DEVELOPMENT OF A COMPRESSED CARBON DIOXIDE PROPULSION UNIT FOR NEAR-TERM MARS SURFACE APPLICATIONS

Size: px
Start display at page:

Download "DEVELOPMENT OF A COMPRESSED CARBON DIOXIDE PROPULSION UNIT FOR NEAR-TERM MARS SURFACE APPLICATIONS"

Transcription

1 DEVELOPMENT OF A COMPRESSED CARBON DIOXIDE PROPULSION UNIT FOR NEAR-TERM MARS SURFACE APPLICATIONS Erin Blass Old Dominion University Advisor: Dr. Robert Ash Abstract This work has focused on the development of a reusable rocket propulsion system for near term Mars surface applications by utilizing Mars atmosphere as a propellant source. Mars atmosphere is more than 95% carbon dioxide, and its low ambient temperatures mean that it is relatively easy to condense dry ice out of the atmosphere. Furthermore, the low critical temperature of carbon dioxide enables the production of a supercritical fluid by heating dry ice at constant density to temperatures only slightly higher than terrestrial ambient temperatures. The goal of this research is to develop a supersonic nozzle for reusable high-thrust propulsion. Due to the complex behavior of supercritical carbon dioxide gas, it is not possible to use the standard linear method of characteristics for nozzle design, via the ideal gas-based, Prandtl-Meyer function. Instead, a Method of Characteristics (MOC) for isentropic axisymmetric flow of a real gas has been used to develop the streamline contour of a supersonic nozzle. The boundary layer that develops along the wall of the nozzle is also taken into consideration and then combined with the non-ideal gas method of characteristics to complete the supersonic nozzle design. A Mach nozzle design has been selected because it is possible to achieve relatively high (though modest) specific impulse over longer durations before predicted performance degrades due to recondensation of carbon dioxide. Introduction There are many Martian geographic features that would be very interesting to explore, but current Mars entry descent and landing systems are not capable of placing payloads at precise locations on rough terrain and current surface rovers cannot ascend or descend large boulders, mountains or canyons. Furthermore, as demonstrated by the Mars Exploration Rovers, it is likely that even advanced wheeled systems will become stuck or trapped when they attempt to access some of the more interesting surface regions. There is a near-term need to develop high-thrust systems that can be used to propel surface vehicles in and around hazardous terrain of great scientific interest and to cover large distances. Ideally, this type of surface propulsion should use local Mars resources in order to permit extended reuse. The most readily accessible Mars resource is its atmosphere, consisting mostly of carbon dioxide. The goal of this research is to develop a supersonic nozzle for reusable high-thrust propulsion utilizing compressed carbon dioxide gas extracted from Martian atmosphere and processed as a supercritical fluid for rocket propulsion. The critical temperature of carbon dioxide is 304. K (3 o C or 88 o F), meaning that solid carbon dioxide (dry ice) in a closed container can be heated with relative ease above its critical temperature to become a supercritical fluid at very high pressures and can in that way be used as a rocket propellant. Due to the complex behavior of supercritical carbon dioxide gas, it is not possible to use the standard linear method of characteristics for nozzle design, via the ideal gas-based, Prandtl-Meyer function. Instead, a method of characteristics approach for a non-ideal gas nozzle design has been used. A supersonic convergent-divergent nozzle consisting of a subsonic, sonic, and supersonic section has been the focus of this work. In the subsonic section of the nozzle, the gas speed increases as the nozzle area decreases and that portion of the nozzle can be designed using the continuity equation for steady flow. At the throat, where the cross sectional area is a minimum, the gas velocity becomes sonic. As the subsequent nozzle cross sectional area increases the gas continues to expand and the gas flow increases to supersonic speeds. For supersonic flow, the equations governing compressible fluid flow are a set of hyperbolic partial differential equations. Hyperbolic governing equations can be solved using the method of characteristics. The method of characteristics employs characteristic lines or surfaces (for axisymmetric flow) to construct ideal streamlines. Along these characteristic lines the flow variables are continuous, but their associated derivatives are indeterminate, making it possible to use Cramer s rule to delineate the characteristic lines and compatibility equations. That is, by treating the governing equations as a set of simultaneous linear Blass

2 algebraic equations and using Cramer s rule, it is possible to make the derivatives indeterminate, e.g. u / r v / x 0 / 0, along those surfaces, the characteristic and compatibility equations can be adjusted. Recently, Aldo and Argrow (995) studied plug nozzle designs for non-ideal, dense gas BZT fluids. They developed a method of characteristics approach based on earlier work by Zucrow and Hoffman (976) who developed an Euler predictorcorrector scheme to solve the real gas characteristic and compatibility equations simultaneously. That approach has been modified here for the specific case of supercritical carbon dioxide. However, the resulting streamline contour design neglects viscous interaction with the nozzle wall and hence must be corrected for boundary layer effects. The boundary layer that develops along the wall of the nozzle is also taken into consideration. Boundary layers can be either laminar or turbulent depending on the pressure gradient and the local Reynolds number. At low Reynolds numbers, the boundary layer is laminar and the streamwise velocity increases uniformly moving away from the wall of the nozzle. At higher Reynolds numbers, the boundary layer becomes turbulent and the streamwise velocity is characterized by unsteady swirling flows inside the boundary layer. Using three different throat diameters of,, and 4 mm, with specified density, viscosity, and speed of sound at the nozzle throat, this study has determined that the flow in the sonic section of each nozzle throat produces Reynolds numbers, ranging from 3,00,000 to,800,000, that are considered to be turbulent. There are many approximate methods for estimating the boundary layer growth along the wall of a supersonic nozzle, and most of these have been described and summarized more than 50 years ago by Rogers and Davis (957). In nozzle design it is often assumed that the boundary layer thickness is negligible at the throat due to the favorable pressure gradient upstream of the throat. While it is true that the favorable pressure gradient inhibits the growth of the boundary layer, experiments have shown that the boundary layer thickness is only effectively zero when the exit design Mach number is above 3, as demonstrated by Rogers and Davis (957). In this design the boundary layer thickness at the throat was calculated using a displacement thickness equation model from McCabe (967). Subsequently, the average boundary layer growth along the nozzle contour was estimated using the methods of Rogers and Davis (957), then iterated to adjust for displacement thickness pressure effects. These boundary layer calculations were then combined with the non-ideal gas method of characteristics based streamline contours to complete the supersonic nozzle design. Method of Characteristics A Method of Characteristics (MOC) for isentropic axisymmetric flow of a real gas has been used to develop the frictionless flow streamline contour for our supersonic nozzle. First, using the above mentioned assumptions, the equations for continuity, Euler s momentum equation, irrotationality for an axisymmetric flow, and a speed of sound relation were developed as below. ( ρu) ( ρv) x r ρv 0 r () V u v dp ρ VdV ρ d ρ d () u v r x (3) p dp a (4) ρ dρ s Eqs. -4 are the governing equations used along with some mathematical techniques, such as Cramer s rule, to develop the characteristic and compatibility equations: C characteristic equation: dr dx ( θ µ ) λ tan C compatibility equation: a v ( a ) du [ uv ( u a ) ] dv 0 (5) u λ dx (6) r Where C and C - are the left and right running characteristics as sketched in Fig. (taken from Aldo and Argrow, 995). The gas is assumed to enter the supersonic portion of nozzle across a flat sonic surface (straight line OA in Fig.), with uniform properties and velocity, flowing parallel to the x-axis. The gas then expands and accelerates through the nozzle before exiting from the Blass

3 nozzle with a uniform flow crossing the conical terminating C characteristic surface, with an exit Mach number of M f. For a two-dimensional nozzle, the centered expansion generated by the sharp throat is a Prandtl-Meyer expansion. In the axisymmetric case, the flow at the wall is locally two-dimensional, thus at the throat the expansion is locally Prandtl- Meyer. Fig. Supersonic flow field geometry, upper halfplane Shown below are the Finite Difference Equations corresponding to the characteristic and compatibility relations of Eqs. 5 and 6. and r λ x, () Q u R v S x 0, () λ θ µ Q R S ( ) tan (3) u a (4) uv ( u a )λ a v (5), (6) r where the or denotes C or C - characteristics. It should be noted that (6) applies only to axisymmetric nozzle flow; for two-dimensional flow, S is zero. Construction of the flow field begins by separating the centered expansion into equally-spaced speed increments. Each speed increment V has a related flow turning angle increment θ. The angle θ is computed from the relation θ θ V V M dv V (7) By selecting evenly spaced increments of V, we can use the trapezoidal rule to solve Eq. 7 which can be rewritten as: where, or M d θ dv f ( V ) dv (8) V M f ( V ) (9) V θ θ V V f ( V ) dv (0) Next we use the second-order-average-property Euler Predictor scheme, based on the development presented in Zucrow and Hoffman (976). This procedure shows how the characteristic and compatibility equations can be solved simultaneously. Fig. Schematic representation of intersecting characteristic surfaces Now if we know the values of x, r, u, and v for locations and in Figure, the left running characteristic from will intersect with the right running characteristic from at some point 4, as shown in Fig. (taken from Zucrow and Hoffman, 976). We can determine the location of point 4 by writing Eq. in terms of points, and 4, in finite difference form, i.e.: ( r4 r) ( x4 x) and ( r r) ( x ) Then, λ (7) λ (8) 4 4 x ( θ µ ) and ( θ µ ) where λ tan (9) λ tan (0) v tan u θ. () Blass 3

4 Hence, we can solve for x 4 and r 4, and the compatibility equation can be used to solve for u 4 and v 4, the finite difference form of the compatibility equations can be written in terms of points, and 4 as: Q Q ( u4 u) R ( v4 v) S ( x4 ) 0 ( u u ) R ( v v ) S ( x x ) 0 x Now, the wall contour corresponds to the streamline that passes through points A and C in Fig.. The streamline is also determined by using the averageproperty Euler predictor-corrector scheme to integrate the equation dyw dx tanθ () w marching from the initial condition θ w θ * at x 0 to the exit condition θ w 0 at x x f. Subscript w refers to quantities at the wall and subscript f refers to the exit conditions. The NIST Thermophysical property tables for carbon dioxide have been used here to estimate the properties throughout the nozzle. The strongly varying thermophysical properties are what cause this linear looking method of characteristics to become challenging. That is, the departure from linear theory occurs because the speed of sound for carbon dioxide varies strongly with temperature and pressure near supercritical and phase change states. Results The supersonic nozzle design will actually be a convergent-divergent nozzle consisting of a subsonic or convergent section and a supersonic or divergent section. In order to determine the conditions at the throat we need to calculate the properties and flow variations in the subsonic part of the nozzle. We have used a nozzle entrance diameter of 9.05 mm (i.e. an entrance radius of m [0.375 in]), with a throat diameter of mm (radius is mm). Furthermore, we will assume that the initial (stagnation) pressure is 3.03 MPa (4500 psi) and the stagnation temperature is K. A subsequent isentropic expansion to sonic conditions is characterized by the data in Table. Table : Subsonic Calculations P (MPa) T (K) ρ (kg/m 3 ) M (4500 psia) (3000 psia) 5.5 (50 psia) Table contains representative carbon dioxide property data using the NIST software for computing thermodynamic and transport properties of pure fluids over an anticipated supersonic operating pressure range. Note that the critical pressure for CO is 7.38 MPa (070.0 psia) and the critical temperature is 304. K (3 o C or 88 o F). Therefore, Table shows that anticipated nozzle exit conditions below the critical temperature and pressure can be encountered. Table : NIST Properties P (MPa) T (K) ρ (kg/m^3) M (50 psia) (050 psia) (850 psia) (650 psia) (450 psia) (50 psia) (050 psia) (850 psia) (650 psia) 3.79 (550 psia) Then using the angle-velocity relation, Eq. 7, we get the conditions for a centered expansion at the throat. Next using the second-order-average-property Euler Predictor scheme to solve Eqs. 5 and 6 we can calculate the results shown in Figs. 3 and 4, predicting the supersonic nozzle contour for a mm throat diameter. Figures 5 and 6 are the predicted thermodynamic property variations through the nozzle. Blass 4

5 .4 x (a) Pressure 400 (b) Temperature. Pressure (psi) Temperature (K) x 0-3 Fig. 3 Supersonic Contour, upper-half Density (kg/m 3 ) (c) Density Enthalpy (kj/kg) 50 0 (d) Enthalpy 500 wall 480 axis 40 0 Fig. 6 (a) Pressure distribution along the wall and axis; (b) Temperature distribution along the wall and axis; (c) Density distribution along the wall and axis ; (d) Enthalpy distribution along the wall and axis Fig. 4 Supersonic Contour The thrust and specific impulse can be calculated using the equations below: m& ρva (3) u eq u Thrust e pe p m& & a A e (4) (5) mu eq Velocity (m/s) Mach Number (a) Velocity 50 0 (c) Mach Number Speed of Sound (m/s) (b) Speed of Sound 00 0 wall axis Fig. 5 (a) Velocity distribution along the wall and axis; (b) Speed of Sound distribution along the wall and axis; (c) Mach Number distribution along the wall and axis I u eq sp (6) g Using eqs. 3-6 we get the following results: Using the conditions at the throat of the nozzle: m& 0.75 kg/s Now using the exit conditions: u m/s eq Thrust 39.9 N ( 3.46 lb) I 5.53 s sp The exit Mach number is M f.047 Blass 5

6 Boundary Layer Corrections In nozzle design it is often assumed that the wall boundary layer thickness is negligible at the throat, due to the favorable upstream pressure gradient. While it is true that the pressure gradient inhibits the growth of the boundary layer, some experimental evidence shows that its thickness is only effectively zero when the design Mach number is above 3. This is shown in the Fig. 7 where the measured throat boundary layer thickness in inches has been compared with Tucker s (95) turbulent theory, taken from Rogers and Davis (957). Although the nozzle considered in the figure is not consistent with the present flow, it still shows that we should not neglect the boundary layer effects at the throat initially. δ x 0.9 Re / 5 x (4) Fig. 8 Variation of Thickness Parameter g with Mach Number and N Fig. 7 Comparison of Theoretical and Experimental Boundary Layer Thickness at Throat McCabe (967) correlated the boundary layer displacement thickness measured in the throats of supersonic nozzles as a function of Reynolds number and a characteristic geometry parameter. His correlation. * δ throat h 0 R.06 Re / 5, (3) where h is the throat half height and R is the ratio of curvature at the throat to the throat half height, has been used here to estimate the displacement thickness correction at the nozzle throat. Then from Rogers and Davis (957), we can estimate the average boundary layer growth along the nozzle contour and employ an estimate of the ratio of the displacement thickness to the boundary layer * thickness, given by the shape factor g δ / δ, which is displayed as a function of Mach number and turbulent power law (for representing the turbulent boundary layer profile) in Figure 8. A nominal turbulent velocity profile power law of N 7, has been assumed here, which is the accepted value in most references for moderate Mach numbers. This is based on the /7 power law for a compressible turbulent boundary layer where the velocity profile is represented: u U y δ / 7 (5) In order to justify a turbulent nozzle boundary layer assumption, we need to estimate the throat Reynolds numbers for the expected carbon dioxide sonic conditions. Using d to represent one of our nozzle diameters (d, and 4 mm), and recognizing that the subsonic flow up to the nozzle throat is nominally the same for all three nozzles, we have: ρ a * d Re 3,00,000d µ For the throat of the nozzle, where the following carbon dioxide properties have been assumed: density, ρ kg/m 3 Blass 6

7 speed of sound, a* m/s diameter, d, or 4 (mm) viscosity, µ.69e-05 Pa/s Hence, the estimated nozzle throat Reynolds numbers are: Re 3,00,000; Re 6,400,000; and Re 4,800,000.6 x BL Correction Nozzle Wall Boundary Layer Now, shown in Figures 9-, the displacement thickness of the boundary layer found from Eqs. 3 and 4 are used to correct the potential flow outline of the nozzle profile, for throat diameters of,, and 4 mm Fig. Comparison of Wall Contours using the Boundary Layer Analysis (4mm throat diameter) 6.4 x BL Correction Nozzle Wall Boundary Layer Fig. 9 Comparison of Wall Contours using the Boundary Layer Analysis (mm throat diameter) Table 3: Values for Different Throat Diameters Nozzle Throat 4 Diameter (mm) Reynolds 3,00,000 6,400,000,800,000 Number Exit Area with.5e e-6.99e-5 BL Correction (m ) Mass Flow Rate (kg/s) Thrust (N) (lb) Specific Impulse (s) x BL Correction Nozzle Wall Boundary Layer Fig. 0 Comparison of Wall Contours using the Boundary Layer Analysis (mm throat diameter) Conclusion This research has focused on the design a supersonic nozzle for a propulsion system utilizing compressed carbon dioxide gas extracted from Martian atmosphere and processed as a supercritical fluid for rocket propulsion. Undergraduate mechanical engineering design teams at Old Dominion University have worked hard to design a system that will be used to test the supersonic nozzles once they are built, but have been using a sonic nozzle in their testing this far and have been getting good results. There design consisted of placing solid carbon dioxide (dry ice) in a tank and heating it above its critical temperature to become a supercritical fluid at very high pressures to be used as a rocket propellant. While testing the sonic nozzle there was visual and audible observations which suggested that the expanding Blass 7

8 carbon dioxide continued to behave like a single phase gas expansion at pressures and temperatures that should have produced two-phase nozzle flows, thus extending observed thrust duration. Therefore, one element of my completed research will be to determine whether subcooled carbon dioxide can support propulsion. For the design of the supersonic nozzle a method of characteristics for isentropic axisymmetric flow of a real gas has been used to develop the streamline contour of our supersonic nozzle. The equations for continuity, Euler s momentum equation, irrotationality for an axisymmetric flow, and a speed of sound relation were developed and used along with some mathematical techniques, such as Cramer s rule, to develop the characteristic and compatibility equations shown in eqs. 5 and 6. The second-order-average-property Euler Predictor scheme was then used to solve the characteristic and compatibility equations simultaneously. To get the conditions of the centered expansion at the throat we used the angle velocity relation in eq. 7. The average-property Euler predictor-corrector scheme is used again to integrate eq. to develop the wall contour and the NIST Thermophysical property tables for carbon dioxide have been used to estimate the properties throughout the nozzle. The results of this design technique are shown in figs. 3-6 which show the nozzle contour and the properties throughout the nozzle. However, the resulting streamline contour design neglects viscous interaction with the nozzle wall and hence must be corrected for boundary layer effects. The boundary layer that develops along the wall of the nozzle is also taken into consideration. Boundary layers can be either laminar or turbulent depending on the pressure gradient and the local Reynolds number. Using three different throat diameters of,, and 4 mm, with specified density, viscosity, and speed of sound at the nozzle throat, this study has determined that the flow in the sonic section of each nozzle throat produces Reynolds numbers that are considered to be turbulent. In this design the boundary layer thickness at the throat was calculated using a displacement thickness equation model shown in eq. 3 and the average boundary layer growth along the nozzle contour was estimated using eq. 4 and then iterated to adjust for displacement thickness pressure effects. These boundary layer calculations were then combined with the non-ideal gas method of characteristics based streamline contours to complete the supersonic nozzle design. The results of the boundary layer analysis are shown in figs. 9- which compares the size of the boundary layer along the wall, the nozzle wall contour, and the boundary layer correction due to the displacement thickness calculations. These supersonic nozzle designs will soon be built and tested. The experimental results will then be compared to the computational results and will be evaluated for future study. References Aldo, A.C. and Argrow, B. M.. Dense Gas Flow in Minimum Length Nozzles. Journal of Fluids Engineering, Vol. 7. ASME, June 995 McCabe, A.. Design of a Supersonic Nozzle. Ministry of Aviation, Aeronautical Research Council Reports and Memoranda. 967 Rogers, E.W.E., Davis, B.M.. A note on Turbulent Boundary Layer Allowances in Supersonic Nozzle Design. Ministry of Supply, Aeronautical Research Council Current Papers. 957 Tucker, M. Approximate Calculation of Turbulent Boundary Layer Development in Compressible Flow. N.A.C.A. TN. 337, 95 Zucrow, Maurice J. and Hoffman, Joe D.. Gas Dynamics, Volume. New York: John Wiley and Sons, Inc., 976. Blass 8

SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations

SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations 1. Is it possible to accelerate a gas to a supersonic velocity in a converging nozzle? Explain. No, it is not possible. The only way to

More information

IX. COMPRESSIBLE FLOW. ρ = P

IX. COMPRESSIBLE FLOW. ρ = P IX. COMPRESSIBLE FLOW Compressible flow is the study of fluids flowing at speeds comparable to the local speed of sound. This occurs when fluid speeds are about 30% or more of the local acoustic velocity.

More information

Introduction to Fluid Mechanics. Chapter 13 Compressible Flow. Fox, Pritchard, & McDonald

Introduction to Fluid Mechanics. Chapter 13 Compressible Flow. Fox, Pritchard, & McDonald Introduction to Fluid Mechanics Chapter 13 Compressible Flow Main Topics Basic Equations for One-Dimensional Compressible Flow Isentropic Flow of an Ideal Gas Area Variation Flow in a Constant Area Duct

More information

Richard Nakka's Experimental Rocketry Web Site

Richard Nakka's Experimental Rocketry Web Site Página 1 de 7 Richard Nakka's Experimental Rocketry Web Site Solid Rocket Motor Theory -- Nozzle Theory Nozzle Theory The rocket nozzle can surely be described as the epitome of elegant simplicity. The

More information

Applied Gas Dynamics Flow With Friction and Heat Transfer

Applied Gas Dynamics Flow With Friction and Heat Transfer Applied Gas Dynamics Flow With Friction and Heat Transfer Ethirajan Rathakrishnan Applied Gas Dynamics, John Wiley & Sons (Asia) Pte Ltd c 2010 Ethirajan Rathakrishnan 1 / 121 Introduction So far, we have

More information

MODELING & SIMULATION OF ROCKET NOZZLE

MODELING & SIMULATION OF ROCKET NOZZLE MODELING & SIMULATION OF ROCKET NOZZLE Nirmith Kumar Mishra, Dr S Srinivas Prasad, Mr Ayub Padania Department of Aerospace Engineering MLR Institute of Technology Hyderabad, T.S Abstract This project develops

More information

Rocket Thermodynamics

Rocket Thermodynamics Rocket Thermodynamics PROFESSOR CHRIS CHATWIN LECTURE FOR SATELLITE AND SPACE SYSTEMS MSC UNIVERSITY OF SUSSEX SCHOOL OF ENGINEERING & INFORMATICS 25 TH APRIL 2017 Thermodynamics of Chemical Rockets ΣForce

More information

1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature

1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature CHAPTER 11 1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature 2.In Equation 11.7 the subscript p on the partial derivative refers to differentiation at

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility

More information

Shock and Expansion Waves

Shock and Expansion Waves Chapter For the solution of the Euler equations to represent adequately a given large-reynolds-number flow, we need to consider in general the existence of discontinuity surfaces, across which the fluid

More information

In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0.

In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0. bernoulli_11 In which of the following scenarios is applying the following form of Bernoulli s equation: p V z constant! g + g + = from point 1 to point valid? a. 1 stagnant column of water steady, inviscid,

More information

Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us

Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us Problems of Practices Of Fluid Mechanics Compressible Fluid Flow Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan

More information

P 1 P * 1 T P * 1 T 1 T * 1. s 1 P 1

P 1 P * 1 T P * 1 T 1 T * 1. s 1 P 1 ME 131B Fluid Mechanics Solutions to Week Three Problem Session: Isentropic Flow II (1/26/98) 1. From an energy view point, (a) a nozzle is a device that converts static enthalpy into kinetic energy. (b)

More information

Part A: 1 pts each, 10 pts total, no partial credit.

Part A: 1 pts each, 10 pts total, no partial credit. Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: -3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,

More information

Analysis of Head Loss in Pipe System Components: Quasi-one-Dimensional Nozzle Flow

Analysis of Head Loss in Pipe System Components: Quasi-one-Dimensional Nozzle Flow Analysis of Head Loss in Pipe System Components: Quasi-one-Dimensional Nozzle Flow Charles Ndambuki Muli School of Education, The Presbyterian University of East Africa, P.O. Box 387-00902, Kikuyu, Kenya.

More information

Notes #4a MAE 533, Fluid Mechanics

Notes #4a MAE 533, Fluid Mechanics Notes #4a MAE 533, Fluid Mechanics S. H. Lam lam@princeton.edu http://www.princeton.edu/ lam October 23, 1998 1 The One-dimensional Continuity Equation The one-dimensional steady flow continuity equation

More information

Design and Optimization of De Lavel Nozzle to Prevent Shock Induced Flow Separation

Design and Optimization of De Lavel Nozzle to Prevent Shock Induced Flow Separation Advances in Aerospace Science and Applications. ISSN 2277-3223 Volume 3, Number 2 (2013), pp. 119-124 Research India Publications http://www.ripublication.com/aasa.htm Design and Optimization of De Lavel

More information

6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s

6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an

More information

Gasdynamics 1-D compressible, inviscid, stationary, adiabatic flows

Gasdynamics 1-D compressible, inviscid, stationary, adiabatic flows Gasdynamics 1-D compressible, inviscid, stationary, adiabatic flows 1st law of thermodynamics ρ const Kontrollfläche 1 2 m u 2 u 1 z Q 12 +P 12 = ṁ } h 2 h {{} 1 Enthalpy Q 12 + 1 2 (u2 2 u2 1 }{{} ) +

More information

To study the motion of a perfect gas, the conservation equations of continuity

To study the motion of a perfect gas, the conservation equations of continuity Chapter 1 Ideal Gas Flow The Navier-Stokes equations To study the motion of a perfect gas, the conservation equations of continuity ρ + (ρ v = 0, (1.1 momentum ρ D v Dt = p+ τ +ρ f m, (1.2 and energy ρ

More information

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer

More information

Introduction. In general, gases are highly compressible and liquids have a very low compressibility. COMPRESSIBLE FLOW

Introduction. In general, gases are highly compressible and liquids have a very low compressibility. COMPRESSIBLE FLOW COMRESSIBLE FLOW COMRESSIBLE FLOW Introduction he compressibility of a fluid is, basically, a measure of the change in density that will be produced in the fluid by a specific change in pressure and temperature.

More information

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives Chapter 17 COMPRESSIBLE FLOW For the most part, we have limited our consideration so far to flows for which density variations and thus compressibility effects are negligible. In this chapter we lift this

More information

Lesson 6 Review of fundamentals: Fluid flow

Lesson 6 Review of fundamentals: Fluid flow Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass

More information

Theoretical analysis on the effect of divergent section with laminar boundary layer of sonic nozzles

Theoretical analysis on the effect of divergent section with laminar boundary layer of sonic nozzles 6th International Flow Measurement Conference, FOMEKO 03 4-6th September 03, Paris Theoretical analysis on the effect of divergent section with laminar boundary layer of sonic nozzles Hongbing Ding, Chao

More information

Thin airfoil theory. Chapter Compressible potential flow The full potential equation

Thin airfoil theory. Chapter Compressible potential flow The full potential equation hapter 4 Thin airfoil theory 4. ompressible potential flow 4.. The full potential equation In compressible flow, both the lift and drag of a thin airfoil can be determined to a reasonable level of accuracy

More information

AEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics

AEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term (2008-2009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:

More information

Steady waves in compressible flow

Steady waves in compressible flow Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique

More information

1. (20 pts total 2pts each) - Circle the most correct answer for the following questions.

1. (20 pts total 2pts each) - Circle the most correct answer for the following questions. ME 50 Gas Dynamics Spring 009 Final Exam NME:. (0 pts total pts each) - Circle the most correct answer for the following questions. i. normal shock propagated into still air travels with a speed (a) equal

More information

Final 1. (25) 2. (10) 3. (10) 4. (10) 5. (10) 6. (10) TOTAL = HW = % MIDTERM = % FINAL = % COURSE GRADE =

Final 1. (25) 2. (10) 3. (10) 4. (10) 5. (10) 6. (10) TOTAL = HW = % MIDTERM = % FINAL = % COURSE GRADE = MAE101B: Advanced Fluid Mechanics Winter Quarter 2017 http://web.eng.ucsd.edu/~sgls/mae101b_2017/ Name: Final This is a three hour open-book exam. Please put your name on the top sheet of the exam. Answer

More information

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303 Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum

More information

1. Introduction Some Basic Concepts

1. Introduction Some Basic Concepts 1. Introduction Some Basic Concepts 1.What is a fluid? A substance that will go on deforming in the presence of a deforming force, however small 2. What Properties Do Fluids Have? Density ( ) Pressure

More information

High Speed Aerodynamics. Copyright 2009 Narayanan Komerath

High Speed Aerodynamics. Copyright 2009 Narayanan Komerath Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil

More information

Turbulent Compressible Flow in a Slender Tube

Turbulent Compressible Flow in a Slender Tube Turbulent Compressible Flow in a Slender Tube Kurt O. Lund* 1, and Christine M. Lord 2 1 COMSOL Consultant, 2 Lord Engineering Corp. *Corresponding author: 135 Sixth Street, Del Mar, CA 92014, kurtlund@roadrunner.com

More information

GAS DYNAMICS AND JET PROPULSION

GAS DYNAMICS AND JET PROPULSION GAS DYNAMICS AND JE PROPULSION 1. What is the basic difference between compressible and incompressible fluid flow? Compressible Incompressible 1. Fluid velocities are appreciable 1. Fluid velocities are

More information

Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)

Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved) Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation

More information

A Computational Study on the Thrust Performance of a Supersonic Pintle Nozzle

A Computational Study on the Thrust Performance of a Supersonic Pintle Nozzle June 30 - July 3, 2015 Melbourne, Australia 9 P-10 A Computational Study on the Thrust Performance of a Supersonic Pintle Nozzle Ruoyu Deng Department of Mechanical Engineering Andong National University,

More information

Numerical Simulation of Supersonic Plume in a Cowl-Plug Nozzle Configuration}

Numerical Simulation of Supersonic Plume in a Cowl-Plug Nozzle Configuration} Freund Publishing House Ltd. London International Journal of Turbo and Jet Engines, 16, 241-253(1999) Numerical Simulation of Supersonic Plume in a Cowl-Plug Nozzle Configuration} Tony W. H. Sheu Department

More information

CFD ANALYSIS OF HYPERSONIC NOZZLE THROAT ANALYSIS

CFD ANALYSIS OF HYPERSONIC NOZZLE THROAT ANALYSIS Vol-4 Issue-4 218 CFD ANALYSIS OF HYPERSONIC NOZZLE THROAT ANALYSIS Gaurav Kumar 1, Sachin Baraskar 2 1 Research Scholar, Department of Mechanical Engineering, SOE, SSSUTMS, M.P., INDIA 2 Assistant Professor,

More information

Flow Analysis and Optimization of Supersonic Rocket Engine Nozzle at Various Divergent Angle using Computational Fluid Dynamics (CFD)

Flow Analysis and Optimization of Supersonic Rocket Engine Nozzle at Various Divergent Angle using Computational Fluid Dynamics (CFD) IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 11, Issue 6 Ver. IV (Nov- Dec. 2014), PP 01-10 Flow Analysis and Optimization of Supersonic Rocket

More information

Compressible Duct Flow with Friction

Compressible Duct Flow with Friction Compressible Duct Flow with Friction We treat only the effect of friction, neglecting area change and heat transfer. The basic assumptions are 1. Steady one-dimensional adiabatic flow 2. Perfect gas with

More information

COMPUTATIONAL ANALYSIS OF CD NOZZLE FOR SOLID PROPELLANT ROCKET

COMPUTATIONAL ANALYSIS OF CD NOZZLE FOR SOLID PROPELLANT ROCKET COMPUTATIONAL ANALYSIS OF CD NOZZLE FOR SOLID PROPELLANT ROCKET Mohammed iliyaas.a PG Student Aeronautical Engineering, Anna University Tirunelveli Region, Tirunelveli, Dr.K.Karuppasamy Assisant Professor,

More information

Influence of Molecular Complexity on Nozzle Design for an Organic Vapor Wind Tunnel

Influence of Molecular Complexity on Nozzle Design for an Organic Vapor Wind Tunnel ORC 2011 First International Seminar on ORC Power Systems, Delft, NL, 22-23 September 2011 Influence of Molecular Complexity on Nozzle Design for an Organic Vapor Wind Tunnel A. Guardone, Aerospace Eng.

More information

for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory?

for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? 1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first

More information

2013/5/22. ( + ) ( ) = = momentum outflow rate. ( x) FPressure. 9.3 Nozzles. δ q= heat added into the fluid per unit mass

2013/5/22. ( + ) ( ) = = momentum outflow rate. ( x) FPressure. 9.3 Nozzles. δ q= heat added into the fluid per unit mass 9.3 Nozzles (b) omentum conservation : (i) Governing Equations Consider: nonadiabatic ternal (body) force ists variable flow area continuously varying flows δq f ternal force per unit volume +d δffdx dx

More information

The Design and Computational Validation of a Mach 3 Wind Tunnel Nozzle Contour

The Design and Computational Validation of a Mach 3 Wind Tunnel Nozzle Contour University of Tennessee, Knoxville Trace: Tennessee Research and Creative Exchange Masters Theses Graduate School 12-2016 The Design and Computational Validation of a Mach 3 Wind Tunnel Nozzle Contour

More information

Brown Hills College of Engineering & Technology

Brown Hills College of Engineering & Technology UNIT 4 Flow Through Nozzles Velocity and heat drop, Mass discharge through a nozzle, Critical pressure ratio and its significance, Effect of friction, Nozzle efficiency, Supersaturated flow, Design pressure

More information

Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras

Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras Module - 3 Lecture - 33 Measurement of Volume and Mass Flow Rate

More information

Computational Analysis of Bell Nozzles

Computational Analysis of Bell Nozzles Proceedings of the 4 th International Conference of Fluid Flow, Heat and Mass Transfer (FFHMT'17) Toronto, Canada August 21 23, 2017 Paper No. 110 DOI: 10.11159/ffhmt17.110 Computational Analysis of Bell

More information

Design And Analysis Of Thrust Chamber Of A Cryogenic Rocket Engine S. Senthilkumar 1, Dr. P. Maniiarasan 2,Christy Oomman Jacob 2, T.

Design And Analysis Of Thrust Chamber Of A Cryogenic Rocket Engine S. Senthilkumar 1, Dr. P. Maniiarasan 2,Christy Oomman Jacob 2, T. Design And Analysis Of Thrust Chamber Of A Cryogenic Rocket Engine S. Senthilkumar 1, Dr. P. Maniiarasan 2,Christy Oomman Jacob 2, T. Vinitha 2 1 Research Scholar, Department of Mechanical Engineering,

More information

FUNDAMENTALS OF GAS DYNAMICS

FUNDAMENTALS OF GAS DYNAMICS FUNDAMENTALS OF GAS DYNAMICS Second Edition ROBERT D. ZUCKER OSCAR BIBLARZ Department of Aeronautics and Astronautics Naval Postgraduate School Monterey, California JOHN WILEY & SONS, INC. Contents PREFACE

More information

Review of Fundamentals - Fluid Mechanics

Review of Fundamentals - Fluid Mechanics Review of Fundamentals - Fluid Mechanics Introduction Properties of Compressible Fluid Flow Basics of One-Dimensional Gas Dynamics Nozzle Operating Characteristics Characteristics of Shock Wave A gas turbine

More information

One-Dimensional Isentropic Flow

One-Dimensional Isentropic Flow Cairo University Second Year Faculty of Engineering Gas Dynamics AER 201B Aerospace Department Sheet (1) 2011-2012 One-Dimensional Isentropic Flow 1. Assuming the flow of a perfect gas in an adiabatic,

More information

BERNOULLI EQUATION. The motion of a fluid is usually extremely complex.

BERNOULLI EQUATION. The motion of a fluid is usually extremely complex. BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over

More information

AEROSPACE ENGINEERING

AEROSPACE ENGINEERING AEROSPACE ENGINEERING Subject Code: AE Course Structure Sections/Units Topics Section A Engineering Mathematics Topics (Core) 1 Linear Algebra 2 Calculus 3 Differential Equations 1 Fourier Series Topics

More information

6.1 According to Handbook of Chemistry and Physics the composition of air is

6.1 According to Handbook of Chemistry and Physics the composition of air is 6. Compressible flow 6.1 According to Handbook of Chemistry and Physics the composition of air is From this, compute the gas constant R for air. 6. The figure shows a, Pitot-static tube used for velocity

More information

Modelling Nozzle throat as Rocket exhaust

Modelling Nozzle throat as Rocket exhaust Vol. 3, Issue. 4, Jul - Aug. 2013 pp-2502-2506 ISSN: 2249-6645 Modelling Nozzle throat as Rocket exhaust Keshava Rao P. 1, Komma Rahul 2, Souda Dinesh 3 1 (Mechanical Engineering, CBIT College, India)

More information

SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30

SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the

More information

Introduction and Basic Concepts

Introduction and Basic Concepts Topic 1 Introduction and Basic Concepts 1 Flow Past a Circular Cylinder Re = 10,000 and Mach approximately zero Mach = 0.45 Mach = 0.64 Pictures are from An Album of Fluid Motion by Van Dyke Flow Past

More information

Numerical Simulation of Supersonic Expansion in Conical and Contour Nozzle

Numerical Simulation of Supersonic Expansion in Conical and Contour Nozzle Numerical Simulation of Supersonic Expansion in Conical and Contour Nozzle Madhu B P (1), Vijaya Raghu B (2) 1 M.Tech Scholars, Mechanical Engineering, Maharaja Institute of Technology, Mysore 2 Professor,

More information

Introduction to Gas Dynamics All Lecture Slides

Introduction to Gas Dynamics All Lecture Slides Introduction to Gas Dynamics All Lecture Slides Teknillinen Korkeakoulu / Helsinki University of Technology Autumn 009 1 Compressible flow Zeroth law of thermodynamics 3 First law of thermodynamics 4 Equation

More information

AOE 3114 Compressible Aerodynamics

AOE 3114 Compressible Aerodynamics AOE 114 Compressible Aerodynamics Primary Learning Objectives The student will be able to: 1. Identify common situations in which compressibility becomes important in internal and external aerodynamics

More information

Continuity Equation for Compressible Flow

Continuity Equation for Compressible Flow Continuity Equation for Compressible Flow Velocity potential irrotational steady compressible Momentum (Euler) Equation for Compressible Flow Euler's equation isentropic velocity potential equation for

More information

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow 1. Consider subsonic Rayleigh flow of air with a Mach number of 0.92. Heat is now transferred to the fluid and the Mach number increases to 0.95.

More information

DISCHARGE COEFFICIENT OF SMALL SONIC NOZZLES

DISCHARGE COEFFICIENT OF SMALL SONIC NOZZLES THERMAL SCIENCE, Year 2014, Vol. 18, No. 5, pp. 1505-1510 1505 Introduction DISCHARGE COEFFICIENT OF SMALL SONIC NOZZLES by Zhao-Qin YIN *, Dong-Sheng LI, Jin-Long MENG, and Ming LOU Zhejiang Province

More information

DESIGN & COMPUTATIONAL FLUID DYNAMICS ANALYSES OF AN AXISYMMETRIC NOZZLE AT TRANSONIC FREE STREAM CONDITIONS

DESIGN & COMPUTATIONAL FLUID DYNAMICS ANALYSES OF AN AXISYMMETRIC NOZZLE AT TRANSONIC FREE STREAM CONDITIONS DESIGN & COMPUTATIONAL FLUID DYNAMICS ANALYSES OF AN AXISYMMETRIC NOZZLE AT TRANSONIC FREE STREAM CONDITIONS S Wasim Akram 1, S. Rajesh 2 1 M.Tech Student, Department of Mechanical Engineering, Krishna

More information

Fluid Mechanics - Course 123 COMPRESSIBLE FLOW

Fluid Mechanics - Course 123 COMPRESSIBLE FLOW Fluid Mechanics - Course 123 COMPRESSIBLE FLOW Flow of compressible fluids in a p~pe involves not only change of pressure in the downstream direction but also a change of both density of the fluid and

More information

Preliminary Design Review

Preliminary Design Review Preliminary Review Supersonic Air-Breathing Redesigned Engine Customer: Air Force Research Lab Advisor: Brian Argrow Team Members: Corrina Briggs, Jared Cuteri, Tucker Emmett, Alexander Muller, Jack Oblack,

More information

AGENA ROCKET NOZZLE: PROPERTIES AND GEOMETRY. Charles R. O Neill. School of Mechanical and Aerospace Engineering. Oklahoma State University

AGENA ROCKET NOZZLE: PROPERTIES AND GEOMETRY. Charles R. O Neill. School of Mechanical and Aerospace Engineering. Oklahoma State University AGENA ROCKET NOZZLE: PROPERTIES AND GEOMETRY Charles R. O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 74078 MAE 443 Project 1 Gas Power Oct 0, 000 Agena

More information

first law of ThermodyNamics

first law of ThermodyNamics first law of ThermodyNamics First law of thermodynamics - Principle of conservation of energy - Energy can be neither created nor destroyed Basic statement When any closed system is taken through a cycle,

More information

Principles of Convection

Principles of Convection Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

More information

Signature: (Note that unsigned exams will be given a score of zero.)

Signature: (Note that unsigned exams will be given a score of zero.) Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (-1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.

More information

Numerical Investigation of Supersonic Nozzle Producing Maximum Thrust For Altitude Variation

Numerical Investigation of Supersonic Nozzle Producing Maximum Thrust For Altitude Variation Numerical Investigation of Supersonic Nozzle Producing Maximum Thrust For Altitude Variation Muhammad Misbah-Ul Islam 1, Mohammad Mashud 1, Md. Hasan Ali 2 and Abdullah Al Bari 1 1 Department of Mechanical

More information

Lecture-2. One-dimensional Compressible Fluid Flow in Variable Area

Lecture-2. One-dimensional Compressible Fluid Flow in Variable Area Lecture-2 One-dimensional Compressible Fluid Flow in Variable Area Summary of Results(Cont..) In isoenergetic-isentropic flow, an increase in velocity always corresponds to a Mach number increase and vice

More information

Development of Two-Dimensional Convergent-Divergent Nozzle Performance Rapid Analysis Project

Development of Two-Dimensional Convergent-Divergent Nozzle Performance Rapid Analysis Project International Forum on Energy, Environment Science and Materials (IFEESM 015) Development of Two-Dimensional Convergent-Divergent Nozzle Performance Rapid Analysis Project Yaxiong YANG 1,a *, Eri Qitai,b,

More information

!! +! 2!! +!"!! =!! +! 2!! +!"!! +!!"!"!"

!! +! 2!! +!!! =!! +! 2!! +!!! +!!!! Homework 4 Solutions 1. (15 points) Bernoulli s equation can be adapted for use in evaluating unsteady flow conditions, such as those encountered during start- up processes. For example, consider the large

More information

EXTERNAL-JET (FLUID) PROPULSION ANALOGY FOR PHOTONIC (LASER) PROPULSION By John R. Cipolla, Copyright February 21, 2017

EXTERNAL-JET (FLUID) PROPULSION ANALOGY FOR PHOTONIC (LASER) PROPULSION By John R. Cipolla, Copyright February 21, 2017 EXTERNAL-JET (FLUID) PROPULSION ANALOGY FOR PHOTONIC (LASER) PROPULSION By John R. Cipolla, Copyright February 21, 2017 ABSTRACT External-jet propulsion uses a narrow jet of high velocity water or conceptually

More information

INFLUENCE OF NOZZLE GEOMETRY ON THE PERFORMANCE OF RECTANGULAR, LINEAR, SUPERSONIC MICRO-NOZZLES

INFLUENCE OF NOZZLE GEOMETRY ON THE PERFORMANCE OF RECTANGULAR, LINEAR, SUPERSONIC MICRO-NOZZLES 20 th Annual CFD Symposium, August 09-10, 2018, Bangalore INFLUENCE OF NOZZLE GEOMETRY ON THE PERFORMANCE OF RECTANGULAR, LINEAR, SUPERSONIC MICRO-NOZZLES K Mukesh 1, K Vijaya Sankaran 1, G Uthaya Sankara

More information

Positron Propelled and Powered Space Transport Vehicle for Planetary Missions

Positron Propelled and Powered Space Transport Vehicle for Planetary Missions Positron Propelled and Powered Space Transport Vehicle for Planetary Missions Positronics Research, LLC, Santa Fe, NM Work performed under Universities Space Research Association Research Subaward No.

More information

Optimization of Divergent Angle of a Rocket Engine Nozzle Using Computational Fluid Dynamics

Optimization of Divergent Angle of a Rocket Engine Nozzle Using Computational Fluid Dynamics The International Journal Of Engineering And Science (Ijes) Volume 2 Issue 2 Pages 196-207 2013 Issn: 2319 1813 Isbn: 2319 1805 Optimization of Divergent Angle of a Rocket Engine Nozzle Using Computational

More information

Compressible Flow Through Solar Power Plant Chimneys

Compressible Flow Through Solar Power Plant Chimneys Theodor W. von Backström e-mail: twvb@ing.sun.ac.za Anthony J. Gannon Department of Mechanical Engineering, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa Compressible Flow Through

More information

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions

Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions Fundamentals of Gas Dynamics (NOC16 - ME05) Assignment - 10 : Solutions Manjul Sharma & Aswathy Nair K. Department of Aerospace Engineering IIT Madras April 18, 016 (Note : The solutions discussed below

More information

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD) Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The

More information

EVALUATION OF THE BEHAVIOUR OF STEAM EXPANDED IN A SET OF NOZZLES, IN A GIVEN TEMPERATURE

EVALUATION OF THE BEHAVIOUR OF STEAM EXPANDED IN A SET OF NOZZLES, IN A GIVEN TEMPERATURE Equatorial Journal of Engineering (2018) 9-13 Journal Homepage: www.erjournals.com ISSN: 0184-7937 EVALUATION OF THE BEHAVIOUR OF STEAM EXPANDED IN A SET OF NOZZLES, IN A GIVEN TEMPERATURE Kingsley Ejikeme

More information

V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)

V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t) IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common

More information

Propulsion Thermodynamics

Propulsion Thermodynamics Chapter 1 Propulsion Thermodynamics 1.1 Introduction The Figure below shows a cross-section of a Pratt and Whitney JT9D-7 high bypass ratio turbofan engine. The engine is depicted without any inlet, nacelle

More information

Fanno Flow. Gas Dynamics

Fanno Flow. Gas Dynamics Fanno Flow Simple frictional flow ( Fanno Flow Adiabatic frictional flow in a constant-area duct * he Flow of a compressible fluid in a duct is Always accompanied by :- ariation in the cross sectional

More information

William В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.

William В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C. William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory

More information

Tutorial Materials for ME 131B Fluid Mechanics (Compressible Flow & Turbomachinery) Calvin Lui Department of Mechanical Engineering Stanford University Stanford, CA 94305 March 1998 Acknowledgments This

More information

10 minutes reading time is allowed for this paper.

10 minutes reading time is allowed for this paper. EGT1 ENGINEERING TRIPOS PART IB Tuesday 31 May 2016 2 to 4 Paper 4 THERMOFLUID MECHANICS Answer not more than four questions. Answer not more than two questions from each section. All questions carry the

More information

Aerothermodynamics of High Speed Flows

Aerothermodynamics of High Speed Flows Aerothermodynamics of High Speed Flows Lecture 5: Nozzle design G. Dimitriadis 1 Introduction Before talking about nozzle design we need to address a very important issue: Shock reflection We have already

More information

58:160 Intermediate Fluid Mechanics Bluff Body Professor Fred Stern Fall 2014

58:160 Intermediate Fluid Mechanics Bluff Body Professor Fred Stern Fall 2014 Professor Fred Stern Fall 04 Chapter 7 Bluff Body Fluid flows are broadly categorized:. Internal flows such as ducts/pipes, turbomachinery, open channel/river, which are bounded by walls or fluid interfaces:

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Introduction to Aerospace Engineering Lecture slides Challenge the future 4-0-0 Introduction to Aerospace Engineering Aerodynamics 3 & 4 Prof. H. Bijl ir. N. Timmer Delft University of Technology Challenge

More information

AME 436. Energy and Propulsion. Lecture 11 Propulsion 1: Thrust and aircraft range

AME 436. Energy and Propulsion. Lecture 11 Propulsion 1: Thrust and aircraft range AME 436 Energy and Propulsion Lecture 11 Propulsion 1: Thrust and aircraft range Outline!!!!! Why gas turbines? Computation of thrust Propulsive, thermal and overall efficiency Specific thrust, thrust

More information

NUMERICAL INVESTIGATION ON THE FLOW CHARACTERISTICS OF A SUPERSONIC JET IMPINGING ON AN AXI-SYMMETRIC DEFLECTOR

NUMERICAL INVESTIGATION ON THE FLOW CHARACTERISTICS OF A SUPERSONIC JET IMPINGING ON AN AXI-SYMMETRIC DEFLECTOR ICAS 2002 CONGRESS NUMERICAL INVESTIGATION ON THE FLOW CHARACTERISTICS OF A SUPERSONIC JET IMPINGING ON AN AXI-SYMMETRIC DEFLECTOR S.Sankaran, M.Rajeswara Rao, T.N.V.Satyanarayana, N.Satyanarayana K.Visvanathan

More information

CHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES

CHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES Thermodynamics: An Engineering Approach 8th Edition in SI Units Yunus A. Çengel, Michael A. Boles McGraw-Hill, 2015 CHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES Lecture slides by Dr. Fawzi Elfghi

More information

NAPC Numerical investigation of axisymmetric underexpanded supersonic jets. Pratikkumar Raje. Bijaylakshmi Saikia. Krishnendu Sinha 1

NAPC Numerical investigation of axisymmetric underexpanded supersonic jets. Pratikkumar Raje. Bijaylakshmi Saikia. Krishnendu Sinha 1 Proceedings of the 1 st National Aerospace Propulsion Conference NAPC-2017 March 15-17, 2017, IIT Kanpur, Kanpur NAPC-2017-139 Numerical investigation of axisymmetric underexpanded supersonic jets Pratikkumar

More information

MONTANA STATE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING. EMEC 426 Thermodynamics of Propulsion Systems. Spring 2017

MONTANA STATE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING. EMEC 426 Thermodynamics of Propulsion Systems. Spring 2017 MONTANA STATE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING EMEC 426 Thermodynamics of Propulsion Systems Spring 2017 Instructor: Dr. Alan H. George Office: Roberts 119 Office Hours: to be announced

More information

UOT Mechanical Department / Aeronautical Branch

UOT Mechanical Department / Aeronautical Branch Chapter One/Introduction to Compressible Flow Chapter One/Introduction to Compressible Flow 1.1. Introduction In general flow can be subdivided into: i. Ideal and real flow. For ideal (inviscid) flow viscous

More information

REPORT DOCUMENTATION PAGE

REPORT DOCUMENTATION PAGE REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions,

More information