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ASHRAE produces the Guideline 33 for Documenting Indoor Airflow and Contaminant Transport Modeling (ASHRAE in Guideline 332013: Guideline for Documenting Indoor Airflow and Contaminant Transport Modeling, 2013). This can be used as the ground for general requirements for reporting engineering CFD simulation and results. In general, four parts are required to form a complete CFD report.
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Example Project: Investigation of cooling efficiency drop of drycooling towers under crosswind conditions
Background:
Naturaldraft drycooling tower is an energyefficient and watersaving cooling equipment in power plants, widely used in the regions lack of water but rich in coal or oil, such as, South Africa, Middle East and North China. However, the performance of drycooling towers is highly sensitive to the environment conditions, particularly the wind conditions that may reduce up to 40% of the total power generation capacity (Ding
1992). The conventional design of cooling towers does not sufficiently consider the impact of wind, which in fact exists most of time in reality. Hence, it is important to investigate the influence of wind on the performance of cooling towers and propose appropriate improving measures. Figure
10.6 displays a typical Helertype dry cooling tower with vertical heat exchangers around the bottom of the tower, which generally confronts the most significant impacts from crosswinds.
where Z
_{ref} = 45 m.
where, C
_{w} is the water heat capacity,
\(\dot{m}_{w}\) is the water mass flow rate in the heat exchangers, T
_{w1} and T
_{w2} are the water inlet and outlet temperature in the heat exchangers; α is the heat transfer coefficient of the heat exchangers and is related to the airflow velocity through the heat exchangers,
\(\overline{{T_{w} }}\) is the mean water temperature in the heat exchangers, T is the air temperature outside the heat exchangers, A is the surface area of the heat exchangers.
Since the air temperature and flow rate as well as water temperature are varying with locations under wind conditions, the numerical simulation divides the heat exchangers into N uniform sections around the bottom of the cooling towers and M layers in vertical direction. For the Jth section,
where Q(J) is the total heat exchange rate between air and water at the Jth section of the heat exchangers, k denotes the kth layer in the vertical direction of the Jth section, T is the local air temperature,
\(\dot{m}_{w} \left( J \right)\), T
_{w1}(J) and T
_{w2}(J) are the water mass flow rate, water inlet and outlet temperature at the Jth section,
\(\overline{{T_{w} \left( J \right)}} = \left[ {T_{w1} \left( J \right) + T_{w2} \left( J \right)} \right]/2\) is the mean water temperature in the Jth section. The heat transfer coefficient α of the heat exchangers can be obtained from the literature (Ding,
1992):
where, L
_{1} and L
_{2} are, respectively, the original and modified air mass flow rate through the heat exchangers per front area, and C
_{k} = 1.11.
Since the heat transfer between air and water influences the airflow velocity while the airflow velocity inversely affects the heat transfer performance, an iterative coupling algorithm is required:
Assume initial fields of air velocity, temperature, turbulence, and the distribution of T
_{w2}(J). T
_{w1}(J) is specified as a constant water temperature based on power generation turbine outputs. Calculate the heat transfer coefficient α with Eqs. (
10.6) and (
10.7) and calculate
\(\overline{{T_{w} \left( J \right)}} = \left[ {T_{w1} \left( J \right) + T_{w2} \left( J \right)} \right]/2\).
Solve Eq. (
10.5) to obtain Q
_{air}(J) and introduce this heat source term into the energy conservation equation of air.
Solve the airflow governing equations to obtain the new distributions of air velocity, pressure, temperature, and turbulence.
Update the heat transfer coefficient α with Eqs. (
10.6) and (
10.7). Calculate Q
_{air}(J) with previous
\(\overline{{T_{w} \left( J \right)}}\) values and Eq. (
10.5).
Calculate the new T
_{w2}(J) with Eq. (
10.5) and update
\(\overline{{T_{w} \left( J \right)}}\).
Go back to (2) until the solution is converged.
The total heat exchange rate
\(Q_{total} = \mathop \sum \nolimits_{J} Q\left( J \right)\) and the distribution of T
_{w2}(J) are two major results for evaluating the cooling performance of the towers under different wind conditions and improving strategies. Q
_{total} represents the overall cooling capacity or efficiency of the cooling towers, while the distribution of T
_{w2}(J) indicates the locations of cooling deficiency and improvement.
Heat exchangers provide not only heat sources but also resistance to air movement. The study uses the same iteration process to account for the airflow resistance effect of the heat exchangers in cooling towers. The field test shows that the air pressure drop through the heat exchangers has the following relationship to the airflow rate (Ding
1992):
L1 is the air mass flow rate through the heat exchangers per front area. Once L
_{1} is updated with current air velocities, the new pressure resistance term can be obtained and introduced to the momentum equation of air to produce the new velocity distribution.
Results and Analysis:
Independence of results on computational grids
The study first examines the independence of numerical results on the grid resolution. Figure
10.8 shows the distribution of water outlet temperature in the air–water heat exchangers around the towers, predicted with two different grids. The difference of two solutions is negligible, indicating good gridindependence of the simulation. Table
10.3 further verifies that the difference of the total heat exchange rates in windy days calculated with the fine and coarse grid is only about 3%.
Please list three industrial examples that CFD can and cannot simulate, respectively.
Please list three advantages of CFD over experimental fluid dynamics.
Please indicate the conventional/practical criteria to define impressible flow.
How many equations need be solved in order to obtain room airflow velocity, temperature and humidity distributions?
What is Einstein notation (or called summation convention)? Give an example.
How many CFD approaches are available and what are they and which one is usually fastest?
What is the Boussinesq Approximation?
What is the general expression of a scalar transport equation?
Which term do turbulence models deal with in the Reynoldsaveraged momentum equations?
What is eddy viscosity model?
What are the pros and cons of the standard ke twoequation model?
What are lowReynoldsnumber ke models used for?
What is symmetric boundary condition?
How many velocity boundary conditions are required at a 3D boundary where the pressure condition is given?
How many numerical discretization methods/approaches are available? What are they?
What is the upwind differencing scheme?
What is TDMA and what for?
What is SIMPLE algorithm and what for?
What is falsetime step?
Which one is better: implicit versus explicit algorithm? Why?
What are, respectively, staggered grid, structure grid, and adaptive grid?
How to judge the grid quality of a structure grid?
Please numerically solve the following equation and compare the results with the analytical solution in graph.
Please test both the upwind and central schemes and comment on how the scheme affects the solutions.
Please test different grid resolutions and comment on how the grid affects the solutions.

Naturaldraft drycooling tower is an energyefficient and watersaving cooling equipment in power plants, widely used in the regions lack of water but rich in coal or oil, such as, South Africa, Middle East and North China. However, the performance of drycooling towers is highly sensitive to the environment conditions, particularly the wind conditions that may reduce up to 40% of the total power generation capacity (Ding 1992). The conventional design of cooling towers does not sufficiently consider the impact of wind, which in fact exists most of time in reality. Hence, it is important to investigate the influence of wind on the performance of cooling towers and propose appropriate improving measures. Figure 10.6 displays a typical Helertype dry cooling tower with vertical heat exchangers around the bottom of the tower, which generally confronts the most significant impacts from crosswinds.×
×
Simulation Details:
The study simulates the two fullscale cooling towers in tandem arrangement with the air–water heat exchangers vertically located at the bottom of the towers (Zhai and Fu
2006). Figure
10.7 illustrates the computational domain, the boundary conditions and the grid system used. Only half of the flow field was simulated because of the symmetry in geometry and flow/thermal conditions. A typical wind speed U
_{ref} = 10 m/s in the winter was applied to study the impact of crosswind on the performance of the cooling towers. The wind profile was set up as:
$$U_{wind} = U_{ref} \left( {Z/Z_{ref} } \right)^{0.16} , V = W = 0$$
(10.2)
×
The investigation uses the multiblock CFD algorithm and program developed by Zhai and Fu (
2002) to simulate the airflow and heat transfer in and around two cooling towers. The program has been verified by many previous studies (Zhai
1999). The computation adopted five blocks of grids—one exterior flow block, two interior flow blocks, and two shell/heat exchanger block—to ensure the generation of high quality grids, as shown in Fig.
10.7. Each grid block was generated individually with the total grid cells of about 220,000. A fine grid with 640,000 cells was also used to verify the grid independence of numerical results.
The numerical simulation solves the steadystate governing conservation equations of mass, momentum and energy, with the standard kε turbulence model and wall function (Launder and Spalding,
1974) to represent the overall turbulence effect. The CFD simulation incorporates the heat exchange process between air and water of the heat exchangers, as well as the resistance effect of the heat exchangers to airflow. The heat released at the water side and absorbed at the air side of the heat exchangers are, respectively,
$$Q_{water} = C_{w} \dot{m}_{w} \left( {T_{w1}  T_{w2} } \right)$$
(10.3)
$$Q_{air} = \alpha \left( {\overline{{T_{w} }}  T} \right)A$$
(10.4)
$$\begin{aligned} Q\left( J \right) & = Q_{{air}} \left( J \right) = \sum\limits_{k} \alpha \left[ {\overline{{T_{w} (J)}}  T} \right]A\left( J \right) \\ & = Q_{{water}} \left( J \right) = C_{w} \dot{m}_{w} \left( J \right)\left[ {T_{{w1}} \left( J \right)  T_{{w2}} \left( J \right)} \right] \\ \end{aligned}$$
(10.5)
$$\alpha = 1372.34L_{2}^{0.515} \left( {\frac{\text{W}}{{{\text{m}}^{2} {\text{K}}}}} \right)$$
(10.6)
$$L_{2} = C_{k}^{0.64} L_{1} \left( {\frac{\text{ton}}{{{\text{m}}^{2} {\text{h}}}}} \right)$$
(10.7)
(1)
Assume initial fields of air velocity, temperature, turbulence, and the distribution of T
_{w2}(J). T
_{w1}(J) is specified as a constant water temperature based on power generation turbine outputs. Calculate the heat transfer coefficient α with Eqs. (
10.6) and (
10.7) and calculate
\(\overline{{T_{w} \left( J \right)}} = \left[ {T_{w1} \left( J \right) + T_{w2} \left( J \right)} \right]/2\).
(2)
Solve Eq. (
10.5) to obtain Q
_{air}(J) and introduce this heat source term into the energy conservation equation of air.
(3)
Solve the airflow governing equations to obtain the new distributions of air velocity, pressure, temperature, and turbulence.
(4)
(5)
Calculate the new T
_{w2}(J) with Eq. (
10.5) and update
\(\overline{{T_{w} \left( J \right)}}\).
(6)
Go back to (2) until the solution is converged.
$$\Delta P = 2.1L_{1}^{1.76} + 0.06L_{1}^{2} \left( {\text{Pa}} \right)$$
(10.8)
(1)
Independence of results on computational grids
The study first examines the independence of numerical results on the grid resolution. Figure
10.8 shows the distribution of water outlet temperature in the air–water heat exchangers around the towers, predicted with two different grids. The difference of two solutions is negligible, indicating good gridindependence of the simulation. Table
10.3 further verifies that the difference of the total heat exchange rates in windy days calculated with the fine and coarse grid is only about 3%.
Table 10.3
Comparison of computed total heat exchange rates of cooling towers with different simulation conditions
Fine grid

Coarse grid



U
_{wind} = 0 m/s

U
_{wind} = 10 m/s windward tower

U
_{wind} = 10 m/s leeward tower

U
_{wind} = 10 m/s windward tower

U
_{wind} = 10 m/s leeward tower


Total heat exchange rate
Q (MW)

248.964

182.956

215.346

186.784

218.272

Relative change (
Q
_{wind}≠ 0 −
Q
_{wind} = 0)/
Q
_{wind} = 0 × 100%

−26.5%

−13.5%

−25.0%

−12.3%

×
(2)
Comparison of numerical results with experimental tests
To verify the creditability of numerical results, the study compares the simulation with the model experiment and available field tests (Ding
1992). Table
10.4 presents the predicted total heat exchange rate without crosswind and with the same operating conditions as those in the design and field test. The calculated result is between the design value and the field test result, and the difference is less than 10%. Figure
10.9 shows the influence curve of crosswind speed versus water outlet temperature of heat exchangers. The predicted trends by this study fairly match those measured from actual cooling towers in the world. The predicted internal upward air velocity profiles also show good agreement with the model experiment. The upward airflow speeds at the windward portion of the towers encounter significant reduction and the velocity peak areas are pushed back to the leeward side of the towers. These validations verify that the simulation can provide reasonable results and the results can be used to develop methods for improving the performance of cooling towers.
Table 10.4
Comparison of computed results with designed and fieldtested values for cooling towers under nowind conditions
Water inlet temperature in heat exchanger
T
_{wl} (°C)

Environmental air temperature
T
_{a} (°C)

Water mass flow rate in heat exchanger
G (ton/h)

Water outlet temperature in heat exchanger
T
_{w2} (°C)

Total heat exchange rate
Q (MW)



Simulation

43.82

15.46

22,760

32.77

291.89

Design

43.82

15.46

22,760

275.63


Fieldtest

43.82

15.46

22,760

31.85

316.85

×
(3)
Wind influence analysis
The cooling performance of cooling towers without wind is quite uniform around the towers as evidenced by the uniform water outlet temperatures in Fig.
10.10. The existence of crosswind of 10 m/s causes 26.5 and 13.5% reduction of the total heat exchange rate for the windward and leeward tower, respectively. This is mainly attributed to the airflow around the cooling towers, destroying the radial flow of surrounding cold air into the towers and thus reducing the heat transfer efficiency of cooling towers. As a result, the water outlet temperatures of the heat exchangers at both lateral sides of the towers (about 0–20°) increase significantly, as shown in Fig.
10.10. Figures
10.11 and
10.12, respectively, display the velocity vector and temperature distributions in the middle section of the cooling towers when U
_{wind} = 10 m/s. Figure
10.13 shows the velocity vector distribution in the middle section of the heat exchanger, and Fig.
10.14 illustrates the predicted flow streamlines in and around the towers. All these explicitly indicate that the airflow around the lateral sides of the cooling towers blocks the cold air entering the towers and therefore affects the cooling efficiency of the towers.
×
×
×
×
×
(4)
Improvement performance analysis
To recover the cooling capacity, windbreak walls were introduced at both sides of the cooling towers, perpendicular to the crosswind direction. This arrangement will not only hinder the strong crossflow over the towers but also induce the fresh airflow into the towers through the heat exchangers. The windbreak walls studied were 16 m high (to cover most of the heat exchanger height), 6 m thick (for structure safety concern), and 3.5 m away from the towers (to avoid significant airflow separations at the back of the walls and facilitate maintenance work of the towers). The study compares the performance of the walls with four different widths (9, 14, 20, and 27 m).
The results show that all the windbreak walls can improve the cooling efficiency of the towers under wind conditions. The water outlet temperatures at both sides of cooling towers are reduced, as evidenced in Fig.
10.10. Figure
10.11 presents the airflow patterns at the height of 8.75 m with and without windbreak walls, exhibiting the forced airflows into the towers at the lateral locations by using windbreak walls. The improving effectiveness is increased with the increase of windbreak wall width. But it is not a linear relationship. Figure
10.15 reveals the relationship between cooling tower efficiency recovery rate and the width of windbreak walls. Note that a wider wall does not always improve the tower performance. In fact, it may even make the situation worse because a large separate vortex at the back of a wide wall may block the inflow of air to the towers. The study indicates that the width of 20 m is a good choice for the practical purpose. Various practical forms such as tree walls can be implemented for both blocking crosswind and cooling surrounding air temperature.
×
Table 10.3
Comparison of computed total heat exchange rates of cooling towers with different simulation conditions
Fine grid

Coarse grid



U
_{wind} = 0 m/s

U
_{wind} = 10 m/s windward tower

U
_{wind} = 10 m/s leeward tower

U
_{wind} = 10 m/s windward tower

U
_{wind} = 10 m/s leeward tower


Total heat exchange rate
Q (MW)

248.964

182.956

215.346

186.784

218.272

Relative change (
Q
_{wind}≠ 0 −
Q
_{wind} = 0)/
Q
_{wind} = 0 × 100%

−26.5%

−13.5%

−25.0%

−12.3%

×
Comparison of numerical results with experimental tests
To verify the creditability of numerical results, the study compares the simulation with the model experiment and available field tests (Ding
1992). Table
10.4 presents the predicted total heat exchange rate without crosswind and with the same operating conditions as those in the design and field test. The calculated result is between the design value and the field test result, and the difference is less than 10%. Figure
10.9 shows the influence curve of crosswind speed versus water outlet temperature of heat exchangers. The predicted trends by this study fairly match those measured from actual cooling towers in the world. The predicted internal upward air velocity profiles also show good agreement with the model experiment. The upward airflow speeds at the windward portion of the towers encounter significant reduction and the velocity peak areas are pushed back to the leeward side of the towers. These validations verify that the simulation can provide reasonable results and the results can be used to develop methods for improving the performance of cooling towers.
Table 10.4
Comparison of computed results with designed and fieldtested values for cooling towers under nowind conditions
Water inlet temperature in heat exchanger
T
_{wl} (°C)

Environmental air temperature
T
_{a} (°C)

Water mass flow rate in heat exchanger
G (ton/h)

Water outlet temperature in heat exchanger
T
_{w2} (°C)

Total heat exchange rate
Q (MW)



Simulation

43.82

15.46

22,760

32.77

291.89

Design

43.82

15.46

22,760

275.63


Fieldtest

43.82

15.46

22,760

31.85

316.85

×
Wind influence analysis
The cooling performance of cooling towers without wind is quite uniform around the towers as evidenced by the uniform water outlet temperatures in Fig.
10.10. The existence of crosswind of 10 m/s causes 26.5 and 13.5% reduction of the total heat exchange rate for the windward and leeward tower, respectively. This is mainly attributed to the airflow around the cooling towers, destroying the radial flow of surrounding cold air into the towers and thus reducing the heat transfer efficiency of cooling towers. As a result, the water outlet temperatures of the heat exchangers at both lateral sides of the towers (about 0–20°) increase significantly, as shown in Fig.
10.10. Figures
10.11 and
10.12, respectively, display the velocity vector and temperature distributions in the middle section of the cooling towers when U
_{wind} = 10 m/s. Figure
10.13 shows the velocity vector distribution in the middle section of the heat exchanger, and Fig.
10.14 illustrates the predicted flow streamlines in and around the towers. All these explicitly indicate that the airflow around the lateral sides of the cooling towers blocks the cold air entering the towers and therefore affects the cooling efficiency of the towers.
×
×
×
×
×
Improvement performance analysis
To recover the cooling capacity, windbreak walls were introduced at both sides of the cooling towers, perpendicular to the crosswind direction. This arrangement will not only hinder the strong crossflow over the towers but also induce the fresh airflow into the towers through the heat exchangers. The windbreak walls studied were 16 m high (to cover most of the heat exchanger height), 6 m thick (for structure safety concern), and 3.5 m away from the towers (to avoid significant airflow separations at the back of the walls and facilitate maintenance work of the towers). The study compares the performance of the walls with four different widths (9, 14, 20, and 27 m).
The results show that all the windbreak walls can improve the cooling efficiency of the towers under wind conditions. The water outlet temperatures at both sides of cooling towers are reduced, as evidenced in Fig.
10.10. Figure
10.11 presents the airflow patterns at the height of 8.75 m with and without windbreak walls, exhibiting the forced airflows into the towers at the lateral locations by using windbreak walls. The improving effectiveness is increased with the increase of windbreak wall width. But it is not a linear relationship. Figure
10.15 reveals the relationship between cooling tower efficiency recovery rate and the width of windbreak walls. Note that a wider wall does not always improve the tower performance. In fact, it may even make the situation worse because a large separate vortex at the back of a wide wall may block the inflow of air to the towers. The study indicates that the width of 20 m is a good choice for the practical purpose. Various practical forms such as tree walls can be implemented for both blocking crosswind and cooling surrounding air temperature.
×
1.
Please list three industrial examples that CFD can and cannot simulate, respectively.
2.
Please list three advantages of CFD over experimental fluid dynamics.
3.
Please indicate the conventional/practical criteria to define impressible flow.
4.
How many equations need be solved in order to obtain room airflow velocity, temperature and humidity distributions?
5.
What is Einstein notation (or called summation convention)? Give an example.
6.
How many CFD approaches are available and what are they and which one is usually fastest?
7.
What is the Boussinesq Approximation?
8.
What is the general expression of a scalar transport equation?
9.
Which term do turbulence models deal with in the Reynoldsaveraged momentum equations?
10.
What is eddy viscosity model?
11.
What are the pros and cons of the standard ke twoequation model?
12.
What are lowReynoldsnumber ke models used for?
13.
What is symmetric boundary condition?
14.
How many velocity boundary conditions are required at a 3D boundary where the pressure condition is given?
15.
How many numerical discretization methods/approaches are available? What are they?
16.
What is the upwind differencing scheme?
17.
What is TDMA and what for?
18.
What is SIMPLE algorithm and what for?
19.
What is falsetime step?
20.
Which one is better: implicit versus explicit algorithm? Why?
21.
What are, respectively, staggered grid, structure grid, and adaptive grid?
22.
How to judge the grid quality of a structure grid?
23.
Please numerically solve the following equation and compare the results with the analytical solution in graph.
$$\frac{dT}{dX} + T = 0,\,0 \le X \le 1;\,T\left( 0 \right) = 1$$
a.
Please test both the upwind and central schemes and comment on how the scheme affects the solutions.
b.
Please test different grid resolutions and comment on how the grid affects the solutions.
$$\frac{dT}{dX} + T = 0,\,0 \le X \le 1;\,T\left( 0 \right) = 1$$
a.
Please test both the upwind and central schemes and comment on how the scheme affects the solutions.
b.
Please test different grid resolutions and comment on how the grid affects the solutions.
ASHRAE (2013) Guideline 332013: guideline for documenting indoor airflow and contaminant transport modeling
ASHRAE (2017) Standard 1202017: method of testing to determine flow resistance of HVAC ducts and fittings
Ding E (1992) Air cooling techniques in power plants. Water and Electric Power Press, Beijing
Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3:269–289
CrossRef
Sleiti A, Zhai Z, Idem S (2013) Computational fluid dynamics to predict duct fitting losses: challenges and opportunities. HVAC&R Res 19(1):2–9
Zhai Z (1999) Study of the flow around drycooling towers. Ph.D. Dissertation, Tsinghua University, Beijing, China
Zhai Z, Fu S (2002) Modeling the airflow around cooling towers with multiblock CFD. In: The 4th international ASME/JSME/KSME symposium, Canada
Zhai Z, Fu S (2006) Improving cooling efficiency of drycooling towers under crosswind conditions by using windbreak methods. Appl Therm Eng 26(10):1008–1017
MathSciNetCrossRef
 Titel
 Write CFD Report
 DOI
 https://doi.org/10.1007/9789813298200_10
 Autor:

Zhiqiang (John) Zhai
 Verlag
 Springer Singapore
 Sequenznummer
 10
 Kapitelnummer
 Chapter 10