EDITOR’S NOTE: This is a continuation of the reporting from the 10-16-2021 flight of the 6-inch rocket design, built and flown by RRS member, Bill Claybaugh.
Post-Flight Motor Inspection
Recovery of the spent motor hardware allowed a detailed disassembly and inspection of the parts. This revealed several useful observations:
Motor Tube
The recovered Motor Tube showed a dent just above the fins that was deep enough to have caused a pressure failure if it had been present while the motor was operating; we thus conclude that the dent occurred during or post impact.
Localized dent in the aluminum case, likely resulting from impact after burnout
Bulkhead
Inspection of the Forward Bulkhead showed it to be in good condition with no evidence of any gas leaks above the two O-rings. The bottom of the Bulkhead showed some damage to the fiberglass heat shield from the ground impact of the rocket but showed plenty of fiberglass heat shield remaining after the about eight second burn. The “nose” of the ignitor assembly remained in place in contrast to previous tests where this part had shattered upon ignition; the change to a steel “gun barrel” liner for the initiator appears to have resolved this issue.
The forward side of the bulkhead showing no leakage or damage.Aft side of the bulkhead showing damage to fiberglass heatshield.
Fins
The four fins were intact and largely undamaged; they appear suitable for reuse in future flight vehicles. Checking with a 0.002” feeler gauge showed there was no gap between the “nose” of any of the fins and the motor tube. A further check using backlighting confirmed that there were no visible gaps between the fins and the motor tube at any location along the fin edges.
Nozzle
The graphite nozzle insert had broken free of its aluminum shell on impact; it was damaged at the exit end and is not suitable for reuse. The aluminum shell showed signs of erosion at the very top of the nozzle. This area was covered by a ring-shaped fiberglass heat shield that was not present upon disassembly. This suggests that the heat shield was fully consumed by hot gas erosion during motor operation; a thicker heat shield is evidently appropriate in future nozzles.
The titanium nozzle extension was undamaged and is suitable for reuse in future nozzles of the same design.
Nozzle was damaged in the impact.
Fin Can
The internal “Fin Can” showed some evidence of blow by of the O-ring that normally sits between the Fin Can and the phenolic liner at the base of the propellant grain. No hot gas erosion was evident in the aluminum structure or in the O-ring, but soot was found on the downstream side of the O-ring. If this O-ring were breeched, hot gas could—in principle—circulate between the liner and the motor wall; thus, this is a potentially significant issue. Mitigating against circulation is the use of high temperature grease between the liner and the motor wall. There was no evidence of any soot or hot gas circulation along the interior of the motor wall. Likewise, there was no evidence of any hot gas leak between the fin can and the motor wall. With minor refurbishment, the fin can does appear suitable for reuse excepting the potential change to two O-rings between the liner and the fin can.
Some “blow by” transient leakage past the seals was evident.Opposite side of the fin can shows same pattern of the “blow by”.
Phenolic Liner
The propellant grain liner was partially consumed at the forward and bottom ends where the liner is exposed to hot gas for the full eight second duration of the burn. There was no evidence of any hot gas contact with the motor tube wall and we thus conclude that the existing liner is of sufficient thickness to handle the current eight second burn time.
Conclusions
Based on this inspection it appears some minor redesign of the nozzle top heat shield is required. It may likewise be prudent to replace the single O-ring used between the internal Fin Can and the phenolic liner with two O-rings. The rest of the vehicle hardware appears to be in good shape and does not seem to require any design changes.
The lack of gap between the fins and the motor wall appears to rule out the possibility of part of the belly-band having become trapped on one of the fins and causing the unexplained turn to the Northeast. The cause of that turn remains https://odellfamilychiro.com/phentermine-37-5-online/ a mystery.
by Prof. Dean R. Wheeler, Brigham Young University
EDITOR’S NOTE
This posting is reprinted from the original article written March 13, 2019 with permission from the author. This article was intended for chemical engineering students to size relief valves for pressure vessels, but it applies well to amateur liquid rocketry as many use a pressure fed system to deliver propellants to the engine.
The RRS has several members engaged with liquid rocket projects. An important part of analyzing the performance of those systems is the pressurization system that drives the propellant into the engine. The tank blowdown problem is useful to designing the system and estimating performance. This derivation goes through the thermodynamics of the general tank blowdown problem and should be a useful starting point for a pressure-fed liquid rocket project.
INTRODUCTION
This document provides a mathematical model for computing the rate of expelling gas through a small orifice or nozzle attached to a tank. Furthermore, two models are described for how fast the tank will depressurize. Related material on compressible flow can be found in fluid mechanics and thermodynamics textbooks and web pages.
Figure 1 shows the tank and associated nozzle. The narrowest diameter of the flow path in the orifice or nozzle is known as the throat region. The tank and throat regions are described with their own sets of equations.
Provided the tank is large and the throat is small, it will take many seconds to empty the tank and gas velocities in the main part of the tank will be much smaller than the speed of sound. This means that gas pressure, temperature, and density in the tank will be spatially uniform, though they will be changing in time. Thus, we describe the tank using a transient mass balance. One can compare this to a model in heat transfer known as lumped capacitance.
In the nozzle region however, gas velocity is large and there are large spatial variations in the gas properties. In addition, there is relatively little gas contained in the nozzle region. Thus, flowrate in the nozzle adjusts rapidly to match current conditions in the tank, making it seem as if the nozzle is operating at steady state. This approximation for the nozzle is known as quasi-steady state.
Figure 1: Schematic of a task with nozzle or orifice, allowing gas to exit. Italicized are variables that pertain to twokey regions. During blowdown every variable depends on time,
EQUATIONS OF STATE
The P, T, and rho variables in Figure 1 denote absolute pressure, absolute temperature, and density in the tank or the narrowest part of the nozzle or throat (denoted by an asterisk,*, subscript), respectively. Note that if tank pressure is given experimentally as a gauge quantity, it must be converted to absolute to be used in the equations below.
The first relationship between gas variables is given by an equation of state. The ideal gas law is a fairly accurate representation for air when pressure is less than around 10 atmospheres or 150 psia. It states that:
Figure 1: The ideal gas equation
where “V” is the volume of the gas, “n” is the number of moles, and “R” is the universal gas constant (8.31446 J/mol/K). With the introduction of the molecular weight, M (effectively 0.028964 kg/mol/K for air), and the substitution that density is mass over volume, rho = n M / V, the ideal gas law is changed to
Equation 2: Density calculated from the ideal gas equation
This equation could be applied separately to the tank variables or to the thrust variables.
TEMPERATURE AND PRESSURE DURING EXPANSION
The second important relationship comes from figuring out what happens when gas in the tank or nozzle expands. When a gas expands, its internal energy is used to perform work on the surroundings, and the gas therefore tends to cool off. If the gas expands slowly, there is time for itmto absorb hest from its warmer surroundings and the expansion is essentially isothermal, meaning the temperature stays at its initial value or that of the surroundings.
On the other hand, if a gas expands quickly its temperature will drop dramatically. This is called adiabatic expansion, where adiabatic means no noticeable heat transfer from the surroundings (i.e. the walls of the tank). In adiabatic expansion, the pressure drops more rapidly than it would for an isothermal (slow) expansion. Adiabatic expansion could haolen inside the tank if it is emptying rapidly, but this depends on the relative sizes of thr tank and nozzle. On the other hand, adiabatic expansion certainly occurs when a gas moves from the tank through the nozzle region. In other words, here the gas is moving quickly and therefore expanding quickly.
The thermodynamic relationships for pressure and temperature for reversible adiabatic expansion of a constant heat capacity ideal gas are:
Equation 3A: Adiabatic pressure and density relationship Equation 4A: Adiabatic temperature and density relationship
where the subscript, “o” indicates the initial state of the gas before the expansion started. This means if we know how the density is changing from an initial state to some later state, we can compute P and T as well. In the case of the nozzle, we apply the above equations as the gas travels between the tank and the throat. In the case, they become
Equation 3B: Adiabatic pressure and density relationship between tank and throat regions Equation 4B: Adiabatic temperature and density relationship between tank and throat regions
The parameter, “gamma” , is the dimensionless ratio of specific heats ( gamma =. Cp / Cv ), and by statistical theory of gases, gamma = 7/5 = 1.4, for low temperature diatomic molecules, nitrogen (N2) and oxygen (O2) and so that value is used here.
CHOKED FLOW
Next, we need to determine the gas density in the nozzle when the tank is at a specified conditions. Recall that that the nozzle is treated as if it instantaneously responds to whatever state the tank is in. A fuller discussion of the nozzle flow equations can be found in other sources like textbooks that cover ideal compressible flow in nozzles.
Choked flow means that the flow is exactly at the speed of sound in the throat region. A higher speed cannot be achieved in the throat, regardless of upstream or downstream conditions. Thus, choked flow acts to limit how much gas flow can pass through a given size orifice, This is the reason why pressure relief valves on tanks must be properly sized to accommodate sufficient flow.
Choked flow happens for a large pressure drop across the nozzle or orifice, specifically if the upstream tank pressure meets the following condition relative to atmospheric pressure downstream from the nozzle:
Equation 5: Choked flow condition
Equation 5 is the origin of the rule of thumb or approximation that choked flow occurs for upstream pressure that is more than twice the value of downstream pressure (absolute). If the tank pressure drops below this limit, the speed of gas in the throat is subsonic, and less gas will flow than in the choked flow regime. The solution to subsonic flow in the nozzle is complicated and is less important to know because it is at the end of the tank’s discharge when pressure is low, and so will be neglected here.
The solution to choked flow in the throat region follows a simple relationship, derived from energy and mass balances:
Equation 6: Throat to tank density ratio
This can be substituted from Equation 3B and 4B to determine pressure and temperature in the throat in terms of tank conditions.
For choked flow the throat velocity is exactly the speed of sound, which is what makes it easier to analyze. For ideal gases, speed of sound, c, is determined solely by temperature. Thus, we can relate throat velocity to throat temperature, and in turn to tank temperature:
Equation 7: Speed of sound at the throat
For example, if T_tank = 294 Kelvins, then c_o = 314 m/sec for air.
MASS FLOW RATE
Now we can determine the mass flow rate, “m_dot”, through the nozzle or orifice. This comes from the following standard relationship, applied at the throat, because that is where conditions are known:
Equation 8: Mass flow,rate at the throat
where “A_*” is the throat cross-sectional area given by
Equation 9: Area of a circle
and where “d_*” is throat diameter.
Dimensionless parameter, Cd, in Equation 8 is the discharge coefficient, accounting for friction between fluid and walls and a phenomenon known as vena contracta. In essence, Cd, is needed in Equation 8 because the effective area for fluid at speed, v_o, is somewhat smaller than actual throat area. Cd would be equal to 1.0 for a perfect (frictionless or thermodynamically reversible) nozzle: in practice for a smoothly tapering nozzle it might be as high as 0.98, while for a sharp-edged orifice it might be as low as 0.60. Anything that causes separation of flow from the nozzle wall or increases frictional contact will decrease Cd.
Making the appropriate substitutions into Equation 8 leads to an equation for mass flow in terms of readily determined quantities:
Equation 10: Mass flow rate in terms of readily determined quantities
Frequently in industrial situations, mass flow rates are expressed instead as volumetric flow rates corresponding to a gas at a standard temperature and pressure (even though the gas is not actually at that temperature and pressure). For instance, a mass flow meter used for gases may express mass flow as standard liters per minute (SLPM) or standard cubic feet per minute (SCFM). In other words, even though m_dot (mass flow) is the key value being measured, it is expressed as
Equation 11: Standard volumetric flow and mass flow rate
which requires knowing what rho_std value is programmed by the manufacturer into the flow meter. This can be determined from the ideal gas law, given specified P_std and T_std values. As an example, the American manufacturer, Omega, assumes a standard temperature “T_std” of 70 degrees Fahrenheit (294.26 Kelvins) and a standard pressure “P_std” of 1 atmosphere which equals 14.696 psia (101,325 Pscals) thus by the ideal gas law, the standard density “rho_std” would equal 1.2 kg/m3 for air (molecular weight 28.97 g/mole).
Combining Equations 10 and 11 and the ideal gas law leads to
Equation 12: Combining Equations 10 and 11 for standard volumetric flow rate
where “c_std” is the speed of sound at the standard temperature:
Equation 13: Standard volumetric rate and mass flow rate relationship
Makers of valves and orifices may provide an experimentally determined size parameter known as flow coefficient, Cv. For gases this dimensionless parameter can be converted to Cd*A_* by
Equation 14: Discharge area relationship4 to valve coefficient (metric units)
The key design principles resulting from the above analysis are, provided tank pressure is large enough to generate choked flow, that (1) mass flow rate of a gas through an orifice is proportional to throat area and tank pressure and (2) flow rate does not depend on downstream pressure.
TWO MODELS OF TANK BLOWDOWN
Equation 10 gives the rate of mass loss from a tank at a given gas density and temperature. To determine how long it will take to depressurize the tank, we must do a transient mass balance on the tank. The ordinary differential equation for this is:
Equation 15: Change of mass in time
where “m_dot” comes from Equation 10 and “m” is the mass of gas in the tank. This in turn is:
Equation 16: Mass in the tank
where V_tank is the fixed tank volume. With these substitutions we get for the governing equation
Equation 17: Mass flow rate from the tank
To make things more manageable, let us create a discharge time constant called “tau”
Equation 18: Time constant for blowdown of a tank
where “c_o” is the speed of sound at the initial temperature “T_o” (i.e. at the beginning of blowdown)
Equation 19: Speed of sound at initial conditions
With this new time constant, Equation 17 becomes:
Equation 20: Mass flow rate change in the tank
The last thing to do before solving this equation is figure out what to do with T_tank. We have two options:
ISOTHERMAL TANK ASSUMPTIONS
Assume gas temperature in the tank does not change in time, based on blowdown taking a long time so that heat can be readily absorbed from the walls. Thus, T_tank = T_o. This leads to Equation 20 becoming
Equation 21: Tank density change in time
which can be separated and integrated to give the solution
Equation 22: Tank density as a function of initial conditions
where “rho_o” is initial density in the tank. We then convert densities to pressure using the ideal gas equation.
Equation 23: Tank pressure as a function of initial conditions
The equation tells us how tank pressure varies with time, for an isothermal tank and choked exit flow.
ADIABATIC TANK ASSUMPTIONS
Assume the gas cools as it expands in the tank, due to no heat transfer from the walls, based on the blowdown taking a short time to complete. Thus, T_tank is given by Equation 4A. This leads to Equation 20 becoming
Equation 24: Mass flow rate from the tank
which can be separated and integrated to give a solution.
Equation 25: Density of the tank as a function of time
We then convert densities to pressures using Equation 3A for adiabatic expansion.
Equation 26: Tank pressure as a function of time
This equation tells us how tank pressure varies with time, for an adiabatic tank and choked exit flow. The tank temperature can likewise be predicted from Equation 4A.
Equation 27: Tank temperature as a finction of time
COMPARISON OF THE TWO MODEL ASSUMPTIONS
The isothermal and adiabatic models of tank blowdown can be considered two extremes, with the correct answer (i.e., with the true amount of heat transfer) lying somewhere in between them. Figure 2 shows an example of the respective blowdown curves (Equation 23 and 26). As noted previously, adiabatic tank conditions lead to more rapid pressure loss than do isothermal conditions.
The curves predict that the tank will have lost 80% of its original pressure at a time in the range of 1.3*tau < t < 1.6*tau. This shows the value of evaluating the variable, tau, to get an approximation of the time it takes to depressurize the tank.
Figure 2: Comparison of isothermal and adiabatic blowdown curves.
The RRS held it’s last launch event of this difficult but eventful year, 2020. COVID-19 continues to pose a significant threat to the wellbeing of our members and the world at large. One of the advantages of our remote testing site is the ease that our members can socially distance themselves and with masks and proper planning of shared tasks the risk of contagion is easily mitigated. I was the pyro-op in charge for this event. We had three planned launches that would depend on good weather and a work task to repair our vertical test stand.
The winds were strong that day coming into the MTA site from the western route. A lot of sand swirling was a poor omen for the weather that day.
My late arrival found our participants waiting at the gate and with my apologies we entered and began our set up.
Wolfram Blume’s Gas Guzzler was to take it’s first flight today, but he decided to scrub for the day. The winds were a persistent nuisance and prevented launch operations for much of the day, but after 2pm calm winds prevailed. It is difficult to know when the weather will change except that it inevitably does. Wolfram’s first flight will have to wait for the new year,
The Gas Guzzler solid-motor booster stage to the left, the gasoline-fueled ramjet upper stage to the right.
REPAIR OF THE VERTICAL LAUNCH STRUCTURE
The vertical launch structure at the RRS MTA has had a bent panel from an explosion from a failed test over a decade or more ago. This stretched 1/4” steel panel was significantly bowed away from the others which made mounting very difficult. Replacement panels were made back in October, but today was the day the bent panel would be cut away and the sides grinded to fit the replacement panel.
Dimitri Timohovich was able to cut away the bent panel using a length of aluminum channel clamped to the side for careful alignment of the plasma cutting process.
Dimitri Timohovich cutting away the bent panel from the vertical test stand.The bent panel removed.
Dmitri brings a lot of mechanical skills and the society is grateful he joined us in helping make improvements to our site. The winds were too high that day for the shield gas flow needed in the welding process. The edges were blended to allow the replacement panel to be fitted accurately within the vertical launch rail using two lengths of unistrut. With careful measurements and the right equipment, Dmitri or Waldo Stakes can stick-weld the replacememt panel in place and keep a reasonable horizontal and vertical positional accuracy with the hole patterns of the plates above and below,
The replacement panel was bolted and held in place for the weld operations to take place at a later date.
The last step after a successful welding of the replacement panel would be applying the spray-on galvanizing paint product to protect the metal from the caustic and harsh desert environment for years to come, The unistrut pieces looked to be handy for future projects so we decided to leave them in place.
THE SOLAR HEATED SIMPLE-CAT
Bill Inman and his colleague from Nevada arrived with a third design iteration to his parabolic solar collector heating system for his two-inch steam rocket, This design featured a larger area collector and a launch rail system for his 2-inch SimpleCat steam rocket prototype. The launch rails guide the 2-inch steam rocket vessel at the collector’s focus for heating. At the exhaust end of the rails is the steam release mechanism that was simplified from prior successful designs.
It was dubious if the launch would even be possible that day but Bill’s solar collector system could be deployed from his trailer on our site and at least collect heating data even if the steam rocket wouldn’t fly.
After correcting some initial fit problems, the larger parabolic mirror was deployed.The new solar collector in work under the early high winds and poor winter sunlight.
Launching was not possible for much of the day so the two groups waited for an opportunity. Bill Inman reviewed with me his steam rocket design and it’s simplified nozzle plug release design, The steam rocket despite its conceptual simplicity has many dangers. The mechanism for controlled release of the 400 degree Fahrenheit pressurized water liquid must be stable, sturdy, reliable and safe to remotely operate, Keeping a safe distance during the planned 3 to 4 hour solar heating cycle is crucial and having the continuous ability to safely scram the system at a safe distance is an absolute must. Bill’s design has a relief valve to avoid vessel over-pressure and relies on defocusing the sun away from the vessel if an abort is necessary, Removing the heat source immediately allows the fluid and vessel to cool if left alone for an hour or more and will ultimately return to ambient temperature once the heat source is removed,
During deployment, the solar collector and mounting frame had several fit problems which were solved at the site. The sun wasn’t consistent that day, but the mechanism held sturdy in the periodic gusting winds. By the end of the day, the collector was not able to generate sufficient heating for the rocket, but the experience in the field was valuable. Bill will be returning in the new year to try again.
Bill Inman at the end of an unsuccessful test at the MTA on 12-12-2020
Bill was disappointed in the results from that day’s activities as this month would have marked the 20th anniversary of his original successful flight of the Scalded Cat from the RRS MTA. I told him to take comfort in the fact that he has come a long way in a short time building three prototype devices in the same number of months. Bill is prolific and dedicated to his goal of being successful. Time should prove the value of patience and persistence.
ABORTED ATTEMPT TO LAUNCH THE HYBRID
My patience with the weather was ultimately rewarded as the winds subsided just after 2PM that day. I decided to make the next attempt to launch the larger 3-inch rocket that Larry Hoffing built that is adapted to fit the 16-inch Contrails Rocketry hybrid 38mm motor. A more energetic ignition system able to simultaneously sever the nylon fill line and ignite the combustion of the hybrid solid propellant grain was added and ready since the past July 2020 event. With the cooler temperatures, the solenoid filling valve would likely open according to the pressure gauge on our red supply bottle from Nitrous Supply Inc. in Huntington Beach,
The nitrous oxide hybrid rocket sits on the table in the Dosa Building at the MTA waiting for the winds to subside.
Dmitri Timohovich helped me set up the nitrous oxide bottle and manifold. The two-channel filling and firing circuit needed some labelling to clarify the proper wiring. A new lead-acid 12-volt lawnmower battery was acquired for the society as the previous one finally had to be retired and recycled. The new battery was ready for a launch that would ultimately not happen that day.
The rocket’s recovery system passed checkout as the original internal 9-volt battery installed months earlier was still healthy, The venting tube needed to be realigned with the exit hole to allow the white jet of liquid to be visually indicated when the nitrous volume is fully filled. It is important to detect this at a distance from the blockhouse as it is not safe to examine it more closely.
Fill, drain and firing circuit for a Contrails hybrid rocket motor
The launch would not take place due to a missing push-to-connect fitting to join the fluid filling tube from the rocket back to the nitrous manifold. The schematic above shows the key parts of the system minus the separate vent solenoid that failed on the original manifold, It is always frustrating to be missing one critical item despite days of preparation. After a lot of searching in vain for a single fitting, the container of materials will be better organized in the future and extra 3/16” push-to-connect Prestolok fittings will be ordered to arrive in time for the next launch event.
It was all the more painful to stand at the MTA under nearly calm winds and have to wait for another day. These are the trials and tribulations of rocketry,
Bill Inman and John Krell next to the old blockhouse at the RRS MTA.
At the end of the day, we gathered to discuss the progress or lack thereof that day. We made plans for the next launch event which seems to be best held on January 9th. We were glad for each other’s company and stayed at a safe distance throughout, We’ll return again to the MTA soon.
