The Performance of Transit Time Flowmeters in Heated Gas Mixtures

An ultrasonic transit time flowmeter was tested over Reynolds numbers from 1000 to 100 000 in a calibration facility that generates gas flows with controlled temperature and composition. The gas mixtures were composed of air, nitrogen, carbon dioxide, water vapor, and argon, and the mixture temperature ranged from 290 K to 450 K. The test program was conducted to determine the sensitivity of the flowmeter output to gas composition and temperature and to find the appropriate dimensionless quantities for the presentation of calibration results. Plots of discharge coefficient versus Reynolds number collapse the data well for all of the conditions tested. Comparisons between the experimentally measured discharge coefficients and those predicted by computer models using postulated velocity profiles are presented, and they show good qualitative agreement. The effects of thermal expansion on sound path length and pipe diameter were significant over the tested temperature range. NOMENCLATURE A Cross sectional area of pipe c Sound speed Cd Discharge coefficient kT Path length thermal correction m Reference mass flow tup , tdn Transit times up and downstream V Path mean velocity (of the fluid) VB Bulk mean velocity (of the fluid) Length of the sound path Angle of sound path Gas density Thermal expansion coefficient subscripts and superscripts H Handbook value m Meter value 0 Reference temperature condition T Actual temperature condition INTRODUCTION In recent years, ultrasonic transit time flowmeters designed for use in gas flows have become commercially available. These meters have good accuracy, do not obstruct the flow (or lead to any significant pressure losses), and have a wide flow rangeability (100 to 1 or more). Transit time flowmeters are good candidates for the measurement of gas mixtures that vary in temperature and composition, such as vehicle exhaust, the exhaust from furnaces, or humid air. PRINCIPLE OF OPERATION An ultrasonic transit time flowmeter uses two ultrasonic transducers to transmit sound pulses alternately upstream and downstream through the flow (Lynnworth, 1989, Brown, 1991). The times required for the sound to travel in the opposite directions can be used to calculate both the sound speed and the mean fluid velocity along the path followed by the sound (“path mean velocity”). The acoustic transducers are generally positioned flush with the inner surface of the pipe wall and at an angle to the pipe axis ( ). The reflective 1 Copyright 1998 by ASME Figure 1. The arrangement of ultrasonic, pressure, and temperature sensors in the tested transit time flowmeter. arrangement used in the present test is shown in Fig. 1. For the transit time flowmeter, assuming only axial velocity components, the governing equations are: V t t dn up 2 1 1 cos( ) , (1) c t t dn up 2 1 1 . (2) The path mean velocity (V ) may be multiplied by a discharge coefficient (Cd ) to obtain a value for the bulk mean velocity (VB ),