Rocket characteristic velocity

Delivered or Characteristic Velocity. This is a term frequently employed to compare the performance of different rocket engines.. It measures the effectiveness with which the chemical reaction is accomplished in the combustion chamber. The characteristic velocity, denoted by Q, is calcd from the formula ... 

The results of several rocket engine investigations are summarized as the variation of characteristic velocity with mixture ratio and are compared with the predicted values based on equilibrium combustion in figure m-A-1. Greater than theoretical performance is obtained at fuel rich mixture ratios while considerably less than theoretical performance is reported at oxidizer rich mixture ratios. The results cannot be dismissed as the consequences of poor injection technique, poor mixing, or insufficient reaction time (L ), especially with the observation of greater than theoretical performance. At near stoichiometric mixture ratios and at chamber pressures of about 300 psia, performance in terms of characteristic velocity is near the theoretically predicted value. 

Other observations of the reaction of hydrazine and nitrogen tetroxide substantiate the production of non-equilibrium combustion products. Non-equilibrium product concentrations were found in combustion gases extracted from a small rocket combustion chamber through a molecular beam sampling device with direct mass spec-trometric analysis (31) (39). Under oxidizer rich conditions excessive amounts of nitric oxide were found under fuel rich conditions excessive amounts of ammonia were found. A correlation between the experimentally observed characteristic velocity and nitric oxide concentration exists (40). Related kinetic effects are postulated to account for the two stage flame observed in the burning of hydrazine droplets in nitrogen dioxide atmospheres (41) (42). 

The observations that the thrust coefficient has its maximum value near the stoichiometric mixture ratio, see figure V. A. 6.,is consistent with the foregoing expectations. Since specific impulse is proportional to the product of the characteristic velocity and the thrust coefficient, it is expected and observed that the optimum mixture ratio in terms of the specific impulse should fall between the optimum mixture ratios for the characteristic velocity and for the thrust coefficient. It is noted that the characteristic velocity is the dominant member of the pair, a property which adds further to the utility of the characteristic velocity as a performance parameter to rocket propulsion development. 

The basic characteristics of a one-dimensional shock wave are described in Chapter 1 of this text. However, the shock waves in supersonic flow propagate not only one-dimensionally but also two- or three-dimensionally in space. For example, the shock waves formed at the air-intake of a ducted rocket are two- or three-dimensional in shape. Expansion waves are also formed in supersonic flow. The pressure downstream of an expansion wave is reduced and the flow velocity is increased. With reference to Chapter 1, brief descriptions of the characteristics of a two-dimensional shock wave and of an expansion wave are given here.Ii-5]... 

The performance of propints is a unique function of the temp of the hot reaction products, their compn and their pressure. The pro-pint bums at constant pressure and forms a set of products which are in thermal and chemical equilibrium with each other. The multiplicity of the reaction products requires that the combustion chamber conditions be calcd from the solution of simultaneous equations of pressure and energy balances. This calcn is best performed by computer, although the manual scheme has been described well by Sutton (Ref 14) and Barr re et al (Ref 10). The chamber conditions determine the condition in the nozzle which in turn characterizes the rocket engine performance in terms of specific impulse and characteristic exhaust velocity... 

An example of bulk modes in solid-propellant rockets is afforded by the low-frequency, or L, instability [7]. A characteristic length of importance in rocket design is the ratio of the gas volume in the chamber to the throat area of the nozzle this ratio often is denoted by L, and its ratio to a characteristic exhaust velocity provides an estimate of the residence time of a fluid element in the gas phase inside the chamber. A mass balance for the gas inside a rocket chamber with a choked nozzle is... 

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