Proposal for a Nuclear Analysis of Clustered Reactor Interations

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Proposal for a Nuclear Analysis of Clustered Reactor Interactions DEPARTMENT OF ENERGY DECLASSIFICATION REVIEW ADVANCED TECHNOLOGY SERVICES

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This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency Portions of this document may be illegible in electronic image products. Images are produced from the best available

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This document is a proposal prepared by the General Electric Company. The material is to be used only for evaluation to determine whether an award should be made, subject to the negotiation of a contract. The General Electric Company, therefore: A. Makes no warranty or representation, express or implied, with respect to any application, except for evaluation, of the information contained in this proposal, or that the use of any information, apparatus, material, method, or process disclosed in this proposal may not infringe privately owned rights; and B. Assumes no liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, material, method, or process disclosed in this

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Proposal for a Nuclear Analysis of Clustered Reactor Interactions NUCLEAR MATERIALS and PROPULSION OPERATION ADVANCED TECHNOLOGY SERVICES

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The ability to cluster nuclear rocket engines would provide increased flexibility to the mission analyst and vehicle designer in the selection of thrust levels for a stage and also reduce the number of engines that would have to be developed. Reducing the required num ber of different size engines would greatly reduce the cost of developing and fabricating engines, conducting qualification testing, and the required facilities. Vehicle and mission studies made to date indicate that the potential flexibility and cost reductions are of great interest. In these studies, however, the interaction of clusters of engines has only been approximated and a quantitative assessment of the actual effect of clustering on system performance has not been possible. However, in order to realistically determine the de sirability of clustering, an accurate evaluation of the problems associated with the use of clustered nuclear rocket engines should be undertaken. Many questions must be answered, such as the weight and cost trade-off of multiple small engines versus a large single engine for a given reliability level and the added or modified shielding requirements. However, a valid assessment of these effects is dependent upon an accurate determination of the nuclear interaction between adjacent engines in the cluster. Several analyses of the nuclear interaction of clustered reactors have been per formed by GE-NMPO personnel with various degrees of sophistication in recent nuclear rocket investigations and earlier design studies. None of these analyses provided com pletely satisfactory solutions. However, they revealed the complexity and difficulty of the problem and illustrated the need for methods of providing accurate interaction information. A well-controlled experiment would provide the best determination of the interaction be tween adjacent nuclear engines. In a ground-based experiment, however, the effects of ground and air scattering as well as irrelevant structural effects, would produce results of questionable reliability. It would be more desirable to perform the experiment under fully controlled conditions. This approach can be closely approximated through the use of computer programmed Monte Carlo techniques. The accuracy of the Monte Carlo solution would be limited only by the uncertainty in the basic nuclear reaction cross sections used in the calculations. Less exact programs than Monte Carlo may also be used. Past experience with some of these approximate methods has resulted in uncertainties of approximately the same size as the effect which was being calculated. However, the use of these approximate methods, when calibrated against either an experiment or an accurate calculation such as proposed here, might be economical and sufficiently accurate for systems analysis work. / The interaction between two nuclear engines consists of an exchange of neutrons and gamma radiation. The neutron exchange appears td up the more significant, for reasons discussed below. The gamma ray exchange is also significant, but it affects individual components of the engines rather than resulting in a systematic interaction^ The neutron interaction of primary importance can be described as the fission power produced in one engine by the neutrons leaking from the other engine. The effect of this

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added power production will vary with the operating condition of the target engine. If the target engine is operating at design power, the added fission power will produce an asym metric perturbation of the power distribution and increase the multiplication factor. The power perturbation causes a fuel element temperature perturbation which can be alleviated by power or flow adjustments. These adjustments will result in a reduction in the average maximum surface temperature and a corresponding reduction in exit gas temperature and The effect of the gamma ray transport between two operating engines will be increased local heating rates in the adjacent nozzle, pressure shell and, depending upon the configura tion, the pump, gimbal, and support structure. The interaction between an operating engine and a shutdown engine presents a more com plex problem. If the target engine has been shut down by virtue of the required mission se quence and is not to be jettisoned, the amount of coolant, if any, required to prevent dam age to it must be determined. If it is to be jettisoned, the only information required is the allowable reaction time before the over-temperature of the target engine produces destruc tive effects on other vehicle components. In the determination of the required coolant flow, several factors must be calculated. Most important of these is the determination of the total amount of fission power produced in the shutdown engine due to the leakage neutrons from the operating engine. As the mul tiplication factor of the shutdown engine will still be significant, the incident neutrons will be multiplied and will produce power in the target engine. Concurrently, secondary heat will be generated in the shutdown engine by fission product decay and neutrons and gamma rays from the operating engine. The magnitude of this total power production in the target engine must be known to determine what coolant flows are required to maintain the integrity of the engine, and subsequently power for pumping the coolant. The target engine's own turbopump may not be able to use the same energy as during normal operation. Therefore, energy storage for this coolant flow may be required or may have to be diverted from the operating engine. Either of these methods of providing coolant flow would result in a degra dation of overall propulsion system performance because the coolant would be discharged from the shutdown reactor at considerably below the design temperature. From this description of the problem, the information required for a quantitative assess ment of the interaction between two engines can be established. Although only the interaction between two engines has been discussed, the interaction between engines in clusters of more than two can be determined by the superposition of the two-engine solution on pairs of en gines in a multiple-engine cluster. The results of the proposed analysis will be the basic standard for evaluation of the inter action between two nuclear engines. This standard would then be used to determine the ade quacy of more approximate, less expensive methods suitable for parametric interaction evaluations. An obvious corollary problem is an evaluation of means of isolating the two engines to reduce the nuclear interaction. An artist's concept of a two-engine cluster is shown in Figure 1.

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GE-NMPO proposes to perforin a study which will provide an accurate determination of the interaction of two clustered nuclear rocket engines. Using the results as a reference, an evaluation will then be made of the accuracy and suitability of more approximate methods for economical use in vehicle and mission parametric studies. The scope of the study con sists of the following: 1. Establish a reference configuration of two identical nuclear rocket engines. The engines chosen will utilize a fast-spectrum, refractory-metal reactor, in the 30,000pound-thrust size, of the type being studied for the Air Force under Contract No. AF 04 (611)-9068. The engines will be separated by a fixed distance for the accurate calculation. This configuration will extend to the upper structure of the engines but will not include vehicle-associated components. 2. Calculate the fission power distribution and reactivity of the sdurce reactor incorpo rating the reflection of neutrons from the target engine. 3. Calculate the fission power distribution and reactivity of the operating target reactor due to neutron leakage from the source engine. 4. Establish the total fission power generation in the target engine in the shutdown con 5. Calculate the heating caused by the gamma rays originating from the source engine in several components of the target engine including, but not restricted to, the nozzle, pressure shell, and representative upper structure. 6. Determine the foregoing quantities utilizing approximation methods for the defined separation and, if the approximation methods are found to be suitable, for three 7. The above calculations will be repeated for a configuration in which isolation is pro vided. The approximation methods will again be compared with the results of the accurate analysis. If the approximate methods are found to be satisfactory, the ef fect of increased barrier thickness will be determined by the approximate methods. If they are not satisfactory, other means of obtaining the parametric information will be recommended. After establishing the configuration, the study will be performed in the following steps. Step 1 - A neutron analysis of the source reactor will be performed by use of one-di Step 2 - Utilizing the neutron source distribution determined in Step 1, the energy and angular distribution of the neutrons leaking from the source reactor will be determined by the use of a cylindrical Monte Carlo method. Step 3 - With the surface source of neutrons established in Step 2, the transport of the neutrons from the surface and the penetration into the target engine will be determined by a flexible geometry Monte Carlo calculation. This calculation will also provide the spatial energy and angular data on the neutrons reflected from the target engine.

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Step 4 - The spatial power distribution in the target engine will be determined as a function of the azimuthal angle; also, the effect on reactivity in both the shutdown and operating conditions will be determined. The method used for these calculations will be a two-dimensional transport theory formulation in the X-Y coordinate system, with the neutron penetration derived in Step 3 considered as a fixed source contribution. Step 5 - The gamma heating in the target engine will be calculated using point kernel techniques. The point kernel calculations will utilize source spatial and energy distri butions determined by the neutron analysis performed in Step 1. Step 6 - The information obtained in Steps 1 to 4 will be obtained, using point kernel calculations to replace the more accurate methods used in Steps 2 and 3. Step 7 - If the correlation of results of Steps 4 and 6 is not satisfactory, the data from Step 2 will be integrated over the surface of the source engine. This source will then be used for the point kernel calculation of the information obtained in Step 3. Step 8 - Using Step 6 methods, or Step 7 if necessary, the information obtained in Step 4 will be determined for three additional and different engine separation distances. Step 9 - Steps 3 to 8 will be repeated to determine the effect of isolation barriers on the interaction of the two engines. The data obtained from the above steps will therefore consist of: 1. The effect on the target engine for both perturbation of the operating power distri bution and the power generation in the shutdown condition. 2. The reactivity change in one engine caused by the adjacent operating engine or the reflecting effect of the adjacent engine. 3. The dependency of the effect in (2.) above on engine separation distances. 4. Gamma heating rates in the target engine due to source engine operation. 5. Leakage neutron patterns in angle, energy, and space suitable for translation to 6. Energy deposition in the barrier region. 7. An evaluation of the advantages and disadvantages of different methods of analyzing a. Fission source distribution in the source reactor. b. Primary and secondary gamma source distribution. c. The spatial, angular, and energy distribution of neutrons striking the target, reflected from the target, and then re-incident on the source engine. d. Neutron fluxes in the target engine due to the transported neutrons. Adequately funded, this clustering study could be performed in about 1 year, as shown in Figure 2. A more detailed discussion of several of the methods that would be used in this study is contained in the following Technical Discussion.

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The first four steps (listed in the Work Statement) of the proposed study will be per formed by means of detailed, cross-matched, one-dimensional transport theory; Monte Carlo computations; and two-dimensional transport theory calculations. For convenience, this is called Phase I of the study. Step 5, determining the gamma heating in the target engine, will be performed con currently with Phase I. Phase II will consist of Steps 6 through 9. 3.1 PHASE I - ANALYSIS OF THE SOURCE REACTOR (STEP 1) One-dimensional transport theory calculations will be made with multienergy, multi region Program S-XI** to predict longitudinal and radial distributions of the fission neu tron production in the source reactor. This code is the result of an extension of SN neutron codes^S to a variational optimum formulation. It uses Carlson's composite discrete-point and piecewise-linear digital representation, as weU as selected portions of his integration method. It calculates the flux and adjoint simultaneously from the flux and adjoint transport equations, respectively, and solves for the eigenvalue of interest in an integrated action principle that essentially eliminates first-order errors in the solution. Perturbation theory integrals are calculated for selected materials for a first-order perturbation theory equa tion that is derived from the integrated action principle and is at the transport level of Unlike the one-dimensional diffusion equation, the one-dimensional transport equation is not separable. Consequently, one-dimensional radial and longitudinal transport cal culations must assume infinite dimensions in the transverse direction. Transverse leak age probabilities in the form of fictitious macroscopic absorption cross sections will be used to account for transverse leakage from the active core. Transverse leakage from extra-core components will be neglected. Initially, a radial calculation will be made assuming no transverse leakage. The output of this analysis will …