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Sustainable design analysis of waterjet cutting through exergy/energy and LCA analysis
h [electronic resource] /
by Matthew Johnson.
[Tampa, Fla] :
b University of South Florida,
Title from PDF of title page.
Document formatted into pages; contains 70 pages.
Thesis (M.S.M.E.)--University of South Florida, 2009.
Includes bibliographical references.
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ABSTRACT: A broad scope analysis of waterjet cutting systems has been developed using thermodynamics, life cycle analysis, and biological system comparison. The typical assessments associated with mechanical design include measures for performance and thermodynamic efficiency. Further analysis has been conducted using exergy, which is not typically incorporated into design practices. Exergy measures the effectiveness of a process with respect to a base state, usually that of the systems surroundings. Comparing Gibbs free energy of biological processes to exergy efficiency has served to illustrate the need for various levels of comparison. Each biological process used in this comparison correlates to a different type of mechanical process and level of complexity. Overall, biological processes display similar properties to mechanical systems in that simpler systems are more energy efficient.In order to determine accurate efficiency and effectiveness values for a mechanical process, in this case waterjet cutting, a set of thermodynamic models was established to account for energy uses. Various output force and velocity models have been developed and are used here for comparison to assess output efficiencies with "no loss" models used as a lossless base. Experimental testing was then conducted using a simple nozzle and a pressure washer with 2 other diameter nozzles. The most energy efficient system used a turbojet nozzle. It was also the most efficient sustained system with energy inputs. However, it had a much lower exergy efficiency compared to the other systems. This implies that it could be significantly improved by more adequately utilizing the energy provided. An effort to assess the green nature of pressurized water systems was done through use of an Economic Input/Output Life Cycle Analysis (EIO-LCA).The EIO-LCA is designed to assess processes for greenhouse gas emissions and total power consumption across the life of a system. Calculations showed that increases in power consumption result in much higher greenhouse gas emissions per unit time than increases in water consumption. Financial cost however showed an opposite trend due to the much greater cost of water with regard to consumption rates in each system. The most "green" system used only a nozzle with no power consumption.
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Advisor: Delcie Durham, Ph.D.
x Mechanical Engineering
t USF Electronic Theses and Dissertations.
Sustainable Design Analysis o f Water j et Cutting Through Exergy / Energy and Lca Analysis by Matthew Johnson A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Delcie Durham Ph.D. Nathan Gallant, Ph.D. David Merkler, Ph.D. Date of Approval: September 13, 2009 Keywords: biological systems, environmental impact, sustainability, exergy analysis, green engineering Copyright 2009 Matthew Johnson
i Table of C ontents L ist of T ables III List o f Figures IV A bstract VI C hapter 1: Introduction 1 C hapter 2: Background 3 2.1. Waterjet Cutters 3 2.1.1. Crack Propagation Model 4 2.1.2. Abrasive Waterjet 4 2.1.3. I mpingement Failure Model 6 2.2. Design Methodology 6 2.2.1. Efficiency 7 2.2.2. Effective ness 7 2.2.3. Sustainable Design 8 184.108.40.206. Life Cycle Analysis 9 2.3. Biological Systems 10 2.3.1. Organelle 10 2.3.2. Cell 11 2.3.3. Organ 12
ii 2.3.4. Gibbs Free Energy 12 C hapter 3: Thermodynamic Model 13 C hapter 4: Experimental Assessment Of Thermodynamic Model 19 C hapter 5: E IO L CA 36 C hapter 6: Discussion 42 6.1. Tradeoffs Between Performance and LCA 44 6.2. Cell Analogy 44 C hapter 7: Conclusions 48 R eferences 50 A ppendices 53 Appendix 1: Experimental Assessment Photos 54 Appendix 2: Experimental Data 59
iii L ist of Tables Table 1: Common Organelles and Associated Functions 10 Table 2: Nozzle Dimensions 20 Table 3: Reynolds Number Values for Systems 1,2 &3 27 Table 4: Work in, Enthalpy, and Kinetic Energy Values for Systems 2 & 3 31 Table 5: Work In, Work Required, and Efficiency Ratings for Systems 2 & 3 32 Table 6: Forces and Impartment Efficiency 33 Table 7: Unpowered Kinetic Impartment Efficiencies 35 Table 8: Resource Consumption & Costs 37 Table 9: System Resource Costs Per Hour 38 Table 10: Water Sector Global Warming Potential & Energy Consumption 39 Table 11: Power Supply Sector Global Warming Potential & Energy Consumption 40 Table 12: Total Global Warming Potential & Energy Consumption 40
iv L ist of Figures Figure 1: Waterjet Cutter Head 5 Figure 2: Animal Cell 11 Figure 3: Model System & Measurements 14 Figure 4: Cross Section of Test Stand 22 Figure 5: System Diagram With Sensor Placement 23 Figure 6: Mass Flow Rate Vs. Cross Sectional Area 24 Figure 7: Input Velocities 25 Figure 8: Input and Output Velocities 26 Figure 9: Force Output 28 Figure 10: Average Force Outputs 29 Figure 11: Pressure Output 30 Figure 12: Energy and Exergy Efficiencies of Systems 2 and 3 34 Figure 13: Volumetric Flow Meter (Gal) 54 Figure 14: Load Cell With Impact Plate & Mount 55 Figure 15: Input Line Pressure Meter (psi) 55 Figure 16: Watts Up Electricity Meter 56 Figure 17: Type J Thermocouple 56 Figure 18: Nozzle Comparison for Each System 57 Figure 19: System Comparison 57
v Figure 20: Experimental Test Stand Assembly 58
vi Sustainable Design Analysis of Waterjet Cutting Through Exergy/Energy and Lca Analysis Matthew Johnson ABSTRACT A broad scope analysis of waterjet cutting systems has been developed using thermodynamics, life cycle analysis, and biological system comparison The typical assessments associated with mechanical design include measures for performance and thermodynamic efficiency Further analysis has been conducted using exergy, which is not typically incorporated into design practices. Exergy measures the effectiveness of a process with respect to a base state, usually that of the systems surroundings. C omparing Gibbs free energy of biological processes to exergy efficiency has served to illu str ate the need for various levels of comparison. Each biological process used in this comparison co rrelates to a different type of mechanical process and level of co mplexity. Overall, biological processes display similar properties to mechanical systems in that simpler systems are more energy efficient. In order to determine accurate efficiency and effectiveness values for a mechanical process, in this case waterjet cutting a set of thermodynamic models was
vii established to account for energy uses. Various output force and velocity models have been developed and are used here for comparison to assess output efficiencies with no loss models used as a lossless base. E xperimental testing was then conducted using a simple nozzle and a pressure washer with 2 other diameter nozzles. The most energy efficient system used a turbojet nozzle. It was also the most efficient sustained system with energy inputs. However, it had a much lower exergy efficiency compared to the other systems. This implies that it could be significantly improved by more adequately utiliz ing the energy provided. An effort to assess the green nature of pressurized water systems was done through use of an Economic Input/Output Life Cycle Analysis (EIO LCA). The EIO LCA is designed to assess processes for greenhouse gas emissions and total power consumption across th e life of a system. Calculations showed that increases in power consumption result in much higher greenhouse gas emissions per unit time than increases in water consumption. Financial cost however showed an opposite trend due to the much greater cost of water with regard to consumption rates in each system. The most "green" system used only a nozzle with no power consumption.
1 C hapter 1: I ntroduction Waterjet cutting is considered a highly efficient manufacturing method. The process involves the use of highly pressurized water as a cutting medium which imparts negligible amounts of heat to the work piece being cut. As such, the parts created by this form of ma nufacturing incur no change in crystal structure typically caused by heat generated in other metal removal processes The analysis of such a manufacturing process from an exergy standpoint may serve as a preliminary indicator as to how effective it is. Ex isting models of this process will be extended to determine both the thermodynamic efficiency and effectiveness of a waterjet machining process. T he model will then be assessed for accur acy through experimental trials and then for evaluating its usefulness in identifying key parameters that affect the efficiencies and effectiveness. Manufacturing process comparison to cellular processes may also be useful in determining sustainable design metrics. Cellular processes are typically assessed on a Gibbs free e nergy basis, which is similar in methodology to an exergy analysis. As some biological systems are highly efficient in the use of available resources while minimizing waste, a comparative analogy between a waterjet and variable scale cellular systems could prove invaluable in determining a set of sustainable design metrics for mechanical
2 systems which may result in higher efficiencies, effectiveness and better resource utilization while minimizing ecological impact and waste. Similarly, a life cycle analys is of waterjet cutting should also identify which aspects of the process have the most impact on those economical and ecological facets.
3 C hapter 2: Background While the focus of this analysis is rooted in mechanical engineering, there are many cross disciplinary terms and ideas which will be introduced. This background is meant to act as a primer for introducing the knowledge required to relate the ideas being presented. 2.1. Waterjet Cutters The advent of what may be considered modern waterjet cutting brought with it what can only be described as an amalgam of manufacturing possibilities. Modern waterjet s use pressures in the range of 200 800 MPa with exit velocities which may approach 1200 m/s.1 10 Water at that velocity acts in much the sam e way a s a saw cutting through very hard materials Cutters are usually attached to a number of servos which a llow for computer numberically controlled (CNC) machining.1 The most influential aspect of using a waterjet cutter over standard machining alter natives, is that the water stream does not heat the material during cutting.1 This prevents the typical heat affected zones and possible sub surface damage which may be present after traditional cutting. As such, material properties can be held at nominal values and are as such, much more likely to act as designed.
4 2.1.1. C rack Propagation Model For waterjet cutting, material removal occurs by crack propagation.1,2,5,7,9 Materials science dictates that in order for cracking to occur, a defect or dislocati on in an a ffected material must be present. In other words, materials which have failed from the extenuation of a crack already had a defect present, such as in the form of a microstructural anomoly. Waterjet s serve to promote crack growth by imparting localized pressure fields on a surface, exploiting the nature of these defects and eventually cutting completely through the material.1 Typically, more brittle materials fail under this mechanism.1 2.1.2. A brasive Waterjet An abrasive waterjet acts similarly to a standard waterjet in that the force imparted comes from a combination of stream velocity and pressure. Abrasive waterjet s differ in that abrasive additives are mixed int o the water stream, typically an abrasive garnet in the range of 80 grit.1 1 0 The addition of hardened particles acts to increase stream cohesion and impart higher levels of kinetic energy.1 1 0 The addition of garnet for instance, will allow a water stream to cut th r ough very hard and brittle materials such as titanium with very l ow resource utilization It has also been suggested that the addition of abrasive particles may serve to decrease the cost per unit length when cutting materials through reduction in the water and electricity required to cut a medium .2 A detailed diagram o f a standard abrasive waterjet cutting head assembly is present in Figure 1.
5 Figure 1: Waterjet Cutter Head; 1 high pressure water inlet, 2 jewel (ruby or diamond), 3 abrasive (garnet), 4 mixing tube, 5 guard, 6 cutting water jet, 7 cut material Source: Zureks, Waterjet Cutter Head, http://commons.wikimedia.org/wiki/File:Water_jet_cut ter_head.svg
6 2.1. 3 I mpingement Failure Model The impingement model for material removal details plastic deformation as the cause of primary failure.1 Ductile materials such as metals typically undergo this type of failure during waterjet cutting.1 ,5,9 Evidence of this has been shown in a variety of papers whereby an abrasive waterjet embeds partiles of abrasive in the metal. This acts to cause localized areas of highly strain hardened material. The m aterial in essence surrounds t he embedded particle in a sheath The bombardment continues this trend until the material has completely flown out of the path of stream travel or until the stream and abrasives have broken through following impact due to cracking .1 ,5,9 Because of the likeli hood of embedding particulates rather than removing material, a non perp e ndicular angle of attack is sometimes used, whereby knicks in the cut zone are created due to glancing impacts .1 2.2. D esign Methodology Common practice for design of modern technology is performance based.1118 In essence, this means that the goal of design is to achieve a particular performance level with product efficiency. In this respect, other design considerations such as resource utilization or environmental impact are often times only taken into account when deemed an economical shortcoming.
7 2.2.1. E fficiency Efficiency is typically assessed on an output vs. input basis.11 In other words, effeciency for a pump is merely a performance measurement which defines the ratio of output to input as defined by E quation 21. The first law of thermodynamics then dictates that output can never exceed input and as such, the ratio must always fall between 0 and 1. For a value of 1, all energy input would be exchanged as output whereas for a value of 0, all energy input would be lost. The amount of energy lost can be the result of friction, heat transfer to th e surroundings, or improperly designed components These losses all act to limit the highest ef ficiency a proccess can achieve, according to a first law analysis.11 (2 1) 2.2.2. E ffectiveness Effectiveness, or Ex ergy eff iciency, uses the standard formula for efficiency but also takes into account exergy destruction. Effectiveness assesses the quality of energy used with regard to the maximum obtainable work in a system.1 1 In essence, the system is being compared to an ide al C arnot engine s use of energy. This means that the energy used is being compared to the maximum potential of heat energy being used in the form of work.17 Equation 22 defines exergy destruction or irreversibilities as surrounding temperature multiplied by the change in entropy from entry to exit.11,17 (2 2)
8 2.2.3 S ustainable Design The idea of sustainable design is not a new one. One recognized application of such a design methodology is intended to minimize negative environmental impact with regard to the 12 Principles of Green Engineering. 18 The 12 principles are listed as follows: 1. Designers need to strive to ensure that all material and ener gy inputs and outputs are as inherently nonhazardous as possible. 2. It is b etter to prevent waste than to treat or clean up waste after it is formed 3. Seperation and purification operations should be designed to minimize energy consumption and materials use. 4. Products, processes, and systems should be designed to maximize mass, energy, space, and time efficiency. 5. Products, processes, and systems should be output pulled rather than input pushed through the use of energy and materials. 6. Embedded entropy and co mplexity must be viewed as an investment when making design choices on recycle, reuse, or beneficial disposition. 7. Targeted durability, not immortality, should be a design goal. 8. Design for unnecessary capacity or capability (e.g., one size fits all) solutions should be considered a design flaw.
9 9. Material diversity in multicomponent products should be minimized to promote disassembly and value retention. 10. Design of products, processes, and systems must include integration and interconnectivity with avail able energy and materials flows. 11. Products, processes, and systems should be designed for performance in a commercial afterlife. 12. Material and energy inputs should be renewable rather than depleting. 2.2.3 .1. L ife Cycle Analysis The intent of a life cycl e analysis is to determine not only economic impact but also environmental impact over the life of a process.1 5 Economic impacts cover the financial costs assessed either per unit time for usage or for the total life if known. Some of the relevant variables include cost of the object, power usage, chemical usage, and any relevant maintence costs. Environmental impa cts cover the creation of any environmental hazards as a result of the process. These may include but are not limited to greenhouse gasses or wastes.15
10 2.3. B iological Systems 2.3.1. O rganelle At the most basic level, an organelle may be considered as on e of the many specialized components that make up a typical eukaryotic cell. Each eukaryotic cell, also known as an animal cell, has a standardized make up. This does not change with differentiation of cell types. In other words, a muscle cell will have th e same organelles as an epithelial cell, albeit in possibly different concentrations.1 9 Table 1 lists a number of these organelles and their functions within a cell.1 9 Table 1: Common Organelles and Associated Functions Organelle Function 1 9 Golgi Apparatus Process all incoming proteins, enzymes, and lipids while at the same time also controlling their export. Lysosomes Break down particles, other cells, and old organelles for reutilization of resources. Nucleus Acts as the brain of the cell, serving to moderate and control internal resources as well as external actions. Mitochondrion Serve to create ATP as a fuel to power cellular functions. Ribosomes Convert nucleic acids into proteins using mRNA as a template.
11 2.3.2. C ell The cell is the smallest living biological entity. Cells are the basic building blocks for any more complex organism.1 9 While cells vary in function and size, each has a number of the same b asic organelles .1 9 Figure 2 details the general makeup of a eukar yotic (animal) cell with some of these common organelles identified. Figure 2: Animal Cell19
12 2.3.3. O rgan Biology defines an organ as a component or system which is made up of a collection of tissues and cells with a common purpose.19 Organs typically have a primary tissue type which is specific to the organ as well as secondary general tissue types which are com mon to most organ ty pes. Organs are similar to organelles in that they operate to serve a larger system such as an organism 2.3. 4 G ibbs Free Energy Gibbs free energy is a term used in the biochemistry field to define the second law of thermodynamics.1 9 In this respect it is similar to exergy in that they both measure how much energy a system can utilize if the conversion energy was directly from heat to work. Gibbs free energy is assessed with regard to the system temperature and the change in enthalpies and entropies from state 1 to 2.1 9 Rather than measure the actual amount of 1 9 The standard G ibbs free energy equation is defined in E quation 23. A more applicable definition for the purposes of comparison is defined in E quation 24. (2 3) (2 4)
13 C hapter 3: Thermodynamic Model A variety of analyse s have been conducted on water jet cutters which encompass its performance aspects. An analysis which assesses both 1st and 2nd law efficiencies has not been done however. As such the implementation of such an analysis requires the use of model designed to assess the energy usage with regard to per formance. Most models for water jet cutting ignore the energy requirements associated with increased water pressurization and as so they are not entirely relevant to determining efficiency or effectiveness. A typical method for assessing energy o utput and requirements for a water stream is to analyze the changes in enthalpy, kinetic energy, and potential energy. Equation 1 identifies the basic equation for assessing these terms. The term is mass flow rate in kg/s and indicates that the stream wi ll be measured with respect to time. Figure 3 displays an ideal system for use with this model and the required measurements. (3 1)
14 Figure 3: Model System & Measurements Wis refers to the isentropic or no loss work associated with a stream and is measured in J/s or Watts. The h1 and h2s terms refer to the specific enthalpy associated with the stream at entry (point 1) and exit (point 2). Typically, specific enthalpy is asse ssed on a J/kg basis and can be measured by temperature and pressure relationships associated w ith a fluid. In a typical water jet system however, there is a minimal increase in temperature whereas pressure may increase drastically. To more accurately asse ss such a relationship, an equation for determining specific enthalpy from internal energy, pressure, and specific volume will be used.
15 (3 2) on a m^3/kg basis. P denotes pressure in Pascals, and u represents internal energy in J/kg. By replacing specific enthalpy with E quation 32 in E quation 31, a difference in pressures with respect to specific volume can be found. Internal energy should most likely remain constant so long as water is cons idered incompressible. This demonstr ates that an increase enthalpy will result not from temperature increase, but from pressure increase. Vel is used to denote velocity and when paired with mass flow rate closely resembles E quation 33, which defines the kinetic energy of an object. This again means that the 2nd set of terms in E quation 31 is actually a measure for the difference of kinetic energy from the entry to exit. When used at just the exit however, E quation 33 may be used to assess the maximum p ossible impact force from a water stream at exit velocity. It may also be used with the cross sectional area A of the stream to find the pressure of the water stream on the impact surface. Force is measured in J/s. (3 3) At this point however, another issue arises. There will be a difference between the actual impact force and calculated impact force. This occurs due to a variety of issues, including that a water stream does not act as a solid object would. A number of factors affect how closely a stream of water will act compared to a solid object. Chief a mong
16 these are Reynolds Number, which defines how laminar or turbulent a stream is, and stream pressure, which acts to increase transmissivity Equation 34 defines the R eynolds (3 4) Finding entry and exit velocities may be easier through base calculation involving water density, cross sectional area, and a measured volumetric or mass flow rate. For this purpose three relationships have been established. The first ( E quation 35) relates volumetric flow rate to mass flow rate using water density. The second equation ( E quation 36) relates mass flow rate to velocity and cross sectional area using density. The third and final relationship ( E quation 37) may be used to find the relation between entry and exit velocities by assuming that mass flow rate in is equivalent to mass flow rate out and that density remains constant. (3 5) (3 6) (3 7) The last of the three terms found in equation 3 1 refers to the difference in potential energy. Fortunately, in most systems, the potential energy difference is in fact not substantial. This is because unlike the velocity terms, the heights are not squared. This means, at a height difference of even 1 m the energy lost in a typical water jet
17 system using roughly 0.1 kg/s mass flow rate would equate to just 0. 98 Watts compare d to the e nergy input of a standard water jet cutter being somewhere near 23 kWatts At this juncture, each of the terms in E quation 31 may be assessed using nominal values based on constant inputs measured such as mass flow rate pressure in, and geometry of both the entry and exit ports. From E quation 37, velocity out may be found an d input to E quation 33. This will yield a lossless force value and associated output pressure. Using the pressure and force values in E quation 31 should then yield an isentropic work value. This is essentially a minimal work required value which signifies the lowest possible amount of energy which could be input to create the equivalent pressure and output force. Due to losses inherent to any system, this value of i sentropic work will never be achieved. With that in mind, an efficiency value can be found through the use of E quation 38. Division of isentropic work values by actual work input will yield an efficiency rating. (3 8) The overall effectiveness or exergy efficiency of the system may then be determined through the addition of a term governing exergy destruction. The exergy destruction is based on the surrounding temperature and the differential between entry and exit specific entropy values. This term is designed to account for the amount of energy which can never be recovered from the exchange of energy occurring within the
18 boundaries of the system. Equation 3 9 shows the basic exergy equation Equation 310 then shows effectiveness utilizing a comparison between exergy and actual work input. (3 9) (3 10) When effectiveness approaches the value calculated as efficiency, it means that low amounts of energy are lost in energy conversion. It is important to note that efficiency compares losses in energy relevant to a system whereas effectiveness compares a system s energy utilization in so much as various types of energy use carry with them a higher transmissivity and innate ability to maintain higher levels of order. For this waterjet cutter model, this suggests that the force comes mostly from the achievement of higher levels of velocity. Velocity increase is therefore obtained through a combination of minimizing nozzle geometry with respect to entry geometry and an increase of mass flow rate through use of pressurization.
19 C hapter 4: Experimental Assessment of Thermodynamic Model To test the validity of the model, an experimental apparatus has been constructed with sensors designed to monitor the needed thermodynamic components of the system. Among these components are volumetric flow rate, ingoing and outgoing temperature, ingoing pressure, and outgoing force. These components may then be used w ith the model to assess efficiencies of the various test systems. The first test system analyzed is that of a simple pressure driven nozzle. Essentially, the force to be imparted comes from the change in cross sectional area from the supply hose to the nozzle. The nozzle is roughly 1/30th the size of the sup ply hose, which in turn amplifies the input velocity by 30 times at the output. The nozzle cross sectional area is about 6.7E 06 m2. It is important to note the water flow is driven solely by standard plumbing water pressure which was measured to be 80 psi The second and third system s analyzed utilize a pressure was her rated for 1800 psi output. The difference between systems two and three is the nozzle type used. System two uses a slightly divergent nozzle with a 0.125 diameter while system three uses a 0.175 diameter flat nozzle. The second system has an approximate nozzle cross section ratio of 1/25th the input hose, whereas the third system has approximately a 1/13th ratio. Based on E quation 37, it is logical to assume that a higher input:output ratio will result
20 in higher velocity output, and as such, higher force output. Table 2 designates the nozzle geometry values and input:output ratios. Table 2: Nozzle Dimensions Implementation of the model assessment (photos available in A ppendix 1: F igure 18) was conducted with respect to the following procedure and was reiterated for each of the three systems being tested: 1. Mount the force load cell on the target grill with the impact plate affixed on top. 2. Mount the nozzle assembly such that the stream impact will be perpendicular to the load cell. Minimal distance between the nozzle and the impact plate s hould be maintained to minimize velocity losses due to strea m dispersion. 3. Once mounted, the load cell is calibrated in order to zero the force readout while the impact plate is affixed. 4. To measure volumetric flow rate, an inline flow meter is utilized and values are recorded on a unit time basis. System 1 System 2 System 3 Nozzle Diameter (m) 2.921E 03 3.175E 03 4.445E 03 Nozzle Area (m 2 ) 6.704E 06 7.920E 06 1.552E 05 Input : Output Area 29.5 25 12.76
21 5. A watts up meter is used to measure and record power input values. 6. Before each trial, the force readout is once again zeroed in order to maintain accuracy and to assess the maximum burst output for each trial. 7. Discharge of the water stream should occur until values reach o r approximate steady state values. Values to record during this period are flow rate, power input, force output, surrounding temperature, output stream temperature, and input stream temperature. 8. Efficiencies, exerg i es and other values are then calculated from the afore mentioned thermodynamic models.
22 Figure 4: Cross Section of Test Stand
23 Figure 5: System Diagram With Sensor Placement The mass flow rates are found by assessing the volumetric flow rate (m3/s) and convert ing to mass flow rate (kg/s) through a relationship described by E quation 35. The mass flow rate does not necessarily correlate to cross s ectional area as denoted by F igure 6. Rather, the flow rate is driven up by increased pressur ization.
24 Figure 6: Mass Flow Rate Vs. Cross Sectional Area Individual volumetr ic flow rates and by extension mass flow rates were found to be constant across trials with minimal variability. As such, a mean value was used for each system as the basic mass flow rate in the calculation of the other associated variables Input velocity values were found using the relationship described by E quation 36. These input velocities are directly associated with the geometry of the input hose, mass flow rate, and a specific volume value related to the temperature of water. As water is considered to be an incompressible Newtonian fluid, the value for specific vo lume was found from thermodynamic tables and used across trials as a constant value. As the mass flow rates between each system varied, input velocities also varied correspondingly. Of 0 0.000002 0.000004 0.000006 0.000008 0.00001 0.000012 0.000014 0.000016 0.000018 0.05 0.07 0.09 0.11 0.13Area (m^2)Mass Flow Rate (kg/s) Mass Flow Rate Vs. Cross Sectional Area System 1 System 2 System 3
25 the three syste ms defined, system 2 had by far the lowest input velocit y as denoted by F igure 7. Figure 7: Input Velocities After calculating input velocities it is a relatively straightforward process to determine the exit velocity. Output velocity corresponds to input velocity through the flux E quation 37. The relation is that of velocity proportional to cross sectional area being equivalent for both entry and exit if mass flow rate is held constant. It is interesting to note that while system 2 had the lowest input velocity, it is in fact not the lowest output velocity. Figure 8 shows the comparison between input and exit velocities with regard to each system. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.546 0.416 0.597Velocity (m/s)Input Velocities System 1 System 2 System 3
26 Figure 8: Input and Output Velocities By using the output velocities, a Reynolds number may be calculated using E quation 34. Reynolds number identifies each system s relevant level of laminar or turbulent flow. Each system was determined to be turbulent in nature. Table 3 shows the Reynolds number calculated in each system using the assumption that each nozzle has a very small convergence length before exit The Reynolds number in these systems denotes the turbulent or laminar nature of the streams and will serve as a comp arison tool in future analyses. 0.25 0.50 1.00 2.00 4.00 8.00 16.00 32.00 System 1 System 2 System 3 0.55 0.42 0.60 16.13 10.39 7.62Velocity (m/s)Input and Output Stream Velocity Ouput Velocity Input Velocity
27 Table 3: Reynolds Number Values for Systems 1,2 &3 The placement of the nozzle with respect to the load cell was such that maximum output was achieved. The distance between the nozzle and the load cell impact plate was roughly 1 mm. This value was observed to have the highest force ratings across each syst em and nozzle impact from recoil during the initial release of the streams. Initial testing showed correlations between exit velocity and impact ratings as expected except in the case of system 3. However, upon further inspection it was found that system 3 s nozzle opening was higher in the assembly than the others. Where system 1 and system 2 each had a nozzle that opened directly at the impact plate, system 3 had a circular shroud that encased the nozzle and prevented the use of a uniform impact distance. The larger distance from stream exit to impact point results in a drastic pressure loss due to a lack of stream confinement as well as lower pressure air surrounding the stream.1 Stream degradation was also observed further from the exit point and as such the value for stream diameter which is observed at the nozzle exit was used for stream diameter. Force measurements were taken as both peak outputs and sustained values. The peak value was typically observed just after stream initiation and may in fact be caused by backpressure in the system. For instance, systems 2 and 3 show extreme peak output forces, well in excess of the energy available at steady state power consumption. This System 1 System 2 System 3 Reynolds Number 27715 19404 19923
28 may be explained by the initial power used to bring the supply reservoir up to output pressure. Essentially, the peak force observed is a result of prior power input. Figure 9 shows the peak output values recorded over the course of 5 trials. Figure 9: Force Output Sustained values by comparison were measured on a per unit time basis and compared to both water usage and power usage. Sustained values were shown to be much lower than peak values. Figure 10 shows the average sustained force output in comparison to the average peak force output for all th ree systems as well as a mode whereby no work was added to the system 0 5 10 15 20 25 30 1 2 3 4 5 Force (N)Trial Number Peak Force Output System 1 System 2 System 3
29 Figure 10: Average Force Outputs From this particular point, a variety of models exist for determining output pressure. Because the emphasis of this analysis is on impact force, pressure was calculated directly from empirically gathered values. As such, pressure was found by dividing the measured force by the measured stream diameter as defined by E quation 33. While this value is almost certainly not the actual output pressure at the nozzle, it was determined to be the most useful value for calculating efficiency. It was also posited that this value would be closest in nature to what can be described as a transmitted pressure associated with the water stream. In other words, this pressure is what a work piece would actually experience regardless of how pressurized the stream may be. By comparison, a secondary value for pressure was also found and defined as the No Loss 0.125 0.25 0.5 1 2 4 8 16 32 1 2 3 Force (N/s)System Average Force Outputs Peak Force Sustained Force No Input Energy
30 Pressure. This particular value is found by modeling the water stream as a projectile and applying the kinetic energy term in the second half of E quation 33 where the velocity term is taken as the velocity out found by the flux equation. A comparison of average peak, average sustained, and no loss pressure values associated with each of the th ree systems is conveyed in Figure 11. Figure 11: Pressure Output The velocity and pressure values then allow for the calculation of both kinetic energy and enthalpy terms. Kinetic energy relies upon the difference between entry and exit velocity where as the enthalpy term relies upon the difference between entry and exi t internal energy, pressure, and specific volume. Because water is modeled as incompressible, specific volume is taken as constant. Temperature at the inlet and exit 0.002 0.004 0.008 0.016 0.031 0.063 0.125 0.250 0.500 1.000 2.000 4.000 System 1 System 2 System 3 Pressure (MPa)Pressure Output Unpowered Sustained Peak No Loss
31 was also measured experimentally as constant. The average enthalpy and kinetic energy term s with respect to average power consumption in each system under steady state are made available in Table 4 System 1 was not included because an accurate input pressure value could not be established while maintaining the same volumetric flow rate. Table 4: Work in, Enthalpy, and Kinetic Energy Values for Systems 2 & 3 When the kinetic energy and enthalpy terms are combined, the power required can be found, and with it an efficiency value. Because the intent of the study was to develop an analysis which would accurately assess a process in continuous action, the efficien cies were calculated under sustained conditions for systems 2 and 3. System 1 had no direct power input and as such did not qualify to be assessed for efficiency as specified by the established model. Table 5 conveys the average power required, actual powe r input, and corresponding efficiency. System 2 System 3 Work in (J/s) 729.60 1246.00 Enthalpy (J/kg) 249.02 140. 47 Kinetic Energy (J/kg) 53.88 28.85
32 Table 5: Work In, Work Required, and Efficiency Ratings for Systems 2 & 3 Bec ause the values used were based on the impact or transmittable force rather than that measured directly at the nozzle, the enthalpy term may have in fact been larger. As such, rather than looking at standard efficiencies, a better option may be to look at how much force was imparted by the water stream compared to what a solid object might do. This will be a comparison of the force out term to calculations of what could be an expected force determined from the calculated velocity out which has been designat ed as the impartment efficiency Measured force out puts and calculated force out puts are used to define the kinetic energy transmission efficiency (impartment efficiency) and can be found in Table 6. System 2 System 3 Work in (J/s) 729.60 1246.00 Work required (J/s) 25.00 20.02 Efficiency 3. 42% 1. 61%
33 Table 6: Forces and Impartment Efficiency To determine the effectiveness of the pressure washer, values for internal energy and entropy were determined through the use of water property tables. Through the use of E quation 32 enthalpy was calculated using input and output pressures along with the internal energy of the water stream at usage temperature. Entropy was then found using a correlated enthalpy value. Calculation of exergy destruction was done through the manipulation of E quation 22. Total exergy is then found by subtracting exergy destru ction from the standard work in equation resulting in E quation 39. The total exergy defines the total energy available with regard to the base state, in this case the temperature of the room. When compared to the actual input energy an exergetic efficien cy may be found. Figure 12 compares 1st law efficiency ( E quation 38) to 2nd law effectiveness efficiency ( E quation 310). System 1 System 2 System 3 Force Out (N/s) 3.78 2.12 2.22 Calculated Force Out (N/s) 14.06 4.44 3.43 Impartment Efficiency 26.91% 47.79% 64.78%
34 Figure 12: Energy and Exergy Efficiencies of Systems 2 and 3 While each system scales up in terms of cross sectional diameter, the outputs and efficiencies do not. This is of particular interest when examining the nozzle geometries. System 1 has a flat nozzle head similar in nature to the nozzle in system 3. Unfortu nately a direct comparison cannot be made because the nozzle to impact distance in system 3 could not be standardized because of the protective shroud. This particular fact comes into play when examining the pressure decrement involved once a turbulent str eam becomes unconfined. As each system was calculated as highly turbulent, system 3 in respect suffers from higher levels of degradation than either of the other 2 systems. Fortunately, once steady state was reached, pressures and impact forces were found to be similar in nature to system 2. 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% System 2 System 3 Energy vs Exergy Efficiency Energy Efficiency Exergy Efficiency
35 Sustained force values showed a decrease which correlated to the calculated output velocities. In other words, as output velocity increased, so too did unpowered force output. When the compressor on the pump was used t o increase the pressure on systems 2 and 3, substantial gains in output force were noticed. System 1 remained the highest total force output. As denoted in T able 6 however, the force out efficiency increased as power input increased. This would seem to suggest that increased pressure of a stream results in a higher level of imparted velocity. In other words, the stream begins to act more as a solid beam pushing on the force sensor rather than splashing against it. Looking at the relatively low imparted kinetic energy efficiency led to the thought of comparing unpowered kinetic impartment efficiency in T able 7. This particular figure conveys how well each nozzle is designed to work without increasing the pressure of the water being used. Table 7: Unpowered Kinetic Impartment Efficiencies System 1 System 2 System 3 Unpowered Force Out (N/s) 3.78 0.67 0.20 Calculated Force Out (N/s) 14.06 4.44 3.43 Efficiency 26.91% 15.03% 5.70%
36 Chapter 5: EIO LCA The environmental impact of waterjet cutter use was assessed using an Economic Input/Output Life Cycle Analysis (EIO LCA) model. The model chosen was designed for the specific case of analyzing processes on a usage or unit time basis. The analysis consists of determining resource requirements and assessing the environmental impact of their use in the process. The initial step in this analysis is to determine the usage costs associated with the waterjet cutting process. In this respect, the primary costs come from the purchase of the unit, the cost of water on a volumetric basis, and the electricity consumption in kWatts. Table 8 details these costs for each of the three experimental systems tested. The water and electricity consumption valu es were gathered during the experimental assessment. Electricity costs were provided by Tampa Electric and are a suggested commercial rate. Water costs were provided by the City of Tampa Water Department.
37 Table 8: Resource Consumption & Costs These values then allow for the calculation of total cost per hour of use. Electricity and water costs per hour of usage were calculated by multiplying consumption rate by cost. Annual cost could be calculated if an assumed value for daily or weekly use w as given. At this time, that data is not available. Table 9 shows the hourly cost for each system with regard to electricity and water consumption. Interestingly, system 2 which was a powered system showed the lowest total cost per hour at just $ System 1 System 2 System 3 Cost ($) 20.00 200.00 200.00 Water Consumption (gal/hour) 102.84 78.26 112.5 Electricity Consumption (kWh) 0 0.73 1.25 Electricity Cost ($/kWh) 0.128 0.128 0.128 Water Cost ($/gal) 0.005 0.005 0.005
38 0.48. Thi s also shows that water cost is much higher per hour usage than the electricity required to power the pressure washer. This may not be the case with a waterjet cutter.17 Table 9: System Resource Costs Per Hour The EIOLCA software assesses impact based on cost sector performance. The intent is to asses, in a specific area, what greenhouse gasses are released as a result of economic activity. In other words, by relating the system usage to cost per hour, the EIOLC A software makes available a per hour greenhouse gas emission and energy consumption value. Higher values are more detrimental to the environment. The emission and consumption values for each system based on water cost for the water, sewage, and other syst ems sector are designated in Table 10 T he calculated emission and power consumption values for each system based on electrical cost assessed in the power generation and supply sector are then available in Table 11 T otal global warming System 1 System 2 System 3 Electricity Cost ($/hour) 0 0.09 0.16 Water Cost ( $ /hour) 0.51 0.39 0.56 Total Cost ( $/hour ) 0.51 0.48 0.72
39 potential values and power consumptions for each system are conveyed through Table 12. Table 10: Water Sector Global Warming Potential & Energy Consumption GWP (mt CO2 equiv.) Energy Consumption (TJ) System 1 0.000570 0.000001 System 2 0.000436 0.000001 System 3 0.000626 0.000001
40 Table 11: Power Supply Sector Global Warming Potential & Energy Consumption Table 12: Total Global Warming Potential & Energy Consumption GWP (mt CO2 equiv.) Energy Consumption (TJ) System 1 0 0 System 2 0.00077 0.000009 System 3 0.001369 0.000016 GWP Total (mt CO2 equiv.) Total Energy Consumption (TJ) System 1 0.000570 0.000001 System 2 0.001206 0.000010 System 3 0.001995 0.000017
41 The distinction between which sectors emit greater amounts of greenhouse gasses is important to notice here. While system 2 had the lowest total cost per hour to run, its green house gas emissions were second highest. This is due in part to the fact that s ystem 1 had no direct power consumption. Power consumption, while cheaper cost per hour in all cases, produced significantly greater amounts of greenhouse gases. As such, it is clearly the case that power supply has a greater negative impact on the environ ment than water consumption in pressurized water systems such as those tested.
42 Chapter 6: Discussion Thermodynamic e fficiency and effectiveness analysis serve to demonstrate how well a process or system is performing with respect to the best possible performance obtainable As detailed in Chapter 2, an effectiveness efficiency which approaches a 1st law efficiency is indicative of a minimal loss of energy in the form of system irreversibilities. Essentially, this means that more of the energy is used and not wasted. In this way, it is acceptable to then say that efficiency measures the losses of energy due to system parameters whereas effectiveness measures how well the energy was used. Increasing entropy of a system typically results in higher losses due to irreversibility and as such lower effectiveness. Such a relationship may prove to show that higher effectiveness may show a lower level of system wastes and by products. Determinations of both performance and efficiency in the tested systems led to a marked cap of available impact potentials. The meaning behind this is in the fact that velocity output remains constant thus establishing the maximum kinetic energy output available to the system. There are potential differences in actual force o utput compared to maximum force output as a result of stream pressurization. This effectively shows that while impartment efficiency increases under higher power input, further output could be achieved through the use of better nozzle geometry most namely lower cross sectional area which tends to result in higher output velocity as defined by Equation 3 7. Since
43 only systems 2 and 3 were able to use the pump, an assessment of the two systems from unpowered to powered may allow for the reasonable extrapolat ion of how system 1 would react under pressurized conditions. Both system 2 and 3 showed higher impartment efficiencies using pressurized water. As such, system 1 would most likely show an increase in impartment efficiency. Further testing may show that the more efficient nozzle designs of system 1 and 3 could show even higher impartment efficiencies under p ressurized conditions if nozzleto impact distance was able to be standardized. System 3 would have to be modified to allow for those conditions. The id ea behind increased impartment efficiency with decreasing energy efficiency due to stream turbulence may allow for an optimization to be associated with a system. In order to further explore this, a system with variable pressure would have to be utilized. A relationship between power input efficiency and the corresponding imparted energy efficiency may then be investigated Furthermore, reducing the Reynolds number of each stream or even allowing the stream to become fully developed may increase impartment efficiency, 1st law efficiency, and effectiveness. The idea behind this is that a more cohesive stream tends to impart more of the energy stored within as seen with system 1 which had the smallest stream and a nozzle designed to reduce diffusion after exi ting. This could be done by increasing the length of the nozzle to an extent which would allow for the stream to become more fully developed as is the case with modern waterjet cutter nozzles.
44 6.1. Tradeoffs Between Performance and LCA Based on the mod el assessment, a correlation can also be found between increasing pressure and power requirements. This would seem to imply that increasing pressure serves to not only significantly increase losses due to irreversibilities, but also to increase the negativ e impact of the process from a global warming perspective. However, manipulation of equation 36 also shows that increased exit velocities may be obtained by reduction in cross sectional area. This is in fact why system 2 had the lowest cost per hour to ru n but still had the highest sustained force output between the powered systems. The lower resource cost per hour then correlated to a lower green house gas emission value. Therefore, it should be a focus to reduce water and electricity consumption while in creasing exit velocity in order to create the highest force output. 6.2. Cell Analogy In thermodynamic analysis of a system or cycle boundaries are established in order to delimit the areas or components to be considered. This is done to establish indepe ndent analytical values for the component or device within the boundaries As such, full analysis may be done starting at component level and moving upward in scale through the level of full system. This is typically done to assess how each compon ent sub assembly, or assembly a ffect s the system as a whole. Often there are concerns about the effect of any change upon both the local and global efficiencies. Parts of the system can be targetted for design refinements aimed at increasing efficiency, performance, or utility.
45 In this case, an organelle may be assessed which is a basic component of a cell which is in turn a basic component of an organ. The organelle, as a component to the entire system, would then be a factor in the overall system s perfo rmance and efficiency ratings. Such dileneations would then prove useful in comparing similar levels of scale in the biological system to that of a thermodynamic system. Analyzing a biological process in the terms a thermodynamic model requires that all i nputs and outputs be quantified to determine all forms of mass and energy entering and exiting the boundaries of the system. Establishment of such parameters has been done on a series of processes with increasing complexity whereby each more complex system makes use of the systems before it. In this case, the most complex system, the heart, makes use of muscle cells for contraction, which are fueled by ATP created in mitochondria. The various inputs and outputs of each system are made available in T able 13.
46 Table 13: Thermodynamic analysis of 3 biological systems Mitochondria 19 (organelle) Muscle Cell 20,21 (cell) Heart 22 (organ) Input Glucose,6 O2, 36 Phosphate, 36 ADP Creatine Phosphate, Glycogen, ATP 75% Oxygen rich blood, O2(pulmonary stage), Contraction by cardiac muscle cells Output 6 CO2, 6 H2O, 36 ATP Contractive force, waste products from ATP generation 97% Oxygen rich blood, waste products from muscle cells and mitochondria Gibbs Free Energy Efficiency 50% 15 35% 15 25% Comparison Energy conversion External work Change in stream energy
47 A relation can then be drawn that as a greater number of energy interactions occur a lower Gibbs free energy efficiency is obtained. When compared to systems 2 and 3 of the experimental assessment a similarity is also found. System 3 used a much greater am ount of energy than system 2 and subsequently had a lower exergy efficiency. Because exergy efficiency and Gibbs free energy efficiency differ only in the reference states, this becomes an adequate manner for comparison. However, biological systems are not assessed for 1st law efficiency values and as such, nothing can be said of the comparison between how effectively the energy was utilized and if there are trends similar in the mechanical processes. Further research in this area could lead to the determin ation of relationships between efficiency and effectiveness of biological systems and would then allow for their comparisons to mechanical systems. The end result of adaptation and evolution achieved by a biological system, in most cases the survivability in a set of environmental parameters may lead toward an understanding regarding designing processes with higher e ffectiveness as a goal The typical assessment of biological processes is done at a reference state of system temperature. Changing the reference state of the biological system's analysis from system temperature to ambient temperature would also serve to strengthen this argument if the same trends were found as those between exergy efficiency and Gibbs free energy with changes in complexity and energy usage types
48 Chapter 7: Conclusions The energy exergy efficiency model with the experimental validation provide the following insight into waterjet design: Nozzle geometry, cross sectional area and design, greatly impact str eam cohesion, imp artment force, and to an extent regulate environmental impact. Higher impartment efficiencies were nearly always the result of increased pressurization of the water stream but tended to reduce 1st law efficiency. Increasing pressure caused the water to impart the impact surface with kinetic energy more closely equivalent to expected values. Higher exit velocity has a much greater impact on force output than mass flow rate. Water consumption, while much more costly than electricity, results in substantially lower amounts of negative environmental impact. In comparison with biological systems at different scales, the following determinations were made: Biological systems showed reductions in 2nd law efficiency as com plexity increased similar to mechanical systems. Biological systems have higher 2nd law efficiencies at optimum reaction temperatures. T his should be explored in manufacturing processes.
49 Further recommendations: Further comparison between other biological systems at the same scale could lead to more efficient and effective system design practices. Testing at supersonic stream speeds could result in different conclusions and should be examined and determine if there is an applicable effect on Gibbs free energy efficiency. Determine 1st law efficiency of cellular and biological processes for comparison with Gibbs free energy efficiency which will allow for direct comparison to mechanical processes.
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54 Appendix 1: Experimental Assessment Photos Figure 13: Volumetric Flow Meter (Gal)
Appendix 1 (Continued) 55 Figure 14: Load Cell With Impact Plate & Mount Figure 15: Input Line Pressure Meter (psi)
Appendix 1 (Continued) 56 Figure 16: Watts Up Electricity Meter Figure 17: Type J Thermocouple
Appendix 1 (Continued) 57 Figure 18: Nozzle Comparison for Each System Figure 19: System Comparison
Appendix 1 (Continued) 58 Figure 20: Experimental Test Stand Assembly
59 Appendix 2: Experimental Data Specific Volume (ft^3/lb) Pressure In (lb/in^2) Pressure In (Pa) 0.016023073 80 551580.583 Specific Volume (m^3/kg) Kinematic Viscosity Temp Surround (C) 0.001000288 0.0000017 21.41 Water Cost ($/gal) 0.005372751 Jet Ratio Turbo Ratio Adjustable Ratio 29.536862 25 12.75510204 Electric Cost ($/kWh) 0.12844 1800 PSI (Pa) Area in (in^2) Area in (m^2) 12410563.1 0.306919643 0.000198012
Appendix 2 (Continued) 60 Trial Diameter (in) Diameter (m) Area (in^2) Jet 1 0.115 0.002921 0.010391071 2 0.115 0.002921 0.010391071 3 0.115 0.002921 0.010391071 4 0.115 0.002921 0.010391071 5 0.115 0.002921 0.010391071 Pressure Washer Turbo 1 0.125 0.003175 0.012276786 2 0.125 0.003175 0.012276786 3 0.125 0.003175 0.012276786 4 0.125 0.003175 0.012276786 5 0.125 0.003175 0.012276786 Pressure Washer Adjust 1 0.175 0.004445 0.0240625 2 0.175 0.004445 0.0240625 3 0.175 0.004445 0.0240625 4 0.175 0.004445 0.0240625 5 0.175 0.004445 0.0240625
Appendix 2 (Continued) 61 Trial Area (m^2) Mass Flow Rate (lb/s) Mass Flow Rate (Kg/s) Temp ( C ) Jet 1 6.7E 06 0.238332 0.108105 38.1 2 6.7E 06 0.238332 0.108105 38.1 3 6.7E 06 0.238332 0.108105 38.1 4 6.7E 06 0.238332 0.108105 38.1 5 6.7E 06 0.238332 0.108105 38.1 Pressure Washer Turbo 1 7.92E 06 0.181369 0.082268 38.1 2 7.92E 06 0.181369 0.082268 38.1 3 7.92E 06 0.181369 0.082268 38.1 4 7.92E 06 0.181369 0.082268 38.1 5 7.92E 06 0.181369 0.082268 38.1 Pressure Washer Adjust 1 1.55E 05 0.260718 0.11826 38.1 2 1.55E 05 0.260718 0.11826 38.1 3 1.55E 05 0.260718 0.11826 38.1 4 1.55E 05 0.260718 0.11826 38.1 5 1.55E 05 0.260718 0.11826 38.1
Appendix 2 (Continued) 62 In Out Isentropic Trial Internal Energy (kJ/kg) Exergy Destruction (J/s) Enthalpy (kJ/kg) Enthalpy (kJ/kg) Pressure Out (lb/in^2) Jet 1 159.2 159.7517 159.8173 304.2759 2 159.2 159.7517 159.731 304.2759 3 159.2 159.7517 159.6912 304.2759 4 159.2 159.7517 159.8173 304.2759 5 159.2 159.7517 159.7668 304.2759 Avg 159.7517 159.7647 304.2759 std dev 0 0.054945 0 Pressure Washer Turbo 1 159.2 22.86975 159.2189 159.5146 81.30888 2 159.2 21.76147 159.2164 159.4977 81.30888 3 159.2 19.63248 159.2215 159.4753 81.30888 4 159.2 14.88437 159.2126 159.405 81.30888 5 159.2 17.16662 159.2253 159.4472 81.30888 Avg 19.26294 159.2189 159.468 81.30888 std dev 3.276992 0.004809 0.043315 0 Pressure Washer Adjust 1 159.2 0.90819 159.2032 159.3634 32.07691 2 159.2 0.618026 159.2019 159.329 32.07691 3 159.2 0.763108 159.2045 159.3376 32.07691 4 159.2 0.980731 159.2032 159.3433 32.07691 5 159.2 0.806633 159.2013 159.3433 32.07691 Avg 0.815338 159.2028 159.3433 32.07691 std dev 0.139384 0.001256 0.012657 0
Appendix 2 (Continued) 63 Isentropic Gun Gun Peak Peak Trial Pressure Out (Pa) Pressure Out (lb/in^2) Pressure Out (Pa) Pressure Out (lb/in^2) Pressure Out (Pa) Jet 1 2097876 120.2975 829408.9 2 2097876 99.12511 683432.9 3 2097876 95.27559 656891.8 4 2097876 116.4479 802867.8 5 2097876 115.8705 798886.6 Avg 2097876 109.4033 754297.6 std dev 0 11.35086 78260.2 Pressure Washer Turbo 1 560596.2 2.746799 18938.22 475.702 3279798 2 560596.2 2.380559 16413.12 457.7817 3156244 3 560596.2 3.113039 21463.32 499.3242 3442665 4 560596.2 1.8312 12625.48 473.2583 3262950 5 560596.2 3.662399 25250.96 461.8545 3184325 Avg 560596.2 2.746799 18938.22 473.5841 3265197 std dev 0 0.6973 4807.639 16.23609 111942.1 Pressure Washer Adjust 1 221159.1 0.467143 3220.786 38.23436 263612.5 2 221159.1 0.280286 1932.471 51.94886 358169.2 3 221159.1 0.654 4509.1 54.02682 372496 4 221159.1 0.467143 3220.786 54.858 378226.7 5 221159.1 0.186857 1288.314 74.80636 515763.7 Avg 221159.1 0.411086 2834.291 54.77488 377653.6 std dev 0 0.182126 1255.693 13.07098 90119.81
Appendix 2 (Continued) 64 Isentropic Peak Sustained Sustained A1*Vel1 = A2*Vel2 F=1/2mv^2 Trial Pressure Out (lb/in^2) Pressure Out (Pa) Velocity Out (m/s) Velocity Out (m/s) Jet 1 89.50131 617080.2 16.13039216 10.14236874 2 76.99037 530821.7 16.13039216 9.206679013 3 71.2161 491010 16.13039216 9.026138369 4 89.50131 617080.2 16.13039216 9.978771425 5 82.18722 566652.1 16.13039216 9.953999923 Avg 81.87926 564528.8 16.13039216 9.661591495 std dev 7.966969 54929.46 0 0.50695133 Pressure Washer Turbo 1 45.61526 314501.2 10.38966983 25.13044796 2 43.17158 297652.9 10.38966983 24.65255659 3 39.91335 275188.6 10.38966983 25.7468465 4 29.73137 204987.4 10.38966983 25.06581747 5 35.84056 247108.1 10.38966983 24.76197815 Avg 38.85442 267887.6 10.38966983 25.07152934 std dev 6.280555 43302.23 0 0.427468538 Pressure Washer Adjust 1 23.68868 163325.2 7.619969937 8.319245279 2 18.70159 128940.9 7.619969937 9.69717028 3 19.94836 137537 7.619969937 9.889212097 4 20.77954 143267.7 7.619969937 9.964992608 5 20.77954 143267.7 7.619969937 11.63660434 Avg 20.77954 143267.7 7.619969937 9.90144492 std dev 1.8352 12653.06 0 1.178987911
Appendix 2 (Continued) 65 Sustained F=1/2mv^2 Trial Velocity Out (m/s) Velocity in Gun (m/s) Velocity in (m/s) Power In (Watts) Jet 1 8.7483442 0.546111 0 2 8.113895 0.546111 0 3 7.8036943 0.546111 0 4 8.7483442 0.546111 0 5 8.3832675 0.546111 0 Avg 8.3595091 0.546111 0 std dev 0.409941 0 0 Pressure Washer Turbo 1 7.781939 4.027536 0.415587 728 2 7.5706251 3.749432 0.415587 729 3 7.2793374 4.28764 0.415587 727 4 6.282612 3.288469 0.415587 731 5 6.8979516 4.650598 0.415587 733 Avg 7.162493 4.000735 0.415587 729.6 std dev 0.5933192 0.518611 6.21E 17 2.408319 Pressure Washer Adjust 1 6.548283 1.939434 0.597406 1250 2 5.8183022 1.502279 0.597406 1245 3 6.0091166 2.294769 0.597406 1243 4 6.133029 1.939434 0.597406 1240 5 6.133029 1.226606 0.597406 1252 Avg 6.128352 1.780504 0.597406 1246 std dev 0.2677377 0.41809 0 4.949747
Appendix 2 (Continued) 66 Peak Peak Sustained Sustained Gun Trial Force Out (lbf) Force Out (N) Force Out (lbf) Force Out (N) Force Out (lbf) Jet 1 1.25 5.560277 0.93 4.136846 2 1.03 4.581668 0.8 3.558577 3 0.99 4.403739 0.74 3.291684 4 1.21 5.382348 0.93 4.136846 5 1.204 5.355659 0.854 3.798781 Avg 1.1368 5.056738 0.8508 3.784547 std dev 0.117946 0.524649 0.082784 0.368242 Pressure Washer Turbo 1 5.84 25.97761 0.56 2.491004 0.15 2 5.62 24.99901 0.53 2.357557 0.13 3 6.13 27.2676 0.49 2.179629 0.17 4 5.81 25.84417 0.365 1.623601 0.1 5 5.67 25.22142 0.44 1.957218 0.2 Avg 5.814 25.86196 0.477 2.121802 0.15 std dev 0.199324 0.886637 0.077104 0.342975 0.038079 Pressure Washer Adjust 1 0.92 4.092364 0.57 2.535486 0.05 2 1.25 5.560277 0.45 2.0017 0.03 3 1.3 5.782688 0.48 2.135146 0.07 4 1.32 5.871653 0.5 2.224111 0.05 5 1.8 8.006799 0.5 2.224111 0.02 Avg 1.318 5.862756 0.5 2.224111 0.044 std dev 0.314516 1.399035 0.044159 0.196428 0.019494
Appendix 2 (Continued) 67 Gun No Loss Peak Peak Peak Trial Force Out (N) Force Out (N) D Enthalpy KE Work In Calculated (Watts) Jet 1 14.06396 277.9083 129.9457 44.09124 2 14.06396 131.8903 129.9457 28.3059 3 14.06396 105.3416 129.9457 25.43583 4 14.06396 251.3596 129.9457 41.22118 5 14.06396 247.3772 129.9457 40.79067 Avg 14.06396 202.7754 129.9457 35.96896 std dev 1.99E 15 78.28274 0 8.462791 Pressure Washer Turbo 1 0.667233 4.440198 3261.799 53.88626 272.7735 2 0.578269 4.440198 3140.736 53.88626 262.8138 3 0.756198 4.440198 3422.187 53.88626 285.9682 4 0.444822 4.440198 3251.261 53.88626 271.9065 5 0.889644 4.440198 3159.984 53.88626 264.3974 Avg 0.667233 4.440198 3247.193 53.88626 271.5719 std dev 0.169383 0 111.57 7.94E 15 9.178598 Pressure Washer Adjust 1 0.222411 3.433309 260.4667 28.85352 34.2149 2 0.133447 3.433309 356.3393 28.85352 45.55275 3 0.311376 3.433309 368.0929 28.85352 46.94272 4 0.222411 3.433309 375.1139 28.85352 47.77302 5 0.088964 3.433309 514.6235 28.85352 64.27137 Avg 0.195722 3.433309 374.9273 28.85352 47.75095 std dev 0.086712 4.97E 16 90.84122 0 10.74285
Appendix 2 (Continued) 68 Peak Peak Peak Peak Peak Trial Work Efficiency Vel Efficiency Vel^2 Efficiency KE Efficiency Re Jet 1 #DIV/0! 62.87738 39.53566 39.53566 27715.81 2 #DIV/0! 57.0766 32.57738 32.57738 27715.81 3 #DIV/0! 55.95734 31.31224 31.31224 27715.81 4 #DIV/0! 61.86317 38.27051 38.27051 27715.81 5 #DIV/0! 61.7096 38.08074 38.08074 27715.81 Avg #DIV/0! 59.89682 35.95531 35.95531 27715.81 std dev #DIV/0! 3.142833 3.73045 3.73045 0 Pressure Washer Turbo 1 37.46888 241.8792 585.0554 585.0554 19404.24 2 36.05128 237.2795 563.0156 563.0156 19404.24 3 39.33538 247.812 614.1078 614.1078 19404.24 4 37.19651 241.2571 582.0499 582.0499 19404.24 5 36.07058 238.3327 568.0246 568.0246 19404.24 Avg 37.22453 241.3121 582.4507 582.4507 19404.24 std dev 1.343901 4.114361 19.96841 19.96841 0 Pressure Washer Adjust 1 2.737192 109.1769 119.1959 119.1959 19923.98 2 3.658855 127.26 161.951 161.951 19923.98 3 3.776566 129.7802 168.429 168.429 19923.98 4 3.852663 130.7747 171.0202 171.0202 19923.98 5 5.133496 152.7119 233.2094 233.2094 19923.98 Avg 3.831755 129.9407 170.7611 170.7611 19923.98 std dev 0.855274 15.47234 40.74887 40.74887 0
Appendix 2 (Continued) 69 Sustained Sustained Sustained Trial D Enthalpy KE Work In Calculated (Watts) Work in Exergy (Watts) Exergy Efficiency Jet 1 65.51847 129.9457 21.13074 2 20.7649 129.9457 11.80304 3 60.588 129.9457 7.497943 4 65.51847 129.9457 21.13074 5 15.07589 129.9457 15.67762 Avg 12.95199 129.9457 15.44802 std dev 54.94528 0 5.939885 Pressure Washer Turbo 1 295.6481 53.88626 28.75535 5.885601 0.808462 2 281.3208 53.88626 27.57668 5.815211 0.797697 3 253.7983 53.88626 25.31247 5.679994 0.781292 4 192.4173 53.88626 20.2628 5.378432 0.735764 5 221.921 53.88626 22.69 5.523382 0.753531 Avg 249.0211 53.88626 24.91946 5.656524 0.775349 std dev 42.36323 7.94E 15 3.485121 0.208129 0.030308 Pressure Washer Adjust 1 160.1505 28.85352 22.35154 21.44335 1.715468 2 127.045 28.85352 18.4365 17.81847 1.431203 3 133.0662 28.85352 19.14856 18.38545 1.479119 4 140.0872 28.85352 19.97887 18.99813 1.532108 5 142.0203 28.85352 20.20746 19.40083 1.549587 Avg 140.4738 28.85352 20.02458 19.20925 1.541497 std dev 12.49918 0 1.478148 1.386125 0.107791
Appendix 2 (Continued) 70 Sustained Sustained Sustained Sustained Trial Work Efficiency Vel Efficiency Vel^2 Efficiency KE Efficiency Jet 1 54.23516 29.41453 29.41453 2 50.30191 25.30282 25.30282 3 48.37883 23.40511 23.40511 4 54.23516 29.41453 29.41453 5 51.97188 27.01076 27.01076 Avg 51.82459 26.90955 26.90955 std dev 2.54142 2.618338 2.618338 Pressure Washer Turbo 1 3.949911 74.90073 56.1012 56.1012 2 3.782809 72.86685 53.09578 53.09578 3 3.48177 70.06322 49.08855 49.08855 4 2.771929 60.46979 36.56596 36.56596 5 3.095498 66.3924 44.07951 44.07951 Avg 3.416384 68.9386 47.7862 47.7862 std dev 0.48515 5.710664 7.724316 7.724316 Pressure Washer Adjust 1 1.788123 85.93581 73.84964 73.84964 2 1.480843 76.35597 58.30235 58.30235 3 1.540512 78.86011 62.18917 62.18917 4 1.611199 80.48626 64.78038 64.78038 5 1.614015 80.48626 64.78038 64.78038 Avg 1.606938 80.42488 64.78038 64.78038 std dev 0.115335 3.513631 5.721249 5.721249