1997年NASA RL10A-3-3A火箭发动机建模项目：关键技术研发与应用

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RL10A3-3A火箭发动机建模NASA项目是一份发表于1997年2月的学术文章，由NASA的三位作者——Michael Binder、Thomas M. Tomsik 和 Joseph P. Veres 主导。这篇研究主要关注于RL10A-3-3A火箭发动机的详细建模工作，这是一项关键的航空航天工程任务，旨在通过数值模拟和数据分析来理解和优化火箭发动机的性能。该研究项目的种子讨论、统计信息以及作者们的个人资料可在ResearchGate上获取（<https://www.researchgate.net/publication/24317266>），展示了18次引用和695次阅读量，反映出其在航天技术领域的专业认可度。Thomas Tomsik和Joseph P. Veres不仅参与了这个项目，还在其他相关项目中发挥着重要作用，如左心室辅助装置设计（LVAD Design View project）和数值推进系统模拟（Numerical Propulsion System Simulation, NPSS）项目。文章内容包括了对RL10A-3-3A火箭发动机的整体概述，详细描述了发动机系统的配置和操作特性。这可能涉及发动机的工作原理、燃烧室的设计、喷射推进系统、涡轮泵性能分析以及控制系统等方面的研究。通过对这些关键组件的模型建立，研究人员能够预测发动机在不同工况下的性能表现，评估其效率和可靠性，并为火箭发射计划提供数据支持。作为NASA的一份技术备忘录（Technical Memorandum），107318号文档，该报告可能是为了内部分享和外部同行评审而编写的，旨在推动火箭发动机技术的发展，同时满足NASA对于精确和安全的航天器动力源的高要求。总体而言，RL10A3-3A火箭发动机建模项目是航天工程领域的重要研究，它结合了理论建模、实验数据和实际应用，对提升火箭发动机的性能、优化火箭发射流程以及推动相关技术进步具有深远的影响。

Use the new system model to characterize the effects of variations in operating

conditions on system performance (time to accelerate, steady-state levels, etc.).

Benchmark our overall analytic capabilities for rocket propulsion systems.

4. COMPONENT MODELING RESULTS

4.1 Turbomachinery Modeling Results

4.1.1 Verification of Pumo Performance Test Data

Several sources of RL10 pump performance data exist. The systems group at Pratt & Whitney

provided NASA LeRC with a set of pump performance maps and polynomial functions. We also

received a separate set of pump test data from the Pratt & Whitney turbomachinery group. The

first task was therefore to consolidate these different sources of data, if possible.

The performance maps provided by the P&W systems group show head coefficient and efficiency

as functions of flow coefficient for each of the three pump stages. Maps of speed correction

factors to pump efficiency were also provided. The performance characteristics of the fuel and

LOX pump inducers had been lumped with those of the impellers in these maps. These maps are

shown in Figures 4.1.1 through 4.1.8.

Comparison of these map data with those provided by the turbomachinery group indicate that the

two data sets are approximately the same. It appears, however, that the maps provided by the

systems group are actually extrapolations from test data for flow coefficients greater than 0.62.

This conclusion was supported by subsequent discussions with P&W engineers. A number of

other small discrepancies (on the order of 1% to 2%) were also noted, and may be due to non-ideal

speed effects, changes in fluid density between pump stages, or differences in rotating clearance.

Despite these minor differences, it was concluded that the performance maps provided by the P&W

systems group axe based on test data for flows near the design conditions. Map data at very high

values of flow coefficient were, however, concluded to be extrapolations only, and can be replaced

when extending the maps to cover start conditions.

4.1.2 Extension of Pumn Maos for Start and Shutdown Conditions

At start, the pumps are n& ro_ting although there is an appreciable cool-down flow. The flow

coefficients during start are much higher than the values found in the test data, and it is necessary

to extend the maps to cover this region of operation. During shutdown, a very wide range of flow-

coefficients are encountered; both cavitation and surge are likely to occur.

The first consideration that must be addressed when extending the pump maps is their form. In

order to represent pump performance for conditions ranging from zero speed with non-zero flow to

the zero flow with non-zero speed, a rather unconventional map form is required. Common

practice is to plot pump performance as efficiency and head-coefficient (which is the head divided

by speed-squared) as a function of flow coefficient (which is volumetric flow divided by speed).

Using this mapping approach, however, the head-coefficient and flow-coefficient would both be

undefined (infinite) at zero speed. A less conventional approach is to map head and torque, divided

by the sum of the squares of the volumetric flow and speed, plotted versus the arctangent of speed

over flOW.

h = AHead / (N2 + Q2) vs. amn(N/Q)

[} = Z / (N2 + Q2) vs. atan(N/Q)

This method eliminates most concerns of zero quantities producing singularities. To simplify the

comparison with generic map curves, it is possible to normalize these relations using the head,

torque, speed, and volumetric flow at the point of maximum pump efficiency (Reference 3).

4.1.2.1 Extension of Pump Maps to START Conditions : In order to extend the RL10

pump maps to cover the start conditions, two approaches were considered. The first

approach considered was to use detailed one-dimensional pump performance analysis

progrmns. These codes use the pump geometry and inlet fluid conditions to predict the

head-rise and efficiency as functions of flow and shaft speed (References 4 and 5). In

order to test the accuracy of the detailed pump models, the predicted performance was

compared first with test data at conditions around the engine design point. The predicted

head maps were reasonably close to test data but the predicted efficiencies were

significantly lower than test data would indicate. Normally, empirical data would be used

to adjust certain parameters in the model to match the pump design performance. This was

not done for the RL10 because one of our research objectives was to test our capability to

model new designs for which test data does not yet exit Because this design-point

adjustment to test data was not done for the RL10, there was some doubt on how accurate

predictions of the low-speed performance would be. Low-speed pump simulations were

done to provide qualitative information about performance at start. A more detailed

discussion of these analyses are given in Appendix B.

The second approach considered was to use a combination of available test data, qualitative

information from the detailed analyses, and generic pump performance curves found in

References 3, 6, and 7. The generic maps were derived primarily for water pumps; their

application to cryogenic pumps appears valid based on the results from the detailed

analyses. The generic pump maps and analysis results were used to define only the shapes

of the map extensions; these curve shapes were fit to match the RL10 pump test-stand data

at near-design conditions.

The generic performance curves for head-rise and torque (from Reference 3) are shown in

Figures 4.1.9. There were two basic shapes that the genetic data could take for head-rise,

one curve levels off at low-speeds and the other shape turns down (depending on pump

specific-speed). The detailed pump analyses indicated that the head curves would turn

down at low speeds for the first stage fuel pump; this might be due to the backward sweep

of the impeller or the axial flow through the inducer section. These analyses also indicated

that the second stage fuel pump and LOX pump head-rise maps should level-out at low

speeds; these pump stages have radial blades, although the LOX pump also has an axial-

flow inducer. Simple subsystem models of the pumps were used to find zero-speed map

values that would be consistent with engine test data. Finally, complete performance

curves were fit to match the test data at higher speeds, pass through the zero-speed

intercepts and have the desired shape for each pump stage. The final results are shown in

Figures 4.1.10 through 4.1.15. The extended torque performance curves shown in the

figures are further modified by the appropriate speed correction curves given in Figures

4.1.5 and 4.1.8.

4.1.2.2Extension of Pumo Mars to SHUT-DOWN Conditions : During the engine

shutdown, a different combination of off-design conditions appears to exist, including

pump cavitation and reverse flow. Proper simulation of these effects is complicated by

their interaction with each other. From available test data and simulation output, it appears

that as the fuel inlet valve closes and the cool-down valves open, the pump first cavitates

due to a combination of changes in pump loading and cut-off of the inlet flow. The

cavitation causes the pump performance to degrade rapidly until the pump cannot prevent

the reverse flow of fluid as it comes backward through the cooling jacket. When the

reversed flow reaches the closed fuel inlet valve, however, extreme transients of pressure

and flow are created. Similar effects are encountered in the LOX pump during shutdown

as well.

The pump bead and torque performance characteristics during, this period of operation are,

of course, not extensively documented in test data. The genenc pump characteristics found

in References 3 and 6 have been used again to extend the .performance .maps for cavitation

and reverse flow. The maxima and minima of the curves m this operating regmn were

varied until a reasonable match with engine shutdown test data was achieved. Due to

limitations of schedule and manpower, no attempt was made to predict the post-cavitation

and stall behavior of the pumps using the detailed component analysis tools available. It is

likely, in any case, that these tools would require significant modification to examine such

pump conditions; modifications of this kind were beyond the scope of this projecL

The pump map extensions for engine shutdown are included in Figures 4.1.10 through

4.1.15. Although the engine start and shutdown models use the same pump performance

maps, the cavitation and reverse flow effects also require additional logic. This logic is not

required (or even desirable) in the start model. The interested reader is referred to

subroutines PUMPSD, FPASDMP, FPBSDMP and OPSDMP in the model (see Appendix

A) for documentation of these changes.

4.1.2.3 Effects of Density Changes on Pumo Performance Models : The issue of

propellant phase-change (liquid to gas) has not been adequately adomssed in the generic

maps or detailed analyses described above. It has been noted that using cryogens,

numerical instabilities were encountered in the start simulation due to the effects of fluid

changing density in the pumps. Engine test data, although limited, appears to indicate that

these density instabilities do not actually occur in the pumps during start. In order to obtain

stable and reliable calculations, it was necessary to limit density changes within each stage

of the pumps until pumped operation begins. For the start simulation, if the discharge

density is lower than the inlet density, the discharge pressure is calculated from head-rise

using only the inlet density.

Pdischarge = Pinlet + AHead * pimet

Once pumped operation begins, the standard expression for discharge pressure is used in

the start model:

Paisclaarge = (PinldPinlet + AHead) * pdischarge

During engine shutdown, the propellant densities at the pump inlets may, in reality,

approach zero. Numerical instabilities will arise using either the upstream or downstream

density alone. For the shutdown model, we will instead use the average fluid density:

Pdischarge = ]>inlet + AHead * Paverage

This expression is used throughout the shutdown model regardless of conditions at the

inlet or discahrge. Because the expressions for discharge pressure differ between start and

shutdown models, the predicted steady-state operating points will also be slightly different

for the two models.

4.1.3 Verification of Fuel Turbine Performance Test Data

The turbine performance maps provided by Pratt & Whimey depict the combined performance of

the two stages. The turbine's flow resistance is modeled as isentropic flow through an orifice and

the map describes the effective area (area times discharge coefficient) as a function of velocity ratio

(u/Co) for several different pressure ratios. In the course of this project, two different flow-

resistance models were found. The fast model was based on linear functions and were intended

for use only near the design operating conditions. The second model was represented by non-

linear map curves and were apparently better suited for start transient engine simulations. The two

models unfortunately disagree at the design point, which has lead to errors in engine steady-state

performance predictions. Attempts to consolidate the two data sets have not been satisfactory.

Nor have we been able to locate additional data or human experts who could resolve the differences

in data. We decided to use the transient (non-linear) data map (as shown in Figure 4.1.16) and

accept the steady-state error for now. Additional research may succeed in resolving this conflict in

the future.

The combined two-stage turbine efficiency map provided by P&W is shown in Figure 4.1.17. No

additional data was available to cross-check this map.

4.1.4 Extension of Turbine Maps

The turbine maps provided by Pratt & Whitney (as discussed above) already extend to the low

speed region (to zero speed) and did not require extension (see Figures 4.1.16 and 4.1.17).

Although these maps may also have been extrapolated from higher speed data, the low-speed

information was judged to be reasonable for the turbine.

In order to calculate the starting torque of the turbine (no rotation as flow starts), it was necessary

to address a zero-divided-by-zero problem (zero efficiency divided by zero speed). This was

resolved using 1-Hopital's Rule, which states that when approaching a 0/0 point, the value of the

ratio is the same as the slope of the ratio at that point. It was found that using this solution, the

predicted starting torque approximately equals the value estimated from engine test data.

A detailed component analysis of the turbine was also performed for this project (Reference 8).

Preliminary analyses predicted overall (two-stage) turbine efficiency values that were 2% to 10%

lower than those specified by Pratt & Whitney. The modeling results for turbine flow resistance

were not able to resolve the conflict between the two different data sets as discussed in the previous

section. As with the pump analysis discussed previously, it is common practice to adjust the

turbine model to better match test data, when available. Such adjustments were considered

inconsistent with the research goal of benchrnarking our capability to model new designs, and

therefore no adjustments were made. The detailed turbine analysis was not pursued further but is

described in Appendix C.

In the course of our modeling work with the RL10 turbine, it was discovered that even slight

differences in the turbine efficiency map may cause sig.nificant differences, in.the s.h_'t,tin_._ g. of the

engine. The extreme sensitivity of the engine start taming to small vanauons m mrome emcaency

may have profound significance for our ability to accurately model the start of new engines for

which detailed component test data is not yet available. This issue is discussed in greater detail in

Appendix C.

4.2 Combustion and Heat Transfer Modeling Results

4.2.1 Enhanced combustion _as properties

The ROCETS code (Referenc_ 9) was originally developed with a built-in set of hydrogen/oxygen

combustion tables. These tables provided gas thermal and transport properties at a specified

pressure, temperature and mixture ratio. Many of the calculations in these tables involved applying

corrections to more basic tables and assumed ideal, isentropic gas behavior. A comparison of the

property table output with the NASA CET93 one-dimensional-equilibrium (ODE) code (Reference

10) indicated some significant discrepancies. The original tables have therefore been replaced with

data tables generated specifically for the RL10A-3-3A model using the CET93 code. CET93 was

used to determine the equilibrium-composition hot-gas properties at several axial locations along

the length of the thrust chamber and nozzle.

Generating a complete set of tables for all conditions and expansion ratios proved to be more

difficult than expected. At the extreme limits of pressure and mixture ratio present during the RL10

start transient, the propellants may actually freeze as they expand through the nozzle, creating a

snow flurry at the engine discharge. Given the injector-face pressure, propellant mixture enthalpy

and mixture ratio, the pressure, temperature and enthalpy of the combustion products were

tabulated at several values of expansion ratio throughout the thrust chamber and nozzle. The other

thermal and transport properties required by the system model were tabulated as functions of

pressure, temperature and mixture ratio (and are not considered explicit functions of expansion

ratio). Table 4.2.1 gives the range of conditions and the expansion ratios included in the new

RL10 hot-gas property tables.

4.2.2 Cooling, Jacket Heat Transfer Model

In this projec-t, several approaches were explored for modeling the heat-transfer in the RL10A-3-

3A cooling jacket. These approaches included empirical models, first-principle physical models,

and several combinations of theory and test data. In this section, we describe only the analytic

approach selected for the final engine system model. The other methods which we considered are

discussed in greater detail in Appendix D.

Predicting heat transfer appears to be something.of an art. "ll_e orig.in_ jacket cooling model for

the RL10 steady-state model was based on test data alone aria was maaequam for predicting

transient heat transfer behavior. Subsequent cooling jacket models used in the RL10 system model

have been more sophisticated and scientific but also tend to be less accurate in reproducing test

data. Several expert sources have indicated that the state of the art in predicting heat transfer

behavior is +/- 20% accuracy (Reference 11). Greater accuracy was desired for the RL10A-3-3A

system model.

The detailed one-dimensional analysis was performed using the RTE (Reference 12) program

developed by NASA. RTE calculates hot-gas-side heat transfer based on the enthalpy gradient,

which predicts the variation of heat transfer coefficient with mixture ratio more accurately than

models based on temperature gradient. The RTE program also calculates the effects of tube

curvature on heat transfer to the coolant. The basic form of the equations used to predict heat

transfer are shown below.

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