Fixing Sensor Position Using Computational Fluid Dynamic Analysis

M.V. Shyla1 , K.B. Naidu2 , G. Vasanth Kumar3

1Department of Mathematics, Sathyabama University, Chennai-600119, India.2Department of Mathematics, Sathyabama University, Chennai-600119, India.

3Department of Aeronautical Engineering, Sathyabama University, Chennai-600119, India. 1shylamv@yahoo.com, 2kbnaidu999@gmail.com, 3vassa.aero@gmail.com

Abstract: This paper aims at fixing an optimal sensor position in indoor environment using Computational Fluid Dynamic (CFD) technique, Finite volume method. CFD Simulation of hydrogen-cyanide is performed around circular sensors fixed at different locations under steady state condition with laminar and turbulent boundary conditions. The CFD model is generated using Gambit software. CFD Analysis is done using Fluent software to compute velocity profile, pressure distribution, and streamline pattern. The effect of hydrogen-cyanide on the circular sensors is studied using which optimal sensor placement can be determined. This information can be used in fixing sensors in an optimal position in industries and indoor environment to increase the efficiency of sensing.

Key words: computational fluid dynamic analysis, laminar; turbulent, steady flow, sensor position, Finite volume method

1. Introduction

In indoor environment, the chemical and biological agent dispersion is very fast. The sensors are used to give early warning in order to escape dangerous situations in case of a terrorist attack or accidents. Early warning before the contaminant reached an occupant in the room is possible only if the sensors are fixed in a suitable position inside the room. Optimal placement of sensors increases the efficiency of sensing. Computational fluid dynamic simulations are much effective and cheaper when compared to the experimental study. A modified multizone model (Arvelo et al., 2002) was used to analyze the suitable placement of chemical and biological toxic sensors in a building. The contaminant flow time in a zone was not considered since the model assumed instantaneous mixing in each zone. The multizone model was not able to give clear and complete information about the sensor position. To obtain more accurate and detailed results researchers (Zhenzhang liu, 2000) prefer CFD modeling. Researchers have also developed different search strategies to localize the source of the leak (Mohamed S. Awadallai et al., 2012) . CFD analysis of spherical gas sensor array ( Ishida et.al., 2003) was studied in a two dimensional flow field with laminar main flow. But optimal sensor position was no analyzed. Later the optimal sensor position for chemical and biological agent releases in buildings were studied (Zhai et al., 2003). Their study revealed that CFD simulation can be used to find the sensor deployment location. Optimal sensor placement during a chemical and biological contaminant threat in a city was studied (Obenschain et al., 2004) with CFD modeling. The contaminant transport details were pre-computed, stored, and interpreted with a nomograph technique. Their analysis depended on the assumed weather conditions. CFD studies also concentrated on optimal sensor placement for hazardous material transports (Löhner and Camelli , 2005) around buildings. Identification of contaminant sources in enclosed environments by inverse CFD modeling (Zhang et.al., 2006) was done. CFD program were used (Zhang et.al., 2007) to monitor cabin air quality, infectious disease transmission, and intentional airborne contaminant releases in commercial aircraft cabins. CFD model for indoor plume propagation (Liu and Lu, 2008) was analyzed using Fluent software to predict a two dimensional plane flow field in a building. CFD model was developed for search strategy to localize the source of leak using robots (Mohamed et.al., 2012). Optimal sensor position on different surfaces like spherical, cylindrical, cubical, and prism using CFD analysis (Shyla et al., 2013) for reducing accidents caused by emission of toxic gas in industries.

Hydrogen cyanide gas in air at concentration over 5.6% is an explosive. It is listed among the chemical warfare agents. It was used during the world war II in the German concentration camp mass killing. In this paper, we study two dimensional flow field with laminar and turbulent flow at low cost to simulate flow of hydrogen cyanide around circular gas sensors used for indoor plume tracing. CFD simulation is performed by fixing sensors at different positions in different models in an indoor set up and the models are compared. The information on the flow pattern can be used in identifying and fixing the optimal sensor position in an indoor environment to sense efficiently.

The paper is organized as follows. The governing differential equations and boundary conditions are given in the first part. The second part discusses the methodology . The third part explains the results of this study in detail. The concluding remarks are presented in the last part.

2. Mathematical Formulation

A. Governing Differential Equation

The governing differential equation for a steady, incompressible flow is given by Navier-Stokes system of equations namely the equation of continuity and the momentum equations.

Equation of continuity: ∇ . q = 0 (1)x-momentum equation:

∇ . ( ρ u q )=−∂ p∂ x

+ ∇ . ( μ ∇ u ) (2)

y-momentum equation:

∇ . ( ρ v q )=−∂ p∂ y

+ ∇ . ( μ ∇ v ) (3)

q = u i +v j is the velocity vector where u & v are the velocity components in the x & y directions respect-

ively, p is pressure, ρ is density, and µ is coefficient of viscosity (M. Pontiggia et al., 2009; H. Versteeg and W. Malalasekra, 2011).

B. Boundary Conditions: The circular sensors are placed at different positions in different models in an indoor environment. When airflows, it brings a gas cloud from the inlet which flows along the circular sensor before it is being carried away into the wake. A two dimensional flow of hydrogen cyanide is simulated around circular sensors under steady state conditions. The operating pressure is kept at 101325 pascals. Body forces are all ignored. The inlet velocity of 0.01m/s and 0.5m/s is taken for laminar flow and turbulent flow respectively. The walls are considered to be rigid. No slip boundary condition is assumed. The physical properties of hydrogen cyanide is taken for analysis with density ρ=1kg/m3 and coefficient of viscosity µ=1.72e-05 kg/m-s.

Fig.1a Grid of Model1

Fig.1b Grid of Model2 generated by Gambit Software.

Fig.1c Grid of Model3

Fig.1 (d). Grid of Model4

Fig.1 (e). Mesh generated using Gambit software

3. Methodology

The computational fluid dynamic model geometry is developed using the CFD software, Gambit as presented in Fig.1a, Fig.1b, Fig.1c, Fig.1d and Fig.1e. The dimensions of the building section are taken as 100m and 50m in the x and y directions respectively with circle radius 1 m. Computational fluid dynamic technique namely finite volume method is applied. It consists of 3 steps. In the first step, discretization of the entire domain into finite number of control volumes is done. In the next step analysis is performed followed by the post processing of the results.

A. Discretization: The quadrilateral pave mesh with interval size 0.25 was generated for the entire domain under consideration for all the models. The number of nodes and quadrilateral cells for each model is presented in Table 1. The two dimensional mesh is exported to Fluent software for analysis.

Table 1. DiscretizationMode

lNo. of Nodes

No. of Quadrilatera

l cells

Minimum Volume

e-002 (m3)

Maximum Volume

e-001 (m3)1 82613 81976 1.543551 1.4308412 82859 82210 1.269687 1.3106773 81929 81292 1.7111163 2.6085644 81862 81225 1.810986 2.194254

The partial differential system of equations is discretized by upwind differencing scheme over each control volume and is reduced to algebraic system of equations as follows:( ρ uA )e − ( ρ uA )w + ( ρ vA )n − ( ρ vA )s= 0

(4)

( ρ uA )e ue − ( ρuA )w uw =( pw − pe )Δx

ΔV u

( ρ vA )n vn − ( ρ vA ) s v s =( ps − pn)Δy

ΔV v

(5)

The RHS represents the pressure gradient integrated over the control volume ΔV . The above equations

represents discretized Navier Stokes equation along the x direction where ΔV is the volume, A is the area, e is the node to the east and w is the node to the west of of u-cell, n is the node to the north and s is the node to the south of v-cell. For laminar flow, the equation of continuity and momentum equations are solved. For turbulent flow, k-ε model is used to indicate the effects of the turbulence. The k-ε model introduces two transport equations for turbulent kinetic energy k and turbulent kinetic energy dissipation rate ε in addition to the equation of continuity and momentum equations, given by following equations.

∂∂ t

( ρk )+ ∂∂ x i

( ρk ui )=∂

∂ x j [(μ+μt

σk) ∂ k

∂ x j ]+ M k+M b−ρε−Y m ¿ (6)

∂∂ t

( ρε )+ ∂∂ x i

( ρε ui )=∂

∂ x j [(μ+μ t

σ ε) ∂ ε∂ x j ]+C ε 1

εk(M ¿¿k+C ε 3 M b)−C ε 2 ρ

ε2

k(7)¿

where ui is the velocity component along x direction, μ is the viscosity, μ t is the turbulent viscosity, Mk is the shear stress-related turbulent kinetic energy production, M b is the buoyancy-related turbulent kinetic energy

production, Ym is the compressibility related kinetic energy production. Cε1=1.44; Cε2=1.92; Cε3=1.0; σk=1, σε=1.3, and Cμ=0.09 are empirical constants (M. Pontiggia et al., 2009). Discretized equations are iteratively solved by segregated solver using Semi-Implicit Method for Pressure Linked Equations known as SIMPLE algorithm in Fluent software where values u0, v0, and p0 are initial guess values. The flow equations are solved using guessed pressure field to obtain velocity components u0, and v0.

The correction p’ is defined as the difference between the correct pressure field p and the guessed pressure field p0 . The correction velocity fields are also similarly defined. P=p0 + p’ ; u=u0 + u’ ;v=v0 + v’ (8)The iteration stops if the solution converges. If not, then p, u, and v are used as initial guess values in the next iteration and the whole process is repeated till the solution converges (John F. Wendt, 2009). In the case of problems involving complex geometries, the entire domain under consideration in physical space with artesian coordinates (x,y) is transformed to computational space with curvilinear coordinates (ξ, η) and then solved. When the solution is obtained, it is transferred back to physical space (Joel Guerrero, 2012; Shyla M.V., 2013). In computational space, the governing differential equations in compact form become

∂ ei

∂ ξ+

∂ hi

∂ η=

∂ ev

∂ ξ+

∂ hv

∂ η (9)

Where

e i=1J

(ξx e i+ξ y hi )

hi=1J

(ηx e i+ηy hi )

ev=1J

(ξx ev+ξy hv)

hv=1J

(ηx ev+η y hv )(10)

(Q) is the vector containing the primitive variables.

e i & hi are the vectors containing the inviscid fluxes in the ξ and η directions.

ev & hv are the vectors containing the viscous fluxes in the ξ & η directions respectively.

Q= 1J [0uv ]; e i=

1J [ U

uU + p ξ x

vU+ p ξ y]; hi=[ V

uV+ p ηx

vV + pηy];

U=u ξx+v ξ y ;V =uηx+vη y

ev=1

J ℜL [ 0(∇ ξ .∇ξ ) uξ+ (∇ξ .∇η ) uη

(∇ξ .∇ξ ) vξ+ (∇ξ .∇η ) vη];

hv=1

J ℜL [ 0(∇η .∇ξ )uξ+(∇ η .∇η)uη

(∇ η .∇ξ ) vξ+(∇ η .∇η)vη]

τ xx=2ℜL

(ξx uξ+ηx uη ) ; τ yy=2ℜL

(ξ y vξ+ηy vη ) ;

τ xy=1ℜL

(ξ y uξ+η y uη+ξx vξ+ηx vη ) ; τ xy=τ yx(11)

B. Validation:

Grid validation is done. Differerent grids have been tried. Perfect mesh combination has been performed to identify the flow pattern by varying the no. of nodes and shape of the mesh. The mass flow rate at the inlet and outlet is measured. Conservation of mass is ensured. Convergence of the solution correct to three decimal places is checked.

Table 2. Mass flow rate(kg/s)Mode

lInlet Outlet

1 0.61249 -0.612492 0.6125 -0.612493 0.6125 -0.612494 0.6125 -0.61249

C. Error Analysis: Discretization error (d) and round off error(r) are the errors done by the computer during each iteration (John F. Wendt, 2009) .

d = A – S1; r = N- S1‘A’ is the analytical solution of the partial differential equation.‘S1’ is the exact solution of the difference equation. ‘N’ is the Numerical solution from a computer with finite accuracy. The solution is unstable if the r i

’s grow bigger during the progression of the solution from nth step to (n+1)th step. The solution is stable if

|ri

n+1

rin

|≤ 1 (12)

D. Limitation: If the Space mesh size is reduced, then more amount of memory and time computation is required.

E. Future Scope: This study can be extended to unsteady state with turbulent flow conditions. Single and multiple flow of various toxic chemicals can be considered. Many other shapes of sensors and geometry of different indoor environments can be studied for CFD analysis.

4. Analysis of Results

In this study, viscous flow of hydrogen cyanide on the circular sensors has been considered. The flow pattern around the circular sensors placed at different locations are visualized for laminar flow conditions from Fig.2a, Fig.2b, Fig.2c, Fig.2d, Fig.2e, Fig.2f, Fig.2g, Fig.2h, and Fig.2i. The turbulent flow pattern around the circular sensors in different models can be viewed from Fig.4a, Fig.4b, Fig.4c, and Fig.4d. The velocity on and around the circular sensors can be visualized with the help of different contours starting from blue to red. Red colour indicates very high velocity and blue colour for very low velocity . The velocity values corresponding to different contours are shown in the figures. Red contours are observed on the region perpendicular to the circular sensors which indicates very high velocities ( Ishida et.al., 2003). This indicates that the contaminants are not captured by the sensors at the region perpendicular to the sensors and the gas cloud keeps moving with high velocity. Blue contours observed at the upstream and downstream sides of the sensors is an indication of low velocity. Stagnation points are identified in the region of low velocity and hence it is an implication of sensing. The contaminants are captured by the sensors at these stagnation points. Comparing the velocity magnitudes of low velocity region in various models, a variation in velocity magnitude is observed in model2, model3 and model4. But the magnitude of velocity around the three sensors in model 1 remains the same. This variation reveals the fact that the flow is disturbed by the placement of sensors in all models except model1. For model1, the velocity magnitude corresponding to the green contour lies between 5.40e-03m/s and 6.07e-03m/s in the fore section of the sensor, the velocity magnitude in laminar flow corresponding to the blue

contour lies between 1.35e-03m/s and 2.02e-03m/s in the aft section of the sensor, and the velocity magnitude corresponding to the red contour lies between 1.15e-02m/s and 1.21e-02m/s in the perpendicular section of the sensor. Similarly for turbulent flow pattern in model1, the velocity magnitude corresponding to the green contour lies between 2.02e-01m/s and 2.35e-01m/s in the fore section of the sensor, the velocity magnitude in laminar flow corresponding to the blue contour lies between 3.36e-02m/s and 6.73e-02m/s in the aft section of the sensor, and the velocity magnitude corresponding to the red contour lies between 5.72e-01m/s and 6.73e-02m/s in the perpendicular section of the sensor. These values remain the same for all the 3 sensors used in model1. It is important to place the sensors in appropriate locations such that the flow remains undisturbed. Hence the placement of sensors given in model1 is considered as as an optimal sensor position. When the flow is undisturbed, the sensing efficiency increases. Pressure distribution at different points on and around the circular sensors are presented in Fig.6a, Fig.6b and Fig.6c. High pressure region is an implication of sensing. The high pressure value in model1 for turbulent flow is found to lie between 8.50e-02pascals and 1.07e-01pascals and the low pressure lies between-2.07e-01 and -1.85e-01. Streamline pattern given in Fig.5a, Fig.5b, Fig.5c, and Fig.5d, gives the direction of flow of fluid particles. Small length of the vector indicates low velocity. Convergence of the solution correct to 3 decimal places are ensured as given in Fig.3a and Fig. 3b. The solution converges at 264 th iteration for model1, 301st iteration for model2, 741st iteration for model3, and 265th iteration for model4 for laminar flow and the solution converges at 272nd iteration for model1, 266th iteration for model2, 331st iteration for model3, and 236th iteration for model4 for turbulent flow conditions. The wall shear stress for laminar flow around circular sensors is calculated as seen in Fig.7a, Fig.7b, Fig.7c and Fig.7d.

Fig.2 (a). Laminar flow pattern around circular sensors in Model1

Fig.2 (b). Velocity Magnitude plot for laminar flow in Model1

Fig.2 (c). Laminar flow pattern around circular sensors in Model2

Fig.2 (d). Velocity Magnitude plot for laminar flow in Model2

Fig.2 (e). Laminar flow pattern around circular sensors in Model3

Fig.2 (f). Velocity Magnitude plot for laminar flow in Model3

Fig.2 (g). Laminar flow pattern around circular sensors in Model4

Fig.2 (h). Velocity Magnitude plot for laminar flow in Model3

Fig.2 (i). Contours of Velocity Magnitude for laminar flow in Model1

Fig.3 (a). Velocity iteration plot for laminar flow around circular sensor in Model1

Fig.3 (b). Velocity iteration plot for turbulent flow around circular sensor in Model1

Fig.4 (a). Turbulent flow pattern around circular sensors in Model1

Fig.4 (b). Turbulent flow pattern around circular sensors in Model2

Fig.4 (c). Turbulent flow pattern around circular sensors in Model3

Fig.4 (d). Turbulent flow pattern around circular sensors in Model4

Fig.5 (a). Streamline pattern for laminar flow around circular sensor in Model1

Fig.5 (b). Streamline pattern for laminar flow around circular sensors in Model2

Fig.5 (c). Streamline pattern for laminar flow around circular sensors in Model3

Fig.5 (d). Streamline pattern for laminar flow around circular sensors in Model4

Fig.6 (a). Pressure distribution for laminar flow around circular sernsors in Model1

Fig.6 (b). Pressure distribution for laminar flow around circular sernsors in Model2

Fig.6 (c). Pressure distribution for laminar flow around circular sernsors in Model4

Fig.7 (a). Wall Shear Stress plot for laminar flow around circular sensors in Model1

Fig.7 (b). Wall Shear Stress plot for laminar flow around circular sensors in Model2

Fig.7 (c). Wall Shear Stress plot for laminar flow around circular sensors in Model3

Fig.7 (d). Wall Shear Stress plot for laminar flow around circular sensors in Model4

5. Conclusion

A two dimensional, viscous, incompressible flow field around circular sensors has been analyzed with laminar and turbulent flow pattern under steady state conditions. The flow pattern of hydrogen-cyanide around the sensor has a great impact on the sensitivity of sensors. The placement of circular sensors in Model1 shows good response in terms of sensing when compared to other models. It is because the flow is not disturbed due to the arrangement of sensors in model1. Hence it increases the efficiency of sensing and thereby give an early warning about the contaminants before it reaches the occupants. This information has been obtained based on the velocity, pressure and streamline pattern of hydrogen-cyanide. Hence the results of this study can be considered in fixing the optimal sensor position to sense effectively and get early warning about the contaminants.

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