Calculation of gas flow parameters through a throttle washer

graphic-analytical calculation of turbulent throttle

Throttle (the term is usually used when describing the flow of a gaseous working fluid), it is also a jet (usually when a liquid working fluid is flowing), it is also turbulent throttle, aka diaphragm, aka throttle washer, it is also a detail with a hole of small diameter for passing the working substance with the required flow rate, in which the diameter of the throttling hole is greater than or approximately equal to its length. (1,5·d > L).

Turbulent flow is the movement of a viscous liquid or gas, in which the layers of the working fluid are mixed.

Determined parameters in the graphic-analytical calculation of the throttle washer

We set or is determined the following parameters:

k - adiabatic exponent;

Re - number Re;

T - temperature of gas, К;

R - gas constant, kg/m*kg.

G - the charge of gas, g/s;

d - diameter of an aperture orifice, mm;

F - the area of an aperture, mm²;

P0 - pressure before a orifice;

P1/P0 - the relation of pressure;

e - factor of the charge;

On the auxiliary diagram of definition of factor of the charge on an input in a orifice (е_in)

F1/F0 - the relation of the area of an aperture of a orifice to the area of through passage section of the channel before a orifice.

On the auxiliary diagram of definition of factor of the charge on an output from a washer (е_in)

F1/F0 - the relation of the area of an aperture of a orifice to the area of through passage section of the channel after a orifice.

Formulas for calculating the gas flow rate at subcritical and supercritical flow through the throttling hole of the throttle washer

The charge of gas at subcritical current:

G = e · F · P0 · [(2 · g/(R · T)) · (k/(k-1)) · ((P1/P0)^2/k - (P1/P0)^(k+1)/k]^0,5

The charge of gas at supercritical current:

G = e · F · P0 · [(2 · g/(R · T)) · (k/(k+1)) · (2/(k+1))^2/(k-1)]^0,5

Critical difference:

[P1/P0]_cr = [2/(k+1)]^k/(k-1)

Formulas are submitted by the following complexes:

C-ex A = e · [2 · g/(R · T) ]^0,5

For subcritical a mode - C-ex B = [(k/(k-1)) · ((P1/P0)^2/k - (P1/P0)^(k+1)/k]^0,5

For supercritical a mode - C-ex B = [(k/(k+1)) · (2/(k+1))^2/(k-1)]^0,5

C-ex C = G/(F · P0)

adiabatic exponent: k = (Cv + R) / Cv = 1 + (R/Cv)

Gas	Number of degrees of freedom	Adiabatic exponent
helium	3	1.66
argon	3	1.667
oxide carbon	5	1.401
oxygen	5	1.398
hydrogen	5	1.408
nitrogen	5	1.41
water steam	6	1.33
carbonic gas	6	1.305
ammonia	6	1.313
methane	6	1.315

For all options, the following parameter ranges are common:

d = 0.2 ... 1.9 mm P0 = 0.4 ... 35 kgf/cm² Т = 200 ... 2500 К

system nom. #1	e = 2...14 RTx10^-3=0.2...7.5 G = 0 ... 400 g/s
system nom. #2	e = 2...14 RTx10^-3=0.2...7.5 G = 0 ... 90 g/s
system nom. #3	e = 1...9 RTx10^-3=0.2...15 G = 0 ... 90 g/s
system nom. #4	e = 1...9 RTx10^-3=0.2...17 G = 0.01 ... 50 g/s
system nom. #5	e = 0.5...6.5 RTx10^-3=0.2...17 G = 0 ... 45 g/s
system nom. #6	e = 0.5...4.1 RTx10^-3=0.6...18 G = 0.005 ... 25 g/s
system nom. #7	e = 0.5...2.5 RTx10^-3=0.6...17 G = 0 ... 23 g/s
system nom. #8	e = 0.2...1.8 RTx10^-3=0.4...17 G = 0 ... 14 g/s
system nom. #9	e = 0.1...1.3 RTx10^-3=0.2...18 G = 0 ... 9 g/s
system nom. #10	e = 0.1...0.5 RTx10^-3=0.4...17 G = 0.01 ... 4.5 g/s

Brief description of the system of nomograms for the graphic-analytical calculation of the parameters of the throttle

The basic system of nomograms consists of four nomograms. Nomograms 1 and 2 have additional nomogram systems consisting of three nomograms. For the first nomogram, this is the definition of the flow coefficient e (Y-axis), which is the sum of the flow coefficients at the inlet and outlet of the orifice, which in turn depend on the area ratio and the Reynolds number (10<Re<10⁴). Also for the first graph, an additional nomogram is used to determine the product of RT (gas constant and gas temperature in K).

For the second nomogram, an additional system of nomograms is used to determine the C-ex B complex. This complex is calculated using different formulas for subcritical and supercritical flow regimes. Knowing the value of the adiabatic coefficient k, we determine the critical pressure drop for this washer from the lower graph of the additional system of nomograms. If the pressure drop across the washer chosen by us is less than [P1/P0]cr, then the flow is supercritical and the C-ex B complex is determined from the right auxiliary graph and depends only on k. If the difference we have chosen is greater than [P1/P0]cr, then the flow is subcritical and C-ex B is determined from the left nomogram and depends already on k and P1/P0.

Section topic: calculation of a throttle washer (turbulent throttle).

The calculation of an extended choke - capillary (laminar choke) is given on the page "Calculation of the characteristics of the throttling channel, made in the form of a coil" .

graphic-analytical systems The contact information: nomogramka@gmail.com