DE102014004846A1 - Low-temperature high-pressure thermoforming - Google Patents

Abstract

Low-temperature high-pressure thermal forming is a process for converting heat into mechanical work at low temperatures and high pressures. The conversion of heat into mechanical work takes place in all conventional power plants. The conversion mainly takes place in expansion machines (eg steam turbines or gas turbines). In a continuous operation, heat is supplied to the operating medium at high pressure in a cycle process. Part of this added heat is converted into mechanical work in expansion machines. The remainder of this added heat must be dissipated at lower temperature and lower pressure and is thus lost to operation. The cycle can be divided into 4 steps. Beginning with Step 1: Expansion of gaseous equipment from high pressure to lower pressure and lower temperature under operating power. (Ideal = adiabatic change of state) Step 2: Dissipation of heat at constant pressure until the operating medium is liquid. (Isobaric state change) Step 3: Compress the fluid to high pressure. Step 4: Heat up to initial state is reached. If the lower pressure of this cycle is still above the critical pressure of the operating medium, then the temperature profile in the heat dissipating step 2 and the temperature profile in the lower part of the heat receiving step 4 in opposite directions. The amount of heat from step 2 can be transferred to the lower part of step 4 and thus is not lost to the process. The upper part of the heat to be supplied in step 4 is taken out of an external heat reservoir. If now the operating temperatures are selected so that the highest temperature is still below the ambient temperature, the ambient heat can be used as heat reservoir. This is possible if the equipment used is a gas whose critical temperature is correspondingly far below the ambient temperature. For example, nitrogen, oxygen, air, etc. The individual components of an installation to this process are so well insulated against each other and against the outside that, except in the heat exchangers, no significant heat exchange takes place.

Description

Low-temperature high-pressure thermal forming is a process for converting heat into mechanical work in a thermodynamic cycle with heat exchangers, expansion machine and feed pump. The conversion happens at low temperatures and high pressures. The medium used for the cyclic process is a medium which is gaseous at normal ambient temperature (about 290 ° K). The cycle can be divided into 4 sub-processes. Initial state is a gas with high pressure and a temperature just below the ambient temperature.

First sub-process:

The gas is released from the high pressure to a lower pressure while working. (Adiabatic change of state). According to the work performance, the temperature will decrease.

Second sub-process:

In one or more heat exchangers, the operating medium is then deprived of heat, much so that it changes state of aggregation and becomes liquid. (Isobare change of state).

Third sub-process:

The liquid is then compressed by a pump to the high outlet pressure. Since its volume only slightly decreases in the increase in pressure of liquid, the resulting increase in temperature is low.

Fourth sub-process:

Next, at the high pressure in heat exchangers, the operating medium is reheated to the starting temperature. (Isobare change of state).

The circuit is closed and can start all over again.

The lower pressure of this cycle is chosen so that it is still above the critical pressure of the operating medium.

At a pressure above the critical pressure, the medium is gaseous when its temperature is above the critical temperature and liquid when its temperature is below the critical temperature. Both at the same time, as it can be below the critical values for pressures and temperatures, is not possible there.

At these high pressures of the temperature profile during cooling in the sub-process 2 and the lower part of the temperature profile during heating in the sub-process 4 is about the same in opposite directions. Accordingly, using an auxiliary circuit, the heat given off in the sub-process 2 can be returned to the main circuit in the sub-process 4.

There are many possibilities for the design of the aid cycle. However, it must be a self-contained cycle (or more).

The auxiliary circuit can be operated with any gas. Prerequisite: It must remain gaseous in the required temperature range and obey largely the gas laws. The pressures are also, within limits, freely selectable. They are only conditionally adapted to the main circuit.

In the main circuit 2 heat is dissipated during the sub-process. This heat is transferred in a heat exchanger to the medium in the auxiliary circuit. Thereafter, the gas in the auxiliary circuit is brought by compression to a higher temperature (adiabatic change of state). Now, the order to the compression work slightly increased amount of heat in another heat exchanger back to the main circuit under sub-process 4 is supplied. Subsequently, the gas is relieved in the auxiliary circuit back to the lower pressure at work. (Adiabatic change of state). The temperature drops to the initial value before heat absorption. The auxiliary circuit is hereby also closed.

The pressure ratio in the auxiliary circuit between the upper and the lower pressure must only be so great that a sufficiently large temperature difference between the two counter-rotating working materials in the heat exchangers arises.

If the individual components of these cycles are dimensioned accordingly, especially if the pressure ratio in the main circuit is chosen high enough, and if the machines do not have too poor efficiency, then the highest temperature in the auxiliary circuit will still be below the initial temperature in the main circuit.

However, this means that in the main circuit under sub-process 4 still more heat must be supplied. This additional heat is taken from a heat reservoir located outside the plant and fed via a further heat exchanger to the main circuit.

If the individual parts of the system are so well insulated against each other that - except in the Heat exchangers - no heat exchange takes place, then, according to the first law of thermodynamics, the externally supplied heat must be available as an excess of mechanical energy.

The first law of thermodynamics says the following: The sum of the heat supplied to a system from the outside and the work input from the outside is equal to the increase of the internal energy.

Mathematical: dU = dQ + dA. In this mean: U = internal energy, Q = supplied heat, A = supplied work. Work done by the system is negative in the equation.

Attention I: In some essays on this topic, the mechanical work delivered is considered positive and the submitted mechanical work negative. The equation is then: dU = dQ - dA.

In a self-contained circulatory system, the internal energy remains the same. That is, dU = 0, and thus, for this case, the above equation is dQ = -dA.

In words, the heat supplied to the system is equal to the mechanical work delivered by the system.

• 1. Die einzelnen Komponenten der Anlage (Turbinen, Kompressor, Pumpe und Wärmetauscher) sind gegeneinander und gegen außen vollkommen bzw. so gut wie möglich gegen Wärmeaustausch zu isolieren.
• 2. Die Komprimierung auf den hohen Anfangsdruck des Hauptkreislaufes erfolgt im flüssigen Zustand.
• 3. Der Hauptkreislauf verläuft oberhalb des kritischen Gasdruckes.

The most important features of the cycle are:

• 1. The individual components of the plant (turbines, compressor, pump and heat exchanger) are to be isolated against each other and against the outside completely or as well as possible against heat exchange.
• 2. The compression to the high initial pressure of the main circuit takes place in the liquid state.
• 3. The main circuit runs above the critical gas pressure.

In the realization of a plant for heat conversion into mechanical work, according to the criteria described above, many variants are possible.

The simplest example:

A set of machines consisting of three heat exchangers, two expansion engines (turbines), a compressor and a feed pump. The interaction of these individual components to a low-temperature high-pressure unit can be done as follows:
The plant is operated with air as a working medium.
Technical data of the air: molecular weight = 28.26, standard weight (at 0 ° C and 1 bar) = 1.2928 kg / m ³ , boiling point (at 1 bar) = 82 ° K, specific gravity of the liquid (at 1 bar) = 0.875 kg / dm ³ , critical temperature T _k = 132.3 ° K, critical pressure P _k = 37.7 bar, volume at the critical state values V _k = 3.23 dm ³ / kg,
Specific heat at constant pressure c _p (at 0 ° C) = 1.001 kJ / kg °,
Specific heat at constant volume c _v = 0.715 kJ / kg °, c _p / c _v = kappa = 1.4

• 1. Der Aufbau ist genau wie oben beschrieben. Siehe dazu Zeichnungen 1.
• 2. In den Wärmetauschern wird mit einer hohen Temperaturdifferenz von 10° zwischen dem Wärme abgebenden und dem Wärme aufnehmenden Medium gerechnet.
• 3. Bei den Maschinen (Turbinen, Kompressor und Pumpe) wird mit einem Wirkungsgrad von nur 80% gerechnet.
• 4. Der obere Druck im Hauptkreislauf wird mit 400 bar und der untere mit 50 bar festgelegt.
• 5. Der untere Druck im Hilfskreislauf wird so gewählt, dass das Gas bei der niedrigsten Temperatur noch gasförmig ist.
• 6. Es wird angenommen, dass – etwa der Realität entsprechend – die spezifische Wärme der Luft in der Nähe des Verflüssigungspunktes beim unteren Druck im Bereich von 15° den doppelten Wert hat. Ebenso wird für die Flüssigkeit der doppelte Wert angenommen.
• 7. Es wird angenommen, dass ein Wärmereservoir mit einer Temperatur von 290°K zur Verfügung steht.

The following assumptions are made:

• 1. The structure is exactly as described above. See drawings 1 ,
• 2. In the heat exchangers is calculated with a high temperature difference of 10 ° between the heat-emitting and the heat-absorbing medium.
• 3. The machines (turbines, compressor and pump) are expected to have an efficiency of only 80%.
• 4. The upper pressure in the main circuit is set at 400 bar and the lower one at 50 bar.
• 5. The lower pressure in the auxiliary circuit is chosen so that the gas is still gaseous at the lowest temperature.
• 6. It is believed that, as is the case in reality, the specific heat of the air near the point of liquefaction at the lower pressure in the range of 15 ° has twice the value. Likewise, twice the value is assumed for the liquid.
• 7. It is assumed that a heat reservoir with a temperature of 290 ° K is available.

The initial state of the air is a pressure of 400 bar and a temperature of 280 ° K. (Main circuit state 0)

For an adiabatic relaxation with work performance, the equation applies: T ₂ = T ₁ * (P ₂ / P ₁ ) ^{kappa-1 / kappa} = 280 * (50/400) ^{0.4 / 1.4} = 154.57 ° K

The mechanical work delivered would be dA = (T ₂ -T ₁ ) · c _v . The work is proportional to the temperature difference. The temperature difference is 280 - 154.57 = 125.43 °. With an efficiency of 0.8, only 80% of it is converted into mechanical work. The remainder remains as heat in the medium. The actual temperature difference is thus 125.43 · 0.8 = 100.34 °.

The temperature after the relaxation is thus 280 - 100.34 = 179.66 ° K (main circuit state 1).

For the air to become liquid, its temperature must fall below 132.3 ° K. Calculated with 129.66 ° K. (Main circuit state 2). So you have to Air to be cooled by 50 °. This corresponds to a dissipated amount of heat of 50 · 1.001 = 50.05 kJ / kg. Since we have assumed that in the lower part the specific heat c _{p has} twice the value, another 15 · 1.001 = 15.015 kJ / kg are added. Total 65,065 kJ / kg.

The compressibility of liquid air is set at 10% volume difference per 1000 bar pressure difference. With water it is about 4%. If the air is now compressed to 400 bar, the volume difference is 3.5%.

3.5% of 3.23 dm ³ is 0.113 dm ³ . The compression work is calculated to be (P ₁ + P ₂ ) / 2 · dV; P ₁ = 50 × 10 ⁵ N / m ² , P ₂ = 400 × 10 ⁵ N / m ² , dV = 0.113 × 10 ^-3 m ³ . A _compr. = (50 + 400) / 2 × 10 ⁵ × 0.113 × 10 ^-3 = 2542.5 Nm. At an efficiency of 80%, 2542.5 / 0.8 = 3178 Nm are to be used as compression work, which appears as heat in the medium. 3178 Nm = 3178 joules. At a specific heat of the liquid of 2.002 kJ / kg °, this results in a temperature increase of 1.58 °, to 129.66 + 1.58 = 131.24 ° K. (Main circuit state 3)

Auxiliary circuit:

The auxiliary circuit is dimensioned so that the same amount of heat as in the main circuit is required to produce a specific temperature difference.

In the low pressure range 65,065 kJ / kg must be recorded. This requires a temperature range of 65.065 / 1.001 = 65 °.

If in the heat exchanger a temperature difference of at least 10 ° should be, then the highest temperature in the heat receiving part of the auxiliary circuit is 179.66 - 10 = 169.66 ° k. (Auxiliary circuit state b). The lowest temperature is 65 ° less then 104.66 ° K. (Auxiliary circuit state a).

The lowest temperature in the heat-releasing part of the auxiliary circuit is 131.2 ° k + 10 ° = 141.2 ° k. (Auxiliary circuit state d).

From these values, the required pressure ratio between high pressure and low pressure in the auxiliary circuit can be calculated, as follows:
The operating medium is depressurized from high pressure at 141.2 ° K to low pressure at 104.66 ° K under operating performance. The temperature difference is 36.54 °. To account for the efficiency of 0.8, divide this value by 0.8. 36.54 / 0.8 = 45.68 °. As a lower temperature value, 141.2 - 45.68 = 95.52 ° k must be included in the calculation. If P _{1 is} assumed to be 10 bar, the following applies:
T ₁ = 141.2, T ₂ = 95.52, P ₁ = 10, P ₂ = P ₁ * (T ₂ / T ₁ ) ^{kappa / kappa-1} = 10 * (95.52 / 141.2) ^{1 , 4 / 0.4} = 2.54. The pressure ratio in the auxiliary circuit is therefore correctly dimensioned with 4/1.

After heat absorption, the pressure in the auxiliary circuit should be increased by a factor of four by compression. The equation applies here: T ₂ = T ₁ · (P ₂ / P ₁ ) ^{kappa-1 / kappa} . Index 1 here means value before the state change and index 2 value after the state change. T ₂ = 169.66 x 4 ^{0.4 / 1.4} = 252.11. The temperature difference is 82.45 °. This value has to be divided by 0.8 because of the efficiency of 80%, which results in a temperature difference of 103.06 °.

The highest temperature in the auxiliary circuit is therefore 169.66 + 103.06 = 272.72 ° K (auxiliary circuit state c).

In the upper heat exchanger, the medium of the auxiliary circuit is cooled to 141.2 ° K and transferred the heat to the main circuit. Its temperature rises accordingly to 262.72 ° K (main circuit state 4).

In order to reach the outlet temperature in the main circuit, heat must be supplied from the outside for a further increase in temperature of 17.28 °.

This value is very low, but: Most important: ER is greater than zero.

• 1. Erhöhung des Druckverhältnisses im Hauptkreislauf.
• 2. Verbesserung der Wirkungsgrade.
• 3. Verbesserung der Wärmetauscher mit kleinerer Temperaturdifferenz.
• 4. Eine kleine Verbesserung ist zu erreichen, wenn die Wärmeübergabe an den Hilfskreislauf mehrstufig ausgeführt wird. Siehe Zeichnungen 2.

For an improvement of the system there are some possibilities:

• 1. Increase of the pressure ratio in the main circuit.
• 2. Improvement of efficiencies.
• 3. Improvement of the heat exchanger with smaller temperature difference.
• 4. A small improvement can be achieved if the heat transfer to the auxiliary circuit is carried out in several stages. See drawings 2 ,

The different specific heats between the heat emitting lower part of the main circuit and the heat receiving auxiliary circuit are better taken into account in this case. Disadvantage: higher machine costs.

In the example above, a correction must be made. The fact that in the main circuit, in the lower temperature range, at lower pressure, the specific heat was assumed to be twice as high and was calculated in the other with constant specific heat, the energy balance is not quite right. For the sum of the added and removed energy = zero, the amount of energy to be supplied must be increased. This can only mean that the specific heat is higher in the high pressure part must be accepted. The amount of heat to be supplied from the outside will thus also increase.

In order for the energy balance to be correct, the specific heat in the high-pressure section of the main circuit must be assumed to be 1.102 kJ / kg °. The intermediate temperature state 4 is then 250.67 ° K. The heat to be supplied from the outside must produce a temperature increase of 29.33 °. This is 29.33 x 1.102 = 32.32 kJ / kg.

As is apparent from various physics documents, the specific heat actually increases at high pressures and high temperatures. Below are some values of specific heat c _p of air at 273 ° K and high pressures:
Pressure 20 bar c _p = 1,043 kJ / kg °, pressure 60 bar c _p = 1,113 kJ / kg °,
Pressure 100 bar c _p = 1.189 kJ / kg °, pressure 140 bar c _p = 1.25 kJ / kg °
Pressure 180 bar c _p = 1,296 kJ / kg °, pressure 220 bar c _p = 1,333 kJ / kg °

With appropriate choice of operating points, it is also possible to combine the main circuit and the auxiliary circuit into a single circuit. See drawings 3 ,

The operating medium in sub-process 1 is still relaxed far below the critical pressure. The temperature also drops below the critical value. The temperature must drop so far that a sufficiently large temperature difference is created in the heat exchanger W1 in order to liquefy the medium in countercurrent.

After the medium in heat exchanger 1 has absorbed the heat to be dissipated there for liquefaction, it is compressed to a pressure value just above the critical pressure. The temperature increases, but remains below the initial temperature. In the heat exchanger 2, the heat is now transferred to the high-pressure part, whereby the temperature decreases to a value just above the critical temperature. The remainder until liquefaction is removed in the heat exchanger 1. The liquid medium is supplied with a pump to the high-pressure part, where it absorbs heat in the heat exchanger 2. In the heat exchanger 3 heat is supplied from the outside to come back to the initial temperature.

With a large difference of the specific heat between the heat-emitting part and the heat-absorbing part, a multi-stage heat transfer can be useful here as well. However, this also means a larger machine cost.

When working in the main circuit with a medium whose critical temperature is close to the ambient temperature or higher (eg carbon dioxide with a critical temperature of T _k = 304 ° K), the main circuit runs at even higher temperatures. The direct heat transfer from the outside, via heat exchangers, to the main circuit is not possible. It is best in this case to supply the required additional heat via the auxiliary circuit to the process. A process setup could look like drawings 4 shown. The temperatures recorded arise when operating the main circuit with carbon dioxide. The upper pressure was used at 338 bar and the lower at 80 bar in the calculation. In the auxiliary circuit, a pressure ratio of 10/4 was calculated and air was assumed as the operating medium. The efficiency of the machines was also assumed to be only 80%, and in the heat exchangers was calculated with 10 ° temperature difference.

In this example too, in order to compensate for different specific heats, the transfer of heat from the main circuit to the auxiliary circuit can take place in several stages. The heat supply from the outside could be done in several stages. Both bring a small improvement in the overall balance, but also requires an increased machine cost.

The summary of main circuit and auxiliary circuit is also possible in a system operated with CO ₂ . See drawings 5 with single-stage heat transfer. drawings 6 shows the schematic structure with two-stage heat transfer in the lower pressure range, whereby the increased specific heat is considered in the vicinity of the liquefaction point. The heat supply from the outside was made in two stages. That brings a small improvement in the overall balance.

The operation of a heat conversion plant as described, with a resource whose critical temperature is close to the ambient temperature, may make sense if one wishes to avoid the difficulties of low temperatures.

In the above description, the term turbine has been used for the expansion machines. It could be that the conventional machines of this type are less suitable because of the extreme operating values.

A way out could be to build the expansion engine as a piston engine with diaphragm cylinders and controlled valves. The compressors and the pumps could work on this principle, with check valves would suffice.

The economics of a plant for the conversion of heat into mechanical work by this method depends very much on the quality of the machines used. A halving of the losses, ie efficiency 90% instead of the previously assumed 80%, would triple the usefulness, under otherwise identical conditions. An improvement of the heat exchanger to half the value of the required temperature difference provides a benefit improvement to about twice the value, all other things being equal.

An even greater benefit or operation at much lower temperatures of the available Wärmereservoire can be achieved if a second auxiliary circuit is added, which, like the main circuit, runs above the critical pressure and, as the main circuit, between liquid and gaseous changes ,

The dissipated in the main circuit to liquefy the equipment heat is transferred using the first, gaseous auxiliary circuit, to the high pressure part of the second auxiliary circuit.

The second auxiliary circuit performs mechanical work in its expansion stage (adiabatic change of state) whereby the temperature of the equipment decreases. The heat to be dissipated until the liquefaction is transferred to the lower part of the high pressure part of the main circuit. This transfer of heat is possible when the working fluid in the second auxiliary circuit has a critical temperature which is higher than the critical temperature in the main circuit and at least as much higher than the required temperature difference in the heat exchanger. Or, if the main circuit is still cooled by the required temperature difference lower than the critical temperature. The sketch (see drawings 7 ) shows the interaction of the individual components. The entered temperature values result when the main circuit is operated with air and the second auxiliary circuit with oxygen. For the first auxiliary circuit z. B. nitrogen can be used as resources. The pressure ratio was set in the main circuit and in the second auxiliary circuit with 400 bar to 50 bar. For the rest, the assumptions made in the first example were retained.

Conclusion:

The second law of thermodynamics states in a strict interpretation: Heat does not spontaneously pass from a low temperature body to a higher temperature body. The inferred, now generally accepted claim that it is impossible to design a machine that does nothing but extract heat from a heat reservoir and convert it into mechanical work is wrong.

Claims (1)

Low temperature high pressure heat forming is a process for converting heat into mechanical work, at low temperatures and high pressures. Characterized in that the amount of heat for conversion normal, existing at the site ambient heat, can be removed. This is made possible by the fact that in a thermodynamic cycle with heat exchangers, expansion machine and feed pump, the return of the gaseous operating medium in the liquid state at a pressure above the critical gas pressure. The individual plant components for such a process are to be isolated against each other and against the outside so well that -except in the heat exchangers-no substantial heat exchange takes place.

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