Its my understanding that the exhaust velocity is inversely proportional to the average molecular wt of the gases. Perhaps that is where the MW enters your equations (hidden in the Ve term).
Nope. Take a close look at the energy equation:
eta*P = 0.5*mdot*v_exh^2
You can solve for v_exh
without knowing M. All you need are mdot (a controllable design parameter), P (which is mdot times specific heat of combustion of the mixture), and eta (which is generally fairly close to 1, at least for a wide-nozzle engine in vacuum).
Given these parameters, what the molecular weight of the combustion products tells you is what the chamber temperature is (temperature is proportional to energy per particle, and when you have more particles sharing the same total energy, the temperature is lower even if the total mass is the same). Chamber temperature can be important, of course, but it doesn't directly affect the performance.
A chemical rocket will always have the highest ratio of P/mdot at the stoichiometric mixture ratio. However, the finite expansion ratio, combined with second-order chemical effects during the expansion, mean that the highest value of eta*P/mdot, at least for a hydrolox engine, is achieved with a fuel-rich mixture.
In other words, molecular weight is
hidden in my equations, but in the efficiency eta, not the exhaust velocity.On the other hand
, a nuclear rocket works not by dumping a given amount of energy per unit mass into the propellant, but by heating it to a certain temperature. At a given chamber temperature, P (and thus v_exh) is strongly
dependent on molecular weight. Thus low M is absolutely paramount for a nuclear thermal rocket.
In any case, low mol wt is desirable. My query was regarding variation in the mixture ratio. Is there any benefit in continuous variation?
I expect its complex to implement, but would there be any theoretical basis for such a practice?
Yes. The efficiency depends on the exit pressure. I'm not entirely sure how it works with a fixed nozzle, but with an altitude-compensating one the optimum definitely moves with altitude.