# Fluid Mechanics Applications/A32:Similarity analysis applied to vehicles

## Similarity analysis applied to vehicles using wind tunnel

### Motivation

With new models of vehicles always being created, wind tunnel testing is needed to evaluate the complex turbulent flow around the vehicle to better understand the capabilities and restrictions of new models and optimize the aerodynamics of new vehicles in wind tunnels.

### Overview

To improve the aerodynamic performance of a vehicles, data regarding the aerodynamic characteristics such as lift and drag force which are considered here mainly has to be obtained. Similarity & modeling are robust tools which helps to simulate the actual conditions on a small prototype and perform analysis and wind tunnels assist in making it true.

### Introduction

The Similarity analysis is applied to vehicles and a reduced scale model of actual prototype is built to determine data on aerodynamic parameters by wind tunnel simulations and hence improve the design which affects the actual vehicle’s performance. Inside the wind tunnel real like conditions are replicated which helps to determine actual dynamic performance of vehicle . Sensors built into the model provide data on aerodynamic forces and moments, as well as pressure values on the surface of the model. Aerodynamicists use both measured and numerically derived characteristics to decide on necessary design changes. A NASCAR 1/12 scale model is considered for the sample analysis.

## What Are Wind Tunnels?

Wind tunnels are large tubes with air moving inside with some artificial source like large propellers or fans. Wind tunnels can be as big as a room .Small ones are also available for laboratory purposes.The tunnels are used to copy the actions of an object in flight whether it is a car or aircraft.

NASA uses wind tunnels to test scale models of aircraft and spacecraft. Some wind tunnels are big enough to hold full-size versions of vehicles. The wind tunnel moves air around an object, making it seem like the object is really moving on the track. Most of the time, powerful fans move air through the tube.[1]

## Why to go for wind tunnel analysis using similarity?

Wind tunnel modeling is a robust technique which allows determination of wind effects on any structure. Due to complexity of flows and induced wind loads, other techniques can not be reliably used in practical analyses of such effects. The instruments attached to the wind tunnel provides accurate and reliable information about the analysis and by applying similarity criterion the data can be converted for actual prototype .A scale model for analysis is also made by similarity criterion which a simple and efficient technique.

## History: Making Aerodynamic Cars -Automotive Wind Tunnels

The first wind tunnel was built a full 30 years before the Wrights' success at Kitty Hawk .In the early days of development the wind tunnel analysis were mostly restricted to aircrafts testing. The Francis Herbert Wenham from the Aeronautical Society of Great Britain invented wind tunnel in 1871, and operated the same delivered many fundamental discoveries.

The wind tunnel analysis reached automobile sector almost after one century, after year of high tech simulations by experts from different fields. Most probable cause for the procrastination accounts to the difference from aircraft aerodynamics in many ways. For example, the geometry and configuration of a road vehicle is much less streamlined compared to an aircraft. [2]

## How do Wind Tunnels Work?

### Working overview

The object to be tested is rigidly fastened in the tunnel so that it will not move. The object can be anything a small model of a vehicle or a big sized plane. It can be a full-size aircraft or spacecraft. It can even be a common object like a tennis ball. The air moving around the still object shows what would happen if the object were moving through the air. Different methods can be adopted for analysis.

Smoke or dye can be placed in the air and can be seen as it moves. Threads can be attached to the object to show how the air is moving. The test object, often called a wind tunnel model is instrumented with suitable sensors to measure aerodynamic forces, pressure distribution, or other aerodynamic-related characteristics. Special instruments are often used to measure the force of the air on the object.

### The Concept:Entrance Region

The concept used in wind tunnel belongs to internal duct flows.An internal flow is constrained by the bounding walls grows and permeate the entire flow as shown in figures.There is a entrance region where a nearly inviscid upstream flow converges and enters the tube. At finite distance from entrance the boundary layer merges and the inviscid core disappears and the viscous layer develops and obstructs the axial flow in the duct.Hence the simulations in wind tunnel are carried out by placing the object in the inviscid part of entrance region to get flow without turbulence and obtain desired results.[3]

To realistically simulate vehicle movements in the wind tunnel, vertical movements of several millimetres in amplitude are induced to the wheel axles, at frequencies up to more than 20 Hz. A hydraulic "shaker" with a control unit has been developed to produce such motions on the wind tunnel model. In the model, the shaker is located beneath the weighing sensor – the balance – that in turn is fixed at the vertically aligned model support protruding through the roof of the model.[4]

## Designing wind tunnels

Wind tunnels are used to test models of proposed automobiles and other objects. The engineer can control the flow conditions inside wind tunnel and make careful measurements on the model. By which the engineer the forces on the full scale prototype can be predicted.

### Compressibility Effects

Wind tunnels are designed for a specific purpose and speed range and there is a wide variety of wind tunnel types. Due to compressibility effects the choice of speed range affects the design of the wind tunnel

### For subsonic flows

The air density remains almost constant and decreasing the cross-sectional area causes the flow to increase velocity and decrease pressure and vice versa.Highest possible velocity in the test section is desired. For a subsonic wind tunnel, the test section is placed at the end of the contraction section and upstream of the diffuser. From a knowledge of the conservation of mass for subsonic flows, the test section to produce a desired velocity or Mach number can be designed since the velocity is a function of the cross-sectional area.The changes in Mach number, velocity and pressure through a subsonic wind tunnel design can be observed in figure. The plenum is the settling chamber on a closed return tunnel, or the open room of an open return design.

### For supersonic flows

Unlike subsonic flows the air density changes in the tunnel because of compressibility. Actually the density changes faster than the velocity by a factor of the square of the Mach number. In a supersonic flow, the flow decreases in velocity and increases in pressure by decreasing the cross-sectional area and vice versa. In addition, compressible flows experience mass flow choking. As a subsonic flow is contracted, the velocity and Mach number increase. When the velocity reaches the speed of sound (M = 1), the flow gets choked and the Mach number can not increase beyond M = 1. For a supersonic wind tunnel, the flow is contracted until it chokes in the throat of a nozzle to get highest velocity. The flow is then diffused which increases the speed supersonically. The test section of the supersonic tunnel is placed at the end of the diffuser. From a consideration of conservation of mass for a compressible flow, the test section can be designed to produce a desired velocity or Mach based on the area in the test section.

### Similarity in supersonic and subsonic designs

In both supersonic and subsonic designs, the velocity is increased and the pressure is decreased relative to the upstream station of the test section. In a subsonic tunnel the area is contracting into the test section; in a supersonic tunnel the area is increasing.[5]

## What is Drag force?

Drag is force which acts in opposite direction to the vehicle and has negative consequences to vehicle performance because of several reasons like it limits the top speed of a vehicle and increases the fuel consumption. Low drag vehicles usually have one or some combination of the following characteristics: Streamlined shape, low frontal area, and minimal openings in the bodywork for windows or cooling ducts. The drag performance of vehicles is characterized by the drag coefficient ${\displaystyle c_{\mathrm {d} }\,}$ is defined as:

${\displaystyle c_{\mathrm {d} }={\dfrac {F_{\mathrm {d} }}{{\dfrac {1}{2}}\rho v^{2}A}}\,}$

where:

${\displaystyle F_{\mathrm {d} }\,}$ is the drag force, which is by definition the force component in the direction of the flow velocity,[6]
${\displaystyle \rho \,}$ is the mass density of the fluid,[7]
${\displaystyle v\,}$ is the speed of the object relative to the fluid,
${\displaystyle A\,}$ is the reference area.

This non-dimensional coefficient allows the drag performance between different vehicles and different setups of the same vehicle to be compared directly.[8]

## What is Lift?

Lift is the force that acts on a vehicle normal to the track surface that the vehicle rides on. It is the other main aerodynamic forces which acts on a race vehicle, but unlike drag, lift can be manipulated to enhance the performance of a racecar and decrease lap times. As its definition implies, lift usually has the effect of “pulling” the vehicle upwards - away from the surface it drives on. It has great use and implication in aircraft design. But for cars it is detrimental. However, by manipulating the racecar geometry like deploying a spoiler it is possible to create negative lift, or down-force. Down-force enhances vehicle performance by increasing the normal load on the tires. This increases the potential cornering force which results in the ability of the vehicle to go around corners faster and reduce lap times. The lift of the vehicle is characterized by the lift coefficient CL and is defined as[9]

${\displaystyle C_{\mathrm {L} }={\frac {L}{{\frac {1}{2}}\rho v^{2}S}}={\frac {2L}{\rho v^{2}S}}={\frac {L}{qS}}}$ ,

where ${\displaystyle L\,}$ is the lift force', ${\displaystyle \rho \,}$ is fluid density, ${\displaystyle v\,}$ is true airspeed, ${\displaystyle S\,}$ is planform area and ${\displaystyle q\,}$ is the fluid dynamic pressure. A negative lift coefficient means that a vehicle is experiencing down force

## Similarity criterion

Reduced scale models are used to study complex fluid dynamics of objects where computer simulations aren't enough. Design can be tested prior to building actual prototype. But conditions apart from design must also be considered such as pressure, temperature or the velocity and type of fluid. Similitude is said to be achieved when testing conditions are developed such that the test results are applicable to the real design.

The three conditions required for a model to have similitude with an application. Following similarity criterion must be satisfied to achieve similitude;

### Geometric similarity

The model and prototype must be of same scaled shape.

### Kinematic similarity

Fluid flow across the model and prototype must have same time rates of change motions

### Dynamic similarity

The forces on model and prototype must possess a constant ratio or are multiple of a constant number.

The actual working conditions should be analyzed properly to have all these similarities and achieve a proper similitude. The greater is the replication of actual conditions better is the analysis

## Rapid Prototyping:How to make a scale model for simulation?

Rapid prototyping is a process of manufacturing which uses the computers and high tech instruments to manufacture scale models of prototypes or anything else.It is highly useful in developing new products as a cost effective model can be made and analysis can be done on it on and if it is fine then actual expensive prototype can be manufactured.These models can be used for testing vehicles etc such as when an airfoil shape is put into a wind tunnel.The computer Aided Designing is also used in the early stage for developing designs.

## Setup:How to determine Lift and Drag force from wind tunnel analysis?

• The scale model is mounted to the dynamometer inside the wind tunnel so that the wheels are just touching the floor of the wind tunnel and the front of model is in the direction of the air flow.
• The dynamometer is attached to a data acquisition box which is plugged into a computer.
• A Pitot probe is properly positioned in the wind tunnel and attached to a pressure transducer using Tygon tubing which is also then connected to the data acquisition box.
• Then dynamometer is zeroed using the attached knobs.
• Results pertaining to the Pitot probe, the lift, and the drag are represented by voltages.
• Data is recorded while the motor is at a particular frequency and repeated in intervals upto a certain range.
• Care is taken to ensure that the flow in the wind tunnel is steady before taking any readings. One student watches the behavior of the car to record any suspicious movements (i.e. the front of the model tipping upwards).[10]

## Sample experiment:Data of 1/12th Scale NASCAR car model on Lift and Drag[11]

Details regarding the obtained experimental data are shown in the lift and drag coefficients versus Reynold’s Number plot.

### Findings

The wind tunnel test results showed that the lift coefficient achieved Reynold’s Number independence after a Reynold’s Number of approximately 5X105. However, the drag coefficient never seemed to achieve Reynold’s Number independence, although it seemed to be approaching Reynold’s Number independence near the upper speed constraints of the wind tunnel. Since lift reached Reynold’s Number independence, beyond a Reynold’s Number of 5.0X105the forces exerted on the model can be scaled to a full size car.

### Analysis

The lift and drag coefficients displayed in graph obtained offer valuable insight into the aerodynamics of the stock car. The force coefficients represent the relative magnitude of the lift/drag forces on the vehicle. The lift and drag coefficients are directly related to the change in momentum of particles flowing past that object, as well as how abruptly those changes in momentum occur. Stock cars designers use a technique called streamlining to achieve minimal lift and drag forces in order to maximize vehicle performance.

Since the drag coefficient doesn’t reach Reynold’s Number independence, dynamic similarity does not exist prior to a Reynold’s Number of 7.15X105. Generally, both the lift and drag coefficients follow a similar trend. They begin high, decrease rapidly, and then increase gradually.

### Analogy

For explanation an analogy to flow around a sphere is made because that behavior is well known and it relates to results of this experiment. In laminar flow around a sphere, separation occurs at the middle of the sphere. A low pressure area on the back of the sphere is created which increases the drag. As the flow becomes turbulent and gains more momentum, the separation occurs past the mid-point and the low pressure area on the back of the sphere gets small. As a result, the drag is decreased. Given that, it is possible that flow around the NASCAR model may behave similarly.

## Data conversion from model to prototype

Considering Reynold's number equivalence for model and prototype:

${\displaystyle \mathrm {Re} _{m}={{\rho _{m}{\mathbf {v} _{m}}L_{m}} \over {\mu _{m}}}={{\rho _{p}{\mathbf {v} _{p}}L_{p}} \over {\mu _{p}}}=\mathrm {Re} _{p}}$

If ρp = ρm and ηp = ηm

${\displaystyle \mathrm {\mathbf {v} _{m}} ={{\ {\mathbf {v} _{p}}L_{p}} \over {L_{m}}}}$ ... (1)

This is the relationship for velocity of model & actual prototype of car, where

Lp / Lm

is scale ratio.

Now drag coefficient ${\displaystyle c_{\mathrm {d} }\,}$ is defined as:

${\displaystyle c_{\mathrm {d} }={\dfrac {F_{\mathrm {d} }}{{\dfrac {1}{2}}\rho v^{2}A}}\,}$

Equating the Coefficient of Drag of actual prototype and model as follows:

FDp/ ρp (vp)2 Lp2 = FDm/ ρm (vm)2 Lm2 ... (2)

Therefore from (1) and (2) ,

FDp = FDm

This shows that Drag force on model and prototype will be equal. Hence we can analyze on model only and accordingly it will be for prototype car.

Similarly,

Lift force for model can be converted to prototype, lift coefficient

${\displaystyle C_{\mathrm {L} }={\frac {FL}{{\frac {1}{2}}\rho v^{2}S}}={\frac {2FL}{\rho v^{2}S}}={\frac {L}{qS}}}$

Where FL is the lift force

By equating (CL)m = (CL)p

2(FL)mm(vm)2Sm = 2(FL)pp(vp)2Sp

FLm = FLp

## Concluding note

Wind tunnel analysis using similarity criterion by making a scale model is an indispensable technique in automobile industry if accurate results based on actual conditions rather than computer simulations are required for developing efficient and robust automotives. It is simple,reliable and inexpensive technique as far as automobile industries are considered.The subject of Fluid Mechanics has provided the core crux and concept for this similarity analysis which is very effective in evolving new hybrid cars and developing the automobile landscape of a country.

## References

1. http://www.nasa.gov/audience/forstudents/
2. Book "Wind Tunnels of NASA" by Donald D. Baals and William R. Corliss
3. Book Fluid Mechanics.Seventh edition by Frank M White
4. Just like real racing: Wind tunnel measurements for simulating the dynamic behavior of a ground vehicle Article by Claus Zimmermann, Peter Aschwanden and Werner Häberli, RUAG Aerospace
5. http://www.grc.nasa.gov/
6. See lift force and vortex induced vibration for a possible force components transverse to the flow direction.
7. Note that for the Earth's atmosphere, the air density can be found using the barometric formula. Air is 1.293 kg/m3 at 0 °C and 1 atmosphere .
8. Race Car Aerodynamics Part 2- Lift and Drag: http://antipasto.union.edu
9. Clancy, L. J.: Aerodynamics. Section 4.15
10. From: RJ Hojnacki, Wes Wall, Sam Caruso
11. From: RJ Hojnacki, Wes Wall, Sam Caruso;http://antipasto.union.edu/~andersoa/mer331