Discrepancies in thrust chamber dimensions for RL10

Question

I've recently been developing some automated scripts in Python for the purpose of calculating engine parameters. I've been using the RocketCEA interface library, which links to NASA's Chemical Equilibrium with Applications (CEA) code and produces combustion data. I've been developing these scripts for a separate application, but I decided to run it using the data for the RL10A-3-3A as a sanity check.

I'm using Barrére et al. (1960) as well as Huzel & Huang (1991), which gives the following steps:

$$\begin{align} \Gamma &= \sqrt{\gamma} \Big( \frac{2}{\gamma + 1} \Big)^{\frac{\gamma + 1}{2(\gamma - 1)}} \\[5pt] c^* &= \frac{\sqrt{\mathfrak{R}T_c}}{\Gamma} \\[5pt] C^{\circ}_{F} &= \Gamma \sqrt{\frac{2\gamma}{\gamma - 1}\Big[1 - \Big(\frac{p_e}{p_c}\Big)^{\frac{\gamma - 1}{\gamma}}\Big]} + \varepsilon \Big(\frac{p_e - p_a}{p_c}\Big) \\[5pt] A_t &= \frac{F}{C^{\circ}_{F} \cdot p_c} \end{align}$$

I used CEA to obtain the frozen-equilibrium thermodynamic parameters for the RL10A-3-3A at a chamber pressure of 475 psia, a mixture ratio of 5.00:1 and an expansion ratio of 61.0:1. Computing the above equations gives $\Gamma = 0.6389$, $c^* = 2,364.4 \,\text{m/s}$, and $(C^{\circ}_{F})_{vac} = 1.9844$. These result in a (purely theoretical, efficiency-unadjusted) $I_{sp}$ of 478.4 s, which is in the ballpark of the RL10A's 440.3 s real-world $I_{sp}$.

However, when I go to calculate the throat dimensions, I obtain values which are not in agreement with published sources. Applying the final throat-area equation for the stated inputs gives an area of 112.9 cm² or a diameter of 11.99 cm (4.72 in). However, Binder, Tomsik, & Veres (1997) (p. 6, Table 2.5.1) give values of 2.47 in for the throat diameter (a 91% difference between the two). However, calculations in an archived sci.space.tech posting is within 10% agreement of my calculated diameter values here for the same RL10 variant (13.1 cm as opposed to 12.0 cm).

Is there an error in my calculations, and if so, how do I rectify it to get better agreement with published engine data?

Answer 1

I think your calculations are OK.

It seems incredible, but the 2.47 inches seems to be the throat radius.

This Pratt paper DESIGN, FABRICATION, AND TEST OF THE RL10 DERIVATIVE II CHAMBER/PRIMARY NOZZLE flat out states

The throat diameter was also reduced from 2.57 inches for the RL10A-3-3 to 2.472 inches for the Derivative II engine

(emphasis mine)

But then shows this image labeling it as a radius

The table on this page (which seems to be extracted from the firewalled paper Evolution of the RL10 liquid rocket engine for a new upperstage application gives throat diameters in the 5 - 6 inch range.

Also the Pratt paper Design Study of RL10 Derivatives Volume 2 says

The Category II engine, as defined in the previous study, uses the same chamber and nozzle as the RL10A-3-3

and then gives the throat diameter as ~5 inches.

Even the Binder etc. paper you quote says

by comparing the effective flow area of the nozzle specified by Pratt & Whitney (18.85 in2) with the actual physical area of the throat (19.19 in2)

Which gives a radius of ~2.5 inches, not a diameter.