Experimental and numerical curved flow study for metrology purposes

Abstract

Most of the current volumetric flow measurement methods represent an important investment for many industries. However, when the accuracy requirements for the processes are not too high, curved pipes could be used as primary elements for this purpose. Unfortunately, there is a lack of information for this device as flowmeter, so more experimental and numerical research is required for its full characterization. This paper reports the experimental work conducted on three commercial 90º elbows, installed horizontally. All of them were short curvature radius with 0.75, 1 and 1.5 inches of internal diameter; water maintained at 24 ºC was employed for the experiments. Pressure taps on the elbows were located at 45 º along the curvature radius, on both inside and outside the wall. The performance of the elbow was compared against a calibrated orifice plate. A numerical study using CFD-2000 provided more information about the pressure and velocity fields, so it was posible to develop a model to describe the curvature effects on the radial pressure gradient. Experimental results show that there is a greater sensibility of the element when the curvature radius decreases, this means, a larger pressure gradient is obtained. If this radial pressure gradient is used in the typical equation for the orifice plate, a good concordance between the measurements of both elements is observed.

Solving the Partial Differential Problems Using Maple

“…The methods adopted in [1][2][3][4][5] are different from the methods used in this paper, and [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] studied the evaluation of the partial derivatives of different types of multivariable functions using differentiation term by term theorem and complex power series method. [25] considered two differential equations whose independent variables involve the partial derivatives. [26] discussed the distance functions whose expressions contain the partial derivatives, and [27] found the solutions of some type of partial differential equation.…”