Review of Thermodynamics and Chemistry in Advanced Rocket Propulsion, Lecture notes of Thermodynamics

Download Review of Thermodynamics and Chemistry in Advanced Rocket Propulsion and more Lecture notes Thermodynamics in PDF only on Docsity! Lecture 3 Review of Thermodynamics and Chemistry AA284a Advanced Rocket Propulsion Stanford University Prepared by Arif Karabeyoglu Mechanical Engineering KOC University Fall 2019 Advanced Rocket Propulsion Stanford University •  System: A group of entities distinguished from its surroundings –  Mass and energy transfer is allowed –  Change of volume is allowed –  Example: Human body •  Transfer quantities –  Heat (transfer to the system): –  Work (done by the system): –  Mass transfer: •  Definitions: –  Open System: Mass transfer allowed –  Closed System: Mass transfer not allowed –  Adiabatic System: Heat transfer is not allowed Review of Thermodynamics-Definitions Mδ Qδ Karabeyoglu 2 Wδ Reference on Thermodynamics: I. Klotz and R. Rosenberg, “Chemical Thermodynamics” Advanced Rocket Propulsion Stanford University •  Second Law: –  Reversible/Irreversible processes •  Imagine a time dependent physical process governed by a set of equations •  If these equations are invariant with regard to the sign of the time variable the process is reversible, else irreversible –  There exists a system variable, entropy, with the following definition for a single component system •  Explicit property –  Second law of thermodynamics Review of Thermodynamics-Laws T q sd δ = Karabeyoglu 5 0≥universeSd eTemperaturT EntropySpecifics EntropyS : : : T Q Sd δ = Advanced Rocket Propulsion Stanford University •  Second Law: –  Or –  For an isolated system –  Entropy is a measure of “disorder” or lack of “information” on the possible microstates –  Boltzmann’s Equation: –  All real processes are irreversible •  Third Law: –  Planck’s Formulation: Value of entropy of a pure liquid or solid approaches zero at 0 K Review of Thermodynamics-Laws ( )microNkS ln= 0≥+ gssurroundinsystem SdSd Karabeyoglu 6 0≥systemSd StatesMicroofNumberN ConssBoltzmannk mic : .': Advanced Rocket Propulsion Stanford University •  Heat machines convert thermal energy into mechanical energy according to the laws of thermodynamics. •  Many machines work in cycles. Working fluid returns to the original state that it started. •  Carnot Cycle: –  Two constant temperature heat transfer processes and two isentropic compression expansion processes –  Carnot cycle efficiency: •  Bryton Cycle: –  Two constant pressure heat transfer processes and two isentropic compression expansion processes –  Bryton cycle efficiency: •  Cycle efficiency increases with increasing temperature ratio •  Carnot cycle is always the best efficiency heat machine operating between two specified temperature extremes (T1 and T3). Review of Thermodynamics-Cycles 3 1 2 1 11 T T Q Q C −=−=η Karabeyoglu 7 3 1 2 1 111 T T T T h h heating cooling B −<−= Δ Δ −=η Efficiency:η Advanced Rocket Propulsion Stanford University •  Work done by the fluid •  For the same extreme temperatures the Carnot cycle is more efficient than the Bryton cycle •  This conclusion is valid for all other cycles. •  Thus Carnot cycle sets the upper limit for the efficiency of a heat engine operating at two set temperatures •  Nonideal behavior is due to –  Non-isothermal heat transfer –  Non-isentropic expansion and compression Review of Thermodynamics – Cycle Comparison ∫= dvPW Karabeyoglu 10 Advanced Rocket Propulsion Stanford University •  State equation relates the state variables of a substance to each other •  Gibb’s Phase Rule: Number of Phases + Independent Intensive Properties = 2 + Number of Components ( P + V = C +2 ) –  Examples •  If P=1 and C=1, V=2 (One phase one component) •  If P=2 and C=1, V=1 (Two phase one component) •  If P=1 and C=2, V=3 (One phase two component) State Equation Karabeyoglu 11 Advanced Rocket Propulsion Stanford University •  State Equation for a one component system: •  Examples –  Ideal Gas Equation: –  Ideal Liquid Equation: State Equation TRP ρ= ( ) 0,, =TvPf Karabeyoglu 12 ( )TvPP ,= .cons=ρ Advanced Rocket Propulsion Stanford University P-h Diagram Molecular Oxygen Karabeyoglu 15 Advanced Rocket Propulsion Stanford University Saturation Pressure and Density Plots for N2O Karabeyoglu 16 Advanced Rocket Propulsion Stanford University Saturation Pressure vs Saturation Density for Popular Oxidizers Karabeyoglu 17 Advanced Rocket Propulsion Stanford University •  In a thermal rocket the propellant molecules are thermalized by addition of heat in a chamber. •  This thermal energy (random motion of the molecules) is converted to the useful directional velocity needed for thrust in the nozzle. •  The heat source varies –  Nuclear energy: Thermonuclear rockets –  Chemical bond energy: Chemical rockets –  Electric energy: Resistojets and Arcjets –  Thermal energy of the stored propellant: Cold gas thrusters Thermal Rocket – General Concept Karabeyoglu 20 Advanced Rocket Propulsion Stanford University •  Note that this is not really a cycle since the propellant never returns to its original state •  The velocity at the nozzle exit, ue, can be estimated using the conservation of energy along a streamline •  The maximum possible exit velocity (or Isp) is obtained for infinite expansion (he=0) •  For calorically perfect gas Thermal Rocket – Thermodynamic Process RTcc vp =− 2 2 1 eetc uhh =− Karabeyoglu 21 ( )etce hhu −= 2 tce hu 2= Mw TRu tcu e 1 2 − = γ γ •  For monatomic gas: Mw TRu tcu e 21.2= Advanced Rocket Propulsion Stanford University •  Lets compare this maximum velocity to the other fundamental velocities that can be defined in a monatomic gas Thermal Rocket – Velocities in Monatomic Gas Mw TRa tcu s 29.1:SoundofSpeedIsentropic = Mw TRa tcu T =:SoundofSpeedIsothermal Mw TRC tcu MP 41.1:on)Distributin(MaxwelliaSpeedMolecularProbableMost = Karabeyoglu 22 Mw TRc tcu38.1*:yticVelocitCharactris = •  Note that all of these speeds are of the same order (order of the average speed of the molecules in the gas) •  Similar results can be produced for other gamma values Mw TRC tcu72.1:SpeedMolecularAvergeSquare 21 2 =⎟⎠ ⎞⎜⎝ ⎛ Mw TRC tcu60.1:on)Distributin(MaxwelliaSpeedMolecularAverage = Mw TRu tcu e 21.2:Velocity lDirectiona Maximum = Advanced Rocket Propulsion Stanford University •  Quantum Mechanics Predicts: –  Shells, subshells, orbitals •  n=1: K shell (2 electrons) –  1s subshell (1 orbital): electrons •  n=2: L shell (8 electrons) –  2s subshell (1 orbital): 2 electrons –  2p subshell (3 orbitals): 6 electrons •  n=3: M shell –  3s subshell (1 orbital): 2 electrons –  3p subshell (3 orbitals): 6 electrons –  3d subshell: (5 orbitals): 10 electrons •  Argononic structures: Completely full shells (Noble elements: He, Ne, Ar …), Octets •  Valance electrons: Electrons in the shell that is not completely filled Review of Chemistry Karabeyoglu Reference on Chemistry: Linus Pauling, “General Chemistry” 25 NumberQuantumincipaln Pr: Advanced Rocket Propulsion Stanford University Periodic Table of Elements Karabeyoglu 26 Advanced Rocket Propulsion Stanford University •  Elements in the same group have closely related physical and chemical properties (same number of valance electrons) •  Elements in the periods have their valance electrons in the same shell •  Left side of the periodic table : Metals (Fuels) –  High electric and thermal conductivity, metallic luster, malleable, ductile •  Right side of the periodic table : Nonmetals (Oxidizers) •  Metalloids in the middle: B, Si, Ge, As •  Chemical Bonds: –  Octet rule: Filled shell rule •  Share or gain electrons to fill their shells to the Argononic structures –  Covalent Bonds: Share pairs of electrons (H-C) –  Ionic Bonds: Take or give electrons (Li+Cl-) •  Electronegativity: Affinity of an atom to an electron –  The difference in electronegativity determines the covalent/ionic nature of the bond (Upper right highly electronegative, lower left poorly electronegative) •  Strained bonds (C3H6, C2H2) and Resonance Structures (N2O) Review of Chemistry Karabeyoglu 27