Turbulent Mixing and its Effects on Thermal Fatigue in Nuclear Reactors
The turbulent mixing of coolant streams of different
temperature and density can cause severe temperature fluctuations in
piping systems in nuclear reactors. In certain periodic contraction
cycles these conditions lead to thermal fatigue. The resulting aging
effect prompts investigation in how the mixing of flows over a sharp
temperature/density interface evolves. To study the fundamental
turbulent mixing phenomena in the presence of density gradients,
isokinetic (shear-free) mixing experiments are performed in a square
channel with Reynolds numbers ranging from 2-500 to 60-000.
Sucrose is used to create the density difference. A Wire Mesh Sensor
(WMS) is used to determine the concentration map of the flow in the
cross section. The mean interface width as a function of velocity,
density difference and distance from the mixing point are analyzed
based on traditional methods chosen for the purposes of
atmospheric/oceanic stratification analyses. A definition of the
mixing layer thickness more appropriate to thermal fatigue and based
on mixedness is devised. This definition shows that the thermal
fatigue risk assessed using simple mixing layer growth can be
misleading and why an approach that separates the effects of large
scale (turbulent) and small scale (molecular) mixing is necessary.
[1] S. Chapuliot, C. Gourdin, T. Payen, J.P. Magnaud, and A. Monavaon,
"Hydro-thermal-mechanical analysis of thermal fatigue in a mixing tee,"
in Nuclear Engineering and Design, vol. 235, 2005, pp. 575-596.
[2] K.J. Metzner and U. Wilke, "European THERFAT project - Thermal
fatigue evaluation of piping system tee-connections," in Nuclear
Engineering and Design, vol. 235, 2004, pp. 473-484.
[3] H.D. Kweon, J.S. Kim, and K.Y. Lee, "Fatigue Design of nuclear class 1
piping considering thermal stratification," in Nuclear Engineering and
Design, vol. 238, 2008, pp. 1265-1274.
[4] R. Kapulla, C. Dyck, M. Witte, J. Fokken, A. Leder, "Optical flow and
cross correlation techniques for velocity field calculation," in 2009
Conf. Proc. Lasermethoden in der strömungsmesstechnik, pp. 284-295.
[5] J. Fokken, R. Kapulla, S. Kuhn, C. Dyck, H.M. Prasser, "Stably
stratified isokinetic turbulent mixing layers: Comparison of PIVmeasurements
and numerical calculation," in 2009 Conf. Proc.
Lasermethoden in der strömungsmesstechnik, pp. 296-303.
[6] C. Walker, M. Simiano, R. Zboray, and H.M. Prasser, "Investigations
on mixing phenomena in single phase flow in a T-junction geometry,"
in Nuclear Engineering and Design, vol. 239, 2009, pp. 116-126.
[7] H. Rouse and J. Dodu, "Turbulent diffusion across a density
discontinuity," in Houille Blanche, vol. 10, 1955, pp. 522-532.
[8] J.S. Turner, "The influence of molecular diffusivity on turbulent
entrainment across a density interface," in Journal of Fluid Mechanics,
vol. 33, 1968, pp. 639-656.
[9] J.S. Turner, "Buoyancy effects in fluids," Cambridge: University Press,
2nd ed., 1980, 368 pp.
[10] H.J.S. Fernando, "Turbulent mixing in stratified fluids," in Annual
Review of Fluid Mechanics, vol. 23, 1991, pp. 455-493.
[11] P. Huq and R. Britter, "Mixing due to grid-generated turbulence of a
two-layer scalar profile," in Journal of Fluid Mechanics, vol. 285, 1995,
pp. 17-40.
[12] P. Huq and R. Britter, "Turbulence evolution and mixing in a two-layer
stably stratified fluid," in Journal of Fluid Mechanics, vol. 285, 1995,
pp. 41-67.
[13] E.C. Itsweire, K.N. Helland, and C.W. Van Atta, "Evolution of gridgenerated
turbulence in a stably stratified fluid," in Journal of Fluid
Mechanics, vol. 162, 1986, pp. 299-338.
[14] T.K. Barrett and C.W. Van Atta, "Experiments on the inhibition of
mixing in stably stratified decaying turbulence using LDA and LIF," in
Physics of Fluids, vol. 3, 1991, pp. 1321-1332.
[15] Jayesh and Z. Warhaft, "Probability distribution, conditional
dissipation, and transport of passive temperature fluctuations in grid
generated turbulence," in Physics of Fluids, vol. 4, 1992, pp. 292-307.
[16] Z. Bubnik, P. Kadlec, D. Urban, M. Bruhns, "Sugar Technologists
Manual," Bartens pub co. Berlin, 1995, pp. 125-170.
[17] H.M. Prasser, A. Böttger, and J. Zschau, "A new electrode-mesh
tomograph for gas-liquid flows," in Flow Measurement and
Instrumentation, vol. 9, 1998, pp. 111-119.
[18] J. Fokken, et al, "LIF-measurements and self similarity considerations in
a stably stratified isokinetic turbulent mixing layer," in 2010 Conf.
Proc. Lasermethoden in der strömungsmesstechnik, pp. 12-19.
[19] J. Fokken, R. Kapulla, G. Galgani, O. Schib, H.M. Prasser, "Stably
stratified isokinetic turbulent mixing layers: Investigation in a square
flow channel," in 2010 Conf. Proc. International Youth Nuclear
Congress, pp. 120.1-120.9.
[20] H. Tenekes, J.L. Lumley, "A first course in turbulence," MIT Press,
1972, 300 pp.
[21] C.G. Koop and F.K. Browand, "Instability and turbulence in a stratified
fluid with shear," in Journal of Fluid Mechanics, vol. 93, 1979, pp.
135-159.
[22] Xuequan E. and E.J. Hopfinger, "On mixing across an interface in
stably stratified fluid," in Journal of Fluid Mechanics, vol. 166, 1986,
pp. 227-244.
[1] S. Chapuliot, C. Gourdin, T. Payen, J.P. Magnaud, and A. Monavaon,
"Hydro-thermal-mechanical analysis of thermal fatigue in a mixing tee,"
in Nuclear Engineering and Design, vol. 235, 2005, pp. 575-596.
[2] K.J. Metzner and U. Wilke, "European THERFAT project - Thermal
fatigue evaluation of piping system tee-connections," in Nuclear
Engineering and Design, vol. 235, 2004, pp. 473-484.
[3] H.D. Kweon, J.S. Kim, and K.Y. Lee, "Fatigue Design of nuclear class 1
piping considering thermal stratification," in Nuclear Engineering and
Design, vol. 238, 2008, pp. 1265-1274.
[4] R. Kapulla, C. Dyck, M. Witte, J. Fokken, A. Leder, "Optical flow and
cross correlation techniques for velocity field calculation," in 2009
Conf. Proc. Lasermethoden in der strömungsmesstechnik, pp. 284-295.
[5] J. Fokken, R. Kapulla, S. Kuhn, C. Dyck, H.M. Prasser, "Stably
stratified isokinetic turbulent mixing layers: Comparison of PIVmeasurements
and numerical calculation," in 2009 Conf. Proc.
Lasermethoden in der strömungsmesstechnik, pp. 296-303.
[6] C. Walker, M. Simiano, R. Zboray, and H.M. Prasser, "Investigations
on mixing phenomena in single phase flow in a T-junction geometry,"
in Nuclear Engineering and Design, vol. 239, 2009, pp. 116-126.
[7] H. Rouse and J. Dodu, "Turbulent diffusion across a density
discontinuity," in Houille Blanche, vol. 10, 1955, pp. 522-532.
[8] J.S. Turner, "The influence of molecular diffusivity on turbulent
entrainment across a density interface," in Journal of Fluid Mechanics,
vol. 33, 1968, pp. 639-656.
[9] J.S. Turner, "Buoyancy effects in fluids," Cambridge: University Press,
2nd ed., 1980, 368 pp.
[10] H.J.S. Fernando, "Turbulent mixing in stratified fluids," in Annual
Review of Fluid Mechanics, vol. 23, 1991, pp. 455-493.
[11] P. Huq and R. Britter, "Mixing due to grid-generated turbulence of a
two-layer scalar profile," in Journal of Fluid Mechanics, vol. 285, 1995,
pp. 17-40.
[12] P. Huq and R. Britter, "Turbulence evolution and mixing in a two-layer
stably stratified fluid," in Journal of Fluid Mechanics, vol. 285, 1995,
pp. 41-67.
[13] E.C. Itsweire, K.N. Helland, and C.W. Van Atta, "Evolution of gridgenerated
turbulence in a stably stratified fluid," in Journal of Fluid
Mechanics, vol. 162, 1986, pp. 299-338.
[14] T.K. Barrett and C.W. Van Atta, "Experiments on the inhibition of
mixing in stably stratified decaying turbulence using LDA and LIF," in
Physics of Fluids, vol. 3, 1991, pp. 1321-1332.
[15] Jayesh and Z. Warhaft, "Probability distribution, conditional
dissipation, and transport of passive temperature fluctuations in grid
generated turbulence," in Physics of Fluids, vol. 4, 1992, pp. 292-307.
[16] Z. Bubnik, P. Kadlec, D. Urban, M. Bruhns, "Sugar Technologists
Manual," Bartens pub co. Berlin, 1995, pp. 125-170.
[17] H.M. Prasser, A. Böttger, and J. Zschau, "A new electrode-mesh
tomograph for gas-liquid flows," in Flow Measurement and
Instrumentation, vol. 9, 1998, pp. 111-119.
[18] J. Fokken, et al, "LIF-measurements and self similarity considerations in
a stably stratified isokinetic turbulent mixing layer," in 2010 Conf.
Proc. Lasermethoden in der strömungsmesstechnik, pp. 12-19.
[19] J. Fokken, R. Kapulla, G. Galgani, O. Schib, H.M. Prasser, "Stably
stratified isokinetic turbulent mixing layers: Investigation in a square
flow channel," in 2010 Conf. Proc. International Youth Nuclear
Congress, pp. 120.1-120.9.
[20] H. Tenekes, J.L. Lumley, "A first course in turbulence," MIT Press,
1972, 300 pp.
[21] C.G. Koop and F.K. Browand, "Instability and turbulence in a stratified
fluid with shear," in Journal of Fluid Mechanics, vol. 93, 1979, pp.
135-159.
[22] Xuequan E. and E.J. Hopfinger, "On mixing across an interface in
stably stratified fluid," in Journal of Fluid Mechanics, vol. 166, 1986,
pp. 227-244.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54055", author = "Eggertson and E.C. Kapulla and R and Fokken and J and Prasser and H.M.", title = "Turbulent Mixing and its Effects on Thermal Fatigue in Nuclear Reactors", abstract = "The turbulent mixing of coolant streams of different
temperature and density can cause severe temperature fluctuations in
piping systems in nuclear reactors. In certain periodic contraction
cycles these conditions lead to thermal fatigue. The resulting aging
effect prompts investigation in how the mixing of flows over a sharp
temperature/density interface evolves. To study the fundamental
turbulent mixing phenomena in the presence of density gradients,
isokinetic (shear-free) mixing experiments are performed in a square
channel with Reynolds numbers ranging from 2-500 to 60-000.
Sucrose is used to create the density difference. A Wire Mesh Sensor
(WMS) is used to determine the concentration map of the flow in the
cross section. The mean interface width as a function of velocity,
density difference and distance from the mixing point are analyzed
based on traditional methods chosen for the purposes of
atmospheric/oceanic stratification analyses. A definition of the
mixing layer thickness more appropriate to thermal fatigue and based
on mixedness is devised. This definition shows that the thermal
fatigue risk assessed using simple mixing layer growth can be
misleading and why an approach that separates the effects of large
scale (turbulent) and small scale (molecular) mixing is necessary.", keywords = "Concentration measurements, Mixedness, Stablystratified turbulent isokinetic mixing layer, Wire mesh sensor", volume = "5", number = "4", pages = "579-8", }
