Lec 13: Machines (except heat exchangers)

For next time: Read: § 5-4 HW7 due Oct. 15, 2003 Outline: Diffusers and nozzles Turbines Pumps and compressors Important points: Know the standard assumptions that go with each device Know how to simplify the governing equations using these assumptions Consider what each device would be used for in real-world applications

Applications to some steady state systems Start simple nozzles diffusers valves Include systems with power in/out turbines compressors/pumps Finish with multiple inlet/outlet devices heat exchangers mixers

We will need everything we have covered Conservation of mass Conservation of energy Property relationships Ideal gas equation of state Property tables Systematic analysis approach

Nozzles and Diffusers Nozzle--a device which accelerates a fluid as the pressure is decreased. V2, p2 V1, p1 This configuration is for subsonic flow.

Nozzles and Diffusers Diffuser--a device which decelerates a fluid and increases the pressure. V2, p2 V1, p1

For supersonic flow, the shape of the nozzle is reversed. Nozzles

General shapes of nozzles and diffusers

Common assumptions for nozzles and diffusers Steady state, steady flow. Nozzles and diffusers do no work and use no work. Potential energy changes are usually small. Sometimes adiabatic.

TEAMPLAY For nozzles, diffusers and other machines--just how important is PE? The energy in the head of a kitchen match is reportedly about 1 Btu. How far does 1 lbm have to fall in a standard earth gravity field to “match” this much energy? Example 5-12 on p. 175 has an enthalpy change h1 - h2 less than 20 Btu. What does your result mean physically for a nozzle or diffuser?

We start our analysis of diffusers and nozzles with the conservation of mass If we have steady state, steady flow, then: And

We continue with conservation of energy We can simplify by dividing by mass flow: Applying the definition that w=0 and using some other assumptions...

We can rearrange to get a much simpler expression: With a nozzle or diffuser, we are converting flow energy and internal energy, represented by Dh into kinetic energy, or vice-versa.

Sample Problem

Sample Problem:Assumptions SSSF (Steady state, steady flow) - no time dependent terms adiabatic no work potential energy change is zero air is ideal gas

Sample problem:diagram and basic information OUTLET P2=167 kPa V2=35 m/s INLET T1=300C P1=100 kPa V1=250 m/s m = 7 kg/s

Sample Problem: apply basic equations Conservation of Mass Solve for A2

How do we get specific volumes? Remember ideal gas equation of state? or and We know T1 and P1, so v1 is simple. We know P2, but what about T2? NEED ENERGY EQUATION!!!!

Sample problem - con’t Energy V1 and V2 are given. We need h2 to get T2 and v2. If we assumed constant specific heats, we could get T2 directly

Sample problem - con’t However, use variable specific heats...get h1 from air tables at T1 = 300+273 = 573 K. From energy equation: This corresponds to an exit temperature of 602.2 K.

Now we can get solution. and

TEAMPLAY Work problem 5-65

Throttling Devices (Valves)

Short tube orifice for 2.5 ton air conditioner

Throttles (throttling devices) A major purpose of a throttling device is to restrict flow or cause a pressure drop. A major category of throttling devices is valves.

Typical assumptions for throttling devices Do no work, have no work done on them Potential energy changes are zero Kinetic energy changes are usually small Heat transfer is usually small

Look at energy equation: Apply assumptions from previous page: We obtain: or

Look at implications: If fluid is an ideal gas: cp is always a positive number, thus:

Discussion Question Does the fluid temperature increase, decrease, or remain constant as an ideal gas goes through an adiabatic valve?

TEAMPLAY Refrigerant 134a enters a valve as a saturated liquid at 200 psia and leaves at 50 psia. What is the quality of the refrigerant at the exit of the valve?

Turbine A turbine is device in which work is produced by a gas passing over and through a set of blades fixed to a shaft which is free to rotate.

Turbines We’ll assume steady state, Sometimes neglected Almost always neglected

Turbines We will draw turbines like this: inlet w maybe q outlet

Compressors, pumps, and fans Machines developed to make life easier, decrease world anxiety, and provide challenging problems for engineering students. Machines which do work on a fluid to raise its pressure, potential, or speed. Mathematical analysis proceeds the same as for turbines, although the signs may differ.

Primary differences Compressor - used to raise the pressure of a compressible fluid Pump - used to raise pressure or potential of an incompressible fluid Fan - primary purpose is to move large amounts of gas, but usually has a small pressure increase

Compressors, pumps, and fans Side view End view Centrifugal pump Axial flow Compressor

Sample Problem Air initially at 15 psia and 60°F is compressed to 75 psia and 400°F. The power input to the air is 5 hp and a heat loss of 4 Btu/lb occurs during the process. Determine the mass flow in lbm/min.

Draw Diagram

Assumptions Steady state steady flow (SSSF) Neglect potential energy changes Neglect kinetic energy changes Air is ideal gas

What do we know? INLET T1 = 60F P1 = 15 psia OUTLET T2 = 400F

Apply First Law: Simplify and rearrange:

Continuing with the solution.. Get h1 and h2 from air tables Follow through with solution

TEAMPLAY Work problem 5-73E

TEAMPLAY Use EES and vary the exit pressure from 5 psia to 0.5 psia in increments of 1.0 psia. Show the results as a table and a plot. Open EES and put in the basic equation

TEAMPLAY You will have to use some new features of EES 1. Under options always check and set unit system, if necessary. 2. Under options, find function info, and select fluid properties. 3. For steam, use Steam_NBS.

TEAMPLAY Parametric studies Under “Tables”, select “New Parametric Table” Click and drag the variables you want to see to the right--P2, Qdot, and h2. See that P2 is not specified in the problem statement in the “Equations Window”.

TEAMPLAY Enter P2 via “Alter Values” under “Tables” Click on the column headings to be able to enter units. You must solve the table before you can plot it. Under “Calculate” select “Solve Table.”

TEAMPLAY Under “Plot” select “New Plot Window” and “X-Y Plot”.