Operating Characteristics of Nozzles

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Operating Characteristics of Nozzles

• P M V Subbarao
• Professor
• Mechanical Engineering Department
• I I T Delhi

From Takeoff to cruising Realizing New Events
of Physics.
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Converging Nozzle
pb Back Pressure
Design Variables
Outlet Condition
p0
pb
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Designed Exit Conditions
Under design conditions the pressure at the exit
plane of the nozzle is applied back pressure.
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Profile of the Nozzle
At design Conditions
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Full Capacity Convergent Nozzle
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Remarks on Isentropic Nozzle Design

• Length of the nozzle is immaterial for an
  isentropic nozzle.
• Strength requirements of nozzle material may
  decide the nozzle length.
• Either Mach number variation or Area variation or
  Pressure variation is specified as a function or
  arbitrary length unit.
• Nozzle design attains maximum capacity when the
  exit Mach number is unity.

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Converging Nozzle
p0
Pb,critical
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Operational Characteristics of Nozzles

• A variable area passage designed to accelerate
  the a gas flow is considered for study.
• The concern here is with the effect of changes in
  the upstream and downstream pressures
• on the nature of the inside flow and
• on the mass flow rate through a nozzle.
• Four different cases considered for analysis are
• Converging nozzle with constant upstream
  conditions.
• Converging-diverging nozzle with constant
  upstream conditions.
• Converging nozzle with constant downstream
  conditions.
• Converging-diverging nozzle with constant
  downstream conditions.

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Pressure Distribution in Under Expanded Nozzle
pbp0
p0
pb,criticalltpb1ltp0
Pb,critical
At all the above conditions, the pressure at the
exit plane of nozzle, pexit pb.
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Variation of Mass Flow Rate in Exit Pressure
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Variation of in Exit Pressure
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1
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Variation of in Mass Flow Rate
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Low Back Pressure Operation
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Convergent-Divergent Nozzle Under Design
Conditions
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Convergent-Divergent Nozzle with High Back
Pressure
plt pb1ltp0
pthroatgt p
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Convergent-Divergent Nozzle with High Back
Pressure

• When pb is very nearly the same as p0 the flow
  remains subsonic throughout.
• The flow in the nozzle is then similar to that in
  a venturi.
• The local pressure drops from p0 to a minimum
  value at the throat, pthroat , which is greater
  than p.
• The local pressure increases from throat to exit
  plane of the nozzle.
• The pressure at the exit plate of the nozzle is
  equal to the back pressure.
• This trend will continue for a particular value
  of back pressure.

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Convergent-Divergent Nozzle with High Back
Pressure
At all these back pressures the exit plane
pressure is equal to the back pressure.
pthroatgt p
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At exit with high back pressure pb
At throat with high back pressure pb
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• For a given value of high back pressure
  corresponding throat pressure can be calculated.
• As exit area is higher than throat area throat
  pressure is always less than exit plane pressure.
• An decreasing exit pressure produces lowering
  throat pressure

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Variation of Mass Flow Rate in Exit Pressure
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Variation of in Mass Flow Rate
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Numerical Solution for Mach Number Caluculation
Use Newtons Method to extract numerical
solution
Define
At correct Mach number (for given A/A)
Expand F(M) is Taylors series about some
arbitrary Mach number M(j)
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Solve for M
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Still exact expression
if M(j) is chosen to be close to M
And we can truncate after the first order terms
with little Loss of accuracy
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First Order approximation of solution for M
Hat indicates that solution is no longer exact
However one would anticipate that
estimate is closer than original guess
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And we would anticipate that
refined estimate . Iteration 1
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Abstracting to a jth iteration
Iterate until convergence j0,1,.
Drop from loop when