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A Multi-Disciplinary Analysis Framework for the Design of Small Launch Vehicles

Between the years of 1995 and 2014 the number of small satellites (1-500 kg) went up from 20 to 180. [1] Out of the 180 launched in 2014 66% were Nano satellites (1-10 kg). [1] With this trend of smaller satellites, one would expect a rise in number of small launch vehicles (SLVs are defined by capability to carry 1-100 kg to orbit), but this has not happened: [3] only 8% of all small satellites are launched on SLVs and the others become secondary payloads on regular launch vehicles. [1] This results in small satellites being placed into either suboptimal orbits or waiting for launch schedules to align with bigger launches, resulting in long waiting times. Dedicated SLVs could improve the responsiveness of small satellite launches, but SLV design is complicated by the large architecture space needed to be explored in order to find efficient and affordable designs. The SLV architecture trade space contains many discrete options, e.g. solid vs. liquid fuels, air launch vs. ground launch, number of stages, etc. [2][3] Performing detailed analysis for all the options at once would be prohibitive. Thus, a sizing environment/framework that is capable of providing necessary information for conceptual-level trade studies and can rapidly explore the vast SLV architecture space is necessary. The framework, illustrated in Figure 1, consists of four disciplines central to the sizing and synthesis of launch vehicles: propulsion, aerodynamics, structures, and trajectory. For the aerodynamics and trajectory disciplines, Missile DATCOM and POST2 are used, respectively. The propulsion and structures disciplines are represented in the framework with tools developed at ASDL Georgia Tech. For propulsion, the Solid Motor Analysis Code (SMAC) is a physics-based conceptual design tool for solid rocket motors. SMAC is capable of geometric burn simulation, ballistic analysis, and prediction of thrust performance. [4] For structures, Launch Vehicle Structural Analysis (LVSA) tool is a physics-based tool that focuses on structural dynamic analysis with sizing capability. These tools are integrated into the framework illustrated in Figure 1 with the corresponding connections described in Table 1. The process flow is as follows: first, SMAC sizes insulation and calculates maximum operating pressures for each vehicle stage. The MEOP and insulation thickness values from SMAC are fed to LVSA which then utilizes this information to size the motor casing. This creates a feedback loop between LVSA and SMAC that converges on the radius available for fuel, casing, and insulation thickness. Once the stage sizing is converged on SMAC creates an engine deck that is passed to POST2. Next, the data from SMAC and LVSA goes into Missile DATCOM which generates an aerodynamics database for POST2. Finally, POST2 performs a targeting optimization while maximizing the payload mass to orbit. Within the framework, POST2 is automated in order to be robust to a wide variety of possible designs by performing a Monte Carlo simulation over the initialization vector of the POST2 optimization variables. To demonstrate the capability of this framework, a sample problem of exploring the design space of an SLV capable of placing satellites into a low Earth orbit (inclination=47 deg, 196.5 by 211.3 nm) is used. This sample problem is a ground-launched SLV consisting of four in-line SRM stages. The multidisciplinary design analysis (MDA) environment is utilized to explore a design space consisting of 22 continuous and 12 discrete variables, shown by Table 1 by blocks 1,2,3. Running a full factorial design of experiments (DOE) would have been prohibitively expensive even with this reduced design space, thus a space filling design with 3,502 and then additional expansion of 2,602 cases was used. The first DOE consisted of 3,502 cases, and all of the variables were varied. These input variables are listed in blocks 1, 2, and 3 in Table 1. Most of the variables are propulsion related with stage lengths determining the delta-V split of the SLV. The expansion consisted of 2,602 cases, and the continuous variables were set to be equal to the most promising designs from the sizing of first DOE. For each set of continuous variables, the discrete variables (grain type, star points, and propellant) were to varied. The results of the DOE can be seen in Figure 2; each of the points in this plot represents a closed launch vehicle that reaches the targeted orbit. For each of the cases, there is information on flown trajectory, structural, and propulsion properties of the SLV. For example, Figure 3 shows changes in altitude and velocity with time for a particular case. The right side of Figure 3 clearly shows the coasting (slow decrease) and burning phases (sharp increase) of the SLV mission. LV mass is positively correlated with the optimized payload mass to orbit because heavier LVs carry more fuel and thus have more stored chemical energy. Furthermore, for any given payload mass to orbit, the most efficient design would result in the smallest LV. The results as visualized in Figure 2 shows this tradeoff, and the Pareto frontier of the efficient designs can be seen along the dotted line. Figure 2 can be divided into regions with the lowest mass vehicles corresponding to the minimum bound on radius, and the highest mass vehicles corresponding to the maximum bound on radius. Within a mass region, the discrete variables, such as propellant type and propellant grain arrangement, have the most effect on payload mass. This paper presents an MDA framework that can perform an automated physics-based sizing of SLV designs and a corresponding methodology to utilize the MDA to explore the design space of SLVs. The proposed methodology was applied to a perform a design space exploration for a four stage SLV. The outputs show the expected pareto frontier forming and provide detailed information about the SLV performance and staging. Using the produced data, it will be possible to select a set of pareto optimal designs that can then be further explored in subsequent design cycles. This demonstration shows that automated design space exploration should be used in the early phase design of future SLV concepts.

Nikita S Birbasov↗

NASA NTRS2002

The M2 Proton Channel of Influenza Virus: How Does It Work?

The transport of protons across membranes is an essential process for both bioenergetics of modem cells and the origins of cellular life. All living systems make use of proton gradients across cell walls to convert environmental energy into a high-energy chemical compound, adenosine triphosphate (ATR), synthesized from adenosine diphosphate. ATR, in turn, is used as a source of energy to drive many cellular reactions. The ubiquity of this process in biology suggests that even the earliest cellular systems were relying on proton gradient for harvesting environmental energy needed to support their survival and growth. In contemporary cells, proton transfer is assisted by large, complex proteins embedded in membranes. The issue addressed in this study was: how the same process can be accomplished with the aid of similar, but much simpler molecules that could have existed in the protobiological milieu? The model system used in the study contained a bilayer membrane made of phospholipid, dimyristoylphosphatidylcholine (DMPC), which is a good model of the biological membranes focusing cellular boundaries. Both sides of the bilayer were surrounded by water which simulated the environment inside and outside the cell. Embedded in the membrane was a fragment of the Influenza-A M2 protein and enough sodium counterions to maintain system neutrality. This protein has been shown to exhibit remarkably high rates of proton transport and, therefore, is an excellent model to study the formation of proton gradients across membranes. The Influenza M2 protein is 97 amino acids in length, but a fragment 25 amino acids long, which contains a transmembrane domain of 19 amino acids flanked by 3 amino acids on each side, is sufficient to transport protons. Four identical protein fragments, each folded into a helix, aggregate to form small channels spanning the membrane. Protons are conducted through a narrow pore in the middle of the channel in response to applied voltage. This channel is large enough to contain water molecules, and is normally filled with water. In analogy to the mechanism of proton transfer in some other channels, it has been postulated that protons are translocated along the network of water molecules filling the pore of the channel. This mechanism, however, must involve an additional, important step because the channel contains four histidine amino acid residues, one from each of the helices, which are sufficiently large to occlude the pore and interrupt the water network. The histidine residues ensure channel selectivity by blocking transport of small such as sodium or potassium. They have been also implicated in gating protons due to the ability of each histidine to become positively charged by accepting an additional proton. Two mechanisms of gating have been proposed. In one mechanism, all four histidines acquire an additional proton and, due to repulsion between their positive charges, move away from one another, thus opening the channel. The alternative mechanism relies of the ability of protons to move between different atoms in a molecule (tautomerization). Thus, a proton is captured on one side of the gate while another proton is released from the opposite side, and the molecule returns to the initial state through tautomerization. The simulations were designed to test these two mechanisms. Large-scale, atomic-level molecular dynamics simulations of the channel, in which the histidine residues were in different protonation states revealed that all intermediate states of the system involved in the tautomerization mechanism are structurally stable and the arrangement of water molecules in the channel is conducive to the proton transport. In contrast, in the four-protonated state, postulated to exist in the gate-opening mechanism, the electrostatic repulsion between the histidine residues appears to be so large that the channel looses its structural integrity and one helix moves away from the remaining three. This result indicates that such a mechanism of proton transport is unlikely. The simulations revealed that translocation along a network of water molecules in the channel and tautomerization of the histidine residues in the M2 proteins in the most likely mechanism of proton transport. The results not only explain how a remarkably simple protein system can efficiently aid in the formation of proton gradients across cell walls, but also suggest how this system can be genetically re-engineered to become a directional, reversible proton pump. Such a pump can provide energy to laboratory-built models of simple cellular systems. If they were successfully constructed it would greatly advance our understanding of the beginnings of life and find important applications in medicine and pharmacology.

Pohorille, Andrew↗

NASA NTRS2001

Proton Transport

The transport of protons across membranes is an essential process for both bioenergetics of modern cells and the origins of cellular life. All living systems make use of proton gradients across cell walls to convert environmental energy into a high-energy chemical compound, adenosine triphosphate (ATP), synthesized from adenosine diphosphate. ATP, in turn, is used as a source of energy to drive many cellular reactions. The ubiquity of this process in biology suggests that even the earliest cellular systems were relying on proton gradient for harvesting environmental energy needed to support their survival and growth. In contemporary cells, proton transfer is assisted by large, complex proteins embedded in membranes. The issue addressed in this Study was: how the same process can be accomplished with the aid of similar but much simpler molecules that could have existed in the protobiological milieu? The model system used in the study contained a bilayer membrane made of phospholipid, dimyristoylphosphatidylcholine (DMPC) which is a good model of the biological membranes forming cellular boundaries. Both sides of the bilayer were surrounded by water which simulated the environment inside and outside the cell. Embedded in the membrane was a fragment of the Influenza-A M$_2$ protein and enough sodium counterions to maintain system neutrality. This protein has been shown to exhibit remarkably high rates of proton transport and, therefore, is an excellent model to study the formation of proton gradients across membranes. The Influenza M$_2$ protein is 97 amino acids in length, but a fragment 25 amino acids long. which contains a transmembrane domain of 19 amino acids flanked by three amino acids on each side. is sufficient to transport protons. Four identical protein fragments, each folded into a helix, aggregate to form small channels spanning the membrane. Protons are conducted through a narrow pore in the middle of the channel in response to applied voltage. This channel is large enough to contain water molecules. and is normally filled with water. In analogy to the mechanism of proton transfer in some other channels, it has been postulated that protons are translocated along the network of water molecules filling the pore of the channel. This mechanism, however, must involve an additional important step because the channel contains four histidine amino acid residues, one from each of the helices, which are sufficiently large to occlude the pore and interrupt the water network. The histidine residues ensure channel selectivity by blocking transport of small ions, such as sodium or potassium. They have been also implicated in gating protons due to the ability of each histidine to become positively charged by accepting an additional proton. Two mechanisms of gating have been proposed. In one mechanism, all four histidines acquire an additional proton and, due to repulsion between their positive charges, move away from one another, thus opening the channel. The alternative mechanism relies of the ability of protons to move between different atoms in a molecule (tautomerization). Thus, a proton is captured on one side of the gate while another proton is released from the opposite side, and the molecule returns to the initial state through tautomerization. The simulations were designed to test these two mechanisms. Large-scale, atomic-level molecular dynamics simulations of the channel with the histidine residues in different protonation states revealed that all intermediate states of the system involved in the tautomerization mechanism are structurally stable and the arrangement of water molecules in the channel is conducive to the proton transport. In contrast, in the four-protonated state, postulated to exist in the gate-opening mechanism, the electrostatic repulsion between the histidine residues appears to be so large that the channel loses its structural integrity and one helix moves away from the remaining three. Additional information is contained within the original extended abstract.

Pohorille, Andrew↗

NASA NTRS2002

Motion of Drops on Surfaces with Wettability Gradients

A liquid drop present on a solid surface can move because of a gradient in wettability along the surface, as manifested by a gradient in the contact angle. The contact angle at a given point on the contact line between a solid and a liquid in a gaseous medium is the angle between the tangent planes to the liquid and the solid surfaces at that point and is measured within the liquid side, by convention. The motion of the drop occurs in the direction of increasing wettability. The cause of the motion is the net force exerted on the drop by the solid surface because of the variation of the contact angle around the periphery. This force causes acceleration of an initially stationary drop, and leads to its motion in the direction of decreasing contact angle. The nature of the motion is determined by the balance between the motivating force and the resisting hydrodynamic force from the solid surface and the surrounding gaseous medium. A wettability gradient can be chemically induced as shown by Chaudhury and Whitesides who provided unambiguous experimental evidence that drops can move in such gradients. The phenomenon can be important in heat transfer applications in low gravity, such as when condensation occurs on a surface. Daniel et al have demonstrated that the velocity of a drop on a surface due to a wettability gradient in the presence of condensation can be more than two orders of magnitude larger than that observed in the absence of condensation. In the present research program, we have begun to study the motion of a drop in a wettability gradient systematically using a model system. Our initial efforts will be restricted to a system in which no condensation occurs. The experiments are performed as follows. First, a rectangular strip of approximate dimensions 10 x 20 mm is cut out of a silicon wafer. The strip is cleaned thoroughly and its surface is exposed to the vapor from an alkylchlorosilane for a period lasting between one and two minutes inside a desiccator. This is done using an approximate line source of the vapor in the form of a string soaked in the alkylchlorosilane. Ordinarily, many fluids, including water, wet the surface of silicon quite well. This means that the contact angle is small. But the silanized surface resists wetting, with contact angles that are as large as 100 degs. Therefore, a gradient of wettability is formed on the silicon surface. The region near the string is highly hydrophobic, and the contact angle decreases gradually toward a small value at the hydrophilic end away from this region. The change in wettability occurs over a distance of several mm. The strip is placed on a platform within a Plexiglas cell. Drops of a suitable liquid are introduced on top of the strip near the hydrophobic end. An optical system attached to a video camera is trained on the drop so that images of the moving drop can be captured on videotape for subsequent analysis. We have performed preliminary experiments with water as well as ethylene glycol drops. Results from these experiments will be presented in the poster. Future plans include the refinement of the experimental system so as to permit images to be recorded from the side as well as the top, and the conduct of a systematic study in which the drop size is varied over a good range. Experiments will be conducted with different fluids so as to obtain the largest possible range of suitably defined Reynolds and Capillary numbers. Also, an effort will be initiated on theoretical modeling of this motion. The challenges in the development of the theoretical description lie in the proper analysis of the region in the vicinity of the contact line, as well as in the free boundary nature of the problem. It is known that continuum models assuming the no slip condition all the way to the contact line fail by predicting that the stress on the solid surface becomes singular as the contact line is approached. One approach for dealing with this issue has been to relax the no-slip boundary condition using the Navier model. Molecular dynamics simulations of the contact line region show that for a non-polar liquid on a solid surface, the no-slip boundary condition is in fact incorrect near the contact line. Furthermore, the same simulations also show that the usual relationship between stress and the rate of deformation breaks down in the vicinity of the contact line. In developing continuum theoretical models of the system, we shall accommodate this knowledge to the extent possible.

Subramanian, R. Shankar↗