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Journal of Hydraulic Research Vol. 44, No. 5 (2006), pp. 663–673 © 2006 Interna

Journal of Hydraulic Research Vol. 44, No. 5 (2006), pp. 663–673 © 2006 International Association of Hydraulic Engineering and Research Scour due to a horizontal turbulent jet: Numerical and experimental investigation Affouillement dû à un jet turbulent horizontal: Recherche numérique et expérimentale CLAUDIA ADDUCE, Post-Doc, Dipartimento di Scienze dell’Ingegneria Civile, Università Roma Tre, via Vito Volterra 62, 00146, Rome, Italy. Tel.: +390655173468; fax: +390655173441; e-mail: adduce@uniroma3.it. (author for correspondence) GIAMPIERO SCIORTINO, Professor, Dipartimento di Scienze dell’Ingegneria Civile, Università Roma Tre, via Vito Volterra 62, 00146, Rome, Italy. Tel.: +390655173448; fax: +390655173441; e-mail: sciorti@uniroma3.it. ABSTRACT In this paper both numerical and experimental investigations of local scour downstream of a sill followed by a rigid apron are presented. Nine laboratory experiments were carried out in clear water scour conditions, with different values of discharge. At the end of each run, velocity measurements both on the apron and on the scour hole were performed by ultrasonic Doppler velocimetry. A mathematical-numerical model was developed, simulating local scour downstream of a sill followed by an apron. The model uses information related both to the measured velocity ﬁelds and to the physical and mechanical properties of the sand constituting the mobile bed. The mathematical structure of the model consists of a second order partial differential parabolic equation whose unknown is the shape of the mobile bed. The numerical integration of this nonlinear equation, with suitable boundary conditions, is in agreement with the measured scour proﬁles at the end of the run. Upon comparing experimental and numerical data, a similar temporal evolution of the maximum scour depth is observed. RÉSUMÉ Cet article présente des recherches numériques et expérimentales sur l’affouillement local en aval d’un seuil prolongé par un tablier rigide. Neuf expériences de laboratoire ont été effectuées en eaux claires, avec des débits différents. À la ﬁn de chaque essai, des mesures de vitesse sur le tablier et sur le trou affouillé ont été exécutées par vélocimétrie Doppler ultrasonique. Un modèle mathématique numérique a été développé, simulant l’affouillement local en aval d’un seuil prolongé par un tablier. Le modèle utilise à la fois l’information des champs de vitesses mesurées et les propriétés physiques et mécaniques du sable constituant le lit mobile. La structure mathématique du modèle se compose d’une équation parabolique aux dérivées partielles du second ordre dont l’inconnue est la forme du lit mobile. L’intégration numérique de cette équation non-linéaire, avec des conditions aux limites appropriées, est en accord avec les proﬁls d’affouillement mesurés après les essais. La comparaison des données numériques et expérimentales, montre une évolution temporelle semblable de la profondeur maximum d’affouillement Keywords: Scour, velocity measurements, UDV, 2D horizontal jet, mathematical model. 1 Introduction Both turbulent plunging and horizontal jets can arise when a ﬂow interacts with hydraulic structures such as underﬂow gates, cul- verts, large dams and stilling basins (Farhoudi and Smith, 1985; Hassan and Narayanan, 1985; Fritz and Hager, 1998). When a jet impinges on a mobile bed it lifts the sediments, which are transported downstream, and a scour hole is formed. Local scour downstream of hydraulic structures is a relevant prob- lem, given its signiﬁcant practical value. Scour can endanger the stability of structures and cause the risk of failure if the foun- dations are not designed taking into account the maximum scour depth. The study of a local scour process is a complex problem, given the numerous variables related to both the heterogeneity of the eroded soil and the turbulent ﬂow producing the erosion. Many experimental investigations have been carried out whose Revision received July 26, 2005/Open for discussion until October 31, 2007. 663 aim was the development of empirical formulae predicting the maximum (or equilibrium) scour depth and length. Schoklitsch (1932), Kotulas (1967) and Bormann and Julien (1991) pro- posed formulae for scour due to plunging jets, Qayoum (1960), Altinbilek and Basmaci (1973), Farhoudi and Smith (1985), Breusers and Raudkivi (1991), Hoffmans (1997) and Chatterjee et al. (1994) suggested relations for scour downstream of 2D hor- izontal jets. A comparative review of the existing formulae can be found in Hoffmans andVerheij (1997). Empirical relations are based mainly on small-scale laboratory studies. They have “to be viewed with caution” if applied to prototypes (Graf, 1998). The possibility of developing mathematical-numerical models pre- dicting scouring processes is becoming more and more attractive and several authors (see Hogg et al., 1997; Istiarto, 2001; Jia et al., 2001; Karim and Ali, 2001; Salehi Neyshabouri et al., 2003) have recently focused on the numerical simulation of local Downloaded by [IAHR ] at 07:23 17 January 2012 664 Adduce and Sciortino scour. These models, tested by laboratory experiments, may lead to a better understanding of this complex phenomena. Hogg et al. (1997) developed an analytical model simulating local scour of an initially ﬂat bed of grains by a two-dimensional turbulent wall jet. They calculated the steady-state proﬁle by applying critical conditions along the bed surface for the incipient motion of a particle. The temporal evolution of the scour hole was obtained by integrating a sediment-volume conservation equation. The predicted proﬁles were compared with experimental studies by Rajaratnam (1981). Karim and Ali (2001) applied the FLUENT CFD package, testing three different closure models (Standard k–M model, the Reynolds Stress Model and the renormalization Group Theory-Based Model) to simulate the ﬂow ﬁeld gener- ated by a turbulent water jet impinging on a rigid horizontal bottom and scoured beds. Istiarto (2001) developed a 3D numeri- cal model to simulate the ﬂow around a cylinder on a scoured bed. The Reynolds-averaged Navier–Stokes and continuity equations for incompressible ﬂow were used, together with a k–ε turbu- lence closure model. Jia et al. (2001) simulated the local scour due to a 2D plane impinging jet in a plunge pool with a loose bed. The sediment transport model of Nakagawa and Tsujimono (1980) was modiﬁed by including the effects of shear stress and a ﬂuctuating lift force, the latter was related to pressure ﬂuctu- ations by using empirical functions. The ﬂow ﬁeld was solved by CCHE3D, a ﬁnite element-based unsteady 3D model, with a k–ε turbulence closure model. Salehi Neyshabouri et al. (2004) presented a numerical simulation of local scour of a ﬂat bed due to a 2D free falling jet. The momentum equations, the continuity equation and the k–ε equations for turbulent ﬂows were applied. First the turbulent ﬂow due to a free falling jet was computed, then the distribution of the sand concentration was determined and the scoured bed was predicted. Making use of both laboratory and numerical experiments, the present paper investigates local scour downstream of a sill followed by a rigid apron. No sediments are supplied from the upstream into the scour zone and the experiments are conducted under clear water scour. Nine laboratory experiments with local scour due to a 2D horizontal jet are conducted. Measurements of both the temporal evolution of the scour hole and its geometry at the end of the run are performed. Ultrasonic Doppler velocime- try is used to measure the velocity ﬁeld on the rigid apron and on the scour hole at the end of the run. A 1D mathematical- numerical model is developed, simulating the temporal evolution of the scour proﬁle due to a 2D horizontal wall jet. The model uses the equation of continuity for the local solid discharge and physical and mechanical properties of the sand. The analysis of the forces acting on a sand particle is performed taking into account the angle of repose of the sand, the instantaneous shape of the mobile bed and a model for the shear stress, following an approach similar to that of Hogg et al. (1997). The proposed model describes the progressive erosion of an initially ﬂat bed of cohesionless grains, but unlike the model proposed by Hogg et al. (1997), the scour proﬁle at the end of the run can be com- puted only by the complete temporal reconstruction of the scour proﬁle. The mathematical model consists of a second order par- tial integro-differential equation with a parabolic-like structure whose unknown is the shape of the mobile bed. The coupling between the shape of the eroded bed and the characteristics of the 2D horizontal jet make this problem highly complex. The developed model requires some empirical assumptions concern- ing the modelling of the bed shear stress. In particular, we assume that the source of the jet momentum is close to the bed and the bed shear stress can be described by a Gaussian-like law (see Hogg et al., 1997), when the shape of the bed is not ﬂat. Numeri- cal integration of this nonlinear equation with suitable boundary conditions, namely absence of solid discharge both at the inlet and at the end of the mobile bed agrees with the laboratory mea- sured scour proﬁles. The absence of solid discharge at the end of the mobile bed was experimentally observed in all the tests. A similar temporal evolution of the maximum scour depth is also observed when the laboratory and numerical data are compared. 2 Experimental set-up The experiments were conducted at uploads/Geographie/ 2006jhr.pdf