A NUMERICAL AND EXPERIMENTAL STUDY ON
TURBULENT FLOW AND HEAT TRANSFERIN COASTAL WATER
Ping Zeng1, Huiquan Chen, Baichuan
Ao and Ping
Ji
Dept. Cooling Water, China Institute of Water
Resources & Hydropower Research (IWHR),
POB
366, Beijing 100044, China
1Corresponding author. Tel:86 10 6845 4997; Fax:86 10 6841 2859;
E-mail:pzeng@iwhr.com.
Abstract: This paper deals with the numerical and experimental modeling of
turbulent tidal flow and heat transfer in coastal water. A depth-averaged k-
turbulence mathematical model is used to present the numerical
prediction. A full-field physical model with scale distortion, carried out in a
specially designed laboratory with some necessary facilities for controlling the
conditions, is described for simulating the turbulent tidal flow and heat
transfer in coastal water. Field investigations and prototype measurements are
concerned to provide the calibration and validation of the numerical prediction
and experimental simulation. In the engineering application study, the modeling
of turbulent heat transfer in coastal water near Daya Bay Nuclear Power Plant is
conducted.
Keywords: heat
transfer, turbulent flow, coastal water
1 INTRODUCTION
In water engineering fields, research
on turbulent tidal flow and heat transfer in coastal water is important for the
purpose of solving the pressing problems involved in water resources, water
quality, environmental protection and engineering design etc. Many similar
studies had been carried out and the necessary modelling techniques to be
utilized in this paper had been solved in the past. Coeffe et al. (1987)
introduced some applications and developments of the numerical simulations in
coastal fields connected to thermal impact due to the heat transfer on tidal
current, by describing the contribution of LNH/EDF, France on heat dilution
studies in the vicinity of coastal power plants. Steiner (1973) carried out a
basic experiment in laboratory to directly measure the overall heat exchange
coefficient and the equilibrium water temperature from water surface to air.
Shaw & Lee (1976) made a semi-theoretical study of turbulent heat and mass
transfer over large bodies of water. Nystrom et al. (1981) conducted two
physical model studies to assist in the evaluation of the environmental impact
of once-through condenser cooling at the Indian Point Nuclear Generating
Station, New York. In recent decades, IWHR successfully conducted a large number
of numerical and experimental studies of engineering based modeling of turbulent
tidal flow and heat transfer in coastal water near power plant. The engineering
applications, concerning a series of numerical predictions, physical model
studies and field surveys, covered nearly all of the nuclear power plants and
most of the large-size thermal power plants in China, some of which give much
contribution for the present work in this paper.
2
NUMERICAL PREDICTION
In most engineering application studies on
turbulent flow and heat transfer problem over natural coastal water, the plane
length is large enough compared with water depth and the bottom is rough enough
so that a nearly uniform vertical distribution of hydrodynamic and thermodynamic
quantities can be supposed. The mathematical modeling equations, based on the
depth-averaged variables, can be expressed as follows (McGuirk & Rodi,
1978),
where
in which,
= tidal level;
= water depth;
= depth-averaged velocity;
= depth-averaged flow temperature;
k = turbulent kinematics energy;
=turbulent dissipation rate; q = flow discharge source or sink;
= heat source input to or output
of the system;
= multiphase conjunction term;
= density of natural water;
= density of air; g = acceleration of
gravity;
= molecular viscosity, turbulent viscosity and effective viscosity
respectively;
and
=velocity and temperature dispersion coefficients;
and
=shear stresses at fluid surface and bed bottom respectively; W = wind speed; q = wind direction angle;
and
=new terms originating from depth-averaging; C = Chezy coefficient;
are
constants obtained from experiments for equilibrium turbulent boundary layers
and isotropic turbulence (Rodi, 1980).
The term
indicates the multiphase
conjunction of atmosphere with heated-water and cooling-water at the water
surface. A simple assumption is applied in the present paper, which supposed
that the atmosphere-phase is not interpenetrated with the fluid domain while the
phase interaction is represented by an additional heat transfer equation. Three
processes are considered to be responsible for the interaction: evaporation,
conduction, and back radiation. The prediction of these processes depends on
meteorological conditions above the coastal water surface, of which, the water
surface temperature, the wind and the air-water temperature difference are
driving forces. Following formulas presented by Chen et al. (1991) is used,
(7)
(8)
(9)
where K = surface heat exchange coefficient, which is the heat change
resulted by per unit variance of water surface temperature for particular values
of air temperature, water temperature, wind speed, and relative humidity; b = (P/0.623)(cP /L); cP = specific heat of water; L = latent heat of vaporization; s = Stefan-Boltzmann
constant; TS = water
surface temperature; T¥ = natural water temperature;
Ta = ambient air
temperature; eS = vapor
pressure at the water surface; ea
= vapor pressure of ambient air; subscript ’1.5’ represents the value at
the height of 1.5m over the water surface; subscript ‘V’ represents the virtual
temperature which defined by expression TV
= T/(1-0.378e/P); e = vapor pressure; P =
atmospheric pressure.
The approximation of the
governing equations is based upon a control volume approach which is expressed
briefly here, and the details was presented by Patankar (1980) and Spalding
(1981). The present calculations are performed on the body-fitted curvilinear
coordinates with a mesh freezing treatment onto the "out-field"
domain; so as to generate a zonal computational domain in which the irregular
coastline can be economically simulated (Zeng et al. 1995). Convergency of the
calculation can be obtained when a normalized residual for the day-averaged
water temperature falls below a small value.
3 EXPERIMENTAL
SIMULATION
The physical experiment in laboratory on the
turbulent flow and heat transfer in coastal water described in this paper is to
simulate both the coastal currents near the area of engineering system such as a
power plant and the temperature distribution due to the heat transfer. The
simulation covers all the process of heat discharged from the cooling water
circulating system of power plant into the coastal water, till the dilution is
developed well. A well designed laboratory experiment which can offer data and
conditions enough for the turbulent flow and heat transfer study will generate
reliable cases to satisfy the engineering applications and verify the numerical
predictions. One of the major problems to overcome is that the limitation of
physical model size in laboratory due to the laboratory area, and the coming
experiment budget, often produce some difficulties for full-field coastal water.
A distortion of model scale seems to be a practical approach for solving this
problem over a large water body. Another major problem to fulfil the experiment
requirement is that the difficulties to simulate a prototype climate in a model,
so as to conduct a correct modeling of heat exchange between coastal water
surface and atmosphere. A practical method is to carry out the experiment in a
specially designed laboratory where some of the conditions, such as wind, air
temperature and air humidity, can be simulated, meanwhile, to provide the
verification by conservative test with respect to ambient effects in a
conditioning chamber.
The experiments are performed in a specially
designed laboratory with coastal tidal flow modeling, and also with some
necessary facilities for controlling the conditions such as wind, air
temperature and air humidity. Four sets of packaged air conditioners, with
cooling capacity of 4´30KW, heating capacity of 4´25KW, air flow of 4´6200m3/h, are used in the
laboratory. The bed and the banks of model are firstly built with brickwork and
moulds filled up with sand, then coated with a layer of cement. The turbulent
tidal current is generated with a coastal hydrodynamics system designed and
manufactured by IWHR supported by The Ministry of Water Resources of China. The
unsteady coastal tidal flow is simulated by a series of tidal generating pumps,
which are set along the periphery of the model area to control the discharges
into or out of the tidal open boundaries on physical model. These pumps work
under the condition of the detailed discharge distribution along every open
tidal boundary on model, which is provided with the numerical prediction or
directly by the prototype measurement. The heated-water discharge and
cooling-water intake of power plant are simulated by a closed circulating
heating system, which consists of constant-temperature electric heater, flow
meter, outlet pump, and intake pump.
The velocity measurements are performed with
Acoustic Doppler Velocimeters (ADV-10MHZ, SonTek), accompanied with the tracing
photography for compensating the surface currents. The distance between the ADV
probes is chosen smaller where high velocity gradients are expected. The
velocity measurement values turn out reliable down to about 1.0cm/s, while the
uncertainty increases when approaching to zero velocity. Temperature
measurements are carried out using a 3-D thermistor system, which consists of a
multi-channel data acquisition system (YODAC-85S) and an infrared thermal video
system (TVS-2000MKII, Nippon Avionics). YODAC-85S has a temperature reading of a
resolution of 0.01°C and a measuring range from 0°C to 50°C in the actual study. TVS-2000MKII has
a sensitivity of 0.01°C, and a measuring range from -40°C to 300°C. The probes in the 3-D thermistor
system are installed on a frame which can trace the water surface movement in
vertical direction to fit the water depth change automatically. The distance
between temperature measuring points should be chosen smaller where closed to
the heat discharging because the high temperature gradients are expected.
4 ENGINEERING
APPLICATION
The engineering application is presented of a
thermal impact study on environment of turbulent heat transfer in coastal water
produced by Daya Bay Nuclear Power Plant. The plant is located on the northern
coast of Daya Bay, which is near the South China Sea and about 80km northeast to
Hongkong. The plant was constructed in 1992, with a capacity of 1,800MW. The
heated water discharge, from the condenser circulating system into coastal
water, is 95m3/s, with a temperature rise of 10°C. To validate and verify the numerical
and experimental results, field investigations regarding tidal flow and
temperature distribution were carried out. The field measurement area covered
30km2 in Daya Bay; much attention was given to the coastal water near
the plant. There were 13 comprehensive measuring stations, which were numbered
with 9401 to 9413, and 3 tidal level measuring stations, which were numbered
with H1 to H3 (see Fig.1), set in the measuring area of Daya Bay. Velocity,
tidal level, water temperature and wind data on these measuring points were
collected simultaneously. Additionally, ocean currents and water surface
temperature distributions in Daya Bay were observed and analyzed by using the
satellite remote sensing pictures.
A full-field physical model was studied which
covered the coastal water area of 590km2 (See Fig.1). The full-field
model was geometrically distorted with a ratio 1:10 of horizontal length to
vertical depth. The horizontal scale was 1:1200 and the vertical scale was
1:120. Fig.1 is a layout of the full-field physical model in the laboratory.
There were 200 temperature measuring points set over the model water, half of
which were set near the middle of the water depth and the others near the bottom
and the top of the water depth respectively. The simulated area with numerical
model was of 830 km2, much larger than that with the full-field
physical model, which covered nearly all of Daya Bay. The computational domain
was subdivided into 6920 quadrilateral meshes. To achieve an adequate and
economic meshing of the coastal water in the vicinity of the power plant, a
multi-grid system was used.
Comparison of simulated and observed tidal flow
patterns, by using the numerical model, the full-field physical model, and the
satellite remote sensing pictures separately, at selected time steps during
flood and ebb tides is shown in Fig.2. Comparison of the simulated time series
tidal levels at selected stations is shown in Fig.3. It can be seen that both
numerical model computation and physical model simulation agree well with the
measurement on prototype. Fig.4 shows the comparison of the calculated
temperature fields by numerical model with the depth-averaged results of
temperature contours simulated by physical model, at maximum flood tide and ebb
tide respectively. Fig.5 shows the comparison of day-averaged water surface
temperature contours obtained by the field investigation and the experimental
simulation separately. The water temperature contours predicted by the numerical
model had some deviation from the water surface temperature contours of the
experimental results. Two reasons were responsible for the deviation: the
numerical model could not fully explain the observed temperature distributions
due to a shortage of the depth-averaged numerical model; and the scale
distortion of the full-field physical model which somewhat amplified the
stratification of the heated flow. Fig.6 shows the comparison of the vertical
temperature distributions between the prototype measurement and the physical
model simulation at Stations 9403, 9405 and 9407 at chosen time steps. It can be
seen that the stratification of water temperature was simulated well by the
physical model although some discrepancies existed due to the influence of scale
distortion as above-mentioned.
5 CONCLUSIONS
The present work has focused on the numerical
and experimental modeling of turbulent tidal flow and heat transfer in coastal
water near power plant, for the purpose of engineering applications. The
engineering application study was conducted by using the depth-averaged k-
turbulence model to obtain the full field temperature distribution, a
full-field physical model with scale distortion to analyze the detailed heat
exchange phenomena in coastal water, and the prototype measurement to calibrate
and validate the modeling. It has been shown that the modelling presented in
this paper can be used to simulate the heat exchange and obtain practical
results in coastal water.
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Fig.1 Layout of the full-field physical
model.(*location of the measuring station corresponding to the prototype)
Fig.2
Comparison of simulated and observed tidal flow patterns, on Sept.5-6 of 1994.
Fig.3 Comparison of time
series of tidal level, simulated by the full-field physical model and numerical
model, with the field measurement data, at selected stations, on Aug.30-31 of
1994.
Fig.4 Comparison of the depth-averaged
temperature rise, on Aug.14-15 of 1994.
(filled area: numerical
prediction; – –
– : experimental simulation.)
Fig.5 Comparison of
the day-averaged water surface temperature rise.
(filled area: field
investigation; –
– – : experimental simulation.)
Fig.6 Comparison of
the vertical water temperature rise, on Aug.14-15 of 1994.
(–––:
prototype measurement; ----: experimental simulation.)