Oblique Shocks in Fluid Dynamics

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Questions and Answers

What is the primary factor that causes an oblique shock at angle β?

The presence of an obstruction in the flow path

The initial Mach number of the flow

The deflection angle θ caused by an object (correct)

The nature of the gas used in the flow

Which statement best describes the relationship between Mach number M₁ and shock angles β?

Higher Mach numbers only produce weak shocks.

A lower shock angle β results in a detached shock.

There is always one unique shock angle for a given Mach number.

Two possible shock angles exist for a given deflection angle. (correct)

What happens if the deflection angle θ exceeds the maximum deflection angle θ_max?

The Mach number decreases significantly.

A detached normal shock forms. (correct)

The flow remains unchanged.

A weak shock is generated.

In the context of air (k=1.4) when M₁ = 3, what is the approximate value of the maximum deflection angle θ_max?

34° Signup and view all the answers

As the deflection θ approaches zero, what occurs to the weak shock?

It becomes a Mach wave. Signup and view all the answers

What happens to the oblique shock angle as the Mach number increases?

It progressively decreases. Signup and view all the answers

At what Mach number does the normal shock first attach and become oblique for an angle of 10°?

1.42 Signup and view all the answers

What is the speed of sound (C₁) at 4°C in the given scenario?

334 m/s Signup and view all the answers

For the upper surface of the airfoil with an angle of attack of 1°, what is the deflection angle θ_u?

2° Signup and view all the answers

What is the upstream Mach number (M₁) calculated for the airfoil traveling at 600 m/s?

1.80 Signup and view all the answers

What method can be used to solve for β_u in the context provided?

Manual iteration or Excel's Goal Seek function. Signup and view all the answers

What does a normal Mach number close to one indicate about the oblique shock strength?

The shock is quite weak. Signup and view all the answers

What is the angle of the leading edge (δ) of the airfoil in the example given?

6° Signup and view all the answers

What is the relationship of the deflection angle θ to the incoming Mach number M₁ and the oblique shock angle β as expressed in Equation 13.49?

tan θ = 2 cot(M12sin2β - 1)M12(k + cos 2β) + 2 Signup and view all the answers

Which statement accurately describes the characteristics of an oblique shock compared to a normal shock?

For a given supersonic flow, an oblique shock will always be weaker than a normal shock. Signup and view all the answers

What does the angle θ represent in the context of oblique shocks?

The total deflection experienced by the flow Signup and view all the answers

In which scenario can M₂ be supersonic?

In specific conditions of oblique shock where M1 is sufficiently high Signup and view all the answers

What is the significance of the Excel workbook mentioned in relation to oblique shocks?

It helps perform complex calculations related to shock dynamics. Signup and view all the answers

Which equation demonstrates the relationship between the normal velocity ratios for oblique shocks?

V1/V2 = tan β tan(β - θ) Signup and view all the answers

What is the effect of increasing the shock angle β on the deflection angle θ for a given Mach number M₁?

θ increases with increasing β. Signup and view all the answers

How does the normal shock function relate to the solution of oblique shock problems?

It provides a baseline for calculating changes in flow direction. Signup and view all the answers

What is the speed of sound calculated for the air at -2°C?

330 m/s Signup and view all the answers

After experiencing a normal shock, what is the value of downstream pressure $P_2$?

2.9 MPa Signup and view all the answers

What is the upstream Mach number $M_1$ before the normal shock?

5.0 Signup and view all the answers

For an oblique shock at angle β = 30°, what is the downstream temperature $T_2$ after the shock?

306°C Signup and view all the answers

What is the ratio of the downstream pressure $P_2$ to upstream pressure $P_1$ after an oblique shock?

7.125 Signup and view all the answers

What is the downstream velocity $V_2$ after the oblique shock calculated from the velocity components?

1450 m/s Signup and view all the answers

What happens to the air's Mach number after it experiences a normal shock?

It becomes subsonic. Signup and view all the answers

What is the tangential component of velocity $V_{1, cos β}$ for the oblique shock?

1429 m/s Signup and view all the answers

What is the deflection angle θ for the air experiencing an oblique shock?

30° Signup and view all the answers

What changes need to be made in the shock equations when analyzing oblique shocks compared to normal shocks?

Replace velocities with normal velocity components only. Signup and view all the answers

Given the normal velocity components $V_1$ and $V_2$, what is the formula for $V_1$?

$V_1 = V_1 sin β$ Signup and view all the answers

What is the final value of downstream Mach number $M_2$ after the oblique shock?

3.01 Signup and view all the answers

What is represented by the equation $M_2^2 = M_1^2 + \frac{2}{k-1} (1 - M_1^2)$?

The Mach number relationship for oblique shocks. Signup and view all the answers

Which parameter is NOT part of the equations governing oblique shocks for an ideal gas?

Velocity magnitude Signup and view all the answers

Which equation denotes the relationship between total pressures before and after an oblique shock?

$P_{02}/P_{01} = (1 + \frac{k}{2}M_1^2)^{k/(k-1)} (1 + \frac{k}{2}M_2^2)^{-k/(k-1)}$ Signup and view all the answers

What is the equivalent normal shock problem used for analyzing oblique shocks?

Application of equations from normal shock analysis. Signup and view all the answers

In the context of oblique shocks, what is needed to obtain ratios like $T_2/T_1$?

Direct calculation from flow functions. Signup and view all the answers

Which specific heat ratio is commonly used for air in relation to oblique shock calculations?

1.4 Signup and view all the answers

Study Notes

Oblique Shocks

Oblique shocks are similar to normal shocks, but the flow is deflected by an angle.
The equations for oblique shocks are the same as for normal shocks, but we replace the velocity with the normal velocity component.
The normal velocity component is the velocity component perpendicular to the shock wave.
We can use the same normal shock equations with the normal velocities for oblique shocks.
The oblique shock equations for an ideal gas with constant specific heats are obtained directly from the normal shock equations.
The normal shock flow functions can be used to analyze oblique shock problems.
Oblique shocks are always weaker than normal shocks for a given supersonic flow.
Oblique shocks can be analyzed as an equivalent normal shock problem.
The deflection angle of an oblique shock is the angle between the upstream flow direction and the downstream flow direction.
The maximum deflection angle for a given Mach number is limited.
There are generally two possible shock angles for a given Mach number and deflection angle: a weak shock and a strong shock.
For zero deflection, the weak shock becomes a Mach wave.

Normal shock vs Oblique shock comparison

The pressure, temperature, and speed after a normal shock are different from those after an oblique shock.
A normal shock is stronger than an oblique shock.
The downstream Mach number can be subsonic or supersonic after an oblique shock, but it is always subsonic after a normal shock.

Example 13.11

Air flows at a certain speed and temperature.
The air experiences a normal shock.
The flow is then compared to that after an oblique shock.
The downstream pressure, temperature, and speed are calculated for both cases.

Example 13.12

An airplane travels at a certain speed.
The airfoil has a sharp leading edge.
The pressures on the upper and lower surfaces of the airfoil are calculated.
The deflection angle for both the upper and lower surfaces are computed.
The oblique shock angle is computed using various methods.
The pressure ratios for both the upper and lower surfaces are computed, implying the oblique shock is weak.

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Description

This quiz explores the concept of oblique shocks, focusing on their similarities and differences with normal shocks. Test your understanding of how oblique shocks affect supersonic flow and the use of normal shock equations for analysis. Ideal for students studying fluid dynamics or aerodynamics.