Gas Dynamics ESA 341 Chapter 1 Dr Kamarul Arifin B. Ahmad PPK Aeroangkasa.

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Presentation transcript:

Gas Dynamics ESA 341 Chapter 1 Dr Kamarul Arifin B. Ahmad PPK Aeroangkasa

Chapter 1 : Introduction Review of prerequisite elements  Perfect gas  Thermodynamics laws  Isentropic flow  Conservation laws Speed of sound  Analogous concept  Derivation of speed of sound Mach number

Review of prerequisite elements Perfect gas: Equation of state For calorically perfect gas Entropy Entropy changes?

Review of prerequisite elements Cont. Forms of the 1 st law The second law

Review of prerequisite elements Cont. For an isentropic flowIf ds=o

Review of prerequisite elements Cont. Conservation of mass (steady flow): Rate of mass enters control volume Rate of mass leaves control volume = 12 flow If  is constant (incompressible):

Review of prerequisite elements Cont. Conservation of momentum (steady flow): Rate momentum leaves control volume Rate momentum enters control volume - Net force on gas in control volume = Euler equation (frictionless flow): 12 flow

Review of prerequisite elements Cont. heat transferenergy transfer due to mass flowwork transfer Basic principle: Change of energy in a CV is related to energy transfer by heat, work, and energy in the mass flow. Conservation of energy for a CV (energy balance):

Review of prerequisite elements Cont. Most important form of energy balance. Analyzing more about Rate of Work Transfer: work can be separated into 2 types: work associated with fluid pressure as mass entering or leaving the CV. other works such as expansion/compression, electrical, shaft, etc. Work due to fluid pressure: fluid pressure acting on the CV boundary creates force.

Review of prerequisite elements Cont. 12 flow For adiabatic flow (no heat transfer) and no work: For calorically perfect gas (dc p =dc v =0):

Conservation of mass (compressible flow): Conservation of momentum (frictionless flow): Conservation of energy (adiabatic): Review of prerequisite elements Cont. Conservation laws

Group Exercises 1 1.Given that standard atmospheric conditions for air at 15 0 C are a pressure of bar and a density of 1.225kg, calculate the gas constant for air. Ans: R=287.13J/kgK 2.The value of Cv for air is 717J/kgK. The value of R=287 J/kgK. Calculate the specific enthalpy of air at 20 0 C. Derive a relation connecting Cp, Cv, R. Use this relation to calculate Cp for air using the information above. Ans: h=294.2kJ/kgK,Cp=1.004kJ/kgK 3.Air is stored in a cylinder at a pressure of 10 bar, and at a room temperature of 25 0 C. How much volume will 1kg of air occupy inside the cylinder? The cylinder is rated for a maximum pressure of 15 bar. At what temperature would this pressure be reached? Ans: V=0.086m2, T=174 0 C.

Speed of sound Sound wave Sounds are the small pressure disturbances in the gas around us, analogous to the surface ripples produced when still water is disturbed Sound wave Sound wave moving through stationary gas Gas moving through stationary sound wave

Derivation of speed of sound Speed of sound cont. Conservation of mass Conservation of momentum Combination of mass and momentum For isentropic flow Finally

Mach Number M=V/a Source of disturbance Distance traveled = speed x time = 4at Zone of silence Region of influence If M=0 M<1Subsonic M=1Sonic M>1Supersonic M>5Hypersonic Distance traveled = at

Mach Number cont. Source of disturbance If M=0.5 Original location of source of disturbance

Mach Number cont. Source of disturbance If M=2 Original location of source of disturbance ut Mach wave: Direction of motion