Settling velocities : Modelling strategy

• If you are not using key_sedim

  : settling velocity is defined by 2 parameters given by user in variable.dat : Defined simulated substances for each particulate variable (PART or NoCP) :

  • minimum value : ws_free_min(iv)
  • maximum value : ws_free_max(iv)

• If you are using key_sedim : a modelling strategy is proposed with a choice of some formulations. Options and parameters are given by user in variable.dat : Defined simulated substances for each particulate variable (MUD, PART or NoCP). Settling velocity is defined by 2 notions : Free settling velocity and Hindered settling velocity.

• Exemple of evolution and values of settling velocities issued from these different choices are presented below (Exemples of evolution of settling velocity according to different options)

Free settling velocity

4 options defined by a parameter (ws_free_opt) given by user in variable.dat : Defined simulated substances for each particulate variable (MUD, PART or NoCP). Some parameters values are proposed below.

• Option free 0 : Constant settling velocity defined by minimum value (ws_free_min(iv)) and maximum value (ws_free_max(iv)) - aditional parameters are not used (ws_free_para(1:4)

• Option free 1 : Formulation of Van Leussen, 1994

  \(Ws=kC^m \frac{1+aG}{1+bG^2}\)

  • \(k=0.0005\) =*ws_free_para(1)*
  • \(m=1.2\) =*ws_free_para(2)*
  • \(a=0.3\) =*ws_free_para(3)*
  • \(b=0.09\) =*ws_free_para(4)*

• Option free 2 : Formulation of Winterwerp, 1999

  \(D_e=D_p+ \frac{k_aC}{k_b \sqrt{G}}\)

  \(Ws=\frac{1}{18} \frac{(\rho_s-\rho)g}{\mu} D_p^{3-n_f} D_e^{n_f-1}\)

  • \(D_p=4.10^{-6}\) =*ws_free_para(13)*
  • \(k_a=14.6\) =*ws_free_para(2)*
  • \(k_b=30000\) =*ws_free_para(3)*
  • \(n_f=2\) =*ws_free_para(4)*

• Option free 3 : Wolanski et al., 1989 : include Hindered settling (ws_hind_opt must be = 3 also; otherwise error and stop)

  \(Ws=k C^m\) * \(k=0.01\) =*ws_free_para(1)* * \(m=2.1\) =*ws_free_para(2)* * ws_free_para(3) and ws_free_para(4) not used

Hindered settling velocity

4 options defined by a parameter (ws_hind_opt) given by user in variable.dat : Defined simulated substances for each particulate variable (MUD, PART or NoCP)

• Option hindered 0 : no hindered settling velocity

• Option hindered 1 : Formulation of Scott, 1984

  \(\Phi=\frac{SPM_{tot}}{cgel}\)

  \(Ws=Ws(1-\Phi)^m\)

  • \(cgel=40\) =*ws_hind_para(1)*
  • \(m=4.5\) =*ws_hind_para(2)*

• Option hindered 2 : Winterwerp 2002

  \(Ws=Ws(1-\Phi_v)^m \frac{(1-\Phi)}{1+2.5\Phi_v}\)

  if Option free = 2 \(\Longrightarrow \Phi_v=\Phi (\frac{D_e}{D_p})^{3-n_f}\)

  • \(m=1\) =*ws_hind_para(2)*

  if Option free \(\neq 2 \Longrightarrow \Phi_v=\frac{SPM_{tot}}{cgel}\)

  • \(cgel=40\) =*ws_hind_para(1)*
  • \(m=1\) =*ws_hind_para(2)*

• Option hindered 3 : Wolanski et al., 1989

  \(Ws=frac{Ws}{(C^2+b_w^2)^{m_w}}\)

  if Option free = 3

  • \(b_w=2\) =*ws_hind_para(1)*
  • \(m_w=1.46\) =*ws_hind_para(2)*

  if Option free \(\neq 3\) : error and stop

Exemples of evolution of settling velocity according to different options

Option free 1 and Option hindered 0 :
Option free 1 and Option hindered 1 :
Option free 1 and Option hindered 2 :
Option free 2 and Option hindered 1 :
Option free 2 and Option hindered 2 :
Option free 3 and Option hindered 3 :