ame 513 principles of combustion n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
AME 513 Principles of Combustion PowerPoint Presentation
Download Presentation
AME 513 Principles of Combustion

Loading in 2 Seconds...

play fullscreen
1 / 14

AME 513 Principles of Combustion - PowerPoint PPT Presentation


  • 153 Views
  • Uploaded on

AME 513 Principles of Combustion. Lecture 7 Conservation equations. Outline. Conservation equations Mass Energy Chemical species Momentum. Conservation of mass. Cubic control volume with sides dx, dy , dz u , v, w = velocity components in x, y and z directions

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'AME 513 Principles of Combustion' - naoko


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
ame 513 principles of combustion

AME 513Principles of Combustion

Lecture 7

Conservation equations

outline
Outline
  • Conservation equations
    • Mass
    • Energy
    • Chemical species
    • Momentum

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation of mass
Conservation of mass
  • Cubic control volume with sides dx, dy, dz
  • u, v, w = velocity components in x, y and z directions
  • Mass flow into left side& mass flow out of right side
  • Net mass flow in x direction = sum of these 2 terms

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation of mass1
Conservation of mass
  • Similarly for y and z directions
  • Rate of mass accumulation within control volume
  • Sum of all mass flows = rate of change of mass within control volume

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation of energy control volume
Conservation of energy – control volume
  • 1st Law of Thermodynamics for a control volume, a fixed volume in space that may have mass flowing in or out (opposite of control mass, which has fixed mass but possibly changing volume):
    • E = energy within control volume = U + KE + PE as before
    • = rates of heat & work transfer in or out (Watts)
    • Subscript “in” refers to conditions at inlet(s) of mass, “out” to outlet(s) of mass
    • = mass flow rate in or out of the control volume
    • h  u + Pv = enthalpy
    • Note h, u & v are lower case, i.e. per unit mass; h = H/M, u = U/M, V = v/M, etc.; upper case means total for all the mass (not per unit mass)
    • v = velocity, thus v2/2 is the KE term
    • g = acceleration of gravity, z = elevation at inlet or outlet, thus gz is the PE term

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation of energy
Conservation of energy
  • Same cubic control volume with sides dx, dy, dz
  • Several forms of energy flow
    • Convection
    • Conduction
    • Sources and sinks within control volume, e.g. via chemical reaction & radiative transfer = q’’’ (units power per unit volume)
  • Neglect potential (gz) and kinetic energy (u2/2) for now
  • Energy flow in from left side of CV
  • Energy flow out from right side of CV
  • Can neglect higher order (dx)2 term

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation of energy1
Conservation of energy
  • Net energy flux (Ex) in x direction = Eleft – Eright
  • Similarly for y and z directions (only y shown for brevity)
  • Combining Ex + Ey
  • dECV/dt term

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation of energy2
Conservation of energy
  • dECV/dt= Ex+ Ey+ heat sources/sinks within CV
  • First term = 0 (mass conservation!) thus (finally!)
  • Combined effects of unsteadiness, convection, conduction and enthalpy sources
  • Special case: 1D, steady (∂/∂t = 0), constant CP (thus ∂h/∂T = CP∂T/∂t) & constant k:

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation of species
Conservation of species
  • Similar to energy conservation but
    • Key property is mass fraction of species i (Yi), not T
    • Mass diffusion rD instead of conduction – units of D are m2/s
    • Mass source/sink due to chemical reaction = Miwi (units kg/m3s)

which leads to

  • Special case: 1D, steady (∂/∂t = 0), constant rD
  • Note if rD = constant andrD= k/CPandthere is only a single reactant with heating value QR, then q’’’ = -QRMiwiand the equations for T and Yi are exactly the same!
  • k/rCPD is dimensionless, called the Lewis number (Le) – generally for gases D ≈ k/rCP ≈n, where k/rCP= a= thermal diffusivity, n = kinematic viscosity (“viscous diffusivity”)

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation equations
Conservation equations
  • Combine energy and species equations
  • is constant, i.e. doesn’t vary with reaction but
    • If Le is not exactly 1, small deviations in Le (thus T) will have large impact on wdue to high activation energy
    • Energy equation may have heat loss in q’’’ term, not present in species conservation equation

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation equations comments
Conservation equations - comments
  • Outside of a thin reaction zone at x = 0
  • Temperature profile is exponential in this convection-diffusion zone (x ≥ 0); constant downstream (x ≤ 0)
  • u = -SL (SL > 0) at x = +∞ (flow in from right to left); in premixed flames, SL is called the burning velocity
  • d has units of length: flame thickness in premixed flames
  • Within reaction zone – temperature does not increase despite heat release – temperature acts to change slope of temperature profile, not temperature itself

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

schematic of deflagration from lecture 1
Schematic of deflagration (from Lecture 1)
  • Temperature increases in convection-diffusion zone or preheat zoneahead of reaction zone, even though no heat release occurs there, due to balance between convection & diffusion
  • Temperature constant downstream (if adiabatic)
  • Reactant concentration decreases in convection-diffusion zone, even though no chemical reaction occurs there, for the same reason

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation equations comments1
Conservation equations - comments
  • In limit of infinitely thin reaction zone, T does not change but dT/dx does; integrating across reaction zone
  • Note also that from temperature profile:
  • Thus, change in slope of temperature profile is a measure of the total amount of reaction – but only when the reaction zone is thin enough that convection term can be neglected compared to diffusion term

AME 513 - Fall 2012 - Lecture 7 - Conservation equations

conservation of momentum
Conservation of momentum
  • Apply conservation of momentum to our control volume results in Navier-Stokes equations:

or written out as individual components

  • This is just Newton’s 2nd Law, rate of change of momentum = d(mu)/dt = S(Forces)
  • Left side is just d(mu)/dt = m(du/dt) + u(dm/dt)
  • Right side is just S(Forces): pressure, gravity, viscosity

AME 513 - Fall 2012 - Lecture 7 - Conservation equations