DT9P 34 - Thermofluids

Energy in Thermofluid Systems

The Principle of Conservation of Energy

The Law of Conservation of Energy in mechanics, only potential and kinetic

energy are usually considered, in thermodynamics this is extended to include

thermal and other forms of energy.

Energy cannot be created or destroyed although it can be changed from one

form to another. This means that a system and its surroundings that contain a

given amount of energy may change the form of energy but the total amount will

remain the same.

e.g. A common example is the motorcar, where a specific amount of thermal

energy is released with the combustion of the fuel in the engine. This energy is

converted into work to move the vehicle, some is released via exhaust gases,

and some is released to the air via the cooling system.

Open and Closed Systems

A System is a region in space containing a quantity of matter whose behaviour is

being investigated. The system is surrounded by a boundary.

An Open System is a system that has breaks in the boundary so that matter

may flow through the system e.g. a turbine.

A Closed System is a system having a continuous boundary and no matter may

enter or leave, e.g. an engine cylinder with the valves closed.

Surroundings

Boundary

System

Energy Transfer

If a system contains a certain amount of stored energy this amount will be

altered when either work or heat (or both) flow across the boundary.

A closed system will contain internal energy and an open system will contain

internal energy and it may also contain potential energy, kinetic energy and flow

energy.

The internal energy that matter contains cannot be measured directly, but

changes in the internal energy due to energy transfer can be inferred (by

measurement of the heat and work transfer).

Stored and Transitional Energy

Energy may be divided into two main groups: -

Stored Energy

A system may have stored energy such as potential energy, kinetic energy,

internal energy and flow energy due to a fluid at some height above a datum,

moving with a specific velocity and having a particular temperature and flow

characteristics.

Transitional Energy

Both heat and work are forms of transitional energy, which is energy being

transferred either from the system or to the system.

Heat and Work cannot exist as stored energy, so that a body cannot

“contain heat” or “contain work”.

A system may contain internal energy and possess both potential and

kinetic energy, but heat and work energy can only exist on their way to, or

from, a system.

So when heat or work transfers take place the total energy of the system

is either increased or decreased.

Stored and Transitional Energy

Enthalpy (H)

Internal energy and flow energy are always present in moving fluid in an Open

System and are normally combined together to form the energy expression: -

Enthalpy, H = U + P V

Heat (Q)

This is a form of “energy transfer” to or from a system due to a difference in

temperature between the system and its surrounding.

Work (W)

Work is a form of “energy transfer” to or from a system and occurs when a

force (or torque) causes a body to move.

Energy in Specific Terms

Normally we work in specific terms i.e. energy per unit mass, where the unit of

mass is defined as 1kg. Therefore the unit of specific energy is J/kg (Jkg-1).

Joules are by definition a small quantity so energy is specified in terms of kJ/kg

(kJkg-1 )

The specific definition of the energy components are therefore as follows: -

Kinetic Energy ke = c2 / 2000 kJ/kg (kJkg-1)

Potential Energy pe = (g Z) /1000 kJ/kg (kJkg-1)

Internal Energy u kJ/kg (kJkg-1) (This value is normally described in kJ terms)

Flow Energy pv kJ/kg (kJkg-1) (Assuming pressure in kNm-2)

Heat Energy q kJ/kg (kJkg-1)

Work Energy w kJ/kg (kJkg-1)

NOTE: The use of lowercase lettering for the specific quantity, absolute values are

represented using UPPERCASE lettering.

Energy Equation Convention

This relates the changes that take place in the stored energies of a system to the

flow of heat and work to, or from the system. A convention must be adopted to

avoid confusion in problems.

The normal convention used is: -

Quantity Convention

PE (pe) +ve when increased and –ve when decreased.

KE (ke) +ve when increased and –ve when decreased.

U (u) +ve when internal energy is increased and –ve when it is decreased.

Q (q) +ve when heat is added and –ve when heat is rejected.

W (w) +ve when work is done by the (expansion) system and –ve when work is done

on the (compression) system.

The First Law of Thermodynamics

This is the same as the Principle of Conservation of Energy.

If Heat (Q) and Work (W) are transferred across the boundary of a system then the

net amount of the transfer must equal the change in the total energy of the system.

Net transfer = Change in Energy

Q – W = E2 – E1

Q = E2 – E1 + W

Note: ‘2’ is the Output Energy State and ‘1’ is the Input Energy State.

General Energy Equation for an Open System

This equation takes into account all the components of energy of an open system,

where matter crosses the boundaries of the system. In this equation we expand the

values of ‘E’ in the First Law defined on the previous slide.

Q = (U2 – U1) + (P2V2 – P1V1) + (PE2 – PE1) + (KE2 – KE1) + W (J or kJ)

Q = ΔU + ΔPV + ΔPE + ΔKE + W (J or kJ)

For specific quantities (i.e. 1 kg):

q = (u2 – u1) + (p2v2 – p1v1) + (pe2 – pe1) + (ke2 –ke1) + w (Jkg-1 or kJkg-1)

q = Δu + Δpv + Δpe + Δke + w (Jkg-1 or kJkg-1)

(Δ = change in)

Open System - Steady Flow Energy Equation (S.F.E.E.)

Consider a system which has reached operational state, for example, when a

gas or steam turbine is in the operating mode, (not warming up or running

down). The mass flow rate of fluid entering the system is the same as the mass

flow rate leaving the system.

Q = ṁ(h2 – h1) + ṁ(pe2 – pe1) + ṁ(ke2 – k1) + Ẇ

Q - rate at which heat enters or leaves the system kJ/s (kJs-1)

ṁ - mass flow rate of fluid kg/s (kgs-1)

h - specific Enthalpy entering or leaving the system kJ/kg (kJkg-1)

ke - specific kinetic energy of the fluid kJ/kg (kJkg-1)

pe - is the specific potential energy of the fluid kJ/kg (kJkg-1)

Ẇ - is the rate of work output or input to the system kJ/s (kJs-1)

J/s (Js-1) = Watts, kJ/s (kJs-1) = kW

Example – S.F.E.E.

Air flows steadily at the rate of 0.4kgs-1 through an air compressor, entering at 6ms-1

with a pressure of 1bar and a specific volume of 0.85m3kg-1 and leaving with a

velocity of 4.5ms-1 with a pressure of 6.9bar and a specific volume of 0.16m3kg-1.

The internal energy of the air leaving is 88kJkg-1 greater than that of the air entering.

Cooling water in a jacket surrounding the cylinder absorbs heat from the air at the

rate of 59kJs-1. Calculate the power required to drive the compressor.

1

2

w

Q = 59kJ/s

q = (u2 – u1 ) + (p2v2 – p1v1) + (ke2 – ke1) + w (No PE) (kJ/kg)

-147.5 = 88 + ((690 x 0.16) – (100 x 0.85)) + ((4.52 – 6.02) / 2 x 103)) + w

(note: pressure in kN/m2)

-147.5 = 88 +25.4 - 0.0078 + w

w = -260.9kJkg-1 (work has to be done to compress!)

Power Required = ṁ x w = 0.4 x 260.9 = 104.4kW

c2 = 4.5ms-1

v2 = 0.16m3kg-1

p2 = 6.9bar

ṁ = 0.4kgs-1

c1 = 6ms-1

v1 = 0.85m3kg-1

p1 =1bar

u2 – u1 = 88kJkg-1

q = Q / ṁ

= 59 / 0.4

= 147.5kJkg-1

(heat loss)

Closed System - Non-Flow Energy Equation (N.F.E.E.)

In the Closed system No fluid crosses the boundary. Heat and Work can cross the

boundary but not the working fluid itself.

The heat and work exchange across the boundary will cause a change in the

Internal Energy of the working fluid within the boundary.

Potential energy, kinetic energy and flow energy are all zero.

Heat (in or out) + Work (in or out) = Change in internal energy of the system.

Q = ΔU + W or Q – W = ΔU (J) (kJ)

Q - heat transfer across the boundary

W - work transfer across the boundary

U - internal energy

System

Boundary

Heat Work

Example – N.F.E.E.

An example of an N.F.E.E. is a gas in a cylinder which has an initial internal

energy of 200kJ. Heat energy of 40kJ enters the system whilst the piston does

30kJ of work. What is the final internal energy of the gas in the cylinder?

Q – W = U2 – U1

40kJ – 30kJ = U2 – 200kJ

240 – 30kJ = U2

The final internal energy of the gas in the system

= 210kJ

U 40kJ

30kJ