기초열역학 (control volume 의 열역학)

4.1 Thermodynamic analysis of control volumes

Control Volume
Control Surface
Steady: No change with time
↔ Unsteady, Transient
Uniform: No change with location

Conservation of Mass Principle

Mass and Volume Flow Rates
Mass Flow Rate: Amount of mass flowing through a cross section per unit time

Mass Flow Rate

It is proportional to the cross-sectional area A, the density ρ, the velocity V of the fluid.

Vn: Velocity component normal to dA

Vav :  Average fluid velocity normal to A

Volume Flow Rate

Volume of the fluid flowing through a cross-section per unit time

The mass and volume flow rate:

Conservation of Energy Principle

In closed system

Net heat(Q) – Work(W) = Energy change(ΔE)

When mass enters or leaves a control volume, the energy increase or decrease within the control volume.

The conservation of energy equation for a control volume

The energy required ot push fluid into or out of a control volume is called the flow work, or flow energy.

Flow Work

If the fluid pressure is P and the cross-sectional area of the fluid element A, the force applied on the fluid element by the imaginary piston F = PA.
The work done in pushing the fluid element
Wflow = FL  =  PAL  =PV

Total Energy of a Flowing Fluid

Three Parts of total energy of a simple compressible system: Internal, Kinetic, and Potential energies.
On a unit mass basis,

Total energy of a flowing fluid on a unit mass basis (θ)

By the definition of enthalpy (h = u + Pv):

θ: Methalphy Metaenthalpy, which means beyond enthalphy

Steady Flow Process

Process during which a fluid flows through a control volume steadily

Steady flow devices: Turbines, compressors, and nozzles operating for long periods of time under the same conditions

Steady means no change with time.

No properties (volume, mass, total energy) within the control volume change with time. The boundary work is zero for steady flow systems since Vcv is constant.
No properties change at the boundaries of the control volume with time. The mass flow rate of the fluid at an opening must remain constant during a steady flow process.
The heat and work interactions between a steady flow system and its surrounding do not change with time

Conservation of Mass

During a steady flow process, the total amount of mass in CV does not change with time. (Entering Mass = Leaving Mass)

Water Heater under steady operation:
The water stream will experience an increase in its total energy as it flows through the water heater, which is equal to the electric energy supplied to the water minus the heat losses.

Some Steady-Flow Engineering Device

Nozzles and Diffusers
Jet engines, rockets, spacecraft, garden hoses
Nozzle: Device to increase the velocity of a fluid
Diffuser: Device to increase the pressure of a fluid by slowing it down.

Turbines
Steam, gas, hydroelectric power plants
As the fluid passes through the turbine, work is done against the blades which are attached to the shaft.
Compressors
Device to increase the pressure of a fluid

Throttling Valves
Adjustable valves, capillary tubes, porous plugs
Any kind of flow-restricting devices that cause a significant pressure drop in the fluid.


Heat Exchangers
Devices to exchange heat with mixing of two moving fluid streams.
Double-tube (tube and shell) heat exchanger

Pipe and Duct Flow
Transport of liquids or gases
Flow through a pipe or a duct usually satisfies the steady flow conditions except the transient start-up and shut-down periods