Solid-Fuel Rocket Motor Efficiency Improvement Scheme - Novel Combustion Concepts for Sustainable Energy Development - page 530

G b ¼ b l t

r t ðr T g Þ

ð 14 Þ

2
3 q k

2
3 l t ðr v Þ

2

2

G k ¼ l t S r v ð 15 Þ

where r v is the velocity divergence, S is the strain parameter, and S is the strain

rate tensor given in Eqs. ( 16 ) and ( 17 ).

p

2S

p

2S S T

S ¼ jj ¼ S ¼ S ð 16 Þ

: :

And

1
2 ðr

v T

v þr Þ ð Þ

S ¼ 17

Also, the product of two tensors is described in Eq. ( 18 ).

s : s ¼ s ij s ji ð 18 Þ

4.3 SST k- ˉ Model

The shear model was addressed by Menter ( 1994 ) and can be

expressed as Eqs. ( 19 ) and ( 20 ):

stress transport k- ˉ

-

Z Z Z

dt

q kd V þ q k ð v v g Þ d a ¼ ðl þ r k l t Þr k d a

V A A

Z

ðc eff G k c 0 qb f b ðx k þ x 0 k 0 ÞÞ d V

V

ð 19 Þ

Z Z Z

d
dt

qx d V þ qxð v v g Þ d a ¼ ðl þ r x l t Þrx d a

V A A

Z

2 2

0

þ ð G x qb f b ðx x Þþ D x Þ

d V

V

ð 20 Þ

where k 0 are the ambient turbulence values in source terms that counteract turbu-
lence decay, c eff is the effective intermittency provided by the Gamma Theta
Transition model, and c 0 ¼

½ ðc eff ; : Þ;

. The turbulent production G k and
G x can be written as follows in Eqs. ( 21 ) and ( 22 ).

min max 0 1 1