Thermal fluid dynamics

The Thermal Fluid Dynamics is one of the sub-regions thermodynamics and fluid mechanics composite field of physics . As these two subject areas for technical applications often interact closely with one another, there is the discipline of thermal fluid dynamics, which forms the interface between them. Furthermore, the thermal fluid dynamics is based on the properties of the fluids , so it is not a discipline in which solids play a major role. It is a more modern area of physics, but it is used in many areas of technology.

Areas

Thermal fluid dynamics includes the areas of energy technology (e.g. compressors, expanders, valves, heat exchangers), supply technology (heating, ventilation, air conditioning, gas, district heating), process technology (material transformations, material transport), environmental technology (sewage treatment plants, flue gas cleaning, pollutant propagation) and traffic technology (Vehicle, aerospace technology → aerodynamics, drive technology).

thermodynamics

Thermodynamics is a sub-discipline of physics. The basics of thermodynamics were developed from the study of volume, pressure and temperature conditions in steam engines. Thermodynamics deals, among other things, with the investigation of the laws governing the conversion of heat into other forms of energy and vice versa. That is why it is also known under the term thermodynamics.

The teaching of thermodynamics is used in areas where heat is involved. For example, in engines, refrigerators or when optimizing reaction conditions with regard to temperature and pressure.

In thermodynamics one differentiates between open, closed and closed systems. Open systems are characterized by the exchange of energy and materials beyond the system boundaries. Closed systems, on the other hand, are impermeable to matter. Such a system always contains the same amount of substance. Its volume, on the other hand, does not need to be constant, because the system boundaries are allowed to move. Closed systems exchange neither energy nor matter with their environment.

Fluid dynamics

Fluid dynamics or fluid dynamics is a branch of physics and deals with the study of gases and fluids that are in motion. Fluid dynamics play a central role when it comes to planning and laying piping systems. Both stationary and unsteady flows can be used here. If the velocity remains constant at a fixed point in space in the flow field, one speaks of a steady flow. If the speed changes, an unsteady flow can be assumed.

Continuity equation

A steady flow can often be assumed in technology. If you consider a control volume (e.g. a piece of pipe) and balance the mass flows around the volume, you arrive at the stationary mass balance of an open system, also known as the continuity equation .

Differentiation between ideal and real fluids

Compressibility

One property of fluids is compressibility, which describes the change in density of a fluid when the pressure changes, and the property of the change in volume when the temperature changes. The compressibility of a fluid is the decision criterion with regard to a distinction between gas (compressible) and liquid (almost incompressible).

The assumption of an incompressible fluid is therefore an idealization of the physical behavior when the fluid opposes a change in volume with great resistance. The distinction between incompressible and compressible fluids also applies to fluid dynamics, because flow kinetics or forces can lead to a change in density in compressible fluids and thus affect the flow again.

The terms hydraulics (almost incompressible fluids such as liquids, mostly oil) and pneumatics (compressible fluids such as gases, mostly air) are understood to mean techniques that realize and control “force movements” with fluids. Furthermore, a distinction is made between ideal and real fluids.

Ideal (frictionless) fluids

Ideal fluids are incompressible, which means that the density of the fluid remains constant when the pressure changes. They are not viscous and therefore frictionless. All flowing fluid particles in a flow of an ideal fluid have an equally large and a rectified velocity. Flows of ideal fluids are called potential flows. Assuming a flow profile that is constant over the flow cross-section, a 1-dimensional flow can be assumed with the simplification. This is of great importance in practical application, since 3-dimensional flow equations can usually only be solved with the help of numerical methods (CFD).

Real fluids

With real fluids, a distinction must be made between laminar and turbulent flow. Every flow is laminar at a correspondingly low speed. If the speed is increased, the flow of a real fluid becomes unstable and becomes a turbulent flow. This is characterized by the fact that the magnitude and direction of the main speed are superimposed by irregular fluctuations. The precalculation of the flow around blunt bodies by ideal fluids provides a flow pattern in which the streamlines nestle against the contour and close again behind the body. If a real fluid is assumed, a similar picture emerges only in the front area. Streamlines come off around the thickest part of the body. This phenomenon is called detachment. The space between the back of the body and the rapidly flowing parts of the fluid fills with fluid that carries out less local and less right, eddy movements.

Thermal fluid dynamics formulas

Ideal gas equation

For an ideal gas, the ideal gas law applies to the density as a function of pressure and temperature.

{\ displaystyle \ rho = \ rho / (R_ {i} \ cdot T)}

with the specific gas constant. ${\ displaystyle R_ {i}}$

Kinematic viscosity

The kinematic viscosity of a fluid is the ratio of the dynamic viscosity to the density of the fluid. It is also known as the specific viscosity:

{\ displaystyle v = \ eta / \ rho.}

with the dynamic viscosity. ${\ displaystyle \ eta}$

Static pressure

The static pressure in a fluid at rest is defined as follows: It is the force that acts perpendicularly on a surface. This pressure is location-dependent and must therefore be defined for very small areas.

{\ displaystyle p = \ lim _ {\ triangle A \ to 0} \ {\ triangle F / \ triangle A}.}

Masses and volume flow

The volume flow is the volume of a fluid that flows through the cross section over a period of time . ${\ displaystyle {\ dot {V}}}$ ${\ displaystyle \ triangle V}$ ${\ displaystyle \ triangle t}$ ${\ displaystyle A_ {c}}$

{\ displaystyle {\ dot {V}} = \ triangle V / \ triangle t.}

If the cross-sectional area is known and the average flow velocity in the cross-section, the volume flow can also be calculated. ${\ displaystyle A_ {c}}$ ${\ displaystyle \ omega _ {m}}$ ${\ displaystyle {\ dot {V}}}$

{\ displaystyle {\ dot {V}} = \ omega _ {m} \ cdot A_ {c}.}

Just like the volume flow , the mass flow is defined. The mass of a fluid that flows through the cross-section per period of time . ${\ displaystyle {\ dot {V}}}$ ${\ displaystyle {\ dot {m}}}$ ${\ displaystyle \ triangle m}$ ${\ displaystyle \ triangle t}$ ${\ displaystyle A_ {c}}$

{\ displaystyle {\ dot {m}} = \ triangle m / \ triangle t.}

The mass flow that flows through a cross-section with a known cross-sectional area can be determined from the mean flow velocity and the density of the fluid in the cross-section. ${\ displaystyle {\ dot {m}}}$ ${\ displaystyle A_ {c}}$ ${\ displaystyle \ omega _ {m}}$ ${\ displaystyle \ rho}$

{\ displaystyle {\ dot {m}} = \ rho \ cdot {\ dot {V}} = \ rho \ cdot \ omega _ {m} \ cdot A_ {c}.}

Often (e.g. with laminar flow) the flow velocity in a flow cross-section is not constant, but depends on the location. Therefore, the mean value of the speed is determined to determine the volume and mass flow through a cross section . ${\ displaystyle \ omega}$ ${\ displaystyle \ omega _ {m}}$

{\ displaystyle \ omega _ {m} = 1 / A_ {c} \ int \ omega \, dA.}

Continuity equation of thermal fluid dynamics

{\ displaystyle {\ dot {m}} _ {1} = {\ dot {m}} _ {2}.}

{\ displaystyle \ omega _ {(} m, 1) \ cdot A _ {(} c, 1) \ cdot \ rho _ {1} = \ omega _ {(} m, 2) \ cdot A _ {(} c, 2) \ cdot \ rho _ {2}.}

Bernoulli's equation

Under steady flow can be (ignoring friction) a balance of pressures seen

{\ displaystyle \ rho _ {1} + \ rho _ {1} \ cdot (w ^ {2}) _ {1} / 2 + \ rho _ {1} \ cdot g \ cdot z_ {1} = \ rho _ {2} + \ rho _ {2} \ cdot (w ^ {2}) _ {2} / 2 + \ rho _ {2} \ cdot g \ cdot z_ {2} = const.}

Torricelli's law of discharge

When considering stationary outflow problems with the simplified assumption that it is an ideal fluid, one can usually calculate with the Bernoulli equation.

The simplest form of application is stationary outflow from an open-topped container of any shape with a constant liquid level. Liquid flows out of this container - through a relatively small opening in the lower area.

With such a container, the Bernoulli equation can be simplified as follows:

{\ displaystyle \ rho _ {1} = \ rho _ {2} = \ rho.}

{\ displaystyle \ rho _ {1} = \ rho _ {2} = \ rho.}

{\ displaystyle \ omega _ {1} \ ll \ omega _ {2} \ longrightarrow \ omega _ {2} ^ {2} - \ omega _ {1} ^ {2} \ approx \ omega _ {2} ^ { 2}.}

The Bernoulli equation then looks like this:

{\ displaystyle \ omega _ {2} ^ {2} / 2 + g \ cdot (h_ {2} -h_ {1}) = 0.}

If we now solve for the velocity, we get Torricelli's discharge law:

{\ displaystyle \ omega _ {2} = {\ sqrt {2 \ cdot g \ cdot h}}.}

Interfaces / areas of application

Accounting

The balance equation is a component of thermal fluid dynamics, as it requires both thermal and fluid dynamics. Balance equations are always structured in the same way, regardless of the quantity X, according to which the balance is calculated. Such quantities can be, for example, mass, energy, entropy or money. The first step in drawing up a balance sheet is to define the balance sheet size and the balance area. The monthly statement of a bank account, for example, is nothing more than a balance sheet of the amount of money over a period of one month. The balance area is the account. Transfers from other accounts and deposits increase the amount of money and withdrawals decrease it.

Transferred to thermodynamics, the balance space is the thermodynamic system. If a quantity of the accounting variable X is transported from the environment over the system boundary, the quantity X in the system increases. If it is discharged from the system through its boundary to the environment, the amount X in the system is reduced. In addition, sources or reductions in the system - if any - can increase or decrease the quantity X in the system. When balancing a partial mass in the system, for example the mass of the gas carbon dioxide (CO ₂ ), a reaction with formation of CO ₂ (e.g. combustion) from a source, a reaction with consumption of CO ₂ (e.g. a Photosynthesis) correspond to a reduction. The system is self-contained. This means that energy can neither be supplied nor withdrawn.

process technology

The process engineering as an engineering discipline explores different material amendment procedure, developed and realized this. It describes all technical processes in which a product is made from a raw material or substance that has changed in terms of type, properties and composition. Even in earlier history, man made use of process engineering, for example when converting ores into pure metals for forging weapons and utensils.

Fluid technology / flow technology

Fluid or flow technology deals with the movement of fluids, i.e. gases or liquids. The transfer of energy through currents plays a decisive role here. Hydraulics and pneumatics are the main technical areas in which fluid technology comes into play. In an ordinary car, several functions are usually based on hydraulic systems, such as:

Fuel and oil-filled units in drives
Vibration damping
Transmission of the braking force
Opening / closing of convertible roofs
Tilting trailer beds

Energy technology / energy conversions

One area of application of thermofluid dynamics can be found in energy technology. In the design and calculation of fluid systems that z. B. are used to generate electricity or heat, one must take into account the thermodynamic and the fluid dynamic portion of the fluid. Such systems are nowadays available in almost every household around the world and many people take it for granted. An application example is a heating system in a single family house. Since electrical heaters are used less and less and more and more such fluid systems (central heating) are used, knowledge of thermofluid dynamics is required when designing and planning these systems. Since in such a heating system water flows through pipes and this is also heated, the thermodynamics and fluid dynamics of this system must be taken into account.

Supply technology

Supply technology includes all technical measures that are used in rooms and buildings, but also in operating facilities and facilities that are not buildings, for energy supply, i.e. H. For example, heating and lighting, as well as the material supply (water, air) and the disposal of all waste products (sewage, garbage) are used. Supply technology includes all building types as well as systems. The term supply engineering is very broad and includes many sub-areas (e.g. heat, water supply), the main purpose of which is to make the building usable for residents. Thermofluid dynamics are used in many sub-areas of supply technology, such as heating, ventilation or air conditioning systems. Thermofluid dynamics helps, among other things, with the dimensioning of pipe and valve cross-sections or the design of conveyor systems. Here, flow calculations for gases and liquids are essential. Furthermore, heat pumps or CHPs, which are based on thermofluid-dynamic processes, are also used for heat supply technology. In the case of heat pumps, for example, technical work is used to absorb thermal energy from a low-temperature reservoir and transfer it as useful heat from a system to be heated at a higher temperature. The process used here is in principle the reverse of a thermal power process in which thermal energy is absorbed and converted into mechanical energy.