tailieunhanh - Aerospace Technologies Advancements Fig Part 9

Tham khảo tài liệu 'aerospace technologies advancements fig part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Integrated Vehicle Health Management for Solid Rocket Motors 265 dt pqv - puA l Pprb Po Ab A - di- dt p0 e0V puAht L HPprb P Ab A t 15 dtR rb P0 . Here puA l L and puAht L are the mass and the enthalpy flow from the whole burning area of the propellant including the propellant surface in the hole and p0 Po and e0 are the stagnation values of the flow parameters. The total mass flow from the burning propellant surface is equal to the sum of the mass flows through the nozzle and hole throats. Assuming that sonic conditions hold both in the nozzle throat and the hole throat we obtain the following result pwa L PhuhAh t pmA t r VYP0P0 At h r MYP0P0 At r-17YP0P0 At h At 16 Here r A li- 2 and Aet At h At is the effective nozzle throat area. This relation means that in the first approximation the hole is seen by the internal flow dynamics as an increase of the nozzle throat area and the dynamics of the stagnation values of the gas parameters are governed by both dynamics of the propellant burning area related to the thickness of the burned propellant layer R and by the hole radius Rh. Substituting results of integration 16 into 15 and using model for nozzle ablation 11 12 and hole melting 13 14 we obtain the low-dimensional model of the internal ballistic of a subscale SRM in the presence of the case breach fault in the form P - C0vAet P A Ab pp - p Pn a1 1 t Vĩb P V1 p - - AR pjị AbAPp - p pn a2Ỉ2 t Vrb P V - - R rbpn Ab f R V AbR f R rbpn 1-0 R 7Ĩ 7Ĩ I p0 I I Rt Ì Rt vabl vm I I Ini I Pm I Rt0 R v f p0At i f Rex i Tex - Tabl Rex Vm K A I Ip I T I pmAex Rex0 Tt T abl R Qc Qr Qb Rh --------- ----- -------- 17 tfmet Cmet Tmel Tm0 pmet where the following dimensionless variables are used -P0 P P t typl R Rl Ab Ab V V Rih R R R Aet Aẻr. 18 Pm Pm L0 1 L0 b lL0 L Lq L0 et L0 266 Aerospace Technologies Advancements Here subscript m refers to maximum reference values of the pressure and density and Lo is characteristic length of the motor. We note that two first equations in 17