Computerized method and system for designing an aerodynamic focusing lens stack
View Patent ↗A computerized method and system for designing an aerodynamic focusing lens stack, using input from a designer related to, for example, particle size range to be considered, characteristics of the gas to be flowed through the system, the upstream temperature and pressure at the top of a first focusing lens, the flow rate through the aerodynamic focusing lens stack equivalent at atmosphere pressure; and a Stokes number range. Based on the design parameters, the method and system determines the total number of focusing lenses and their respective orifice diameters required to focus the particle size range to be considered, by first calculating for the orifice diameter of the first focusing lens in the Stokes formula, and then using that value to determine, in iterative fashion, intermediate flow values which are themselves used to determine the orifice diameters of each succeeding focusing lens in the stack design, with the results being output to a designer. In addition, the Reynolds numbers associated with each focusing lens as well as exit nozzle size may also be determined to enhance the stack design.
1. A computerized method for designing an aerodynamic focusing lens stack, said computerized method comprising:
receiving as input in a computer the design parameters of: (1) the particle size range to be considered (d particle (min) , d particle (max) ) and the particle density thereof (ρ particle ); (2) pa characteristics of the gas to be flowed through the aerodynamic focusing lens n stack design, including dynamic viscosity (μ), standard gas mean free path (λ standard ), heat ratio (γ), gas constant (R), molecular mass (M), and flow type, either isothermal flow or isentropic flow; (3) the temperature (T[ 1 ]) and pressure (P[ 1 ]) upstream of a first focusing lens [i=1] of the aerodynamic focusing lens stack design; (4) the flow rate through the aerodynamic focusing lens stack equivalent at atmosphere pressure (Q equ ); and (5) a Stokes number range defining the focusing tightness (Stk min , Stk max );
based on said received design parameters, determining the number of focusing lenses and their respective orifice diameters (d lens [i]) required to focus the particle size range to be considered, and including the steps of:
(a) solving for the orifice diameter (d lens [i]) of the i th focusing lens, in the Stokes number equation: FOCUS(T[i], Q[i], P[i], λ standard , μ, d lens [i], d particle [i], ρ particle , Stk max )=0, beginning with the first focusing lens [i=1] where d particle [1]=d particle (max) and
Q
[
1
]
=
Q
equ
(
P
atm
P
[
1
]
)
;
(b) using the value of the orifice diameter (d lens [i]) in step (a) to solve for a new maximum particle size d particle [i+1] to be focused in the next [i+1] th focusing lens, in the Stokes number equation: FOCUS(T[i], Q[i], P[i], λ standard , μ, d lens [i], d particle [i+1], ρ particle , Stk min )=0;
(c) determining the pressure drop across the [i] th focusing lens by solving for a pressure P[i+1] downstream of the [i] th focusing lens and upstream of the next [i+1] th focusing lens, in the Prandtl derivation: DROP (T[i], Q[i], P[i], P[i+1], d lens [i], γ, R, M)=0;
(d) setting the temperature T[i+1] and flow rate Q[i+1] of the next [i+1] th focusing lens according to: if the flow type is isothermal flow, then
T
[
i
+
1
]
=
T
[
i
]
and
Q
[
i
+
1
]
=
Q
[
i
]
(
P
[
i
]
P
[
i
+
1
]
)
=
Q
equ
(
P
atm
P
[
i
+
1
]
)
;
and if the flow type is isentropic flow, then
T
[
i
+
1
]
=
T
[
i
]
(
P
[
i
+
1
]
P
[
i
]
)
γ
-
1
γ
and
Q
[
i
+
1
]
=
Q
[
i
]
(
P
[
i
]
P
[
i
+
1
]
)
=
Q
equ
(
P
atm
P
[
i
+
1
]
)
1
γ
;
and
(e) setting i=i+1 and iteratively performing steps (a) through (d) using the values for d particle [i+1], P[i+1], T[i+1], and Q[i+1] determined in the previous iteration, until d particle [i+1] in step (b) is less than d particle (min) ; and
outputting to a designer the respective orifice diameters of all the number of focusing lens determined to be required to focus the particle size range to be considered.
2. The method of claim 1 , further comprising:
determining the flow stability through each focusing lens of the aerodynamic focusing lens stack design by solving for the Reynolds number (Re[i]) in the formula:
Re
[
i
]
=
(
Q
[
i
]
·
d
lens
[
i
]
1000
·
60
·
π
·
(
d
lens
[
i
]
2
)
2
)
(
ρ
μ
)
,
where ρ is the density of the gas; and
outputting to the designer the respective Reynolds numbers of all the number of focusing lens.
3. The method of claim 1 , further comprising:
determining the orifice diameter of an exit nozzle of the aerodynamic focusing lens stack design operating in a choked mode to lock the operating pressure and flow, by solving for the orifice diameter (d exitnozzle ) of the exit nozzle in the Prandtl formula:
Q
exitnozzle
=
π
(
d
exitnozzle
2
)
2
·
R
0
T
top
M
·
γ
(
2
γ
+
1
)
γ
+
1
γ
-
1
,
where Q exitnozzle is estimated using the formula
Q
1
=
Q
2
·
P
2
P
1
for the pressure downstream of the last focusing lens, and the pressure downstream of the last focusing lens is itself determined from the final iteration of step (c); and
outputting to the designer the orifice diameter of the exit nozzle.
4. A computerized method for designing an aerodynamic focusing lens stack, said computerized method comprising:
receiving as input in a computer the design parameters of: (1) the particle size range to be considered (d particle (min) , d particle (max) ) and the particle density thereof (ρ particle ); (2) characteristics of the gas to be flowed through the aerodynamic focusing lens stack design, including dynamic viscosity (μ), standard gas mean free path (λ standard ), heat ratio (γ), gas constant (R), molecular mass (M), and flow type, either isothermal flow or isentropic flow; ( 3 ) the temperature (T[ 1 ]) and pressure (P[ 1 ]) upstream of a first focusing lens [i=1] of the aerodynamic focusing lens stack design; (4) the flow rate through the aerodynamic focusing lens stack equivalent at atmosphere pressure (Q equ ); and (5) a Stokes number range defining the focusing tightness (Stk min , Stk max );
based on said received design parameters, determining the number of focusing lenses and their respective orifice diameters (d lens [i]) required to focus the particle size range to be considered, and including the steps of:
(a) solving for the orifice diameter (d lens [i]) of the i th focusing lens, in the Stokes number equation: FOCUS(T[i], Q[i], P[i]), λ standard , μ, d lens [i], d particle [i], ρ particle , Stk max )=0, beginning with the first focusing lens [i=1] where d particle [1]=d particle(max) and
Q
[
1
]
=
Q
equ
(
P
atm
P
[
1
]
)
;
(b) using the value of the orifice diameter (d lens [i]) in step (a) to solve for a new maximum particle size d particle [i+1] to be focused in the next [i+1] th focusing lens, in the Stokes number equation: FOCUS(T[i], Q[i], P[i], λ standard , μ, d lens [i], d particle [i+1], ρ particle , Stk min )=0;
(c) determining the pressure drop across the [i] th focusing lens by solving for a pressure P[i+1] downstream of the [i] th focusing lens and upstream of the next [i+1] th focusing lens, in the Prandtl derivation: DROP (T[i], Q[i], P[i], P[i+1], d lens [i], γ, R, M)=0;
(d) setting the temperature T[i+1] and flow rate Q[i+1] of the next [i+1] th focusing lens according to: if the flow type is isothermal flow, then
T
[
i
+
1
]
=
T
[
i
]
and
Q
[
i
+
1
]
=
Q
[
i
]
(
P
[
i
]
P
[
i
+
1
]
)
=
Q
equ
(
P
atm
P
[
i
+
1
]
)
;
and if the flow type is isentropic flow, then
T
[
i
+
1
]
=
T
[
i
]
(
P
[
i
+
1
]
P
[
i
]
)
γ
-
1
γ
and
Q
[
i
+
1
]
=
Q
[
i
]
(
P
[
i
]
P
[
i
+
1
]
)
=
Q
equ
(
P
atm
P
[
i
+
1
]
)
1
γ
;
and
(e) setting i=i+1 and iteratively performing steps (a) through (d) using the values for d particle [i+1], P[i+1], T[i+1], and Q[i+1] determined in the previous iteration, until d particle [i+1] in step (b) is less than d particle (min) ;
determining the flow stability through each focusing lens of the aerodynamic focusing lens stack design by solving for the Reynolds number
(
Re
[
i
]
)
in
the
formula
:
Re
[
i
]
=
(
Q
[
i
]
·
d
lens
[
i
]
1000
·
60
·
π
·
(
d
lens
[
i
]
2
)
2
)
(
ρ
μ
)
,
where ρ is the density of the gas;
determining the orifice diameter of an exit nozzle of the aerodynamic focusing lens stack design operating in a choked mode to lock the operating pressure and flow, by solving for the orifice diameter (d exitnozzle ) of the exit nozzle in the Prandtl formula:
Q
exitnozzle
=
π
(
d
exitnozzle
2
)
2
·
R
0
T
top
M
·
γ
(
2
γ
+
1
)
γ
+
1
γ
-
1
,
where Q exitnozzle is estimated using the formula
Q
1
=
Q
2
·
P
2
P
1
for the pressure downstream of the last focusing lens, and the pressure downstream of the last focusing lens is itself determined from the final iteration of step (c); and
outputting to a designer the respective orifice diameters of all the number of focusing lens determined to be required to focus the particle size range to be considered, the respective Reynolds numbers of all the number of focusing lens; and the orifice diameter of the exit nozzle.
5. A computer system for designing an aerodynamic focusing lens stack, said computer system comprising:
input means for receiving the design parameters of: (1) the particle size range to be considered (d particle (min) , d particle (max) ); particle density of the particle size range to be considered (ρ particle ); (2) characteristics of the gas to be flowed through the aerodynamic focusing lens stack design, including dynamic viscosity (μ), standard gas mean free path (λ standard ), heat ratio (γ), gas constant (R), molecular mass (M), and flow type, either isothermal flow or isentropic flow; (3) the temperature (T[ 1 ]) and pressure (P[ 1 ]) immediately upstream of a first focusing lens [i=1] of the aerodynamic focusing lens stack design; (4) a flow rate through the aerodynamic focusing lens stack equivalent at atmosphere pressure (Q equ ); and (5) a Stokes number range defining the focusing tightness (Stk min , Stk max );
computer processor means for determining, based on said received design parameters, the number of focusing lenses and their respective orifice diameters (d lens [i]) required to focus the particle size range to be considered, said computer processor means for determining adapted to:
(a) solve for the orifice diameter (d lens [i]) of the i th focusing lens, in the Stokes number equation: FOCUS(T[i], Q[i], P[i], λ standard , μ, d lens [i], d particle [i], ρ particle , Stk max )=0, beginning with the first focusing lens [i=1] where d particle [1]=d particle (max) and
Q
[
1
]
=
Q
equ
(
P
atm
P
[
1
]
)
;
(b) use the value of the orifice diameter (d lens [i]) in step (a) to solve for a new maximum particle size d particle [i+1] to be focused in the next [i+1] th focusing lens, in the Stokes number equation: FOCUS (T[i], Q[i], P[i], λ standard , μ, d lens [i], d particle [i+1], ρ particle , Stk min )=0;
(c) determine the pressure drop across the [i] th focusing lens by solving for a pressure P[i+1] downstream of the [i] th focusing lens and upstream of the next [i+1] th focusing lens, in the Prandtl derivation: DROP (T[i], Q[i], P[i], P[i+1], d lens [i], γ, R, M)=0;
(d) set the temperature T[i+1] and flow rate Q[i+1] of the next [i+1] th focusing lens according to: if the flow type is isothermal flow, then T[i+1]=T[i] and
Q
[
i
+
1
]
=
Q
[
i
]
(
P
[
i
]
P
[
i
+
1
]
)
=
Q
equ
(
P
atm
P
[
i
+
1
]
)
;
and if the flow type is isentropic flow, then
T
[
i
+
1
]
=
T
[
i
]
(
P
[
i
+
1
]
P
[
i
]
)
γ
-
1
γ
and
Q
[
i
+
1
]
=
Q
[
i
]
(
P
[
i
]
P
[
i
+
1
]
)
=
Q
equ
(
P
atm
P
[
i
+
1
]
)
1
γ
;
and
(e) set i=i+1 and iteratively performing steps (a) through (d) using the values for d particle [i+1], P[i+1], T[i+1], and Q[i+1] determined in the previous iteration, until d particle [i+1] in step (b) is less than d particle (min) ; and
output means for communicating to a designer the number of focusing lenses and their respective orifice diameters (d lens [i]) determined to be required to focus the particle size range to be considered.
6. The computer system of claim 5 , further comprising:
computer processor means for determining the flow stability through each focusing lens of the aerodynamic focusing lens stack design by solving for the Reynolds number
(
Re
[
i
]
)
in
the
formula
:
Re
[
i
]
=
(
Q
[
i
]
·
d
lens
[
i
]
1000
·
60
·
π
·
(
d
lens
[
i
]
2
)
2
)
(
ρ
μ
)
,
where ρ is the density of the gas; and
wherein the output means also communicates to a designer the respective Reynolds numbers of all the number of focusing lens.
7. The computer system of claim 5 , further comprising:
computer processor means for determining the orifice diameter of an exit nozzle of the aerodynamic focusing lens stack design operating in a choked mode to lock the operating pressure and flow, by solving for the orifice diameter (d exitnozzle ) of the exit nozzle in the
Prandtl
formula
:
Q
exitnozzle
=
π
(
d
exitnozzle
2
)
2
·
R
0
T
top
M
·
γ
(
2
γ
+
1
)
γ
+
1
γ
-
1
,
where Q exitnozzle is estimated using the formula
Q
1
=
Q
2
·
P
2
P
1
for the pressure downstream of the last focusing lens, and the pressure downstream of the last focusing lens is itself determined from the final iteration of step (c); and
wherein the output means also communicates to a designer the orifice diameter of the exit nozzle.
8. A computer program product comprising:
a computer useable medium and computer readable code embodied on said computer useable medium for causing the automatic determination of an optimal aerodynamic focusing lens stack design based on a set of design parameters, said computer readable code comprising:
computer readable program code means for causing a computer to receive as input the following design parameters: (1) the particle size range to be considered (d particle (min) , d particle (max) ); particle density of the particle size range to be considered (ρ particle ); (2) characteristics of the gas to be flowed through the aerodynamic focusing lens stack design, including dynamic viscosity (μ), standard gas mean free path (λ standard ), heat ratio (γ), gas constant (R), molecular mass (M), and flow type, either isothermal flow or isentropic flow; (3) the temperature (T[ 1 ]) and pressure (P[ 1 ]) immediately upstream of a first focusing lens [i=1] of the aerodynamic focusing lens stack design; (4) a flow rate through the aerodynamic focusing lens stack equivalent at atmosphere pressure (Q equ ); and (5) a Stokes number range defining the focusing tightness (Stk min , Stk max );
computer readable program code means for causing the computer to determine, based on said received design parameters, the number of focusing lenses and their respective orifice diameters (d lens [i]) required to focus the particle size range to be considered, by:
(a) solving for the orifice diameter (d lens [i]) of the i th focusing lens, in the Stokes number equation: FOCUS(T[i], Q[i], P[i], λ standard , μ, d lens [i], d particle [i], ρ particle , Stk max )=0, beginning with the first focusing lens [i=1] where d particle [1]=d particle(max) and
Q
[
1
]
=
Q
equ
(
P
atm
P
[
1
]
)
;
(b) using the value of the orifice diameter (d lens [i]) in step (a) to solve for a new maximum particle size d particle [i+1] to be focused in the next [i+1] th focusing lens, in the Stokes number equation: FOCUS(T[i], Q[i], P[i], λ standard , μ, d lens [i], d particle [i+1], ρ particle , Stk min )=0;
(c) determining the pressure drop across the [i] th focusing lens by solving for a pressure P[i+1] downstream of the [i] th focusing lens and upstream of the next [i+1] th focusing lens, in the Prandtl derivation: DROP (T[i], Q[i], P[i], P[i+1], γ, R, M)=0;
(d) setting the temperature T[i+1] and flow rate Q[i+1] of the next [i+1] th focusing lens according to: if the flow type is isothermal flow, then T[i+1]=T[i] and
Q
[
i
+
1
]
=
Q
[
i
]
(
P
[
i
]
P
[
i
+
1
]
)
=
Q
equ
(
P
atm
P
[
i
+
1
]
)
;
and if the flow type is isentropic flow, then
T
[
i
+
1
]
=
T
[
i
]
(
P
[
i
+
1
]
P
[
i
]
)
γ
-
1
γ
and
Q
[
i
+
1
]
=
Q
[
i
]
(
P
[
i
]
P
[
i
+
1
]
)
=
Q
equ
(
P
atm
P
[
i
+
1
]
)
1
γ
;
and
(e) setting i+1 and iteratively performing steps (a) through (d) using the values for d particle [i+1], P[i+1], T[i+1], and Q[i+1] determined in the previous iteration, until d particle [i+1] in step (b) is less than d particle (min) ; and
computer readable program code means for outputting to a designer the number of focusing lenses and their respective orifice diameters (d lens [i]) determined to be required to focus the particle size range to be considered.
9. The computer program product of claim 8 , computer readable program code means for causing the computer to determine the flow stability through each focusing lens of the aerodynamic focusing lens stack design by solving for the Reynolds number (Re[i]) in the formula:
Re
[
i
]
=
(
Q
[
i
]
·
d
lens
[
i
]
1000
·
60
·
π
·
(
d
lens
[
i
]
2
)
2
)
(
ρ
μ
)
,
where ρ is the density of the gas; and
wherein the computer readable program code means for outputting to a designer also provides as output to the designer the respective Reynolds numbers of all the number of focusing lens.
10. The computer program product of claim 8 ,
computer readable program code means for causing the computer to determine the orifice diameter of an exit nozzle of the aerodynamic focusing lens stack design operating in a choked mode to lock the operating pressure and flow, by solving for the orifice diameter (d exitnozzle ) of the exit nozzle in the Prandtl formula:
Q
exitnozzle
=
π
(
d
exitnozzle
2
)
2
·
R
0
T
top
M
·
γ
(
2
γ
+
1
)
γ
+
1
γ
-
1
,
where Q exitnozzle is estimated using the formula
Q
1
=
Q
2
·
P
2
P
1
for the pressure downstream of the last focusing lens, and the pressure downstream of the last focusing lens is itself determined from the final iteration of step (c); and
wherein the computer readable program code means for outputting to a designer also provides as output to the designer the orifice diameter of the exit nozzle.