10-×5×104500 =0.0304m 0.263 30.4 From (24)then 0.263= 1.171 which can be solved to rL=0. 805. Then, from(28) m=1-0805)=0352;m= mY =0284g/s and from(25),(27),r(=14)=0685,and m=06g5Px(25×10 =2.33×10P ×500 Yo.oo 0.284×10 2.33×10-91218×105N/m2=1.202am From the paper AIAA-90-2531, the experimental value under these conditions is 1.16 atm, a good agreement. Repeating for other conditions would yield r(g/s) I(A) Ra(calc PO R (data) 0.1 100 0.805 1.20 (1.16) 0.2 100 0.686 (180) 0.616 0.1 0.718 0.88 0.870 Table 1 As expected, the agreement is only approximate, but trends are well predicted Notice how increasing the flow reduces the arc radius(higher buffer layer density, less adius growth for similar heated mass). The increase in pressure with current is also indicated, but the model exaggerates the effect 16.522, Space Propulsion Lecture 11-12 Prof. Manuel Martinez-Sanchez Page 12 of 18xref = 1 2π 10−4 × 5 ×104 7 500 7000 = 0.0304m x* = 8 30.4 = 0.263 From (24) then, 0.263 = 1 1.171 ln 1 + r a, L 1 − ra, L − ra,L ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ which can be solved to ra, L =0.805. Then, from (28) m Ý * = 1 − ( ) 0.805 2 = 0.352 ; m Ý ref = m Ý m Ý * = 0.284g /s and from (25), (27), Γ( ) γ = 1.4 = 0.685, and m Ý ref = 0.685 Ptπ 1.25 ×10−3 ( )2 8.31 0.002 × 500 = 2.33 ×10−9 Pt Pt = 0.284 ×10 −3 2.33 ×10 −9 = 1.218 ×105 N / m 2 = 1.202atm] ⎡ ⎣ ⎢ From the paper AIAA-90-2531, the experimental value under these conditions is 1.16 atm, a good agreement. Repeating for other conditions would yield: m g Ý( ) / s I(A) Ra R (calc.) Pt(atm) (calc.) Pt(atm) (data) 0.1 100 0.805 1.20 (1.16) 0.2 100 0.686 1.60 (1.80) 0.3 100 0.616 2.05 (2.55) 0.1 60 0.718 0.88 (0.97) 0.1 150 0.870 1.74 (1.28) Table 1 As expected, the agreement is only approximate, but trends are well predicted. Notice how increasing the flow reduces the arc radius (higher buffer layer density, less radius growth for similar heated mass). The increase in pressure with current is also indicated, but the model exaggerates the effect. 16.522, Space Propulsion Lecture 11-12 Prof. Manuel Martinez-Sanchez Page 12 of 18