Mci Modelagem Stanford Program

An Overview of Stanford ESP Program ! An engine simulation program for the simulation of the thermodynamics performance of homogeneous charge engines !Zero dimensional thermodynamic analysis • energy and mass balance • turbulent modeling • two zones flame propagation plus ignition analysis !Fluid Mechanics • Isentropic compressible flow for intake and exhaust flow • Manifold analysis using method of characteristics !Heat Transfer • heat loss through the walls (two zones model)

Detailed Procedures ! Four stage calculation: compression, burn (ignition and flame propagation), expansion, and gas exchange (inlet, exhaust, and overlap). (1) Compression stage (the same procedures for expansion stage) Energy balance: dU C ! + QC + W! P = 0 ( A) dt dz ! where WP = PAP and dt Q! C = hC AC (TC − TW )

dQC/dt TDC

dWp/dt

hC = StC ρ cPVt , StC is the Stanton number

z

Compression stage (cont.) • Integrate equation A to advance Uc to the next step. Divided Uc by Mc to obtain the specific internal energy uc. • Determine new temperature Tc from uc (using pre-determined thermodynamic table) • Calculate specific volume (v) using the new cylinder volume • Determine pressure using v and TC using thermodynamic table • Calculate heat transfer using new Tc. Stanton number is updated using turbulent kinetic energy model (8-35) through the turbulent velocity Vt. • Repeat until the end of stage

Burn Stage (ignition and flame propagation) ! First, the spark ignition stage is a short period between the compression and burn stages at a user-specified crank angle. ! A user-specified mass fraction (0
b

flame (B)

u

M! b hu

where uu and ub are the specific internal energies and Tu and Tb are the temperatures of the two zones.

dQu/dt

Ignition stage Total volume has to be conserved also: M u v u (Tu ,P+ )+M b v b (Tb ,P+ )=VC (C) where v u and v b are the specific volumes of the two zones and P+ is the pressure after ignition. To determine the pressure and temperature after the ignition, we assume that the unburned gas is undergoing an isentropic compression due to the ignition, that is, su (Tu , P+ ) = su (T− , P− ) (D) where T- is the unburned gas after ignition, T- and P- are the temperature and pressure in the cylinder before ignition. Use equations (B), (C), and (D) to solve for three unknowns: P+ , Tu , and Tb .

Burn Stage (ignition and flame propagation) ! After ignition, a flame front is generated between the unburned and burned zones. The flame is defined as the thin region where rapid exothermic chemical reaction is taking place. The flame can propagate as a result of strong coupling between chemical reaction, mass and heat diffusions, and fluid flow behavior. • premixed (spark-ignition) or diffusion (diesel) • laminar (for low Reynolds number) or turbulent • steady or unsteady ! There will be mass exchange between the two zones and the energy balance can be modeled as: dU u dV + PC u + Q! u + M! b hu = 0 dt dt Energy transfer due to dU b dVb ! mass leaving unburned Burned zone: + PC + Qb = M! b hu zone dt dt Unburned zone:

Flame propagation Mass conservation: dM u dM b dM u + M! b = 0 (E) and M! b = =− (F) dt dt dt This mass exchange is very important since when unburned gases enter the burned zone, the reaction is assumed to be completed (up to a user-specified percentage). Therefore, the enthalpy values for the products will be used instead of the reactants. The energy equations of two zones can be better presented using the enthaply instead of energy as: H=U+PV. dP dH u − Vu C + Q! u + M! b hu = 0 (G) dt dt dPC ! dH b − Vb + Qb = M! b hu (H) dt dt

Flame propagation Combining equations (G) & (H) and the ideal gas relation: h=c p dT, we can obtain: (VC -β uVu − β bVb )

dPC dt

dVC + β b M! b ( hu − hb ) − ( β u Q! u − β bQ! b ) + M! b (α b − α u ) (I) dt α' dα β α = α = where (T)= , (T ) RT , ' dT cP

= − PC

dPC . With the pressure, equations (G) & (H) dt can be used to advance the total enthaplies in both zones. Equation (I) is used to calculate

Then equations (E) & (F) will be used to advance the zonal mass balances. Finally, the new masses and total enthaplies determine the zonal temperatures.

Flame propagation The new unburned volume is calculated using: Vu ( MRT )u = and the burned volume Vb = VC - Vu . VC ( MRT )u + ( MRT )b The pressure is calculated from PV=MRT for whichever zone is larger. Additional information needed, ! = St V ρ c A (T − T ) Heat losses to the walls: (Unburned zone) Q u tu u pu u u w u ! = St V ρ c A (T − T ) (Burned zone) Q b

b tb

b pb

b

b

w

! = A ρ V , where V is the flame propagation speed relative to the Burn rate: M f u f b f unburned gases. A f is the flame front area. V f = VL + C f Vtu , where VL is the specified laminar flame speed, C f is a specified coefficient, and Vtu is the turbulence velocity.

Gas Exchange Stage (Intake and Exhaust) Q! eV

Intake Backflow into intake

 hi M! i − Q! iV   = !  − hC M ib 

hC M! ib

hC M! e

exhaust

  hC M! e dU C ! ! + W p + QC +  ! + Q!  dt − h M eV   e eb

he M! eb

hi M! i

Q! iV

Backflow from exhaust

M! = Cd F ( A, ρ , P, Pb , γ ) : Cd is the specified discharge coefficient, F is the isentropic flow rate.