
Implications of Changing Inlet Conditions Using Diaphragm Pumps
Whenever a gas pump is used, there are certain requirements for its flow rate. As shown in a previous blog post, flow can be presented using volume flow or mass flow. For maximum reliability and precision, the flow rate of KNF gas pumps is measured with the help of mass flow meters and then converted to a volumetric flow. This volumetric flow is specified in accordance with ISO 8778 at 20 °C (293.15 °K, 68 °F) and 1,000 mbar absolute (14.5 psi, 750.06 torr).
Real Life Implications
The specified conditions do not reflect the conditions that occur in most applications. Imagine an application that requires a very accurate mass flow of a gas. In this application, a tank filled with gas is stored outside. The outlet of the tank is connected to a pump and the pump transfers the gas to an apparatus. This apparatus requires a constant mass flow of gas. Therefore, the mass flow is measured directly after the pump, between the pump and the apparatus. The outdoor storage tank is subject to strong seasonal temperature changes. The pressure in the tank as well as the pressure in the apparatus is always constant, resulting in a constant inlet and outlet pressure of the pump.
Over the year, the mass flow rate measured between the pump and the apparatus fluctuates considerably even though the inlet and outlet pressure of the pump are constant and describe the operation point of a pump. In the wintertime, the mass flow is much higher than during the summer. After checking the equipment and finding that it works as intended, one question arises “Does mass flow rate change with temperature?”. In the following, we will provide the theoretical background necessary to answer this question.
Theoretical Basics of Positive Displacement Pumps
Diaphragm pumps are positive displacement pumps, which means that their working principle is based on changing the volume of a chamber or cavity thus moving fluid in and out. The volume flow rate of a positive displacement pump at the inlet can therefore be described as:
\begin{equation} \dot{V}_{\text{S,eff}} = n(V_1 - V_3 \Pi^{1/\gamma}) \end{equation}
related to the thermal reference state of the inlet condition with the inlet pressure \(p_{\text{i}}\) and inlet temperature \(T_{\text{i}}\) . Where \( \eta \) is the rotational speed, \(V_1\) respective \(V_3\) is the working chamber volume at maximum downstroke position or maximum upstroke position, \( \Pi := \frac{p_{\text{o}}}{p_{\text{i}}} \) is the pressure ratio with the outlet pressure \(p_{\text{o}}\) and the isentropic exponent \( \gamma \).
Gas Temperature Affects Mass Flow
The conveyed mass flow is therefore calculated as follows:
\(\dot{m} = \rho_{\text{i}} \dot{V}_{\text{S,eff}}\)
with the gas density \( \rho_{\text{i}}\) at the inlet of the pump, and also corresponds to the measured mass flow, provided the pump is operating ideally. Together with the ideal gas equation \( \varrho = \frac{p}{RT} \), the influence of the inlet temperature and pressure on the mass flow becomes more visible.
\(\dot{m} = \frac{p_{\text{i}}}{RT_{\text{i}}} \dot{V}_{\text{S,eff}}\)
The effective suction speed \( \dot{V}_{\text{S,eff}} \) of a pump is constant for constant pressure ratio \( \pi \), constant fluid represented by the isentropic exponent \( \gamma \) and constant rotational speed \( \eta \). Changing only the inlet temperature, the mass flow will change as well like the equation above indicates. For increasing inlet temperature, the mass flow reduces and vice versa for decreasing inlet temperature.
Reducing Uncertainty in Flow and Suction at Changing Inlet Conditions
To reduce this uncertainty, it is desirable to divide the measured mass flow rate by the inlet density to obtain the effective suction speed. The effective suction speed is independent of the thermal inlet condition and the influence of the thermal inlet conditions becomes directly visible by calculating or analyzing the mass flow.
Finally, even though the pump is seemingly working at a constant operation point, meaning the inlet and outlet pressures are constant, changing inlet conditions, such as inlet temperature, will change the amount of gas transferred and therefore the true operating point of the pump.
Get in touch with our experts to discuss your mass flow requirements!
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