×

Close

- Compressive Flow and Gas Dynamics - CFG
- Note
- 6 Topics
**689 Views**- 31 Offline Downloads
- Uploaded 10 months ago

Touch here to read

Page-2

Topic:

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Euler’s equation Momentum equation A review of equations of conservation Isentropic condition Speed of sound — Mach number Results from the energy equation The area-velocity relationship On the equations of state Bernoulli equation — dynamic pressure Constant area flows Shock relations for perfect gas — Part I Shock relations for perfect gas — Part II Shock relations for perfect gas — Part III The area-velocity relationship — revisited Nozzle flow — converging nozzle Gasdynamics — Lecture Slides 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Nozzle flow — converging-diverging nozzle Normal shock recovery — diffuser Flow with wall roughness — Fanno flow Flow with heat addition — Rayleigh flow Normal shock, Fanno flow and Rayleigh flow Waves in supersonic flow Multi-dimensional equations of the flow Oblique shocks Relationship between wedge angle and wave angle Small angle approximation Mach lines Weak oblique shocks Supersonic compression by turning Supersonic expansion by turning The Prandtl-Meyer function Gasdynamics — Lecture Slides

46 Detached shocks 47 Shock-expansion theory 48 Reflection and intersection of oblique shocks 49 Cones in supersonic flow 50 Derivation of perturbation equation 51 Irrotational flow 52 Governing equations for small perturbation flows — Part I 53 Governing equations for small perturbation flows — Part II 54 Pressure coefficient 55 Boundary conditions 56 Flow past a wave-shaped wall — an example 57 Flow past a wave-shaped wall — subsonic case 58 Flow past a wave-shaped wall — supersonic case Gasdynamics — Lecture Slides Compressible flow In a nutshell, the term compressible flow refers to the fluids of which there can be found significant variation of density in the flow under consideration. Compressibility is strongly related to the speed of the flow itself and the thermodynamics of the fluid. A good grasp of thermodynamics is imperative for the study of compressible flow. For low-speed flow, the kinetic energy is often much smaller than the heat content of the fluid, such that temperature remains more or less constant. On the other hand, the magnitude of the kinetic energy in a high-speed flow can be very large, able to cause a large variation in the temperature. Some important phenomena strongly associated with compressibility are the flow discontinuity and choking of the flow. Gasdynamics — Lecture Slides

Compressible flow To illustrate, consider a car at sea-level, 1 atm and 15 ◦ C, going at a speed of 90 km/h. The density is 1.225 kg/m3 . At a stagnation point, the density there is found to be 1.228 kg/m3 , a mere 0.27 % difference. The temperature rises by 0.311 ◦ C and the pressure changes by 0.38 %. Here, the incompressible assumption can be applied. Now, consider a typical air flow around a cruising jetliner at 10 km altitude. The speed is now 810 km/h, while the ambient conditions are 0.413 kg/m3 , 0.261 atm and −50 ◦ C. At the stagnation point the temperature rises by over 25 ◦ C, while density and pressure changes by more than 30 % and 45 %, respectively. It is clear that compressibility must now be taken into account. Gasdynamics — Lecture Slides Compressible flow Figure 1: Breaking the sound barrier. . . ? An extreme example of compressible flow in action is the re-entry flow. Another is shown here on the left as a jet fighter seemingly punches through the “sound barrier”. However, more daily mundane applications can also be found in flows through jet engines, or around a transport aircraft. Gasdynamics — Lecture Slides

Zeroth law of thermodynamics The concept of equilibrium is fundamental to the study of thermodynamics, yet it was not wholly appreciated until later. Thus, it is deemed necessary to define the zeroth law of thermodynamics, as a way to say that it precedes even the first law, as follows: When two objects are separately in thermodynamic equilibrium with a third object, they are in equilibrium with each other. A system is said to be in equilibrium if it is free of currents. The term “currents” here refers to the flux of quantities such as mass, momentum, or energy, which is caused by gradients in the system. Gasdynamics — Lecture Slides First law of thermodynamics The first law is a statement of energy conservation. It states that the increase in the internal energy level of a system E is equal to the amount of heat Q flowing in from the surroundings and work W done on the system by the surroundings. Mathematically, it can be written as: ∆E = Q + W (1) Note that E is a variable of state, while Q and W depend on the process involved in the state change. And, for a small change of state the law can be written in a differential form as: dE = δQ + δW Gasdynamics — Lecture Slides (2)

## Leave your Comments