Nearshore Sediment Transport Modeling: Collaborative Studies with the U. S. Naval Research Laboratory

Transcription

1 Nearhore Sediment Tranport Modeling: Collaborative Studie with the U. S. Naval Reearch Laboratory Donald N. Slinn Department of Civil and Coatal Engineering, Univerity of Florida Gaineville, FL , Phone: (352) x 1431 Fax: (352) linn@coatal.ufl.edu Award #: N Joeph Calantoni and K. Todd Holland Naval Reearch Laboratory, Littoral Dynamic Team Code Building 1005 Stenni Space Center, MS Phone: (228) ; Fax (228) joce@nrlc.navy.mil LONG-TERM GOALS The goal of thi work are to obtain better undertanding of ediment mobilization, tranport, and depoition acro the wave bottom-boundary layer (WBBL) in the urf and wah zone and to improve predictive capabilitie for bed load and upended ediment tranport a a function of environmental parameter, including wave height, breaker characteritic, ediment propertie, beach lope, bottom roughne, local water depth, wave frequency pectra, and the preence of low frequency circulation uch a along hore current and undertow. OBJECTIVES We are preently focued on addreing two key apect of ediment tranport: 1.) to imulate coupled two-phae flow, particularly for bed-load dominated flow regime, utilizing three-dimenional hydrodynamic direct numerical imulation of the turbulent, wave bottom boundary layer and dicrete particle modeling. 2.) to ae the trength and weaknee of the hydrodynamic and dicrete particle model capabilitie and addre deficiencie a guided by the lab and field data. APPROACH The work involve theoretical and model development, numerical computation, and comparion with laboratory data. The primary experimental tool are three-dimenional dicrete particle and direct numerical imulation hydrodynamic model of ocillatory, turbulent boundary layer. 1

2 WORK COMPLETED The coupled model being developed here will challenge and refine exiting parameterization for bedload and upended load tranport rate. Fundamental concept ued in decribing the phenomena of ediment tranport uch a the reference concentration, bed failure criterion, and the more recently introduced concept of acceleration-induced tranport will be more acceible for tudy with the new model. It will produce the high level of detail neceary to refine our preent undertanding of ediment tranport procee and clarify new direction in the meauring technique needed to improve preent predictive capabilitie. Our approach integrate the turbulent boundary layer hydrodynamic model of Moneri and Slinn (2005) (Figure 1) with the dicrete particle model of Drake and Calantoni (2001) (Figure 2). The model are being integrated with two-way coupling between the fluid and olid phae. The hydrodynamic model ue control-volume lightly larger than individual grain ize. The fluid model pae the three intantaneou Carteian component of momentum in a turbulent boundary layer under ocillatory free-tream flow to the particle location. By coupling preure, lift, and drag force between the model, turbulent upenion of the dicrete particle i imulated. The drag and lift component of the momentum exchange (updated approximately 1000 time per econd) i calculated uing empirical drag coefficient and the local preure gradient in the fluid can act to lift the particle. Global momentum i conerved, and a a particle accelerate, the local fluid velocity decreae, or a the particle decelerate, the local fluid velocity increae. It i not a perfectly phyical model, but it i, arguably, a rational tep toward increaed realim in both the hydrodynamic and dicrete particle modeling approache. In order to model a domain that contain ufficient number of particle and turbulent eddie to make a tatitically meaningful repreentation of the flow (Barr, Slinn, Pierro, Winter, 2004) the model domain ha been choen to be approximately 5 cm x 3 cm x 5 cm. We can imulate approximately 100,000 particle for econd of imulation time in about a day or two of CPU time. We have focued ome effort on calculating exact olution to the portion of the particle volume that i located in each fluid control volume. Thi i neceary to approximate with accuracy becaue a the particle move acro the domain they reide in multiple fluid control volume and we need to know the ma of each particle in each control volume to a high degree of accuracy in order to appropriately attribute the exchange of momentum between the fluid and particulate phae, we needed to know the portion of each particle in each fluid control volume a a function of time. Thi detail ha been worked out for a particle croing through a corner (a illutrated in Figure 3 below) it can occupy portion of up to 8 control volume imultaneouly and a manucript on the analytic olution i in preparation. There i a new level of complexity developed in the model becaue the fluid doe not occupy all of the pace. Thi complicate the mathematical method required for olution of the fluid preure field. For a uniform denity flow field, the coefficient that appear in front of the Poion equation for preure are contant (the denity). However, for the variable denity field (ariing from portion of the control volume being filled with and particle), the coefficient are patially and temporally variable. They can be calculated, by integrating forward the particle poition, but the computationally efficient direct preure olution method that worked in the old fluid model mut be replaced with a lower multi-grid preure olver (a ued by Barr, Slinn, Pierro, and Winter, 2004) or an iterative technique (a ued by Slinn, Allen, Holman, 2000). Iterative technique introduce new mathematical uncertainty to the model olution, becaue they require convergence criteria and tolerance level. Thi 2

3 apect of the problem i the main technical challenge remaining. We are eeking to optimize the algorithm. RESULTS The model equation for the two-phae flow are v d( εu) v v 2 v v v ρ + ( u ) εu = ε p+ μ ( εu) + ρεg freaction + ε FApplied, (1) dt dε and the modified continuity equation i + ()= εv u 0, (2) dt where ε = 1 c i the local poroity of the fluid, c i the particle concentration at the grid volume, ρ i v the fluid denity, u i the fluid velocity, p i the preure, μ i the dynamic fluid vicoity, g v i the acceleration due to gravity, and f v reaction repreent the coupling force which i the component of the particle drag force acting back on the fluid volume and F i an applied external preure gradient that drive the wave bottom boundary layer flow. The preure field i determined iteratively becaue n 1 of the non-contant coefficient ε + n 1 in front of p + at the new (n+1) time level in the 3 rd order Adam-Bahforth time tepping cheme uing the projection method. The governing equation for the motion of a pherical particle i given by (e.g. Maden, 1991) du v ρ V v = ( ρ ρ)v g + 1 dt 2 ρ C A v d u u v u v v Du ( v u )+ ρv + F v φ, (3) Dt z= where ρ i the ediment denity, V i the particle volume, u v i the particle velocity, C d i the modified drag coefficient, A i the projected area of the phere and F v φ i the um of inter-particle force. The firt term on the right hand ide of the equation repreent the particle buoyancy. The econd term repreent the particle drag force where the drag coefficient i calculated from a fit to the Applied empirical drag law for a phere, C d = c * (24Re 1 + 4Re ), where baed on the local particle concentration (e.g. Richardon and Zaki, 1954), c * repreent a modification c * = (1 c 1 3 c2 ) 5 2. The third term repreent the applied horizontal preure force, which i the driving force of fluid and particle motion in the model, written here in term of the free tream fluid acceleration. A number of fluid-particle interaction force (e.g. added-ma, Baett hitory, Magnu force) have been ignored with thi initial formulation. Conider the reaction term, f v reaction, in (1) i the equal and oppoite force to the particle drag force. The reaction term ha dimenion of force per unit volume in (1). The particle drag found in (3) ha dimenion of force. In general, the reaction term in (1) may be written a f reaction = 1 1 ρ C d A u v v v u ( u u v ). The particle drag force i aumed to be a body force 2 V acting through the center of ma of the particle. The fluid velocity, u v, found in (1) i the etimated velocity at the center of the phere. When the fluid velocity i contant over a large volume compared to the particle then the etimate i trivial; the velocity of the fluid at the center of the particle i etimated to equal the velocity of the fluid volume where the center of the particle i located. However, for our problem a ediment particle could pan many grid volume (of fluid) in the vertical, while at 3

4 mot four volume in the horizontal, the tak of etimating the particle drag force uing the empirical drag law for a phere while imultaneouly atifying Newton Third Law become problematic. Due to the tretched vertical grid a ediment particle may occupy volume in over 20 different fluid grid point imultaneouly. Determining a reaonable etimate of the fluid velocity at the particle center for ue in the empirical drag law i no longer trivial. There i NO clear choice that i obviouly better than the other poibilitie. Some method will be more computationally efficient than other, but one could argue that their ue acrifice accuracy and more importantly, fidelity to the phyic. We have choen a method for computing the velocity at the center of a particle for our baeline imulation that i omewhere in between the extremely difficult and trivial. In practice, there are at leat two neceary contraint that need to be atified when determining how to compute the reaction term. The concentration of particle in fluid grid volume mut alway be le than unity. More realitically the concentration hould not be allowed to exceed about 0.7. A a reult of thi contraint, there will be ome trade off between the cale of the turbulence reolved and the larget particle allowed in the imulation. The econd contraint i that Newton Third Law mut be trictly enforced! When a ediment particle i much maller than the fluid grid volume the eaiet method for obeying Newton Third Law i clear. The fluid velocity ued to compute the drag force i jut the velocity of fluid at the grid point where the center of the particle reide. The computed drag force i generated entirely from a ingle grid point and i imply projected back onto that grid point with equal magnitude and oppoite direction. For our configuration the particle may occupy volume in many grid point imultaneouly and it i not poible to chooe a ingle grid point for fluid-particle interaction without violating the firt contraint. Implicitly aumed i that the total ma of fluid and particle will be conerved for all time and pace in the imulation. Figure 1. Turbulent kinetic energy diipation rate in a imulation of a turbulent wave bottom boundary layer during a phae of flow reveral. The left panel how a vertical plane, and the right panel how a horizontal plane located 2.7 mm from the boundary during flow tranition. 4

5 Figure 2. Dicret particle during a imulation. Figure 3. The poition of particle croing control urface mut be accounted for preciely to accurately determine the ma of fluid and olid in each control volume. A complex algorithm ha been developed to efficiently determine the location of the ma of each particle in motion. IMPACT/APPLICATIONS Our model are the mot ophiticated, coupled model of turbulence and ediment tranport ever implemented. Thi approach hould allow much more detailed undertanding of the complex phyic of two-phae flow. The model reult will permit evaluation of bulk tranport formula. RELATED PROJECTS Modeling project for the Sand Ripple DRI are related. 5

6 REFERENCES Barr, B., D. N. Slinn, T. Pierro, K. Winter, 2004, Numerical imulation of the wave bottom boundary layer over and ripple, Journal of Geophyical Reearch, Vol. 109, doi: /2002jc001709, 19 page. Drake, T. G., and J. Calantoni, 2001, Dicrete particle model for heet flow ediment tranport in the nearhore, Journal of Geophyical Reearch, 106, 19,859-19,868. Maden, O.S., Mechanic of coheionle ediment tranport in coatal water, Coatal Sediment, 15-27, Moneri, S. S., D. N. Slinn, 2005, Numerical imulation of the wave bottom boundary layer over a mooth urface. Part 1: Three-dimenional imulation, ubmitted to the Journal of Geophyical Reearch. Richardon, J.F., and W.N. Zaki, Sedimentation and fluidiation, Tran. Intn. Chem. Engr., 32, 35-53, Slinn, D. N., J. S. Allen, R. A. Holman, Alonghore current over variable beach topography, Journal of Geophyical Reearch, 105, C7, 16,971-16,998. 6