Four Performance Parameters

In using values of thrust, specific impulse, propellant flow, and other performance parameters, one must be careful to specify or qualify the conditions under which a specific number is presented. There are at least four sets of performance parameters and they are often quite different in concept and value, even when referring to the same rocket propulsion system. Each performance parameter, such as F, Is, c, v2 and/or m, should be accompanied by a clear definition of the conditions under which it applies, namely:

a. Chamber pressure; also, for slender chambers, the location where this pressure prevails (e.g., at nozzle entrance).

b. Ambient pressure or altitude or space (vacuum).

c. Nozzle expansion area ratio and whether this is an optimum.

d. Nozzle shape and exit angle (see Table 3-3).

e. Propellants, their composition or mixture ratio.

/. Key assumptions and corrections made in the calculations of the theoretical performance: for example, was frozen or shifting equilibrium used in the analysis? (This is described in Chapter 5.)

g. Initial temperature of propellants.

1. Theoretical performance values are defined in Chapters 2, 3, and 5 and generally apply to ideal rockets, but usually with some corrections. Most organizations doing nozzle design have their own computer programs, often different programs for different nozzle designs, different thrust levels, or operating durations. Most are two dimensional and correct for the chemical reactions in the nozzle using real gas properties, and correct for divergence. Many also correct for one or more of the other losses mentioned above. For example, programs for solid propellant motor nozzles can include losses for throat erosion and multiphase flow; for liquid propellant engines it may include two or more concentric zones, each at different mixtures ratios and thus with different gas properties. Nozzle wall contour analysis with expansion and compression waves may use a finite element analysis and/or a method of characteristics approach. Some of the more sophisticated programs include viscous boundary layer effects and heat transfer to the walls. Typically these computer simulation programs are based on computer fluid dynamics finite element analyses and on the basic Navier-Stokes relationships. Most companies also have simpler, one-dimensional computer programs which may include one or more of the above corrections; they are used frequently for preliminary estimates or proposals.

2. Delivered, that is, actually measured, performance values are obtained from static tests or flight tests of full-scale propulsion systems. Again, the conditions should be explained (e.g., define pi,A2/At, T{, etc.) and the measured values should be corrected for instrument deviations, errors, or calibration constants. Flight test data need to be corrected for aerodynamic effects, such as drag. Often empirical coefficients, such as the thrust correction factor, the velocity correction factor, and the mass discharge flow correction factors are used to convert the theoretical values of item 1 above to approximate actual values and this is often satisfactory for preliminary estimates. Sometimes sub-scale propulsion systems are used in the development of new rocket systems and then scale factors are used to correct the measured data to full-scale values.

3. Performance values at standard conditions are corrected values of items 1 and 2 above. These standard conditions are generally rigidly specified by the customer. Usually they refer to conditions that allow ready evaluation or comparison with reference values and often they refer to conditions that can be easily measured and/or corrected. For example, to allow a good comparison of specific impulse for several propellants or rocket propulsion systems, the values are often corrected to the following standard conditions (see Examples 3-4 and 3-5):

b. p2=p3 = 14.69 psia (sea level) or 1.0132 x 105 Pa or 0.10132 MPa.

d. Nozzle divergence half angle a = 15° for conical nozzles, or some agreed-upon value.

e. Specific propellant, its design mixture ratio and/or propellant composition.

/. Propellant initial temperature: 21°C (sometimes 20 or 25°C) or boiling temperature, if cryogenic. A rocket propulsion system is generally designed, built, tested, and delivered in accordance with some predetermined requirements or specifications, usually in formal documents often called the rocket engine or rocket motor specifications. They define the performance as shown above and they also define many other requirements. More discussion of these specifications is given as a part of the selection process for propulsion systems in Chapter 17.

4. Rocket manufacturers are often required by their customers to deliver rocket propulsion systems with a guaranteed minimum performance, such as minimum F or Is or both. The determination of this value can be based on a nominal value (items 1 or 2 above) diminished by all likely losses, including changes in chamber pressure due to variation of pressure drops in injector or pipelines, a loss due to nozzle surface roughness, propellant initial ambient temperatures, manufacturing variations from rocket to rocket (e.g., in grain volume, nozzle dimensions, or pump impeller diameters, etc.). This minimum value can be determined by a probabilistic evaluation of these losses and is then usually validated by actual full-scale static and flights tests.

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