Added mass matrix Particle Matrix Element Value Sphere(T) Mi 号pCTR3 Disc (T) M11 号pcR3 Ellipsoids(T) 123 Mis a/6 K11 K22(K33) =Ka号0cTab2 0.209 0.702 5 0.059 0.895 10 0.021 0.960 Sphere near Plane Ma Wall (T) 2(or3) =KpoTR3 (R/H《1) K33=K22 H Sphere near Free Mi H/R Ku Surface (E) =K美PcrR3 8.0 0.52 (R/H《1) 4.0 0.59 2.0 0.54 1.0 0.44 0.0 0.25
Added mass matrix
Unsteady effect .Mrelated to Re and Kc,Re=2UMR/vC Ke=UMt/2R -Umt*10R,'added mass'term dominates -Umt*>20R,pathological coefficients Concentration effect M(@_=1+2a=1+3a+0(a2) M(0)(1-a)
Unsteady effect • M related to Re and Kc, – Umt* < 10R, ‘added mass’ term dominates – Umt* > 20R, pathological coefficients • Concentration effect