After another request to Yandex about refrigeration equipment, a link to an article from Habr about a vortex tube based on the Ranque-Hilsch effect appeared in the selection. At the same time, the most interesting thing was that it is not clear how it works, generating cold air from compressed air from a compressor.
https://habr.com/ru/companies/ruvds/articles/558356/ Ss Трубная Машина
The article caught my attention, and I decided to look into the Ranque-Hilsch effect from the standpoint of the data I had previously obtained on the outflow of a supersonic jet into the atmosphere from small holes in a receiver under a pressure of 2-6 atm. (see my article on Habr). https://habr.com/ru/articles/699564/
I first heard about vortex tubes and their strange work 20 years ago in 2003, but at that time the Internet was not yet so well developed to easily and quickly obtain the necessary information. All that has been learned is that the effect has been known since 1931, but has not yet been properly explained.
Nevertheless, the effect itself and devices built on it are used in industry for the purpose of local cooling of something, for example: cooling of cutting tools (cutters, drills, etc.) in cases where it is impossible to use a cutting fluid (coolant). And the cooling device itself is called the Ranque-Hilsch Vortex Tube.
Further in the text of the article, we will abbreviately call vortex tubes based on the Ranque-Hilsch effect VTR.
Fig.1. Schemes for the execution of VTR: 1 - an extremely ineffective scheme, created based on a “mythical” explanation of the principle of operation of the VTR. 2- The original version of the single-nozzle Hilsch vortex tube (the efficiency is also extremely low).
Fig.2. Schematic section of a modern VTR.
Fig.3. A modern serial vortex tube with a multi-entry (6 nozzles) volute for supplying tangential air flows. In the same way, water is supplied to Francis turbines at large hydroelectric power plants through a volute with a multi-blade guide vane. Also in this VTR, the hot pipe is shortened in length due to the conical expansion and installation of the “swirler” braking blades at the outlet end of the hot pipe.
Numerical assessment of the Ranque-Hilsch effect using the example of modern industrial high-tech equipment.
To understand what is happening in the HTR and to numerically evaluate the heat-cold effect obtained from the HTR, I turned to the data of the manufacturers of modern HTRs.
It turned out that such information is available from many VTR manufacturers and the numbers in them are almost the same.
I will give the most understandable tables from the websites of VTR sellers on the Russian market (see Fig. 4-5)
Fig.4. Table of performance characteristics of serial VTR (Vortex)
Fig.5. Table of temperature characteristics of the outgoing air flows from the VTR type 3215 (Vortex) at different ratios of air flow at the ends of the pipe: Green - dT decrease at the cold end, White - dT increase at the hot end depending on the air temperature in the receiver.
It is clear that the behavior of compressed air when entering the VTR must obey the laws of physics known to us.
So in this case, the equations of a gas during adiabatic expansion suit us.
During adiabatic expansion (compression) of air, the following relationship holds:
P1*V1^k= P2*V2^k
where k=1.4 for air is the adiabatic index.
Or P1/P2=(V2/V1)^k
Where does V2/V1= (P1/P2)^(1/k)
To expand the outflowing gas with a pressure of 9 atm to a pressure of 1 atm in the surrounding space, we obtain the ratio of the temperatures of the initial and final states from the Mendeleev-Cliperon equation:
Where n is the number of moles of gas.
Knowing that in the final and initial states the number of moles in the process is unchanged, then in the future this indicator in the relationship is reduced.
From here we can find the maximum cooling temperature of compressed air from an excess pressure of 8 bar (9 bar absolute), to an ambient pressure of 1 bar (absolute).
T2/T1=R2*V2/(R1*V1)= (R2/R1)*(P1/P2)^(1/k)
As a result of substituting the volume values for adiabatic expansion into the equation, we obtain:
T2/T1=P2*V2/(P1*V1)= (1/9)*(9/1)^(1/1,4)=0.534
That is, if the initial temperature is taken as T1=293K (+20C), then we get the final temperature:
T2=0.534*293=156K (or T2s=156-273= -116S)
We compare with the data from the VTR table (see Fig. 5) for a pressure of 8 bar and 20% output, where a total of dT = 71K is indicated
Thus, we can calculate the efficiency of cooling in a vortex tube:
That is, for 100 W of the resulting cold, up to 1 kW of electricity is consumed with an efficiency of 10% of the coolest air stream!!!
Considering that the refrigeration coefficient of the compressor-condenser cycle with freon in a regular home air conditioner is as much as Kx = 3, that is, 300% (THREE HUNDRED percent), this is for household split air conditioners with a freon boiling point of +6C.
For freezers at a freon boiling point of -18C, the refrigeration coefficient drops significantly to Kx=2.
It is also necessary to add to the calculation of the efficiency of the VTR process the efficiency of the air compressor, which at high pressures can be about 40%.
Such a low efficiency is associated with strong heating of the air during adiabatic compression by a factor of 9, which results in heating up to +435C at a pressure of 22 bar (as in a diesel engine) followed by cooling to +20C at P1=9 bar in the receiver.
As a result, it is possible to obtain an interesting comparative assessment of the effectiveness of VTR.
Taking into account the compressor efficiency of 40%, we obtain comparative energy efficiency in relation to freon condensation coolers with Kx = 2 (for freezers up to -18C):
That is, the freon condenser cycle is 28-48 times more efficient in terms of energy consumption per unit of cold than the HTR from a compressor.
Here is a real explanation of why vortex tubes are used only in factories, where the extremely low energy efficiency of a vortex tube is outweighed by the simplicity, compactness and reliability of the local refrigeration device.
For the purposes of experimental observations, I wanted to buy myself the smallest VTR from a dealer in Moscow. But when I found out that even the smallest Canadian-made HTR with a cold power of 42 W costs as much as 45 thousand. rub, it shocked me.
A tiny piece of iron (fitting in the palm of your hand) without any drive mechanisms costs as much as a hefty household refrigerator with its own compressor!
For this money, you could buy an ordinary household freezer (down to -18C) and drive compressed air through it to a regular nozzle, while a freezer costing 30 thousand rubles would produce cold with a power of 80 W (productivity 20 kg of ice per day) while consuming would be about 40W.
That is, performing air cooling of something by cooling compressed air in the chamber of a freon freezer would be 3 times cheaper than using high-pressure air cooler from high-pressure compressed air.
In this case, for cooling with air from the freezer, you can use low-pressure compressed air of 0.5-1 bar, which is energetically cheaper to obtain than with a pressure of 6-8 bar.
True, on Aliexpress there is something similar to VTR, but entirely made of aluminum, it costs only 4 thousand rubles. (see Fig. 6), that is, 10 times cheaper than Canadian VTR from Vortex. It turns out that the Chinese actually produce simple metal gizmos at quite reasonable prices, making their use in industry a much more rational solution.
Fig. 6 Appearance and price of a Chinese-made VTR from Aliexpress, which turns out to be 10 times cheaper than its North American-made counterpart.
Checking heat separation in HTR using scientific and academic data
Data from equipment dealers cannot be unconditionally trusted, and therefore it is worth looking for alternative data from academic sources.
So, on the Internet, I came across a course of lectures on the “Theory of Vortexes” [1].
It contained extremely interesting theoretical-calculation dependencies and experimental graphs of the operation of high-tech equipment in various modes (see Fig. 7-8)
Fig.7. A page from a course of lectures on “Theory of Vortexes” [1].
Fig.8 Graph from a course of lectures on vortex tubes [1]. An extremely interesting graph of a complex indicator of the product of % of the cold fraction (mu) by dT of cold air.
Applying the dependencies from the lecture course to the data from the Vortex table (P = 5 bar at 80% cold fraction) we obtain:
It seems that traders hardly deceive consumers, giving completely verifiable information: 21/19 = 1.08 or 8% of the difference.
At the same time, checking similar data from the graph (see Fig. 8) from a recent PhD thesis [2] gives a much larger gap in values:
The energy balance for thermally insulated HTR does not converge: that is, 16/12 = 1.33 or 33% error.
This means that these scientists somewhere have some serious errors in the experiment with the conditions of the experiment or with the quality of the measurement.
Fig.9. Graph of air temperatures from the VTR at various compressed air pressures Po and a variable parameter of the cold fraction fraction by oh. Fragment from the dissertation [2].
Physics of the cooling process in a Ranque-Hilsch vortex tube
As is known, gas must do work for adiabatic cooling.
What kind of work does air do when cooling in a VTR?
Here it is necessary to move from air in general to considering the behavior of a single molecule with a field of universal repulsion around it.
This model of gas structure is called “Static Theory of Gas” (hereinafter STG).
It is by using the STG that it is possible to consider the behavior of an individual molecule in the process of vortex motion inside the VTR.
So, according to STG, in order to cool an individual molecule, it needs to expand its volume of individual emptiness around itself, that is, increase the specific molecular volume.
The air flow rotates inside the VTR, creating excess pressure on the pipe walls due to centripetal acceleration from individual layers of air.
A detailed description of the effect of pressure differences along and across the flow in curvilinear fast-moving flows is presented in my previous article (see link)
https://habr.com/ru/articles/759094/
Thus, the centripetal pressure in the vortex decreases from the periphery to the center of the tube.
That is, an individual molecule, when moving from the outer edge of the tube to the axis of the vortex, will pass through layers of air with increasingly less static pressure. With such an ascent along the pressure gradient, the observed volume of gas will increase, and the own molar volume of this molecule will also expand.
It is precisely this expansion of the molecular volume when the molecule moves from the edge of the vortex to the center that can lead to cooling of the flow on the VTR axis.
In this case, the tangential rotation speed on the VTR axis will be zero at a pressure close to atmospheric.
Thus, the pressure from the center to the periphery will gradually increase with a proportional increase in air density from 1 bar to Pmax.
With a large pressure gradient along the radius of the VTR, an individual air molecule will tend to rise towards the axis of the VTR pipe, while expanding in its individual volume. This is similar to how bubbles of air rise from the depths of dense water, swelling as they rise from the depths.
With such an ascent against centripetal acceleration, the molecule will perform the work of adiabatic expansion by pushing away surrounding molecules, while reducing its temperature.
It is precisely this line of thought that could lead to the creation of a “mythical” interpretation of the Ranque-Hilsch effect.
The problem with this “mythical” explanation is the fact that before it adiabatically expanded and cooled while “ascending” along the radius of the vortex in the VTR, the same gas was first also adiabatically compressed by centripetal acceleration to exactly the same additional pressure and heated at the same additional temperature, which will be reset during ascent.
That is, the total effect of these two successive adiabatic processes of compression and expansion to the original parameters will be equal to pure zero.
Acceleration of the vortex towards the center.
Among the “mythical” versions of the interpretation of the Ranque-Hilsch effect, there is a model where the separation of molecules by speed and temperature is carried out on certain microvortices that arise inside the general vortex in the VTR pipe.
So, as the molecule ascends along the pressure gradient towards the axis, it still maintains a constant speed in the tangential direction.
A decrease in the radius of curvature at a constant tangential velocity leads to an increase in the angular velocity. This phenomenon is known as Coriolis acceleration.
This is where the idea for the second version of the “mythical” version of the explanation of the operating principle of the VTR arises.
Thus, with an increase in angular velocities towards the center of the VTR, “mythologists” declare the occurrence of intense sliding of layers relative to each other on circular concentric nested trajectories. True, the “mythologists” do not explain why the neighboring layers suddenly slowed down relative to each other?
However, with such braking with sliding, local vortices may arise when uneven layers are broken into fragments. The microvortices themselves will seem to roll along the underlying layers.
With such rotation, the microvortex will help the molecules to float up behind itself and press the layers to the periphery of the pipe in front of it, as if acting as a virtual expander turbine.
Molecules pressed against the walls of the pipe receive an additional impulse from the vortex, that is, they will be forced to heat up more when extinguishing at a higher speed than when leaving the nozzle. That is, the heating will be higher than up to the initial supply temperature of +20C.
This is how a retarded layer of superheated air begins to form on the inner wall of the “hot pipe”.
On the axis of the pipe there will be its own central vortex, rotating in engagement with the microvortices of the intermediate layer.
That is, the layers of air inside the pipe will rotate in the same direction as the cold air vortex on the axis of the pipe, but between them there will be a spacer of microvortices of opposite rotation, similar to rollers inside a rolling bearing.
It seems that it was precisely this line of thought about what was happening inside the VTR that led to the creation of a “mythological” explanation of the operation of the VTR as a turbine made of air vortices.
True, we have already refuted the basic version of gas cooling from “ascent” along the pressure gradient in a vortex a little higher. So the stated mechanism of molecular separation on microvortices did not add anything new to the “mythical” model.
Nonequilibrium structure of the jet according to the STG.
But the operation of VTR can also be explained using other physical scenarios.
So, instead of the “Kinetic Theory of Gases” (KTG), you can use the model of the “Static Theory of Gases” (STG), where in a gaseous environment individual molecules are surrounded by central repulsive forces from neighboring molecules.
That is, according to the STG, molecules in a stationary gas hang motionless in space, and do not rush through space like crazy billiard balls with the speed of a gun bullet.
At the entrance to the VTR pipe, the air stream from the nozzle, according to the STG, has a nonequilibrium structure, where the pressure across the jet is greater than along the axis.
Along the axis, the pressure is zero (all the potential energy of the pressure has been converted into the kinetic energy of the velocity pressure), and across the jet the pressure will be the value according to the adiabatic expansion of air with a drop in absolute temperature by one third, that is, from 300K (+27 C) to 200K (-73C ) .
dT=100K turns into the kinetic energy of the jet, which results in a speed of air molecules of about 470 m/s, that is, 1.4 times greater than the speed of a sound wave in air.
An article is devoted to this issue, which also describes an experiment on instrumental measurement of the speed of a stream of air from a receiver under an excess pressure of 2-7 bar through a short small hole (Ф1.5mm).
https://habr.com/ru/articles/699564/
That is, immediately after leaving the nozzle, the air already has an extremely low temperature of minus 73C.
It is for this reason that it is advantageous to select a cold jet in the immediate vicinity of the air supply nozzles in the VTR. In this case, the metal body of the nozzle and the side wall with a hole on the axis are used to remove cold from the “ice” jet from the nozzle.
That is, the “ice” jet from the nozzles cools the end wall of the VTR with a hole for the “cold” air to escape.
It is this cooling of the side wall that determines the entire effect of cooling part of the air in the VTR itself.
It turns out that the bell at the cold end of the VTR is not a Laval nozzle at all, as it might seem, but a deceleration zone for an intensely rotating air jet. In this case, intensive heat transfer occurs from the air that is braking and warming up during braking to the cold massive wall of the cone, cooled by the ice jet from the nozzles.
In fact, this thermal energy exchange through the metal wall could be limited by diverting the most heated and still uninhibited air flows to the distant “hot outlet” of the VTR pipe.
But it will not be possible to simply pull a cold stream of air out of the vortex, since the stream is still accelerated to a very high speed and is pressed by centripetal pressure to the hot layers near the wall of the “hot” VTR pipe.
Calculation of air flow velocities in VTR
We can assume that the speed of the molecules after leaving the nozzle will be 470 m/s. It is this speed of an individual molecule that will need to be suppressed when working against centripetal acceleration as it ascends to the axis of the pipe.
Considering the ratio of the areas of the inlet nozzles and outlet holes as 1:4 according to the data from the textbook (see table Fig. 10. line 1.), then the air speeds (at constant air density) will be with a mirror ratio of 4:1 = 470:118
That is, from the cold hole of the VTR (before braking in the diffuser cone), air will fly out at a speed of 118 m/s, and the kinetic energy of the cold jet (before braking in the conical diffuser) will be 1/16 of the original (or 7%). True, at the same time, the central “cold” jet on the VTR axis still rotates at a tangential speed of the same 470 m/s, because there was simply nothing for the air in the empty pipe to slow down against.
Fig. 10. Table of VTR sizes of various models tested in experiments and showing good efficiency.
Heating by 7% of the theoretical dT = 100C will increase the jet temperature by about 7C.
These 7C will need to be added to the existing dT = 100C from the braking of the jet from the initial speed from the vortex generator nozzles.
Speed 118m/s corresponds to velocity pressure
It is precisely this excess pressure of 10 kPa = 0.1 atm that should be near the axial zone inside the VTR in order to push the vortex along the axis outward.
It is precisely to create this backing pressure inside the VTR that a flow control screw is needed at the end of the “hot pipe” of the VTR.
Based on this model of the operation of the VTR, it turns out that in order to increase the efficiency of the VTR due to heat transfer through the nozzle wall in the “gas-metal-gas” process, it is necessary to ensure thermal insulation of the still warm (+27C) vortex generator from the cold wall (-73C) of the “cold” one. end of the VTR.
It is also necessary to exclude the flow of heat from the “hot pipe” to the vortex generator, which is also achieved by using heat-insulating gaskets at the junction of the pipe and the vortex generator.
The insertion of thin polymer “spacer washers” into a serial HTR will allow one to correctly compare and evaluate their effect on the operation of well-studied serial HTRs.
It is precisely this solution with polymer inserts that can be seen in the VTR from the Vortex company, which uses plastic vortex generators with a long polymer insert in the “hot pipe”, which reduces the heat flow along the steel wall from the hot zone to the cold one (see Fig. 11).
Also, the photo of the vortex generator liner shows that the flat side wall of the “cold” end of the VTR is much larger than the inner diameter of the outlet tube-liner in the “hot pipe”.
In this way, a larger area of contact of the cold jet from the nozzles with the wall of the “cold outlet cone” is achieved, which gives maximum cold heat transfer towards the outlet “cold” end of the VTR.
Also, by replacing one plastic vortex generator with another (with a different internal size), as well as installing a corresponding replaceable “cold cone bell”, you can obtain a wide range of VTR in terms of power and air flow within a single external durable housing.
Fig. 11. External view of the durable steel casing of the VTR and plastic liners-vortex generators of various standard sizes according to air flow (the different radius of the “hot pipe” is visible).
Features of the design and conflict-free operation of the vortex generator as part of the VTR
When turning, the flow of gas (water) is forced to twist into a spiral bundle (as was already found out in the previous article)
https://habr.com/ru/articles/759094/
If there is only one supply nozzle in the VTR, then the spiral flow will meet with itself, describing a full circle inside the “hot pipe” of the VTR.
When a vortex bundle collides with itself, the edges of the vortex will come into contact with high counter tangential velocities, which will lead to an immediate explosion of the jets with the formation of a retarded cloud of air over the entire cross-section of the hot VTR pipe.
To avoid such an explosive scenario, it is necessary to feed two jets with opposite directions of flow turbulence into the VTR.
Then, when two oppositely rotating flows meet on their lateral surfaces, the tangential velocities will be equally directed at the points of contact. With such coordinated contact, the flows will continue to wind parallel spirals along the “hot” VTR pipe without explosive destruction of their structures.
This is exactly how the VTR is modified (in line 2) relative to the original Hilsch odonospeller tube (line 1, see Fig. 10).
It is also possible to increase the number of nozzles by adding new pairs, that is, the number of nozzles must be even (2-4-6-8...etc.). In this case, the direction of the smoke in adjacent nozzles should alternate: right-left-right-left, etc.
Modern serial VTRs are produced with standard multi-pass guide vanes with an even number of nozzles and factory profiling of the relative direction of rotation of the flow in adjacent jets (see Fig. 10)
Pressure difference between the axis and the inner surface of the VTR
Let us estimate the centripetal acceleration and the magnitude of the pressure drop from the axis to the edge of the VTR pipe.
To estimate the speed of rotation of the vortex in the VTR, we need to know the speed of air outflow from the nozzle apparatus of the VTR.
From a previously conducted experiment on measuring the thrust of a thin jet from a receiver, we found that for air at +20C the air outflow speed will be about 470 m/s (1.42 times the speed of sound at +20C)
See article https://habr.com/ru/articles/699564/
True, according to the STG, exactly a third of the internal energy of the gas is spent in one of 3 directions to accelerate air to supersonic V = 1.42 * Va = 470 m/s at T = 300 K (+ 27 C), while the temperature of the air in the stream decreases in the same way by 33% or by dT=100K.
This is slightly less than the previously calculated dT = 137K according to generally accepted CTG.
Thus, the effectiveness of the VTR cycle according to HTG will be higher by 137/100 = 1.37 times (or 30-40%) than according to CTG.
Nevertheless, to simulate the operation of the high-speed jet, it is enough for us to cool the supersonic jet “only” by dT = 100K.
Let's take the dimensions of the VTR from the table (see Fig. 10), where our modern VTR most closely corresponds to the multi-nozzle design from the bottom line of paragraph 6.
So the initial data for the calculation will be the following geometric parameters:
D1=6.1 mm - diameter of the “hot” VTR pipe
D2=1.75 mm - diameter of the “cold” hole at the end of the VTR
S=0.8 mm.sq. - nozzle inlet area.
The volumetric air flow will be
G=470*0.8/10^6=0.000377 m3/s or 0.377l/s=22.6l/min
It turns out that the experimental HTR is almost 3 times less productive than the smallest modern serial HTR with an air flow of 57 l/min.
Such miniaturization is quite logical for scientific installations, where they save on the power of laboratory equipment.
The centripetal acceleration at the periphery of the pipe will be:
A=V^2/(0.5*D1)=470^2/(0.5*0.0061)=72,426,229 m/s^2 or 7.38 million g
Overheating of air in a “hot” pipe
When a vortex flow of cold air passes through a “hot pipe”, heat inevitably transfers through the wall of the tube from the warm outside room to the cold air environment inside the HTR.
Thus, the still uninhibited cold stream can be greatly heated by the external heat of the room. As a result, when the already warm air stream at the end of the “hot pipe” is decelerated, the air will heat up to a temperature higher than the initial temperature of +27C at the entrance to the VTR.
So, the excessive overheating of the air in the “hot pipe” in the VTR is not associated with the mysterious separation of hot and cold air molecules in the vortex, but with the banal flow of heat through the wall from hot to cold, including when heated by ambient heat from the room of a still cold stream into “hot pipe” VTR.
Various crazy “innovation-breakthrough” projects are built on this misunderstanding of the essence of the VTR operation, where they try to add expensive turbines to the ends of the VTR (see Fig. 12), while forgetting about the already extremely low energy efficiency of the VTR.
Fig. 12. An example of the crazy idea of “increasing the efficiency of a high-speed turbine by installing additional turbines at its ends”
Calculation of centripetal pressure in the VTR.
Based on the given dimensions of the VTR, the centripetal pressure from the vortex on the wall of the “hot pipe” can be calculated.
So, with an outflow speed of 470 m/s and an air density of about q = 1.5 kg/m3 (cooling to -70 C and excess pressure of 0.1 bar) at a layer thickness of dh = 2 mm (distance from the edge of the “cold” hole to the wall of the “hot” pipe ) and pipe diameter R=3mm we obtain the pressure
P= q*dh*V^2*/R =1.5*0.002*470^2/0.003=220900 Pa or 221 kPa =2.2 bar
That is, the excess centripetal pressure along the height of the thin vortex layer rises by more than 2 bar on the pipe wall and decreases along the height of the layer to zero at the cut of the hole in the “cold” wall.
With such excess pressure, the vortex layer of air from the nozzles in the VTR is compressed transversely, becoming 3 times thinner and denser.
True, this will have little effect on the pressure, since the increase in air density will be compensated in the calculation by a decrease in the thickness of the layer, and we have already used the maximum radius for the diameter of the “hot” pipe.
Ultimately, the accuracy of calculating the pressure increase from centripetal pressure will not in any way affect the final temperature of the gas at the outlet of the VTR, since the adiabatic centripetal compression at the walls will be fully compensated by the equally rapid adiabatic expansion when the gas “floats” to the axis of the VTR (see the chapter on "mythical" explanations above).
Although, in this case, the very fact of increasing the pressure and temperature of the vortex at the exit of the nozzles at the “cold” wall of the VTR can affect the optimization of the design of the heat-removing sections of the “cold” end of the VTR.
It is also possible that the centripetal compression of the jet in the vortex completely compensates for the temperature drop when the air jet accelerates to supersonic speed from the nozzle.
By the same principle, turning a flow of any radius in a pipe ultimately creates the same thrust impulse from the jet as a whole from the turn.
It is this balance of curvature and degree of compression of the jet across the flow that explains that until now a cold jet from the nozzle at the outer wall in the cyclone has not been detected, but in the center of the vortex, the air that “floated up” along the gradient expanded many times and cooled to the calculated low temperatures. At the same time, it also became possible to fix the temperature of the still supersonic jet on the vortex axis at a near-zero translational flow velocity.
Ultimately, in a fast adiabatic process, the path from the initial state to the final state is not important, but only the parameters of these two extreme states are important.
Therefore, in the center of the rotating vortex there must really be an extremely low temperature. But it’s extremely difficult to use it to cool anything.
Removal of cold from the rarefied, unstopped central vortex.
In a standard VTR, the speed along the pipe axis is only about 118 m/s. While the peripheral speed in the vortex remains supersonic 470 m/s.
Question: How to use the cold air in the central vortex if the air heats up again during braking?
When braking in a conical bell, the high-speed vortex is no longer pressed from below by high-speed passing layers of air, and therefore can expand following the diverging walls and is decelerated against them.
It is with such close contact of the decelerating and heating gas that the real process of cooling the air against the cooled metal of the bell begins.
At the same time, the uninhibited cooling air (which previously gave up its cold to the metal of the bell and therefore warmed up) went into the “hot” VTR pipe to be discharged at the far hot end of the hot pipe.
Only this amount of cold from the air escaping into the warm exhaust is useful cold generated in the VTR.
Realistic version of VTR operation without “microvortexes”
Heat transfer of cold from a supersonic jet to the socket of the “cold pipe”.
According to STG, compressed air (1.4 atm or more) from a small-diameter nozzle escapes into the atmosphere at a speed greater than sound, while losing 33% of its temperature to convert heat into kinetic energy.
As a result, when the VTR is operating in a room at T = 300K (+30C), a stream of air with a temperature Tx = 200K (minus 70C) comes into contact with the cold end of the pipe, which makes it possible to greatly cool the metal wall and the socket of the “cold” end of the VTR.
The power of VTR in air at dT=30C and the flow rate in the “cold” hole V=118v/c is
It is interesting that with a translational speed Vx = 118 m/s in a cold hole, at the same time in a “hot pipe” the speed will be only about Vg = 7 m/s, that is, 16 times less. So 4 times less consumption for a “hot” discharge 80/20=4 is multiplied by 4 times the cross-sectional area of the “hot pipe”, a total of 4*4=16.
For the accepted standard size of the VTR, it is possible to calculate the approximate heat flow through the metal when the air stream is heated at dT = 30C.
So the area of the annular wall is
S=(D1^2-D2^2) *3.14/4= (6^2-2^2) *3.14/4=25mm.sq
To calculate heat transfer through a wall, it is necessary to know the thermal conductivity characteristics of metals (see Fig. 13).
Fig. 13. Table of thermal conductivity coefficients for different metals.
Let us also take the average thermal pressure over the area of the heat transfer ring dT = 30C. That is, we obtain a total taken into account difference of 30+30=60С, which is less than the value of the total supercooling of the supersonic jet by dT=100С.
The difference of 100-60=40С will be released into unproductive leaks.
With a thermal conductivity of steel of 45 W/S*m and a metal wall thickness of 5 mm (0.005 m), a heat flow will be transferred through a ring area of 25 mm2 (0.000025 m2) to the “cold socket”:
Qst = 6.75 W - this is two times less than the design power of 13 W required for VTR.
Therefore, the steel “cold bell” of the VTR in its thermal conductivity does not correspond to the necessary power parameters of the VTR.
To ensure the required heat transfer power of the cold end of the HTR, it is necessary to use a material with greater thermal conductivity than steel, namely aluminum or copper.
Aluminum has a thermal conductivity of 209 W/S*m, which is 4 times higher than that of steel.
Copper has a thermal conductivity of 389 W/S*m, which is 8 times higher than that of steel.
Aluminum is cheaper than copper, so we use an aluminum socket for the cold end of the VTR.
Thus, for HTP it is necessary to make a conical socket of a “cold pipe” from aluminum, since the thermal conductivity of steel is insufficient for the calculated heat flow.
I note that in modern VTR the cold end sockets are made of aluminum.
At the same time, what happens in the “hot” VTR pipe no longer affects the cooling capacity of the VTR.
In addition, using VTR for heating is a completely pointless exercise, since electric heaters are tens of times more efficient and cheaper than VTR from a compressor.
Installations for non-turbine separation of heat flows.
In addition to VTR, there are other technical systems for cooling gases when they come into contact with a supersonic jet cooled during acceleration.
In the installation diagrams below, the presence of a supersonic cold flow is declared explicitly (see Fig. 14-16), while the presence of a supersonic flow from the nozzles inside the HTR is not recognized (or not advertised) at all.
Fig. 14 Description of the installation for transferring heat from a warm subsonic to a cold supersonic flow through a gas-tight solid heat-conducting wall. Drawing from the dissertation[2].
Rice. 15. Installation for cooling air leaking through a solid heat-conducting wall from a cooled supersonic flow. Drawing from the dissertation[2]. The leakage of inhibited gas through micro-holes in the side wall of a supersonic nozzle is an ultra-miniature equivalent of the operation of a high-pressure jet (in a realistic physical version).
Fig. 16. Description of an installation for transferring heat from a warm subsonic to a cold supersonic flow through a solid heat-conducting wall. Fragment of a page from the dissertation[2]. The situation is equivalent to the heating of a supersonic flow in the “hot pipe” of the VTR.
An alternative VTR design with separation of the flow of cooled air to the consumer and the supersonic flow (cold working fluid from the compressor).
By combining individual design solutions of VTP and the above-discussed supersonic heat separation installations with Laval nozzles, one can try to create a new synthetic design that will combine the advantages of these systems, partially reducing the impact of their disadvantages.
Let's call the new design this: Vortex tube with separate circuits (VTRC)
As part of the HTRK, an air flow with room temperature and low excess pressure (sufficient to overcome the resistance of the HTRK path itself and the pipe to the consumer after it) will be used as a “cold” flow.
High pressure compressed air from the compressor (5-8 bar) will be used as a source of cold.
Air from different circuits does not mix, contacting only through a thin heat-conducting wall.
Outwardly, this is similar to a supersonic heat separator on a Laval nozzle (Fig. 14), only instead of a single Laval nozzle with a single hole of the central critical section, a multi-nozzle vortex generator will be used, launching supersonic jets across the nozzle exactly like the vortex generator in the VTR (see Fig. 17) .
To obtain the same amount of cold, the VTRK will require 3 times less compressed air from the compressor than was needed in a conventional VTR.
Such large savings arise because in a conventional HTR, the theoretical maximum heat transfer was achieved in the region of 60-80% of the cold fraction, and only less than 20-40% of the high-pressure air flow was left for thermal discharge.
In the proposed VTRC, the entire compressed air consumption will be limited to this 20-40%, which goes to the “hot” discharge.
An additional increase in the efficiency of the VTR will be due to the fact that heat transfer through a thin copper plate of increased area occurs more intensely than through the elongated part of the aluminum brake bell of the “cold” end of the classic VTR.
Separately, it is necessary to take into account the flow of high-pressure compressed air directed into the ejection jet, which encourages pumping of outside air past the copper heat exchanger.
Since the speed of the cooled air on the heat exchanger is relatively low (10-20 m/s), that is, 20-50 times lower than the supersonic speed of the injection jet (470 m/s), the mixing of flows during ejection will occur in the same ratios from 1:20 until 1:50. In this case, the additional air consumption from the compressor for ejection will be only 6-15% of the air consumption in the supersonic circuit of the VTRC.
Fig. 17. Schematic section of a vortex “tube” with separated circuits of cooled and heated air (VTRC). The word “tube” is in quotation marks, since the design of the VTRC is more like a disk than a tube.
VTRC is presented in two versions:
A-Heat exchanger in the form of a flat disk,
B - heat exchanger in the form of a disk with a tube and countercurrent heat exchange in the coaxial pipe of the air duct.
In both options, the main body does not change. Only the copper heat exchangers are changed and a plug is added to the vortex generator (in option B).
The purple, green and yellow parts are molded plastic, the red disk is a hard plastic sheet with holes, the blue disk (option A) and the blue disk with a tube (option B) are a heat exchanger made of a thin copper sheet 1-2mm thick.
The colored rings in the side views correspond to the projections of the hidden ring receivers of the corresponding halves of the VTRC housing. The use of plastic housings (with a thermal conductivity of 0.15-0.4 W/m*C) can dramatically reduce unproductive cold leaks to the outside, since the thermal conductivity of plastic is 1000-2500 times lower than that of copper. In addition, a single plastic case with a complex shape is much easier to print on a 3D printer than to turn it out of metal.
The supersonic duct of the high-tech rocket engine is somewhat similar to a flattened and inverted multi-nozzle rocket engine with a central body (see Fig. 18-19). Only in the VTRK the external supersonic nozzle needs to be heated by outside air (the supersonic flow is “cold”), while in the liquid rocket engine the gases in the nozzle are hot (1800C), and the outer jacket of the nozzle with cryogenic fuel cools the nozzle to protect it from melting. By the way, the nozzles of Russian liquid-propellant rocket engines are also made of copper in order to better remove heat through the wall to the cryogenic fuel-cooler.
Fig. 18. Variants of liquid propellant rocket engines with a central body and a single annular combustion chamber.
Fig. 19. A variant of the liquid-propellant rocket engine with a central body and individual combustion chambers arranged in a circle with individual Laval nozzles.
1. As a result of the analysis of the operation options of the VTR, two alternative models were obtained, namely:
a) Thermal-mechanical model (heat exchange cooling of a warm air stream through a metal wall from a cold stream).
b) “Mythological” vortex model (mysterious process of cooling the central jet from the rotation of hot air).
2. Thermal-mechanical option (version A) can easily be calculated within the boundaries of the known laws of physics, and the technical solutions are optimized in terms of execution.
3. At the present time in the real HTP model, the default figure is the extremely low temperature of the supersonic air jet from the nozzle (down to minus 70C), which the usual ideal gas flow model does not allow to obtain. Whereas according to STG, it is quite logical that a supersonic jet speed is obtained when 33% of the internal energy of the gas is converted into kinetic energy in one direction, while simultaneously reducing the absolute temperature of the gas by 33% (from 300K to 200K for compressed air in everyday life).
4. As for the “mythological” version of the VTR operation model (var.B), the “microvortexes” described in it are not observable at all: both due to the small size of the VTR, and because of the invisibility of air as such. As a result, microvortices are the same philosophical and speculative construct as the unobservable structures of the atomic nucleus.
5. Now there are models of installations with supersonic Laval nozzles for without turbine heat separation in gases. So, on their basis, taking into account the obtained thermal-mechanical model (var.A), it was possible to create a hybrid design with VTR, called “Vortex tube with separate circuits” (VTRC), where the air flows in the cooled and heated paths are separated, but the generation of a cooling supersonic vortex is carried out on a multi-nozzle vortex generator with a torus-shaped receiver, that is, the same as in VTR.
6. VTRC turn out to be structurally no more complicated than VTR, but at the same time they are much more energy efficient, since the consumption of high-pressure compressed air is reduced by 3 times.
PS If you have read to the end and you have something to tell me personally, then I will gladly accept your objections and comments to my e-mail. I answer everyone!
1. V.A. Arkhipov. "Course of lectures on the theory and practice of swirling flows." Part 3.
Ministry of Education of the Russian Federation, Tomsk State University, Center for Research and Education in the Field of Missile and Artillery Sciences
Digital Library (repository) of Tomsk State University http://vital.lib.tsu.ru
2. Khazov Dmitry Evgenievich. “Numerical modeling of energy separation processes in compressible gas flows.”
Dissertation for the degree of candidate of physical and mathematical sciences.
Specialty 1.3.14 — “Thermophysics and theoretical heat engineering”
Scientific supervisor: Doctor of Technical Sciences, Academician of the Russian Academy of Sciences, Professor
Research Institute of Mechanics, Moscow State University named after M.V. Lomonosov
Завод По Производству Продольных Сварных Труб https://jiht.ru/science/dissert-council/diss_texts/diss_Khazov_online2.pdf