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a98a101a108a105a101a118a101a100 a116a111 a104a97a118a101 a99a114a101a97a116a101a100 a115a105a103a110a105a28a99a97a110a116 a98a105a97a115 a101a114a114a111a114a115a46 a84a104a101a114a101a102a111a114a101a44 a116a104a101a115a101 a104a105a103a104 a118a111a105a100a97a103a101 a100a97a116a97 a97a114a101 a111a109a105a116a116a101a100 a102a114a111a109 a116a104a101 a112a114a101a115a101a110a116 a115a116a117a100a121a46 F a ce V e l o ci ty [ m / s ] ? P/ L [ Pa / m ] 0 0. 2 0. 4 0. 6 0. 8 1 1. 2 0 500000 1E + 0 6 1. 5E + 0 6 2E + 0 6 2. 5E + 0 6 Vo i d F r a c t i o n ( ? ) = 0. 41 Vo i d F r a c t i o n ( ? ) = 0. 47 a70a105a103a117a114a101 a52a46a50a58 a80a114a101a115a115a117a114a101 a100a114a111a112 a116a104a114a111a117a103a104 a56 ?a109 a78a105a47a65a67a80 a109a101a115a104 a40a100a97a116a97 a102a114a111a109 a67a97a104a101a108a97 a101a116 a97a108 a91a51a93a41 a52a46a50 a67a104a101a109a105a99a97a108 a67a111a110a118a101a114a115a105a111a110 a69a120a112a101a114a105a109a101a110a116a115 a119a101a114a101 a99a111a110a100a117a99a116a101a100 a98a121 a89a97a110a103 a91a52a93 a116a111 a115a116a117a100a121 a116a104a101 a101a27a101a99a116 a111a102 a102a97a99a101 a118a101a108a111a99a105a116a121 a40a114a101a115a105a100a101a110a99a101 a116a105a109a101a41 a111a110 a116a104a101 a98a114a101a97a107a116a104a114a111a117a103a104 a99a97a112a97a99a105a116a105a101a115 a97a110a100 a97a112a112a97a114a101a110a116 a114a97a116a101 a99a111a110a115a116a97a110a116a115 a105a110 a112a97a99a107a101a100 a54a49 a98a101a100a115a46 a84a104a101 a112a97a114a116a105a99a108a101a115 a105a110 a116a104a101 a112a97a99a107a101a100 a98a101a100a115 a119a101a114a101 a83a105a792 a99a111a97a116a101a100 a119a105a116a104 a90a110a79 a111a110 a116a104a101 a112a111a114a101 a115a117a114a102a97a99a101a46 a65a108a108 a116a104a101 a90a110a79a47a83a105a792 a115a111a114a98a101a110a116a115 a119a101a114a101 a116a101a115a116a101a100 a97a116 a52a48a480a67 a119a105a116a104 a97 a99a104a97a108a108a101a110a103a101 a103a97a115 a111a102 a50 a118a111a108a46a37 a722a83 a105a110 a722a46 a68a117a114a105a110a103 a116a104a101 a101a120a112a101a114a105a109a101a110a116a44 a48a46a49 a103 a111a102 a112a114a101a112a97a114a101a100 a90a110a79a47a83a105a792 a115a111a114a98a101a110a116 a119a97a115 a108a111a97a100a101a100 a105a110 a116a104a101 a114a101a97a99a116a111a114 a119a105a116a104 a97 a98a101a100 a116a104a105a99a107a110a101a115a115 a111a102 a50a46a48 a109a109 a97a116 a97 a103a97a115 a102a97a99a101 a118a101a108a111a99a105a116a121 a111a102 a49a46a51 a99a109a47a115a46 a73a110 a116a104a101 a101a120a112a101a114a105a109a101a110a116a115a44 a116a104a101 a97a109a111a117a110a116 a111a102 a115a111a114a98a101a110a116 a97a110a100 a116a104a101 a102a97a99a101 a118a101a108a111a99a105a116a121 a119a101a114a101 a100a111a117a98a108a101a100 a97a116 a115a105a109a117a108a116a97a110a101a111a117a115a108a121 a117a110a116a105a108 a116a104a101 a115a111a114a98a101a110a116 a108a111a97a100a105a110a103 a114a101a97a99a104a101a100 a48a46a56 a103 a97a110a100 a116a104a101 a102a97a99a101 a118a101a108a111a99a105a116a121 a114a101a97a99a104a101a100 a49a48a46a52 a99a109a47a115a46 Time(min) C / C 0 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 m:v 2m:2v 4m:4v 8m:8v a70a105a103a117a114a101 a52a46a51a58 a66a114a101a97a107a116a104a114a111a117a103a104 a99a117a114a118a101 a115a104a111a119a105a110a103 a116a104a101 a101a27a101a99a116 a111a102 a118a101a108a111a99a105a116a121 a111a110 a116a104a101 a114a101a97a99a116a105a118a105a116a121 a111a102 a116a104a101 a112a97a99a107a101a100 a98a101a100 a40a100a97a116a97 a102a114a111a109 a89a97a110a103 a91a52a93a41 a54a50 a84a104a101 a98a114a101a97a107a116a104a114a111a117a103a104 a99a117a114a118a101a115 a97a110a100 a101a27a101a99a116 a111a102 a116a104a101 a102a97a99a101 a118a101a108a111a99a105a116a121 a111a110 a116a104a101 a97a112a112a97a114a101a110a116 a114a97a116a101 a99a111a110a115a116a97a110a116 a97a114a101 a115a104a111a119a110 a105a110 a70a105a103a117a114a101a115 a52a46a51 a97a110a100 a52a46a52a46 Velocity[cm/s] Appa r en t R at e C o n s t an t [ s - 1 ] 2 4 6 8 10 0.5 1 1.5 2 2.5 3 3.5 4 GFE PackedBed k expt. =0.7824V 0.6732 a70a105a103a117a114a101 a52a46a52a58 a69a27a101a99a116 a111a102 a118a101a108a111a99a105a116a121 a111a110 a116a104a101 a97a112a112a97a114a101a110a116 a114a97a116a101 a99a111a110a115a116a97a110a116 a40a100a97a116a97 a102a114a111a109 a91a52a93a41 a70a105a103a117a114a101 a52a46a51 a115a104a111a119a115 a116a104a97a116 a97a108a108 a111a102 a116a104a101 a112a97a99a107a101a100 a98a101a100a115 a105a110 a116a104a105a115 a115a101a116 a111a102 a116a101a115a116a115 a104a97a100 a116a104a101 a115a97a109a101 a116a104a101a111a114a101a116a105a99a97a108 a115a97a116a117a114a97a116a105a111a110 a116a105a109a101 a116 a40a111a114 a1161 2 a41 a111a102 a49a50 a109a105a110a117a116a101a115 a97a110a100 a116a104a101 a115a97a109a101 a114a101a115a105a100a101a110a99a101 a116a105a109a101 a111a102 a48a46a48a55a53 a115a46 a84a104a101 a98a114a101a97a107a116a104a114a111a117a103a104 a99a117a114a118a101a115 a98a101a99a111a109a101 a115a104a97a114a112a101a114 a97a115 a116a104a101 a102a97a99a101 a118a101a108a111a99a105a116a121 a111a102 a99a104a97a108a108a101a110a103a101 a103a97a115 a105a115 a105a110a99a114a101a97a115a101a100a46 a71a108a97a115a115 a28a98a101a114 a101a110a116a114a97a112a112a101a100 a115a111a114a98a101a110a116 a99a111a110a116a97a105a110a105a110a103 a48a46a49 a103 a111a102 a90a110a79a47a83a105a792 a115a111a114a98a101a110a116a44 a115a104a111a119a110 a105a110 a70a105a103a117a114a101 a52a46a53a44 a119a101a114a101 a97a108a115a111 a116a101a115a116a101a100 a97a116 a116a104a101 a118a101a108a111a99a105a116a121 a111a102 a49a46a50 a99a109a47a115a46 a54a51 161 particles, and the amount of active catalyst or sorbent is only one-third of that in the packed bed of ZnO/SiO2 sorbents. (a) (b) Figure V-2. Morphologies of several microfibrous entrapped sorbents. (a) Al2O3 particles in Ni fiber media; (b) SiO2 particles in glass fiber media. Table V-1. Comparison between microfibrous entrapped ZnO/SiO2 sorbent (MFE), packed bed composed of ZnO/SiO2 particles (PB) and packed bed of commercial sorbents (PBC). Wt.% Vol.% Component MFE PB PBC MFE PB PBC ZnO 13 17 100* N.A.+ N.A. 60 SiO2 66 84 N.A. 22+ 60 N.A. Fiber 22 N.A. N.A 3 N.A. N.A Void N.A. N.A. 0 75 40 40 * The commercial sorbent contains 90 wt.% ZnO and 10 wt.% Al2O3 as binder + ZnO was loaded in the pores of SiO2 particles 8 ?m glass fiber SiO2 100 ?m 8 ?m glass fiber SiO2 100 ?m a70a105a103a117a114a101 a52a46a53a58 a77a111a114a112a104a111a108a111a103a105a101a115 a111a102 a83a105a792 a112a97a114a116a105a99a108a101a115 a105a110 a103a108a97a115a115 a28a98a101a114a115 a40a99a111a117a114a116a101a115a121 a89a97a110a103 a91a52a93a41 a70a105a103a117a114a101 a52a46a54 a115a104a111a119a115 a116a104a101 a99a111a109a112a97a114a105a115a111a110 a111a102 a98a114a101a97a107a116a104a114a111a117a103a104 a99a117a114a118a101a115 a119a105a116a104 a112a97a99a107a101a100 a98a101a100 a40a109a58a118 a101a120a112a101a114a105a109a101a110a116a41 a97a110a100 a103a108a97a115a115 a28a98a101a114 a101a110a116a114a97a112a112a101a100 a115a111a114a98a101a110a116a115 a97a116 a115a97a109a101 a108a111a97a100a105a110a103a46 a84a104a101 a98a114a101a97a107a116a104a114a111a117a103a104 a99a117a114a118a101 a111a102 a103a108a97a115a115 a28a98a101a114 a101a110a116a114a97a112a112a101a100 a115a111a114a98a101a110a116a115 a115a104a111a119a115 a116a104a101 a99a97a112a97a99a105a116a121 a97a116 a98a114a101a97a107a116a104a114a111a117a103a104 a105a110a99a114a101a97a115a101a115 a97a98a111a117a116 a53a48a37 a99a111a109a112a97a114a101a100 a119a105a116a104 a116a104a101 a112a97a99a107a101a100 a98a101a100 a101a120a112a101a114a105a109a101a110a116a44 a119a104a105a108a101 a105a110 a98a111a116a104 a99a97a115a101a115a44 a116a104a101 a115a97a109a101 a116a121a112a101 a111a102 a115a111a114a98a101a110a116 a40a90a110a79a47a83a105a792a41 a119a105a116a104 a116a104a101 a115a97a109a101 a97a109a111a117a110a116 a111a102 a90a110a79 a99a97a116a97a108a121a115a116 a119a97a115 a117a115a101a100a46 a84a104a101a114a101a45 a102a111a114a101a44 a116a104a101 a114a101a115a117a108a116a105a110a103 a105a109a112a114a111a118a101a109a101a110a116 a105a115 a114a101a108a97a116a101a100 a116a111 a116a104a101 a103a101a111a109a101a116a114a121 a111a102 a116a104a101 a103a108a97a115a115 a28a98a101a114 a109a101a100a105a97a46 a84a97a98a108a101 a52a46a49 a115a104a111a119a115 a116a104a101 a112a101a114a99a101a110a116 a108a111a97a100a105a110a103 a98a121 a119a101a105a103a104a116 a97a110a100 a118a111a108a117a109a101 a111a102 a101a97a99a104 a99a111a109a112a111a110a101a110a116 a105a110 a116a104a101 a112a97a99a107a101a100 a98a101a100a115 a97a110a100 a109a105a99a114a111a28a98a114a111a117a115 a109a97a116a101a114a105a97a108a115 a117a115a101a100 a98a121 a89a97a110a103 a91a52a93 a100a117a114a105a110a103 a104a105a115 a101a120a112a101a114a105a109a101a110a116a115a46 a54a52 a84a97a98a108a101 a52a46a49a58 a67a111a109a112a97a114a105a115a111a110 a98a101a116a119a101a101a110 a103a108a97a115a115 a28a98a101a114 a101a110a116a114a97a112a112a101a100 a90a110a79a47a83a105a792 a115a111a114a98a101a110a116 a40a71a70a69a83a41 a97a110a100 a112a97a99a107a101a100 a98a101a100a115 a99a111a109a112a111a115a101a100 a111a102 a90a110a79a47a83a105a792 a112a97a114a116a105a99a108a101a115 a40a80a66a41 a87a116a46a37 a86a111a108a46a37 a67a111a109a112a111a110a101a110a116a115 a71a70a69a83 a80a66 a71a70a69a83 a80a66 a90a110a79 a49a51 a49a55 a78a65 a78a65 a83a105a792 a54a53 a56a51 a50a50 a54a48 ? a70a105a98a101a114a115 a50a50 a78a65 a51 a78a65 a86a111a105a100 a78a65 a78a65 a55a53 a52a48 Time(min) C / C 0 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 m:v-PB m:v-GFE a70a105a103a117a114a101 a52a46a54a58 a67a111a109a112a97a114a105a115a111a110 a111a102 a98a114a101a97a107a116a104a114a111a117a103a104 a99a117a114a118a101a115 a111a102 a71a70a69 a97a110a100 a80a66 a40a101a120a112a101a114a105a109a101a110a116a97a108 a100a97a116a97 a102a114a111a109 a89a97a110a103 a91a52a93a41 a54a53 a67a104a97a112a116a101a114 a53 a69a109a112a105a114a105a99a97a108 a67a111a114a114a101a108a97a116a105a111a110a115 a102a111a114 a80a114a101a115a115a117a114a101 a68a114a111a112 a53a46a49 a69a114a103a117a110 a69a113a117a97a116a105a111a110 a84a104a101 a108a105a110a101a97a114 a69a114a103a117a110 a101a113a117a97a116a105a111a110 a105a115 a117a115a101a100 a116a111 a112a114a101a100a105a99a116 a116a104a101 a112a114a101a115a115a117a114a101 a100a114a111a112 a116a104a114a111a117a103a104 a112a97a99a107a101a100 a98a101a100a115a46 a73a110 a116a104a105a115 a115a101a99a116a105a111a110a44 a84a104a101 a69a114a103a117a110 a101a113a117a97a116a105a111a110 a105a115 a100a101a114a105a118a101a100 a102a111a114 a108a97a109a105a110a97a114 a97a110a100 a116a117a114a98a117a108a101a110a116 a29a111a119a115 a102a114a111a109 a116a104a101 a72a97a103a101a110a45a80a111a105a115a101a117a105a108a108a101 a108a97a119a46 a65a115a115a117a109a105a110a103 a116a104a101 a104a121a100a114a97a117a108a105a99 a114a97a100a105a117a115 rh a40a116a104a101 a114a97a116a105a111 a111a102 a99a114a111a115a115a45a115a101a99a116a105a111a110a97a108 a97a114a101a97 a116a111 a119a101a116a116a101a100 a112a101a114a105a109a101a116a101a114a41 a97a115 a116a104a101 a108a101a110a103a116a104 a115a99a97a108a101a44 a116a104a101 a102a114a105a99a116a105a111a110 a102a97a99a116a111a114 a99a97a110 a98a101 a100a101a28a110a101a100 a97a115 f = 2(?P/L)rh?V 2 i a40a53a46a49a41 a119a104a101a114a101 a116a104a101 a105a110a116a101a114a115a116a105a116a105a97a108 a118a101a108a111a99a105a116a121 Vi a105a115 a100a101a28a110a101a100 a97a115 a116a104a101 a102a97a99a101 a118a101a108a111a99a105a116a121 a100a105a118a105a100a101a100 a98a121 a116a104a101 a118a111a105a100a97a103a101 a40Vi = Vf/epsilon1a41a46 a84a104a101 a104a121a100a114a97a117a108a105a99 a114a97a100a105a117a115 a99a97a110 a98a101 a119a114a105a116a116a101a110 a97a115 rh = epsilon1a v (1?epsilon1) a119a104a101a114a101 a54a54 av = Surface AreaVolume = 6d p a40a102a111a114 a97 a115a112a104a101a114a101a41 a84a104a117a115 a119a101 a99a97a110 a119a114a105a116a101 rh = epsilon1dp6(1?epsilon1) a40a53a46a50a41 a83a117a98a115a116a105a116a117a116a105a110a103 a102a97a99a101 a118a101a108a111a99a105a116a121 a97a110a100 a104a121a100a114a97a117a108a105a99 a114a97a100a105a117a115 a40a105a110a116a111 a69a113a117a97a116a105a111a110 a53a46a49a41 a119a101 a103a101a116 f = parenleftbigg?P L parenrightbigg epsilon12dp 3?V 2f (1?epsilon1) . a40a53a46a51a41 a70a111a114 a108a97a109a105a110a97a114 a29a111a119a115a44 a72a97a103a101a110a45a80a111a105a115a101a117a105a108a108a101 a108a97a119 a99a97a110 a98a101 a119a114a105a116a116a101a110 a97a115 f = 16Reprime . a40a53a46a52a41 a70a111a114 a112a97a99a107a101a100 a98a101a100a115a44 a116a104a101 a109a111a100a105a28a101a100 a82a101a121a110a111a108a100a115 a110a117a109a98a101a114 a99a97a110 a98a101 a119a114a105a116a116a101a110 a97a115a58 Reprime = Vf (4rh)?? = 23 Vfdp??(1?epsilon1) a40a53a46a53a41 a83a117a98a115a116a105a116a117a116a105a110a103 a82a101prime a105a110a116a111 a69a113a117a97a116a105a111a110 a53a46a52 a119a101 a103a101a116 a54a55 f = 24?(1?epsilon1)V fdp? . a40a53a46a54a41 a69a113a117a97a116a105a110a103 a69a113a117a97a116a105a111a110a115 a53a46a51 a97a110a100 a53a46a54 a114a101a115a117a108a116a115 a105a110 ?P L epsilon1 2dp 3?V 2f (1?epsilon1) = 24?(1?epsilon1) Vfdpepsilon1 a111a114 a40a53a46a55a41 fprime = ?Pdpepsilon1 3 L?V 2f (1?epsilon1) = 72 (1?epsilon1) ?Vfdp ? . a66a121 a97a112a112a108a121a105a110a103 a116a104a101 a108a101a97a115a116 a115a113a117a97a114a101 a109a101a116a104a111a100 a116a111 a101a120a105a115a116a105a110a103 a101a120a112a101a114a105a109a101a110a116a97a108 a100a97a116a97a44 a69a114a103a117a110 a105a110a45 a99a114a101a97a115a101a100 a116a104a101 a110a117a109a101a114a105a99a97a108 a99a111a101a30a99a105a101a110a116 a111a102 a55a50 a116a111 a49a53a48 a91a56a48a93a46 a84a104a105a115 a109a111a100a105a28a99a97a116a105a111a110 a105a115 a97 a115a105a109a112a108a101 a101a109a112a105a114a105a99a97a108 a99a111a114a114a101a99a116a105a111a110 a116a111 a116a104a101 a110a117a109a101a114a105a99a97a108 a99a111a101a30a99a105a101a110a116 a111a110a108a121a46 a69a113a117a97a116a105a111a110 a53a46a56 a105a115 a99a97a108a108a101a100 a116a104a101 a66a108a97a107a101a45a75a111a122a101a110a121 a101a113a117a97a116a105a111a110a58 fprime = ?Pdpepsilon1 3 L?V 2f (1?epsilon1) = 150 (1?epsilon1) ?Vfdp/? a40a53a46a56a41 a70a111a114 a116a117a114a98a117a108a101a110a116 a29a111a119a115a44 a116a104a101 a102a114a105a99a116a105a111a110 a102a97a99a116a111a114 a102a111a114 a29a111a119 a116a104a114a111a117a103a104 a112a97a99a107a101a100 a98a101a100a115 a99a97a110 a98a101 a101a120a112a101a99a116a101a100 a116a111 a102a111a108a108a111a119 a80a114a97a110a100a116a108a39a115 a114a101a115a105a115a116a97a110a99a101 a108a97a119a46 a72a111a119a101a118a101a114a44 a116a104a101 a80a114a97a110a100a116a108a39a115 a114a101a115a105a115a116a97a110a99a101 a108a97a119 a105a115 a118a97a108a105a100 a40a97a110a100 a97a103a114a101a101a115 a119a101a108a108a41 a102a111a114 a115a109a111a111a116a104 a116a117a98a101a115 a97a110a100 a112a105a112a101a115 a111a110a108a121a46 a82a111a117a103a104a110a101a115a115 a111a110 a116a104a101 a115a117a114a102a97a99a101 a54a56 a105a110a99a114a101a97a115a101a115 a116a104a101 a102a114a105a99a116a105a111a110 a102a97a99a116a111a114 a97a116 a104a105a103a104 a82a101a121a110a111a108a100a115 a110a117a109a98a101a114a115 a119a104a101a114a101 a111a110 a99a97a110 a97a115a115a117a109a101 a116a104a101 a102a114a105a99a116a105a111a110 a102a97a99a116a111a114 a105a115 a105a110a100a101a112a101a110a100a101a110a116 a111a102 a82a101a121a110a111a108a100a115 a110a117a109a98a101a114a46 a84a104a117a115a44 a102a111a114 a116a117a114a98a117a108a101a110a116 a29a111a119a115 a119a101 a104a97a118a101a58 f = ?Pdpepsilon1 3 L?V 2f (1?epsilon1) = a99a111a110a115a116a97a110a116 a40a53a46a57a41 a65 a99a111a110a115a116a97a110a116 a111a102 a49a46a55a53 a28a116a115 a116a104a101 a100a97a116a97 a102a114a111a109 a101a120a112a101a114a105a109a101a110a116a115a46 a87a105a116a104 a116a104a105a115 a99a111a110a115a116a97a110a116a44 a69a113a117a97a45 a116a105a111a110 a53a46a57 a105a115 a99a97a108a108a101a100 a116a104a101 a66a117a114a107a101a45a80a108a117a109a109a101a114 a101a113a117a97a116a105a111a110 a91a56a48a93a46 a84a104a101 a102a114a105a99a116a105a111a110 a102a97a99a116a111a114 a102a111a114 a29a111a119a115 a119a105a116a104 a82a101a121a110a111a108a100a115 a110a117a109a98a101a114a115 a114a97a110a103a105a110a103 a102a114a111a109 a49a48 a116a111 a49a48a48a48 a99a97a110 a98a101 a111a98a116a97a105a110a101a100 a98a121 a99a111a109a98a105a110a105a110a103 a66a108a97a107a101a45 a75a111a122a101a110a121 a101a113a117a97a116a105a111a110 a40a69a113a117a97a116a105a111a110 a53a46a56a41 a97a110a100 a66a117a114a107a101a45a80a108a117a109a109a101a114 a101a113a117a97a116a105a111a110 a40a69a113a117a97a116a105a111a110 a53a46a57a41a58 f = ?Pdpepsilon1 3 L?V 2f (1?epsilon1) = 150 (1?epsilon1) Vfdp?/? + 1.75 a40a53a46a49a48a41 a70a114a111a109 a116a104a101 a66a117a114a107a101a45a80a108a117a109a109a101a114 a101a113a117a97a116a105a111a110 a40a69a113a117a97a116a105a111a110 a53a46a49a48a41a44 a116a104a101 a112a114a101a115a115a117a114a101 a103a114a97a100a105a101a110a116 a99a97a110 a98a101 a119a114a105a116a116a101a110 a97a115 ?P L = ?V 2f (1?epsilon1) dpepsilon13 bracketleftbigg 150(1?epsilon1)?V fdp? + 1.75 bracketrightbigg a40a53a46a49a49a41 a53a46a50 a80a111a114a111a117a115 a77a101a100a105a97 a80a101a114a109a101a97a98a105a108a105a116a121 a69a113a117a97a116a105a111a110 a84a104a101 a69a114a103a117a110 a101a113a117a97a116a105a111a110 a105a115 a100a101a115a105a103a110a101a100 a102a111a114 a112a97a99a107a101a100 a98a101a100a115 a97a110a100 a100a111a101a115 a110a111a116 a97a112a112a108a121 a102a111a114 a112a111a114a111a115a105a116a105a101a115 a103a114a101a97a116a101a114 a116a104a97a110 a53a48a37 a97a115 a105a116 a100a111a101a115 a110a111a116 a99a111a110a115a105a100a101a114 a102a111a114a109 a100a114a97a103 a108a111a115a115a101a115 a119a104a105a99a104 a97a114a101 a115a109a97a108a108 a97a116 a108a111a119 a112a111a114a111a115a105a116a105a101a115a46 a77a111a115a116 a111a102 a116a104a101 a28a108a116a101a114 a109a97a116a101a114a105a97a108a115 a99a111a109a112a111a115a101a100 a111a102 a109a105a99a114a111a28a98a114a111a117a115 a109a97a116a101a114a105a97a108a115 a104a97a118a101 a104a105a103a104 a54a57 a112a111a114a111a115a105a116a121 a103a114a101a97a116a101a114 a116a104a97a110 a56a48a37 a91a49a55a93a46 a84a104a101 a118a105a115a99a111a117a115 a102a111a114a109 a100a114a97a103 a108a111a115a115a101a115 a97a114a101 a99a97a108a99a117a108a97a116a101a100 a117a115a105a110a103 a83a116a111a107a101a115a39 a108a97a119 a97a110a100 a97a114a101 a97a100a100a101a100 a116a111 a116a104a101 a118a105a115a99a111a117a115 a102a114a105a99a116a105a111a110 a108a111a115a115a101a115 a119a104a105a99a104 a105a109a112a114a111a118a101 a116a104a101 a97a103a114a101a101a109a101a110a116 a111a102 a116a104a101 a69a114a103a117a110 a101a113a117a97a116a105a111a110 a102a111a114 a104a105a103a104 a118a111a105a100a97a103a101 a109a97a116a101a114a105a97a108a115a46 a84a104a105a115 a109a111a100a105a28a101a100 a69a114a103a117a110 a101a113a117a97a116a105a111a110 a105a115 a99a97a108a108a101a100 a80a111a114a111a117a115 a77a101a100a105a97 a80a101a114a109a101a97a98a105a108a105a116a121 a40a80a77a80a41 a101a113a117a97a116a105a111a110 a97a110a100 a119a97a115 a100a101a114a105a118a101a100 a98a121 a67a97a104a101a108a97 a101a116 a97a108a46 a91a51a93a46 a84a104a101 a112a111a114a111a117a115 a109a101a100a105a97 a99a97a110 a98a101 a109a111a100a101a108a101a100 a97a115 a97 a99a111a108a108a101a99a116a105a111a110 a111a102 a99a97a112a105a108a108a97a114a105a101a115 a111a102 a108a101a110a103a116a104 Lea46 a84a104a101 a105a110a116a101a114a115a116a105a116a105a97a108 a118a101a108a111a99a105a116a121 a40Via41 a99a97a110 a98a101 a119a114a105a116a116a101a110 a97a115 Vi = ?Pr 2 h 2?Le . a40a53a46a49a50a41 a83a105a110a99a101 a116a104a101 a112a97a114a116a105a99a108a101a115 a105a110 a116a104a101 a112a111a114a111a117a115 a109a101a100a105a97 a97a114a101 a110a111a116 a115a109a111a111a116a104 a115a112a104a101a114a101a115a44 a97a110 a101a113a117a105a118a97a108a101a110a116 a100a105a97a109a101a116a101a114 a105a115 a100a101a28a110a101a100 a98a97a115a101 a111a110 a116a104a101 a115a104a97a112a101 a102a97a99a116a111a114 a40?a41 a97a115 deq = ?dp a119a104a101a114a101 ? = 6d pav a46 a73a110a99a111a114a112a111a114a97a116a105a110a103 a116a104a101 a115a104a97a112a101 a102a97a99a116a111a114 a105a110 a116a111 a116a104a101 a104a121a100a114a97a117a108a105a99 a114a97a100a105a117a115 a40a69a113a117a97a116a105a111a110 a53a46a50a41 a114a101a115a117a108a116a115 a105a110 rh = epsilon1deq6(1?epsilon1) = epsilon1(?dp)6(1?epsilon1) . a40a53a46a49a51a41 a73a116 a105a115 a111a98a115a101a114a118a101a100 a116a104a97a116 a116a104a101 a105a110a116a101a114a115a116a105a116a105a97a108 a118a101a108a111a99a105a116a121 a102a111a114 a97 a112a111a114a111a117a115 a98a101a100 a105a115 a103a114a101a97a116a101a114 a116a104a97a110 a116a104a101 a102a97a99a101 a118a101a108a111a99a105a116a121 a100a105a118a105a100a101a100 a98a121 a118a111a105a100 a102a114a97a99a116a105a111a110 a91a56a49a93a46 a70a108a117a105a100 a29a111a119a105a110a103 a116a104a114a111a117a103a104 a97 a116a111a114a116a117a111a117a115 a112a97a116a104 a116a114a97a118a101a108a115 a109a111a114a101 a100a105a115a116a97a110a99a101 a116a104a97a110 a106a117a115a116 a116a104a101 a108a101a110a103a116a104 a111a102 a116a104a101 a112a111a114a111a117a115 a98a101a100a46 a70a111a114 a97 a116a111a114a116a117a111a117a115 a112a97a116a104 a105a110 a55a48 a97 a112a111a114a111a117a115 a109a101a100a105a97 a111a110a101 a28a110a100a115 a116a104a97a116 ? ??? ??? a84a105a109a101 a116a111 a116a114a97a118a101a108 a100a105a115a116a97a110a99a101 a76 a97a116 a97 a118a101a108a111a99a105a116a121 Vf/epsilon1 ? ??? ???= ? ??? ??? a84a105a109a101 a116a111 a116a114a97a118a101a108 a97 a116a111a114a116a117a111a117a115 a112a97a116a104 a111a102 a108a101a110a103a116a104 Le a97a116 a97 a118a101a108a111a99a105a116a121 Vi ? ??? ??? a84a104a117a115a44 Lepsilon1 Vf = Le Vi ?Vi = Vf?t epsilon1 a111a114 Vi = Vf epsilon1 parenleftbiggL e L parenrightbigg . a40a53a46a49a52a41 a84a111a114a116a117a111a115a105a116a121 a40?ta41 a111a102 a116a104a101 a112a111a114a111a117a115 a109a101a100a105a97 a105a115 a101a115a116a105a109a97a116a101a100 a117a115a105a110a103 a97 a99a117a98a105a99 a99a101a108a108 a119a105a116a104 a111a110a101 a115a112a104a101a114a101 a105a110 a116a104a101 a99a101a110a116a101a114 a97a110a100 a105a115 a100a101a28a110a101a100 a97a115 ?t = 1 + (1?epsilon1)/2. a40a53a46a49a53a41 a84a104a101 a111a114a105a101a110a116a97a116a105a111a110 a111a102 a28a98a101a114a115 a105a110 a97 a28a120a101a100 a98a101a100 a97a108a115a111 a97a27a101a99a116a115 a116a104a101 a105a110a116a101a114a115a116a105a116a105a97a108 a118a101a108a111a99a105a116a121 a91a56a50a93a46 a76a101a116 ? a98a101 a116a104a101 a97a110a103a108a101 a98a101a116a119a101a101a110 a116a104a101 a29a111a119 a100a105a114a101a99a116a105a111a110 a40a114a41 a97a110a100 a112a101a114a112a101a110a100a105a99a117a108a97a114 a100a105a114a101a99a116a105a111a110 a116a104a114a111a117a103a104 a116a104a101 a98a101a100 a40a120a41a44 a116a104a101a110 dx = drcos? ?Vx = Vr cos? Vi = Vf?tepsilon1cos? a40a53a46a49a54a41 a55a49 a66a121 a115a117a98a115a116a105a116a117a116a105a110a103 Vi a97a110a100 rh a105a110a116a111 a69a113a117a97a116a105a111a110 a53a46a49a50 a119a101 a103a101a116 Vf ?t epsilon1cos? = ?P L parenleftbiggL Le parenrightbiggbracketleftbigg epsilon1(?d p) 6(1?epsilon1) bracketrightbigg2 1 2? a40a53a46a49a55a41 ?P L vextendsinglevextendsingle vextendsinglevextendsingle a70a114a105a99a116a105a111a110 a76a111a115a115a101a115 = 72 ? 2 t cos2 ? ?Vf epsilon13 (1?epsilon1)2 (?dp)2 a115a105a110a99a101a44 L Le = cos? ?t a40a53a46a49a56a41 a84a104a101 a97a98a111a118a101 a101a113a117a97a116a105a111a110 a97a99a99a111a117a110a116a115 a111a110a108a121 a102a111a114 a102a114a105a99a116a105a111a110 a108a111a115a115a101a115a46 a70a114a111a109 a83a116a111a107a101a115 a108a97a119a44 a116a104a101 a102a111a114a99a101 a111a110 a116a104a101 a115a112a104a101a114a101 a105a110 a97 a108a97a109a105a110a97a114 a29a111a119 a105a115 a103a105a118a101a110 a98a121a44 F = 6pi?RV? = pi?dpVi a40a53a46a49a57a41 a84a104a101 a112a114a101a115a115a117a114a101 a108a111a115a115 a100a117a101 a116a111 a102a111a114a109 a100a114a97a103 a112a101a114 a116a111a114a116a117a111a117a115 a98a101a100 a108a101a110a103a116a104 a105a115 a116a104a101 a112a114a111a100a117a99a116 a111a102 a102a111a114a109 a100a114a97a103 a102a111a114a99a101 a112a101a114 a112a97a114a116a105a99a108a101 a97a110a100 a116a104a101 a110a117a109a98a101a114 a111a102 a112a97a114a116a105a99a108a101a115 a112a101a114 a118a111a108a117a109a101 a111a102 a98a101a100a46 a84a104a101 a110a117a109a98a101a114 a111a102 a112a97a114a116a105a99a108a101a115 a112a101a114 a118a111a108a117a109a101 a111a102 a98a101a100 a105a115 a116a104a101 a114a97a116a105a111 a111a102 a118a111a108a117a109a101 a102a114a97a99a116a105a111a110 a111a99a99a117a112a105a101a100 a98a121 a112a97a114a116a105a99a108a101a115 a116a111 a116a104a101 a118a111a108a117a109a101 a111a102 a111a110a101 a112a97a114a116a105a99a108a101 a91a49a55a93a58 ?P L vextendsinglevextendsingle vextendsinglevextendsingle a70a111a114a109 a68a114a97a103 a76a111a115a115a101a115 = 6 ? 2 t cos2 ? ?Vf epsilon1 (1?epsilon1)3 (?dp)2 a40a53a46a50a48a41 a84a111a116a97a108 a112a114a101a115a115a117a114a101 a100a114a111a112 a100a117a101 a116a111 a118a105a115a99a111a117a115 a108a111a115a115a101a115 a105a115 a116a104a101 a115a117a109 a111a102 a116a104a101 a102a114a105a99a116a105a111a110 a108a111a115a115a101a115 a40a69a113a117a97a45 a116a105a111a110 a53a46a49a55a41 a97a110a100 a102a111a114a109 a100a114a97a103 a108a111a115a115a101a115 a40a69a113a117a97a116a105a111a110 a53a46a50a48a41 a55a50 ?P L vextendsinglevextendsingle vextendsinglevextendsingle a86a105a115a99a111a117a115 a76a111a115a115a101a115 = ?PL vextendsinglevextendsingle vextendsinglevextendsingle a70a114a105a99a116a105a111a110 a76a111a115a115a101a115 + ?PL vextendsinglevextendsingle vextendsinglevextendsingle a70a111a114a109 a68a114a97a103 a76a111a115a115a101a115 = 72 ?Vfepsilon13 ? 2 cos2 ? (1?epsilon1)2 (?dp)2 bracketleftbigg 1 + 112 epsilon1 2 (1?epsilon1) bracketrightbigg a59 epsilon1 2 12(1?epsilon1) = xFD a40a53a46a50a49a41 a77a105a99a114a111a28a98a114a111a117a115 a109a97a116a101a114a105a97a108a115 a103a101a110a101a114a97a108a108a121 a99a111a110a115a105a115a116 a111a102 a97 a109a97a116a114a105a120 a111a102 a28a98a101a114a115 a99a111a110a116a97a105a110a105a110a103 a112a97a114a116a105a99a108a101a115a46 a67a97a104a101a108a97 a101a116 a97a108a46 a91a49a55a93 a100a101a114a105a118a101a100 a97a110 a101a113a117a97a116a105a111a110 a116a111 a112a114a101a100a105a99a116 a116a104a101 a112a114a101a115a115a117a114a101 a100a114a111a112 a116a104a114a111a117a103a104 a97 a109a105a120a116a117a114a101 a111a102 a28a98a101a114a115 a97a110a100 a112a97a114a116a105a99a117a108a97a116a101a115 a98a121 a100a101a28a110a105a110a103 a97a110 a101a113a117a105a118a97a108a101a110a116 a100a105a97a109a101a116a101a114 a98a97a115a101a100 a111a110 a116a111a116a97a108 a115a117a114a102a97a99a101 a97a114a101a97 a97a110a100 a116a111a116a97a108 a118a111a108a117a109a101 a111a102 a116a104a101 a112a97a114a116a105a99a108a101a115 a97a115 1 deq = SAp 6 a86a111a108p = summationdisplay xi ?idi . a40a53a46a50a50a41 a65a110 a101a113a117a105a118a97a108a101a110a116 a104a121a100a114a97a117a108a105a99 a114a97a100a105a117a115 a99a97a110 a98a101 a100a101a28a110a101a100 a97a115a58 rh = epsilon1 6 (1?epsilon1)summationtext xi(?d i) a40a53a46a50a51a41 a70a105a110a97a108a108a121a44 a116a104a101 a116a111a116a97a108 a112a114a101a115a115a117a114a101 a100a114a111a112 a102a111a114 a108a97a109a105a110a97a114 a29a111a119a115 a116a104a114a111a117a103a104 a97 a109a105a120a116a117a114a101 a111a102 a115a111a108a105a100 a112a97a114a116a105a99a108a101a115 a97a110a100 a28a98a101a114a115 a111a102 a97a110a121 a115a104a97a112a101 a97a110a100 a115a105a122a101 a105a115 a103a105a118a101a110 a98a121a58 ?P L = 72 ? Vf ?2t cos2 ? (1?epsilon1)2 epsilon13 bracketleftBiggparenleftbiggsummationdisplay xi ?idi parenrightbigg2 + xFD summationdisplay xi (?idi)2 bracketrightBigg a40a53a46a50a52a41 a55a51 a69a113a117a97a116a105a111a110 a53a46a50a52 a105a115 a99a97a108a108a101a100 a116a104a101 a112a111a114a111a117a115 a109a101a100a105a97 a112a101a114a109a101a97a98a105a108a105a116a121 a40a80a77a80a41 a101a113a117a97a116a105a111a110a46 a55a52 a67a104a97a112a116a101a114 a54 a78a117a109a101a114a105a99a97a108 a77a111a100a101a108a105a110a103 a54a46a49 a71a101a111a109a101a116a114a105a99 a77a111a100a101a108a105a110a103 a71a65a77a66a73a84a44 a97 a99a111a109a109a101a114a99a105a97a108 a112a114a101a45a112a114a111a99a101a115a115a111a114 a105a115 a117a115a101a100 a116a111 a103a101a110a101a114a97a116a101 a103a101a111a109a101a116a114a105a99 a109a111a100a101a108a115 a117a115a101a100 a105a110 a116a104a105a115 a115a116a117a100a121a46 a70a76a85a69a78a84a44 a97 a99a111a109a109a101a114a99a105a97a108 a67a70a68 a99a111a100a101a44 a105a115 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P / L w .r . t . E x p er i m et al D a t a 0 0.3 0.6 0.9 1.2 -10 0 10 20 30 % Error - CFD Simulation % Error - PMP Equation % Error - Ergun Equation % Error- ExperimentalData a70a105a103a117a114a101 a55a46a49a56a58 a69a114a114a111a114 a105a110 a112a114a101a100a105a99a116a105a110a103 a112a114a101a115a115a117a114a101 a100a114a111a112 a105a110 a109a105a99a114a111a28a98a114a111a117a115 a109a97a116a101a114a105a97a108a115 a119a105a116a104 a114a101a115a112a101a99a116 a116a111 a101a120a112a101a114a105a109a101a110a116a115 a91a51a93a58 a88pa61a53a51a37 a109a101a97a115a117a114a101a109a101a110a116a115a46 a84a104a101 a100a101a118a105a97a116a105a111a110 a111a102 a112a114a101a115a115a117a114a101 a100a114a111a112 a111a98a116a97a105a110a101a100 a117a115a105a110a103 a116a104a101 a67a70a68 a115a105a109a117a108a97a116a105a111a110a115 a97a110a100 a101a109a112a105a114a105a99a97a108 a99a111a114a114a101a108a97a116a105a111a110a115 a114a101a108a97a116a105a118a101 a116a111 a101a120a112a101a114a105a109a101a110a116a115 a104a97a118a101 a116a104a101 a115a97a109a101 a116a114a101a110a100 a102a111a114 a98a111a116a104 a116a104a101 a115a111a108a105a100 a102a114a97a99a116a105a111a110a115 a97a114a101 a115a104a111a119a110 a105a110 a70a105a103a117a114a101a115 a55a46a49a56 a97a110a100 a55a46a49a57a46 a84a104a105a115 a99a111a110a115a105a115a116a101a110a116 a116a114a101a110a100 a115a117a103a103a101a115a116a115 a116a104a97a116 a101a105a116a104a101a114 a116a104a101a114a101 a97a114a101 a112a104a121a115a105a99a97a108 a109a101a99a104a97a110a105a115a109a115 a109a105a115a115a105a110a103 a102a114a111a109 a98a111a116a104 a116a104a101 a115a105a109a117a108a97a116a105a111a110a115 a97a110a100 a116a104a101 a116a104a101a111a114a121a45a98a97a115a101a100 a99a111a114a114a101a108a97a116a105a111a110a115a44 a111a114 a116a104a97a116 a116a104a101a114a101 a97a114a101 a101a120a112a101a114a105a109a101a110a116a97a108 a98a105a97a115 a101a114a114a111a114a115 a119a104a105a99a104 a99a111a114a114a101a108a97a116a101 a119a105a116a104 a102a97a99a101 a118a101a108a111a99a105a116a121a46 a49a49a53 Face Velocity[m/s] %E r r o r i n ? P / L w .r .t . 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