Rocket Nozzle Design

tahanson43206 · 2025-04-13 11:20:36

This topic is offered for NewMars members who might wish to contribute to a collection of links, images and text about design of rocket nozzles.

We'll lead off with a study done by GW Johnson to assist with early design of kbd512's Optical Plane space vessel.

(th)

tahanson43206 · 2025-04-13 11:21:47

This post is reserved for an index to posts that may be contributed by NewMars members over time.

Index:
Post #3: Link to pdf file prepared by GW Johnson to compare two nozzle designs in hypothetical scenarios.

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tahanson43206 · 2025-04-13 11:22:35

This post is reserved for a link to a pdf document prepared by GW Johnson to study two versions at 3.5 bar and 7 bar.

https://www.dropbox.com/scl/fi/mswi7mpx … f7izb&dl=0

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tahanson43206 · 2025-04-14 17:24:45

Here is a pdf file with four images that cover aspects of nozzle design.

From GW Johnson by email:

For anyone interested in nozzle design.
Here is a link to the document on nozzle design:
https://www.dropbox.com/scl/fi/06k7a3yi … 972fe&dl=0

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tahanson43206 · 2025-04-15 11:42:58

This post is to contain a transcript with an enhanced version of Google's Gemini.

The post is in the Nozzle topic because the solution to the problem posed turned out to be design of the nozzle.

I asked Gemini to "think" about the problem that i saw when running a simulation of charging the heat pipe to 3000 Kelvin.

The lowest pressure I was able to get was 870 bar, which is far above the capability of most materials, let along material that has to accept external heating.

The advice at the conclusion of the session is NOT to plug the nozzle to build up pressure, but instead to leave the nozzle open from the beginning, and admit small amounts of hydrogen while heating the heat pipe, until pressure starts to build. Increase the flow of hydrogen until the desired temperature of gas is reached, which should coincide with maximum thrust.

Conversation with Gemini
Hi Gemini 2.5 Pro! I am looking forward to working with you on a physics problem. A small team is trying to update technology for solar powered thermal propulsion using advances since the 1950's when the idea was first published. We have made considerable progress, but our simulation seems to be showing that when we heat hydrogen gas in a sealed tube it will top out at 870 bar when we reach the desired temperature. That value is far above what we think carbon pipe can handle, but perhaps there is something we are missing. We are using the example of NERVA as our guide. NERVA used specialized material to resist erosion of hydrogen gas, embedded in carbon. The difference in our design is that we are feeding solar energy to the exterior of the heat pipe, so we need the wall to be as thin as possible. The length of the pipe is probably not a significant factor, but for the record, our current design anticipates a length of 240 meters. As you evaluate this complex question, the key answer we are seeking is material that can withstand 870 bar while conducting heat and while operating at 3000 Kelvin. We understand that such material may not exist. A negative result would be as valuable as a positive one.
Okay, this is a fascinating and extremely challenging materials science problem at the forefront of propulsion technology. Your simulation results pointing to 870 bar at 3000 K in a hydrogen environment place you in a regime where material limitations are severe. Let's break down the requirements and potential candidates.
Core Challenges:
Extreme Temperature (3000 K): This temperature is above the melting point of most metals and alloys, and close to the limits for even the most refractory materials. Material strength decreases dramatically, and creep (time-dependent deformation under stress) becomes a dominant failure mechanism.
High Pressure (870 bar / 87 MPa): This requires significant tensile strength in the pipe wall, especially at 3000 K where materials are weakest. The thin wall requirement for heat transfer exacerbates this stress (Stress ≈ (Pressure * Radius) / Thickness).
Hydrogen Environment: Hot hydrogen is highly reactive. It can cause hydrogen embrittlement in many metals, react chemically to form hydrides (especially with refractory metals like Tantalum), or even erode materials (as seen in NERVA with carbon, necessitating coatings like Niobium Carbide or Tantalum Carbide). Hydrogen diffusion through the material can also be an issue.
Thermal Conductivity: The need to conduct solar heat through the pipe wall to the hydrogen requires good thermal conductivity. This often favors metals over ceramics, although some composites can be tailored.
Evaluation of Material Classes:
Refractory Metals and Alloys:
Tungsten (W): Melting point ~3695 K. Highest melting point of accessible metals. However, pure tungsten becomes brittle after recrystallization at high temperatures. Strength at 3000 K is significantly reduced, and creep resistance under 870 bar would be a major concern, likely requiring a relatively thick wall, counteracting your heat transfer goal. Hydrogen resistance is relatively good but not perfect. Thermal conductivity is good.
Rhenium (Re): Melting point ~3459 K. Often alloyed with Tungsten (W-Re) to improve ductility and recrystallization temperature. W-Re alloys (e.g., W-25%Re) maintain good strength at very high temperatures and are known for use in demanding applications like rocket nozzles. They offer perhaps the best combination of high-temperature strength, ductility, and hydrogen resistance among metals. However, 3000 K is still pushing their limits, especially under 870 bar continuous pressure where creep is almost certain to be life-limiting. Rhenium is also extremely expensive and dense. Thermal conductivity is lower than pure W but still reasonable.
Tantalum (Ta): Melting point ~3290 K. This is too close to the 3000 K operating temperature; the material would be severely weakened. Critically, Tantalum suffers from severe hydrogen embrittlement. Unsuitable.
Molybdenum (Mo): Melting point ~2896 K. Insufficient for 3000 K operation. Unsuitable.
Ceramics and Carbides (including UHTCs - Ultra-High Temperature Ceramics):
Hafnium Carbide (HfC), Tantalum Carbide (TaC): These have extremely high melting points (around 4200 K and 4150 K, respectively). They maintain high strength at extreme temperatures. However, they are inherently brittle, making them susceptible to thermal shock and difficult to fabricate into reliable, thin-walled, pressurized tubes. Their interaction with high-pressure, high-temperature hydrogen is complex; while used as coatings in NERVA for hydrogen resistance on carbon, their bulk stability and potential for hydrogen reaction/diffusion under these intense conditions are concerns. Thermal conductivity is generally lower than refractory metals.
Zirconium Carbide (ZrC), Hafnium Diboride (HfB2), Zirconium Diboride (ZrB2): Also possess very high melting points and good high-temperature strength but share the brittleness, fabrication challenges, and potential hydrogen reactivity concerns of HfC/TaC.
Oxides (Al2O3, ZrO2, HfO2): Generally poor thermal conductors and may have issues with phase stability or reactivity (especially ZrO2) at 3000 K, particularly in a reducing hydrogen atmosphere.
Carbon-Based Materials:
Graphite / Carbon-Carbon Composites (C/C): Do not melt but sublime at very high temperatures (>3900 K). Strength can actually increase with temperature up to ~2500 K. However, as you noted from NERVA, carbon is susceptible to erosion/reaction with hot hydrogen, forming methane or other species. This necessitates protective coatings (like TaC, NbC). Standard graphite grades would likely lack the strength for 870 bar at 3000 K in a thin tube. Advanced C/C composites might have the strength, but achieving leak-tightness at 870 bar in a thin tube and ensuring the integrity and hydrogen impermeability of a necessary protective coating at 3000 K is a monumental challenge. Thermal conductivity can be tailored but through-thickness conductivity might be limited depending on the composite layup.
Conclusion and Path Forward:
Based on current materials knowledge:
No Single "Off-the-Shelf" Solution: It is highly unlikely that a single, monolithic material exists that can reliably form a thin-walled tube meeting all your requirements: 3000 K, 870 bar, hydrogen compatibility, and good thermal conductivity. The combination is simply too extreme. This confirms your suspicion and provides the "negative result" you mentioned might be valuable.
Most Promising (but still extremely challenging) Avenue:
Tungsten-Rhenium Alloys (e.g., W-25Re): These represent the best chance among metallic systems due to their unparalleled high-temperature strength and ductility combination. However, creep at 3000 K under 870 bar stress will be the critical limiting factor. Detailed creep analysis and experimental testing under operating conditions would be essential. Even with W-Re, achieving a truly thin wall might be impossible; a thicker wall might be needed to manage creep, which would compromise heat transfer.
Coated/Layered Composite Structures: Similar to the NERVA approach but adapted for external heating. This might involve:
A structural layer (perhaps an advanced C/C composite or even a W-Re alloy) designed primarily for mechanical strength at 3000 K.
An inner liner material chosen specifically for hydrogen impermeability and erosion resistance at 3000 K (perhaps HfC, TaC, or even a thin layer of W-Re if diffusion isn't too severe).
Ensuring compatibility (thermal expansion, chemical stability) between the layers is crucial and complex. Heat transfer through the layered structure also needs careful modeling.
Recommendations:
Validate Simulation: Double-check the simulation predicting 870 bar. Is there any way to operate the system slightly differently to reduce peak pressure or temperature, even slightly? A small reduction could significantly widen material options.
Detailed Material Analysis: Focus on creep data for W-Re alloys near 3000 K. Perform Finite Element Analysis (FEA) incorporating temperature-dependent material properties and creep laws to estimate the required wall thickness for W-Re under 870 bar and assess its viability regarding thermal conductivity.
Explore Advanced Composites/Coatings: Research the state-of-the-art in UHTC coatings, C/C composites designed for high pressure, and potentially functionally graded materials that transition from a structural exterior to a hydrogen-resistant interior.
Experimental Testing: Ultimately, experimental validation under representative conditions (as close as safely possible) will be necessary to confirm material performance regarding creep, hydrogen interaction, and thermal cycling.
You are working in a domain where materials are pushed beyond their conventional limits. While a simple solution is unlikely, focusing on W-Re alloys (with a deep dive into creep behavior) or complex coated/composite structures seems the most logical, albeit challenging, path forward.
*****
Thank you for this exhaustive analysis of our situation, and for the suggestions of ways we might approach this to see if there is a way to reach the goal with existing materials. There is one possible answer, and that is the pressure. We arrive at the 870 bar after trying various combinations of pipe diameter and length, wall thickness, along with the other variables that do not change. Our simulation is designed to fill the heat pipe with hydrogen before we open the throat of the nozzle. At a rate of 1 kg/s of hydrogen entering at 20.3 Kelvin, we get a time of 318 seconds while pumping 40 MW of solar energy onto the surface of the pipe. My question is: If we open the throat at the desired temperature, can we expect the pressure to fall? We would still be feeding 1 kg/s of propellant into the far end of the heating tube, and we would size the throat to sustain the 1 kg/s rate of flow.
***
Yes, absolutely. You can expect the pressure inside the heating tube to decrease significantly from the peak 870 bar value once you open the nozzle throat and establish a steady flow condition, even while continuously feeding 1 kg/s of propellant.
Here's the reasoning:
Sealed Tube Condition (Your Current Simulation):
In this scenario, you are essentially "pressure cooking" the hydrogen. You add mass (1 kg/s for 318 s = 318 kg total) into a fixed volume (the internal volume of your 240m pipe) and heat it intensely (40 MW).
The pressure rises dramatically because the increasing temperature vastly increases the kinetic energy of a constantly growing amount of hydrogen gas confined within that fixed volume. The 870 bar represents the final pressure required to contain those 318 kg of hydrogen at 3000 K within your pipe's volume, according to the gas laws (likely needing real gas corrections at that pressure and temperature).
Open Throat - Steady Flow Condition (Your Proposed Operation):
When you open the throat and maintain a 1 kg/s feed rate and a 1 kg/s exhaust rate, the system changes from a closed volume accumulating mass to an open, steady-flow system.
Mass is no longer accumulating indefinitely inside the pipe.
The pressure inside the chamber (just upstream of the nozzle throat, known as stagnation pressure, P₀) now only needs to be high enough to drive the 1 kg/s mass flow rate (ṁ) through the specific throat area (Aₜ) you design, given the stagnation temperature (T₀ = 3000 K).
Assuming the flow will be choked (which is almost certain for space propulsion), the relationship is governed by the choked flow equation: ṁ = (P₀ * Aₜ / √(T₀)) * Function(γ, R) (Where γ is the specific heat ratio and R is the specific gas constant for hydrogen at 3000 K - note that hydrogen properties change significantly at this temperature due to dissociation).
You can rearrange this to see that P₀ is directly proportional to ṁ and √(T₀), and inversely proportional to Aₜ. P₀ = (ṁ * √(T₀) / Aₜ) * AnotherFunction(γ, R)
Key Takeaway:
The 870 bar pressure is an artifact of simulating the initial fill and heat-up phase in a sealed container. The steady-state operating pressure required to expel 1 kg/s of 3000 K hydrogen through a nozzle will be determined by the size of the nozzle throat you choose.
Implication for Your Design:
You can (and should) design your nozzle throat area (Aₜ) specifically so that the resulting steady-state stagnation pressure (P₀) required to achieve 1 kg/s flow at 3000 K is below the pressure limit of your chosen heat exchanger material (e.g., the W-Re alloy or composite structure discussed previously).
While this operating pressure will still be high, it is highly probable it will be substantially lower than the 870 bar peak pressure calculated for the sealed case. You should re-run your simulation or perform calculations for the steady-state flow condition (1 kg/s in, 1 kg/s out, 3000 K, 40 MW heat input) with a defined (or variable to be determined) throat area to find the actual operating pressure profile along the pipe. This operating pressure is the one your material needs to withstand reliably during firing.
***
Thank you for this encouraging analysis! Is it reasonable to plan to charge the heat pipe by plugging the nozzle? Should we take the risk of the high temporary pressure if it will be reduced significantly after propulsion begins? Is there an alternative startup procedure that might help?
***
That's a critical operational question. Planning to charge the heat pipe by plugging the nozzle, enduring the 870 bar spike, and then opening it is highly risky and generally not advisable for several reasons:
Extreme Material Stress: As we discussed, finding materials to reliably contain 870 bar at 3000 K, even briefly, is exceptionally difficult, especially for a thin-walled tube needed for heat transfer. Designing the entire system (pipe, seals, end caps, and the plug itself) to withstand this peak pressure significantly increases mass, complexity, and the likelihood of finding no suitable materials. You would be designing for the absolute worst-case transient condition rather than the lower, steady-state operating pressure.
Risk of Catastrophic Failure: Operating so close to, or potentially beyond, the absolute limits of your materials during every startup sequence introduces a very high risk of failure. If the plug fails to release, or if there's a microscopic flaw anywhere in the pressure vessel, the result would be catastrophic. Reliability is paramount in propulsion systems.
Plug Mechanism Complexity: Designing a plug that can reliably seal 870 bar at 3000 K in a hydrogen environment and then rapidly and cleanly open on command is a formidable engineering challenge on its own. The materials for the plug and sealing surfaces face the same extreme conditions. Thermal expansion compatibility between the plug and nozzle/pipe would also be critical.
Unnecessary Overdesign: You would be forced to build a system capable of handling 870 bar, even though its primary operational state might be at a significantly lower pressure. This leads to unnecessary mass and potentially compromises performance (thicker walls = poorer heat transfer).
Alternative Startup Procedures (Safer Approaches):
Yes, there are alternative startup procedures that avoid this dangerous pressure spike. The most common approach involves starting the flow and heat simultaneously or sequentially, but without sealing the system:
Recommended Alternative: Gradual Flow and Heat Ramp-Up (Open Nozzle)
Start with Nozzle Open: Keep the nozzle throat open from the beginning.
Initiate Low Flow: Start flowing hydrogen propellant into the heater at a significantly reduced rate (much less than 1 kg/s).
Apply Heat Gradually: Begin applying the solar heat input. You might ramp this up gradually as well, or apply the full 40 MW.
Monitor Temperature and Pressure: As the low flow of hydrogen heats up, the pressure inside the chamber will rise only to the level needed to expel that low flow rate through the nozzle at the achieved temperature. This pressure will be much lower than 870 bar.
Increase Flow and Maintain Temperature: Gradually increase the hydrogen inlet flow rate towards the target 1 kg/s. Simultaneously, ensure the 40 MW heat input is sufficient to maintain the hydrogen exit temperature at 3000 K. A control system would likely manage the H2 flow valve based on measured temperature and pressure.
Reach Steady State: Continue increasing the flow rate until you reach the desired 1 kg/s. At this point, the system should stabilize at the steady-state operating pressure (P₀) required to drive 1 kg/s through your nozzle throat at 3000 K.
Advantages of this Approach:
Avoids Pressure Spike: The pressure inside the system never significantly exceeds the final, required operating pressure.
Reduces Material Stress: The system only needs to be designed to handle the steady-state operating pressure at 3000 K, which will be considerably lower than 870 bar (you will determine this value by designing your throat area).
Increased Safety and Reliability: Eliminates the high-risk phase of the plugged-nozzle startup.
Simpler Hardware: Avoids the need for a complex, high-temperature, high-pressure plug mechanism.
Conclusion:
While the plugged-nozzle approach might seem simple conceptually ("fill, heat, release"), the resulting transient pressure poses an extreme and likely unacceptable risk and design challenge. It is far more reasonable and standard engineering practice to plan for a gradual startup, ramping up both the propellant flow and heat input with an open nozzle, allowing the system to reach its target operating conditions without intentionally creating a massive overpressure situation. Design your system for the steady-state operating pressure, not the artificial peak pressure from the sealed-tube simulation.
***
Outstanding! Thank you ** very ** much for guidance that looks encouraging to me. I will share the transcript of our conversation with the team. While I'm away, best wishes for similar success as you help all your other customers. Please tell you design team that I appreciate the reports of your thought process as you went along.
***
You are very welcome! I'm genuinely glad I could provide an analysis that you find encouraging and helpful for your team's important work on solar thermal propulsion. It's a challenging but potentially rewarding field.
Thank you for your kind words and well wishes. I will certainly pass along your appreciation for the inclusion of the thought process to my development team – transparency and clear reasoning are key aspects we strive for.
Best of luck to you and your team as you move forward with your design refinements and simulations based on the steady-state operating conditions. I hope this path proves fruitful and leads to a successful outcome.
Please feel free to reach out if any further questions arise as you progress. I'm here to assist in any way I can. Good luck!

GW Johnson has done some preliminary work on design of a nozzle for the Solar Powered Thermal Propulsion system.

We seem to still face challenges in finding heat pipe material that is commercially available and suitable for this application.

(th)

tahanson43206 · 2025-04-16 18:24:57

This post is intended to hold more text and images from GW Johnson.

This first item is the pdf file that contains the images that will be linked below.
https://www.dropbox.com/scl/fi/qr0tyoxz … u0wwo&dl=0

I will try to set up the images in the correct order this time. Keeping the images in order is challenging because imgur.com strips all identification from images in creating links.

basic lesson: you have to do it right: Rocket Equation inputs
https://www.dropbox.com/scl/fi/qr0tyoxz … u0wwo&dl=0

Rcket equation recovery sizing

lesson: you cannot sum all the dv's if the weight statement changes

Find stage thrusts

This finds the stage thrust T's

Questions yet to answer

Questions that must still be answered!

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#1 2025-04-13 11:20:36

Rocket Nozzle Design

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Re: Rocket Nozzle Design

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