Study Of Recirculation Zone Downstream Of An Expansion In A Shallow Open-Channel Flow

This research concerns the study of recirculation zones developing downstream of a sudden expansion in a shallow open-channel flow,combining both numerical simulations and the design of an experimental set-up.Such zones are common occurrences in nature,they are situated in Groynes fields,behind islands,in bays or in harbors.The study focuses on shallow flow,that is to say the water height is significantly smaller than the flow direction and the transverse dimensions.Understanding the flow's behavior in such zones is essential for river engineering and have an impact on made-man constructions in coastal areas.It is also essential to understand the impact of the flow on the fauna and the flora of the areas,because of the circulation of sediments and pollutants in such areas.From the literature,it is known that the mapping of the zone shows that it is a deposition zone for particles,sediments or pollutants,and this mapping depends on the shape of the flow.Knowing the behavior of the flow and know how to predict the shape of the flow enables to avoid heap of particles,which are potentially noxious for the fauna and flora or for human health.Recirculation zones are complex because they are zero-discharge zone,and the water velocity is lower than in the free stream flow.The free stream reattaches downstream the expansion at a point where the velocity is equaled to zero.From this point,the flow separates into two zones,the recirculation zone,with a water flow developing vortex of low velocity,and the free stream.The zero-velocity point where the free stream reattaches the side wall is called the reattachment point.The development of vortex of low velocity is favorable for the settlement of constructions since it will not disturb the structures.The available literature,first through the study of the backward facing-step problem and then with pioneer work about the characterization of recirculation zones,introduces the main parameters influencing on this zon e,which is characterized by the length of recirculation L,that is to say the distance from the expansion to the reattachment point downstream the expansion.The dimensionless reattachment length is used: L/d where d is the length of the expansion.This study focuses on characterize the effect of variation of the different parameters on L,thus,on the flow.The flow is mainly influenced by the bed-friction number S,the friction of the bottom of the flow tends to influence its behavior.The deeper the flow,the more important the influence of the friction.The water height h,needless to say,has a direct effect of the dimensionless reattachment length,and it is studied by the way of the dimensionless water height: h/d.The total width of the expansion,via the ratio called R_b,is also influencing the flow.The bed-friction number S is a function of the dimensionless water height,but also of the Darcy-Weisbach head loss coefficient ? and it is expressed following the relationship: S=(?.d)/(8h).The roughness of the bottom and of the side walls has an impact on ?,and thus S.? is a function of the roughness and of Reynolds number Re.Reynolds number slightly influences the length of recirculation,with very small variations which is considered negligible in this study.However,the shape of the flow is influenced by Re,especially for high value of Re.In order to characterize these influences on the reattachment length,experiments and numerical simulations are performed.An experimental set-up is designed and built following a simple geometry using the juxtaposition of two elementary flows with different widths.This creates a sharp edge with a right-angle expansion with a fixed length of d=20 centimeters.To modify the value of R_b,the set-up must enable to move the total expansion width B,which is done using a moveable board.The range of R_b values available is from 0.74 to 0.33.The velocity in the canal is also controlled by changing the section in the pipe and measured using a flowmeter incorporated in the pipe.Controlling the water velocity makes Reynolds number,and thus the b ed-friction number S,to vary.The discharges available,as measured by the flowmeter,are between 20m3/h and 48m3/h.The water height h is directly depending on the water velocity and on the total expansion width.Thus,the independence between those parameters is not assured by the experiments.In order to study independently the different parameters,numerical simulations in ANSYS-CFX are performed.The modeling of the wall function is essential since the walls and the bottom have a significant effect on the flow,the boundary layer slows the velocity down,especially if the roughness of the wall is high.Thus,the k-? Shear Stress Transport is chosen,it combines the advantages of the k-? model for the wall function and the efficiency of the k-? model to treat the free-stream flow.The free surface,and especially the interface between the air and the water,is the second critical zone to control.The Volume of Fluid(VOF)method is chosen to model this interface.By calculating the volume fractions of the different phases,this method accurately models the interface between the water and the air.The representation of the interface is also done by using the methods using VOF model.The mesh used for this numerical model must fit the constraint of the critical areas.It is then very thin at the interface of the water and even thinner near the walls.To study independently the three parameters,two out of three are fixed.Modifying the water velocity fixes Reynolds number,and thus,by modifying the roughness,it is possible to fix S.Fixing the water height and the expansion width is done by modifying the geometrical parameters.The first parameter studied is the water height using the dimensionless water height h/d with the configuration R_b=0.75 and a bed-friction number S=0.030.The values of h/d are from 0.11 to 0.21.The results bring the following conclusion s: as the normalized water height h/d increases,the normalized length of reattachment L/d decreases,and the relationship is linear between those two parameters.The water height has a significant impact on the reattachment point position.Concerning the bed-friction number,two different values of h/d,as well as two different value of Reynolds number,were tested to get a wider range of available value of S: from 0.010 to 0.045.The results obtained show that as the bed-friction number increases,the normalized length of recirculation L/d decreases,and this for each value of h/d,and in the logarithmic representation,the relationship is linear.However,it seems that,for a fixed value of R_b,if S and the h/d vary at the same time,the evolution of the ratio L/d as a function of S is a parabola.The parameter R_b is calculated for values from 0.75 to 0.33.The relationship between R_b and L/d is similar than the one with h/d: when R_b increases,the ratio L/d decreases,in a linear evolution.However,the values reached by L/d are higher than the one reached by stud ying h/d,especially when it concerns the lower value of R_b.