roger gregory <roger <at> halfwaytoanywhere.com> writes: > > The thrust is just sufficient to pump the propellant to the exhaust > velocity. So that's not the answer. However the energy imparted to the > fuel is same as in the exhaust (the same v after all) and thus the > temperature of the reaction is pushed higher and the fuel is more > disassociated. The higher energy and temperature raise the exhaust > velocity until this converges. The energy is thus in the disassociated > combustion products and heat. >
Not entirely true. I am assuming that "energy imparted to the fuel" refers to the heat released from the reaction in the combustion/catalyst chamber. Some of the energy released is converted to work, to accelerate the propellants out through the nozzle, causing an increase in the speed of the gases (a rocket isn't just a giant heater, after all) while the rest is rejected as waste heat, i.e. the hot exhaust. Therefore, the exhaust does not contain all of the heat released in the reaction, and the velocities in the combustion chamber and at the exhaust are not the same. As for the notion that the heat in the exhaust can be harnessed to create additional thrust, the portion of heat that a system can convert to work is limited according to the temperatures at which the heat is added and rejected, ultimately due to the Second Law of Thermodynamics. This is best illustrated by the idea of Carnot efficiency, the maximum portion of the heat put into a system that can be released as work. However, back to the rocket, the _mass flow rate_ is the same at both the combustion chamber and the nozzle. In the combustion chamber, where the pressure is high, the density is high and the velocity is low, whereas at the exhaust, the density is low and the velocity is high. Although the cross sectional area of the combustion chamber and nozzle sections also affect velocity and density, the main reason for the increase in velocity is the decrease in density, i.e. expansion of the gases in the nozzle. Since momentum flux equals mass flow rate * velocity, the momentum fluxes (flow rates) through the combustion chamber and nozzle are not equal, giving rise to a force, the thrust. This occurs because the mass flow rates are the same at both locations, but the velocities are different. Dissociation occurs simply because the gases are at high temperature, and is not directly connected to the process of generating thrust. [EMAIL PROTECTED] > On a not so theoretical level, this means the exhaust velocity increases > till some limit of pressure, then drops off as we increase the angle > from zero. The maximal ISP also involves changing the fuel mix toward > stoichiometric as the pressure increases. > > Roger Gregory > roger <at> halfwaytoanywhere.com > http://www.halfwaytoanywhere.com > > On Sat, 2004-06-12 at 13:05, ShadowMem <at> aol.com wrote: > > The rocket, at each time step, has a certain momentum already. Additional > > fuel burned in the next time step will increase its momentum and so on until > > the fuel is depleted. In the absense of any drag, the rocket will keep > > accelerating > > as long as thrust is being made. If drag is larger than thrust, the rocket > > will slow > > down, just more rapidly with no thrust. My wishalloy is platinum, when can > > I pick > > it up? > > > > Dan > > > > In a message dated 6/12/04 12:17:12 PM, erps <at> wolfkeeper.plus.com writes: > > > > > > > Whilst mulling over the mechanics of rocket tipped rotors I came up with > > > the following paradox. > > > > > > Consider a low ISP rocket, say 20 seconds; mounted on an arm pivoting on > > > a central spindle. The propellent enters the rocket along a tube up the > > > central spindle, goes through a frictionless coupling and then follows > > > the tube along to the rocket tip. > > > > > > The rocket is oriented so that the exhaust points at 90 degrees to the > > > rotation axis. > > > > > > Now from momentum considerations you can show that the tip speed should > > > be equal to the exhaust velocity- in this case ~200 m/s (fuel has to be > > > accelerated up to the tip and then leaves it at ~200m/s. Clearly the > > > momentum balances when the tip goes at 200m/s.) > > > > > > However this implies that the exhaust leaves the nozzle and stops; and > > > hence has no energy, and hardly any heat, (rockets are typically 90% > > > efficient at turning hot gas into moving gas, so the exhaust gas is > > > relatively cool). > > > > > > And yet the rocket clearly isn't accelerating and we have burnt all this > > > fuel, which has liberated energy. Conservation of energy is the law! > > > > > > Assuming there is no air drag or other friction; where has the fuel > > > energy gone? > > > > > > Winner gets 1kg of wishalloy. > > > > > > "Lisa, in this house we *obey* the laws of thermodynamics" - H. Simpson > > > > > > > _______________________________________________ > > ERPS-list mailing list > > ERPS-list <at> lists.erps.org > > http://lists.erps.org/mailman/listinfo/erps-list > > > _______________________________________________ ERPS-list mailing list [EMAIL PROTECTED] http://lists.erps.org/mailman/listinfo/erps-list
