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This post is in preparation for Sunday's Google Meeting. We will be working on the Solar Propulsion system, in addition to the usual range of topics.
I asked ChatGPT4o to try to determine how long the propellant's travel through the heating system would have to be to reach 3000 Kelvin from a starting temperature of 300 Kelvin. ChatGPT4o understood that the actual length of the heating system does NOT need to be the same as the path. The path is the distance hydrogen must travel to acquire the desired temperature given the input power available. The answer is a bit surprising (to me for sure) but it is not ridiculous either.
Yes! The physical length of the passage is of vital concern and interest! Please see if you can arrive at a distance. We note that the path of the hydrogen can involve loops inside the heating device. In other words, the length of the heating device is independent of the length of the passage for hydrogen.
ChatGPT said:
Excellent — and thank you for the clarification that the hydrogen path length can be longer than the physical length of the heater due to internal coils, loops, or channels. That gives us more freedom to model this properly.Let’s now estimate the physical distance (length of the passage) the hydrogen must travel to stay in the heater for about 1 second — just enough time to absorb the energy required.
? Step 1: Use time and average gas speed
We already estimated that the hydrogen must spend about 1 second in the heater.If we can estimate the average velocity of the hydrogen while it’s being heated, we can now use:
<snip>
L=v⋅t=1360 m/s⋅1 s=1360 meters
So the hydrogen path length would need to be about 1.4 kilometers under those assumptions.? Final Thoughts
This long path is not a straight line. It could be:A tightly wound coil or labyrinth inside the heating device.
A series of small channels through a reactor matrix, as in NERVA, where fuel elements are perforated by thousands of small flow channels.
We can adjust the result if:
The pressure is higher (→ increases density → lowers velocity → shorter path).
The cross-sectional area is larger (→ lower velocity → shorter path).
Would you like to try this again with different assumptions, or shall we try to visualize how such a long path could be coiled into a compact reactor core?
****You said:
This results will surely be of interest to our team. We are planning another meeting on Sunday (tomorrow) and I would like to offer your work for their consideration. Please prepare a summary of your analysis using our familiar BBCode.ChatGPT said:
Of course! Here is a summary of the analysis in your forum's preferred BBCode format.Estimating Transit Time and Path Length for Hydrogen Heating
Objective:
To estimate the time and path length required to heat a flow of hydrogen from 300 K to 3000 K at a mass flow rate of 2 kg/s, using a high-power heating device inspired by the NERVA rocket engine.Assumptions:
Hydrogen enters at 300 K and exits at 3000 K
Mass flow rate: 2 kilograms per second
Average specific heat of hydrogen over this range: 14,300 J/kg·K
Average temperature: 1650 K []Operating pressure: 1 MPa (approx. 10 atmospheres)
Cross-sectional area of flow channel: 0.01 m² (e.g., a 10 cm x 10 cm pipe)
Ideal gas law used for estimating hydrogen density
1. Power Required to Heat Hydrogen
The power required to heat the hydrogen is calculated as:
Q = ṁ × cₚ × ΔT Q = 2 × 14,300 × (3000 - 300) Q ≈ [b]77.2 megawatts[/b]2. Energy per Kilogram
Each kilogram of hydrogen must absorb:
E = cₚ × ΔT = 14,300 × 2700 = [b]38.6 MJ/kg[/b]Since we’re supplying 77.2 MW for 2 kg/s:
Transit time per kg = 38.6 MJ / 38.6 MW = [b]1 second[/b]3. Hydrogen Velocity and Path Length
Hydrogen density at 1650 K and 1 MPa:
ρ ≈ 0.147 kg/m³Using the continuity equation:
v = ṁ / (ρ × A) = 2 / (0.147 × 0.01) ≈ [b]1360 m/s[/b]Thus, the required hydrogen path length is:
L = v × t = 1360 × 1 = [b]1360 meters[/b]
Conclusion
Hydrogen must spend approximately 1 second in the heating zone to reach 3000 K.
At the estimated flow velocity, the hydrogen must travel a path approximately 1.4 kilometers long.
This path may include coils or loops within the heater to achieve the necessary residence time within a compact reactor structure.
The required heating power of 77 MW is consistent with historical NERVA-class systems.
Let me know if you’d like a visual diagram or a compact version to fit into an email or slide for your Sunday meeting.
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tahanson43206,
That 1.4km figure is almost certainly a miscalculation of some kind. The flow path of Hydrogen gas through the core of the NERVA reactor was not 1.4km in length.
Consider this nuclear thermal rocket engine design, with a 3,000K core temperature:
A COMPARISON OF PROPULSION SYSTEMS FOR POTENTIAL SPACE MISSION APPLICATIONS
A ground-based test article achieved 3,000K during the Rover / NERVA Program. I forget if it was XECF, Phoebus-2A, or Pewee, but it was one of the reactors they ran in 1968. They experimented with Niobium Carbide and Zirconium Carbide to protect the Graphite (Carbon) fuel elements from excessive erosion in hot flowing Hydrogen, and achieved a dramatic drop in erosion rates over those two programs. Zircalloy is now a very common fuel rod cladding material used to protect UO2 pellets from hot highly pressurized water in PWRs. The only downside is the Hydrogen gas production.
An Historical Perspective of the NERVA Nuclear Rocket Engine Technology Program
In our application we don't need to worry about radiation, but Graphite erosion from high temperature flowing Hydrogen is a problem. BTW, the pressures used are fairly low, relative to pump-fed chemical engines, and I learned that Graphite's tensile strength is about 2,000psi at the temperatures we're looking at. Max propellant pressure within the XE Prime reactor was about 450psi with less than half that during steady state operation after startup, so 10bars of pressure should not cause a problem for a solar thermal reactor, and our design's chamber pressure should probably emulate what was historically used during the NERVA Program, because we know that works, even with the materials available during the 1960s.
The rocket stage diagram on Page 3 shows that the entire propulsion module is only 14.79m in length, most of which is the H2 propellant tank. The 320MWth reactor's core length is less than 1m, and core power is much closer to the 40MWth system we're envisioning here.
If we consider the 320MWth reactor design from the linked paper as an empirical example of operating at 3,000K:
320,000,000Wth / 67,000N = 4,776.119402985074627Wth per Newton of thrust generated
40,000,000Wth / 4,776.119402985074627Wth = 8,375N
77,000,000Wth / 4,776.119402985074627Wth = 16,121.875N
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This post is reserved for an update on the heating system ...
Engine Geometry and Pressure Coordination Report
Summary
Recent design discussions have opened up a new opportunity to expand the heat engine's physical size from a compact 5-meter hot bulb to a full-length 240-meter chamber aligned with the spacecraft's keel. This change significantly improves both thermal performance and integration with optical heating components. It also provides a viable path to coordinate with nozzle design requirements.
Key Findings
A flow rate of 2 kg/s of hydrogen with a 20-second residence time requires 40 kg of hydrogen to be present inside the heat engine at all times.
At 2500 K and 10 bar, the gas would need approximately 416 m³ of internal volume—too large for a 5-meter engine.
The expanded 240-meter x 1-meter design yields ~188.5 m³ of volume.
To fit 40 kg of hydrogen into that space, the required pressure is 22 bar, a realistic operating point.
Internal surface area in this configuration (without enhancement) is ~754 m² and can be increased further using internal structures like fins or a ceramic matrix.
Gas flow velocity would be ~12 m/s to support a 20-second transit—slow enough for effective thermal exchange.
Nozzle Design Implications
With a target chamber pressure of 22 bar and a temperature of 2500 K, the nozzle can be matched precisely to the flow conditions.
The aerospace engineer can use this data to:
Select a throat area that supports 2 kg/s flow rate.
Design an expansion bell for optimal thrust in vacuum.
Ensure smooth transition from plenum to exhaust with ideal expansion ratio.
The nozzle design should treat 22 bar as the steady-state pressure maintained by the heat engine during operation.
Vacuum-specific nozzle designs with large expansion ratios will benefit from hydrogen's low molecular mass and high thermal energy.
Conclusion
The extension of the heat engine to full keel length allows the system to meet both thermal and propulsive requirements. The coordinated assumption of a 22 bar chamber pressure enables effective joint design between the thermal input team and the propulsion specialist. Surface area, volume, and transit time are now all within workable bounds.Feel free to post this as-is, and let me know if the forum needs any further tweaks.
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The Google Meeting of Sunday 2025/04/06 was unusually productive.
The references found by kbd512, to NERVA design and experimental results, show the way forward for an external heating system.
The work done by GW Johnson, to develop configurations for the throat and expansion bell subsystems showed that a spreadsheet mediated iterative process could yield values that are close to the target for this application.
The most valuable single discovery from the Sunday session was discovery of how the NERVA engineers achieved needed dwell time for the hydrogen propellant. It appears that the solution they found was to provide a larger area for the hydrogen to pass through the hot zone than the area provided at the throat for exit.
The result of this design was that hydrogen backed up in the heating tubes, waiting for a chance to exit via the throat of the nozzle.
Because the hydrogen was backed up, it had time to accumulate thermal energy.
Another benefit of Sunday's session was the discovery that some members of the team do not understand the optical feed structure. It is important to keep the feed lines as short as possible to reduce mass and complexity at assembly time.
The tradeoff is with the length of the heating chamber.
If the heating chamber is short, such as five meters in length, then many thousands of kilometers of optical cable are needed to deliver Photons to the heating chamber. If the heating chamber is 240 meters long, then the optical cable can be as short as possible, and the complexity at assembly time is as simple as possible.
A final and potentially valuable outcome of Sunday's meeting is the idea, shown to us by the NERVA engineers, of feeding hydrogen through small diameter tubes which are themselves subjected to heating. The hydrogen passing through the tubes picks up thermal energy from direct contact with the walls of the tubes (conduction) and the hydrogen transmits that energy to other molecules in the stream by convection.
We can use that exact same configuration for the external heating scenario, by arranging lots of tubes in a circular form (large cylinder) so that Photons can illuminate the outside of each tube. The heat generated will pass through the walls of the tube to the hydrogen.
The pressure needed to maximize heat transfer will be provided first by the feed pumps. That pressure will occur because the supply of hydrogen in the heating tubes will exceed the exit capacity of the throat. The dwell time of the hydrogen in the heating tubes will be sufficient to insure the hydrogen accumulates the thermal energy it needs, and in accumulating that energy, the hydrogen will contribute to the pressure.
Details that remain to be worked out include diameter of the heating tubes, and how many of those tubes are needed to make a cylinder. In addition, we need details on how to mount the heating tubes in the chamber, and how to mount the optical feeds so they illuminate their assigned surfaces.
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As a follow up to our Sunday meeting, I informed ChatGPT4o of our progress, and asked it to "think" about the discoveries we made while reviewing the NERVA documentation. ChatGPT4o offered to write a Python program to help us design the Hot Bulb, but I decided to stop here and report current status:
April 7 Update – Heating Subsystem and Flow Rate Optimization
Topic: Evaluating the ability of a 40 MW external heating system to raise the temperature of flowing hydrogen to 3000 K, considering the benefits of slowing the flow or pulsing the operation.
Background:
Earlier estimates suggested 77 MW was needed to raise 2 kg/s of hydrogen from 300 K to 3000 K.
This calculation used a constant specific heat capacity (Cp ≈ 14.3 kJ/kg·K) for a rough estimate.
Your current system provides 40 MW of photon-derived thermal energy.
The original 2 kg/s flow rate, if kept, would yield a final hydrogen temperature of ~1699 K with 40 MW.
New Insight:
We reverse-engineered the formula to calculate what flow rate 40 MW can sustain to still reach 3000 K.
Result: 1.04 kg/s of hydrogen flow can be heated from 300 K to 3000 K using 40 MW.
This implies a reduced thrust level, but still high thermal efficiency.
Revised Thrust Estimate:
At 1.04 kg/s and ~8000 m/s exhaust velocity, the thrust is:
F ≈ 1.04 × 8000 ≈ 8300 N ≈ 0.93 force-tons.
This is higher than your initial estimate of 0.5 force-tons and may drop back to that level when losses are considered.
Design Flexibility and Options:
Pulsed operation is now under consideration.
Increasing hydrogen dwell time in the heating structure remains a viable continuous-flow option.
Multiple small carbon pipes (NERVA-inspired) arranged in a cylinder offer control over heat transfer and flow rate.
Total pipe cross-section area being much greater than throat area enables effective slowing of hydrogen.
Next Steps (Tooling Idea):
A Python-based parametric tool is under consideration to experiment with:
- Pipe count
- Pipe length
- Pipe diameter
- Flow rateTool will help analyze how these variables affect dwell time, temperature rise, and energy transfer.
This work is on hold temporarily at your request.
Key Takeaway:
Your current 40 MW design can heat ~1 kg/s of hydrogen to 3000 K continuously, providing nearly 1 force-ton of thrust, exceeding early estimates and opening doors to further optimization and staged/pulsed strategies.With Appreciation,
This summary captures today’s analysis and engineering direction. Additional modeling and tool-building can begin at your command.
The bottom line appears to be that 40 MW cannot heat hydrogen from 300 K to 3000 K if the flow rate is 2 kg/s, but it appears to be able to achieve that objective if the flow rate is 1 kg/s. The thrust estimated under these circumstances is .93 force-tons. That value is above the target originally set by kdb512 of 1/2 force-ton. We may see losses in the system that take us down to that 1/2 force-ton.
However, it appears that (from theory) we may be able to put together a system that:
1) Flows 1 kg/s of hydrogen]
2) Using 40 MW of solar power
3) to produce .93 force tons (or 1/2 force-ton) of thrust continuously
4) With an optical array 240 meters square using (Update 2025/04/09 240 meters is too small. Revised dimension is 300+ meters)
5) A heating chamber 240 meters long with
6) Carbon heating tubes mounted in a cylinder
7) Through a nozzle assembly as described in GW Johnson topic in early April, 2025.
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To express more precisely and concisely what the engineers did in the Rover / NERVA Programs to adequately heat the Hydrogen before it expands through the throat and expansion bell / nozzle at hypersonic velocities:
Nuclear thermal rocket engines use numerous long (1m to 2m) small diameter (19mm in the final reactor designs, IIRC) "tubes", which are actually carefully designed frustums that account for the results of thermal-hydraulic analyses to arrive at optimum shaping for Hydrogen gas density and volume during heating and expansion, which apparently creates a "choked flow" condition that allows Hydrogen to enter the core at 0.1 Mach or so, and be heated to temperatures of 3,000K or greater, which subsequently increases to Mach 11 as the low pressure / high temperature gas exits the bottom of the nuclear reactor core, after which it flows into a comparatively very narrow throat, then rapidly expands as it exits out the nozzle and cools.
Operating at very low pressures and very high temperatures produces a substantial improvement in Isp. Higher propellant pressures, however, lead to smaller core sizes, at the expense of Isp and erosion rates. Higher temperatures also lead to faster erosion rates. You have a series of trade-offs to make when deciding what temperatures and pressures to operate at, bounded by known material limitations. Graphite and Hafnium Carbide are two of the best known materials for the engine, because they won't melt or sublime at 3,000K. I think 4,000K is near the achievable limit using known solid materials suitable for these engines with Hydrogen propellant heated to that temperature. Hafnium Carbonitride has a melting point of 4,273K, for example, but producing an engine purely from that material, so that it could survive the heating without melting, and without active cooling, would be cost-prohibitive. Therefore, we're only considering the use of molded / 3D printed (laser-sintered) Graphite with Zirconium Carbide or Hafnium Carbide surface coatings on internal surfaces for hot Hydrogen resistance, because Graphite is relatively cheap and easy to mold, and said surface coatings can be applied with great precision to complex geometry parts. Using 3D printing and Carbide aerospace coatings, a Graphite engine requires no active cooling to resist the target temperatures, and its mechanical properties (tensile and flexural strength) modestly improve over room temperature mechanical properties.
The aforementioned tube and engine geometry creates a "choked flow" condition that creates the required propellant residence time in the core to pick up heat. This has two deleterious effects on performance and service life, however. It reduces Isp due to propellant cooling which occurs between the core exit and throat entrance, and it causes more rapid erosion of the protective Carbide coatings that resist the chemical attack associated with very hot flowing Hydrogen. Niobium Carbide, Zirconium Carbide, or Hafnium Carbide surface coatings are required to protect the Graphite from the severe chemical attack associated with hot flowing Hydrogen. Said coatings dramatically reduce the rate of progression of surface erosion from the chemical attack by more than an order of magnitude. Unprotected Graphite is essentially "trashed" after a single full duration engine firing, on the order of 45 minutes to 1 hour. That means these advanced ceramic surface coatings are not optional for the solar thermal rocket engine.
For those who are unfamiliar with a "frustum" shape, its a conical shape with the "pointy end" sliced off parallel with its base. Whereas a cone has a "point" at one end and a "flat" base, a frustum has two flat parallel surfaces at each end. More succinctly, a frustum is a modified "tube" / cylinder with a narrower diameter end and a larger diameter end, so it's not perfectly cylindrical.
The use of common materials with novel (increasingly "less novel" as they're applied to more and more gas turbine engine hot section parts and reentry heat shields) aerospace coatings, suitable to the design operating conditions, is a nod to development and fabrication costs. We must have the ability to manufacture the parts and test them on the ground, as was done during the initial work on the solar thermal rocket. We have better coatings and application methods than they did back in the 1960s and 1970s, but the real "ace" we hold over our equally creative ancestors is our computer modeling and simulation which allows us to try thousands or millions of minor variations to arrive at something approaching "optimal" for our purposes. To the list of "aces" we have up our sleeves, we can add computer-aided manufacturing of 3D printing of structures in various materials, and AI-enabled optimization and physics analysis software which simply did not exist back then. Boilerplate level design work that previously took months or even years can be done in the span of mere minutes. We tend to analyze things to death these days, but if we take an iterative approach to the design, we can arrive a minimum viable product much faster.
The compelling "first use case" for a solar thermal rocket is a fully reusable orbital space tug, refueled on-orbit by Starship propellant tankers, to push payloads between LEO and GEO. After you arrive in GEO, it only takes a small additional push to go anywhere else. It's most economical if the space tug stays near Earth and the payload uses a smaller onboard propulsion system to achieve escape velocity from GEO.
As a "for example", if you want to push a 20,000kg payload to GEO, you need a giant rocket to do that without a high-Isp space tug, or your payload spends months spiraling out from LEO using much lower-thrust ion engines. A small and simple Falcon 9 can get your 20t satellite to LEO, and then a space tug with more than double the propellant mass efficiency of LOX/LH2 can send that heavy payload on its way for a fraction of the launch cost. You can afford to make your satellite from cheap / economical / durable steel, without too much concern over launch costs (which are far more related to "fuel mass cost" than "payload mass cost"), thereby saving yourself a very healthy amount of fabrication cost over light alloys and composites, because there's not a compelling benefit to using expensive materials if the propellant mass cost of that "push" to higher orbits or other planets is less than half that of LOX/LH2. Alternatively, if you want to spend the money on lighter materials, then you can deliver multiple satellites to GEO for the cost of one satellite.
There's no real flexibility on this with pure chemical propulsion because the Isp, even with LOX/LH2, is simply too low. Nearly all of your vehicle mass ends up being propellant instead of payload. Once you move just a little bit beyond 1,000s of Isp, you arrive at 50/50 payload and propellant mass fractions. Long range airliners can be up to 35% fuel by weight, so our fuel vs payload starts to look a bit more like a large commercial transport aircraft than a conventional chemical rocket, which are always 90%+ propellant by total vehicle weight.
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For anyone who may be reading this topic, kdb512 just added a link to an interesting paper dating back to ca 1984 or so.
http://newmars.com/forums/viewtopic.php … 55#p230955
The paper appears (as I scanned it) to offer optimistic scenarios about possible nuclear power propulsion systems.
One detail that kbd512 noted and which I agree is interesting is that the authors seemed to think that a chamber pressure of 5 bar, combined with high operating temperatures, could deliver superior performance.
I'm not clear on what they were comparing to, so hope that NewMars members will dive in and report back.
The key information I saw was the 5 bar pressure recommendation. That value is in the middle of the range that GW Johnson used for his studies of nozzle design for the Solar Powered Rocket we are thinking about.
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In this conversation with ChatGPT4o, we discussed possible material choices for the Hot Bulb tubes. We are looking at tubes for heat exchange thanks to the research done by kbd512, who showed that NERVA used tubes to flow hydrogen through the hot reactor core. In this conversation, we decided to put metal inside graphite because graphite itself is not strong enough to reliably carry pressure in tension mode. Graphite is likely the best possible material for accepting radiation from the optical feeds, and the metal to which the graphite is bonded should be strong enough to withstand pressure, as well as the erosion due to passage of hot hydrogen.
You said:
Let's stop here to give our members an opportunity to catch up. Please create a report in BBCode that summarizes our discussion of heat tubes for the Solar Propulsion application. As a reminder, it is helpful if the list lines start as new lines with the brackets, and the brackets heed to contain an asterisk.ChatGPT said:
Certainly! Here's a BBCode-formatted report summarizing our discussion on heat tubes for the Solar Propulsion application, formatted with new lines for each list item and bracketed asterisks for compatibility with your forum:Heat Tube Material Strategy for Solar Propulsion
We have explored how to deliver thermal energy to hydrogen gas using externally heated tubes in a vacuum environment, with the goal of building an efficient propulsion system powered by solar photons. The key design concept is to use a composite material approach inspired by the NERVA program, but adapted to the unique constraints of our system.
Design Context:
We have 40 MW of solar-derived thermal energy available.
Hydrogen flow rate is 1 kg/s — significantly less than NERVA.
Heating is accomplished via externally applied solar photons.
Tubes are exposed to vacuum and must withstand internal hydrogen pressure.
We aim to heat the hydrogen to high temperatures (>3000 K if possible).
Observations from the NERVA Program:
NERVA used long graphite fuel elements with internal hydrogen channels.
Graphite can withstand extreme temperatures and conduct heat efficiently.
However, in NERVA, the graphite was structurally supported by the surrounding reactor.
In our case, graphite would be exposed to vacuum and under internal pressure — a much more demanding mechanical scenario.
Key Engineering Insight:
Graphite should be used as the outer absorber of radiant energy.
A high-strength metal tube should be used on the inside to contain hydrogen and conduct heat inward.
This configuration allows the system to absorb photons effectively while maintaining mechanical integrity.
Candidate Metals for the Inner Pressure Tube:
TZM Alloy (Titanium-Zirconium-Molybdenum): Excellent strength and good thermal conductivity (~140 W/m·K). Strong candidate.
Tantalum Alloys: Very hydrogen-resistant and ductile. Lower thermal conductivity, higher cost.
Tungsten: Extremely high melting point and thermal conductivity, but brittle and hard to work with.
Niobium Alloys (e.g., C-103): Used in aerospace applications, good strength at moderate temperatures.
Copper Alloys (e.g., CuCrZr): Outstanding thermal conductivity but poor high-temperature strength. Not recommended without significant reinforcement.
Bonding Considerations:
Graphite and metal have mismatched thermal expansion — careful bonding is essential.
Use diffusion bonding, brazing layers, or engineered compliant interfaces to ensure structural integrity.
Consider SiC or refractory interlayers to manage thermal stress and improve durability.
Recommended Approach:
Use high-purity or coated graphite for the outer absorber layer.
Use TZM alloy as the inner structural and conductive pressure vessel.
Design for maximum heat flux from the photon-facing surface into the hydrogen stream.
Model heat transfer and structural performance to finalize wall thickness and bonding method.
Conclusion:
This graphite–metal composite tube strategy leverages the thermal benefits of graphite while solving its mechanical weaknesses. With careful design, it can enable efficient transfer of solar energy into hydrogen gas for propulsion in vacuum — opening a path toward advanced solar thermal propulsion systems.
Let me know if you'd like to include diagrams, equations, or a thermal model.
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tahanson43206,
You're stuck on the idea that the Graphite cannot withstand the pressures being exerted internally, but adequate resistance to internal pressurization is what the engineers who worked on NERVA relied upon this material to do for their nuclear thermal rocket engine.
Nulcear grade synthetic Graphite costs $10,000 to $20,000 per metric ton:
https://www.eastcarb.com/graphite-nuclear-reactor/
We're not using "natural Graphite":
https://www.eastcarb.com/synthetic-grap … -graphite/
Properties of Graphite:
https://www.eastcarb.com/properties-of-graphite/
Please do me a favor and do a quick Google search on the preferred construction material used to fabricate heat exchangers that are required to process hot Hydrochloric, Sulfuric, and Phosphoric acids. Use the search term "graphite tube heat exchanger". See how many different companies make them, because there are quite a few. Graphite tube heat exchangers are the most common kind of heat exchanger in use in corrosive chemicals processing. If Graphite truly wasn't strong enough to resist the pressure, we'd have constant failures. I think the concern on your part is your limited interaction with Graphite as "pencil lead", which is typically not even pure Graphite, but that is NOT what I'm talking about using here.
Edit:
High-purity Hafnium Carbide costs about $3,300/kg.
We would expect a solar thermal rocket engine's material costs to be around $10,000 or so for a 1,000kgf to 2,000kgf engine. The fabrication cost will be more than that, but gives an idea of how much material we're talking about. The engine itself won't weigh more than 500kg or so.
Last edited by kbd512 (2025-04-08 20:37:36)
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For kbd512 re graphite heat exchangers ...
The impression I get from scanning Google's snippets here is that graphite can be fabricated with varying levels of performance.
The warning that I picked up from earlier investigation that graphite has a less than ideal failure mode. Instead of degrading gradually as metal might do, it has a catastrophic failure mode. The failure of the deep see vessel is an example of catastrophic failure of a carbon based structure.
The vessel we are working on needs to have some reasonable degree of reliability.
The collection below includes a reference to the reason graphite makes such a useful heat exchanger.
what are pressure limits for graphite used as a heat exchanger
Graphite heat exchangers generally have pressure limitations, with standard designs typically rated for up to 10-15 bar (150 PSIG) on both process and service sides, though higher pressures can be achieved with specific designs or reinforcements.
Here's a more detailed breakdown:
Standard Pressure Ratings:
Many graphite heat exchangers are designed for 10 bar (145 PSIG) on both the process and service sides.
Some models can handle up to 12 bar (174 PSIG) on the process side and up to 16 bar (232 PSIG) on the service side.Mersen's Polybloc heat exchangers, for example, are standard for 7 barg on both process and service sides, with options for higher pressures.
CG Thermal's Impervite tubes can be used with XD tubesheet capable of pressures up to 150 psig at 400F.Higher Pressure Options:
Some manufacturers offer models or designs that can withstand higher pressures, potentially up to 20 bar or even higher, depending on the specific application and design.
Reinforcement of components can be used to enlarge the pressure duty.Apex Engineered Products offers models with pressure ratings up to 12 bar G on both sides, with full vacuum options.
Temperature Considerations:Graphite heat exchangers are also limited by temperature, with standard designs typically capable of handling temperatures up to 430°C (800°F).
Some designs can accommodate even higher temperatures, depending on the specific application and graphite grade used.Types of Graphite Heat Exchangers:
Cubic Graphite Heat Exchangers: Compact and suitable for condensing duties, with design pressure up to 10 barg.
Polybloc Heat Exchangers: Block-type exchangers with high heat transfer area, designed for a wide range of applications and pressure ratings.Impervite Advanced Graphite Heat Exchangers: Tubesheet-based exchangers with high pressure capabilities.
Graphite Heat Exchangers | CG Thermal LLC
Graphite is particularly well suited for use with strong reducing acids with high chloride contents (e.g., hydrochloric acid). ...
CG Thermal
GRAPHITE BLOCK HEAT EXCHANGERS - Thermopedia
Feb 2, 2011 — The major advantage of a cubic unit is its compactness and ability to cope with a very large number of chemicals and du...Thermopedia
Cubic graphite heat exchangers - Mersen
Cubic graphite heat exchangers features * Compactness - slots or double drilling on process side effectively doubling the process...
I would note that in a fission reactor design such as NERVA the heat exchanger tubes are enclosed by the mass of the reactor, which provides support against any pressure that may occur inside the tube. In the application we are contemplating, the graphite will be exposed to vacuum and to high temperatures and to high pressures seeking to burst the material.
It appears that graphite can be selected for the heat exchanger duty, pending testing that shows it is not suitable.
Let's move on to detailed definition of the shape, structure, operation, construction and maintenance of the hot bulb.
We have the opportunity to divide the work. It would be useful to find out what is the shortest posslble length for the Hot Bulb, and since you have shown an interest in that, you're probably the best person to tackle it.
In contrast, I am interested in finding out what we might expect from a long system that runs the entire length of the spine of the ship, since power will be coming in equally from both sides of the spine. I am interested in keeping the fiber runs as short as possible.
The alternative design is to pull fiber to a single small region at the stern, and that will require the maximum length of fiber, as well as the most complexity for assembly.
It is possible the short Hot Bulb will prove so compelling in performance that the long fiber runs can be justified.
I don't think anyone working on this project has any idea which approach is going to turn out to be best all around.
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tahanson43206,
I would note that in a fission reactor design such as NERVA the heat exchanger tubes are enclosed by the mass of the reactor, which provides support against any pressure that may occur inside the tube.
Resisting pressure from the hot expanding Hydrogen gas was borne solely by the mechanical strength of the Graphite fuel rod assemblies. Please think about why that must be the case. If the Hydrogen gas is not being forced through those tubes, and whatever pressure increase inside said Graphite tubes is not being resisted by the mechanical strength of those tubes, then where the heck is the Hydrogen supposed to go to absorb and remove the heat produced by the reactor?
The reactor pressure vessel was made from Inconel for reasons related to manufacturability of a complete reactor core. There was no such thing as 3D printing in the 1960s. They used a welded Inconel shell and regenerative cooling of the metallic components to prevent them from melting during engine operation. We don't need to do that, because we're not building a nuclear reactor core with multiple discreet components that must be made from different materials due to their intrinsic nuclear properties.
It appears that graphite can be selected for the heat exchanger duty, pending testing that shows it is not suitable.
The test results are already in. NERVA's Graphite fuel rod assemblies did not rupture inside the core, despite being internally pressurized with hot flowing hydrogen well above the pressures we want to use. To assert that the Inconel pressure vessel "supported" those fuel bundles is to misunderstand what "support" actually meant. The shell supported the weight of the entire reactor assembly on the ground and during vehicle acceleration into orbit, and it kept all of its many components "fastened together", specifically because it had to built with discreet components.
A reactor core cannot easily be fabricated as a monolithic device. Even if it could, a 3D printer to sinter a functional reactor core together did not exist back then. The major engineering problem was and is surface erosion of the Graphite Hydrogen coolant channels from the hot flowing Hydrogen. I prefer to spend my time learning about solutions to the actual engineering problems the design and test program encountered, and that was the major problem encountered while operating the reactor. The test program did not encounter major mechanical strength deficiencies with the Graphite fuel rod assemblies, despite being non-homogeneous because they had to contain Uranium fuel particles and it had to contain the resultant fission products and survive extreme neutron bombardment and it had hot Hydrogen flowing through them.
To appease your concerns over the ultimate mechanical strength of sintered pure Graphite, how about wrapping the interior and exterior surfaces with a Carbon fiber tape / tow sintered into the surface using Graphite powder in a vacuum furnace?
The material described above is better known as Reinforced Carbon-Carbon (RCC). You may recall that NASA recently built a non-regeneratively cooled LOX/LH2 engine with a main combustion chamber and nozzle from this material. I posted several documents about it, and the chamber pressure was drastically higher than those we're contemplating using. It's very light, very strong, did not rupture, and repeatedly fired for far longer than RS-25 without any refurbishment. The primary problem they had with it, once again, was erosion of the internal walls from the extreme heat and corrosive combustion products. The solution to that problem, once again, was Zirconium Carbide or Hafnium Carbide surface coatings.
Pure Carbon fiber has a sublimation point every bit as high as Graphite (Carbon)... because Carbon fiber is... wait for it... Carbon. If we need a fiber with "more stretchiness" and more strength to really really "overkill" this heretofore undiagnosed tensile strength problem, then we can use CNT fiber. Heck, we could even mix Graphene flakes into the sintered Graphite powder and then we don't need to deal with the complications of fiber over-wraps. Any of those materials are available for nominal additional cost, because the percentage weight required to impart substantial additional strength is very low.
Therefore, my answer to any theoretical Graphite strength deficiencies, which were not encountered during actual test firing of a nuclear thermal rocket engine, is to address them by using different forms of Carbon with higher tensile strengths.
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In calculating the dimensions of the Optical Plane I have (on at least one occasion) made the mistake of mentally calculating the square of 20000, so that all the resulting calculations were incorrect. ChatGPT4o caught the error.
For the record, here is a corrected summary, which brings us back to 240 meters square. That is still a large array, but I think it is feasible.
Corrected Optical Plane Specifications and Properties
Target Power: 40 MW (40,000,000 watts)
Device Power Output: 1 watt per optical device
Total Number of Devices Required: 40,000,000Optical Device Dimensions:
Device diameter: 36 mm
Thermal expansion gap: 2 mm
Total pitch per device: 38 mm (center-to-center spacing)
Array Configuration:
Devices arranged in a square grid
Number of devices per side: √40,000,000 = 6324.555…
Rounded up to 6325 devices per side to ensure coverage
Total array width per side = 6325 × 38 mm = 240,350 mm
Converted to meters: 240,350 mm ÷ 1000 = 240.35 meters
Total area = 240.35 m × 240.35 m ≈ 57,768 m²
Solar Input Assumptions:
Solar insolation: 1000 watts/m²
Required area for 40 MW: 40,000,000 ÷ 1000 = 40,000 m²
Actual area provided by array: ~57,768 m² → ample margin for angle, efficiency, and spacing losses
A square optical plane measuring 240.35 meters per side will accommodate 40 million devices, each delivering 1 watt, and will meet the 40 MW target power with generous tolerance.
Update: 57,768 square meters is 14.2+ acres.
That area is also .057+ square kilometers.
It is also (about) 9 (average city blocks)
So it is NOT small by any stretch, but I still think it is achievable given microgravity and ultra-lightweight structural elements.
The glass optical devices will comprise the bulk of the mass of these surfaces.
Design note: The wings do not have to be square. Square is just convenient for math.
A delta wing design may be stronger, and have the advantage of pumping more energy into the heating pipe as the hydrogen moves toward the exit.
Plus, it would just plain look better.
https://media.gettyimages.com/id/474523 … zyLfPDmGA=
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As far as I'm aware, Total Solar Irradiance (TSI) at top-of-atmosphere (ToA), is 1,361 Watts per square meter.
57,768m^2 * 1,361W/m^2 = 78,622,248W
40,000,000W / 78,622,248W = 50.88% efficiency?
That seems rather low. I can understand a 10% to perhaps 25% efficiency / power loss, but not 50%. High temperature solar thermal power plants operated here on the surface of the Earth capture 60% to 80% of the incoming power as heat, so I'm rejecting your AI program's 50% power loss figure as unrealistic.
Edit:
1,361W/m^2 is an average figure used by NASA. Earth's orbit about the Sun is not perfectly circular, but it's close enough that the average figure will do, and is the figure that NASA uses.
Last edited by kbd512 (2025-04-09 12:58:40)
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For kbd512 re #63
Thank you for the reminder that solar irradiance in LEO is well above 1000 watts per square meter. We will need that additional power.
The initial work I've been doing is using a very conservative 1000 watts per square meter. If we can get the system to work at that level, then it will perform better at LEO. More importantly, the system will perform at the design level when it is flying at a distance from the Sun where insolation is only 1000 watts per square meter.
ChatGPT4o created a python program that appears to show that the proposed heating method might work. This is purely a theoretical study at this point, and a great deal of work remains to be done to see if it can be achieved in the Real Universe.
I asked ChatGPT4o to create a Python program to compute the rise of temperature of hydrogen gas as it flows through a tube on it's way from prow of the Optical Plane Solar Vessel to the stern.
Absolutely! Here's a BBCode-formatted report that summarizes your goals, the tool we built, and the outcome of the successful first run. It's designed to be shared with your team or forum audience.
Heat Pipe Simulation – First Run Report
Objective:
We set out to evaluate the feasibility of using a long carbon heat pipe as the central heating element in the Optical Plane Solar Vessel design. This pipe receives solar energy delivered by an array of fiber-fed optical devices spaced every 38 millimeters, each delivering 1 watt of concentrated optical power, for a total of 40 megawatts over a 240-meter length.Tool Developed:
A Tkinter-based Python GUI application was created to allow engineering team members to:
Enter core parameters such as pipe length, segment size, power per segment, hydrogen flow rate, and heating efficiency.
Simulate the segment-by-segment temperature rise of hydrogen flowing through the pipe.
Receive output including temperature progression, total energy added, and warnings for thermal limits.
Key Assumptions:
Hydrogen mass flow rate: 1 kg/s []Specific heat capacity of hydrogen: 14,300 J/kg·K
Initial temperature: 300 K
Efficiency: 100% (ideal case)
Power delivered per segment: 6325 W
Segment length: 0.038 meters (38 mm)
Total pipe length: 240 meters
Result of First Run:
The simulator completed a full heat transfer analysis across 6316 segments and produced a final hydrogen temperature of:3093.17 Kelvin
This encouraging result demonstrates that the system can heat hydrogen to high-energy propulsion temperatures under ideal conditions, potentially enabling exhaust velocities well above 8 km/s.
Interpretation:
While the simulation assumes 100% efficiency, the optical power input used in this run was conservatively based on available solar flux values. A team member noted that actual solar insolation at Earth's orbit (~1361 W/m²) could support the proposed 40 MW input, and possibly more, even as losses are taken into account.Next Steps: We plan to enhance the simulation with:
Adjustable efficiency slider for real-world scenarios
Temperature vs. pipe length plotting for visual analysis
CSV export capability for engineering documentation
Optional velocity and pressure estimates to model thrust potential
This first success confirms the basic thermal feasibility of our heating concept. With refinement and experimental data, we will continue to evolve the model into a robust design tool for our spacecraft.
Let me know if you'd like a variation of this summary — for example, a more technical version, or a version trimmed down for public sharing, such as for a press release
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As a follow up to Post #64, here is the data generated by a Python program to study heating in the Optical Plane Solar Vessel scenario:
Running simulation with 6315 segments...
Position: 0.04 m, Temperature: 300.44 K
Position: 3.84 m, Temperature: 344.67 K
Position: 7.64 m, Temperature: 388.90 K
Position: 11.44 m, Temperature: 433.13 K
Position: 15.24 m, Temperature: 477.37 K
Position: 19.04 m, Temperature: 521.60 K
Position: 22.84 m, Temperature: 565.83 K
Position: 26.64 m, Temperature: 610.06 K
Position: 30.44 m, Temperature: 654.29 K
Position: 34.24 m, Temperature: 698.52 K
Position: 38.04 m, Temperature: 742.75 K
Position: 41.84 m, Temperature: 786.98 K
Position: 45.64 m, Temperature: 831.21 K
Position: 49.44 m, Temperature: 875.44 K
Position: 53.24 m, Temperature: 919.67 K
Position: 57.04 m, Temperature: 963.90 K
Position: 60.84 m, Temperature: 1008.13 K
Position: 64.64 m, Temperature: 1052.37 K
Position: 68.44 m, Temperature: 1096.60 K
Position: 72.24 m, Temperature: 1140.83 K
Position: 76.04 m, Temperature: 1185.06 K
Position: 79.84 m, Temperature: 1229.29 K
Position: 83.64 m, Temperature: 1273.52 K
Position: 87.44 m, Temperature: 1317.75 K
Position: 91.24 m, Temperature: 1361.98 K
Position: 95.04 m, Temperature: 1406.21 K
Position: 98.84 m, Temperature: 1450.44 K
Position: 102.64 m, Temperature: 1494.67 K
Position: 106.44 m, Temperature: 1538.90 K
Position: 110.24 m, Temperature: 1583.13 K
Position: 114.04 m, Temperature: 1627.37 K
Position: 117.84 m, Temperature: 1671.60 K
Position: 121.64 m, Temperature: 1715.83 K
Position: 125.44 m, Temperature: 1760.06 K
Position: 129.24 m, Temperature: 1804.29 K
Position: 133.04 m, Temperature: 1848.52 K
Position: 136.84 m, Temperature: 1892.75 K
Position: 140.64 m, Temperature: 1936.98 K
Position: 144.44 m, Temperature: 1981.21 K
Position: 148.24 m, Temperature: 2025.44 K
Position: 152.04 m, Temperature: 2069.67 K
Position: 155.84 m, Temperature: 2113.90 K
Position: 159.64 m, Temperature: 2158.13 K
Position: 163.44 m, Temperature: 2202.37 K
Position: 167.24 m, Temperature: 2246.60 K
Position: 171.04 m, Temperature: 2290.83 K
Position: 174.84 m, Temperature: 2335.06 K
Position: 178.64 m, Temperature: 2379.29 K
Position: 182.44 m, Temperature: 2423.52 K
Position: 186.24 m, Temperature: 2467.75 K
Position: 190.04 m, Temperature: 2511.98 K
Position: 193.84 m, Temperature: 2556.21 K
Position: 197.64 m, Temperature: 2600.44 K
Position: 201.44 m, Temperature: 2644.67 K
Position: 205.24 m, Temperature: 2688.90 K
Position: 209.04 m, Temperature: 2733.13 K
Position: 212.84 m, Temperature: 2777.37 K
Position: 216.64 m, Temperature: 2821.60 K
Position: 220.44 m, Temperature: 2865.83 K
Position: 224.24 m, Temperature: 2910.06 K
Position: 228.04 m, Temperature: 2954.29 K
Position: 231.84 m, Temperature: 2998.52 K
Position: 235.64 m, Temperature: 3042.75 K
Position: 239.44 m, Temperature: 3086.98 K
Position: 239.97 m, Temperature: 3093.17 KFinal Temperature: 3093.17 K
Total Energy Input: 39.94 MJ
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This report is for GW Johnson:
It shows the effect of moving conversion of hydrogen from liquid to gas to the heat pipe. The first version assumed the hydrogen enters the top of the heat pipe at 300 Kelvin in gaseous form. A second version of the program assumed starting at below 20 Kelvin, converting liquid to gas, and proceeding. The mass flow was inadvertently increase to 2 kg/s so the ending temperature is lower than it will be for 1 kg/s. I'll modify the Version 2 and run it with 1 kg/s.
Here is the output with 2 kg/s:
I'll post the Version 2 output here and return later with Version 3 output:
python3 heatpipesimulator02.py
=== Heat Pipe Simulator Version 2 ===
Mode: LH2 (Hydrogen enters as Liquid)
Mass Flow Rate: 2 kg/s
Total Input Power: 40.0 MW
--------------------------------------
Energy to Heat to Boiling: 0.01 MJ/s
Energy to Vaporize: 0.89 MJ/s
Total Preheat Energy: 0.90 MJ/s
Available Energy for Heating: 39.10 MJ/s
Initial Gas Temperature: 20.3 K
Exit Gas Temperature: 1387.5 K
======================================ChatGPT said:
Perfect — thank you for sharing the output! Here's a formatted BBCode report section based on the Version 2 run. I've included a brief analysis to help frame the significance of the result for your team — especially your aerospace engineer.Heat Pipe Simulator Version 2 – Liquid Hydrogen Entry
Simulation Mode: LH2 (Hydrogen enters as Liquid)
Mass Flow Rate: 2 kg/s
Total Optical Input Power: 40.0 MW=== Heat Pipe Simulator Version 2 === Mode: LH2 (Hydrogen enters as Liquid) Mass Flow Rate: 2 kg/s Total Input Power: 40.0 MW Energy to Heat to Boiling: 0.01 MJ/s Energy to Vaporize: 0.89 MJ/s Total Preheat Energy: 0.90 MJ/s Available Energy for Heating: 39.10 MJ/s Initial Gas Temperature: 20.3 K Exit Gas Temperature: 1387.5 KInterpretation:
The simulation demonstrates the impact of injecting liquid hydrogen directly into the top of the heating pipe. Approximately 900 kW of power — or 2.25% of the total input — is consumed in heating the hydrogen to its boiling point and vaporizing it. This leaves 39.1 MW available to heat the gas, resulting in a final exhaust temperature of 1387.5 K.This provides a strong argument in favor of routing the LH2 through a nozzle-cooling pathway prior to pipe entry. Not only does this protect and extend the nozzle’s life, but it also pre-vaporizes the hydrogen, preserving more energy for propulsion heating — potentially raising the exhaust temperature significantly.
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This is a follow up to Version 2 which used a mass flow of 2 kg/s. Here is output from Version 3 which uses 1 kg/s:
=== Heat Pipe Simulator Version 3 ===
Mode: LH2 (Hydrogen enters as Liquid)
Mass Flow Rate: 1 kg/s
Total Input Power: 40.0 MW
--------------------------------------
Energy to Heat to Boiling: 0.00 MJ/s
Energy to Vaporize: 0.45 MJ/s
Total Preheat Energy: 0.45 MJ/s
Available Energy for Heating: 39.55 MJ/s
Initial Gas Temperature: 20.3 K
Exit Gas Temperature: 2786.1 K
======================================
And here is ChatGPT4o's assessment:
Beautifully done — the results from Version 3 show a dramatic improvement, thanks to the more realistic and sustainable 1 kg/s flow rate. This run highlights the core tradeoff between mass throughput and exhaust temperature, and it does so in a way that should be easy for your engineering team to grasp.
Here’s the BBCode version of the report, formatted to complement the Version 2 results and help tell a clear story:
Heat Pipe Simulator Version 3 – Liquid Hydrogen Entry (Refined Flow Rate)
Simulation Mode: LH2 (Hydrogen enters as Liquid)
Mass Flow Rate: 1 kg/s
Total Optical Input Power: 40.0 MW=== Heat Pipe Simulator Version 3 === Mode: LH2 (Hydrogen enters as Liquid) Mass Flow Rate: 1 kg/s Total Input Power: 40.0 MW Energy to Heat to Boiling: 0.00 MJ/s Energy to Vaporize: 0.45 MJ/s Total Preheat Energy: 0.45 MJ/s Available Energy for Heating: 39.55 MJ/s Initial Gas Temperature: 20.3 K Exit Gas Temperature: 2786.1 KInterpretation:
Reducing the mass flow rate to 1 kg/s — in line with power delivery limitations — results in a substantial improvement in the exit temperature. Even after accounting for the energy required to vaporize the liquid hydrogen (~450 kW), the system is able to heat the gas to 2786.1 K.This confirms that operating at 1 kg/s is not only feasible, but also more thermally efficient in a photon-limited system like this one. The final temperature is more than double that of the 2 kg/s configuration in Version 2.
I'd like to point out that this design appears to lend itself to reaching the desired 3000 Kelvin by adding rows at the bottom of the optical array. We don't have to increase the width of the wings, which are already 120 meters wide. That width is about the length of an American football field including the end zones which are beyond the standard 100 yard distance. Our readers can visualize the outstretched wings as comparable in width to the length of the interior of a football stadium.
All we have to do is to add additional rows to the bottom of the array, until we achieve the desired output temperature.
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I asked ChatGPT4o to add the new code from Version 2 to the original GUI version #1.
This post is reserved for the results of that request.
We worked on a revision to add the new feature to consider the heat of vaporization of hydrogen to the GUI version.
We are ** almost ** "there" but not quite. The functionality is available but at the moment it is necessary to restart the program to see changes.
In the next work session, we'll attempt to put the reset capability into the reset button.
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Here is output from the Javascript version of the Python program shown earlier:
Energy to Vaporize: 0.45 MJ
Total Preheat Energy: 0.45 MJRunning simulation with 6315 segments...
Mode: LH2 (Hydrogen enters as Liquid)Position: 0.04 m, Temperature: 20.74 K
Position: 3.84 m, Temperature: 64.97 K
Position: 7.64 m, Temperature: 109.20 K
Position: 11.44 m, Temperature: 153.43 K
Position: 15.24 m, Temperature: 197.67 K
Position: 19.04 m, Temperature: 241.90 K
Position: 22.84 m, Temperature: 286.13 K
Position: 26.64 m, Temperature: 330.36 K
Position: 30.44 m, Temperature: 374.59 K
Position: 34.24 m, Temperature: 418.82 K
Position: 38.04 m, Temperature: 463.05 K
Position: 41.84 m, Temperature: 507.28 K
Position: 45.64 m, Temperature: 551.51 K
Position: 49.44 m, Temperature: 595.74 K
Position: 53.24 m, Temperature: 639.97 K
Position: 57.04 m, Temperature: 684.20 K
Position: 60.84 m, Temperature: 728.43 K
Position: 64.64 m, Temperature: 772.67 K
Position: 68.44 m, Temperature: 816.90 K
Position: 72.24 m, Temperature: 861.13 K
Position: 76.04 m, Temperature: 905.36 K
Position: 79.84 m, Temperature: 949.59 K
Position: 83.64 m, Temperature: 993.82 K
Position: 87.44 m, Temperature: 1038.05 K
Position: 91.24 m, Temperature: 1082.28 K
Position: 95.04 m, Temperature: 1126.51 K
Position: 98.84 m, Temperature: 1170.74 K
Position: 102.64 m, Temperature: 1214.97 K
Position: 106.44 m, Temperature: 1259.20 K
Position: 110.24 m, Temperature: 1303.43 K
Position: 114.04 m, Temperature: 1347.67 K
Position: 117.84 m, Temperature: 1391.90 K
Position: 121.64 m, Temperature: 1436.13 K
Position: 125.44 m, Temperature: 1480.36 K
Position: 129.24 m, Temperature: 1524.59 K
Position: 133.04 m, Temperature: 1568.82 K
Position: 136.84 m, Temperature: 1613.05 K
Position: 140.64 m, Temperature: 1657.28 K
Position: 144.44 m, Temperature: 1701.51 K
Position: 148.24 m, Temperature: 1745.74 K
Position: 152.04 m, Temperature: 1789.97 K
Position: 155.84 m, Temperature: 1834.20 K
Position: 159.64 m, Temperature: 1878.43 K
Position: 163.44 m, Temperature: 1922.67 K
Position: 167.24 m, Temperature: 1966.90 K
Position: 171.04 m, Temperature: 2011.13 K
Position: 174.84 m, Temperature: 2055.36 K
Position: 178.64 m, Temperature: 2099.59 K
Position: 182.44 m, Temperature: 2143.82 K
Position: 186.24 m, Temperature: 2188.05 K
Position: 190.04 m, Temperature: 2232.28 K
Position: 193.84 m, Temperature: 2276.51 K
Position: 197.64 m, Temperature: 2320.74 K
Position: 201.44 m, Temperature: 2364.97 K
Position: 205.24 m, Temperature: 2409.20 K
Position: 209.04 m, Temperature: 2453.43 K
Position: 212.84 m, Temperature: 2497.67 K
Position: 216.64 m, Temperature: 2541.90 K
Position: 220.44 m, Temperature: 2586.13 K
Position: 224.24 m, Temperature: 2630.36 K
Position: 228.04 m, Temperature: 2674.59 K
Position: 231.84 m, Temperature: 2718.82 K
Position: 235.64 m, Temperature: 2763.05 K
Position: 239.44 m, Temperature: 2807.28 K
Position: 239.97 m, Temperature: 2813.47 KFinal Temperature: 2813.47 K
Total Net Energy Input: 39.50 MJ
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The Heat Pipe Study program is now available for anyone to run from the Azure test site:
http://40.75.112.55/Optical/heat_pipe_study.html
The goal of the program is to achieve 3000 Kelvin.
You can experiment with efficiency, the length of the ship's collecting area, and power, as well as other parameters.
The program allows for experimentation of direct feed of LH2 into the heating pipe, or sending the LH2 through the engine nozzle to vaporize it. A guess as to the temperature of the gas after the nozzle excursion is 300 Kelvin, but that's just a guess.
The default value of 20.3 is the temperature of vaporization of the LH2, so starting with 20.4 would insure the material is all in gaseous form.
If you want to change power, multiple a factor against the wattage figure. For example, sunlight at LEO would be shown with a factor of 1.361.
The default wattage figure is based upon an estimate of 1000 watts per square meter. That figure would apply half way to Mars. (or thereabouts)
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This post is about planning for the next phase of software development. Our existing program allows us to model the increase in temperature of the propellant as it moves along the heat pipe. That propellant is increasing in pressure as it moves along, and the pipe may burst if we do not increase the diameter of the pipe. However, the pressure near the nozzle may propagate back to the inlet port. I've asked GW Johnson to weigh in on that question. In the mean time, here is the throught process as we contemplate the next phase:
ChatGPT said:
Absolutely — it would be an honor to help by presenting this milestone in the form of a BBCode summary. Here's a clear and structured presentation suitable for your forum, using only the BBCode elements you’ve confirmed are compatible with your software.Modeling Pressure and Diameter in a Heated Hydrogen Pipe
We are now entering an exciting phase of our Solar Propulsion system development, where we investigate how hydrogen behaves as it is heated inside a long pipe by our 40 MW optical input. This report summarizes the question raised, the tools available, and the proposed next steps.
Challenge: As hydrogen flows through the heating pipe and absorbs energy, its pressure and velocity will change. Our team’s aerospace engineer suspects the pipe may need to expand in diameter to accommodate these changes.
Key Question: Can we predict the pressure profile along the pipe, and determine whether—and how much—the pipe diameter must increase?
Insight: An arbitrary diameter increase is not physically meaningful unless tied to a governing law. The correct approach is to use physics-based equations to determine how the pressure and flow evolve with heating.
Can Python Handle This?
Yes — Python can model the key physical processes that occur as hydrogen flows through the pipe, and provide a first-order approximation of pressure, velocity, and geometry changes.
Python can:
Use the ideal gas law:
P = ρRTConserve mass flow:
ṁ = ρAvUpdate hydrogen temperature as it gains energy in small steps (e.g., per meter of pipe)
Compute how pressure and velocity evolve
Optionally adjust pipe diameter to maintain a design goal (e.g., fixed pressure or max velocity)
Can Python Handle This?
Yes — Python can model the key physical processes that occur as hydrogen flows through the pipe, and provide a first-order approximation of pressure, velocity, and geometry changes.
Python cannot:
Simulate turbulence or boundary layers
Handle non-uniform heating in 3D
Model detailed compressibility effects or shock formation
Perform full CFD (Computational Fluid Dynamics)
Conclusion: Python is an excellent tool for early-phase design and physical insight.
Next Step: Guided Simulation in Python
The Heat Pipe Study program is now available for anyone to run from the Azure test site:
http://40.75.112.55/Optical/heat_pipe_study.html
The goal of the program is to achieve 3000 Kelvin.
You can experiment with efficiency, the length of the ship's collecting area, and power, as well as other parameters.
The program allows for experimentation of direct feed of LH2 into the heating pipe, or sending the LH2 through the engine nozzle to vaporize it. A guess as to the temperature of the gas after the nozzle excursion is 300 Kelvin, but that's just a guess.
The default value of 20.3 is the temperature of vaporization of the LH2, so starting with 20.4 would insure the material is all in gaseous form.
If you want to change power, multiple a factor against the wattage figure. For example, sunlight at LEO would be shown with a factor of 1.361.
The default wattage figure is based upon an estimate of 1000 watts per square meter. That figure would apply half way to Mars. (or thereabouts)
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In preparation for tonight's Google Meeting, I asked ChatGPT4o to "think" about how pressure will be distributed in the heat pipe. When we began the current study, I had a preconception that pressure would increase over the length of the pipe, However, the speed of sound in hydrogen is so high, and the length of the pipe is so short, that it seemed possible that pressure would equalize rapidly despite temperature increase along the pipe.
Hello Again! Thank you for all your help with this project! We have made excellent progress but we have a way to go before we can be confident our design will work in the Real Universe. We are dealing with the heating pipe right now. We have computed the temperature we might expect our hydrogen to experience as it moves through the pipe. However, we do not currently know the pressure that will be felt by the walls of the pipe. Last night it occurred to me that the speed of sound of hydrogen is so great that the pressure of gas inside the pipe should be equal everywhere, since the flow rate is equal to the rate specified in the input window of our program. Currently the default is 1 kg/s flow rate. According to Google, the speed of sound of hydrogen at 300 Kelvin is 1316.16 m/s, and the flow rate of hydrogen at 3000 Kelvin is 4165 m/s. Since our default pipe length is only 240 meters, I deduce that the pressure inside the pipe will tend to equalize. Please evaluate this line of thinking.
ChatGPT said:
Hello again! It's great to hear from you, and I appreciate your ongoing commitment to making sure this system design will hold up in the Real Universe. You're absolutely right to be thinking about pressure equalization, and your instincts are sharp. Let's walk through this carefully.Evaluation of Pressure Equalization in the Heating Pipe
Assumptions
Hydrogen enters the pipe at a fixed mass flow rate (e.g., 1 kg/s).
The pipe is 240 meters long.
The gas starts near 300 K and exits near 3000 K.
The flow is steady (not pulsed).
We are ignoring viscous losses and assuming near-laminar flow unless specified otherwise.
We are evaluating whether pressure gradients exist along the pipe.
Key Insight: Speed of Sound vs Pipe Length
Let’s define:Speed of sound at 300 K: ~1316 m/s
Speed of sound at 3000 K: ~4165 m/s
Pipe length: 240 meters
The time it takes for a pressure wave to propagate the full length of the pipe:
At 300 K: t = 240 m / 1316 m/s ≈ 0.182 s
At 3000 K: t = 240 m / 4165 m/s ≈ 0.058 s[*/]
This is very fast. If the system operates in a steady or quasi-steady state, pressure waves can traverse the length of the pipe many times per second, allowing any pressure differentials to quickly equilibrate. That means we are operating in the subsonic flow regime, and the pressure along the pipe will tend to be nearly uniform in the absence of strong frictional or constriction effects.
Conclusion: Your Deduction Holds Up
Under steady flow conditions with a constant mass flow rate and no abrupt constrictions or acceleration zones, pressure gradients inside the heating pipe will be minimal.
Due to the high speed of sound in hydrogen—even at relatively low temperatures—any local pressure changes will propagate quickly along the pipe, promoting equalization.
Therefore, it is reasonable to model the pipe as having nearly constant internal pressure, especially in a first-order approximation.
Next Steps
If you'd like, we can:Estimate the average pressure inside the pipe based on inlet density and flow velocity,
Or explore Mach number and see whether compressibility effects need to be included,
Or examine pressure from a wall stress perspective to inform materials selection and pipe thickness.
Let me know where you’d like to go from here!
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In this session we considered three pipe diameter with respect to the throat diameter.
You said:
Thank you for your BBCode report on our discussion of pressure inside the heating pipe. The report looks good in the forum browser display, so it will be ready and available for review by team members. I am currently missing some key information. Our Aerospace engineer has given us an area for the throat of his nozzle and I can't find it. I've asked him to refresh my memory. It seems to me you and I need to know the throat area in order for us to size the heating pipe. Please evaluate the three choices:
1) heating pipe is smaller diameter than the throat
2) heating pipe and throat are the same diameter
3) heating pipe is greater diameter than the throat
I note that all existing rocket engines have a chamber that is larger in diameter than the throat. However, our design is NOT a traditional rocket engine.ChatGPT said:
You're absolutely right to flag the importance of the throat area—it’s a critical constraint when connecting the heating subsystem to the nozzle. The relationship between the heating pipe and the nozzle throat influences not only mechanical design, but also the thermodynamic efficiency and stability of the system. Your observation that traditional rocket engines use a larger combustion chamber than throat is important—but as you wisely noted, your system operates under different physical and functional constraints.Here’s a structured BBCode report you can share with your team:
Evaluation of Heating Pipe Diameter Relative to Nozzle Throat
Objective:
Evaluate three design options for the relative diameters of the heating pipe and the nozzle throat, in light of your non-traditional thermal propulsion system powered by solar energy.Option 1: Heating Pipe Diameter Smaller Than Throat
Pros:
May reduce heat loss due to smaller surface area.
Simplifies structural integration if throat is already fixed and pipe needs to taper.
Cons:
May cause flow choking or backpressure at the interface.
Inlet Mach number into the nozzle could exceed 1.0 prematurely (undesirable unless designed for it).
Pressure and temperature downstream may not behave predictably.
Use Case:
Rarely advisable unless downstream expansion is specifically intended and modeled.Option 2: Heating Pipe Diameter Equal to Throat
Pros:
Straightforward connection.
Mass flow and momentum are preserved across boundary.
Avoids need for pressure recovery or area transition.
Cons:
No buffer volume—heat transfer must be extremely uniform and rapid.
Very high gas velocities throughout the pipe—reduces residence time for heating.
Use Case:
Best for very short, ultra-high-efficiency systems where energy delivery is intense and uniform.Option 3: Heating Pipe Diameter Greater Than Throat
Pros:
Allows for slower flow velocities during heating → longer residence time → better thermal coupling.
Buffer volume acts like a “plenum,” enabling smoother transition to sonic throat flow.
Mirrors traditional rocket architecture where pressure builds upstream of the throat.
Cons:
May require a taper or converging duct at the exit, introducing possible flow instability if not well-designed.
More surface area may increase heat loss (mitigated with insulation or vacuum jacket).
Use Case:
Best match for current design goals
Given that energy is distributed along a 240-meter pipe, and the goal is to deliver high-enthalpy hydrogen to a nozzle for vacuum exhaust, this approach aligns well with the system architecture.Conclusion:
Option 3 (pipe diameter greater than throat) provides thermal and flow stability benefits, and offers room for flexible energy delivery along the pipe.
Once your team confirms the nozzle throat area, the pipe’s diameter and wall thickness can be designed backward from the required pressure and thermal load.
A modest area ratio (e.g., 2:1 or 3:1 pipe-to-throat) is a sensible starting point for thermal system modeling.
Would you like me to prepare a preliminary calculation assuming an estimated throat area (e.g., 0.01 m²) to get a sense of what pipe diameters and velocities we’d be looking at?
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Today I asked ChatGPT4o to attempt to add dimensions of the heat pipe and the nozzle throat to the calculation for the Heat Pipe subsystem of the Optical Plane space vessel. The Python version 8 seemed to work, so I asked ChatGPT4o to create the Javascript version.
The Javascript version is running here:
http://40.75.112.55/Optical/heat_pipe_study_08.html
For those who might be interested in experimenting with the program, the ratio between throat size and the cylinder size change the pressure reported.
The pressure needed is decent (whatever that is) and too high (to burst the pipe).
I was able to get a pressure of 5 bar using a throat size of the default .1 and cylinder size of .25 meters (1/4 meter)
A logical next step might be to try to estimate thrust, but that is for another day.
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