The Reaction Research Society held an event at the Mojave Test Area (MTA) on May 1, 2021. Dave Crisalli was the pyrotechnic operator in charge. RRS president, Osvaldo Tarditti, was also present along with myself, It was not to be a launch event as all planned tests were static firings by the UCLA liquid rocket team and the UCLA hybrid motor team. The winds were very high that day consistently above 20 MPH and gusts above 50 MPH at times. The weather otherwise was very cooperative with comfortable temperatures.
Dave Crisalli gave a safety briefing in the George Dosa building to all attendees before the first static fire campaign would begin. The RRS pyrotechnic operator in charge is responsible for the safety of all during the event. Hazard identification (spiders, snakes, sharp objects) and good practices (hydration, sunscreen) are always part of the briefing, One of the most important things, Dave Crisalli mentioned was not to be in a hurry. It is very important to take the proper time to do things correctly and safely even if it means not proceeding with the intended test that day. Taking your time means avoiding mistakes and improving your chances for success.
RRS members, Bill Inman and John Wells came to the MTA for the event, but only as spectators. The Solar Cat project is still active and undergoing improvements to its sun tracking method. Bill is also expanding the collector area and adjusting the necessary support structures. It is likely Bill and John will be back for the next RRS MTA event.
Also in attendance was the Compton Comet team who have all recently joined the society as members. It was their first time visiting the MTA and getting a chance to see another university team conduct liquid rocket test operations at our vertical test stand.
RRS member, Wolfram Blume came by the RRS MTA to take measurements of the vertical test stand for a future static fire test of his ramjet upper stage engine. He intends to use a leaf-blower compressor motor to simulate foward air flow, but a lot of calculations and planning is required before proceeding. The vertical test stand has a winch and pulley system still attached from Richard Garcia’s liquid motor test in 2017. It should be adequate for Wolfram’s lifting needs when mounting the test equipment to the stand.
The UCLA team spent the night before on our site setting up their equipment. This advanced planning paid off as they were ready for the first of two hot-fires of the liquid rocket just past noon.
Often, it can take several hours to verify all systems are in good working order before testing especially with a liquid rocket, The hybrid rocket was no exception that day.
One of the two load cells had failed so the two teams had to share the same load cell between the hybrid motor and liquid motor firings. UCLA chose to let the hybrid team go next after successful results were seen with the first firing, The UCLA hybrid motor team corrected a few issues and were able conduct a successful hot-fire by late afternoon.
The society members in attendance also had time to make some minor repairs to the new mobile trailer asset, A steel plate was added to keep intruders from entering. Thanks to Waldo Stakes for doing the welding for this temporary fix.
There was sufficient daylight remaining for a second hot-fire of the UCLA liquid rocket, The team had another engine with the previous injector design from last built and ready with a fresh internal ablative liner. They had retanked another load of ethanol and the liquid oxygen cylinder had sufficient stores for another loading cycle.
Thanks to the hard-won, acquired experience of the UCLA team and their commitment to training new members and holding to their proven procedures, they were able to conduct the second firing safely for an impressive finish that day.
Initial data from both UCLA static firings of their liquid motor suggest that the 650 lbf nominal thrust motor outperformed expectations and will be ready for vehicle integration and flight by May 29, 2021. The UCLA team had reason to celebrate at the end of the day. The RRS was glad to be a part of UCLA’s continued campaign to fly liquid rockets that are competitive with any university team in the country.
For other universities interested in working with the RRS, please contact the society president submitting a Standard Record Form downloaded from our website,
by Prof. Dean R. Wheeler, Brigham Young University
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.
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.
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:
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
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:
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
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.
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 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:
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:
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:
where “A_*” is the throat cross-sectional area given by
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:
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
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
where “c_std” is the speed of sound at the standard temperature:
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
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:
where “m_dot” comes from Equation 10 and “m” is the mass of gas in the tank. This in turn is:
where V_tank is the fixed tank volume. With these substitutions we get for the governing equation
To make things more manageable, let us create a discharge time constant called “tau”
where “c_o” is the speed of sound at the initial temperature “T_o” (i.e. at the beginning of blowdown)
With this new time constant, Equation 17 becomes:
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
which can be separated and integrated to give the solution
where “rho_o” is initial density in the tank. We then convert densities to pressure using the ideal gas equation.
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
which can be separated and integrated to give a solution.
We then convert densities to pressures using Equation 3A for adiabatic expansion.
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.
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.
The RRS held its monthly meeting on November 13th. The teleconference brought several of us together again from different parts of the city and around the country.
The society discussed the prior launch event at the MTA held on November 7, 2020. Details of the event are in the firing report posted this month. More RRS members are buidling more rockets and this is a good trend, We were not able to work on site improvements at the event, but these tasks can be resumed at the next event.
The 2020 Constitution Committee is almost ready to release the recommended draft with updated policy listings according to RRS vice-president Frank Miuccio who is the single executive council representative on the committee. Release of the draft will go out in December 2020. If ratified by the voting membership, this new Constitution will clarify RRS rules and policies and supersede all past revisions.
FACILITY UPGRADES AT THE MOJAVE TEST AREA
The society discussed the current progress of facility upgrades approved by the executive council. At the top of the list is a new restroom facility. A couple contractor bids are forthcoming with one being delivered just a few hours before the meeting. Cost is an important consideration and other designs besides a block and concrete design are being considered. Containerized, portable systems may offer an effective solution with fewer complications.
The council approved the construction of a similar pit toilet like the one being used now at the MTA. The second toilet is meant to replace the first as it will not be usable for much longer. A few RRS members are already working to put in this stop-gap measure until the better facility can be selected and funded.
Other site upgrades discussed at the meeting was replacement of the roof structure on the existing blockhouse which would be a temporary but safer solution until a new structure can br funded and built. Another was removal and replacement of the bent panel on the vertical thrust stand which may be done at the next launch event. Still another improvement option is purchasing some of the existing containers from our tenant for more storage space at the site and a water storage tank.
Other improvements include locked and secured areas for high-pressure gas bottles and cryogenic liquid cylindeers. Towable water-spraying trailers have also been discussed to augment fire-fighting at the MTA. A larger launch rail system for heavier liquid rockets at the RRS MTA is also being considered.
DONATE TO THE RRS THROUGH AMAZON SMILE
Amazon Smile is a program that allows Amazon to donate a small percentage of eligible purchases to a non-profit group, such as the Reaction Research Society.
You first enter: smile.amazon.com
then select the Reaction Research Society as your chosen recipient. There is no extra cost to you and you allow the RRS to recieve quarterly donations from Amazon when sufficient purchase amounts have been made in that quarter. With the holiday season approaching, this is a simple way to benefit the RRS and the many activities we support.
For more details and assistance, contact Chris Lujan or just go to Amazon Smile.
NOMINATIONS FOR EXECUTIVE COUNCIL
As per the Constitution, the society holds nominations at the November monthly meeting for the four elected executive council positions. Terms will start in the new calendar year, First, an election chairman is appointed by the council. This person can not run for office in that election cycle. Dave Nordling was selected as election chairman.
Only administrative members in active status can be nominated and hold office. The nominees will be listed on the ballots going out to the eligible voting membership. Ballots will be sent by email which underscores the importance of all members keeping their contact information up to date with the RRS treasurer. Also, one of the requirements of active membership is being current with dues payments also tracked by the RRS treasurer.
ANNUAL MEMBERSHIP DUES
RRS policy is that all annual dues are to be paid on January 1 of each calendar year. New members joining the society throughout the year can pay a pro-rated dues for their first partial calendar year. Membership dues are $40 per year and student membership is $20 per year.
The executive council voted to keep dues at their current levels for the new calendar year, 2021. However, dues will increase to $50 per year starting in 2022 (January 1). All payments are made to the society to the RRS treasurer or the RRS president.
NEXT MTA EVENT
The next launch event at the Mojave Test Area will be held on December 12th. The nitrous oxide hybrid will be launched with the upgraded igniter and new airframe. Other rocket launches are planned.
The next monthly meeting will be held on December 11 by teleconference. Anyone with questions or suggestions should contact the RRS secretary.