Article pubs.acs.org/IECR
Analysis of a Gas Supply Unit Based on Hydrogen Peroxide Decomposition for Wearable Robotic Applications Luca Turchetti,*,† Flavia Vitale,‡,§,∥ Dino Accoto,¶ and Maria C. Annesini‡ †
Faculty of Engineering, University “Campus Bio-medico” of Rome, via Alvaro del Portillo 21, 00128 Roma, Italy, Department of Chemical Engineering Materials & Environment, University “La Sapienza” of Rome, via Eudossiana 18, 00184 Roma, Italy, and ¶ Biomedical Robotics and Biomicrosystems Laboratory, University “Campus Bio-medico” of Rome, via Alvaro del Portillo 21, 00128 Roma, Italy ‡
S Supporting Information *
ABSTRACT: With the aim of developing new solutions for powering pneumatic actuators in the field of wearable robotics, a principle scheme of a pressurized gas supply unit (GSU) based on hydrogen peroxide decomposition is proposed and a dynamic mathematical model is developed to simulate its operation. In the application scenario considered for the simulations, the GSU feeds a pneumatic ankle prosthesis during a standard daily living at-home activity. Furthermore, experiments of hydrogen peroxide decomposition on manganese dioxide powder have been carried out in an apparatus that partially mimics the behavior of the GSU. The results show that the GSU proposed is suitable for the implementation in a mobile robotic system, and, more in general, the use of the hydrogen peroxide decomposition process as a gas source for pneumatic actuators can be a viable approach to solve the principal issues related to powering wearable robotic devices.
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INTRODUCTION Since the 1960s, robotics evolved into a multifaceted engineering domain, with robots designed not only to operate in structured environments, as the industrial ones, but also in an environment shared with humans. In this case, when a robot operates autonomously, safety becomes more important than performance (e.g., speed, accuracy, velocity, etc.). This change in priorities generated a technological fork, which reverberated on the design paradigm, fostering the development of novel design methodologies.1 More recently, robotic technology has also been applied to orthotic and prosthetic devices, giving birth to the so-called wearable robotics, that work in close contact with humans, establishing a continuous physical interaction with the human body. The ideal actuator for a wearable robot should have high power and high energy density, in order to allow the effective actuation of mechanics, while keeping weight as low as possible and energetic autonomy as high as possible. Electric motors are still by far the most used actuators in robotics (especially DC servomotors, thanks to their good controllability), but their energy density, limited by batteries, is not well suited for wearable robotics. Conversely, hydraulic and pneumatic actuators show good performance figures, but their applicability to wearable robotics is hindered by the need of machines, such as pumps and compressors, which in turn need a primary, usually battery-powered, motor. An alternative approach for developing fast and lightweight pneumatic actuators, without the need of compressors, consists in using a liquid monopropellant to generate a compressed gas in a controlled manner by catalytic decomposition. A typical monopropellant is hydrogen peroxide, which can be used to produce oxygen with the following reaction © 2013 American Chemical Society
H 2O2 → H 2O +
1 O2 2
(1)
Pioneering works on the use of this monopropellant in the field of robotics were made by Goldfarb and collaborators.2 Since then, the use of H2O2 decomposition has been suggested or implemented in demonstrative devices as a pressurized gas source for direct or indirect powering of robotic actuators. McGee et al.3 investigated a novel type of monopropellantdriven free piston hydraulic pump. Fite et al.4 realized an antropomorphic upper limb prosthesis powered by injecting H2O2 on a catalytic packed bed. A similar solution was suggested by Wu et al.5 to power a lower limb orthesis. Finally, Wu et al.6 developed a small mobile soft robot based on the same principle. All the above-mentioned works are mainly focused on the actuation system and lack a quantitative analysis of the kinetics and thermodynamics of the decomposition reaction used for gas production. However, these aspects appear of fundamental importance for the proper design of monopropellant-powered pneumatic actuation systems. Recently, efforts have been made to fill this knowledge gap. Vitale et al.7 studied H2O2 decomposition catalyzed by Pb−Sn wires in alkaline liquid solutions; furthermore, Turchetti et al.8 performed a kinetic characterization of H2O2 decomposition catalyzed by MnO2 powder. Both of these works were aimed at Special Issue: Giulio Sarti Festschrift Received: Revised: Accepted: Published: 8946
November 15, 2012 February 7, 2013 February 13, 2013 February 13, 2013 dx.doi.org/10.1021/ie303147b | Ind. Eng. Chem. Res. 2013, 52, 8946−8952
Industrial & Engineering Chemistry Research
Article
internal pressure, causing a volume expansion of the vessel and loading of the elastic component. As the vessel volume increase, the catalytic element is progressively extracted from the liquid, slowing down the reaction. The expansion continues until the force exerted by the elastic component balances the internal pressure; in this condition, pressure attains the set-point value (Figure 1b)
assessing the suitability of the H2O2 decomposition process for applications in wearable robotics. The aim of this paper is to provide proof of concept of a H2O2-based gas supply unit (GSU) for pneumatic actuators and to develop a mathematical model that can be a valuable tool for its design and optimization. To that end, a principle scheme of the GSU is proposed and a dynamic mathematical model is developed to simulate its operation. In the application scenario considered for the simulations, the GSU feeds a pneumatic ankle prosthesis during a standard daily living at-home activity. This choice was aimed at performing a conservative assessment of the GSU performance, because the ankle is the most demanding among the joints of the human body in terms of exerted torque. Furthermore, in order to obtain reliable kinetic parameters for the model, the experimental campaign presented by Turchetti et al.8 was extended by performing new experiments aimed at widening the experimental temperature range. This paper is entirely focused on the GSU, that may be seen as a catalytic chemical reactor equipped with a passive pressure control system. Nevertheless, most of the specifications of the GSU, such as the flow rate and pressure of supplied gas, are set upon the requirements of the actuation system. Therefore, a short description of the prosthesis and its requirements are included as Supporting Information.
PSP = Pext +
kelλ S
(2)
and the catalytic element is completely extracted from the liquid solution. This first phase in which the pressure reaches the set-point value will be hereafter referred to as autopressurization. When the actuator is operated, a gas flow rate F is withdrawn from the GSU chamber. As a consequence, the chamber pressure drops, and the catalyst is partially dipped in the liquid (Figure 1c). Oxygen production triggered by the immersion of the catalyst will tend to compensate for gas withdrawal and bring the pressure back to the set-point value. When the actuation system is stopped, gas is still produced, and the chamber expands until the catalyst is completely extracted and pressure goes back to the set-point value, if a sufficient quantity of H2O2 is still present in the liquid. It is worth noting that pressure control in the chamber (and then at GSU outlet) is obtained with a passive system relying only on mechanical signaling.
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PRINCIPLE SCHEME OF THE GAS SUPPLY UNIT The principle scheme of the catalyst-in-liquid gas supply unit proposed here is reported in Figure 1.
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DYNAMIC MODEL
The mathematical model of the GSU represented in Figure 1 was developed under the following hypotheses: 1. 2. 3. 4.
both phases in the reactor behave as ideal mixtures H2O2 evaporation is negligible gas absorption in the liquid phase is negligible in each instant, H2O is in vapor−liquid equilibrium conditions 5. ideal gas law holds 6. the decomposition reaction follows first-order kinetics 7. friction and inertial effects on the piston are negligible
Figure 1. Principle scheme of the GSU: (a) initial condition after liquid loading; (b) set-point condition; (c) gas feed to the actuation system.
The unit is basically a variable-volume vessel constituted by a cylinder-piston arrangement. The vessel is partially filled with liquid H2O2 solution and provided with a solid catalytic element solidal to the piston; furthermore, an elastic component (elastic constant kel) is connected to the piston in order to oppose to the volume expansion of the vessel. The catalytic element is a solid monolithic bar made either of pure or supported catalyst. In order to allow for high reaction rates, the specific interfacial area per unit volume of the catalytic element, avCE, should be as high as possible. Monolithic structures with open porosities, like open-cell solid foams or solid honeycombs, may be used. Indeed, the use of catalytic honeycombs has also been previously considered for other chemical processes involving H2O2.9,10 The liquid solution is loaded in the vessel when the elastic component is at rest: in this condition, the pressure inside the vessel equals the external pressure Pext and the catalytic element is immersed in the liquid for a length λ (Figure 1a). The contact between catalyst and liquid triggers the decomposition reaction; therefore, the production of gaseous oxygen raises the
The validity of hypotheses 1 and 2 was assessed by comparing predictions of H2O−H2O2 liquid−vapor equilibrium obtained by assuming the liquid mixture as ideal and using the activity coefficient model proposed by Scatchard et al.:11 at 30 °C, for H2O2 molar fractions in the liquid up to about 0.2, the ideal liquid mixture model overestimates the bubble point pressure by less than 6%. Furthermore, in these conditions, the H2O2 molar fraction in the vapor is less than 0.01. These results are also confirmed by experimental vapor−liquid equilibrium data reported in the literature.12 As for reaction kinetics, earlier studies12−14 showed that a first-order expression with respect to H2O2 concentration is applicable to the decomposition reaction on different catalysts. Under the above-mentioned hypotheses, the dynamic model of the GSU can be written as a set of differential-algebraic equations that includes (for the sake of brevity, all symbols used in the model are defined in Table 1) the following: • the mass balances for the three components 8947
dx.doi.org/10.1021/ie303147b | Ind. Eng. Chem. Res. 2013, 52, 8946−8952
Industrial & Engineering Chemistry Research
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P[VGSU − (vH2On HL 2O + vH2O2n HL 2O2)] = (nOG2 + n HG2O)RT
Table 1. Summary of the Symbols Used in the Mathematical Model of the GSU symbol
dn HL 2O2 dt
• the vapor−liquid equilibrium condition for water
definition
Latin a cp d Ea F H k0 kel M n ps P R S t T x v V Script 9 Greek λ ν Superscript 0 a G L m v Subscript CE ext GSU H2O H2O2 min O2 pwd s
−
(5)
n HG2O
specific area heat capacity diameter activation energy supplied gas flow rate height pre-exponential factor elastic constant mass number of moles vapor pressure pressure gas constant cross section area time temperature vertical displacement of the piston (see Figure 1) molar volume volume
n HG2O + nOG2
n HL 2O n HL 2O + n HL 2O2
pHs O (T ) 2
• the stress−strain relationship of the elastic element x P = Pext + kel SGSU
(6)
(7)
• and variations in vessel volume 0 VGSU = (HGSU + x)SGSU
(8)
The system of equations can be integrated by considering that, at the beginning of the autopressurization phase, the following initial conditions hold: n H2O2(t = 0) = n H0 2O2
(9)
P(t = 0) = Pext
(10)
n HL 2O(t = 0) + n HG2O(t = 0) = n H0 2O
(11)
reaction rate
P[VGSU − (vHL 2On HL 2O(t = 0) + vHL 2O2n H0 2O2)]
length of the catalytic element (see Figure 1) frequency
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initial state per unit area gas phase liquid phase per unit mass per unit volume catalytic element external Gas Supply Unit (chamber) water hydrogen peroxide minimum oxygen MnO2 powder step (single gait cycle)
=
dn HL 2O dt
+
dn HG2O dt
+
n HG2O n HG2O + nOG2
=9
F
(3)
• the expression of the reaction rate accounting for the extent of immersion of the catalytic element v k 0aaCE SCE(λ
= (nO02 + n HG2O(t = 0))RT
(12)
APPLICATION SCENARIO AND GAS REQUIREMENTS OF THE ACTUATION SYSTEM In order to perform a conservative assessment of the GSU performance, the application scenario chosen for the simulations is the operation of an ankle prosthesis, because the ankle exerts the highest torque among the joints of human body. A standard daily living at-home activity, in which about 600 steps are performed, has been considered (in agreement with the required number of steps for autonomous living of an amputee subject15). Assuming about 15 h of daily activity, 30 cycles of 20 consecutive steps, with 30 min intervals between each cycle, have been simulated. The analysis of the standard human gait cycle and dynamics of an ankle prosthesis allowed the definition of specifications on the flow rate and pressure of the gas supplied by the GSU. The details of this analysis are beyond the main focus of this paper, and only the relevant results are reported here. However, the whole procedure followed to obtain such results is described in the Supporting Information of this paper. Figure 2 shows the instantaneous gas flow rate that the GSU must supply to the actuation system during the execution of a single step (a gait frequency νs of 0.9 s−1 has been assumed). The time-average flow rate defined is
⎛ dn G ⎞ nOG2 O2 ⎟ = 2⎜⎜ + G F n H2O + nOG2 ⎟⎠ ⎝ dt
9=
P=
F ̅ = νs
∫0
1/ νs
F dt = 10.8 mmol/s
which corresponds to an amount of gas to perform each step, Δns, of 12 mmol (this latter figure does not depend on gait frequency). As for the supplied gas pressure, it must be considered that a gas pressure at the actuators as high as 5 bar is required; therefore, the GSU must operate at a minimum pressure Pmin of
n HL 2O2 ⎛ E ⎞ − x)exp⎜ − a ⎟ ⎝ RT ⎠ vH On HL O + vH O n HL O 2 2 2 2 2 2 (4)
• the ideal gas law 8948
dx.doi.org/10.1021/ie303147b | Ind. Eng. Chem. Res. 2013, 52, 8946−8952
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Table 2. Summary of Experimental Trials Used for the Determination of the Kinetic Parameters
Figure 2. Gas molar flow rate required by the actuation system during a single step. A gait frequency of 0.9 s−1 was assumed.
run
thermostatic bath temperature [°C]
MnO2 powder mass [mg]
initial H2O2 concentration [M]
A
80
3.6
1.18
B
80
3.6
1.74
C
80
3.4
3.46
D E F G H I
50 50 50 25 25 25
3.5 7.8 7.8 3.5 7.8 7.8
1.10 1.68 1.10 1.14 1.70 3.46
9=
5.4 bar, in order to account for pressure losses in the gas distribution system.
k 0mM pwd
n HL 2O2 ⎛ Ea ⎞ ⎜ ⎟ exp − ⎝ RT ⎠ vH On HL O + vH O n HL O 2 2 2 2 2 2
ref this work this work this work 8 8 8 8 8 8
(13)
The mathematical model of the reactor was fitted simultaneously to the pressure data collected in all the experiments listed in Table 2, by using the Arrhenius preexponential factor (per unit catalyst mass) km0 and the activation energy Ea of the decomposition reaction 1 as adjustable parameters. The experimental temperature time courses were provided as input to the model. The optimal values found for the parameters are km0 = 1.0 L s−1 μg−1 and Ea = 44.6 kJ mol−1. It is worth noting that the activation energy obtained is consistent with the values reported by Kanungo et al.13 The rate constant per unit area was then calculated as ka0 = km0 /ampwd, with an external area per unit mass of the MnO2 powder, ampwd, of 0.5 m2/g (estimated on the basis of an average particle diameter of 2.4 μm and a density of about 5000 kg/ m3). The calculated pressure time courses obtained with the optimal parameters are reported in Figure 3 as dashed lines and superimposed to the experimental data collected in this work. It may be seen that the model well fits the data. GSU Size and Operating Conditions. A preliminary sizing of the GSU was performed by taking into account the general requirements of small size and reasonable autonomy (i.e., sufficiently long operating time before refilling is necessary) and the specifications on the supplied gas. Table 3 reports a summary of GSU dimensions and the value of other parameters used in the simulations. The maximum volume of the GSU chamber (at full expansion) is about 3.6 l. The initial volume (1.5 L) and concentration (31.3% w/w, 10.4 M) of the liquid H2O2 solution were chosen in order to grant a full-day autonomy; to that end, both the amount of H2O2 consumed during autopressurization and execution of 600 steps were accounted for. As for the catalytic element, a specific surface area per unit volume of 3000 m−1 was assumed. This value lies in the range 2000−3300 m−1 reported by Boger et al.16 for monolithic honeycombs. It is worth noting that only the external geometric area of the monolith open porosities was accounted for because, even if the solid is internally porous, the liquid is excluded from contact with the surface of internal pores, due to the rapid production of gas bubbles at the external solid surface.12 Isothermal operation at a temperature (30 °C) slightly higher than room temperature was assumed in GSU simulation, since
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MODEL PARAMETERS Experimental Determination of Kinetic Parameters of the Reaction. In order to obtain reliable kinetic parameters for the model, the experimental campaign presented by Turchetti et al.8 in the temperature range 25−50 °C was extended by performing higher temperature experiments (80 °C). The apparatus and the methods used in the experimental tests are the same as those used in the previous work8 and will only be briefly described here. Hydrogen peroxide solution 30% w/w was purchased from Sigma Aldrich (Italy) and used for the preparation of all solutions by dilution with distilled water. Manganese dioxide powder was purchased from Carlo Erba Reagenti (Italy) and used as catalyst. Experimental runs were carried out in a stainless steel closed reactor with an available internal volume of 323.6 mL. The reactor was immersed in a thermostatic bath at 80 °C; furthermore, water from the thermostatic bath was also circulated in a coil immersed in the liquid phase inside the reactor. In each experimental run, the reactor was initially loaded with a given mass of MnO2 powder and immersed in the thermostatic bath. About 100 mL of H2O2 solution of known concentration were injected in the reactor, and, immediately after, the reactor was sealed. A summary of the experiments performed in this work and by Turchetti et al.8 is reported Table 2. Pressure and temperature time courses in the reactor were measured and recorded during each run by means of a pressure sensor connected to the gas ceiling and a resistance thermometer immersed in the liquid solution, respectively. The pressure time courses obtained in this work are reported as solid lines in Figure 3. The experimental reactor behaves like a GSU with a rigid (i.e., constant volume) chamber, no gas withdrawal, and constant amount of catalyst immersed in the liquid solution. Therefore, a modified version of the model of the GSU presented in the previous section has been used to analyze the experimental pressure time courses. More specifically, eqs 7 and 8 were removed by setting VGSU = 323.6 mL and x = 0; furthermore, the reaction rate was expressed on a mass basis 8949
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small amplitude temperature oscillations can be expected with the application scenario considered here. In order to support this hypothesis, an extremely conservative estimation of the temperature increase ΔT during a sequence of 20 steps may be performed by assuming adiabatic operation and neglecting the heat capacity of GSU shell and gas phase. If the initial conditions are considered, the liquid solution has a heat capacity cLp = 3.7 kJ kg−1 K−1 and a mass ML = 1.7 kg; furthermore, the heat of the decomposition reaction is Δh = rx
−98 kJ mol−1. Therefore 2·20Δns( −Δh) ΔT
