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Film Cooling in LF RocketsErin Schmidt
Watch the Heat!
Temperatures in LF rocket engines can reach 3600 K
Heat transfer rates are on the order of 200 MW/m^2
The basic problem is keeping the nozzle and combustion chamber walls from
vaporizing
Rocket Engine Heat Transfer
There are a few classical approaches to dealing with this problem:
Passive cooling -> ablation, radiative cooling, heat sinksActive cooling -> regenerative cooling, film cooling
● LOX-H2 Staged Combustion● 3000 psi Chamber pressure● 2300 kN Thrust Ea.
Late 1960’s technology, but remains the current state-of-the-art
cryogenic engine.The SSME used film cooling
Source: NASA MSFC
RS-25 SSME
Film Cooling
Source: NASA SP-8124, Anon., 1977
Ultimately the thing we care about is Tw
Skipping straight to the solution (similarity solution for B.L. from Schlichting):
(Tw-Ti )/(Tm-Ti )=1-exp[h2αt/k2]erfc[h sqrt(αt)/k]
A Conceptual Model
All of the assumptions implicit in this result are wrong
Big Problems● Flow has 3D wakes due to injector geometry,
lateral flows, separation, and vorticity ● Homogenous reactions within the film● Turbulent mixing within the film● Shear mixing at the film interface● Compressibility-> pressure, density and
temperature gradients● Flow discontinuities (e.g. shock)
For any practical rocket engine the simple model has laughably bad predictive power
Big Problems Cont.
For an isentropic converging-diverging nozzle it is ill-advised to make any of the constant properties assumptions
Besides making the governing equations really complex, this adds several levels of coupling between the governing eqns Source: Huzel and Huang,
1967
Big Problems Cont.
One specific example of coupling is that the reactions in the film are weakly diffusion controlled
But binary diffusion coefficients depend on temperature and pressure (which are changing axially in the isentropic flow). Also the reactions couple the energy and species conservation eqns. because the reactions are not isothermal
Combustion Products
We need to relate T and r. We can do this by balancing enthalpy
Hess’s law states that “if a reaction can be carried out as a series of steps, ∆H for the entire reaction is the sum of all ∆H for each step”...
∆Hrxn= ∑np∆Hf,products- ∑nr∆Hf,reactants
Combustion Products
When a chemical reaction is in equilibrium there are no changes in the molar concentrations of products and reactants with time
For a general reaction aA + bB cC + dD
there is a constant s.t. Kc= [C]c[D]d/[A]a[B]b
Combustion Products
If Kc > 1 equilibrium favors productsIf Kc < 1 equilibrium favors reactants
You can also write Kc in terms of partial pressures
Kc=pCcpD
d/pAapB
b
Equilibrium Constant Method
Example: chemical species at equilibrium2H2(g) + O2(g) 2H2O(g)
a) H2 + ½ O2 H2Ob) ½ O2 + ½ H2 OHc) ½ H2 Hd) ½ O2 O
Equilibrium Constant Method
Equilibrium constants are known functions of temperature! Using the equilibrium constant eqns...
a) Kp,a= pH2O/pH2p1/2O2
b) Kp,b= pOH/p1/2H2p1/2
O2
c) Kp,c= pH/p1/2H2
d)Kp,d= pO/p1/2O2
Equilibrium Constant Method
Solve for pi , but we only have 4 eqns. in 6
unknowns…Using continuity and the ideal gas law:2pH2O+ pOH+ 2pH2+ pH=NH(RT/V)
pH2O+ pOH+ 2pO2+ pO=NO(RT/V)With NH and NO being determined by the concentration gradient
Combustion Temperature
Now we can solve for pi (and thus ni moles of gas per chemical species) ...
We can use ni to get the temperature in the reacting B.L.
Combustion Temperature
Using a simple iterative method:1. Assume a chamber temperature T’ at a
given pressure
2. Determine equilibrium composition of combustion species at T’
3. Calculate:Qavailable=∆Hrxn+ ∑ini,reactants∫TiTrefCp,idT
Combustion Temperature
4. Calculate:
(Use a curve fit equation for Cp , usually found in thermodynamic tables, or use lookups from an enthalpy table in lieu of the integral)
Qrequired= -∑ini,products∫T’TrefCpdT
Combustion Temperature
5. Compare Qavailable and Qrequired ; if the difference is greater than your chosen threshold assume a new T’
6. Iterate until T converges7. Use P, T to compute D with Chapman-Engkog or other
The point is realistic film-cooling simulations accounting
for all these problems are incredibly difficult to do
In fact no one has managed to make one yet
Std. NASA CorrelationBecause analytical and numerical approaches leave much to be desired propulsion engineers rely on empirical correlations. This one is the standard for liquid films:
where,
Reference1. “Liquid Rocket Engine Self-Cooled Combustion Chambers.” 1977.
http://ntrs.nasa.gov/search.jsp?R=19780013268.
2. Huang, D. H., and D. K. Huzel. 1971. “Design of Liquid Propellant
Rocket Engines Second Edition.”
http://ntrs.nasa.gov/search.jsp?R=19710019929.
3. Schlichting, H., and K. Gersten. 2000. Boundary-Layer Theory.
8th edition. Berlin ; New York: Springer.
Thanks!Source: NASA
MSFC