Механизм работы и самая малая модель мотора стирлинга
Август 17th, 2014
This chapter concentrates on the calculations involved when testing engines. A selection of base calculations is described, with appropriate usage and suitability of the calculations. The chapter starts with some brief descriptions of the most common ones.
Torque Backup
Torque backup is best described as
(Maximum torque — Torque at maximum speed)
Torque at maximum speed
Development of advanced common rail systems and associated equipment has introduced additional freedom to vary fuel delivery over the speed range of an engine. For example, the turbocharger matching process must be linked closely with the fuel system matching, even after optimum injection rates, pressures, nozzle sizes, and swirl have been achieved.
Motoring Mean Effective Pressure
The motoring mean effective pressure (MMEP) is determined from the torque required to motor an engine at a predetermined condition and can be calculated as
. „ . 1000 x Motoring torque (Nm) x Number of strokes
MMEP (bar) — —————————— —— ———— ———————————
Capacity (cc)
Volumetric Efficiency
Volumetric efficiency fj is a measure of the effectiveness of the induction and exhaust processes. It is convenient to define volumetric efficiency as
, _ Volume of ambient density air inhaled per cylinder per cycle v Swept volume per cylinder at ambient pressure and temperature
Assuming that air obeys the gas laws, this can be written as
Volume of ambient density air inhaled per cylinder per cycle
V 
T1
Cylinder volume (cc)
, va
Where
Va = volumetric flow rate of air with ambient density Vs = engine swept volume
N = revolutions per second for a twostroke unit, or revolutions per second divided by 2 for a fourstroke engine
Specific Fuel Consumption
The specific fuel consumption (SFC) can be defined as
Mass flow rate of fuel
SFC ————————————
Power output
Correction Factors
Pressure:
RL
A
For example,
25 psig = 25 + 14.504 = 39.504 psia 25 psig = 25 x 6894.76 Pa
= 172,368 Pa (gauge)
= 172,368 Pa + 101,325 Pa (1 atmosphere)
= 273,693 Pa (absolute)
Phase
Phase is the nature of a substance. Matter can exist in three phases: solid, liquid, or gas.
Cycle
If a substance undergoes a series of processes and returns to its original state, then it is said to have been taken through a cycle.
Process
A substance can be said to have undergone a process if the state is changed by operation of that process having been carried out on it.
• Constant temperature process
• Isothermal process
• Constant pressure process
• Isobaric process
• Constant volume process
• Isometric process or isochoric process
Heat
Temperature t (Celsius) = T — 273.15 (Kelvin)
Q — heat energy in joules/kg Specific heat capacity:
Heat transfer per unit temperature
Dt
The unit is joules/kg K (joules per kilogram per Kelvin).
Calorific value is the heat liberated by burning the unit mass or volume of a fuel (e. g., gasoline: 43 MJ/kg).
Work done in a polytropic process:
V2 v2
Work done =  PdV = C J V~ndV
Vi V,
= _c_(vr“+1vrn+1l = PlVl~P^2 —n +1 ‘ ‘ n — 1
Enthalpy
A themodynamic quantity equal to the internal energy of a system plus the product of its volume and pressure.
H = U + PV
Where
U = internal energy P = pressure
V = volume
Specific Enthalpy
The specific enthalpy of a working mass is the property of that mass used in terms of dynamics. The S. I. unit for specific enthalpy is joules per kilogram.
H = U/m = u + Pv
Principle of the Thermodynamic Engine
„ Work done Power =——————— Time taken 
Where the unit is J/s = watt. 
The engine converts chemical energy into usable power and torque.
That which is transmitted through a mechanical system and used to perform work. 
Electrical Power
The product of voltage and current.
W = I V
Where the unit is J/s = watt.
Laws of Thermodynamics
The Zeroeth Law: If bodies A and B are in thermal equilibrium, and bodies A and C are in thermal equilibrium, then bodies B and C must be in thermal equilibrium.
The First Law:
W = Q
This means that if some work W is converted to heat Q, or some heat Q is converted to work W, then W = Q. It does not mean that all work can convert to heat in a particular process. .
The Conservation of Energy
For a system,
Initial energy + Energy entering = Final energy + Energy leaving
Potential energy = gZ
• 1 /~i2 Kinetic energy = — mC
Joule’s Law
Internal energy of gas is the function of temperature only and independent of changes in volume and pressure,
PlVf = P2V2n
Pl_ 
1 
N 
’V 
N And 
Vi _ 
>1* 
P2 
L vi. 
V2 
1 NT 
The specific heat capacity at constant volume is Cv.
U2 — Uj = mcv (T2 — Tj) (change in internal energy) The specific heat capacity at constant pressure is Cp.
U2U1+P(V2V1) = mcp(T2T1)
From the characteristic equation
H T2 
PlVl _ P2V2
PlVl _ 
N 
Vi _ 

P2V2 
IvJ 
V2 
IVJ 
N1 
And
1 
Nl 

/ ^ 
— 
Z’ 
—— 
I 11 
N 
I 11 
N 
Lp2J 
L?2J 
Ti P. V. Pi T2 P2V2 P2 
That is,
II 
FV 
T2 
Nl N 

Entropy
A measure of the unavailability of a system’s energy to do work.
DQrev =Tds 
Revisable heat transfer is Qri
Mill 1 T2 Cr, 
S2 _ S1 — c 
= — cp‘n+(cpc»)^: 
NlnlL 1 t, 
— n 
In—= Cp — Cv" In — 
N — 1 Tt n — 1 
= c. 
















T, 
(cp — cv = R) 
= cnln — — Rln p T,
That is,
T2 di„P2
S7 — Si = cnln—— — Rln p T.
For example, the air at T = 288 K and standard atmosphere is compressed to P = 5 times of standard atmospheric pressure with a temperature of 456.1 K. Calculate the entropy values.
For air, Cp = 1005 J/kgK and R = 287 J/kgK.
Before compression,
S2 = 1005 In 288 2871n^^ = 53
273.15 TOC o "15" h z 0.101
After compression,
I™* . 456 1 „о,, 5×0.101 „
S2 = 1005 In ———— 287 In—:—:—— =53
0.101 
273.15
There is no change in entropy.
The pressure, humidity, and temperature of the ambient air inducted into an engine, at a given speed, affect the air mass flow rate and hence the potential power output. Correction factors are used to adjust measured wide open throttle power to standard atmospheric conditions to provide a more accurate basis for comparison among engines.
The basis for these correction factors is the equation for onedimensional steady compressible flow through an orifice.
1.2 
0.6 
99 
T + 273 
298 1.01325 bar 20°C (293°K) ps= 1.205 kg/m3 
Correction Formulae • 88/195/EEC • EEC80/1269 • ISO 1585 • JISD 1001 • SAEJ1349 • DIN 70 020 Correction formulae: 88/195/EEC = 
Pressure: Standard atmosphere Temperature: Corresponding density: where 
P = barometric pressure (atmospheric) — partial vapor pressure (kPa) T = ambient intake air temperature in degrees Celsius (°C) ps = density of air
The standard conditions are considered to be a barometric pressure of 99 kPa and a temperature of 298°K (25°C).
The partial vapor pressure required to calculate the dry barometric pressure term P in the equation 88/195/EEC can be obtained in two ways.
1. Using wet and dry air bulb temperature measurements and psychometric tables
2. Using relative humidity and ambient air temperature measurements and the following equations:
Dry barometric pressure = Atmospheric pressure — Partial vapor pressure
P = Pa — Ppv
When
Relative humidity (%) x Saturated vapor pressure (kPa)
Ppv =
100
The saturated vapor pressure Psv (kPa) is given by
Log10Psv = 
30.59051 8.2 xlog10(T) +(2.480E — 3) xT — (3.142 x 3l)
T
Where
T(k) = Ta(°C) + 273.15 Ta = ambient air temperature Correction formulae (DIN):
Correction factor = 760(273 + T/P)293
Where
760 
273 + T P + 293
P = barometric pressure (mm Hg)
T = ambient intake air temperature (°C)
Examples of Calculations Required Within the Test Cell Environment Test Bed Fuel Flow Measurement
Many test beds are equipped with gravimetric fuel measuring devices that provide an output in the form of mass of fuel used per selected time interval (e. g., grams of fuel consumed in 30 seconds).
Test Bed Airflow Measurement
To calculate the air/fuel ratio, we need to know the fuel flow and the air used by an engine. This can be done chemically using gaseous emission measuring equipment, but a crossreference is a prerequisite of intelligent testing.
The actual measurement of air mass flow rate is not carried out on a regular basis because it can be calculated from SPINDT AFR (exhaust gas) and from brakespecific fuel consumption. However, various airflow meters are available for measuring engine air consumption, namely, the following:
• Lucas Dawe hot wire corona discharge
• Hot wire wheat stone bridge balance system
• Alcock viscous airflow meter
• Base orifice plate
All types of measuring devices should be used upstream of any intake pressure pulsations to allow for stable readings to be taken and logged. (This usually means prior to an air cleaner/resonator volume.)
Brake Specific Fuel Consumption
Having measured the fuel mass flow rate by one of the methods highlighted in this book, a more useful parameter—the brake specific fuel consumption (BSFC)—can be calculated. It is defined as
„„„„ Fuel mass flow rate mf
BSFC =—————————— =——
Measured brake power P P
With units of grams of fuel consumed to deliver 1 kW over 1 hour (g/kWh).
The BSFC provides a measure of how efficiently an engine is using fuel supplied to produce work. For spark ignition engines, typical values of BSFC at wide open throttle are between 250 and 260 g/kWh.
Figure 13.1 gives an example of a specific fuel consumption contour map for the complete operating range of an engine. The contour lines represent lines of constant specific fuel consumption; the lower the figure, the more efficient the running condition.
Brake specific fuel consumption also can be applied to other items whose output is compared with the brake power delivered by the engine. For example, in emissions, one will note brake specific hydrocarbons (BSHC).
/ / / 
^ і r УПГгч 
Ц—1—1—1 

4 ZL J’ ‘ t 
Arv 1 ^ 

f — A i / 
A ( 
^N4 
ІГх]—1 
VI K 
ЛVvjjj b1 V 245 
1J J 1 [ і 
F 
Щ 
ZЩ 
Wfff 
/ Г7 1 / 
Zip 
AJK 
LLl A І Jo L7 ! 
Щ 
—і ——— r^T^ii—. 
Ш± 
Ш 
ВМЕР (bar) 
Rev/Mis 
Figure 13.1 Oyster curve example. 
Brake Specific Air Consumption
Similarly, brake specific air consumption (BSAC) is defined as the air mass flow rate per unit power output
BSAC = Airflow/power (units kg/kWh)
Where power is the brake power output. This provides a measure of how efficiently an engine is using the air supplied to produce work.
Factors that affect the BSFC and BSAC are as follows:
• Compression ratio
• Air/fuel ratio and ignition settings
• Friction—Rubbing in the engine and accessories
• Pumping losses—Intake system restrictiveness/cylinder head design and exhaust system design
• Calorific value of the fuel
• Barrel swirl ratio
• Heat pickup through the induction system
• Heat transfer from the combustion chamber
• Mixture preparation
• Fuel/air mixture distribution
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