Temperature Behind Oblique Shock For Given Upstream Temperature And Normal Upstream Mach Number Calculator

Formula Used:

\[ T_{s2} = T_{s1} \times \frac{1 + \frac{2\gamma_o}{\gamma_o + 1}(M_{n1}^2 - 1)}{\frac{(\gamma_o + 1)M_{n1}^2}{2 + (\gamma_o - 1)M_{n1}^2}} \]

Temperature Ahead of Oblique Shock (Ts1):

Specific Heat Ratio Oblique Shock (γo):

Upstream Mach Normal to Oblique Shock (Mn1):

Temperature Behind Oblique Shock (Ts2):

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1. What is Temperature Behind Oblique Shock?

Temperature Behind Oblique Shock signifies the temperature of a fluid or airflow after passing through an oblique shock wave. This temperature change is a critical parameter in compressible flow analysis and aerodynamics.

2. How Does the Calculator Work?

The calculator uses the oblique shock temperature ratio formula:

\[ T_{s2} = T_{s1} \times \frac{1 + \frac{2\gamma_o}{\gamma_o + 1}(M_{n1}^2 - 1)}{\frac{(\gamma_o + 1)M_{n1}^2}{2 + (\gamma_o - 1)M_{n1}^2}} \]

Where:

\( T_{s2} \) — Temperature Behind Oblique Shock (K)
\( T_{s1} \) — Temperature Ahead of Oblique Shock (K)
\( \gamma_o \) — Specific Heat Ratio Oblique Shock
\( M_{n1} \) — Upstream Mach Normal to Oblique Shock

Explanation: This formula calculates the temperature ratio across an oblique shock wave based on the normal Mach number component and specific heat ratio.

3. Importance of Temperature Calculation

Details: Accurate temperature calculation behind oblique shocks is crucial for aerodynamic design, propulsion systems, and high-speed flow analysis. It helps determine thermal loads, heat transfer characteristics, and flow properties in supersonic applications.

4. Using the Calculator

Tips: Enter temperature ahead of shock in Kelvin, specific heat ratio (typically 1.4 for air), and normal upstream Mach number. All values must be positive and valid for physical consistency.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of temperature increase across a shock?
A: The temperature increase represents the conversion of kinetic energy to thermal energy due to the compression process across the shock wave.

Q2: How does specific heat ratio affect the temperature rise?
A: Higher specific heat ratios generally result in greater temperature increases across the shock for the same Mach number.

Q3: What is the normal Mach number component?
A: The normal Mach number is the component of the upstream Mach vector perpendicular to the shock wave, calculated as \( M_{n1} = M_1 \times \sin(\beta) \), where β is the shock angle.

Q4: Are there limitations to this equation?
A: This equation assumes ideal gas behavior, steady flow, and perfect gas properties. It may not be accurate for real gas effects at very high temperatures or for reacting flows.

Q5: What are typical values for specific heat ratio?
A: For air at standard conditions, γ = 1.4. For other gases: monatomic gases γ = 1.67, diatomic gases γ = 1.4, triatomic gases γ ≈ 1.33.