**1.3 CFD as a visual and graphical quantification tool**

CFD is a tool for testing and quantifying fluid dynamics over an internal or external body where fluid flow is involved. CFD saves material cost and manufacturing time for analyzing aerodynamics of an initial design concept that has been created [3]. Aerodynamics is a study of airflow in either the internal or

**Figure 1.** *Flowchart of FDM.*

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)… DOI: http://dx.doi.org/10.5772/intechopen.91895*

external side of the body. The aerodynamics concerned in this chapter is related to the external flow over an unknown aircraft body. CFD helps to simulate actual size of computer-aided design (CAD) model, in an enclosed control volume. Any property in the control volume is controlled using Reynolds transport theorem as shown in Eq. (1), and further this approach is applied on velocities over three-dimensional space and time using Eulerian technique as shown in Eq. (2):

$$\frac{DB\_{\rm sys}}{Dt} = \frac{\partial}{\partial t} \left[ \rho b d\Psi + \int\_{\rm c} \rho b \, \mathbf{V} \cdot \mathbf{\hat{n}} dA \right] \tag{1}$$

$$\frac{Du}{Dt} = u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} + w\frac{\partial u}{\partial z} + \frac{\partial u}{\partial t} \tag{2}$$

Partial differential equations are used for describing system of fluids (i.e., gasses and liquids) that are represented by the general laws of conservation of mass, momentum, and energy [4].

The principle of mass balance is used in light of law of conservation of mass for fluid element, and it is written in Eq. (3) [5].

$$\frac{d\rho}{dt} + \nabla \times (\rho \times \nu) = \mathbf{0} \tag{3}$$

where *<sup>∂</sup><sup>ρ</sup> dt* with derivation of density with time change and ∇ � ð Þ *ρ* � *v* is time rate of change of volume of moving fluid.

The momentum equations in the *x*-, *y*-, and *z*-axes, respectively, are expressed in Eq. (4).

$$\frac{\partial(\rho u)}{\partial t} + \nabla \times (\rho uV) = -\frac{\partial p}{\partial x} + \frac{\partial \tau\_{xx}}{\partial x} + \frac{\partial \tau\_{yx}}{\partial y} + \frac{\partial \tau\_{xx}}{\partial z} + \rho f\_x$$

$$\frac{\partial(\rho v)}{\partial t} + \nabla \times (\rho vV) = -\frac{\partial p}{\partial y} + \frac{\partial \tau\_{xy}}{\partial x} + \frac{\partial \tau\_{yy}}{\partial y} + \frac{\partial \tau\_{xy}}{\partial z} + \rho f\_y \tag{4}$$

$$\frac{\partial(\rho w)}{\partial t} + \nabla \times (\rho wV) = -\frac{\partial p}{\partial z} + \frac{\partial \tau\_{xx}}{\partial x} + \frac{\partial \tau\_{yx}}{\partial y} + \frac{\partial \tau\_{xx}}{\partial z} + \rho f\_z$$

The energy equations used were derived from Navier-Stokes which depends upon the first law of thermodynamics [6]. The derivation for conservation of energy on a finite fluid element consists of a single equation which is expressed in Eq. (5).

$$\begin{aligned} &\frac{\partial}{\partial t}\left[\rho\left(\varepsilon + \frac{V^2}{2}\right)\right] + \nabla \times \left[\rho\left(\varepsilon + \frac{V^2}{2}\right)V\right] = \rho\dot{q} \\ &+ \frac{\partial}{\partial \mathbf{x}}\left(\mathbf{k}\frac{\partial T}{\partial \mathbf{x}}\right) + \frac{\partial}{\partial \mathbf{y}}\left(\mathbf{k}\frac{\partial T}{\partial \mathbf{y}}\right) + \frac{\partial}{\partial \mathbf{z}}\left(\mathbf{k}\frac{\partial T}{\partial \mathbf{z}}\right) - \frac{\partial (up)}{\partial \mathbf{x}} \\ &- \frac{\partial (vp)}{\partial \mathbf{y}} - \frac{\partial (wp)}{\partial \mathbf{z}} + \frac{\partial (u\boldsymbol{\tau}\_{\text{xx}})}{\partial \mathbf{x}} + \frac{\partial (u\boldsymbol{\tau}\_{\text{yx}})}{\partial \mathbf{y}} + \frac{\partial (u\boldsymbol{\tau}\_{\text{xx}})}{\partial \mathbf{z}} \\ &+ \frac{\partial (v\boldsymbol{\tau}\_{\text{xy}})}{\partial \mathbf{x}} + \frac{\partial (v\boldsymbol{\tau}\_{\text{yy}})}{\partial \mathbf{y}} + \frac{\partial (v\boldsymbol{\tau}\_{\text{xy}})}{\partial \mathbf{z}} + \frac{\partial (w\boldsymbol{\tau}\_{\text{xx}})}{\partial \mathbf{x}} + \frac{\partial (w\boldsymbol{\tau}\_{\text{yx}})}{\partial \mathbf{y}} \\ &+ \frac{\partial (w\boldsymbol{\tau}\_{\text{xz}})}{\partial \mathbf{z}} + \rho \mathbf{f} \times \mathbf{V} \end{aligned} \tag{5}$$

from the high rate of hiring of new pilots and indulgence of the airlines whether it is in Pakistan or international forum. As the hiring and training of new pilots is expensive, for this reason internationally, ground training with respect to particular aircraft is being catered by flight simulators. For this reason, high-fidelity FDM is a concerning aspect. In line with the above, it is significantly necessary to train new pilots from a realistic approach, keeping in mind the existing piloting reviews from old fellows of that aircraft to adopt for a dynamically changing environment whether that be in terms of standard operating procedures (SOPs) of flight, systems, or navigation [2]. Moreover, the need of designing a realistic FDM for flight simulators can also reduce the amount of actual flight time pilots put on aircrafts by which fuel and CO2 emission can be saved. This effort will inline flight organizations to act according to the ICAO Programme of Action on International Aviation and Climate Change, which enforces the ways to save material cost, i.e., fuel economy, and protect the environment which are the key concerns [1] that can be a

The era of FDM has changed the pathway of flight simulations. FDM consist description of flight model of a certain aircraft, which are the propulsion, navigation, controls, avionics, and aerodynamic data. The major part of this FDM is the aerodynamic data, as it handles the attitude behavior of the aircraft during flight. This aerodynamic data is acquired from either wind tunnel testing or computational fluid dynamics (CFD). Acquiring from wind tunnel is a difficult task as it is timeconsuming and requires scaling down of the design, as it is hard to test actual size model since they are bigger than the wind tunnel test sections. Therefore, CFD is

CFD is a tool for testing and quantifying fluid dynamics over an internal or

manufacturing time for analyzing aerodynamics of an initial design concept that has been created [3]. Aerodynamics is a study of airflow in either the internal or

external body where fluid flow is involved. CFD saves material cost and

driving factor for designing flight simulators.

*Computational Fluid Dynamics Simulations*

**1.3 CFD as a visual and graphical quantification tool**

**1.2 What actually is FDM?**

preferred [2] (**Figure 1**).

**Figure 1.** *Flowchart of FDM.*

**146**

CFD is a cost-effective and easy to use method which empowers engineers to virtually simulate and visualize the experiments carried out using wind tunnels. As far as the visualization of flow is concerned, CFD helps in depicting pattern of the fluid flow, which is difficult with regular wind tunnel experiments. However, wind tunnel experiments are expensive to conduct, and their real flow characteristics are hard to analyze due to the limitation of size of the test section for which scaling down of the geometry is required. Moreover, to determine the forces and moments in a wind tunnel, several pressure orifices are required and mounted over the model of interest to determine the pressure distribution on the surface of the model [7], due to which it is hard to set up the experiment as compared to CFD. Now keeping in mind our application, i.e., related to aerospace industry, Menter's shear stress transport (SST) model initially developed by F.R. Menter in 1994 is suitable. Moreover, according to the F.R. Menter study [8], it is noted that the SST Kω model outperforms and predicts the reduction of kinematic eddy viscosity quantity due to the adverse pressure gradient profiles in very good agreement for all x-station of a flat plate with that of the experiments. Moreover, in his study, SST Kω model is capable of predicting the accurate velocity profile charts as acquired from experimental study. In addition to this, SST Kω solves two equations, viz., turbulent kinetic energy "k" and the eddy dissipation rate "*ω*" which are given in Eqs. (6) and (7), where the variables are in italic and constants are in non-italic format:

elevator deflection cases conducted. "Rudder" in first column third row shows the number of rudder deflection cases conducted, and finally "Aileron" in first column fourth row shows the number of aileron cases conducted. These cases were carried

Subtotal 275 80 16 **Total** 372

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)…*

Generic settings required for setting up any CFD requires the three basic

The object of the study was C-130, and its CAD model was acquired from FlightGear database, which is an open-source platform. Preprocessing involves CAD import, generating and optimizing mesh using various techniques, physics, and environmental settings. The CAD model is imported using inbuilt feature which only supports listed file formats. In this study ".stl" format file is used from

Note: It is worth noting here that STAR-CCM+ requires considerable computer hardware resources to work in a faster pace. Loading times, mesh generation, and simulation times are significantly reduced with improvement in hardware. It has been tested by running same simulations at different desktop configuration machines and noticed significant reduction with respect to elapsed time.

After successful importing, the CAD model is visible in current scene. The next step is to generate mesh. "STAR-CCM+ has all-around mesh generating feature that creates unstructured form fitted finite volume meshes of fluid and solid domains. Software is designed such that mesh generation is automatically informed by the surface tessellation and CAD elements defining the geometry, such as local curvature, surface proximity, and retained feature elements, and is further controlled by user-specified meshing parameters. The latter are organized into a hierarchy of global specifications and local refinements that enables precise control to achieve cell quality metrics, such as skewness, connectivity, conformity, near-wall cell

out with properties already mentioned before in **Table 1**.

**Type AoA Beta Flaps** All 11 8 16

**2. CFD setup**

• Preprocessing

Elevator 88

Aileron 88

*Total number of cases for CFD simulation.*

Rudder 88 72

*DOI: http://dx.doi.org/10.5772/intechopen.91895*

• Post-processing

• Processing

**2.1 Preprocessing**

CAD software.

**149**

processes:

**Table 1.**

$$\frac{\partial(\rho \mathbf{k})}{\partial t} + \frac{\partial(\rho u\_j \mathbf{k})}{\partial \mathbf{x}\_j} = \rho \mathbf{P} - \mathfrak{F}^\* \rho \alpha \mathbf{k} + \frac{\partial}{\partial \mathbf{x}\_j} \left[ (\mu + \sigma\_\mathbf{k} \mu\_t) \frac{\partial \mathbf{k}}{\partial \mathbf{x}\_j} \right] \tag{6}$$

$$\frac{\partial(\rho \alpha)}{\partial t} + \frac{\partial(\rho u\_j \alpha)}{\partial \mathbf{x}\_j} = \frac{\chi}{v\_t} \mathbf{P} - \mathfrak{F}^\* \rho \alpha^2 + \frac{\partial}{\partial \mathbf{x}\_j} \left[ (\mu + \sigma\_\mathbf{a} \mu\_t) \frac{\partial \mathbf{k}}{\partial \mathbf{x}\_j} \right] + 2(\mathbf{1} - \mathbf{F}\_1) \frac{\partial \mathbf{k}}{\partial \mathbf{x}\_j} \frac{\partial \alpha}{\partial \mathbf{x}\_j} \frac{\rho \alpha^2}{\alpha} \tag{7}$$

Variables in Eqs. (6) and (7) are as follows: i.e., *ρ* is the density; *t* is the time; *uj* and *xj* are the velocity and position vectors, respectively; *μ*<sup>t</sup> is the eddy viscosity; *ν<sup>t</sup>* is the kinematic eddy viscosity; γ is the intermittency factor; F1 is a blending function; and β\* , σt, σω are constants. It is basically a combination of the *K*�ε model in the freestream and *K*�ω model near the walls of the geometry and is well suited for external aerodynamic flows around complex geometries and highly separated flows like airfoils at high angles of attack. In this study Siemens STAR-CCM+ software is used to carry out CFD analysis. This software includes numerous fluid dynamic models that are widely used in industry-level simulation requirements. Moreover, in STAR-CCM+ different wall treatment methods like all y+, low y+, and high y+ for treating boundary layer formation can be incorporated with the SST Kω model for true shear stress depiction.

For conducting CFD analysis, numerous test settings are permutated for gathering the aerodynamic data. However, out of different test scenarios, significance is given to cruise profile for which assumptions that are adopted for constraining our simulation are as follows:

Altitude: 1000 m Air density: 0.9075 kg/m<sup>3</sup> Air viscosity: 1.581 m<sup>2</sup> /s Velocity: 115 m/s � 220 knots Attitude cases: 372

**Table 1** shows that the total number of cases conducted for CFD simulations were 372. In **Table 1**, "All" in first column first row means all control surfaces at zero deflection level. "Elevator" in first column second row shows the number of *Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)… DOI: http://dx.doi.org/10.5772/intechopen.91895*


**Table 1.**

CFD is a cost-effective and easy to use method which empowers engineers to virtually simulate and visualize the experiments carried out using wind tunnels. As far as the visualization of flow is concerned, CFD helps in depicting pattern of the fluid flow, which is difficult with regular wind tunnel experiments. However, wind tunnel experiments are expensive to conduct, and their real flow characteristics are hard to analyze due to the limitation of size of the test section for which scaling down of the geometry is required. Moreover, to determine the forces and moments in a wind tunnel, several pressure orifices are required and mounted over the model of interest to determine the pressure distribution on the surface of the model [7], due to which it is hard to set up the experiment as compared to CFD. Now keeping in mind our application, i.e., related to aerospace industry, Menter's shear stress transport (SST) model initially developed by F.R. Menter in 1994 is suitable. Moreover, according to the F.R. Menter study [8], it is noted that the SST Kω model outperforms and predicts the reduction of kinematic eddy viscosity quantity due to the adverse pressure gradient profiles in very good agreement for all x-station of a flat plate with that of the experiments. Moreover, in his study, SST Kω model is capable of predicting the accurate velocity profile charts as acquired from experimental study. In addition to this, SST Kω solves two equations, viz., turbulent kinetic energy "k" and the eddy dissipation rate "*ω*" which are given in Eqs. (6) and

(7), where the variables are in italic and constants are in non-italic format:

<sup>¼</sup> *<sup>ρ</sup><sup>P</sup>* � <sup>β</sup> <sup>∗</sup> *ρω*<sup>k</sup> <sup>þ</sup>

*∂ ∂x <sup>j</sup>*

Variables in Eqs. (6) and (7) are as follows: i.e., *ρ* is the density; *t* is the time; *uj* and *xj* are the velocity and position vectors, respectively; *μ*<sup>t</sup> is the eddy viscosity; *ν<sup>t</sup>* is the kinematic eddy viscosity; γ is the intermittency factor; F1 is a blending

in the freestream and *K*�ω model near the walls of the geometry and is well suited for external aerodynamic flows around complex geometries and highly separated flows like airfoils at high angles of attack. In this study Siemens STAR-CCM+ software is used to carry out CFD analysis. This software includes numerous fluid dynamic models that are widely used in industry-level simulation requirements. Moreover, in STAR-CCM+ different wall treatment methods like all y+, low y+, and high y+ for treating boundary layer formation can be incorporated with the SST Kω

For conducting CFD analysis, numerous test settings are permutated for gathering the aerodynamic data. However, out of different test scenarios, significance is given to cruise profile for which assumptions that are adopted for constraining our

**Table 1** shows that the total number of cases conducted for CFD simulations were 372. In **Table 1**, "All" in first column first row means all control surfaces at zero deflection level. "Elevator" in first column second row shows the number of

*∂ ∂x <sup>j</sup>*

*<sup>μ</sup>* <sup>þ</sup> σω*μ<sup>t</sup>* ð Þ <sup>∂</sup><sup>k</sup>

, σt, σω are constants. It is basically a combination of the *K*�ε model

*∂x <sup>j</sup>*

*<sup>μ</sup>* <sup>þ</sup> <sup>σ</sup>k*μ<sup>t</sup>* ð Þ <sup>∂</sup><sup>k</sup>

*∂x <sup>j</sup>*

∂k *∂x <sup>j</sup>*

*∂ω ∂x <sup>j</sup>*

þ 2 1ð Þ � F1

(6)

*ρω*<sup>2</sup> *ω* (7)

*<sup>∂</sup>*ð Þ *<sup>ρ</sup>*<sup>k</sup> *∂t* þ

*Computational Fluid Dynamics Simulations*

model for true shear stress depiction.

simulation are as follows: Altitude: 1000 m

Attitude cases: 372

**148**

Air density: 0.9075 kg/m<sup>3</sup> Air viscosity: 1.581 m<sup>2</sup>

Velocity: 115 m/s � 220 knots

/s

¼ γ *vt*

*∂ ρu <sup>j</sup>ω ∂x <sup>j</sup>*

*<sup>∂</sup>*ð Þ *ρω ∂t* þ

function; and β\*

*∂ ρu <sup>j</sup>*k *∂x <sup>j</sup>*

*<sup>P</sup>* � <sup>β</sup> <sup>∗</sup> *ρω*<sup>2</sup> <sup>þ</sup>

*Total number of cases for CFD simulation.*

elevator deflection cases conducted. "Rudder" in first column third row shows the number of rudder deflection cases conducted, and finally "Aileron" in first column fourth row shows the number of aileron cases conducted. These cases were carried out with properties already mentioned before in **Table 1**.
