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Analyzing the performance of a kitchen exhaust air duct with regards to recent standards--a CFD/thermal-stress simulation.

INTRODUCTION

Kitchen exhaust air ducts are widely used and are built to specific standards; ASHRAE Handbook--HVAC Applications (2015) is widely used for this purpose. This Handbook refers to a reduced exhaust air velocity that was regarded as sufficient to expel obnoxious particles/fluids from cooking facilities, practically reducing exhaust fan capacity and saving energy.

Now that these reductions in exhaust air duct velocity are part of a standard, computational fluid dynamics (CFD)/thermal stress analysis can be used to carry out a comprehensive analysis and explore how such an air duct behaves and whether there is a possibility to reduce steel duct thickness by using standard industrial software simulation methods. Naturally, to ensure the integrity of a reduced air duct steel wall thickness, steel mechanical characteristics under elevated temperatures specified under ASHRAE Handbook--HVAC Applications (2015) will have to be accounted for. Therefore, it is possible to say that a criterion can be set to accept a reduced steel duct thickness operating under elevated temperatures. Such a decision will have to be justified technically, such as by the use of CFD/thermal stress analysis.

KITCHEN STEEL EXHAUST AIR DUCTS

According to ASHRAE Handbook--HVAC Applications (2015), Type 1 kitchen hoods are designed to cater to a range of appliances categorized as light, medium, heavy duty, and extra heavy duty, with operating temperatures ranging from 200[degrees]C to 370[degrees]C (392[degrees]F to 698[degrees]F). Assumed air duct temperature in this paper will be based on the most extreme temperature condition, 370[degrees]C (698[degrees]F).

William Gerstler (2002) notes the following: "Commercial kitchen design professionals were concerned that the minimum exhaust air duct velocity of 7.62 m/s (1500 fpm)," which was an NFPA requirement, "was too restrictive." The completed research work addresses "the relationship between grease deposits and exhaust velocity.... Research resulted in several published documents." NFPA 96, Standard for Ventilation Control and Fire Protection of Commercial Cooking Operations, then in March 2002, reduced exhaust velocity to 2.54 m/s (500 fpm). This reduction in exhaust velocity can be further enhanced by providing duct insulation, as explained by William Gerstler (2002): "Lowering velocity reduces grease deposition in virtually all cases when duct work with insulation of R-10 or greater is used."

John Clarke (2012) notes: "Type 1 duct construction consists of at least 16-gage black steel or 18-gage stainless steel. This duct must slope 6 mm per 0.3 m (0.25 in. per ft) toward the hood or an approved grease reservoir."

This paper will simulate (at the first instant) a typical kitchen exhaust air duct constructed out of a 16-gage steel duct sheet material but without insulation. The aim is to investigate air duct mechanical characteristics near 2.54 m/s (500 fpm) exhaust air velocity and an extreme inlet air temperature of 370[degrees]C (698[degrees]F) (see Discussions section). Investigation will then continue to simulate an 18- and 24-gage steel duct (not stainless steel) and validate performance as an alternative thinner material but with lower cost than stainless steel.

CFD MODEL

The model was prepared as shown in Figure 1. A CFD analysis was carried out using Fluent[R] software (ANSYS 2016) with the following assumptions and settings:

a. Steady-state analysis with CFD/thermal stress analysis: Once the CFD analysis was setup and run using the custom system, select from the software toolbox Fluid Flow (Fluent) > Static Structural tool, thermal stress analysis. This action will link the CFD software tool with the thermal/stress analysis software tool.

b. Number of cells used is 98,103. It is important to check the quality of mesh, therefore select the following: Mesh Metrics--Element Quality; Minimum Jacobian element 0.27, Maximum Jacobian element 0.99, Average Jacobian element 0.82, Standard Deviation 9.86 e-2. A Jacobian element close to 1 indicates a good element quality, while a Jacobian element close to 0 indicates a poor element quality. Element sizing, use advanced Size function; On: Proximity and Curvature. Number of cells across gap, 3.

c. Settings not mentioned in this paper can be left at software default settings.

d. Air as an ideal gas was assumed.

e. Used the k-omega shear stress transport (k-ra SST) turbulence model. See section "Discussions" on performance of this model.

f. Inlets shown in Figure 1 were set at 0 gage pressure, temperature at 370[degrees]C or 643 K (698[degrees]F). Outlet was assumed to be exhaust fan with a capacity of 30 Pa (0.0003 bar).

g. In the Boundary Conditions settings, select Thermal tab. Enter the following information to define duct walls thermal settings:

Select from main menu: Thermal Conditions > Mixed, and then enter the following data:

* Heat transfer coefficient 7.9 W/([m.sup.2] x K)

(1.40 Btu/[h x [ft.sup.2] x [degrees]F])

* Free stream temperature 26.8[degrees]C (80.24[degrees]F)

* External emissivity 0.9

* External Radiation Temperature 26.8[degrees]C (80.24[degrees]F)

* Wall thickness, varies depending on selected sheet metal thickness.

h. Duct wall 16-gage galvanized sheet steel, assumed to be 1.61e-3 m (0.0635 in.). This gage thickness was then changed for the various simulations. See Tables 1 and 2 for simulated gage thickness.

i. A check on maximum air velocity can be checked in the postprocessor. In this example, maximum velocity is 3.339 m/s (657.11 fpm), as shown in Figure 1.

j. Link the two Geometries items shown in the Fluid Flow and Static Structural menus. Link the Solution item in the Fluid Flow menu with the Setup item in the Static Structural menu.

k. At the structural model settings, select steel sheet from the Engineering Data tool, and then select and open the Model item. Fix supports as shown Figure 1, and then import solution data, which is pressure in duct acting on all duct walls. Carry out the same for thermal solution. Import from Fluid Flow thermal settings.

l. When meshing the steel duct walls, select the mesh tool and allow for a medium mesh setting: Number of elements used is 1608. To check the quality of mesh select Mesh Metrics--Element Quality; this gives Minimum Jacobian element 0.24, Maximum Jacobian element 0.99, Average Jacobian element 0.70, Standard Deviation 0.17. A Jacobian element close to 1 indicates a good element quality, while a Jacobian element close to 0 indicates a poor element quality.

m. Finally, select outputs which are Equivalent Stress (von Mises) and Total deformation.

RESULTS

Graphical and numerical results were generated using the software postprocessor. Results for minimum and maximum von Mises stress values are shown in Table 1, extrapolated from Figures 2 to 4, while Table 2 shows maximum total deformation figures, extrapolated from Figures 5 to 7.

Refer to Figure 2 for an example of how maximum and minimum stress readings were extrapolated and entered in Table 1. The minimum value shows that this stress contour substantially covers the duct surface area.

Figures 2 to 4 are thermal stress analysis results:

* Figure 2 shows a kitchen exhaust duct made of sheet metal 0.7 mm (0.028 in.) thick, 24-gage galvanized steel sheet metal. The top image represents an inlet temperature of 200[degrees]C (392[degrees]F), while the bottom image represents an inlet at 370[degrees]C (698[degrees]F).

* Figure 3 shows a kitchen exhaust duct made of sheet metal 1.31 mm (0.0524 in.) thick, 24-gage galvanized steel sheet metal. The top image represents an inlet temperature of 200[degrees]C (392[degrees]F), while the bottom image represents an inlet at 370[degrees]C (698[degrees]F).

* Figure 4 shows a kitchen exhaust duct made of sheet metal 1.61 mm (0.0644 in.) thick, 24-gage galvanized steel sheet metal. The top image represents an inlet temperature of 200[degrees]C (392[degrees]F), while the bottom image represents an inlet at 370[degrees]C (698[degrees]F).

Figures 5 to 7 are total (exaggerated) deformation images:

* Figure 5 shows a kitchen exhaust duct made of sheet metal 0.7 mm (0.028 in.) thick, 24-gage galvanized steel sheet metal. The top image represents an inlet temperature of 200[degrees]C (392[degrees]F), while the bottom image represents an inlet at 370[degrees]C (698[degrees]F).

* Figure 6 shows kitchen exhaust duct made of sheet metal 1.31 mm (0.0524 in.) thick, 24-gage galvanized steel sheet metal. The top image represents an inlet temperature of 200[degrees]C (392[degrees]F), while the bottom image represents an inlet at 370[degrees]C (698[degrees]F).

* Figure 7 shows kitchen exhaust duct made of sheet metal 1.61 mm (0.0644 in.) thick, 24-gage galvanized steel sheet metal. The top image represents an inlet temperature of 200[degrees]C (392[degrees]F), while the bottom image represents an inlet at 370[degrees]C (698[degrees]F).

DISCUSSIONS

CFD Discussions on Turbulence Model Used

According to Ghiaasiaan (2011), the shear stress transport (SST) model uses the k- ra model at near wall conditions, taking an advantage of its effectiveness at the inner boundary layer, and then switches to k- e at the free-stream conditions, where k-e performs better than the k-ra model.

As expected in this simulation, where adverse pressure gradients do exist, particularly near duct walls and around corners, the model performed well and confirms what is stated above.

Discussions on Heat Transfer

Heat transfer selections made in the CFD Model section, item g, were comprehensive, considering convective, conductive, and thermal radiation. Hence, the mixed function settings was selected.

Faye McQuiston et al. (2000) describes thermal radiation as "the transfer of thermal energy by electromagnetic waves, an entirely different phenomenon from conduction and convection." In fact, thermal radiation can occur in a perfect vacuum and is actually impeded by an interrupting medium. Therefore, the different methods in heat transfer were addressed separately or as mixed settings as shown in the software settings.

The following paragraphs are mechanical discussions and observations made on simulation/results:

1. Because the steel duct in this analysis is subjected to high temperatures, the first discussion will focus on creep failure. According to S.S. Manson and G.R. Halford (2009), "Creep is a time dependent deformation that occurs at high temperature relative to the melting point of metallic materials. The creep regime for metals is commonly regarded to begin at a temperature of approximately half the absolute temperature (degrees Kelvin or Rankine) of the metal melting point."

Therefore, if the melting point of carbon steel is 1698 K (2597[degrees]F), the creep range will begin at 849 K (1068[degrees]F). This is well above the 643 K (698[degrees]F) figure mentioned in item F in the FD Model section. Thermal stress analysis results will exclude this concern of creep failure.

2. Fatigue limit as explained by N.E. Frost et al. (1974) notes that the "fatigue limit/tensile strength ratio lay between 0.4 and 0.5." For practical purposes and little error, steels having tensile strengths up to about 1250 MN/[m.sup.2] (181.3 kpsi) that the fatigue limit/ultimate tensile strength, ratio can be assumed to be 0.5. In other words,

Fatigue limit for steel = 0.5 x 460 = 230 MN/[m.sup.2] (33,358.7 psi)

Note, wrought steels have tensile strengths ranging from 310 to 2000 MN/[m.sup.2] (45 to 290 kpsi). The 460 MN/[m.sup.2] (67 kpsi) figure was obtained from the software-selected engineering data.

3. Exhaust duct velocities: Velocity in duct was selected such that maximum values are near and slightly above the standardized 2.54 m/s (500 fpm) exhaust air velocity, which is 3.339 m/s (657.11 fpm) as shown in Figure 1. This was done as an added insurance to allow for possible imperfections that may occur when fan is selected, in other words, an added design safety factor.

4. The investigation has shown that by using the reduced airflow velocities, thinner steel sheets can be used, such as the 0.7 mm (0.03 in.) 24-gage galvanized steel sheets.

This is demonstrated in Figures 2 to 4. However, only certain sections of the steel duct can be effected by high stress values. This occurs because of geometry imperfections, where stress concentrations occur at the grease collection point. Therefore, it can be said that with careful design, where sudden changes in geometry or stress concentration areas are avoided, thinner sheet metal can be used. That is, provided the three criteria (items 1 to 3 in the Discussions on Heat Transfer section) are complied with and demonstrated through this similar procedure as one way of validating steel duct material reductions.

A simple solution to avoid this grease collecting sump would be, for example, to keep the lower part of duct flat and slope towards one side and avoid introducing any sudden changes in geometry where stress concentrations can occur. However, if it is necessary to keep such an arrangement, then a higher steel thickness can be used in specific areas to overcome such weaknesses and continue using the thinner sheet material as demonstrated in the remainder duct sections.

5. Graphical stress results have shown the following observations (Figures 2 to 4):

a. Maximum stress levels decrease as sheet metal thickness increases.

b. In all cases, the larger dark stress contour areas indicate that stress levels are lower than fatigue limit calculated in item 2 in the Discussions on Heat Transfer section, 230 MN/[m.sup.2] (33.3 kpsi).

c. Exceptions are in the lower part of the duct, at inlets and the grease collection areas. See recommendations made in item 4 in the Discussions on Heat Transfer section.

6. Graphical total deformation results have shown the following observations (Figures 5 to 7):

a. In all cases, as temperature increases, deformation increases. This is because of the metal softening up as temperature increases.

b. In all cases, as the material sheet thickness increases, total deformation decreases.

7. It is possible to suggest that, based on the previous discussions, a CFD/thermal stress analysis can be used as an alternative way or a standard/code in producing a low-cost steel kitchen exhaust ducts.

Importance of Sustainable Development

According to Stephen A. Roosa (2010), describing suitability: "The ability of physical development and environmental impacts to sustain long term habitation on the planet Earth by human and other indigenous species while providing:

1. An opportunity for environmentally safe, ecologically appropriate physical development.

2. Efficient use of natural resources.

3. A framework which allows improvement of the human condition and equal opportunity for current and future generations.

4. Manageable urban growth."

CONCLUSION

It was demonstrated that by using a CFD/thermal stress analysis, thinner sheet metal exhaust ducts can be used., provided that the mechanical thermal stress limitations and fatigue limit of materials used are not exceeded.

Turbulence model k-ra SST was used successfully, with the numerical solution stabilizing at an early stage. CFD simulation was carried to cover (Type 1 kitchen exhaust ducts) light and extra heavy duties considering exhaust inlet temperatures of 200[degrees]C and 370[degrees]C (392[degrees]F and 698[degrees]F), respectively.

Using lower in-duct exhaust air velocities not only reduces fan power requirements but produces a lower negative pressure on duct walls. Therefore, thinner duct materials can be used as demonstrated. Simulations were carried out to demonstrate that steel gage thicknesses as low as 24 can be used, rather than the specified standards of 16- and 18-gage.

ACKNOWLEDGMENTS

Thanks to Mr. Abdulkadir Benzamia, Qatar Rail, POB 29988, Doha, Qatar, for his recommendations on best practices in model settings, and Dr. Lik Sim of Qatar University, Qatar, for software setting up and providing access.

REFERENCES

ANSYS. 2016. ANSYSFluent. Canonsburg, PA: ANSYS, Inc.

ASHRAE. 2015. Sections A33.6 and A33.9, ASHRAE Handbook--HVACApplications. Atlanta: ASHRAE.

Clarke, John. 2012. Design considerations for commercial kitchen ventilation. ASHRAE Journal 54(2):58.

Frost, N.E., K.J. Marsh, and L.P. Pook. 1974. Fatigue strength at long endurances. Mineola, NY: Dover Publications. pp. 46.

Gerstler, William D. 2002. New rules for kitchen exhaust. ASHRAE Journal 44(11):26.

Ghiaasiaan, S.M. 2011. Convective heat and mass transfer. Cambridge: Cambridge University Press, p. 474.

Manson, S.S., and G.R. Halford. 2009. Chapter 1, Fatigue and durability of metals at high temperatures. Materials Park, OH: ASM International. pp. 1.

McQuiston, Faye C., Jerald D. Parker, and Jeffrey D. Spitler 2000. Heating, ventilating and air conditioning analysis and design, 5th ed. New York: John Wiley & Sons Inc. pp. 133.

Roosa, Stephen A. 2010. Sustainable development handbook, 2nd ed. Lilburn, GA: Fairmont Press. pp. 44.

Ali M. Hasan, CEng

Member ASHRAE

Ali M. Hasan is a senior mechanical engineer at KEO International Consulting Engineers, Doha, Qatar.

Table 1. Maximum and Minimum Equivalent
(von Mises) Stress Obtained
per a Simulated Duct Category:

Light Duty 20[degrees]C (392[degrees]F)
and Extra Heavy Duty 370[degrees]C (698[degrees]F)

             Light Duty

             Equivalent
Duct          Stress,          Max
Category   Min MPa (kPsi)   MPa (kPsi)

16-gage        28.462         256.09
18-gage        28.47          256.17
24-gage        28.492         256.37

             Heavy Duty

             Equivalent
Duct          Stress,          Max
Category   Min MPa (kPsi)   MPa (kPsi)

16-gage        28.495         256.39
18-gage        28.51          256.52
24-gage        28.55          256.92

Results obtained at the postprocessor stage.
See Figures 2 to 4 for locations.

Table 2. Total Deformations Obtained per a
Simulated Duct Category:

Light Duty 200[degrees]C (392[degrees]F)
and Extra Heavy Duty 370[degrees]C (698[degrees]F)

Light Duty

Duct Category   Total Deformation, mm (in.)

16-gage              0.18741 (0.00749)
18-gage              0.18822 (0.00753)
24-gage              0.18972 (0.00759)

Heavy Duty

Duct Category   Total Deformation, mm (in.)

16-gage              0.36544 (0.01462)
18-gage              0.36654 (0.01466)
24-gage              0.36857 (0.01474)

Results obtained at the pos tprocessor stage.
See Figures 2 to 4 for locations. Maximum
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Author:Hasan, Ali M.
Publication:ASHRAE Transactions
Article Type:Report
Date:Jul 1, 2016
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