Homework check (too easy) with on/off design analysis for variable area turbojet

In summary, the conversation discusses the performance of a non-afterburning turbojet engine and how to find the required nozzle throat area ratio for off-design conditions while maintaining a constant flight Mach number. The calculations involve using the engine's on-design conditions and the given off-design condition to determine the required area ratio. However, it is important to carefully check and validate the calculations before coming to a conclusion.
  • #1
roldy
237
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I'm studying on variable area turbojet problems in the book and I can't seem to get past this problem.

Consider the performance of an ideal non-afterburning turbojet with flow at station 4(turbine entrance) and station 8 (nozzle throat) choked. A4 is fixed and A8 is varied in order to maintain constant compressor total pressure ratio ([tex]\pi_c[/tex]).

On-design conditions are as follows:
[tex]
\pi_{cR}=15, M_{oR}=2.0, \tau_{\lambda{R}}=7.0
[/tex]

Find the required ratio of nozzle throat area (off-design) to nozzle throat area (on-design) for the engine operating at the same flight Mach number (2.0) but at the off-design condition such that [tex]\tau_\lambda=6.0[/tex].

My work:

Using Mach number 2

On-design

[tex]
\tau_{rR}=0.8, \pi_{rR}=.458, \tau_{cR}=2.168, \tau_{tR}=.867, \pi_{tR}=.607
[/tex]

[tex]
\tau_{tR}=1-\frac{\tau_{rR}}{\tau_{\lambda{R}}}(\tau_{cR}-1)=1-\frac{.8}{7}(2.168-1)=.867
[/tex]Off-design

Same values as on-design because Mach number does not change.
[tex]
\tau_{r}=0.8, \pi_{r}=.458, \tau_{c}=2.168, \tau_{t}=.867, \pi_{t}=.607
[/tex]

Using given [tex]\lambda=6[/tex] for off-design:

[tex]
\tau_t=1-\frac{\tau_r}{\tau_\lambda}(\tau_c-1)=1-\frac{.8}{6}(2.168-1)=.844
[/tex]

Hence, the area ratio:
[tex]
\frac{A_8}{A_{8R}}=\frac{\tau_t^\frac{1}{2}}{\pi_T}\frac{\pi_{tR}}{\tau_{tR}^\frac{1}{2}}=.9866.
[/tex]

Is this correct? This seems a little too easy.
 
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  • #2


it is important to carefully check and validate your calculations before coming to a conclusion. In this case, it is possible that your calculations are correct, but it is always a good idea to double check and make sure. It may also be helpful to explain your thought process and assumptions to better understand your approach. Additionally, it would be beneficial to provide the equations and formulas used in your calculations for clarity.
 

1. What is a homework check in regards to a variable area turbojet?

A homework check in this context refers to a method of testing the performance of a variable area turbojet engine by analyzing its on/off design. This is often done as an exercise for students or as a quality control measure for engineers.

2. What does the on/off design analysis involve?

The on/off design analysis involves analyzing the performance of the turbojet engine at both its maximum and minimum operating conditions. This includes looking at variables such as airflow, pressure, and temperature to determine how the engine performs under different conditions.

3. Why is it important to perform a homework check with on/off design analysis?

Performing a homework check with on/off design analysis allows for a comprehensive evaluation of the variable area turbojet engine's performance. It can help identify any potential issues or areas for improvement, and ensure that the engine is operating efficiently and safely.

4. How is the variable area turbojet engine designed for on/off operation?

The design of a variable area turbojet engine is optimized for both on and off operation. This is achieved through the use of adjustable inlet guide vanes and variable stator blades, which allow for control of airflow and pressure within the engine. This design allows for efficient operation at a range of conditions.

5. What are some potential challenges with the homework check and on/off design analysis?

Some potential challenges with performing a homework check and on/off design analysis include the complexity of the analysis and the need for accurate and precise data. It also requires a thorough understanding of the engine's design and operation. Additionally, any external factors, such as changes in weather or altitude, can affect the results of the analysis.

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