A computational conjugate heat transfer methodology was developed and anchored with data obtained from a hot-hydrogen jet heated, non-nuclear materials tester, as a first step towards developing an efficient and accurate multiphysics, thermo-fluid computational methodology to predict environments for hypothetical solid-core, nuclear thermal engine thrust chamber. The computational methodology is based on a multidimensional, finite-volume, turbulent, chemically reacting, thermally radiating, unstructured-grid, and pressure-based formulation. The multiphysics invoked in this study include hydrogen dissociation kinetics and thermodynamics, turbulent flow, convective and thermal radiative, and conjugate heat transfers. Predicted hot hydrogen jet and material surface temperatures were compared with those of measurement. Predicted solid temperatures were compared with those obtained with a standard heat transfer code. The interrogation of physics revealed that reactions of hydrogen dissociation and recombination are highly correlated with local temperature and are necessary for accurate prediction of the hot-hydrogen jet temperature

Foote, John

Litchford, Ron

Wang, Ten-See

NASA Technical Reports Server

Source of Acquisition 
NASA Marshall Space Flight Center 
An extended abstract for Heat Transfer in Nuclear Systems, 9th AIMASME Joint Thermophysics and Heat 
Transfer Conference, San Francisco, CA, 5-8 June 2006 
Analysis of Material Sample Heated by Impinging Hot 
Hydrogen Jet in a Non-Nuclear Tester 
Ten-See Wang*, John Foote, and Ron Litchford 
NASA Marshall Space Flight Center, Huntsville, Alabama, 35812 
A computational conjugate heat transfer methodology was developed and anchored with 
data obtained from a hot-hydrogen jet heated, non-nuclear materials tester, as a first step 
towards developing an efficient and accurate multiphysics, thermo-fluid computational 
methodology to predict environments for hypothetical solid-core, nuclear thermal engine 
thrust chamber. The computational methodology is based on a multidimensional, finite- 
volume, turbulent, chemically reacting, thermally radiating, unstructured-grid, and 
pressure-based formulation. The multiphysics invoked in this study include hydrogen 
dissociation kinetics and thermodynamics, turbulent flow, convective and thermal radiative, 
and conjugate heat transfers. Predicted hot hydrogen jet and material surface temperatures 
were compared with those of measurement. Predicted solid temperatures were compared 
with those obtained with a standard heat transfer code. The interrogation of physics 
revealed that reactions of hydrogen dissociation and recombination are highly correlated 
with local temperature and are necessary for accurate prediction of the hot-hydrogen jet 
temperature. 
I. Introduction 
uclear thermal propulsion (NTP) may open up the solar system to far broader and faster exploration than is N now possible with chemical propulsion. The feasibility of NTP systems was established by extensive testing in 
the Rover/NERVA programs and the technical merits of NTP have been identified and summarized.’ The heat 
transfer efficiency and degree of hydrogen dissociation are two important performance factors for NTP. On the other 
hand, the need to push fuel element temperature to extremes in order to maximize performance also intensifies 
hydrogen induced corrosion rates, which are known to increase in direct proportion to reactor operating 
temperature.’ In order to develop candidate high temperature fuel materials that would be compatible with the hot- 
hydrogen environment of a high performance solid core NTP engine, a non-nuclear test effort entitled “Hot 
Hydrogen Materials and Component Development” is underway at NASA’s Marshall Space Flight Center (MSFC), 
while a parallel task entitled “Multiphysics Thrust Chamber Modeling” is also in progress in order to develop a 
computational methodology capable of predicting the thermal-fluid environment in a nuclear thermal engine thrust 
chamber. This computational methodology is based on an Unstructured-grid Navier-Stokes Internal-external 
computational fluid dynamics (CFD) Code (UNIC). Physical and numerical models pertinent to solid-core NTP will 
be developed and implemented. In this effort, as a first step, the hot gas and material temperatures to be measured in 
the hot-hydrogen materials development tests will be used to benchmark the UNIC code, while the computed solid 
temperatures will be compared with those obtained from a standard heat transfer code. The physics invoked in 
heating the materials with an impinging hot hydrogen jet are discussed and factors that may reduce the thermal 
gradient in the materials are investigated. 
11. Computational Methodology 
A. Computational Fluid Dynamics 
*Technical Assistant, ER43, Thermal and Combustion Analysis Branch, Propulsion Structure, Thermal, and Fluids 
Analysis Division, Senior Member AIAA. 
1 
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https://ntrs.nasa.gov/search.jsp?R=20060046690 2019-08-29T23:50:48+00:00Z
The CFD methodology is based on a multi-dimensional, finite-volume, viscous, chemically reacting, 
unstructured grid, and pressure-based formulation. Time-varying transport equations of continuity, species 
continuity, momentum, total enthalpy, turbulent kinetic energy, and turbulent kinetic energy dissipation were solved 
using a time-marching sub-iteration scheme and are written as: 
*+-(ou a j ) ' o  
at a x j  
A predictor and corrector solution algorithm was employed to provide coupling of the governing equations. A 
second-order central-difference scheme was employed to discretize the diffusion fluxes and source terms. For the 
convective terms, a second-order upwind total variation diminishing difference scheme was used. To enhance the 
temporal accuracy, a second-order backward difference scheme was employed to discretize the temporal terms. 
Details of the numerical algorithm can be found in Refs  3-7. 
An extended k-E turbulence model' was used to describe the turbulence. A modified wall function approach was 
employed to provide wall boundary layer solutions that are less sensitive to the near-wall grid spacing. 
Consequently, the model has combined the advantages of both the integrated-to-the-wall approach and the 
conventional law-of-the-wall approach by incorporating a complete velocity profile and a universal temperature 
profile6. A 2-species, 3-reaction detailed mechanism' was used to describe the hydrogen dissociation and 
recombination chemical kinetics. 
B. Computational Conjugate Heat Transfer in Solids 
The solid heat conduction equation can be written as: 
The solid heat conduction equation is solved with the gas-side heat flux distributions as its boundary conditions. 
--"(.%)=a, JpcT +Q, 
at axi 
where Q, and Q, represent source terms from volumetric and 
the thermal conductivity and capacity of the solid material, 
(7) 
boundary contributions, respectively. K and C denote 
respectively. The temperature value at the gas-solid 
interface is obtained by enforcing the heat flux conservation condition. The boundary heat flux is, 
qw = ( KZ) where qw is the heat flux from the fluid side. 
b 
Numerically, it is expressed as: 
2 
American Institute of Aeronautics and Astronautics 
Tc -Tb 
Y n  
qw = K- 
where yn represent the normal distance from the boundary to the center of the solid cell next to the boundary, T, is 
the temperature at the center of the solid cell and Tb is the temperature at the interface boundary. The source term for 
the cell is then calculated as: 
To avoid numerical oscillations, an under-relaxation parameter is assign when evaluating the boundary 
temperature from Eq. (9). This step affects the source term accuracy using Eq. (10). Also, the source term calculated 
from (10) can be very large when a case is started, depending of the initial condition specified. This also contributed 
to numerical instability in the solution procedure. To fix this problem, the source term, Eq. (lo), is separated into an 
explicit and an implicit parts. This source term linearization modification makes the solution procedure stable even 
for very large boundary heat fluxes. They are, 
The explicit source is added to the right-hand-side of the heat conduction equation while the implicit source term 
contributes to the diagonal terms of the final system of linear algebra equations. 
111. Test Fixture Description 
The test apparatus for testing tubular fuel materials is 
shown in Fig. 1. It is directly mated to an arc-heater (not 
shown) that provides hot-hydrogen flow. Optical ports 
are fitted to allow real-time pyrometer and laser 
diagnostics measurements for material surface 
temperature and centerline gas temperature, respectively. 
As the hot-hydrogen jet travels the length of the 
chamber, it loses energy to the water-cooled copper 
chamber and sample material. As the sample material 
heats up, it loses energy to the colder chamber wall by 
thermal radiation. A shield serving as both convective 
and radiative shielding was added through a detailed 
design analyses, resulting in minimum heat load on the 
water-cooled copper chamber wall and maximum hot 
hydrogen delivering temperature. 
I Optical Po? 
/ 
optical Port 
Fig 1. Test apparatus. 
IV. Computational Grid Generation 
Hybrid computational grids were generated using a software package GRIDGEN. A series of grid verification 
studies were performed to determine the current grid size. It was also found during the grid study that the computed 
gas-solid interface temperature is most stable when structured-grid layers are present on both sides of the interface. 
3 
American Institute of Aeronautics and Astronautics 
V. Boundary Conditions 
No-slip condition was applied to the solid walls. Fixed 
mass flow rate boundary condition was used at the inlet, 
and mass conservation boundary condition was used at the 
exit. For a conservative calculation of the chamber wall 
heat flux, a fixed temperature of 400 K was estimated for 
the chamber wall and the hot-hydrogen temperature was 
set at 3500 K. The wall temperature of the shield facing the 
chamber wall was estimated to be 2600 K from a separate 
one-dimensional heat transfer calculation. Adiabatic 
condition was applied to walls of opposing-side shield and 
flanges, and graphite insert (the convergent section). The 
hydrogen inlet mass flow rate was 10 g/s and the chamber 
pressure was 35 atm. An emissivity of 0.6 was applied to 
the copper chamber wall, whereas an emissivity of 0.4 was 
applied to the shield. The emissivity for the rest of the solid 
walls was set at 0.9. The inlet boundary was considered as 
a radiating wall to approximate the radiation h m  the arc- 
heater section. A series of pre-calculations were performed 
to iterate the inlet temperature and species concentrations 
such that the inlet species concentrations correspond to a 
state of temperature at 3500 K. 
VI. Results and Discussion 
Figure 2 shows typical computed temperature, H 
concentration contours and streamlines under normal test 
conditions. It can be seen from the temperature contours 
I I 
I I 
Fig. 2 From top to bottom, computed temperature and H 
Mass Fraction Contours and Streamlines. 
that the entire thrust chamber is almost uniformly heated, except for the region between the shield and the cooled 
chamber wall. This is because the shield serves as both convection and radiation shields. Nevertheless, the hot hydrogen 
jet loses energy as it heats up the sample. When that happens, H recombines to become H2. This is shown in the H 
contours where its concentration decreases as the hot jet approaches the sample. The streamlines show an expanding 
hot-hydrogen jet impinging on and flowing around the sample coupon, and later exhausting into the convergent exit 
section. A large recirculation zone appears in the divergent section of the chamber, while a small recirculation region 
forms behind the sample holder; both of which are strongly affected by the turbulence. Note although the plots in Fig. 2 
showing a distinctive strong hot-hydrogen jet and two 
recirculated flow regions, the pressure and Mach number 
contours are fairly uniform inside the chamber (not shown), 
due to the largely low subsonic flow field and the protection 
of the shield. The integrity of the sample being heated by 
such a high temperature environment is the subject of the 
test. 
Figure 3 shows typical temperature contours surrounding 
and inside the sample coupon. It can be seen that heat is 
being transferred from the impinging hot hydrogen jet to the 
sample coupon. For different materiais with different thermal 
properties, the thermal gradient inside the sample coupon 
will be different. The computed temperature contours inside the sample coupon appears to be reasonable. 
VII. Summary 
A computational conjugate heat transfer methodology was developed, to study the effect of hot hydrogen jet 
impinging on sample coupon made of different materials. The computational result of check out runs appears to be 
reasonable. A series of tests are scheduled from November to December. The test results will be used to benchmark 
the computational methodology. The computational methodology will then be used to perform parametric studies to 
assess factors that might reduce thermal gradient inside the sample material. 
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Acknowledgments 
This study was partially supported by a Nuclear Systems Office task entitled “Muliphysics Thrust Chamber 
Modeling” and by a MSFC Internal Research and Development focus area task entitled “Hot-Hydrogen Materials 
and Component Development.” 
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7Wang, T.-S., “Transient 3-D Analysis of Nozzle Side Load in Regeneratively Cooled Engines,” AIAA Paper 2005-3942, 
‘Chen, Y.-S., and Kim, S .  W., “Computation of Turbulent Flows Using an Extended k-e Turbulence Closure Model,” NASA 
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American Institute of Aeronautics and Astronautics 


Analysis of Material Sample Heated by Impinging Hot Hydrogen Jet in a Non-Nuclear Tester

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