pressure. In their method, the properties (heat of formation, specific heat, molecular mass of the species) of the burnt gases are used to determine the regression rate. Since many parameters (chamber temperature, chamber volume, O/F ratio) required in their analysis are unknown during combustion, they are forced to make use of theo retical values, which were obtained from NASA SP-273 [35] and it makes their method complicated to use and prob ably less reliable. Fig. 1 shows the two trend lines obtained by Risha et al. [31,33]. Both were for HTPB and oxygen combination and using the same motor. Both were obtained using the pressure time data. It is evident from Fig. 1 that these two do not match well. Here, an attempt was made to determine the regression rate using combustion chamber pressure for a high regres sion ratefuel ,where C⋆ changes due to the variation of O/F ratio with burn time. It is possible that the L⋆ (due to increase in chamber volume with burn time) also varies significantly with burn time. These results were further compared with the regression rates obtained with the weight loss method using the same motor, fuel and oxidizer combination. These were obtained keeping all other operational parameters similar. Lastly, an attempt was made to test the robustness of the procedure devel oped with the pressure time data reported by Karabeyogluet al. [18], when the motor size is large.
The high regression rate fuel used in the present study was wax (combination of 30% of micro-crystalline wax and 70% of paraffin wax) [36]. Commercially available gaseous oxygen was used as the oxidizer.
2. Experimental setup and test procedure
The experimental setup used in the current study is shown in Fig. 2. It consists of two to four (for high flow rates) commercial grade oxygen cylinders mounted on a weighing balance. The reduction in mass of oxygen was measured with the help of a weighing balance, which had
a least count of 1 g and can measure a maximum of 150 kg. Constant mass flow rate was obtained by allowing the oxidizer to flow through a settling chamber as shown in Fig. 2. The pressure downstream of the pressure regulator was maintained constant. The outlet diameter of the settling chamber was chosen such that the flow was choked. The settling chamber pressure was measured with the help of pressure transducer (P1) obtained from UV Enterprises and fast response piezoresistive transducer (P2) obtained from DRUCK Ltd. UK. The piezoresistive transducer (P3) was used to measure the combustion chamber nozzle end pressure. The temperature of the settling chamber was also measured with the help of a T-type thermocouple and data were acquired with the help of National Instruments (NI) USB-9211A data acquisi- tion system. With the known settling chamber pressure and temperature, mass flow rate of oxidizer was calculated using Eqs. (1)–(3). A ball valve was placed just before the settling chamber to control the flow manually when ever required. A sequential timer was used to control the functioning of the solenoid valve and the igniter battery. The sequential timer keeps the electrical circuit connected for a pre-determined time after which it was disconnected. Hence, it controls the time of the ignition process, as well as the time for which the solenoid valve is open. An igniter consists of a small amount of solid composite propellant (0.2 g) in which a nichrome wire is embedded. This com- bination along with a sufficient length of the electrical wiring was then inserted into the rocket motor through the nozzle such that the solid propellant is located near the head end of the motor. An igniter battery supplied a voltage of 12 V to the nichrome wire for a period of 0.7 s. This caused the small solid propellant to burn, which in turn ignited the hybrid rocket motor. The oxidizer flowwas switched on after this 0.7 s period and was kept on for either 0.5 s or 4 s as needed.
The lab scale hybrid rocket motor used for this study with the relevant dimensions is shown in Fig. 3. Length of the combustion chamber was 134mm and inner diameter was 50mm. The initial port diameter used for the experi- ments was 9 mm. The injector diameter used was 5 mm. A convergent nozzle made of high density graphite was used, having a throat diameter of 8 mm. The wax was cast in a polyethylene tube, whose outer diameter was same as the inner diameter of the rocket motor, i.e., 50 mm. The inner diameter of the polyethylene tube was 42mm. A mild steel rod of 9 mmwas used as a mandrel while casting. As shown in Fig. 3, there is no pre- or post-combustion chamber.
3. Results and discussions
As discussed earlier, the use of combustion chamber pressure is an alternate method to obtain the regression rate. Detailed studies on how to obtain regression rates are presented hereafter for wax.
3.1. Measurement of regression rate using 134 mm length hybrid rocket motor
Before proceeding to obtain the regression rate, it was decided to check whether the pressure time data was
ความกดดัน ในวิธีการของพวกเขา คุณสมบัติ (ความร้อนความร้อนเฉพาะ ผู้แต่ง มวลโมเลกุลของสายพันธุ์) ของก๊าซเผาไหม้จะใช้เพื่อกำหนดอัตราถดถอย เนื่องจากในระหว่างการเผาไหม้จะไม่รู้จักพารามิเตอร์มาก (อุณหภูมิหอการค้า หอการค้าปริมาณ อัตราส่วน O/F) จำเป็นต้องใช้ในการวิเคราะห์ของพวกเขา พวกเขาถูกบังคับให้ใช้ทีค่า retical ซึ่งได้รับมาจาก NASA SP-273 [35] และ ทำให้วิธีการซับซ้อนการใช้ prob สามารถน้อยเชื่อถือได้ Fig. 1 แสดงแนวโน้มสองบรรทัดได้โดย Risha et al. [31,33] ทั้งสองได้ HTPB ชุดออกซิเจน และใช้มอเตอร์ตัวเดียวกัน ทั้งสองได้รับโดยใช้ข้อมูลเวลาความดัน จะเห็นได้จาก 1 Fig. ที่สองไม่ตรงกัน นี่ เป็นความพยายามที่จะกำหนดอัตราถดถอยที่ใช้ความดันในห้องเผาไหม้สูง regres น ratefuel, C⋆ เปลี่ยนแปลงเนื่องจากการเปลี่ยนแปลงของอัตราส่วน O/F กับเวลาเขียนที่ มันเป็นไปได้ที่ L⋆ (เนื่องจากการเพิ่มปริมาณหอด้วยเวลาเขียน) ยังแตกต่างกันไปมากเวลาเขียน ผลลัพธ์เหล่านี้ได้เพิ่มเติมเปรียบเทียบกับอัตราถดถอยได้ ด้วยวิธีการสูญเสียน้ำหนักที่ใช้มอเตอร์เดียว น้ำมันเชื้อเพลิงและ oxidizer เหล่านี้ได้รับการรักษาพารามิเตอร์อื่น ๆ ในการดำเนินงานที่คล้ายกัน สุดท้าย มีความพยายามในการทดสอบเสถียรภาพของ devel กระบวน oped ข้อมูลเวลาความดันที่รายงาน โดย Karabeyogluet al. [18], เมื่อมอเตอร์ขนาดใหญ่ น้ำมันอัตราถดถอยสูงที่ใช้ในการศึกษาปัจจุบันมีขี้ผึ้ง (ชุด 30% ของไมโครผลึกขี้ผึ้งและ 70% ของขี้ผึ้งพาราฟิน) [36] มีใช้ออกซิเจนเป็นต้นใช้ได้ในเชิงพาณิชย์เป็น oxidizer ที่ 2. ทดลองตั้งค่าและการทดสอบขั้นตอน การตั้งค่าการทดลองที่ใช้ในการศึกษาปัจจุบันจะแสดงใน Fig. 2 ประกอบด้วย 2-4 (สำหรับอัตราไหลสูง) ค้าเกรดถังออกซิเจนที่ติดตั้งอยู่บนสมดุลน้ำหนักด้วย การลดมวลของออกซิเจนที่วัดช่วยดุลน้ำหนัก ซึ่งมี a least count of 1 g and can measure a maximum of 150 kg. Constant mass flow rate was obtained by allowing the oxidizer to flow through a settling chamber as shown in Fig. 2. The pressure downstream of the pressure regulator was maintained constant. The outlet diameter of the settling chamber was chosen such that the flow was choked. The settling chamber pressure was measured with the help of pressure transducer (P1) obtained from UV Enterprises and fast response piezoresistive transducer (P2) obtained from DRUCK Ltd. UK. The piezoresistive transducer (P3) was used to measure the combustion chamber nozzle end pressure. The temperature of the settling chamber was also measured with the help of a T-type thermocouple and data were acquired with the help of National Instruments (NI) USB-9211A data acquisi- tion system. With the known settling chamber pressure and temperature, mass flow rate of oxidizer was calculated using Eqs. (1)–(3). A ball valve was placed just before the settling chamber to control the flow manually when ever required. A sequential timer was used to control the functioning of the solenoid valve and the igniter battery. The sequential timer keeps the electrical circuit connected for a pre-determined time after which it was disconnected. Hence, it controls the time of the ignition process, as well as the time for which the solenoid valve is open. An igniter consists of a small amount of solid composite propellant (0.2 g) in which a nichrome wire is embedded. This com- bination along with a sufficient length of the electrical wiring was then inserted into the rocket motor through the nozzle such that the solid propellant is located near the head end of the motor. An igniter battery supplied a voltage of 12 V to the nichrome wire for a period of 0.7 s. This caused the small solid propellant to burn, which in turn ignited the hybrid rocket motor. The oxidizer flowwas switched on after this 0.7 s period and was kept on for either 0.5 s or 4 s as needed. The lab scale hybrid rocket motor used for this study with the relevant dimensions is shown in Fig. 3. Length of the combustion chamber was 134mm and inner diameter was 50mm. The initial port diameter used for the experi- ments was 9 mm. The injector diameter used was 5 mm. A convergent nozzle made of high density graphite was used, having a throat diameter of 8 mm. The wax was cast in a polyethylene tube, whose outer diameter was same as the inner diameter of the rocket motor, i.e., 50 mm. The inner diameter of the polyethylene tube was 42mm. A mild steel rod of 9 mmwas used as a mandrel while casting. As shown in Fig. 3, there is no pre- or post-combustion chamber. 3. Results and discussions As discussed earlier, the use of combustion chamber pressure is an alternate method to obtain the regression rate. Detailed studies on how to obtain regression rates are presented hereafter for wax. 3.1. Measurement of regression rate using 134 mm length hybrid rocket motorBefore proceeding to obtain the regression rate, it was decided to check whether the pressure time data was
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