Proceedings of the Eleventh (2001) International Offshore and Polar Engineering Conference
Stavanger, Norway, June 17-22, 2001
Copyright © 2001 by The International Society of Offshore and Polar Engineers
ISBN 1-880653-51-6(Set); ISBN 1-880653-53-2 (Vol. ll); ISSN 1098-6189 (Set)
An Experimental Study of Heated Surface Jet in a Wave Environment
M. Di Natale and D. Vicinanza
The Second University of Naples
Aversa (Caserta), Italy
ABSTRACT
This paper presents an experimental study on a heated jet
discharged into a stagnant ambient and in a wave environment for
small Richardson numbers. Improving a previous research
(Di Natale and Vicinanza, 2000), extensive measurements of
veloeity and temperature profiles in lateral direction have been
carried out. The aim of the work was firstly to study the hehaviour
of heated jet-wave interaction and secondly to work out equations
to predict the variation of velocity and temperature excess
correlated with some dimensionless parameters.
KEY WORDS: Heated jet, wave environment, velocity profiles,
temperature profiles, thermograph, current meter.
INTRODUCTION
In the last years the increase in electric power request have intensified
the problem of discarding heated water rejected by the plant cooling
system. When this operation is not well controlled, the receiving
waterbodies (lakes, rivers, coastal areas) present induced water
temperature changes, with relevant water quality modifications.
The most important consequence of increased temperature is the
decreased solubility of oxygen in the receiver that it is essential for
many forms of aquatic life. Even though international laws give criteria
on thermal discharges, fixing the temperature excess ranges, some
countries still rely on it for economical reasons.
Three dimensional surface heated jets discharged into a stagnant
ambient have been studied experimentally by many authors (Wiegel et
al., 1964; Jen et al., 1966; Hayashi and Shuto, 1967; Stefan, 1972;
Pande and Rajaratnam, 1977; Wiuff, 1978) considering different outlets
(circular, rectangular or square) and source Richardson numbers (small,
moderate or large), Rio, where:
g" h o • AP°~pa
Rio = U2 °
[1]
in which g is the acceleration due to gravity, ho is the depth of outlet
section, Apo is the difference in mass densities of the hot water
discharge/9o and the ambient Pa, and Uo is the velocity at the outlet.
Particularly interesting are the measurements made by Pande and
Rajaratnam (1977) for moderate and large Rio (0.15+ 1.14). The Authors
found that (mean) velocity and (mean) temperature profiles in the
lateral direction are similar and well described by the exponential
(Gaussian) following equations:
-0.693( ff-.)2
urns - e ~ b,, )
ttmm
[21
--=e [31
AT.,
where urns and Umm are the generic and maximum surface velocity;
Airs = Ts- ira and ATm = Tin- ira being T~ and Tm the generic and
maximum surface temperature and Ta the ambient temperature; bu and
br are the values ofy where um~= 0.5 u~m and AT~ = 0.5 zlTm.
Moreover they correlated the decay Of velocity and excess
temperature with the dimensionless longitudinal distance from the
outlet, x/~ o , and the source Richardson numbers:
Umm 5.68" R~/o 3
~ = (Rio = 0.15+0.56) [41
Umm = 1.43' R~o 1/6
Umso ~/~o~/3 (Rio = 0.79+1.14)[51
AT m 4.42.R//o 3
396