Axial Flow Compressor Mean Line Design

Size: px
Start display at page:

Download "Axial Flow Compressor Mean Line Design"

Transcription

1 Axial Flow Compressor Mean Line Design Niclas Falck February 2008 Master Thesis Division of Thermal Power Engineering Department of Energy Sciences Lund University, Sweden

2 Niclas Falck 2008 ISSN ISRN LUTMDN/TMHP 08/5140 SE Printed in Sweden Lund 2008

3 Preface This master thesis has been conducted at the division of Thermal Power Engineering, department of Energy Science, Lund University, Sweden. This experience has been very educational in terms of modeling and computing thermal energy devices. This thesis has been about axial flow compressors, but the approach and methodic that I have implemented in this thesis will also be useful in my future career as an Engineer regardless of branch. I want to thank my supervisor Magnus Genrup for his support and expertise in the field of turbomachinery. I also want to thank the rest of the department of Energy Science, especially my fellow master thesis workers, for an enjoyable time here in Lund.

4 Abstract The main objective in this thesis is creating a method on how one can model an axial flow compressor. The calculation used in this thesis is based on common thermodynamics and aerodynamics principles in a mean stream line analyses. Calculations based on one stream line i.e. one dimension, is a good first start to model a compressor. Most of the correlations and thermodynamics are based on one stream line, or they can be modified to work on one stream line. By just a handful of design specifications an accurate model can be generated. These specifications can be mass flow, rotational speed, number of stages, pressure ratio etc. The pressure ratio is also the one parameter that the calculation aims to satisfy. If the calculation results in a pressure ratio that is not what was specified in the beginning an adjustment must be made on one parameter. In this case the stage load coefficient is selected. By changing the stage loading coefficient and keeping the other parameters constant the pressure ratio will vary. This is done in an iterative process until the pressure ratio is converged. The purposes of modeling compressors based on correlations and thermodynamics and not model them in a CFD (Computational Fluid Dynamics) simulation program at once is that it takes a long time for a calculation to converge in a CFD program. Finding better correlations and methods on how one can model a compressor will result in fewer hours fine tuning them in advanced fluid dynamic programs and hence same time and not to mention money.

5 Content Nomenclature... 4 Introduction Background Gas turbine Compressor Stagnation property Compressor Fundamentals Compressor operation Blade to Blade Flow path Rothalpy Compressor Losses Profile-loss Endwall-loss Blade geometry Dimensionless Parameters Stage load coefficient Stage flow coefficient Stage reaction de Haller number Pressure rise coefficient Efficiency Isentropic efficiency Polytropic efficiency Operating Limits Methods of Calculation State properties Incidence and Deviation Incidence Angle

6 Content Axial Flow Compressor Mean Line Design Deviation Angle Diffusion Factor and Diffusion Ratio Losses Profile loss model Endwall loss model Total loss Pitch Chord ratio Diffusion Factor Method Hearsey Method McKenzie Method Stall/Surge Calculation procedure Input parameters Main specification Detailed specification Inlet specification Parameter variations throughout the compressor Calculation limitations Mean stream line analyses Convergence criteria s Structure of the calculation Module Module Module Module Newton-Rhapson Method Calculation process Module 0, Inlet geometry Module 1, Rotor-inlet Module 2, Rotor-outlet/stator-inlet Module 2.1 start Module Module 2.2 start

7 Axial Flow Compressor Mean Line Design Content Module Module 3, Stator-outlet Module 3.1 start Module Module 3.2 start Module Outlet Guide Vane, OGV Blade angles calculation Result LUAX-C Structure of the program User Guide to LUAX-C References Appix A, polynomial coefficients for the graphs B, MATLAB script for the calculations B.1 Main Calculation B.2 Inlet geometry calculation B.3 Pitch chord ratio B.4 Diffusion Factor and Diffusion Ratio B.5 Compressor losses B.6 Blade angles Appix C

8 Nomenclature Symbol Unit Description a [m/s] Speed of sound A [m2] Area c p [kj/kgk] Specific heat at constant pressure c v [kj/kgk] Specific heat at constant volume c [m] Chord C [m/s] Absolute velocity C [m/s] Tangential absolute velocity C m [m/s] Meridional velocity C p [-] Static pressure rise coefficient DF [-] Diffusion factor D eq [-] Equivalent diffusion ratio h [kj/kg] Static enthalpy h 0 [kj/kg] Stagnation enthalpy H [m] Blade height i [ ] Incidence I [-] Rothalpy m [kg/s] Massflow Ma [-] Mach-number N [rev/s] Rotational speed p [bar] Static pressure p 0 [bar] Stagnation pressure r [m] Radius R [J/kgK] Gas constant s [kj/kg] entropy S [m] Staggered spacing t [m] Maximum blade thickness T [K] Static temperature T 0 [K] Stagnation temperature U [m/s] Blade velocity W [m/s] Relative velocity W [m/s] Tangential relative velocity 4

9 Axial Flow Compressor Mean Line Design Nomenclature Symbol Unit Description [ ] Angle between absolute velocity and axial direction [ ] Angle between relative velocity and axial direction [ ] Stagger angle [ ] Deviation [m] Endwall clearance [%] Efficiency [-] Heat capacity ratio, Isentropic exponent Heat conductivity [Kg/m2] Density [m2/s] Kinematic viscosity Pressure loss coefficient [ ] Camber angle [-] Stage load coefficient [-] Stage flow coefficient 5

10 Introduction The development of gas turbines has in the recent years come a long way. Serious development began during the Second World War with the key interest of shaft power, but attention was shortly transferred to the turbojet engine for aircraft propulsion. The gas turbine began to compete successfully in other fields in the mid 1950s, since then it has made a successful impact in an increasing variety of applications. When combining a gas turbine with a heat recovery steam generator the heat, that otherwise would be wasted from the gas turbine outlet, can be extracted. Together with a conventional steam generator this will form a combined cycle. The efficiency of a combined cycle power plant is far better than regular gas turbine power plants. The question is than, how could we improve the efficiency of a gas turbine? One can either focus on the compressor, the combustion chamber or the turbine. In this thesis the compressor, especially the axial flow compressor, will be investigated. When designing a new compressor, a good start is to create a base design for the compressor. By just a handful of design specifications an accurate model can be generated. The modelling techniques used are based on combinations of thermodynamic and aerodynamic correlations. This base design will make up for about % of the finished design. In this first stage in designing a new compressor, designs that would not work or have pore efficiency can be avoided. Further on in the process powerful CFD (Computational Fluid Dynamics) simulation programs are being used. A CFD calculation takes a long time and hence cost a lot of money. The solution to cutting down the number of simulations is then to make the base design more accurate. 6

11 1 Background 1.1 Gas turbine A gas turbine consists mainly by three components, the compressor, the combustion chamber and the turbine, see Figure 1.1. The compressor is one a part of the entire gas turbine, but never the less, an important and probably the most complicated component to design in an aerodynamic point of view. The working fluid enters an inlet duct and continues to the compressor. The compressor pressurises the fluid and will also lead to an increase in temperature. Deping on the application it can either have a radial or an axial design deping on mass flow and pressure ratio. After the compressor, the pressure of the working fluid will have increased to bar, even above 40 in aero engines, and will have a temperature of about 500 C. By combustion of fuel in the combustion chamber, energy is added to the working fluid. A gas turbine is very flexible in terms of what sort of fuels can be used. The working fluid which now has a temperature of about C enters the last stage in the process, the turbine. Here the fluid expands and thus transferring its energy to the turbine blade in form of mechanical work. The turbine is connected to the compressor by a shaft and this lead the mechanical work from the turbine to the compressor. If the gas turbine is to be used in a multi-shaft configuration, the work provided by the turbine will just be enough to drive the compressor otherwise a load can be connected like a pump, a propeller or a generator. Combustion chamber Load Compressor Turbine Figure 1.1, Schematic figure over the main components in a gas turbine 7

12 1 Background Axial Flow Compressor Mean Line Design 1.2 Compressor There are two types of compressor designs, radial and axial flow compressors, see Figure 1.3 and Axial flow compressors are divided in a series of stages, each stage consistss of a rotating rotor and a stationary one called stator. It is difficult to get a high pressuree rise in a single stage. Unlike axial flow compressor rs, the radial compressor often consists of a single stage. It is possible to obtain a higher pressure rise over one stage in a radial compressor. An axial flow compressor can handle a much larger mass flow compared to a radial flow compressor. If one would like to have a small compact compressor a radial design is the best choice. But if high power is required, for an examplee in a jet engine for a big airliner, an axial flow is not just the best but probably the only choice. An example of a radial compressor in an aircraft is the Swedish aircraft SAAB J29 also known as Tunnan (in eng. The Barrel ) ). This has a very wide fuselagee because of the large radial compressor design, see Figure 1.2. Figure 1.2, SAAB J29 A deeper insight of the axial flow compressors construction and its design will follow and be discussed in this thesis. Figure 1.3, Axial flow compressor 8

13 Axial Flow Compressor Mean Line Design 1 Background Figure 1.4, Radial flow compressor 1.3 Stagnation property When the kinetic and potential energies of a given fluid are negligible, as is often the case, the enthalpy represents the total energy of the fluid. For high speed flows, M>0.4, the kinetic energy is highly noticeable, but the potential energy is still negligible. It is the convenient to combine the kinetic energy with the enthalpy of the fluid into a single term called stagnation (or total) enthalpy h 0, which is defined as. (1.1) If the kinetic energy is negligible the enthalpy is the referred as the static enthalpy, h. Consider a duct such as a nozzle or a diffuser where a fluid is flowing through, see Figure 1.5. The flow takes place under an adiabatic process where there is no work input or output. Assuming there is no potential energy difference through the duct for the fluid, the energy balance can then be reduced to. or 9

14 1 Background Axial Flow Compressor Mean Line Design 2 1 Figure 1.5, Steady flow of a fluid through an adiabatic duct The stagnation enthalpy will not change through a duct if there is no heat or work done to the system. Flows through nozzles or diffusers usually satisfy these conditions, and any changes in the fluid velocity will create a change in the static enthalpy of the fluid. Substituting the enthalpy with temperature instead results in the following expression or (1.2) C p represents the specific heat value for the fluid for an ideal gas. T 0 is called stagnation (or total) temperature. The term V 2 /2C p is called the dynamic temperature and corresponds to the temperature rise during an adiabatic process. The pressure a fluid obtains when brought to rest is called stagnation pressure, P 0. For ideal gases with constant specific heats, P 0 is related to the static pressure of the fluid by, represents the specific heat ratio, C p /C v. 10

15 2 Compressor Fundamentals 2.1 Compressor operation A typical axial flow compressor consists of a series of stages; each stage has a row of moving rotor blades followed by a row of stator blades which is stationary, see Figure 2.1. The rotor blades accelerates the working fluid thus gaining energy, this kinetic energy is then converted into static pressure by decelerating the fluid in the stator blades. The process is then repeated as many times as necessary to get the required pressure ratio. The number of stages in a compressor is important especially when the engine will be used in an aircraft. The main reason is that too many stages will result in an increase in weight and a large core engine length. For land based gas turbines the main reason is the cost, which will increase when adding more stages. Some different compressors used in aircrafts are shown in Table 2.1, and here one can see how compressor improvement has come along over the years. Figure 2.1, Cross-section view over a compressor flow path Engine Date Thrust Pressure Stages [kn] ratio Avon Spey RB Trent Table 2.1, Compressor evolution, aircraft engine 11

16 2 Compressor Fundamentals Axial Flow Compressor Mean Line Design As discussed earlier all the power is absorbed in the rotor and the stator transforms the kinetic energy which has been absorbed by the rotor into an increase in static pressure. The stagnation temperature remains constant throughout the stator since there is no work feed into the fluid. Figure 2.2 shows a sketch of a typical compressor stage. T 02, T 03 Temperature, T T 03 p 02 p 3 p 03 p 2 T p 01 T 01 T 1 p 1 R S Entropy, s Figure 2.2, Compressor stage and T-s diagram The stagnation pressure rise occurs wholly in the rotor, but in practice, there will be some losses in the stator due to fluid friction which will result in a decrease in stagnation pressure. There are also some losses in the rotor and the stagnation pressure rise will be less than of an isentropic compression. 2.2 Blade to Blade Flow path To get a clear picture in how a compressor works, blade to blade flow path analysis is the most fundamental part. The velocity components of the working fluid can be expressed in two velocity vectors, absolute and relative velocity. The fluid enters the rotor with an absolute velocity, C 1, and has an angle, 1, from the axial direction. Combining the absolute velocity with the blade speed, U, gives the relative velocity, W 1, with its angle 1. The mechanical energy from the rotating rotors will be transferred to the working fluid. This energy absorption will increase the absolute velocity of the fluid. After leaving the rotor the fluid will have a relative velocity, W 2, with an angle, 2, determined by the blade outlet angle. The fluid leaving the rotor is consequently the air entering the stator where a similar change in velocity will occur. Here the relative 12

17 Axial Flow Compressor Mean Line Design 2 Compressor Fundamentals velocity, W 2, will be diffused and leaving the stator with a velocity, C 3, at an angle, 3. Typically the velocity leaving the stator will be the same as the velocity entering the rotor in the next row, C 3 = C 1 and 3 = 1. By creating so called velocity triangles, see Figure 2.3, will make it easier to visualize the change of velocities and angles in a compressor stage [1]. 1 C 1 W C 1 C a1 C 1 U 2 C 2 W 2 C C a2 C 2 C Rothalpy Figure 2.3, Velocity triangles for one stage The work, W, is expressed as the enthalpy change. For adiabatic machines the heat flux, Q, is zero. Introducing the Euler equation and expanding the stagnation enthalpy gives after rearrangement. Consider the left-hand side, expanding C 2 2 as C C x2 2 + C R2 2 and then expressing the absolute tangential velocity in terms of that in the moving frame of reference C 2 = W 2 + U 2. After some manipulation to the left-hand side of the equation one obtains. This can then be used for obtaining the difference between the inlet and outlet. 13

18 2 Compressor Fundamentals Axial Flow Compressor Mean Line Design Or alternatively The term (h 02 ) rel is the stagnation enthalpy in the relative frame of reference. The rothalpy is defined as the quantity (2.1) In rotating blade rows rothalpy has properties analogous to stagnationn enthalpy in stationary passages. If the same concept of rothalpy is applied to a stationary blade row the equation reverts to conservation of stagnation enthalpy [2]. 2.4 Compressor Losses The flow in a compressor is complicated 3-D, unsteady and dominated by viscous effects, see Figure 2.4. This dissipative nature increases the entropy and a loss in pressuree occurs due to the flow effects. Figure 2.4, Flow fields in a cascade 14

19 Axial Flow Compressor Mean Line Design 2 Compressor Fundamentals The individual losses are lumped into profile- and wall-losses. These pressure losses are depent on a numerous parameters which include tip clearance, blade aspect ratio, pitch chord ratio, thickness chord ratio, Mach number and Reynolds number. The different loss models are based on mid radius and will be modelled individually for the rotor/stator Profile-loss Profile-losses are based on the effect of blade boundary layer growth (including separated flow) and wakes through turbulent and viscous dissipation. The effect of these losses is an increase of entropy due to the heat developed by the mechanical energy within the boundary layers. This results in a stagnation pressure loss [3] Endwall-loss In addition to the losses which arise from the blade surfaces, i.e. profile losses, additional losses generated on the walls. These are often called secondary losses which arises from -wall boundary layer build up, secondary flow and tip clearance. When a flow that is parallel but non-uniform in velocity and density is made to follow a curved path, the result is a three-dimensional motion with velocity normal to the overall flow direction. Cross-flow of this type is referred as secondary flow. A good analogy of this is a simple teacup. When stirring the tea in a teacup, the tea leafs will move towards the center of the cup driven by the secondary flow. The formation, development, diffusion and dissipation of these vortices as well as the kinetic energy in secondary velocities generate secondary flow losses. Somewhere between 50-70% of the losses may come from wall losses, deping of the type of turbo machinery [3]. 15

20 2 Compressor Fundamentals Axial Flow Compressor Mean Line Design 2.5 Blade geometry 1 W 1 t b1 C Profile Camber line W 2 2 b2 S Figure 2.5, Cascade notation 1 b1 2 b2 i c S t Relative air inlet angle Blade inlet angle Relative air outlet angle Blade outlet angle Stagger angle Camber angle Incidence angle, 1 - b1 Deviation angle, 2 - b2 Chord length Staggered spacing Maximum thickness Solidity, c/s Table 2.2, Cascade notation 2.6 Dimensionless Parameters Introducing a set of dimensionless parameters will give a useful guidance in designing a compressor stage. These dimensionless performance parameters define the performance of a single stage in a compressor. 16

21 Axial Flow Compressor Mean Line Design 2 Compressor Fundamentals Stage load coefficient The total enthalpy rise through a rotor blade row is expressed by the well-known Euler turbine equation, i.e. (2.2) where H is the total enthalpy rise through the rotor. It is often useful to introduce dimensionless stage performance parameters for a repeating stage, i.e. the rotor-inlet (station 1) and the stator-outlet (station 3) from the previous stage has identical velocity diagrams. Then, the stage load coefficient,, can be defined as (2.3) Stage flow coefficient The stage flow coefficient,, is defined as followed. (2.4) This expresses the ratio between the meridional velocity and the blade velocity. A high stage flow coefficient indicated a high flow through the stage relative to the blade velocity. A low whirl velocity change in a stage would also indicate a high stage flow coefficient and vice versa [1] Stage reaction The stage reaction, R, is defined as the fraction of the rise in static enthalpy in rotor compared to the rise in stagnation enthalpy throughout the entire stage. (2.5) If a compressor stage would have a stage reaction of 1.0 or 100%, the rotor would do all of the diffusion in the stage. Similar if the stage reaction is 0 than the stator will do all of the diffusion of the working fluid. It is never good to have either a stage reaction of 1.0 or 0. The literature, reference 1, suggest that a stage reaction about 0.5 i.e. the diffusion is equally divided between the two blade rows. But in practice a higher stage reaction is preferred. Increasing the stage reaction results in a decrease in whirl prior to the rotor. A smaller whirl will create a larger relative inlet velocity to the rotor row, at a constant C p, and hence make it easier for the rotor to increase the static pressure de Haller number In most compressor stages both the rotors and the stators are designed to diffuse the fluid, and hence transform its kinetic energy into an increase in static enthalpy and static pressure. The more the fluid is decelerated, the bigger pressure rise, but boundary layer growth and wall stall is limiting the process. To avoid this, de Haller proposed that the 17

22 2 Compressor Fundamentals Axial Flow Compressor Mean Line Design overall deceleration ratio, i.e. W 2 /W 1 and C 2 /C 3 in a rotor and stator respectively, should not be less than 0.72 (historic limit) in any row [1] Pressure rise coefficient Another parameter is the pressure rise coefficient. (2.6) (2.7) If axial velocity is assumed constant and the working fluid is assumed to be incompressible, then the pressure rise coefficient can also be expressed as a function of the dehaller number. This is done by applying Bernoulli s principle. (2.8) 2.7 Efficiency The term efficiency finds very wide application in turbo machinery. For all machines or stages, efficiency is defined as. There are several different ways of evaluating efficiency and these reveal different information. Two of the most widely used efficiencies are the isentropic efficiency and the polytropic efficiency Isentropic efficiency The isentropic efficiency can be expressed as the ratio between enthalpy change in an ideal compressor and the actual enthalpy change. An ideal compressor which is both adiabatic and reversible cannot alter the entropy of the gas flowing through it. These types of compressors are usually referred to as isentropic. Since there will be some 18

23 Axial Flow Compressor Mean Line Design 2 Compressor Fundamentals losses which generates an entropy rise, the actual work into the compressor will differ from an ideal one. The efficiency can then be described as, (2.9) The subscript s denotes entropy held constant. Figure 2.6 shows a typical schematic diagram over a reversible adiabatic compression. Temperature T p 02 2s 2 p 01 1 Entropy S Figure 2.6, isentropic compression The constant pressure lines in the T-S diagram, Figure 2.6, have a slope proportional to the temperature and diverge as the temperature increases. For a given pressure rise the work input needed is greater for the later stages in a compressor, this because the temperature is higher and also that the work input required by the later stages is raised because of the previous stages. The isentropic efficiency therefore gets lower as the overall pressure ratio is increased. To cope with this problem, another efficiency the socalled polytropic or small-stage efficiency may be used instead [2] Polytropic efficiency The definition of polytropic efficiency is as follows. By applying Gibbs law and the relationship between temperature and enthalpy it can be rewritten so it deps on temperatures and pressures instead. 19

24 2 Compressor Fundamentals Axial Flow Compressor Mean Line Design Integrating the expression on pressure, p leads to the following equation. (2.10) One can also assume that the specific heat capacity is constant, which is not the case in this thesis. If this is assumed, the following expression can be found [2]. (2.11) 2.7 Operating Limits There are mainly two phenomena that can cause a compressor to break down, rotating stall and surge. Gas turbines, for example, may encounter severe performance and durability problems if the compressor is not able to avoid stall and surge. In preliminary designs there is a need for reliable methods for computing the compressors stall margin capability. This because it is difficult to correct and change the compressor stall margin after its basic design has been chose. In a typical compressor it is normal that if the mass flow is reduced the pressure rise increases. At a certain point in an operating range the pressure rise is at its maximum, in a further reduction in mass flow will lead to an abrupt and definite change in flow pattern in the compressor. This change in flow pattern is known as surge and can cause the flow to start oscillating backwards and forwards, and after a while the compressor will break down. A mild version of surge causes the operating point to orbit around the point of maximum pressure rise. An audible burble is a clear indicator when the compressor is on the limit of the more severe surge [2]. The other phenomena that one should be looking for is stall. If the mass flow is reduced the axial velocity will, according to the continuity equation, also decrease. This will increase the air inlet angle and, due to the difference in air inlet angle and blade inlet angle, create incidence. With an increasing incidence angle the flow will eventually separate from the surface at the trailing edge. The separation will grow with a further 20

25 Axial Flow Compressor Mean Line Design 2 Compressor Fundamentals increase of incidence angle, and finally cover the whole upper blade. This phenomenon is called stall, and will change the performance of a compressor drastically. Rotating stall means that the stall is moved from one blade to another and an uninformed pattern will occur, see Figure 2.7. The annulus then contains regions of stalled flow, usually referred as cells, and regions of unstalled flow. Rotating stall is a mechanism which allows the compressor to adapt to a mass flow which is too small. Instead of trying to share the limited flow over the whole annulus the flow is shared unequally, so that some areas have a larger mass flow than other. The overall mass flow remains constant but the local mass flow varies as the rotating cell passes the point of observation. The cells always rotate in the direction of the rotor. Part-span cells very often rotate at close to 50 percent of the rotor speed, full-span cells usually rotate more slowly in the range of percent. Full-span cells ext axially through the whole compressor while part-span cells can exist in a single blade row [2]. Cell Unstalled flow Full-span stall Part-span stall Figure 2.7, Different types of rotating stall 21

26 3 Methods of Calculation 3.1 State properties In order to calculate the state of a fluid, an approach according to the Gibbs-Dalton is used. The model used is the NASA SP-273, and by integration, the enthalpy and entropy are known. The specific heat is expressed as fifth order polynomial. The reference values are set to zero at kpa and K. as seen in the equations above. As seen in the equation above, the temperature and the pressure must be known if the entropy and enthalpy are to be found. If let say that the enthalpy and the temperature are known instead, an iterative process is needed since the specific heat value is expressed as a fifth order polynomial. This iterative procedure uses the standard Newton method, see chapter 4.5 Newton Rhapson Method. Introduction of other property libraries are straightforward, as long as they are semi-perfect (specific heat only a function of temperature) [11]. 3.2 Incidence and Deviation There are several different methods on how to get the blade angles in a cascade. In this thesis, one method is used to calculate the angles based on a number of input variables. Howard, see reference 4, has put together a number of correlations and equations based on Johnsen and Bullock (1965), which commonly is referred to as NASA SP-36 correlations. These correlations are largely based on low speed cascade test; he also introduces some correlations for advanced transonic compressor blades by Köning, et al (1996), but this will not be taken in consideration in this thesis. 22

27 Axial Flow Compressor Mean Line Design 3 Methods of Calculation Incidence Angle Incidence is the difference between the inlet blade angel and the inlet flow angle. As the fluid flows towards the leading edge it will experience induced incidence. There is one pressure surface and one suction surface at a given blade. This different of pressure will change the ingoing flow angle as it approaches the leading edge, see Figure 3.1. _ + Figure 3.1, induced incidence By performing experimental tests on a given cascade, the incidence can be established. This incidence angle is referred as reference incidence. When testing a given cascade at different inlet flow angles, the loss coefficient,, varies with incidence. There will be an increase in both positive and negative incidence angles with a range of low values for. The pressure loss at twice the minimum loss will be the range in which the reference incidence will be located. Outside this range stall blade stall occurs. If this range of incidence is split in the middle, the point of reference incident angle will be found, see Figure 3.2. Pressure loss, Reference incidence angle i/2 i/2 Min. loss 2 x Min. loss Incidence angle, i Figure 3.2, Definition of reference incidence angle 23

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 06 One-dimensional Gas Dynamics (Contd.) We

More information

Gas Turbine Engine Performance Analysis. S. Jan

Gas Turbine Engine Performance Analysis. S. Jan Gas Turbine Engine Performance Analysis S. Jan Jul. 21 2014 Chapter 1 Basic Definitions Potential & Kinetic Energy PE = mgz/g c KE = mv 2 /2g c Total Energy Operational Envelopes & Standard Atmosphere

More information

COMPUTATIONAL FLUID DYNAMICS (CFD) ANALYSIS OF INTERMEDIATE PRESSURE STEAM TURBINE

COMPUTATIONAL FLUID DYNAMICS (CFD) ANALYSIS OF INTERMEDIATE PRESSURE STEAM TURBINE Research Paper ISSN 2278 0149 www.ijmerr.com Vol. 3, No. 4, October, 2014 2014 IJMERR. All Rights Reserved COMPUTATIONAL FLUID DYNAMICS (CFD) ANALYSIS OF INTERMEDIATE PRESSURE STEAM TURBINE Shivakumar

More information

ME 239: Rocket Propulsion. Nozzle Thermodynamics and Isentropic Flow Relations. J. M. Meyers, PhD

ME 239: Rocket Propulsion. Nozzle Thermodynamics and Isentropic Flow Relations. J. M. Meyers, PhD ME 39: Rocket Propulsion Nozzle Thermodynamics and Isentropic Flow Relations J. M. Meyers, PhD 1 Assumptions for this Analysis 1. Steady, one-dimensional flow No motor start/stopping issues to be concerned

More information

Relevance of Modern Optimization Methods in Turbo Machinery Applications

Relevance of Modern Optimization Methods in Turbo Machinery Applications Relevance of Modern Optimization Methods in Turbo Machinery Applications - From Analytical Models via Three Dimensional Multidisciplinary Approaches to the Optimization of a Wind Turbine - Prof. Dr. Ing.

More information

Keywords: CFD, heat turbomachinery, Compound Lean Nozzle, Controlled Flow Nozzle, efficiency.

Keywords: CFD, heat turbomachinery, Compound Lean Nozzle, Controlled Flow Nozzle, efficiency. CALCULATION OF FLOW CHARACTERISTICS IN HEAT TURBOMACHINERY TURBINE STAGE WITH DIFFERENT THREE DIMENSIONAL SHAPE OF THE STATOR BLADE WITH ANSYS CFX SOFTWARE A. Yangyozov *, R. Willinger ** * Department

More information

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4 Theory of turbo machinery / Turbomaskinernas teori Chapter 4 Axial-Flow Turbines: Mean-Line Analyses and Design Power is more certainly retained by wary measures than by daring counsels. (Tacitius, Annals)

More information

Compressor and turbines

Compressor and turbines Compressor and turbines In this chapter, we will look at the compressor and the turbine. They are both turbomachinery: machines that transfer energy from a rotor to a fluid, or the other way around. The

More information

University Turbine Systems Research 2012 Fellowship Program Final Report. Prepared for: General Electric Company

University Turbine Systems Research 2012 Fellowship Program Final Report. Prepared for: General Electric Company University Turbine Systems Research 2012 Fellowship Program Final Report Prepared for: General Electric Company Gas Turbine Aerodynamics Marion Building 300 Garlington Rd Greenville, SC 29615, USA Prepared

More information

Theory of turbo machinery / Turbomaskinernas teori. Chapter 3

Theory of turbo machinery / Turbomaskinernas teori. Chapter 3 Theory of turbo machinery / Turbomaskinernas teori Chapter 3 D cascades Let us first understand the facts and then we may seek the causes. (Aristotle) D cascades High hub-tip ratio (of radii) negligible

More information

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4

Theory of turbo machinery / Turbomaskinernas teori. Chapter 4 Theory of turbo machinery / Turbomaskinernas teori Chapter 4 Note direction of α 2 FIG. 4.1. Turbine stage velocity diagrams. Assumptions: Hub to tip ratio high (close to 1) Negligible radial velocities

More information

Applied Fluid Mechanics

Applied Fluid Mechanics Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

More information

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

More information

CFD Analysis of Swept and Leaned Transonic Compressor Rotor

CFD Analysis of Swept and Leaned Transonic Compressor Rotor CFD Analysis of Swept and Leaned Transonic Compressor Nivin Francis #1, J. Bruce Ralphin Rose *2 #1 Student, Department of Aeronautical Engineering& Regional Centre of Anna University Tirunelveli India

More information

is the stagnation (or total) pressure, constant along a streamline.

is the stagnation (or total) pressure, constant along a streamline. 70 Incompressible flow (page 60): Bernoulli s equation (steady, inviscid, incompressible): p 0 is the stagnation (or total) pressure, constant along a streamline. Pressure tapping in a wall parallel to

More information

1. A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work.

1. A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. Impulse Turbine 1. A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. 2. Early turbine examples are windmills and waterwheels. 3. Gas, steam,

More information

CO 2 41.2 MPa (abs) 20 C

CO 2 41.2 MPa (abs) 20 C comp_02 A CO 2 cartridge is used to propel a small rocket cart. Compressed CO 2, stored at a pressure of 41.2 MPa (abs) and a temperature of 20 C, is expanded through a smoothly contoured converging nozzle

More information

INTRODUCTION TO FLUID MECHANICS

INTRODUCTION TO FLUID MECHANICS INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION

More information

THE EVOLUTION OF TURBOMACHINERY DESIGN (METHODS) Parsons 1895

THE EVOLUTION OF TURBOMACHINERY DESIGN (METHODS) Parsons 1895 THE EVOLUTION OF TURBOMACHINERY DESIGN (METHODS) Parsons 1895 Rolls-Royce 2008 Parsons 1895 100KW Steam turbine Pitch/chord a bit too low. Tip thinning on suction side. Trailing edge FAR too thick. Surface

More information

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all

More information

Pushing the Envelope

Pushing the Envelope CENTRIFUGAL COMPRESSORS Pushing the Envelope CFD simulation contributes to increasing the operating envelope of a centrifugal compressor stage. By James M. Sorokes, Principal Engineer; Jorge E. Pacheco,

More information

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 10 Steam Power Cycle, Steam Nozzle Good afternoon everybody.

More information

Investigations of the Performance on Vaned Diffusers for Low Specific Speed Centrifugal Compressor

Investigations of the Performance on Vaned Diffusers for Low Specific Speed Centrifugal Compressor International Journal of Gas Turbine, Propulsion and Power Systems February 2014, Volume 6, Number 1 International Journal of Gas Turbine, Propulsion and Power Systems Investigations of the Performance

More information

COMPARISON OF COUNTER ROTATING AND TRADITIONAL AXIAL AIRCRAFT LOW-PRESSURE TURBINES INTEGRAL AND DETAILED PERFORMANCES

COMPARISON OF COUNTER ROTATING AND TRADITIONAL AXIAL AIRCRAFT LOW-PRESSURE TURBINES INTEGRAL AND DETAILED PERFORMANCES COMPARISON OF COUNTER ROTATING AND TRADITIONAL AXIAL AIRCRAFT LOW-PRESSURE TURBINES INTEGRAL AND DETAILED PERFORMANCES Leonid Moroz, Petr Pagur, Yuri Govorushchenko, Kirill Grebennik SoftInWay Inc. 35

More information

Performance. 10. Thrust Models

Performance. 10. Thrust Models Performance 10. Thrust Models In order to determine the maximum speed at which an aircraft can fly at any given altitude, we must solve the simple-looking equations for : (1) We have previously developed

More information

Pushing the limits. Turbine simulation for next-generation turbochargers

Pushing the limits. Turbine simulation for next-generation turbochargers Pushing the limits Turbine simulation for next-generation turbochargers KWOK-KAI SO, BENT PHILLIPSEN, MAGNUS FISCHER Computational fluid dynamics (CFD) has matured and is now an indispensable tool for

More information

Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics

Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics Lecture 6 - Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.

More information

Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS

Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Lecture slides by Hasan Hacışevki Copyright

More information

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

More information

Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any

Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate Flow rate can be expressed in terms of volume flow rate (volume/time) or mass

More information

du u U 0 U dy y b 0 b

du u U 0 U dy y b 0 b BASIC CONCEPTS/DEFINITIONS OF FLUID MECHANICS (by Marios M. Fyrillas) 1. Density (πυκνότητα) Symbol: 3 Units of measure: kg / m Equation: m ( m mass, V volume) V. Pressure (πίεση) Alternative definition:

More information

df dt df dt df ds df ds

df dt df dt df ds df ds Principles of Fluid Mechanics Fluid: Fluid is a substance that deforms or flows continuously under the action of a shear stress (force per unit area). In fluid mechanics the term fluid can refer to any

More information

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22 BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

More information

EXPERIMENTAL RESEARCH ON FLOW IN A 5-STAGE HIGH PRESSURE ROTOR OF 1000 MW STEAM TURBINE

EXPERIMENTAL RESEARCH ON FLOW IN A 5-STAGE HIGH PRESSURE ROTOR OF 1000 MW STEAM TURBINE Proceedings of 11 th European Conference on Turbomachinery Fluid dynamics & Thermodynamics ETC11, March 23-27, 2015, Madrid, Spain EXPERIMENTAL RESEARCH ON FLOW IN A 5-STAGE HIGH PRESSURE ROTOR OF 1000

More information

Design and testing of a high flow coefficient mixed flow impeller

Design and testing of a high flow coefficient mixed flow impeller Design and testing of a high flow coefficient mixed flow impeller H.R. Hazby PCA Engineers Ltd., UK M.V. Casey PCA Engineers Ltd., UK University of Stuttgart (ITSM), Germany R. Numakura and H. Tamaki IHI

More information

Dimensional analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena.

Dimensional analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena. Dimensional Analysis and Similarity Dimensional analysis is very useful for planning, presentation, and interpretation of experimental data. As discussed previously, most practical fluid mechanics problems

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

Analysis of the entire surge cycle of a multi-stage high-speed compressor

Analysis of the entire surge cycle of a multi-stage high-speed compressor Center for Turbulence Research Annual Research Briefs 2008 205 Analysis of the entire surge cycle of a multi-stage high-speed compressor By S. Teramoto 1. Motivation and objectives Both surge and rotating

More information

FRANCIS TURBINE EXPERIMENT

FRANCIS TURBINE EXPERIMENT FRANCIS TURBINE EXPERIMENT 1. OBJECT The purpose of this experiment is to study the constructional details and performance parameters of Francis Turbine. 2. INTRODUCTION Turbines are subdivided into impulse

More information

Dynamic Process Modeling. Process Dynamics and Control

Dynamic Process Modeling. Process Dynamics and Control Dynamic Process Modeling Process Dynamics and Control 1 Description of process dynamics Classes of models What do we need for control? Modeling for control Mechanical Systems Modeling Electrical circuits

More information

FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER

FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER? What type of fluid flow is observed? The above pictures show how the effect

More information

Fundamentals of Fluid Mechanics

Fundamentals of Fluid Mechanics Sixth Edition. Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department

More information

FLUID MECHANICS. TUTORIAL No.7 FLUID FORCES. When you have completed this tutorial you should be able to. Solve forces due to pressure difference.

FLUID MECHANICS. TUTORIAL No.7 FLUID FORCES. When you have completed this tutorial you should be able to. Solve forces due to pressure difference. FLUID MECHANICS TUTORIAL No.7 FLUID FORCES When you have completed this tutorial you should be able to Solve forces due to pressure difference. Solve problems due to momentum changes. Solve problems involving

More information

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 12 Steam Turbine - Impulse Good afternoon. We were studying

More information

ENSC 283 Introduction and Properties of Fluids

ENSC 283 Introduction and Properties of Fluids ENSC 283 Introduction and Properties of Fluids Spring 2009 Prepared by: M. Bahrami Mechatronics System Engineering, School of Engineering and Sciences, SFU 1 Pressure Pressure is the (compression) force

More information

Laminar flow in a baffled stirred mixer (COMSOL)

Laminar flow in a baffled stirred mixer (COMSOL) AALTO UNIVERSITY School of Chemical Technology CHEM-E7160 Fluid Flow in Process Units Laminar flow in a baffled stirred mixer (COMSOL) Sanna Hyvönen, 355551 Nelli Jämsä, 223188 Abstract In this simulation

More information

Transient Performance Prediction for Turbocharging Systems Incorporating Variable-geometry Turbochargers

Transient Performance Prediction for Turbocharging Systems Incorporating Variable-geometry Turbochargers 22 Special Issue Turbocharging Technologies Research Report Transient Performance Prediction for Turbocharging Systems Incorporating Variable-geometry Turbochargers Hiroshi Uchida Abstract Turbocharging

More information

Comparative Analysis of Gas Turbine Blades with and without Turbulators

Comparative Analysis of Gas Turbine Blades with and without Turbulators Comparative Analysis of Gas Turbine Blades with and without Turbulators Sagar H T 1, Kishan Naik 2 1 PG Student, Dept. of Studies in Mechanical Engineering, University BDT College of Engineering, Davangere,

More information

1 Theoretical Background of PELTON Turbine

1 Theoretical Background of PELTON Turbine c [m/s] linear velocity of water jet u [m/s) runner speed at PCD P jet [W] power in the jet de kin P T [W] power of turbine F [N] force F = dj Q [m 3 /s] discharge, volume flow ρ [kg/m 3 ] density of water

More information

Algopithm for Design Calculation of Axial Flow Gas Turbine Compressor Comparison with GTD 350 Compressor Design

Algopithm for Design Calculation of Axial Flow Gas Turbine Compressor Comparison with GTD 350 Compressor Design Mechanics and Mechanical Engineering Vol. 15, No. 3 (2011) 207 216 c Technical University of Lodz Algopithm for Design Calculation of Axial Flow Gas Turbine Compressor Comparison with GTD 350 Compressor

More information

Modelling and CFD Analysis of Single Stage IP Steam Turbine

Modelling and CFD Analysis of Single Stage IP Steam Turbine International Journal of Mechanical Engineering, ISSN:2051-3232, Vol.42, Issue.1 1215 Modelling and CFD Analysis of Single Stage IP Steam Turbine C RAJESH BABU Mechanical Engineering Department, Gitam

More information

PELTON TURBINE EXPERIMENT

PELTON TURBINE EXPERIMENT Fluid Machines PELTON TURBINE EXPERIMENT 1. OBJECT The purpose of this experiment is to study the constructional details and performance parameters of Pelton Turbine. 2. INTRODUCTION Energy may exist in

More information

Ideal Jet Propulsion Cycle

Ideal Jet Propulsion Cycle Ideal Jet ropulsion Cycle Gas-turbine engines are widely used to power aircrafts because of their light-weight, compactness, and high power-to-weight ratio. Aircraft gas turbines operate on an open cycle

More information

Natural Convection. Buoyancy force

Natural Convection. Buoyancy force Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

More information

O.F.Wind Wind Site Assessment Simulation in complex terrain based on OpenFOAM. Darmstadt, 27.06.2012

O.F.Wind Wind Site Assessment Simulation in complex terrain based on OpenFOAM. Darmstadt, 27.06.2012 O.F.Wind Wind Site Assessment Simulation in complex terrain based on OpenFOAM Darmstadt, 27.06.2012 Michael Ehlen IB Fischer CFD+engineering GmbH Lipowskystr. 12 81373 München Tel. 089/74118743 Fax 089/74118749

More information

TwinMesh Grid Generator and CFD Simulation with ANSYS CFX

TwinMesh Grid Generator and CFD Simulation with ANSYS CFX TwinMesh Grid Generator and CFD Simulation with ANSYS CFX 2nd Short Course on CFD in Rotary Positive Displacement Machines London, 5th 6th September 2015 Dr. Andreas Spille-Kohoff Jan Hesse Rainer Andres

More information

Fluent Software Training TRN Boundary Conditions. Fluent Inc. 2/20/01

Fluent Software Training TRN Boundary Conditions. Fluent Inc. 2/20/01 Boundary Conditions C1 Overview Inlet and Outlet Boundaries Velocity Outline Profiles Turbulence Parameters Pressure Boundaries and others... Wall, Symmetry, Periodic and Axis Boundaries Internal Cell

More information

Advances in Military Technology Vol. 6, No. 1, June Gas Turbine Engine Off-Design Calculations Using Matlab. J. Pečinka 1*, M.

Advances in Military Technology Vol. 6, No. 1, June Gas Turbine Engine Off-Design Calculations Using Matlab. J. Pečinka 1*, M. AiMT Advances in Military Technology Vol. 6, No. 1, June 2011 Gas Turbine Engine Off-Design Calculations Using Matlab J. Pečinka 1*, M. Poledno 1 Department of Airspace and Rocket Technologies, University

More information

4.7 DIFFUSER. h c ¼ T. ¼ isentropic stagnation temperature at the diffuser outlet) or. (where T 03

4.7 DIFFUSER. h c ¼ T. ¼ isentropic stagnation temperature at the diffuser outlet) or. (where T 03 (where T 03 0 ¼ isentropic stagnation temperature at the diffuser outlet) or h c ¼ T 01 T 03 0 =T 01 2 1 T 03 2 T 01 Let P 01 be stagnation pressure at the compressor inlet and; P 03 is stagnation pressure

More information

NUMERICAL ANALYSIS OF WELLS TURBINE FOR WAVE POWER CONVERSION

NUMERICAL ANALYSIS OF WELLS TURBINE FOR WAVE POWER CONVERSION Engineering Review Vol. 32, Issue 3, 141-146, 2012. 141 NUMERICAL ANALYSIS OF WELLS TURBINE FOR WAVE POWER CONVERSION Z. 1* L. 1 V. 2 M. 1 1 Department of Fluid Mechanics and Computational Engineering,

More information

Understanding Plastics Engineering Calculations

Understanding Plastics Engineering Calculations Natti S. Rao Nick R. Schott Understanding Plastics Engineering Calculations Hands-on Examples and Case Studies Sample Pages from Chapters 4 and 6 ISBNs 978--56990-509-8-56990-509-6 HANSER Hanser Publishers,

More information

Engineering Problem Solving as Model Building

Engineering Problem Solving as Model Building Engineering Problem Solving as Model Building Part 1. How professors think about problem solving. Part 2. Mech2 and Brain-Full Crisis Part 1 How experts think about problem solving When we solve a problem

More information

Chapter 6 Energy Equation for a Control Volume

Chapter 6 Energy Equation for a Control Volume Chapter 6 Energy Equation for a Control Volume Conservation of Mass and the Control Volume Closed systems: The mass of the system remain constant during a process. Control volumes: Mass can cross the boundaries,

More information

Mass and Energy Analysis of Control Volumes

Mass and Energy Analysis of Control Volumes MAE 320-Chapter 5 Mass and Energy Analysis of Control Volumes Objectives Develop the conservation of mass principle. Apply the conservation of mass principle to various systems including steady- and unsteady-flow

More information

J. Szantyr Lecture No. 2 Principles of the Theory of Turbomachinery

J. Szantyr Lecture No. 2 Principles of the Theory of Turbomachinery J. Szantyr Lecture No. 2 Principles of the Theory of Turbomachinery a) Axial ventilator or pump b) Diagonal (mixed flow) ventilator or pump c) Centrifugal compressor or pump d) Axial-radial water turbine

More information

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation

More information

Mechanical Design of Turbojet Engines. An Introduction

Mechanical Design of Turbojet Engines. An Introduction Mechanical Design of Turbomachinery Mechanical Design of Turbojet Engines An Introduction Reference: AERO0015-1 - MECHANICAL DESIGN OF TURBOMACHINERY - 5 ECTS - J.-C. GOLINVAL University of Liege (Belgium)

More information

Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 Web Site:

Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670   Web Site: Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Brayton Cycle (Gas Turbine) for Propulsion Application

More information

MODULE SPECIFICATION FORM

MODULE SPECIFICATION FORM MODULE SPECIFICATION FORM Module Title: Thermo-fluid and Propulsion Level: 5 Credit Value: 20 Module code: (if known) ENG538 Cost Centre: GAME JACS2 code: H141/H311/ H450 Semester(s) in which to be offered:

More information

Turbulence Modeling in CFD Simulation of Intake Manifold for a 4 Cylinder Engine

Turbulence Modeling in CFD Simulation of Intake Manifold for a 4 Cylinder Engine HEFAT2012 9 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 16 18 July 2012 Malta Turbulence Modeling in CFD Simulation of Intake Manifold for a 4 Cylinder Engine Dr MK

More information

ME 6404 THERMAL ENGINEERING. Part-B (16Marks questions)

ME 6404 THERMAL ENGINEERING. Part-B (16Marks questions) ME 6404 THERMAL ENGINEERING Part-B (16Marks questions) 1. Drive and expression for the air standard efficiency of Otto cycle in terms of volume ratio. (16) 2. Drive an expression for the air standard efficiency

More information

COMPUTATIONAL ANALYSIS OF CENTRIFUGAL COMPRESSOR WITH GROOVES ON CASING

COMPUTATIONAL ANALYSIS OF CENTRIFUGAL COMPRESSOR WITH GROOVES ON CASING INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 6340(Print), ISSN ISSN 0976 6340 (Print) ISSN 0976

More information

AN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL

AN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL 14 th European Conference on Mixing Warszawa, 10-13 September 2012 AN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL Joanna Karcz, Lukasz Kacperski

More information

THERMODYNAMICS NOTES - BOOK 2 OF 2

THERMODYNAMICS NOTES - BOOK 2 OF 2 THERMODYNAMICS & FLUIDS (Thermodynamics level 1\Thermo & Fluids Module -Thermo Book 2-Contents-December 07.doc) UFMEQU-20-1 THERMODYNAMICS NOTES - BOOK 2 OF 2 Students must read through these notes and

More information

Performance 4. Fluid Statics, Dynamics, and Airspeed Indicators

Performance 4. Fluid Statics, Dynamics, and Airspeed Indicators Performance 4. Fluid Statics, Dynamics, and Airspeed Indicators From our previous brief encounter with fluid mechanics we developed two equations: the one-dimensional continuity equation, and the differential

More information

A LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW. 1998 ASME Fluids Engineering Division Summer Meeting

A LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW. 1998 ASME Fluids Engineering Division Summer Meeting TELEDYNE HASTINGS TECHNICAL PAPERS INSTRUMENTS A LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW Proceedings of FEDSM 98: June -5, 998, Washington, DC FEDSM98 49 ABSTRACT The pressure

More information

ME 305 Fluid Mechanics I. Part 4 Integral Formulation of Fluid Flow

ME 305 Fluid Mechanics I. Part 4 Integral Formulation of Fluid Flow ME 305 Fluid Mechanics I Part 4 Integral Formulation of Fluid Flow These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey

More information

Boundary Conditions in Fluid Mechanics

Boundary Conditions in Fluid Mechanics Boundary Conditions in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University The governing equations for the velocity and pressure fields are partial

More information

CRANFIELD UNIVERSITY ELEFTHERIOS ANDREADIS DESIGN OF A LOW SPEED VANEAXIAL FAN SCHOOL OF ENGINEERING. MPhil THESIS

CRANFIELD UNIVERSITY ELEFTHERIOS ANDREADIS DESIGN OF A LOW SPEED VANEAXIAL FAN SCHOOL OF ENGINEERING. MPhil THESIS CRANFIELD UNIVERSITY ELEFTHERIOS ANDREADIS DESIGN OF A LOW SPEED VANEAXIAL FAN SCHOOL OF ENGINEERING MPhil THESIS CRANFIELD UNIVERSITY SCHOOL OF ENGINEERING DEPARTMENT OF POWER ENGINEERING AND PROPULSION

More information

FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES

FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES FREESTUDY HEAT TRANSFER TUTORIAL ADVANCED STUDIES This is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection. The tutorials are designed to bring the

More information

1. Why are the back work ratios relatively high in gas turbine engines? 2. What 4 processes make up the simple ideal Brayton cycle?

1. Why are the back work ratios relatively high in gas turbine engines? 2. What 4 processes make up the simple ideal Brayton cycle? 1. Why are the back work ratios relatively high in gas turbine engines? 2. What 4 processes make up the simple ideal Brayton cycle? 3. For fixed maximum and minimum temperatures, what are the effect of

More information

Macroscopic Balances for Nonisothermal Systems

Macroscopic Balances for Nonisothermal Systems Transport Phenomena Macroscopic Balances for Nonisothermal Systems 1 Macroscopic Balances for Nonisothermal Systems 1. The macroscopic energy balance 2. The macroscopic mechanical energy balance 3. Use

More information

Boston University BRAYTON CYCLE EXPERIMENT -JET ENGINE

Boston University BRAYTON CYCLE EXPERIMENT -JET ENGINE Boston University ENG EK 304 Energy and Thermodynamics Laboratory Exercise II BRAYTON CYCLE EXPERIMENT -JET ENGINE (Based on an instruction set provided by Turbine Technologies Limited, 2002 Modified by

More information

Airflow through Mine Openings and Ducts Chapter 5

Airflow through Mine Openings and Ducts Chapter 5 Airflow through Mine Openings and Ducts Chapter 5 Fundamentals of Airflow Ventilation the application of the principles of fluid mechanics & thermodynamics to the flow of air in underground openings Fluid

More information

Module 6 Case Studies

Module 6 Case Studies Module 6 Case Studies 1 Lecture 6.1 A CFD Code for Turbomachinery Flows 2 Development of a CFD Code The lecture material in the previous Modules help the student to understand the domain knowledge required

More information

Impact of Power Frequency on the Performance of a Scroll Compressor

Impact of Power Frequency on the Performance of a Scroll Compressor Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 28 Impact of Power Frequency on the Performance of a Scroll Compressor Michael M. Cui Trane

More information

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 36 Pipe Flow Systems Welcome back to the video course on Fluid Mechanics. In today

More information

Turbine Design for Thermoacoustic

Turbine Design for Thermoacoustic Turbine Design for Thermoacoustic Generator Design of a bi-directional turbine to convert acoustic power into electricity 8/20/2012 Company: FACT-Foundation Author: Tim Kloprogge Student number: 443943

More information

ME 239: Rocket Propulsion. Over- and Under-expanded Nozzles and Nozzle Configurations. J. M. Meyers, PhD

ME 239: Rocket Propulsion. Over- and Under-expanded Nozzles and Nozzle Configurations. J. M. Meyers, PhD ME 239: Rocket Propulsion Over- and Under-expanded Nozzles and Nozzle Configurations J. M. Meyers, PhD 1 Over- and Underexpanded Nozzles Underexpanded Nozzle Discharges fluid at an exit pressure greater

More information

PEMP RMD M.S. Ramaiah School of Advanced Studies

PEMP RMD M.S. Ramaiah School of Advanced Studies Axial Turbines Session delivered by: Prof. Q.H. Nagpurwala 1 Session Objectives This session is intended to introduce the following: Construction and types of axial turbines Euler turbine equation and

More information

NUMERICAL ANALYSIS FOR TWO PHASE FLOW DISTRIBUTION HEADERS IN HEAT EXCHANGERS

NUMERICAL ANALYSIS FOR TWO PHASE FLOW DISTRIBUTION HEADERS IN HEAT EXCHANGERS NUMERICAL ANALYSIS FOR TWO PHASE FLOW DISTRIBUTION HEADERS IN HEAT EXCHANGERS B.Babu 1, Florence.T 2, M.Punithavalli 3, B.R.Rohit 4 1 Assistant professor, Department of mechanical engineering, Rathinam

More information

Jet Propulsion. Lecture-2. Ujjwal K Saha, Ph.D. Department of Mechanical Engineering Indian Institute of Technology Guwahati 1

Jet Propulsion. Lecture-2. Ujjwal K Saha, Ph.D. Department of Mechanical Engineering Indian Institute of Technology Guwahati 1 Lecture-2 Prepared under QIP-CD Cell Project Jet Propulsion Ujjwal K Saha, Ph.D. Department of Mechanical Engineering Indian Institute of Technology Guwahati 1 Simple Gas Turbine Cycle A gas turbine that

More information

GT2011 46090 ANALYSIS OF A MICROGASTURBINE FED BY NATURAL GAS AND SYNTHESIS GAS: MGT TEST BENCH AND COMBUSTOR CFD ANALYSIS

GT2011 46090 ANALYSIS OF A MICROGASTURBINE FED BY NATURAL GAS AND SYNTHESIS GAS: MGT TEST BENCH AND COMBUSTOR CFD ANALYSIS ASME Turbo Expo 2011 June 6 10, 2011 Vancouver, Canada GT 2011 46090 ANALYSIS OF A MICROGASTURBINE FED BY NATURAL GAS AND SYNTHESIS GAS: MGT TEST BENCH AND COMBUSTOR CFD ANALYSIS M. Cadorin 1,M. Pinelli

More information

Bi-directional turbines for converting acoustic wave power into electricity

Bi-directional turbines for converting acoustic wave power into electricity Bi-directional turbines for converting acoustic wave power into electricity Kees de BLOK 1, Pawel OWCZAREK 2, Maurice-Xavier FRANCOIS 3 1 Aster Thermoacoustics, Smeestraat 11, 8194LG Veessen, The Netherlands

More information

CFturbo Modern turbomachinery design software

CFturbo Modern turbomachinery design software COMPRESSOR Tech Magazine CFturbo Modern turbomachinery design software Designing new compressors from scratch and compressor redesign By Ralph-Peter Mueller & Gero Kreuzfeld Ralph-Peter Mueller and Gero

More information

Gas Turbine Plant Modeling for Dynamic Simulation

Gas Turbine Plant Modeling for Dynamic Simulation Gas Turbine Plant Modeling for Dynamic Simulation Samson Endale Turie October, 2011 Master s Thesis Master of Science Thesis KTH School of Industrial Engineering and Management Department of Energy Technology

More information

The First Law of Thermodynamics

The First Law of Thermodynamics The First Law of Thermodynamics (FL) The First Law of Thermodynamics Explain and manipulate the first law Write the integral and differential forms of the first law Describe the physical meaning of each

More information

Transient Mass Transfer

Transient Mass Transfer Lecture T1 Transient Mass Transfer Up to now, we have considered either processes applied to closed systems or processes involving steady-state flows. In this lecture we turn our attention to transient

More information

Chapter 1. Governing Equations of Fluid Flow and Heat Transfer

Chapter 1. Governing Equations of Fluid Flow and Heat Transfer Chapter 1 Governing Equations of Fluid Flow and Heat Transfer Following fundamental laws can be used to derive governing differential equations that are solved in a Computational Fluid Dynamics (CFD) study

More information

PEMP RMD510. M.S.Ramaiah School of Advanced Studies, Bengaluru

PEMP RMD510. M.S.Ramaiah School of Advanced Studies, Bengaluru Turbine and Compressor Matching Session delivered by: Prof. Q. H. Nagpurwala 1 Session Objectives To discuss the operating characteristics of compressors and turbines To understand the basic conditions

More information