Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach...
-
Upload
barry-mills -
Category
Documents
-
view
214 -
download
0
Transcript of Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach...
![Page 1: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/1.jpg)
Film Cooling in LF RocketsErin Schmidt
![Page 2: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/2.jpg)
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
![Page 3: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/3.jpg)
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
![Page 4: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/4.jpg)
● 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
![Page 5: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/5.jpg)
Film Cooling
Source: NASA SP-8124, Anon., 1977
![Page 6: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/6.jpg)
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
![Page 7: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/7.jpg)
All of the assumptions implicit in this result are wrong
![Page 8: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/8.jpg)
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
![Page 9: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/9.jpg)
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
![Page 10: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/10.jpg)
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
![Page 11: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/11.jpg)
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
![Page 12: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/12.jpg)
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
![Page 13: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/13.jpg)
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
![Page 14: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/14.jpg)
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
![Page 15: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/15.jpg)
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
![Page 16: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/16.jpg)
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
![Page 17: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/17.jpg)
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.
![Page 18: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/18.jpg)
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
![Page 19: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/19.jpg)
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
![Page 20: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/20.jpg)
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
![Page 21: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/21.jpg)
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
![Page 22: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/22.jpg)
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,
![Page 23: Film Cooling in LF Rockets Erin Schmidt. Watch the Heat! Temperatures in LF rocket engines can reach 3600 K Heat transfer rates are on the order of 200.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649e755503460f94b76369/html5/thumbnails/23.jpg)
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