Scientific Paper on Injector with Injection of High Density Fluid
1. INJECTOR WITH THE INJECTION OF A HIGH DENSITY FLUID
INTO A DIFFUSER (A MIXING CHAMBER) APPLIED IN A POWER CYCLE
Date: ___________February / 10 / 2015 _
Personal Identification No.: 0203974500203_____
Investigator Name: ______Marijo Miljkovic_______
Street Address: __Milutina Milankovica 98_______
City/State/Zip + 4: _Belgrade / Serbia / 11070_____
Email Address: _marijo.miljkovic@ymail.com_____
Organization / Individual Person:
The papers are made by an independent scientist: Marijo Miljkovic________________________________
Author(s) / Principal Investigator / Phone / Email:
Marijo Miljkovic / Marijo Miljkovic / +381 64 282 69 80 / +381 11 21 24 144 /+381 217 22 66 / mkonc@sezampro.rs / marijo.miljkovic@ymail.com
Title: INJECTOR WITH THE INJECTION OF A HIGH DENSITY FLUID INTO A DIFFUSER (A MIXING CHAMBER) APPLIED IN A POWER CYCLE
Key Words: Power Cycle, Thermodynamic Cycle, Power Plant, Ocean Thermal Energy Conversion, Injectors, Ejectors, Thermal Compressors
2. ABSTRACT
The motive stream of vapor enters the nozzle of the injector (state 3), where it expands to the state A and its velocity and kinetic energy increase (its
enthalpy decrease), as well as its pressure is reduced to the pressure p13. Then a motive stream of vapor withdraws the suction stream of vapor and they
are mixed in the mixing chamber of the injector (state BI). Then the mixture of vapors (mBI=m3+m13) enters the diffuser where a high density fluid is also
injected through the nozzle. After that the process of further mixing with a high density fluid takes place simultaneously with the process of compression of
the mixture in a diffuser. As the high density fluid is going through the nozzle, it accelerates and its heat potential (enthalpy) decreases, but its kinetic
energy increases. This increase in kinetic energy is later used to increase the pressure of this fraction (mE) of the working fluid. Since the velocity of the
injected high density fluid is similar to the velocity of the mixture of vapor, the efficiency of further mixing is not taken into consideration in this paper. At last,
the new mixture (mmix=m1+m2+mE) is compressed to the state CIII and its velocity and kinetic energy decrease (its enthalpy increases), as well as its
pressure increases to the condensing pressure pCIII=p1.
3. INTRODUCTION
The losses of kinetic energy of the working fluid due to the friction and turbulence in all processes in an injector (expansion, mixing and compression),
actually are not losses of its total energy. A part of its kinetic energy is only converted to heat and absorbed by the working fluid. This results in an increase
of the enthalpy (the heat potential) of the working fluid. Therefore its total energy is preserved.
The Law of Conservation of Energy (the 1 Law of Thermodynamics) could be used in a wise manner in order to increase the overall efficiency of an
injector.
As a goal is not to increase the enthalpy of a working fluid and in order to increase its pressure in an efficient manner, we could inject a high density fluid
into the fluid mixture. In this way, the compression of the mixture in a diffuser takes place simultaneously with mixing with a high density fluid. So the kinetic
energy of both streams, in the first place, is used for increasing the pressure of the new mixture, while reducing its entropy. Therefore a fraction of kinetic
energy of the mixture is used for reduction of its entropy instead for the increase of its enthalpy. In this way, the compression of the mixture is intensified.
Finally, this results in the increase of the overall efficiency of an injector.
This example presents only one aspect of compression process of many possible ones. It implies maintaining a constant value of the enthalpy of a mixture
in a diffuser. In general, if we observe an isenthalpic process (e.g. h=484.5084kJ/kg=const) from a starting point BI (at p=1.25bar and ρ=49.80kg/h) with
mixing with a high density fluid (e.g. ρ=659.39kg/h), then the density of a mixture will rise and therefore its entropy will decrease.
Working
Fluid:
R32
p bar 11.07 1.25 0.58
h kJ/kg 484.5084 484.5084 484.5084
v m/s 0.00 246.36 0.00
ρ kg/m3
136.38 49.80 23.86
s kJ/kgK 2.0045 2.3083 2.4096
εt=h/(p/ρ) - 59.6890 193.0146 199.2984
x - 0.8927 0.9614 0.9822
ε[-] ......Thermal Coefficient
Also, the goal is not to reach a state of a mixture with a certain enthalpy (CII), but to increase its pressure. So, the enthalpy of the final state of a mixture can
be lower than the enthalpy of the state CII, i.e. hCIII<hCII.
In order to behave the same as the first mixture (m3+m13) leaving the mixing chamber, a high density fluid should have the same velocity, i.e. vD≈vBI.
Therefore, it is necessary to inject a fluid with a higher enthalpy from the evaporator instead a liquid from the outlet of a pump.
4. The initial assumptions (as well as conditions and restrictions) for the calculation of an injector with the injection of a high density fluid into the
diffuser (mixing chamber) applied in a power cycle with all irreversible processes:
- A high density fluid of the state E is injected into the inlet of a diffuser of an injector. It expands in the nozzle to the state D.
- The velocity of a high density fluid and a vapor mixture entering the diffuser are similar: vD≈vBI.
- The compression of a mixture in a diffuser takes place simultaneously with the mixing with a high density fluid injected into a diffuser. The final state of the
second mixture (m3+m13+mE) is CIII.
- The final enthalpy of the second mixture (m3+m13+mE) is the same as the final enthalpy of the first mixture (m3+m13), i.e. hCIII=hBI. The kinetic energy of
both streams, (m3 + m13) and mE:
Ekmix= mE x vD^2/2 + (m3 + m13) x vBI^2/2
is used only for increasing the pressure of the mixture while maintaining a constant value of the enthalpy of the second mixture. In other words, the total
energy (heat potential + kinetic energy) of the second mixture (m3+m13+mE) is the same as the final enthalpy (heat potential) of the first mixture (m3+m13),
i.e. hCIII=hBI.
CALCULATION
OF THE INJECTOR WITH THE INJECTION OF A HIGH DENSITY FLUID
INTO A DIFFUSER (A MIXING CHAMBER) APPLIED IN A POWER CYCLE WITH ALL IRREVERSIBLE PROCESSES
The equations that determinate the states of a mixture with respect to the 1st
Law of
Thermodynamics:
- for the 1st mixing of two vapor streams (motive and suction) in the mixing chamber:
hCII x (m3 + m13) = h3 x m3 + h13 x m13
(hBr + vBr^2/2) x (m3 + m13) = (hA+vA^2/2) x m3 + (h13 + v13^2/2) x m13
5.
6.
7. - for the 2nd mixing of a vapor mixture and a high density fluid in a diffuser:
hCIII x (mE + m3 + m13) = hCII x (m3 + m13) + hE x mE
(hCIII + vCIII^2/2) x (mE + m3 + m13) = (hBI+vBI^2/2) x (m3 + m13)+ (hD + vD^2/2) x mE
where:
m ....................... mass fluid flow kg/s
The overall efficiency of an injector with the injection of a high density
fluid into a diffuser:
ηinj = EICR x PDIIL / (EIIIL x PDCR)
- EICR .......................... Energy Input for a conventional injector with all reversible
processes (expansion, mixing and compression).
- PDCR .......................... Pressure difference for a conventional injector with all
reversible processes (expansion, mixing and compression).
- EIIIL ........................... Energy Input for an injector with the injection of a high
density fluid into a diffuser.
- PDIIL ........................ Pressure difference for an injector with the injection of
a high density fluid into a diffuser.
ηinj = h3 x mCR3 x (pCIII - p13) / ((m3 x h3 + mE x hE) x (pCIII - p13))
8. where: mCR3 ....................... mass flow of a motive stream in a conventional
injector with all reversible processes.
kI = m3 / m13 = 7.8510
hCII=(kI x h3 + h13)/(kI+1)= 514.8559 kJ/kg
vA=√(2 x (h3-hA))= 369.73 m/s
vBr=kI x vA / (kI+1) = 327.96 m/s
hBr=((hA+vA^2/2) x kI+h13)/(kI+1)-vBr^2/2= 461.08 kJ/kg
vBI=Ψ x vBr= 246.36 m/s
Ψ= 0.751207
hBI=hBr+vBr^2 x (1-Ψ^2)/2= 484.5084 kJ/kg
10. ηent= ηB = (kI+1) / kI x (vB / vA)^2= 0.5006
Etot=(kI+1) x (hBI+vBI^2)= 4,556.99 Etot=kI*(hA+vA^2/2)+h13= 4,556.99 kJ/kg
hCII=Etotal/(kI+1)= 514.8559 kJ/kg
hE-hD=vD^2/2≈vBI^2/2= 30.3475 kJ/kg
hCIII=(hCII+kII x hE)/(kII+1)= 484.5084 kJ/kg
hCIII=(hBI+vBI^2/2+kII x hE)/(kII+1)= 484.5084 kJ/kg
kII=mE/mBI= 0.1873425 kII=(sF-sCII)/(sCII-sEI)
xCIII=(hCIII-h')/(h"-h')= 0.8927380
ktot=mtot/m13= 10.5092 ktot=(kI+1) x (kII+1)
mtot=m3+m13+mE kg/s
vD=√(2 x (hE-hD))= 246.48 m/s
hE=hD+vD^2/2= 322.5187 kJ/kg
11. The technical work of the turbine:
lt = lt3-6+lt8-9+lt10-11+lt12-13+mtot x lt1-2 = 84.830 kJ/kg
The heat brought to the tehnical system:
qin = ktot x q2-E + (kI+1) x q3E + q6-8 + q9-10 + q11-12= 2,886.56 kJ/kg
The heat taken from the tehnical system:
qout = ktot x qCIII-1 = 2,801.73 kJ/kg
The 1st
Law of Thermodynamics applied to the whole power cycle:
qin - qout - lt= 0.00000 kJ/kg
(sE - s1) x ktot + (s3 - sE) x (kI + 1) + s13 - s3 - (sCIII - s1) x ktot = 0.00000 kJ/kgK
kII= 0.1873425
kI= 7.851000
ktot= 10.509168
12. The thermal efficiency of a power system with applied a real Injection Power Cycle with all
irreversible processes:
ηterm = lt / qin = 0.029388
The pressure difference in a power system with applied a real Injection Power Cycle (IPC):
∆pIPC = 13.49 bar
as well the temperature difference:
∆tIPC = 67.50 °C
The final state of the new (second) mixture, after mixing of vapor mixture from mixing chamber
with a high density fluid in the diffuser:
hCIII=(kI x h3 + h13 + hE x kII x (kI + 1))/((kI + 1)x(kII + 1))= 484.5084 kJ/kg
sCIII=(kI x s3 + s13 + sE x kII x (kI + 1))/((kI + 1)x(kII + 1))= 2.004471 kJ/kgK
The technical work of the working fluid R32 in a system with applied
Rankine Power Cycle, the heat brought to it , as well as taken from it
are as follows:
lt = lt3-6 + lt1-2 = 9.24 kJ/kg
13. qin = q2-3 = 298.16 kJ/kg
qout = q6-1 288.92 kJ/kg
The 1st
Law of Thermodynamics for the Rankine Power Cycle:
qin - qout - lt = 0.00 kJ/kg
The thermal efficiency of the real Rankine Power Cycle:
ηterm = lt / qin = 0.030990
The pressure difference in a power system with applied a real Rankine Power Cycle (RPC):
∆pRPC = 3.67 bar
as well the temperature difference:
∆tRPC = 10.00 °C
14. The overall efficiency of an injector with the injection of a high density
fluid into the diffuser:
ηinj = h3 x k x (pCIII-p13)/((kI*h3+kII*(kI+1) x hE)*(pCIII-p13))
ηinj = h3 x k / (kI x h3+kII x (kI+1) x hE) = 0.952
where the coefficient k is for the conventional type of injector with
all reversible processes (expansion, mixing and compression):
k = 8.46
15. CONCLUSION
At this stage of development of a mathematical model of calculation, it is already clear that the injector with the injection of a high density fluid into a diffuser
(mixing chamber) has a much greater efficiency than the conventional one. Therefore, the further development of an injector with the injection of a high
density fluid into the diffuser (mixing chamber) promises to revolutionize the future of thermal compressors.
Also, in this example the Injection Power Cycle did not reach the efficiency of the Rankine Power Cycle. On the other hand, the IPC is the only power cycle
in which the temperature drop, i.e. temperature difference of a working fluid in its expansion is significantly larger than the temperature difference between
the heat source and the heat sink. This results in an increase in fluid pressure difference in its expansion in the turbines, as well as in a significant increase
in the technical work of a working fluid.
I believe that it is possible to reach the efficiency of the Rankine Power Cycle with the appropriate design of an injector with the injection of a high density
fluid into a diffuser (a mixing chamber).
Finally, I believe that I presented a sufficient proof for prototyping of the injector with the injection of a high density fluid into a diffuser (mixing chamber), as
well as its testing. This is crucial for the commercialization of the new type of injectors with significantly increased efficiency, as well as the new power cycle
(IPC) and advanced type of injection (ejection) refrigeration machine (IRM) with significantly increased efficiency.
In such injection refrigeration machine (IRM), the conventional (mechanical) compressor would be replaced with a pump and the advanced type of injector
(ejector, thermal compressor with no moving parts). For the same refrigeration effect, the work of a pump would be significantly lower than the work of a
mechanical compressor. This results in reducing power input for a refrigeration machine while maintaining the same cooling capacity. The best type of a
heat source for injection refrigeration machine (IRM) would be solar-thermal energy, geothermal energy or waste heat from thermal or nuclear power
plants, as well as foundries.
Author:
Marijo Miljkovic
Personal I.D.No.: 0203974500203
Milutina Milankovica 98
11 070 New Belgrade
Serbia
Europe
+381 64 282 69 80
+381 61 654 66 41
+381 11 21 24 144
marijo.miljkovic@ymail.com
mkonc@sezampro.rs
