Creating a better mass flow meter
05/01/2004
The mass flow meter (MFM), in its current design, is good but has limitations — especially as process requirements change. Standard configurations in MFM designs are being challenged by a need to provide more reliable and accurate readings in spite of the increased thermodynamic difficulties with current chemicals and processes.
The principle behind MFMs is clever but fairly straightforward. If tubing carries fluid (gas or liquid) through a heated region, the fluid temperature will rise in proportion to the amount of heat energy it receives. The rise in temperature and the energy flow rate (i.e., power) correspond to the fluid flow rate. Calibration requires consideration of such factors as pressure, viscosity, density, specific heat, and ambient temperature, but the underlying thermal principle remains the same.
Consider the basic parameters: temperature rise, specific heat, and power. If the power supplied is not lost or confused by other heat or cooling sources, it would seem like a dependable measurement value. Specific heat may vary with conditions, but it is a fundamental property of the fluid. If conditions are repeatable, the value for specific heat is repeatable.
But what about temperature? How does one know that the temperatures being measured are relevant? There is a fundamental physical principle about any thermometer that should make one suspicious: a thermometer can only measure its own temperature. To measure the temperature of anything else, the thermometer must be in equilibrium with it. How can equilibrium be assured?
Taking a temperature. The change in fluid temperature has to be measured or there is no flow measurement. There are complicated equations (Graetz, late 1800s) relating to forced convection and heat transfer influencing a nearby temperature, which can be used for measurement. The equations say that a temperature A (e.g., the fluid) can be mathematically related to another temperature B (e.g., the heat source), provided the conditions are known and consistent. The MFM measures B, whereas the required temperature is A. However, a close look shows there are inconsistencies. Conditions can — and do — change. One must be very careful that the use of B to mean A doesn't turn into a case of apples representing oranges.
Figure 1 illustrates the (thermal) MFM principle. Standard configurations include a tube with heating element wires wrapped around it. The element heats the fluid flowing through the tube, and the fluid also cools the element. The electrical resistance of the element increases with temperature. Thus, the power circuitry can measure resistance and temperature. For a given power level, the element temperature varies with fluid flow. The element heats, the fluid cools, and the balance point (the measurement) is an indication of fluid flow.
 Figure 1. A typical illustration of the (thermal) MFM principle. |
The element is commonly divided into two sections. The section at fluid inlet is at a colder temperature [T(in)] because the colder fluid is a more effective coolant. The section at fluid outlet is hotter [T(out)] because the heated fluid is a less effective coolant. The difference between T(out) and T(in) will show up as a voltage signal as a result of the effect on circuit resistance, which then becomes the flow-rate signal.
Since fluid mass in motion always produces the flow response, all flow meters could be called mass flow meters. The MFM measures flow but doesn't control it. The mass flow controller (MFC) is an MFM in combination with a suitable regulating valve, which is operated by a (generally electronic) controller using signals from the MFM to achieve and maintain flow control. The regulating valve is another component with a tough assignment, which needs improvement and can be a separate subject.
No material or fluid can be instantaneously heated. Even light beams take time, and heat travels far more slowly. Figure 1 shows that if the fluid enters the tube at temperature T1 (throughout its cross section), the location of T1 moves inward as the fluid moves through the tube. At the entrance, the fluid and tube are all at T1. As the fluid moves, the tube gets hotter, and the surface of the fluid column gets hotter. T1 is not the same as T(in). In the heated area, the tube temperature must be hotter than the fluid temperature because the difference is required for heat to flow — no temperature difference, no heat flow.
The challenges. If the changing edge location of T1 does not reach the center of the fluid column, then there's a portion of the fluid flow that does not contribute to the electrical signal at all. The heated portion is thus a dynamic portion. The highest temperatures have to be outside to make heat flow inside. While there is a relationship between outside and inside temperature, it's not a simple one. Use of outside temperature to measure flow — because it's related to inside temperature — is a challenging task. And the challenges do not stop there. Consider these factors:
- The fluid-flow velocity at the tubing wall is nearly zero, while the maximum is at the center. This means the temperature gradient along the fluid column radius is a complicated function that must be accounted for in an accurate flow signal.
- At an interface, such as the fluid-tubing wall, there is almost always some jostling of temperature gradient due to material properties. If, in service, the tubing wall changes due to corrosion or deposit, further jostling of the flow signal occurs.
- A temperature drop through the thickness of the tubing wall has to exist for heat to flow. This will be a function of power density (such as W/cm2), wall thickness, and material thermal conductivity. If any corrosion occurs, the wall gets thinner and the corrosion layer introduces another interface of different thermal conductivity. It may also roughen the surface, changing the laminarity of the fluid flow surface and the heat flow into the fluid.
- Figure 1 does not show the electrical insulation that would support the heating elements. For MFMs, this insulation typically is an elevated-temperature adhesive that bonds the tubing and the elements into an assembly. Electrical insulation tends to have poor heat transfer just like thermal insulation. The underlying mechanisms of electrical and thermal conductivities tend to be the same. This means that at the tubing outer wall, there is another dissimilar material interface that would jostle the temperature gradient. In addition, because of the thermal expansion mismatch between the insulation and the tubing, the bond may be lost over part of the surface, further jostling the temperature gradient in an uneven fashion.
- There is a temperature drop across the layer of insulation depending on its thickness and thermal properties.
- There is another interface between the insulation and the heating element with uncertain adhesive bond, again jostling the temperature gradient.
All of these factors add questions of accuracy and reliability on the chance of T(in) and T(out) being valid indicators of fluid temperature. In many respects, considering the difficulties, it's remarkable that MFMs work as well as they do. Most of the MFM history involves gaseous fluids. With increased need for liquid measurement, the problems increase dramatically.
First, there is the risk of change of state of dissolved gases bubbling out of solution, severely disrupting thermal conditions in the flow tube. Heat of the gases in the solution may add to the measurement confusion. Second, the risk of boiling and the heat of vaporization cause similar disruptions.
To minimize the problems, the flow tube is usually a small capillary. Small size minimizes the extent of accumulated disruptions in temperature gradient and improves the chances that T(in) and T(out) represent fluid temperature and thus fluid flow rate. Small capillaries bring up another problem, however, in that flow rate through the capillary may be insufficient for the application. A bypass structure is then used, but it introduces another uncertainty in knowing the proportion of total flow bypassed (see Fig. 2). Typically, the capillary only carries 5% of the total flow; thus, a 1% error in the measured flow may mean a 20% error in the total flow.
 Figure 2. Bypass structures can be used for the flow rate measurement. |
The small capillary can also improve the chance that thermal equilibrium can be reached in a small space so that the actual measurement is less confounded by the complex dynamic temperature gradient. This brings up an interesting point: the temperature measured is T(out) vs. T(in), but the measurement temperature required is the fluid temperature (power required = specific heat × temperature change × mass flow), not the heating-element temperature. Measuring temperature at the far end of the heat flow path, even at supposed equilibrium, invites many uncertainties.
Why wouldn't it make sense to measure the fluid temperature in the first place, instead of the heating-element temperature? Obviously, it's very hard to do without stirring up many other problems. But here's another question: If thermal equilibrium in the capillary makes sense, could it be possible to redesign the capillary so that 100% of the flow reaches equilibrium, even including the change of state from liquid to gas? If so, nearly insurmountable problems are reoriented into simply becoming part of the measurement signal.
 Figure 3. New design places temperature sensors in the flow path and out of the heat path to minimize errors. |
Figure 3 shows a design that measures the change in fluid temperature in a way that is less vulnerable to assumptions about thermal conditions. The temperature sensors are located internal to the flow path and out of the heat flow path to minimize errors introduced by corrosion, debris, changing thermal gradients, etc. The heat source is also internal to minimize unaccounted losses to surroundings. The flow path is designed to keep the fluid in the sensing region longer to facilitate equilibrium. In doing so, there's a much better chance to measure all of the flow (eliminating bypass uncertainties) and achieve change of state (liquid to gas) if required. Gases or liquids, mixtures of compatible gases and liquids, even combinations of gases and combinations of liquids can be measured and vaporized (provided the combinations are known and one of the flow rates, gas or liquid, is known).
The complexities, compromises, and uncertainties of pumps, bubblers, and other traditional arrangements are reduced,compared to conventional designs. This approach appears to support a simpler, less expensive, and more accurate way to get the job done in mass flow metering.
Nicholas Gralenski received his BS in physics from the U. of Massachusetts in 1954. While working at Watkins-Johnson Co. for 35 years, Gralenski was the originator of atmospheric-pressure chemical-vapor deposition equipment and techniques as a staff scientist. He is the founder of Creative Associates, 1797 Cheryl Way, Aptos, CA 95003; ph 831/688-4671, fax 831/662-8743, e-mail [email protected].