The propellants, which are the working substance of rocket engines, constitute the fluid that undergoes chemical and thermodynamic changes. The term liquid propellant embraces all the various liquids used and may be one of the following:

1. Oxidizer (liquid oxygen, nitric acid, etc.)

2. Fuel (gasoline, alcohol, liquid hydrogen, etc.).

3. Chemical compound or mixture of oxidizer and fuel ingredients, capable of self-decomposition.

4. Any of the above, but with a gelling agent.

A bipropellant rocket unit has two separate liquid propellants, an oxidizer and a fuel. They are stored separately and are not mixed outside the combustion chamber. The majority of liquid propellant rockets have been manufactured for bipropellant applications.

A monopropellant contains an oxidizing agent and combustible matter in a single substance. It may be a mixture of several compounds or it may be a homogeneous material, such as hydrogen peroxide or hydrazine. Monopropellants are stable at ordinary atmospheric conditions but decompose and yield hot combustion gases when heated or catalyzed.

A cold gas propellant (e.g., nitrogen) is stored at very high pressure, gives a low performance, allows a simple system and is usually very reliable. It has been used for roll control and attitude control.

A cryogenic propellant is liquified gas at low temperature, such as liquid oxygen (-183°C) or liquid hydrogen (-253°C). Provisions for venting the storage tank and minimizing vaporization losses are necessary with this type.

Storable propellants (e.g., nitric acid or gasoline) are liquid at ambient temperature and can be stored for long periods in sealed tanks. Space storable propellants are liquid in the environment of space; this storability depends on the specific tank design, thermal conditions, and tank pressure. An example is ammonia.

A gelled propellant is a thixotropic liquid with a gelling additive. It behaves like a jelly or thick paint. It will not spill or leak readily, can flow under pressure, will burn, and is safer in some respects. It is described in a separate section of Chapter 7.

The propellant mixture ratio for a bipropellant is the ratio at which the oxidizer and fuel are mixed and react to give hot gases. The mixture ratio r is defined as the ratio of the oxidizer mass flow rate m0 and the fuel mass flow rate rhf or r = m0/mf (6-1)

The mixture ratio defines the composition of the reaction products. It is usually chosen to give a maximum value of specific impulse or Tx /®t, where Tx is the combustion temperature and 9Jf is the average molecular mass of the reaction gases (see Eq. 3-16 or Fig. 3-2). For a given thrust F and a given effective exhaust velocity c, the total propellant flow is given by Eq. 2-6; namely, m — w/g0 — F/c. The relationships between r, m, m0, and rhf are m0 + rhf — m (6—2)

These same four equations are valid when w and w (weight) are substituted for m and m. Calculated performance values for a number of different propellant combinations are given for specific mixture ratios in Table 5-5. Physical properties and a discussion of several common liquid propellants and their safety concerns are described in Chapter 7.

Example 6-1. A liquid oxygen-liquid hydrogen rocket thrust chamber of 10,000-lbf thrust operates at a chamber pressure of 1000 psia, a mixture ratio of 3.40, has exhaust products with a mean molecular mass of 8.9 lbm/lb-mol, a combustion temperature of 4380°F, and a specific heat ratio of 1.26. Determine the nozzle area, exit area for optimum operation at an altitude where />3 = p2 = 1.58 psia, the propellant weight and volume flow rates, and the total propellant requirements for 2 min of operation. Assume that the actual specific impulse is 97% of the theoretical value.

SOLUTION. The exhaust velocity for an optimum nozzle is determined from Eq. 3-16, but with a correction factor of g0 f°r the foot-pound system.

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The theoretical specific impulse is c/g0, or in this case v2/g0 or 13,900/32.2 = 431 sec. The actual specific impulse is 0.97 x 431 = 418 sec. The theoretical or ideal thrust coefficient can be found from Eq. 3-30 or from Fig. 3-6 (p2 = />3) to be CF = 1.76. The actual thrust coefficient is slightly less, say 98% or CF = 1.72. The throat area required is found from Eq. 3-31.

A, = F/{CFp\) = 10,000/(1.72 x 1000) = 5.80 in.2 (2.71 in. diameter)

The optimum area ratio can be found from Eq. 3-25 or Fig. 3-5 to be 42. The exit area is 5.80 x 42 = 244 in.2 (17.6 in. diameter). The weight density of oxygen is 71.1 lbf/ft3 and of hydrogen is 4.4 lbf/ft3. The propellant weight flow rate is (Equation 2-5)

The oxygen and fuel weight flow rates are, from Eqs. 6-3 and 6-4, w0 = wr/(r + 1) = 24.0 x 3.40/4.40 = 18.55 lbf/sec wf = w/(r + 1) = 24/4.40 = 5.45 lbf/ sec

The volume flow rates are determined from the densities and the weight flow rates.

K = w0/p0 = 18.55/71.1 = 0.261 ft3/sec Vf = wf/pf = 5.45/4.4 = 1.24 ft3/ sec

For 120 sec of operations (arbitrarily allow the equivalent of two additional seconds for start and stop transients and unavailable propellant), the weight and volume of required propellant are w0 = 18.55 x 122 = 2260 lbf of oxygen wf = 5.45 x 122 = 665 lbf of hydrogen V0 = 0.261 x 122 = 31.8 ft3 of oxygen Vf = 1.24 x 122 = 151 ft3 of hydrogen

Note that, with the low-density fuel, the volume flow rate and therefore the tank volume of hydrogen are large compared to that of the oxidizer.

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