Introduction to fluid machines and thermodynamics fundamentals

Introduction to Fluid Machines

In this course fluid machines will be investigated along with their main components in order to provide the fundamentals necessary for both understanding the operation and a rational choice oriented towards the best use of the energy.

A fluid machine is an object consisting of a set of fixed and mobile elements that interact with a working fluid (liquid, vapor and gas), creating an energy exchange with it. The machine transforms an incoming energy, of a certain type, into an outgoing energy, generally of a different nature. This definition actually sees the machine as an energy system, i.e. capable of processing and/or converting energy to make it available in a more useful form.

P-V Diagram in Machine Study

The dynamic diagram is used in the study of machines to represent the pressure variations as a function of the volume (or viceversa).

Important curves are those which represent the isentropic transformations (non-equilateral hyperbolas of equation pvk=cost, with k=cp/cv) and the isothermal ones (equilateral hyperbolas of equation pv=const, having the axes of the diagram as asymptotes ) in the gas field.

The dynamic diagram is particularly useful for directly evaluating the work exchanged with the outside due to pressure and volume variations in the system, as the areas subtended by the curves of the p-v diagram represent precisely this work: in fact, for an open system, along an isentropic transformation we have 2 L = [vdp 1 . In case of a closed system, the mechanical work along an isentropic transformation is: L = [ pdv . It should be noted that the p-V diagram (indicator diagram) used in the study of reciprocating machines is not a thermodynamic diagram because in these systems there are variations in the mass and composition of the fluid during operation (intake, combustion and exhaust phases in endothermic reciprocating engines).

Thermodynamic Systems: Open and Closed

A thermodynamic system, or simply system, is defined as the amount of matter or the region of space under consideration.

The mass or region outside the system is called the environment, while the real or imaginary surface that separates the system from the environment is called the system boundary.

The boundary of a system can be fixed or mobile. The boundary is the surface shared by the system and the environment. In mathematical terms, the contour has zero thickness and therefore can neither contain mass nor occupy volume.

Systems can be closed or open depending on whether a fixed quantity of matter or a fixed volume has to be considered. A closed system, also known as a control mass, consists of a certain amount of matter and is characterized by a boundary that prevent the passage of matter. While mass can neither enter nor leave a closed system, energy can pass through its boundary in the form of heat or work. In the particular case in which even the energy is not allowed to cross the boundary, the system is said to be isolated.

• massa NO SISTEMA CHIUSO m = costante energia SÌ

Open and Closed Systems in Detail

Considering the cylinder-piston device shown in the previous slide, if the attention is focused on the gas, the latter constitutes the system. The internal surfaces of the piston and cylinder form the boundary of the system which, since no mass can cross the boundary, is a closed system. Energy can cross the boundary and that part of the latter (the inner surface of the piston, in this case) can move. Everything outside the gas, included piston and cylinder, constitutes the environment.

An open system, often called control volume, is a region of space delimited by a boundary, called control surface, which at least partially allows the passage of matter. Open systems include devices affected by mass flow such as compressors, turbines or nozzles.

Forms of Energy in a System

The energy of a system can exist in many forms: thermal, kinetic, potential, electric, magnetic, chemical and nuclear. The sum is the total energy E of the system. The total energy of a system per unit mass is denoted by e and is defined by the relationship:

e = E m (J/kg)

Thermodynamics does not provide any information about the absolute value of the total energy of a system, because it deals exclusively with the variations of the total energy, the only ones that are important in engineering problems. We can then assign zero value (E =O) to the total energy of a system in a reference state, as the variations of the total energy of the system are independent of the chosen reference state.

In thermodynamic analysis it is often useful to classify the various forms of energy constituting the total energy of a system into two groups: macroscopic and microscopic. The macroscopic forms of energy are those that a system has as a whole, with respect to some external reference system: for example, kinetic energy or potential energy. Instead, the microscopic forms of energy are those linked to the molecular structure of the system and to the degree of molecular activity; they are independent of the external reference system. The sum of all the microscopic forms of energy is called internal energy of the system and is denoted by U.

Macroscopic Energy and Total Energy

The macroscopic energy of a system is linked to the movement and to the influence of some external phenomena such as gravity. The energy that a system possesses due to its motion, with respect to a fixed reference system, is called kinetic energy Ec. If all the parts of a system move with the same speed, the kinetic energy is expressed by the relation:

mw2 c =m2 S

where w is the velocity of the system in the reference system.

The energy that a system possesses due to its altitude in a gravitational field is called potential energy:

Ep = mgz (J)

where g is the gravity acceleration and z is the height of the center of mass with respect to an arbitrary reference. The total energy of a system is given by the sum of kinetic energy, potential energy and internal energy:

E = Ec + Ep + U = mw 2 2 + mgz + U (J)

State and Equilibrium in Thermodynamics

If a system is not subject to any change, all properties can be measured or calculated anywhere within it, so that a set of properties can be obtained to fully describe the condition, or state, of the system. In a well-defined state, all the properties of a system assume well-defined values. If the value of even one property changes, the state of the system changes.

Thermodynamics deals with systems in a state of equilibrium. In an equilibrium state there are no unbalanced potentials (or driving forces) within the system. A system in an equilibrium state is not subject to any change when isolated from its environment.

There are different types of equilibrium. A system is in thermodynamic equilibrium if the conditions for all types of equilibrium are satisfied, including those of thermal, mechanical, phase and chemical equilibrium. A system is in thermal equilibrium if the temperature is the same at every point in the system; in other words, if the system does not have temperature gradients that are the cause of the heat flow. A system is in mechanical equilibrium if there are no pressure changes at any point over time. A system comprising several phases is in phase equilibrium when the mass of each phase reaches and remains in a state of equilibrium. Finally, a system is in chemical equilibrium if its chemical composition does not vary over time, i.e. if no chemical reactions occur.

Thermodynamic Transformation

Each change that a system undergoes when moving from one equilibrium state to another is called a transformation, and the series of states through which the system passes during a transformation is called a transformation line. To fully describe a transformation, its initial and final states must be specified, as well as the line followed and interactions with the environment.

When a transformation occurs in such a way that, at every instant, the system remains infinitesimally close to the previous equilibrium state, it is called a quasi-static or quasi-equilibrium transformation. A quasi-static transformation can be viewed as a transformation that is slow enough to allow the system to change internally so that properties in one part of the system do not change faster than those in other parts. When a gas inside a cylinder-piston system is compressed rapidly, the molecules close to the face of the piston do not have enough time to move away and end up condensing in a small area near the piston, where they determine an area of greater pressure. Due to this pressure difference, the system can no longer be said to be in equilibrium and this makes the entire transformation non-quasi-static.

Enthalpy Definition

The combination U + pV often encountered. Therefore, it is useful to define such combination as a new property, called enthalpy (H):

H = U + pV (J)

Referring to the unit of mass:

h = u +pv (J/kg)