Assessment of a Simpler Friction Factor in an Algebraic Solution for Adiabatic Coiled Capillary Tubes

2020 ◽  
Vol 28 (04) ◽  
pp. 2050033
Author(s):  
Thiago Torres Martins Rocha ◽  
Sara Isabel De Melo Resende ◽  
Hélio Augusto Goulart Diniz ◽  
Fernando Antônio Rodrigues Filho ◽  
Raphael Nunes De Oliveira
Keyword(s):  
Friction Factor ◽  
Algebraic Solution ◽  
Maximum Deviation ◽  
Empirical Correlations ◽  
Capillary Tubes ◽  
Average Deviation ◽  
Flow Rates ◽  
Mass Flow Rates ◽  
Rms Error ◽  
Dimensionless Correlations

In this work, the performance of an existing algebraic solution for adiabatic coiled capillary tubes, in subcritical cycles, is investigated. However, the C-M&N friction factor, commonly used, was replaced by Schmidt friction factor, which is less complex. Two existing dimensionless correlations were also evaluated for comparison. To assess the effect of altering the friction factor, experimental data collected in the literature were used as reference. Analyzing the present results and that with C-M&N friction factor, it was observed that adopting the Schmidt friction factor does not cause a relevant impact on the solution. The deviations of the predicted versus experimental mass flow rates were comprised in a range between –8% and 12%, with average deviation (AD), absolute average deviation (AAD) and root mean square (RMS) error of –0.1%, 2.7% and 3.4%, respectively. The empirical correlations presented unsatisfactory results, with maximum deviation around 40%. Therefore, it was concluded that using the Schmidt friction factor is adequate to reduce the complexity of the algebraic solution and to maintain the accuracy.

EXPERIMENTAL INVESTIGATION OF R134a FLOWING THROUGH ADIABATIC HELICALLY COILED CAPILLARY TUBES

2012 ◽  
Vol 20 (01) ◽  
pp. 1250001 ◽  
Author(s):  
JATUPORN KAEW-ON ◽  
SAKARIN CHINGULPITAK ◽  
SOMCHAI WONGWISES
Keyword(s):  
Mass Flow ◽  
Flow Characteristic ◽  
Flow Conditions ◽  
Capillary Tubes ◽  
Local Pressure ◽  
Flow Rates ◽  
Temperature Distributions ◽  
Coil Diameter ◽  
Copper Tubing ◽  
Mass Flow Rates

The effects of the relevant parameters on the flow characteristic of R134a flowing through adiabatic helical capillary tubes were experimentally studied. The capillary tubes' diameter, coil diameter, and parameters relating to flow conditions such as inlet pressures and degree of subcooling were the major parameters investigated. The test section was made from copper tubing with inner diameters of 1.07, 1.27, and 1.62 mm. The coil diameters were 25, 50, and 100 mm. The local pressure and temperature distributions along the length of the capillary tubes were measured at inlet pressures ranging from 10 to 14 bar, mass flow rates from 8 to 20 kg/h, and degrees of subcooling from 0.5°C to 15°C. The metastable flow and the delay of vaporization of R134a are also presented and discussed. The results showed that the capillary diameter had more of a significant effect on the mass flow rate than the other variables.

Calculation of the Theoretical Critical Flow Rate of Saturated Steam

1982 ◽  
Vol 104 (1) ◽  
pp. 211-214
Author(s):  
J. W. Murdock
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Theoretical Method ◽  
Ideal Gas ◽  
Saturated Steam ◽  
Critical Flow ◽  
Maximum Deviation ◽  
Average Deviation ◽  
Flow Rates ◽  
Critical Flow Rate

This paper is concerned with the computation of the theoretical critical flow of dry saturated steam through passages over a range of 1 psia (7 kPa) to the critical pressure of 3208.2 psia (22.12 MPa). Two computational methods are used: a theoretical method using ideal gas relations, and a flow maximization method using actual saturated steam properties. An equation is developed and based on the theoretical equation that yields flow rates that have an average deviation of 0.1 percent and a maximum deviation of 0.3 percent from the flow rate found by flow maximization. It is also demonstrated that Napier’s equation currently recommended by PTC 25.3-1976 “Safety and Relief Valves” is unsatisfactory for the calculation of theoretical critical flow rates.

scholarly journals Net-exergetic, hydraulic and thermal optimization of coaxial heat exchangers using fixed flow conditions instead of fixed flow rates

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Tobias Blanke ◽  
Markus Hagenkamp ◽  
Bernd Döring ◽  
Joachim Göttsche ◽  
Vitali Reger ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Mass Flow ◽  
Flow Rate ◽  
Heat Exchangers ◽  
Circular Ring ◽  
Flow Conditions ◽  
Flow Rates ◽  
Mass Flow Rates ◽  
Pipe Radius

AbstractPrevious studies optimized the dimensions of coaxial heat exchangers using constant mass flow rates as a boundary condition. They show a thermal optimal circular ring width of nearly zero. Hydraulically optimal is an inner to outer pipe radius ratio of 0.65 for turbulent and 0.68 for laminar flow types. In contrast, in this study, flow conditions in the circular ring are kept constant (a set of fixed Reynolds numbers) during optimization. This approach ensures fixed flow conditions and prevents inappropriately high or low mass flow rates. The optimization is carried out for three objectives: Maximum energy gain, minimum hydraulic effort and eventually optimum net-exergy balance. The optimization changes the inner pipe radius and mass flow rate but not the Reynolds number of the circular ring. The thermal calculations base on Hellström’s borehole resistance and the hydraulic optimization on individually calculated linear loss of head coefficients. Increasing the inner pipe radius results in decreased hydraulic losses in the inner pipe but increased losses in the circular ring. The net-exergy difference is a key performance indicator and combines thermal and hydraulic calculations. It is the difference between thermal exergy flux and hydraulic effort. The Reynolds number in the circular ring is instead of the mass flow rate constant during all optimizations. The result from a thermal perspective is an optimal width of the circular ring of nearly zero. The hydraulically optimal inner pipe radius is 54% of the outer pipe radius for laminar flow and 60% for turbulent flow scenarios. Net-exergetic optimization shows a predominant influence of hydraulic losses, especially for small temperature gains. The exact result depends on the earth’s thermal properties and the flow type. Conclusively, coaxial geothermal probes’ design should focus on the hydraulic optimum and take the thermal optimum as a secondary criterion due to the dominating hydraulics.

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