Cai(1963), Mason and his co-authors(1985, 1989) once ade an assess about the forulas of scour depth in the orld and suggested these forulas aaited on further study. Regarding effects of air entrainent on jet scour, an identical conclusion has not been reached yet. The earlier researcher of effect of air entrainent on ipinging jet scour is Vizko (1947). Thereafter, Nanjing Hydraulic Research Institute of China (1959), Yu (196) et al also conducted this experiental investigation. Vizko suggested the epirical forula of scour depth t as follos t = AK q (10) 1 P 0 here A denotes a coefficient of air entrainent, the value is 0.4~0.9; K 1 a coefficient

6 of scour,q discharge per unit idth and P 0 action head. It follos fro Eq.(10) that air entrainent ould itigate scour. Sokolov (1958) suggested that air entrainent ould itigate the jet scour because of interaction beteen air and ater that increased energy dissipation. Yu(196) experientally investigated effect of oblique jet ith splitting air entrainent on scour. He suggested that effect of splitting air entrainent on scour as not only related to splitting range, but also internal structures of splitting aerated flo. Unifor ixing air-ater jet flo as superior to splitting thin jet flo fro the vie of energy dissipation, so it should try to force jet to uniforly entrain air as uch as possible in the engineering design. Mitigation of jet ith splitting air entrainent to scour ould increase ith plunge pool depth. Under a sei-round nozzle and air concentration of 50%, Johnson (1967) investigated effect of jet ith air entrainent on scour. After copared 4 types of jets, i.e. solid ater jet ith oving tail ater, splitting ater jet, air-ater ixture jet and solid ater jet ith static tail ater, he obtained that air-ater ixture jet diffused rapidly, and the corresponding tail ater that needed to stop scouring as equivalent to half of tail ater that solid ater jet stopped scouring. At the sae ater level, air entrainent ade scour depth decrease. Mason s (1989) experients shoed that scour hole profile for the jet ith air entrainent as flattener than that for the jet ithout air entrainent, and reoved ith air entrainent ore bed aterials than that ithout air entrainent. Based on odel tests and prototype observations, Mason and Aruuga(1985) checked over 30 epirical forulas of scour hole, and suggested the reasonable expression should be ritten as x y z t = K q H d (11) here D, q, H and d denote scour depth, unit discharge, action head and grain size, respectively; the values of x, y and z are 0.5~0.6, 0.1~0.5, 0.5, respectively. After the contrastive experients ith and ithout air entrainent, Mason(1989)obtained that the values of x and y ithout air entrainent ere 1 and 0, respectively; Whereas, x and y ith air entrainent ere 0.59~0.71 and 0.08~0.0, respectively. These values approached the ones as above-entioned. Therefore he concluded that the values of x and y ould be related to air entrainent. Further experiental study shoed that H in the Eq.(11) can be ore reasonably expressed by air-ater ratio βbecause air entrainent as not only function of H, but also jet thickness, turbulence and ipinging angle. On the

7 basis of 47 runs data of odel experient, Mason suggested calculation forula of three-diensional jet scour as follos ( Hβ ) q h t = (1) g d here h denotes tail ater depth, β denotes ratio of air volue to ater volue, and the other sybols are the sae as the above-entioned. It follos fro Eq.(1) that jet ith air entrainent ould ake scour hole increase under the sae conditions. 4 Concluding Rearks With the developent of hydropoer and progress in da technology, ore and ore high das ill be constructed in China. Flos released fro discharge orks ould entrain a large aount of air. So it is very significant to correctly estiate or predict loer scour depth. Naturally, air entrainent by ipinging jet is an iportant fact that can not be ignored in the riverbed scour because flip bucket jet of prototype is high aerated flo. References Beltaos S. (1976). Oblique ipingeent of plane turbulent jets. J. Hydraulics Div., Proc. ASCE, 10(HY9), Chen C.T. (1980). Soe advances in flood discharging and energy dissipation of high da. Progress in hydraulic Engineering and Hydroelectric Poer, Hydraulic Engineering Press, Vol.1, (in Chinese). Chou P Y. (1945). On velocity correlations and the solutions of the equations of turbulent fluctuation. The Quarterly of Applied Matheatics. 3(1), Dong Z.Y., Wu C.G. and Yang Y.Q.(1994). Effects of aeration on properties of frequency spectru of pressure fluctuation on the botto of the receiving pool plunged by jets. Journal of Chengdu University of Science and Technology, No1, 9~13(in Chinese). Dong Z.Y., Yang Y.Q. and Wu C.G.(1994). Effects of aeration on dynaic pressure in the receiving pool by plunging jets. Science in China, Ser. A, No.4, 431~439(in Chinese). Dong Z.Y.(1993). A study on effects of aeration on hydraulic characteristics in receiving pool by plunging jet. Ph.D. Thesis, Chengdu University of Science and Technology(in Chinese).

8 Dong, Z.Y.(1997). Ipinging jets. China Ocean Press(in Chinese). Hartung, F. and Hausler, E.(1973). Scour, stilling basins and donstrea protection under free overfall jets at das. Transaction 11 th ICOLD, Vol., Madrid, Johnson, G.(1967): The effects of entrained air on the scouring capacity of ater jets. Proc. 1 th Congress of IAHR, Fort Collins, paper C.6, 1-9. Luo, M. and Guo, Y.K.(199). Study of to-diensional suberged aerated jet. Journal of Hydraulic Engineering, CHES, No.7, Mason, P.J. and Aruuga, K.(1985). Free jet scour belo das and flip buckets. J. Hydraulic Engineering, ASCE, 111(), Mason, P.J.(1989). Effects of air entrainent on plunge pool scour. J. Hydraulic Engineering, ASCE, 115(3), Nanjing Hydraulic Research Institute(1959). Coprehensive study of loer local scour of hydraulic structures. Hydraulic Engineering and Electric Poer Press, Vol.1(in Chinese). Sokolov, G. V.(1958). Study of air entrainent of flo in the overflo hydropoer odel. A Series of Translation of High Velocity flo, Science Press, Vol.1(in Chinese). Vizko, M.C. (1947). Scour decrease and increase of jets diension. Hydraulic Engineering Construction, No.7, 13-15(in Russian). Xu D.M., Yu C.Z.(1983). Ipingeent pressure of plane ater jet on the botto and its fluctuation characteristics. Journal of Hydraulic Engineering, CHES, No.5, 5-58(in Chinese). Yu, C.Z.(196). Studies on the role of jet in scouring and effects on dispersing aeration. Journal of Hydraulic Engineering, CHES, No., -35(in Chinese). Yuditski G.A. et al(1979). Model test and prototype observation of effects of dynaic pressure on loer riverbed scour behind flip bucket of overflo da. Translation Collections of High Velocity Flo, Hydraulic Engineering and Electric Poer Press. 4-5(in Chinese). Zhu, R.L. and Cai, F.C.(1963). Discussion of soe probles about flip nappe scouring and coparison of estiation relation for scour depth. Collected Research Papers of Water Conservancy and Hydroelectric Poer Research Institute, China Industry Press, Vol.3, 41-58(in Chinese)