ME 239: Rocket Propulsion Real Nozzles J. M. Meyers, PhD 1
Most Typical Real Nozzle Effects 1) Divergence of the flow 2) Low nozzle contraction ratios ( / ) 3) Boundary Layer Flow 4) Multiphase Flow 5) Unsteady Combustion 6) Chemical Reactions in Nozzle Flow 7) Transient Pressure Operation 8) Erosion of the throat region 9) Non-uniform Gas Composition 10) Real Gas Properties 11) Non-optimum expansion ratio 2
1) Divergence of the Flow Real nozzle flow is not 1-D Normally flow is axis-symmetric with a velocity profile being a function of the axial and radial component (, constant) Even at the throat the flow is not perfectly axial! These losses occur due to divergence angle of the wall at nozzle exit This loss varies as a function of the cosine of the divergence angle: 1 2 1cos Losses can be reduced with the use of a contoured nozzle 3
2) Low Contraction Ratio Small nozzle contraction ratios ( / ) cause pressure losses in the chamber This loss in pressure will result in reduced thrust and exit velocity Increasing the chamber to throat area ratio will improve this loss but at a weight penalty 4
3) Boundary Layer Flow The loss owes to viscous fluid flow The no-slip condition at the nozzle wall causes the fluid to decelerate toward stagnation conditions The drop in kinetic energy results in an increase in thermal energy owing to the energy balance h 2 For large rocket motors the viscous portion of the flow (within the BL or 99% of the free jet velocity) is quite small when compared to the core flow Owing to this, the BL losses are normally between 0.5% and 1.5% However for micorpropulsion applications (scale nozzles) the BL losses are much more significant Potential substantial loss for attitude adjustment thrusters as well 5
3) Boundary Layer Flow Underexpanded Case 6
3) Boundary Layer Flow Low velocity laminar region and M<1 Peak in local temperature gradient due to shear in BL which is high % h 2 7
4) Multiphase Flow For some liquid and solid propulsion systems other phases of propellant or contaminants might be present Small particles (< 0.01 mm or <10 µm in diameter) tend to follow the flow and exchange energy appropriately (equilibrium). Large particles (>15 µm in diameter) do not follow flow path and do not exchange energy resulting in performance losses.! particle fraction, -./0123, 4-1! 5 3 & 6 8
5) Unsteady Combustion Transients in the thrust chamber due to intermittent incomplete combustion events can also cause losses This is different than transient start-up and stopping effects Could be a result of bad mixing or fuel/oxidizer ratio injection mass flow variations 9
6) Chemical Reactions in Nozzle Chemical reactions in the nozzle will change the gas composition and gas properties This will result in varying chamber pressure and temperature We will cover this in more detail in Chpt. 5 which deals with chemistry 10
7) Transient Operation Lower pressure occurs during transients These transient processes include motor starting, motor stopping, and motor pulsing. 11
8) Nozzle Throat Erosion The interaction of environmental conditions together with the usual requirement that dimensional stability in the nozzle throat be maintained makes the selection of suitable rocket nozzle materials extremely difficult. Erosion of the throat (recall throat temperature is generally the highest!) Gradual erosion of nozzle throat material changes 8 over time 12
8) Nozzle Throat Erosion Ablative cooling may be applied either to the entire combustion chamber liner or to the throat section alone Typically all solid rocket boosters have ablative cooled nozzles 13
9) Nonuniform Gas Composition Reduces performance due to incomplete mixing, turbulence, or incomplete combustion Impingement of oxidizer and fuel species (for liquid motors) is key as it promotes good mixing and atomization Swirl injectors which introduce a tangential velocity component to both propellants are typical for small thrusters are often some type of coax injector. They usually create (due to the numerous small recirculation zones in the vicinity of the face plate) a very good mixing and combustion performance They also allow as well for a simple establishment of a cooling film. Shear coaxial injector element 14
9) Nonuniform Gas Composition A major concern of any injector is the injector/wall interaction. In the vicinity of the face plate where propellant mixing is poor oxidizer-rich gases mixed with cryogenic droplets may get in contact with the combustion chamber walls. The result of this process, a combined physical and chemical attack, clearly visible on the wall of the combustion chamber liner of the Vulcain engine This process is referred to as blanching. Smooth inner wall Visible blanching in Vulcain motor combustion chamber 15
9) Nonuniform Gas Composition 16
10) Real Gas Properties Real gas properties affect the values of 9 and M used in the ideal analysis Also depends on if frozen, chemical equilibrium, or chemical non-equilibrium assumptions are being made as the gases expand and accelerate through the nozzle 17
11) Nonoptimum Nozzle Expansion Operation at nonoptimal expansion ratio reduces thrust and specific impulse No loss if motor operates at design point (; 2 ; 3 ) 18