is sufficient. In terms of the total pressure Pt, and temperature tt (the upstream conditions ), we must then have m= RT with T= (26) and with Ra L representing the arc radius at X-L, the constrictor exit. A non-dimensional mass flow rate is defined as m PR 27) and(25)reads then These equations can be used in a variety of ways. Two of them are (a)"Design"mode. Given P, T,, I, Y,R, etc, find the required constrictor length L(or given L, find R) (b)"Analysis"mode. Given Tt, I, m, L, R, etc find the pressure Pt. This then will determine the thrust 上 Xample For H2 gas, say a=0.8Si//K,Te=7000K and(eyeballing from the chart handed out in clas.k≡Tw/m/K. Use also c≡5×10°J/Kg. If the constrictor dimensions are R=1. 25mm, L=8mm, and the buffer gas temperature is T,= T= 500K, find the chamber pressure Pt at operating conditions mY=0.1g/s, 1=100A From 9) =×1.25×102×08×7(70005008544mp r=100=171 854 From(22) 16.522 Space Propulsion Lecture 11-12is sufficient. In terms of the total pressure Pt, and temperature Tt (the upstream conditions), we must then have m Ý = Γ Ptπ R2 ( ) − Ra, L RgTt (25) with Γ = γ 2 γ +1 ⎛ ⎝ ⎜ ⎞ ⎠ γ +1 2( ) λ −1 ≅ 2 3 (26) and with Ra,L representing the arc radius at x-L, the constrictor exit. A non-dimensional mass flow rate is defined as m Ý * = m Ý m Ý ref ; m Ý ref = Γ PtπR2 RgTt (27) and (25) reads then m Ý (28) * = 1 − ra, L 2 These equations can be used in a variety of ways. Two of them are: (a) “Design” mode. Given Pt, Tt, I, m Ý, R, etc., find the required constrictor length L (or given L, find R). (b) “Analysis” mode. Given Tt, I, m Ý, L, R, etc., find the pressure Pt. This then will determine the thrust. Example For H2 gas, say a=0.8Si/m/K,Te=7000K and (eyeballing from the chart handed out in class), k ≅ 7w / m / K. Use also cp ≅ 5 ×104 J / Kg. If the constrictor dimensions are R=1.25mm, L=8mm, and the buffer gas temperature is Tt ≅ Tw ≅ 500K , find the chamber pressure Pt at operating conditions m Ý= 0.1g / s,I = 100A. From (9), Iref = π × 1.25 ×10−3 2 × 0.8 × 7(7000 − 500)= 85.4Amp I * = 100 85.4 = 1.171 From (22) 16.522, Space Propulsion Lecture 11-12 Prof. Manuel Martinez-Sanchez Page 11 of 18