Methods and apparatus for pressure based mass flow ratio control
A system and method for dividing a single mass flow into secondary flows of a desired ratio. The system and method include paths for the secondary flows that include a laminar flow element and two pressure sensors. The nonlinear relationship between flow and pressure upstream and downstream of the laminar flow elements can be transformed into a function comprised of the upstream and downstream pressure that has a linear relationship with the flow. This transformation allows for flow ratio control applications using signals from pressure sensors even if there is no information the fluid species and the flow rate into the flow ratio controller.
1. A system for dividing a single mass flow into secondary flows comprising:
an inlet configured to receive an inlet flow;
secondary flow lines connected to the inlet, each secondary flow line including:
a flow path configured to carry a secondary flow with a secondary flow rate;
a pressure drop element configured to create a linear relationship between the secondary flow rate and a function of a pressure upstream of the pressure drop element and a pressure downstream of the pressure drop element;
a first pressure sensor configured to provide a first pressure signal dependent on the pressure upstream of the pressure drop element;
a second pressure sensor configured to provide a second pressure signal dependent on the pressure downstream of the pressure drop element; and
a valve configured to control the secondary flow rate based upon a control signal; and
a controller configured to calculate, utilizing the linear relationship, for each secondary flow line, a ratio of the secondary flow rate to a total flow rate based upon the first pressure signal and the second pressure signal and further configured to generate the control signal to each valve to obtain a desired ratio of secondary flow to the total flow rate.
2. The system of claim 1 wherein the pressure drop element is a laminar flow element.
3. The system of claim 2 wherein the laminar flow element is one of an annulus, bundled tubes, corrugated plates, or multiple-layer plates.
4. The system of claim 1 wherein the pressure drop element is a compressed laminar flow element.
5. The system of claim 1 wherein the pressure drop element is a flow nozzle or orifice.
6. The system of claim 1 further comprising a temperature sensor configured to measure the temperature of the inlet flow.
7. The system of claim 1 wherein the valves are located in the flow path of the secondary flow lines upstream from the upstream pressure sensor.
8. The system of claim 1 wherein the valves are located in the flow path of the secondary flow lines downstream from the pressure sensors.
9. The system of claim 8 wherein a single pressure sensor is used as the first pressure sensor for all secondary flow lines.
10. The system of claim 1 wherein the function of the pressure upstream of the pressure drop element and the pressure downstream of the pressure drop element is the following:
ƒ( Pu,Pd )= Pu 2 −Pd 2
where ƒ(Pu, Pd) is the function, Pu is the pressure upstream of the pressure drop element and Pd is the pressure downstream of the pressure drop element.
11. The system of claim 1 wherein the secondary flow rates are calculated by the following:
Q=k*ƒ ( Pu,Pd )
where Q is the secondary flow rate, ƒ(Pu, Pd) is the function of the pressure upstream of the pressure drop element and the pressure downstream of the pressure drop element, and k is a function of dimensions of the pressure drop element, fluid properties, and fluid temperature.
12. The system of claim 11 wherein k=k(∈, d, L, mw, r, μ, T) where ∈, d, and L are the dimensions of the pressure drop element, mw, r, and μ are the fluid properties, and T is the fluid temperature.
13. The system of claim 1 wherein the secondary flow rates can be determined based on a 3D map composed of calibration points having variables Pu, Pd, and Q where Q is the secondary flow rate, Pu is the pressure upstream of the pressure drop element and Pd is the pressure downstream of the pressure drop element.
14. A method for dividing a single mass flow into secondary flows of desired ratios of secondary flow rates, comprising;
receiving an inlet flow at an inlet;
dividing the inlet flow into secondary flow lines connected to the inlet, each secondary flow line including:
a flow path configured to carry a secondary flow with a secondary flow rate;
a pressure drop element configured to create a linear relationship between the secondary flow rate and a function of a pressure upstream of the pressure drop element and a pressure downstream of the pressure drop element;
a first pressure sensor configured to provide a first pressure signal dependent on a pressure upstream of the pressure drop element;
a second pressure sensor configured to provide a second pressure signal dependent on a pressure downstream of the pressure drop element; and
a valve configured to control the secondary flow rate based upon a control signal;
determining, by a controller, using the linear relationship, for each secondary flow line, a ratio of the secondary flow rate to a total flow rate based upon the first pressure signals and the second pressure signals; and
obtaining a desired ratio of secondary flow rate to the total flow rate by generating, by the controller, the control signal to each valve.
15. The method of claim 14 wherein the pressure drop element is a laminar flow element.
16. The method of claim 15 wherein the laminar flow element is one of an annulus, bundled tubes, corrugated plates, or multiple-layer plates.
17. The method of claim 14 wherein the pressure drop element is a compressed laminar flow element.
18. The method of claim 14 further comprising measuring the of the inlet flow using a temperature sensor.
19. The method of claim 14 wherein a single pressure sensor is used as the first pressure sensor for all secondary flow lines.
20. The method of claim 14 wherein the function of the pressure upstream of the pressure drop element and the pressure downstream of the pressure drop element is the following:
ƒ( Pu,Pd )= Pu 2 −Pd 2
where ƒ(Pu, Pd) is the function, Pu is the pressure upstream of the pressure drop element, and Pd is the pressure downstream of the pressure drop element.
21. The method of claim 14 wherein the secondary flow rates are determined by the following:
Q=k*ƒ ( Pu,Pd )
where Q is the secondary flow rate, ƒ(Pu, Pd) is the function of the pressure upstream of the pressure drop element and the pressure downstream of the pressure drop element, and k is a function of dimensions of the pressure drop element, fluid properties, and fluid temperature.
22. The method of claim 21 wherein k=k(∈, d, L, mw, r, μ, T) where ∈, d, and L are the dimensions of the pressure drop element, mw, r, and μ are the fluid properties, and T is the fluid temperature.
23. The method of claim 14 further comprising creating a 3D map composed of calibration points having variables Pu, Pd, and Q where Q is the secondary flow rate, Pu is the pressure upstream of the pressure drop element and Pd is the pressure downstream of the pressure drop element, and the controller determines the secondary flow rates based on the 3D map.