THERMAL EFFECT ON MASS FLOW-RATE OF SONIC NOZZLE

Main Article Content

Chao WANG Hong-bing DING Gang WANG

Abstract

Sonic nozzles are widely used as flow measurement and transfer standard. The thermal effect of sonic nozzle is significant at low Reynolds number. It includes two correction factors, CT for the thermal boundary layer and Cα for constrained thermal deformation of throat area. Firstly, using the similarity solution, the formula for correction factor CT over wall temperature range from 0.8T0 to 1.2T0 was obtained. For γ = 1.33, CT = 1 - 3.800Re-1/2ΔT/T0; for γ = 1.4, CT = 1 - 3.845Re-1/2ΔT/T0; for γ = 1.67, CT = 1 - 4.010Re-1/2ΔT/T0. Secondly, thermal and stress models for partially constrained expansion were built. Unlike the free expansion, truth slopes of Cα for three nozzles are +1.74×10-6, -2.75×10-5 and -3.61×10-5, respectively. Lastly, the experimental data of copper nozzle was used to validate present results. It revealed that modified experimental values are in good agreement with the present result.

Article Details

How to Cite
WANG, Chao; DING, Hong-bing; WANG, Gang. THERMAL EFFECT ON MASS FLOW-RATE OF SONIC NOZZLE. Thermal Science, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2228>. Date accessed: 26 sep. 2017. doi: https://doi.org/10.2298/TSCI151104146D.
Section
Articles
Received 2017-03-06
Accepted 2017-03-13
Published 2017-03-13

References

[1] Yin Z. Q., et al., Discharge coefficient of small sonic nozzles, Thermal Science, 18(2014), 5, pp. 1505-1510
[2] ISO 9300, Measurement of gas flow by means of critical flow venturi nozzles, British Standard, October 21, 2005
[3] Wright, J. D., et al., Thermal effects on critical flow venturis, Proceedings, ISSFM 9th, Arlington, Virginia, April 14-17, 2015
[4] Ünsal, B., et al., Numerical assessment of discharge coefficient and wall temperature dependence of discharge coefficient for critical-flow Venturi nozzles, Proceedings, ISSFM 9th, Arlington, Virginia, April 14-17, 2015
[5] Bignell, N., Choi, Y. M., Thermal effects in small sonic nozzles, Flow Measurement and Instrumentation, 13(2002), 1, pp.7-22
[6] Li, C. H., Mickan, B., Flow characteristics and entrance length effect for MEMS nozzles, Flow Measurement and Instrumentation, 33(2013), pp. 212-217
[7] Hu, C. C., et al., Discharge characteristics of small sonic nozzles in the shape of pyramidal convergent and conical divergent, Flow Measurement and Instrumentation, 25(2012), pp. 26-31
[8] Illingworth, C. R., The laminar boundary layer associated with retarded flow of a compressible fluid, ARC RM 2590, 1946
[9] Li, T. Y., Nagamatsu, H. T., Similar solutions of compressible boundary-layer equations, Journal of the Aeronautical Sciences (Institute of the Aeronautical Sciences), 22(1955), pp. 607-617
[10] Cohen, C. B., Reshotko, E., The compressible laminar boundary layer with heat transfer and arbitrary pressure gradient, NACA Report 1294, 1956
[11] Ball, K. O. W., Similarity solutions for the compressible laminar boundary layer with heat and mass transfer, Physics of Fluids, 10(1967), 8, pp. 1823-1826
[12] Back, L. H., Acceleration and cooling effects in laminar boundary layers-subsonic, transonic, and supersonic speeds, AIAA Journal, 8(1970), 4, pp. 794-802
[13] Aziz, A., A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Communications in Nonlinear Science and Numerical Simulation, 14(2009), 4, pp. 1064-1068
[14] Kendoush, A. A., Theoretical analysis of heat and mass transfer to fluids flowing across a flat plate, International Journal of Thermal Sciences, 48(2009), 1, pp. 188-194
[15] Tang, S. P., Theoretical determination of the discharge coefficients of axisymmetric nozzles under critical flows, Project SQUID Technical Report, PR-118-PU, 1969
[16] Geropp, D., Laminare Grenzschichten in ebenen und rotation-symmetrischen Lavaldüsen, Deutsche Luft- und Raumfahrt Forschungsbericht, 1972, pp. 71–90 (in German)
[17] Ishibashi, M., Takamoto, M., Theoretical discharge coefficient of a critical circular-arc nozzle with laminar boundary layer and its verification by measurements using super-accurate nozzles, Flow Measurement and Instrumentation, 11(2000), pp. 305–313
[18] Johnson, A. N., et al., Numerical characterization of the discharge coefficient in critical nozzles, Proceedings of the NCSL Workshop and Symposium, Albuquerque, New Mexico, USA, 1998, pp. 407–422
[19] Teodorescu, P. P., Introduction to Thermoelectricity, Treatise on Classical Elasticity. Springer Netherlands, (2013), pp: 671-698
[20] Thomas, B. G., et al., Analysis of thermal and mechanical behaviour of copper molds during continuous casting of steel slabs, Iron and Steelmaker(USA), 25(1998), 10, pp. 125-143
[21] Park, J. K., et al., Analysis of thermal and mechanical behaviour of copper mould during thin slab casting, 83rd Steelmaking Conference Proceedings, (Pittsburgh, PA, March 26-29, 2000), 83(2000), pp. 9-22
[22] Cragun, R., Howell, L. L., A constrained thermal expansion micro-actuator, Micro - electro - mechanical Systems (MEMS), (1998), pp. 365-371
[23] Isfahani, A. H. G., Brethour, J. M., Simulating thermal stresses and cooling deformations, Die Casting Engineer, (2012), pp. 34-36
[24] Ansola, R., et al., Evolutionary optimization of compliant mechanisms subjected to non-uniform thermal effects, Finite Elements in Analysis and Design, 57(2012), pp: 1-14
[25] Stavely, R. L., Design of contact-aided compliant cellular mechanisms for use as passive variable thermal conductivity structures, Doctor Thesis, The Pennsylvania State University, USA, 2013
[26] Schlichting, H., Gersten, K., Boundary-layer theory, Springer, 8th edition, March 22, 2000
[27] Johnson, A., Numerical characterization of the discharge coefficient in critical nozzles, Doctor Thesis, The Pennsylvania State University, Pennsylvania, USA, 2000
[28] Hall, I. M., Transonic flow in two-dimensional and axially-symmetric nozzles, Quarterly Journal of Mechanics and Applied Mathematics, 15(1962), 4, pp. 487–508
[29] Wang, C., et al.. Influence of wall roughness on discharge coefficient of sonic nozzles, Flow Measurement and Instrumentation, 35(2014), pp. 52-62
[30] Fluent Inc., Fluent user’s guide. Fluent Inc.; 2003
[31] Versteeg, H. K., Malalasekera, W., An introduction to computational fluid dynamics: the finite volume method, Wiley Press, New York, 1995
[32] Sridhar, M. R., Yovanovich, M., Review of elastic and plastic contact conductance models-Comparison with experiment, Journal of Thermophysics and Heat Transfer, 8(1994), 4, pp. 633-640
[33] Ding, H. B., et al., An analytical method for Wilson point in nozzle flow with homogeneous nucleating. International journal of heat and mass transfer, 73(2014), pp. 586-594