Definitions

Coordinate System

Forces and moments are defined according to a right hand coordinate system.

• Positive drag force is along the X-axis
• Positive side force is along the Y-axis
• Positive lift force is along the Z-axis

Moments are calculated about the model origin where:

• Rolling moment is about the X-axis
• Pitching moment is about the Y-axis
• Yawing moment about the Z-axis.

The yaw angle is defined as the angle between the wind vector and the model x-axis and is positive counter-clockwise.

Your requested yaw angles are also indicated in the model preview window when setting up your model.

Pressure

The surface pressure shows the force per area, normal to the surface of the body. The surface pressure decomposed along the three coordinate axes and integrated around the surface, gives drag, lift and side pressure force.

The total pressure field shows the energy in the flow around an object. The total pressure is defined as the sum of the static pressure and the dynamic pressure.

When the boundary layer separates from an object, a low pressure, turbulent wake will form behind the object, and the resulting pressure difference around the object causes pressure drag.

Skin friction

In viscous fluid flows a frictional force will be excerted by the fluid on the surface of immersed objects. This is called skin friction.

The frictional force is caused by a viscous stress component (shear) that exerts a force parallel to the local flow direction due to a normal velocity gradient. The shear stress on a solid boundary is called wall shear stress, and can be interpreted as a frictional force which is directed along the local flow direction, tangential to the surface of the body. It is caused by the velocity gradient in the boundary layer and fluid viscosity. The force is directed along the local velocity vector.

Areas of low wall shear stress have a low local flow velocity. Along separation lines the wall shear stress will be zero.

The wall shear stress is normalized by the dynamic free stream pressure to give the non-dimensional friction coefficient:

$$ C_f={{\tau_w}\over{{1\over2}\rho U_{\infty}^2}}$$

Forces and moments

Fluid dynamic forces on an object are the sum of pressure forces and viscous forces.

In general, pressure forces are dominant for high Reynolds number flows around bluff bodies, while viscous forces are dominant for streamlined bodies and low Reynolds numbers.

The directions & sign conventions for the forces & moments are discussed here.

Normalized variables

Non-dimensional force and moment coefficients are calculated by normalizing the aerodynamic force and moment components by the freestream dynamic pressure and predefined length scales.

$$C_F=\frac{F}{\frac{1}{2}\rho_{\infty} U_{\infty}^2A}$$

$$C_M=\frac{M}{\frac{1}{2}\rho_{\infty} U_{\infty}^2AL}$$

The reference area $A$ is the projected frontal area of the model and the reference length $L$ is 1 meter.

Non-dimensional static and total pressure coefficients are calculated by normalizing the respective pressures by the freestream dynamic pressure.

$$C_{p_{static}} = \frac{p_{static}}{\frac{1}{2}\rho_{\infty} U_{\infty}^2}$$

$$C_{p_{total}}=\frac{p_{static}+\frac{1}{2}\rho \vert u \vert^2}{\frac{1}{2}\rho_{\infty} U_{\infty}^2} $$

The ISO standard atmosphere (ISO 2533:1975) air density of 1.225 $kg/m^3$ is used for all normalizations for air. A value of 1020 $kg/m^3$ is used for water.

The freestream wind speed ($U_{\infty}$) is used for normalization for all yaw angles, implying that the model-aligned wind will decrease for increasing yaw angle.

Drag Pressure

The drag pressure field visualizes the local drag force on the surface of a body. This variable is a decomposition of the surface forces acting on the object along the drag axis (x-axis). It includes both the pressure and the skin friction contributions.

The drag pressure coeffcient is calculated as:

$$ C_{P_x}={{\tau_{w_x}+p_x} \over {{1\over2}\rho U_{\infty}^2}}$$

where $\tau_{w_x}$ and $p_x$ is wall shear stress and pressure along the x-axis, $\rho$ is fluid density and $U_\infty$ is free stream velocity.

This plot is useful for identifying which regions of the model generate drag (or thrust).

The colormap for drag pressure includes a grey midrange around zero, which makes it easy to identify drag regions (positive values), thrust regions (negative values) & regions where drag is negligible (grey).

Heat Transfer

The convective heat transfer from model surfaces is estimated from using surface friction and the Reynolds analogy.

This theory describes the similarity between momentum transfer and heat transfer between a surface and a fluid. It provides an approximation of the heat transfer from the velocity field without solving a thermal energy equation.

As it is based on an analogy, the accuracy and applicability of the method varies and these results should only be regarded as a first approximation of heat transfer.

It does however provide a useful way to compare designs where heat transfer from model surfaces is important (for example, cycling helmet ventilation).

The heat transfer coefficient ($h$) is calculated as:

$$ h = \rho U_\infty C_p {C_f\over2}$$

$$ C_f = {\tau_w \over {1\over2}\rho U^2_\infty} $$

where $C_f$ is the friction coefficient, $\tau_w$ is wall shear stress, $U_\infty$ is free stream velocity and $C_p$ is the specific heat capacity at constant pressure.

The physical properties of the fluid are evaluated at standard atmospheric conditions.

Note: The averaged heat transfer coefficient values are based on the wetted surface area of the model or part. If parts or models are intersecting, this area will be smaller than the area of the original model or part.

Acoustic Power

The acoustic power field is calculated using Proudman’s formula, a technique that uses steady-state turbulence data to predict flow-induced noise.

This method is perfectly suited to AeroCloud simulations & produces a good prediction of flow-induced noise, without having to resort to much slower (& more expensive) simulation methods.

It is particularly useful for comparing the relative performance of options in early-stage design studies.

The process first calculates acoustic power $P_A$ in $\text{W}/{\text{m}^3}$

$$ P_A = \alpha_\epsilon \rho \epsilon M^5_t $$

where $k$ & $\epsilon$ are the turbulent kinetic energy & dissipation rate respectively.

$\alpha_\epsilon$ is an empirical constant, equal to $0.1$ and

$$ M_t = {\sqrt{2k} \over a_0}$$

where $a_0$ is the speed of sound in air.

We display the acoustic power in decibels, using the following conversion:

$$ L_P = 10 \log {P_A \over P_{ref}} $$

where the reference power, $P_{ref}$, is constant at $1e^{-12}$ $\text{W}/{\text{m}^3}$.