Question Converging Diverging Nozzle Design You are tasked to design a converging diverging (CD) nozzle for rocket propulsion system. The working fluid is air (k = 1.4). The proposed dimensions of the nozzle are: 1. Inlet radius = 0.10 m 2. Throat radius = 0.075 m 3. Outlet radius = 0.12 m The rocket is to launch from sea level and fly to an altitude of 100km. The total pressure upstream of the nozzle, Po, inlet = 250 kPa (absolute) for most of rocket trajectory. Between the altitudes of 80km and 100km the total pressure drops to 0 in a linear fashion. The designed inlet pressure and temperatures are as follows. 1. Piniet = 210 kPa 2. To, inlet = 300 K To verify the design, determine the exit flow conditions at every 10km variations in altitude (use reference tables for Pressure and Temperature at various altitudes exit). In case of shock, determine the location of the shock in the CD Nozzle, and propose design alternations to have no shock in CD nozzle through out the length of its planned trajectory.

NPGZSH The Asker · Mechanical Engineering

Transcribed Image Text: Converging Diverging Nozzle Design You are tasked to design a converging diverging (CD) nozzle for rocket propulsion system. The working fluid is air (k = 1.4). The proposed dimensions of the nozzle are: 1. Inlet radius = 0.10 m 2. Throat radius = 0.075 m 3. Outlet radius = 0.12 m The rocket is to launch from sea level and fly to an altitude of 100km. The total pressure upstream of the nozzle, Po, inlet = 250 kPa (absolute) for most of rocket trajectory. Between the altitudes of 80km and 100km the total pressure drops to 0 in a linear fashion. The designed inlet pressure and temperatures are as follows. 1. Piniet = 210 kPa 2. To, inlet = 300 K To verify the design, determine the exit flow conditions at every 10km variations in altitude (use reference tables for Pressure and Temperature at various altitudes exit). In case of shock, determine the location of the shock in the CD Nozzle, and propose design alternations to have no shock in CD nozzle through out the length of its planned trajectory.

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Page-1SOLUTIONLets evaluate areas at L//2 and L//3 Given linear variation.Length is not given.Assume l=1m. Please refer to this Solution as a methodology 10 solve such problem.By geometry{:[(0.045)/(1)=(x)/( 0.5)],[x=0.045 xx0.5=0.0225],[gamma1//2=0.075+0.0225],[gamma1//2=0.0975m^(2)],[AY//2=pigamma^(2)],[AY//2=0.03m^(2)]:}Similarly(0.045)/(1)=(x)/(1//3)Page - 2{:[x=0.015],[gamma//1//3=x+0.075],[gamma1//3=0.09m],[" A "1//3=0.0254m^(2)],[" A exit "=pi xx0.12^(2)],[=0.045m^(2)]:}consider the region 1known parameters areP_(0)=220kpa,T_(0)=300k. To get the properties at 1, The throat area is known to us. Since shock is expected un diverging section, Throat of the nozzle will be chocked. i-e. Mach =1 at throat. So, area of the Throat itself is the A^(**){:[A" th "=A^(**)=0.0177m^(2)],[A_(1)=0.03m^(2)" (calcalated in the above "]:}Page-3The area Ratio for the flow in this region is A_(1)//A^(**)=1.695The Supersonic solution for Mach and Pressure ratio at this area Ratio are{:[" Mach "M_(1)=2],[P_(1)//P_(0)=01267quad(:.P_(0)=220kPa:}],[{:P_(1)=27.9kpa)]:}we now known the mach and pressure values ahead of the shock. using normal Shock relations, we lan arrive at Mach and pressure values behind the shock.Normal shock parameters at H=2 are" mach "{:[M_(2),=0.577,<=>P_(1),=27.9kpa],[P_(2)//P_(1),=4.5,P_(2),=125.55kpa],[P_(O_(2))//P_(01),=0.72,<=>P_(01),=220kpa],[,P_(0_(2)),=158.4kPa]:}The flow conditions at region2 follow mach 0.577 properties SO for A^(**), is A_(2)//A_(1)=1.2165. A_(2) is the area at shock which is 0.03m^(2)page-4A_(2)=0.0247m^(2). The critical area is Consistent throughout the flow till esit consider region 3, where flow is change in flow properties are Isentropic, Which obeys the properties.{:[A_(2)^(**)=A_(3)^(**)],[P_(O_(2))=P_(03)]:}The area Ratio at exit in the area at exit divided by A_(3)^(**).A_(3)//A_(3)**=(A_("esit "))/(A_(2)^(**))=(0.045)/(0.0247)=1.822Since it is known t ... See the full answer