DEGREE PROJECT IN TECHNOLOGY, FIRST CYCLE, 15 CREDITS
STOCKHOLM, SWEDEN 2020
Venturi Undertray
KTH Bachelor Thesis Report
Selma Boudali and Mattias Olausson
BACHELOR THESIS TRITA-ITM-EX 2020:134
KTH ROYAL INSTITUTE OF TECHNOLOGY
Bachelor thesis TRITA-ITM-EX 2020:134 Venturi Undertray
Boudali, Selma Olausson, Mattias Approved
2020-05-12
Examinator Ulf Sellgren
Supervisor Ulf Sellgren
. Commissioner
KTH Formula Student
Contact person Aaron Poutiainen
ABSTRACT
This bachelor thesis aims to describe the work performed for the design of the undertray for the Kungliga Tekniska Högskolan Formula Student(KTHFS) race car. The goal was to achieve an aerodynamically optimized undertray design that follows the regulations of the competition and the targets set by KTHFS concerning the weight, the size, the materials needed for its manufacture and costs. After some research on previous work, the concept, on which we decided that the undertray would rely on, is Venturi tunnels inspired by the Aston Martin Valkyrie, chosen for its ability to provide a large amount of downforce with a negligible amount of drag using ”ground effect”.
Numerous CAD design models were created in Solid Edge and a finalized design was then ported over to Siemens NX to be analyzed using Star-CCM+ and its Design Manager feature. The CFD analyses and optimization was performed in Star-CCM+ with regards to pressure gradient, streamline velocity and downforce. These were done with variable parameters in areas such as expansion height, inlet area and ride height. Contained within this report is a more detailed description of how the CFD analysis was performed as well as suggestions for manufacturing said undertray.
Given the time constraints and the societal impacts of COVID-19, manufacturing had to be removed from the scope of the project, however, a step-by-step manufacture guide is provided within.
Analysis of uur final design showed 428 N of downforce, a weight of 2.55 kg and a production cost of approximately 2320 SEK. It therefore passes the requirements for weight, cost and ride-height rule regulations set by Formula Student and internal KTHFS targets.
Keywords
Race car aerodynamics, undertray, Venturi effect, Formula student, CFD analysis, Topology optimization.
Kandidatexamens arbete TRITA-ITM-EX 2020:134 Venturi Underrede
Boudali, Selma Olausson, Mattias Godkänd
2020-05-12
Examinator Ulf Sellgren
Handledare Ulf Sellgren
. Uppdragsgivare
KTH Formula Student
Kontaktperson Aaron Poutiainen
SAMMANFATTNING
Detta kandidatexamesarbete syftar till att beskriva arbetet som utförts för konstruktions- designen av Kungliga Tekniska Högskolan Formula Student (KTHFS) racerbils underrede. Målet var att uppnå en aerodynamisk optimerad underredes design som följer de regler och krav fastställda av KTHFS gällande vikt, storlek, material som behövs till tillverkningen och kostnader. Efter en litteraturstudie på tidigare arbete, blev Venturi tunnlar, inspirerade av Aston Martin Valkyrie, konceptet som vi beslutade att uderreden skulle bygga på och valda på grund av deras förmåga att förbättra bilens prestanda genom sitt nedkraftsbildande och försumbar mängd drag med hjälp av ”ground effect”.
Många CAD-designmodeller skapades i Solid Edge och en slutgiltig design överfördes sedan till Siemens NX för att analyseras med Star CCM+ och dess Design Manager- funktion. CFD-analyserna och optimeringen utfördes i Star CCM+ med avseende på tryckgradient, strömlinjehastighet och nedkrafter. Dessa gjordes med variabla parametrar i områden som utvidgningshöjd, inloppsarea och frigångshöjd. I denna rapport finns en mer detaljerad beskrivning av hur CFD-analysen utfördes samt förslag för tillverkning.
Med tanke på tidsbegränsningarna och samhällseffekterna av COVID-19 fick vi ta
bort tillverknink från projektets omfattning, men en steg-för-steg tillverkningsguide tillhandahålls i rapporten.
Analyser av vår slutgiltiga design visade på 428N downforce, en vikt på 2,55 kg och en produktionskostnad på cirka 2320 SEK. Den överenstämmer därför kraven för vikt, kostnad och frigångshöjd som fastställdes av Formula Student.
Nyckelord
Aerodynamiken på racerbil, underrede, Venturi effekt, CFD analys, Topologioptimering
ACKNOWLEDGEMENTS
First and foremost we would like to especially thank Per Niva, multidisciplanary technical problem solver at Avalon Innovation, for taking the time to share his expertise in the subject and guiding us.
We would also like to express our sincere gratitude to Yushi Murai for discussion on fluid- mechanic topics and the thesis manuscript.
We would like to thank our fellow KTHFS teammates, especially Aaron Poutiainen and Vivek J Shah for the support they showed us during the course of this project. We also wish to express a special thanks to Selma Rahman for her continued support and input into the structure of the thesis report.
Last but not least, we would like to thank our supervisor Ulf Sellgren for letting us turn our passion project into a thesis.
Selma Boudali & Mattias Olausson Stockholm, May 2020
NOMENCLATURE
Denominations
Symbol Description
ρ Density of flowing fluid
ps Total pressure
P Static pressure
q Dynamic pressure
u, v, w Velocity of fluid in x, y, z direction
g Acceleration due to gravity
h Elevation of fluid with respect to ground
T Stress deviator tensor
f Body force
ν Kinematic viscosity
Abbreviations
CAD Computer Aided Design
CFD Computational Fluid Dynamics
AC Aerodynamics and Composites
KTHFS Kungliga Tekniska Högskolan Formula Student
KTH Kungliga Tekniska Högskolan
FS Formula Student
VIM Vacuum Injection Molding
FEM Finite Element Method
Table of Contents
ABSTRACT 2
SAMMANFATTNING (SWEDISH) 4
ACKNOWLEDGEMENTS 5
NOMENCLATURE 7
TABLE OF CONTENTS 9
1 INTRODUCTION 11
1.1 Background
. . . 111.2 Problem Statement
. . . 111.3 Purpose
. . . 121.4 Goal
. . . 121.5 Methodology
. . . 131.6 Delimitations
. . . 142 FRAME OF REFERENCE 15 2.1 Ground Effect
. . . 152.2 Related Work
. . . 193 EXECUTION 23 3.1 Pre-thesis work
. . . 233.2 Initial design
. . . 243.3 Second design
. . . 253.4 The McDonald’s design
. . . 273.5 Design Manager
. . . 293.6 Potential production
. . . 323.7 Costs and weight
. . . 364 RESULTS 39
5 DISCUSSION AND CONCLUSIONS 41
5.1 Discussion
. . . 415.2 Conclusion
. . . 446 RECOMMENDATIONS AND FUTURE WORK 45
7 REFERENCES 47
A Material Properties 49
A.1 Material Description
. . . 49B Excerpt from Formula Student regulations 55 B.1 Formula student rules
. . . 55APPENDICES 49
1 INTRODUCTION
1.1 Background
Kungliga Tekniska Högskolan Formula Student (KTHFS), is a non-profit student organization with the sole purpose of designing, constructing and racing an electrically driven race car to compete in Formula Student competitions.
In order to produce an optimally performing car, a number of areas have to be taken into account and therefore is KTHFS divided into a number of subgroups: Mechanical Design, Vehicle Dynamics, Powertrain & Electronics, Driverless, Business Marketing, Management and lastly there is Aero & Composites (AC), in charge of the entire aero package of the car. This is the group of which we are members, working on the construction of the undertray. To be able to have a functioning car, a lot of communication is necessitated between the team groups. This can be challenging especially for decision- makings concerning the placement, shape and size of our undertray but is a really good learning experience for us as engineering students.
1.2 Problem Statement
The competitions of Formula Student require that each team follows a list of rules. These have an impact on the decisions related to the design of the race car and some of the rules may be constraining especially for the aerodynamic design of the undertray. The one that is significantly important to focus on is about the static ground clearance. Any part of the vehicle other than tires must be at least 30 mm clear with a driver in the seat (Formula Student, 2020).
Apart from the rules, within the team some constraints are decided together. One of these is the budget of 42 000 SEK which plays a determining role in the manufacturing aspect of the undertray. There is also a maximum weight target of 7.5 kg, set internally, that impacts its design and material choices that need to be sustainable. Of course, the placement of other car parts made by other subgroups conflicts also with the construction and placement of the undertray.
Our mission as members of the AC subgroup is to find a solution for how to construct an undertray achieving an optimal aerodynamical performance while respecting the above-
mentioned rules.
1.3 Purpose
As a vehicle reaches higher velocities the amount of air passing around the car increases as well. Normally this would lead to an increase in drag as the vehicle encounters increase resistance in correspondence with the increased velocity. But the usage of the air flow contouring the car makes it possible to benefit in an improvement of downforce with less drag thus increasing stability at higher speeds. The Venturi effect is a principle that makes this air flow useful and that we want to employ in our undertray in order to be able to improve the performance of the car. It helps generate downforce without adding too much drag as the addition of an undertray barely increases the frontal area of the car.
With the use of the Venturi principle, this undertray construction project aims to answer a couple of questions:
• How can the space behind the driver be used beneficially?
• What type of design is optimal regarding downforce and drag?
• Is it possible to make an undertray that gives half as much downforce as the cars weight and if so how?
• Which core material is the most suitable?
1.4 Goal
At the start of this project, some goals were formulated. The desired result was, in the beginning, a completed undertray design optimized aerodynamically generating as much downforce as possible. It was obvious that the undertray has to satisfy the requirements made by KTHFS regarding the weight, size, material and costs. Also, by the end of the project, it was planned that we would have manufactured the undertray for the team race car. But with the coronavirus pandemic, this was no longer a realizable objective. That is why the goal had to be reformulated during the month of March with the decision of not including manufacture in the project.
1.5 Methodology
To be able to achieve a finalized product by the end of this project different steps needed to be taken. In the beginning, previous solutions of undertrays were studied such as a flat plate design, double diffuser design and a fan car design. After coming up with these different ways of tackling the problem we then gathered information on how other car manufacturers and previous Formula Student teams have made their designs. Our different ideas were then eliminated for different reasons and we ended up with large Venturi tunnels with elongated diffusers, mainly inspired by the design of the Aston Martin Valkyrie. With this conceptual idea, different CAD-models could be made in Solid Edge and Siemens NX. Varying different parameters on the CAD-models such as intake height and width, changing the length of the central low cross-sectional area, airfoil shape, battery placement and battery cavity design as well as Venturi tunnel expansion, was an important step for the optimization of the design. In addition to this, we wanted to add flat plates on the sides for the purpose of gaining additional downforce while at the same time diverting the airflow that otherwise would be hitting the back tires above them. Using programs, such as Star-CCM+ for CFD analysis helped us get a better grasp as to what constitutes a good design as opposed to a bad one.
This process was an iterative one, where the parts from other subgroups had to be taken into account as well as manufacturability – a design that is good from an aerodynamic perspective might not be from a manufacturing one, so special care needed to be taken with respect to this at all times. Unlike at a Formula One design studio, this may very well be our most limiting factor due to the teams comparatively underdeveloped manufacturing capabilities.
When it comes to the choice of materials and manufacturing, our initial analyses pointed toward having a balsa wood core with a carbon fiber outer shell in a sandwich structure.
This was decided via CES EduPack due to its lightweight properties. The core material was especially chosen for its recyclability.
With our limiting weight factor of 7.5 kg and our budget of 42000 SEK, the chosen materials more than pass these requirements.
Following the finalization of the design, manufacturing should have begun. Due to the pandemic of the coronavirus, this was no longer realisable during the time frame of the
project. KTH Campus is closed for students along with KTHFS garage which forced the whole team to give up on manufacture in addition to the fact that importing material in time was not longer possible.
If the pandemic would not have had an impact on our thesis, the core material of balsa wood would have been inquired from 3A Composites Core Materials, an American company. These would then have been formed into the desired shapes, covered with epoxy and a carbon fiber shell would have been applied. This process would have taken about a week and would have been done in the team garage at KTH V-building.
1.6 Delimitations
In order to complete this project within a reasonable time frame we have chosen to limit our scope slightly. Unfortunately, manufacture was planned to be a part of the project before the Covid-19 outbreak. We decided to still discuss in this report the manufacturing process for our undertray that could be considered in the future and give suggestions on potential useable materials. That is why we will have no finished product at the end of the thesis. In the beginning, as we thought that manufacture was possible we had decided that we will not test the finished product in a wind tunnel. Our results will be assumed from simulations and calculations during the writing of this report. However, following the presentation of the thesis and after the reopening of KTH, further testing will be done on the assembled car where in vivo numbers can be produced. We will not be performing, during the timeframe of this report, any solid mechanics analysis on the finished product, where stress and strain limits would be observed and either any optimization post-production. Due to the lax time constraints of the other groups of KTHFS, assembly will also not be performed yet.
2 FRAME OF REFERENCE
2.1 Ground Effect
Ground effect, with respect to car design, is a ”catch-all” term for a group of aerodynamic concepts, such as the Venturi effect, that are used to increase the downforce capability of the aerodynamic devices of the underside of the car by taking advantage of the interaction with the ground at proximity. In the review ”A Review of Ground-Effect Diffuser Aerodynamics” by Ehirim, Knowles and Saddington, Ground effect diffuser is explained as a benefit for race cars due to the fact that a significant increase in downforce with less drag is observed in Formula One cars compared to their front and rear wings (Ehirim, Knwoles and Saddington, 2019). The more downforce creating a low-pressure region on the underside of the car, the faster the car is during corner takings as it increases the tires grip and keeps the car glued to the ground, making it possible to do a cornering manoeuvre with higher speed. This is important since FS circuits consists of mostly corners. In this chapter, relevant theories used to model the flow around the undertray is discussed, followed by some previous examples of ground effect cars. Bernoulli’s principle is used to explain the Venturi effect concept of the undertray. Couette flow was used to model the interaction of the flow with the ground and the undertray.
2.1.1 Bernoulli’s Principle
Bernoulli’s Principle, named after the mathematician and physicist Daniel Bernoulli, states that along a horizontal flow of fluid with density ρ the total pressure, ps, must stay constant (Khan Academy, no date). This means that the static pressure, P , must decrease in concordance with an increase dynamic pressure, q. Since dynamic pressure is dependant on the velocity, v, of the fluid, an increase in velocity will lead to an increase in dynamic pressure. This is expressed in the Bernoulli’s principle formula taken from the book ”Prandtl’s Essentials of Fluid Mechanics” (Oertel et al, 2004):
ps= P + q = P + 1
2ρv2 = constant. (1)
This can also be written in a more developed form. If there is a change in height then h1 ̸= h2. There will also be a resulting change in either velocity or static pressure or both
as presented in the following equation:
p1+1
2ρv21+ ρgh1 = p2+1
2ρv22+ ρgh2. (2)
Given that in the case of the undertray development, the change in height is not considered drastic and can therefor be disregarded, giving us the simplified equation:
p1+1
2ρv12 = p2+1
2ρv22. (3)
This gives us the simplified Bernoulli equation that only compares a point 1 with static pressure p1and speed v1and at point 2 with static pressure p2and speed v2. This principle can only be applied for flows that are steady, incompressible, and irrotational and with negligible any friction.
2.1.2 Venturi Effect
As a fluid travelling in the subsonic regime gets routed through a section with a comparatively smaller cross-sectional area, the static pressure of the fluid drops in accordance with the conservation of mechanical energy (Felföldi, 2020). Simultaneously, due to the principle of mass conservation, the fluid velocity must therefore increase.
Meaning any increase in the kinetic energy of the fluid as a result of its increased velocity is subsequently balanced out by a drop is static pressure. This is an application of Bernoulli’s Principle, called the Venturi Effect, published in 1797 by Giovanni Venturi and represented in the following figure:
Figure 2.1: Venturi Effect. (Felföldi,A. 2020)
The increase in fluid velocity, flowing through cross-section A1 then cross-section A2, in synchronization with the change of pressure in the pipe shown in Figure 2.1, creating the Venturi Effect is described in a variant of the Bernoulli equation:
p1− p2 = ρ
2 ·(v22− v12
)
. (4)
If a fluids velocity nears the speed of sound, the flow enters a state of choked flow. An increase of the mass flow rate will not happen after that the fluid passes through the smaller cross-sectional area that causes a drop in pressure. In this case, the Venturi Effect is no longer applicable as the speed of the sound limits the pressure changes expressed in equation .
It should be pointed out that the Bernoulli equation is invertible. This means that when flow velocity decreases, the pressure should instead increase. However in reality, turbulence appears in the expanding pipe-section which makes the theory invalid.
Therefore, the smallest section is always compared to the input section and never the output one.
2.1.3 Viscosity and Couette Flow
Couette flow is defined as the “laminar flow that arises when a viscous material lies between two parallel plates, where one of the plates is in relative motion to the other plate” ( Earth-Science Reviews, 2017 cited in ScienceDirect, 2018) .
In the case of our undertray, what happens is that the boundary layer of the air between the ground and the undertray, due to viscosity, work to hinder the flow of the air underneath the car which will in turn lead to a reduction of the effectiveness of the Venturi Effect. This would be the case for two stationary objects, the ground and the undertray, in the case of the car being parked. However, as the car moves, the ground will from the reference frame of the car, move backwards at equal speed. The ground will apply viscous drag forces upon the air travelling underneath and pull it backwards. This will result in an increased speed of the air and subsequently a decrease in static pressure.
Figure 2.2 is a representation of our Couette flow. The undertray have the velocity U and the distance between the undertray and the ground is h, the ground clearance which is fixed at 30 mm because of the Formula Student rules.
Figure 2.2: Couette flow between the undertray and the ground.
The velocity distribution of Couette flow can be derived from the Navier-Stokes equations.
These describe the flow of incompressible fluids and are defined in this vector form,
ρ(∂v
∂t + v· ∇v) = −∇p + ∇ · T + f (5)
with ρ being the density, v the velocity field,−∇p the pressure force, T the stress deviator tensor and f the body force (Weisstein, no date).
Equation (5) is quite complex and it is for this reason we are going to use a simplified form by just looking at the x-component as it is the dominant one for the case of our undertray:
∂u
∂t + u∂u
∂z + v∂u
∂y + w∂u
∂z =−1 ρ
∂p
∂x + ν(∂2u
∂x2 +∂2u
∂y2 + ∂2u
∂z2). (6)
u, v, w are the velocities in respectively x-direction, y-direction and z-direction. p is the pressure while ρ is the density of the fluid (air) and ν its kinematic viscosity.
If we assume that the car is running straight and very fast then we can say that the flow is uni-directional. We only have to study the flow field in 2D as nothing happens in z- direction. Therefore we can consider that w = 0 and∂z∂ = 0.
The flow can be seen as steady and therefore no deviation in time can occur. This gives us that ∂t∂ = 0. No pressure gradient is also assumed and for this reason ∂p∂x = 0.
The flow is parallel and fully developed. As seen in Figure 2.2, the streamlines are indeed parallel. This means that v = 0 and ∂u∂x = 0 which explains why ∂∂x2u2 = 0.
The Navier-Stokes equation (6) reduces, for the above mentioned reasons, to a simpler one:
ν· ∂2u
∂y2 = 0⇔ ∂2u
∂y2 = 0. (7)
This equation gives us the velocity in function of y defined as
u(y) = Ay + B, (8)
where A and B are unknown constants.
We know that the ground is stationary meaning that the velocity of the ground is zero and that the velocity of the undertray is U . We end up with these boundary conditions:
u(y = 0) = 0, (9)
u(y = h) = U. (10)
By inserting the above mentioned boundary conditions (9) and (10) in equation (8), we can find the values of A and B. We get that B = 0 and that A = U /h. This is why we get that:
u(y) = U
hy, (11)
which is the Couette solution of our flow.
2.2 Related Work
The idea of exploiting Ground Effect for racing cars by using their underside to create low pressure regions underneath the car and pull the car downwards was first developed for the Canadian-American Challenge Cup sports cars series in the 1960’s (Hughes, Piola, 2018). It inspired many others to work further with the concept.
2.2.1 Lotus 78 and 79
The Lotus 78 is a car that made Formula One™, according to an article posted on their website, understand the advantages of Ground effect and implement it on their cars (Hughes, Piola, 2018). The car is described as having skirts along the bottom of its sidepods forming a seal between the circuit and the cars underside. It is explained in the article, that those skirts are preventing outside air from slipping beneath the sides and consequentially negative pressure is created underneath the car. A Venturi shape is formed by the placement and angle of the radiators together with the shape of the auxilary fuel tanks housed inside the sidepods. The air passes through the Venturi shape and expands into a diffuser at the sidepod’s exit over the rear wheel and suspension making the air flow leave faster and reduce the pressure along the car’s underside due to the Bernoulli principle. With this decrease in pressure, the racing car’s downforce, barely generating any drag, increases which explains the effect of suction seen on the car when racing.
Unfortunately, its center of aerodynamic pressure is located too far ahead which makes the car performance not optimal. This is the reason why the car carries a big rear wing making it keep its balance. Despite this defect, it still has an asset of 15% in downforce compared to other racing cars at that time according to the article. The Lotus 78 has won a couple of races in the 1977 Formula One season, demonstrating the big advantage of a ground effect race car. (Hughes, Piola, 2018)
The Lotus 79 is an improved version of the previous Lotus 78 and is the first race car using Ground Effect that won the world championship in 1978 inspiring others to study further and exploit the concept. (Hughes, Piola, 2018)
2.2.2 Brabham Formula 1 BT46B
The Brabham BT46B, known as the “fan car” is another racing car that exploited Ground effect to generate low pressure on its underside. A radiator is indeed fixed horizontally over the engine and is cooled at the back of the car thanks to a fan driven by a gearbox (Taylor, 2008). The engine compartment is sealed by flexible skirts. The later gets the radiator fed with air and creates a resembling suction effect as the rival Lotus 78 and 79 which gave excellent downforce results at that time according to Simon Taylor (2008).
The car has only participated in one race, Sweden’s Grand Prix in 1978 at Anderstorp making it the only Formula One car ever to win every competition it has participated in
(Dahlin, 2017). After the race the car got tested with an anemometer to measure the flow of air through the fan and the radiator (Taylor, 2008). The car apparently exploits 60% of the air for cooling while 40% is dedicated for generating downforce.
2.2.3 Aston Martin Valkyrie
The Aston Martin Valkyrie is a hypercar built in collaboration with Red Bull Racing with the look of a Formula One car despite being street-legal (Aston Martin™, no date). With its aerodynamic design, the car maximizes downforce thanks to the fully open underfloor with an undertray shaped into two Venturi tunnels making ugly thick-bodied rear wings useless compared to it (McEachern, 2017). It should produce around 1800kg of downforce, almost twice its weight (Kotwal, 2018). This car ended up being the main inspiration for our design, with its expanding and contracting undertray. This shape was deemed ideal for us as a starting point given that it efficiently exploits the Venturi effect. Due to the rules limitations, such as that no aerodynamic parts can be closer than 3 cm off the ground (Formula Student, 2020), this seemed like the ideal choice to replace our initial idea of the
”KTH fan car”.
3 EXECUTION
3.1 Pre-thesis work
This project was initiated before the start of the thesis, as it is our work for KTHFS as team members. The first thing we did was to look at different car designs that exploited Ground Effect. The one that caught our eyes was the Brabham Fan car, with it’s immense downforce numbers given the recent rules changes that now allowed fans in the aerodynamic package. We started to make a CAD-model for it in Solid Edge due to our familiarity with it. After having meetings with experts, we weighed the pros and cons shown in Table 3.1.
Table 3.1: Pros and cons of different aerodynamic alternatives considered for the project .
We got dissuaded mainly because of the FS rules regarding ground clearance and scoring that restrained three of the alternatives we had except for the Venturi tunnels and went for a design more akin to the Aston Martin Valkyrie. It was for us the most interesting undertray shape to work with knowing that in the coming up Formula One competitions
starting from 2021, a new rule allowing ground effect exploitation will be reestablished (J. Noble, 2019).
3.2 Initial design
For the thesis, we chose to focus on a conceptual undertray design inspired by the Aston Martin Valkyrie. We made a model of it on Solid Edge. CFD was not directly performed on the model due to a license issue the KTHFS team had with Star CCM+. Therefore, the design was entirely based on us stitching together ideas from previous cars, deciding what would be ideal based on knowledge gained from our course in Fluid Mechanics. This is the design brought to the initial KTHFS Design Presentation:
Figure 3.1: Seen from below the front Figure 3.2: Seen from below the back
3.3 Second design
Following our initial design we faced a new challenge: our idea of the underside of the monocoque was deemed to not be viable. The boat-shaped center was thrown out and replaced with a ”double-tunnel” design, so as to more easily be fastened to what ever chassis design the team would end up going with. Additionally, large flat plates were added to the sides to provide both a barrier to make it harder to air to flow in from the sides, but also to provide us with additional downforce. We decided to also curve them upward, allowed air that pass over the top of the flate plate to flow over the tires. The following figures show the CAD-model of our second design.
Figure 3.3: Overview.
Figure 3.4: Seen from the front
Figure 3.5: Seen from the back
Figure 3.6: Seen from the right side.
Coinciding with this change we managed to get our licensing issues with Star-CCM+
resolved and initial CFD analyses were now underway (see following figures). By importing the CAD-model of the undertray to Star-CCM+ and then meshing its surface into many cells, we were able to estimate downforce, velocity and pressure.
Figure 3.7: Pressure gradient and streamline velocity
Figure 3.8: Lift force vs number of iterations.
After a meeting with other subgroups, we realized that our undertray design had to be modified as it was conflicting with the needs of other team members concerning the battery placement and suspensions. We also got notified that the team decided on new tires that were larger than the previous ones.
3.4 The McDonald’s design
Due to us having to collaborate with other teams, we had to fit our undertray to their needs.
That is why we had to come up with a new model that we named the McDonald’s design due to its resembling ”M” shape. This one was also made on Solid Edge (see Figure 3.9) and analyzed on Star CCM+ giving a downforce of approximately 800N (see Figure 3.10 3.11), which was a significant drop compared to the previous model even if we still had to optimize it.
Figure 3.9: CAD-model of the M-shaped undertray
Figure 3.10: Pressure gradient and streamline velocity
Figure 3.11: Lift force vs number of iterations.
The team leaders, shortly after we had made our CFD analysis on our first version of the McDonald’s design, announced to us that we had to change from Solid Edge to NX, a program which we had never worked with and were very unfamiliar with the layout. It is the program that the rest of the team uses. As it would be best in the long run and facilitate our teamwork with other subgroups, CAD-software was switched and unified in middle of the design process for long-term integrations purposes. It was associated with an adaptation period that lasted for a couple of weeks.
Work stalled while we waited for a ”close to finalized” version of the monocoque to work around. During this adaptation time, we got a rough design in place shown in Figure
3.12.
Figure 3.12: CAD-model of the cars monocoque and undertray.
Our project lead made this design to help show us how to do it and this was the first one we worked off of. This initial design was made just to try and learn the tools and it pulled a measly 28N of downforce. We then tried to optimize it while looking at the CFD numbers and decided to lower the intake area as it produced a significant pressure drop on top of it with a pressure increase inside it due to its shape. We made some changes and got numbers around 150N, but this was far from optimized.
3.5 Design Manager
Design manager is a feature in Star CCM+ that sets up an automated parameter study and the resulting effects of the changes enabling to topologically optimize CAD-models.
Thinking that this would save us some time instead of manually optimizing our CAD- models, we opted for this feature. Eventually we managed to get Star CCM Design Manager to work and we ran a number of different parameter studies in it. A half-car simulation, with 1.8 million cells, was set up with three design variables tested at different values: WH, height of the throat, was tested between 80 and 120 mm. OpeningArea, the area of the intake, was tested between 230 and 270 mm. Diff_height, end height of the expansion tunnel, was tested between 300 and 350 mm. You will find the initial run in Figure 3.13:
Figure 3.13: Initial Design Manager run.
After the initial run we narrowed down our numbers to values around the previous ideal.
This process was repeated 2 more times and then we got our finalized numbers presented in Figure 3.14:
Figure 3.14: OpeningArea: 230mm, Diff_height: 310mm, WH: 110mm.
From this point we went to a design that was resemblant to our ”McDonald’s” design, hoping that it would improve our values. Assistance was provided by our team and a more updated design was created:
Figure 3.15: Ported version, half car.
Figure 3.16: Slits were added to the flat plate to prevent air (black streamline) from entering from the sides.
3.6 Potential production
Considering that this project will be pursued even after the submission of this thesis, we have thought about the manufacturing process of the undertray. We made a step-by-step guide we can follow when creating the physical undertray: main instructions as well as an alternative one to accommodate variable availability of material and equipment.
• Step 1: Mold Manufacturing
When designing the mold it is important that the chosen material is stiff enough to be machined without crumbling. Moreover it has to be able to withstand the temperatures involved in the curing process, which is dependant on the choice of the process. We have decided to ignore materials related to autoclave curing due to its high pressure and temperature requirements. That coupled with the fact that it is an expensive process and we do not have an easy access to the autoclave.
When choosing a core material for the mold we have decided to narrow our scope to foam materials. We chose to compare the Young’s modulus of different foam materials available on CES Edupack to determine which materials are the stiffest as the final chosen one needs to bare being machined and also stand the resin curing temperature. Therefore, the material needs to have a high-density. In Figure 3.17, the materials are organized by their Young’s modulus in function of their density.
The best materials with both a high Young’s modulus and density according to Figure 3.17 are PC foam, ABS foam, PS and PVC foam. In the descriptions of these four materials, only PVC foam is mentioned as thermo-moldable. The PVC foam is readily available, cheap and more than capable of withstanding the temperatures we would need. Moreover, we have previous, albeit limited, experience working with it. For this reason, we consider that the semi-rigid PVC foam is the best choice (see Appendix A.1.1 for material description) .
Once the core material is chosen, it will be machined with a CNC machine in a single piece, or in multiple pieces to be combined later using glue if the workspace is not over the size. Once the desired core shape has been achieved, we will sand the part to get rid of potential surface irregularities followed by application of the release agent and gel coating.
Figure 3.17: Young’s modulus vs. Density material chart for foam materials.
• Step 2: Sandwich material and core
For the sandwich structure we decided that we will use non-crimp fabric (NCF) or other woven fabrics as reinforcement to obtain homogeneous bending properties in every in-plane direction. For the matrix material we will use epoxy, if possible a partially bio-based one in order to come closer to our goal of recyclability. For our core material we have chosen to go with Baltek balsa wood for its excellent specific (see Appendix A.1.2).
• Step 3: Lamination
Once the mold has been prepared we have two options for lamination depending on our core material: Vacuum Injection Molding (VIM) or hand lay-up process. The one we would ideally use, is VIM and is schematized in Figure 3.18.
Figure 3.18: Schematization of the Vacuum Injection Molding.
This process involves laying dry non-crimp carbon fiber fabric of desired thickness into the mold, on top of which we will place the core material followed by other reinforcement layers. After that we will lay down peel ply (white weave with red stripes in Figure 3.19), followed by a distribution media (blue net shown in Figure 3.19) that helps the resin to move, reducing infusion time. Lastly, a vacuum bag will be placed on top with two hoses connected to either end of the structure. One will be connected to an epoxy resin container, the other to a vacuum pump. The vacuum pump will remove any air and suck the epoxy resin from one side to the other as illustrated in Figure 3.20. Once the epoxy resin has been evenly distributed throughout the structure, the hoses will be disconnected and the structure, with the vacuum bag still on, will be placed in an oven in order to let the resin cure completely.
Following the curation, any imperfections and excess materials will be removed.
Figure 3.19: Sandwich structure. Figure 3.20: Resin travelling via vacuum throughout.
In the case that Baltek balsa wood is unavailable, we will use a hand lay-up process.
We begin by spreading a layer of resin over the mold surface on top of which we will position a fiber mat. During the process, it is ensured that all air pockets are removed with a brush or roller as demonstrated in Figure 3.21.
Multiple layers of fiber mat will be placed until a desired thickness is reached. This is followed by placing the core material on top and repeating the same procedure for the other side of the core. This will complete the sandwich structure, after which we will place a peel ply and a breather to absorb any excess resin. Lastly, we will seal the sandwich structure in a vacuum bag, vacuum out the air inside the bag and finally place the mold into an oven to let the resin cure.
Figure 3.21: Schematization of the hand lay-up process.
3.7 Costs and weight
To estimate the cost of production of the undertray, we gathered information regarding material and consumable prices from probable future suppliers. Thanks to the CAD-model we got a volume of 0.0044 m3for the undertray. We made the assumptions that the volume needed of PVC foam is equal to the volume of the undertray to get approximate cost values as well as the assumption that the volume of carbon fiber is 35times 26 of the volume of the undertray and that the volume of Epoxy is25 times 26 of the volume of the undertray. With this, an approximate cost for material was possible to calculate which resulted in 1400 SEK. To this, we added an extra cost regarding a scrap rate of 30% and the consumables cost for the VIM process which gave us a total manufacture cost estimated to 2320 SEK.
Compared to the budget of 45 000 SEK given to us for the production of the undertray, the manufacturing will only consume about 5% of the budget which makes it more than enough (see Table 3.2).
Table 3.2: Cost estimation for the undertray production by VIM.
4 RESULTS
Presented below in Figure 4.1 is our final design. It provided 428N of downforce as seen in Figure 4.2 were the downforce of the half car simulation is presented. The undertray passed the requirements for weight, cost and ride-height rule regulations. In fact, the undertray weighs 2.55 kg and its production will cost us around 2320 SEK (see previously Table 3.2).
Figure 4.1: CAD-model of the Undertray and Chassis together.
Figure 4.2: Optimal Design Manager run.
5 DISCUSSION AND CONCLUSIONS
5.1 Discussion
Figure 5.1: Nose shape. Figure 5.2: Obstructed volume.
Our initial “McDonald’s design” gave better downforce values compared to the final design. This, we believe, was in large part due to the change in the chassis design and how it interacted with the undertray. In the latest design, as seen in Figure 5.1, the nose has a non-uniform shape where the bottom part has an angle. As the air hits the nose, we will get a resulting force that has a positive z-directed component lifting the nose upward.
The streamlines traveling underneath the chassis then becomes compressed, however, the chassis has an s-shape, causing the air volume to expand which leads to an increase in static pressure and once again causes the chassis to lift. The volume of air is then compressed again before reaching the mouth of the undertray. This compression and expansion of the volume underneath the chassis leads to a net-positive upward force, causing the front of the car to tilt upward. As seen in Figure 5.2, the later chassis design also decreased the volume underneath the vehicle which resulted in a small air throughput, meaning that even if we were to increase the volume of the intake, the lack of space underneath the car has caused a bottleneck in our flow. Additionally, due to the guide vane following the interior of the expansion tunnel not have a variable height and width. This has caused a creation of a small obstruction leading to a disturbance in the air flow, rather than its intended purpose of creating a protrusion for which the boundary layer of the airflow to stay attached, reducing the risk of separation.
Furthermore, the gap between the back half of the chassis and the undertray has led to some issues as well. The gap creates a small vacuum, causing a drop in pressure in that
area and therefore lift. It also has created an issue in CFD when it comes to meshing.
When meshing, this particular area requires smaller and more numerous cells in order to prevent instability in the residuals. This has caused both an increase in meshing and iteration time as well as the amount of iterations needed before reaching acceptable residual values.
All this combined, as well as the issues involved with getting Design Manager to work, has led us to reevaluate our choice in switching to Siemens NX this early in the design process. Even though the Design Manager was very useful, the 2 months it took to get it running could have been spent doing manual changes to the CAD in Solid Edge. This would have been a tedious process, but given our comparatively vast experience in Solid Edge as opposed to Siemens NX, it would have lessened the workload considerably and would, in all likelihood, have led to a superior design from both an aerodynamic, FEM and aesthetic perspective.
Regardless, almost all of our designs gave better results than that of previous undertray designs at KTHFS as well as those of other Formula Student cars that we have looked at.
The most common design prior to this has been that of a flat plate. While flat plates do provide the car with a significant amount of downforce, the abrupt expansion of the air after the undertray leads to a massive amount of drag. This not only causes an increase in fuel consumption, but also leads to a slower lap-time. Moreover, by optimizing the shape of the undertray, it is possible to obtain a better design in terms of downforce to drag ratio compared to the flat plate configuration.
5.1.1 CFD accuracy
Some discussion can be made about which turbulence model to use: K-omega or K- epsilon. As stated in the article ’Choosing the Right Turbulence Model for Your CFD Simulation’ by Shawn Wasserman, K-omega is more sensitive to initial conditions and requires a longer processing time to reach acceptable residual values but it will provide more accurate near-wall values and allows for a movable ground surface. K-epsilon, on the other hand, requires less processing time, is not especially sensitive to the initial conditions and is more common, better in the freestream and therefore easier to verify. While the drag values were already suspected to be low enough as to be considered insignificant in comparison to the downforce, the reason for choosing the K-omega turbulence model
comes down to the fact that we are especially interested in the air interaction with the undertray itself. Given its intricate shape, the flow is defined with shear layers making the effects of the undertray walls important to consider. Hence, we decided on the K-omega turbulence model (Wasserman, 2016).
Initially we also ran full-car simulations but later chose to switch to half-car simulations to save on processing time. This proved to be of no significance to the accuracy of the results, as the values were exactly half of the full-car values with the same model.
When it comes to cell number, we felt that values between 800 000 and 1.8 million cells were enough. Our philosophy was to focus on producing multiple rough designs, where the values were just good enough to be able to be stacked up against one another for us to quickly be able to tell which design was superior.
5.1.2 Potential Improvement
When it comes to improving the performance of the undertray, our initial suggestions are to change the object of which it is attached to: the chassis. It should be noted that this will change the longitudinal location of the centre of pressure and affect the results given when optimizing the undertray. We suggest a more cylindrical design, where the nose is not tilted upwards, and therefore not providing lift to the front of the vehicle, as well as removing the S-shaped underside of the front and making that uniform as well. We also suggest that the bottom of the chassis either be slimmed down in order to increase the volumetric airflow or to stray away from the idea that the bottom of the chassis should be a substitute for the center of the undertray, if the change in chassis shape underneath is non-negotiable. Additionally we would suggest removing the gap between the undertray and the chassis, for the reasons mentioned above.
Furthermore, we suggest including cylindrical rods to the inside of the undertray, as well as slits on the side to allow vertical movement of these cylindrical rods within the CFD model.
This is to simulate the A-arms of the suspension, and the impact that they would have on the aerodynamic performance of the undertray. We also suggest studying the impact of varying the number of slits on the flat plate, as a large number will indeed provide us with the desired vortices to prevent air from entering from the sides. However, aforementioned impact to the overall downforce might be less than that lost from the numerous slits.
Another aspect worth looking into, is the impact of adding additional wings above the
end of the flat plate, with varying number of wings and their angles of attack. This might provide us with an even larger increase in downforce, but the added drag will counteract the benefits of our chosen design and hence, has to be assessed carefully.
We also suggest looking into different attachment methods. For instance, the top two A-arms can be integrated into the top of the expansion tunnels, providing us with less aerodynamic disturbances. This would lead to added complexity, both in the design of the A-arms but also in the design of the undertray itself, however it could provide us with the potential of further vertical expansion. But this expansion increases the risk of flow separation and might not even be desirable.
5.2 Conclusion
To beneficially use the space behind the driver, we chose to make an undertray shaped in Venturi tunnels inspired by the Aston Martin Valyrie as it takes advantage of its interaction with the ground to create more downforce, improving the performance of the car by making it possible to do cornering maoeuvre with higher speed. Though the final design provides half the downforce of one of our previous iterations, the resulting values are still superior to that of previous KTHFS and other Formula Student undertrays. The undertray meets the required specifications in weight, stiffness and budget. We noticed that it was possible to make an undertray that gives half as much downforce as the cars weight but with the ”McDonald’s design” that we deem to be the optimal design with respect to downforce and drag values but not from a KTHFS team perspective. Regarding manufacturing, for core material, we have found Baltek balsa wood to be the most suitable in a sandwich structure of carbon fiber fabric and cured with epoxy resin. The ideal manufacturing process seem to be VIM.
6 RECOMMENDATIONS AND FUTURE WORK
To better the shape of the undertray, the monocoque provided for us should slightly be modified mainly into a more cylindrical design with a nose not tilting upwards as it can be influencing the results of CFD analysis. Further CFD studies on the shape should be performed to get an optimal undertray for the KTHFS car as well as a FEM analysis. The later was not performed during this project as it is quite difficult for composite materials and necessitate help.
Studying if adding a certain number of slits in the inside of the undertray as well as in the sides, is important to understand if they have a positive impact on the undertray by creating vortices and preventing air for entering from the side.
With a final design obtained, a more detailed mesh in Star CCM+ is recommended for more detailed refinement. Afterwards, a CAD-assembly of the whole car will be possible.
This step is important to make sure that the dimensions of the undertray does fit with other car components.
Additionally, manufacture should be done according to the recommendation guide regarding material, method and cost given in this report. Following this, the undertray should be Solid Mechanics analysed and a research on different attachment methods should be performed before the real assembly.
Eventually, the finished product in the assembled car could be tested in a wind tunnel which will give more accurate and real results than the ones obtained in Star CCM+. This will then give us the opportunity to improve the undertray after the production.
7 REFERENCES
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Dahlin, N. (2017) ’Bilen som körde ett enda lopp’, Teknik Historia, 7 January [online].
Available at: https://www.nyteknik.se/teknikhistoria/
bilen-som-korde-ett-enda-lopp-6816365 (Accessed: 22 April 2020)
Felföldi,A.(2020) What Is the Venturi Effect? [online]. Available at: https://
www.simscale.com/blog/2018/04/what-is-venturi-effect/ (Accessed:10 April 2020)
Formula Student (2020) Formula Student Rules 2020, p.25 and p.117.
Hughes, M., Piola G (2018) ’TECH TUESDAY: The Lotus 79, F1’s ground effect marvel’, Formula One™ , 21 August [online]. Available at: https://www.formula1.com/en/
latest/article.tech-tuesday-the-lotus-79-f1s-ground-effect-marvel.
sAD9PXt7mC8iMSwwe6CCw.html (Accessed: 22 April 2020)
Khan Academy, What is Bernoulli’s equation? [online]. Available at: https://www.khanacademy.org/science/physics/fluids/fluid-dynamics/
a/what-is-bernoullis-equation (Accessed:10 April 2020)
Kotwal, S. (2018), ’Aston Martin Valkyrie: An in-depth
look’, Auto Car, 7 October [online]. Available at: https://www.autocarindia.com/
car-news/aston-martin-valkyrie-an-in-depth-look-409968 (Accessed: 22 April 2020)
McEachern, S. (2017), ’5 Things You Need to Know About the Aston Martin Valkyrie’, Auto Guide, 12 July [online]. Available at:https://www.autoguide.com/auto-news/
2017/07/5-things-you-need-to-know-about-the-aston-martin-valkyrie.
html (Accessed: 22 April 2020)
Noble, J. (2019), ’F1 commits to reintroducing ground effect aero concept with ’21 rules’, Auto Sport, 17 July [online]. Available at: https://www.autosport.com/f1/news/
144841/f1-commits-to-reintroducing-ground-effect-for-2021 (Accessed: 2 May 2020)
Oertel, H. et al. (2004) Prandtl’s Essentials of Fluid Mechanics. 2nd edn. Germany:
Springer, p.71.
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https://www.sciencedirect.com/topics/earth-and-planetary-sciences/
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Wasserman, S. (2016), ’Choosing the Right Turbulence Model for Your CFD Simulation’
[online]. Available at: https://www.engineering.com/DesignSoftware/
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gps.caltech.edu/~cdp/Desktop/Navier-Stokes%20Eqn.pdf (Accessed: 26 April 2020)
APPENDICES A MATERIAL PROPERTIES
A.1 Material Description
A.1.1 PVC Foam (semi-rigid, closed cell, 0.700)
General information
Designation Polyvinylchloride semi-rigid closed cell ”linear” foam, 0.700 specific gravity (based on Forex Classic)
Tradenames FOREX Classic, Vestolit
Typical uses Thermal insulation, Refrigeration, Shop fittings, Interior cladding, Packaging, Signs, Display boards, Air ducts / ventilation, External construction.
Composition overview
Compositional summary (CH2-CHCl)n Form Foam
Material family Plastic (thermoplastic, amorphous)
Base material PVC (Polyvinyl chloride, rigid, unplasticized) Polymer code PVC
Composition detail (polymers and natural materials)
Polymer 100 %
Price
Price *43,5 - 47,9 SEK/kg
Price per unit volume *2,91e4 - 3,49e4 SEK/m3
Physical properties
Density 670 - 730 kg/m3 Relative density 0,5 - 0,53 Cell type Closed-cell Cells/volume *2 - 20 /mm3 Anisotropy ratio *1 - 1,5
Mechanical properties
Young’s modulus 0,84 - 0,88 GPa Specific stiffness 1,17 - 1,29 MN.m/kg Yield strength(elastic limit) *8 - 10 MPa Tensile strength 14 - 18 MPa
Specific strength *11,4 - 14,4 kN.m/kg
Elongation strain 32 - 36 %
Compressive modulus 0,719 - 0,943 GPa Compressive strength *8 - 10 MPa Cell type Closed-cell
Compressive stress at 25% strain *13 - 17 MPa Flexural modulus 1,2 - 1,4 GPa
Flexural strength (modulus of rupture) 26 - 30 MPa Shear modulus *0,315 - 0,33 GPa
Shear strength 4 - 5 MPa Bulk modulus *0,84 - 0,88 GPa Poisson’s ratio *0,28 - 0,31 Shape factor 2,6
Hardness - Vickers *0,8 - 1 HV
Elastic stored energy (springs) *37,6 - 57,6 kJ/m3 Fatigue strength at 107cycles *9,8 - 12,6 MPa Densification strain 0,3 - 0,4
Impact fracture properties
Fracture toughness *0,177 - 0,193 MPa.m0.5 Toughness (G) 0,0363 - 0,0433 kJ/m2
Thermal properties
Glass temperature 74 - 88 °C
Heat deflection temperature 0.45MPa *62 - 82 °C Heat deflection temperature 1.8MPa *57 - 77 °C Maximum service temperature *77 - 92 °C Minimum service temperature *-33 - -28 °C Thermal conductivity *0,08 - 0,082 W/m.°C Specific heat capacity 1e3 - 1,1e3 J/kg.°C Thermal expansion coefficient 54 - 58 µstrain/°C Thermal shock resistance *165 - 209 °C
Thermal distortion resistance *0,00139 - 0,0015 MW/m
Electrical properties
Electrical resistivity *1e14 - 1e15 µohm.cm Electrical conductivity 1,72e-13 - 1,72e-12 %IACS Dielectric constant (relative permittivity) 1,85 - 1,95 Dissipation factor(dielectric loss tangent) 0,012 - 0,015 Dielectric strength (dielectric breakdown) 11 - 12 MV/m
Magnetic properties
Magnetic type Non-magnetic
Optical, aesthetic and acoustic properties
Transparency Opaque
Acoustic velocity 1,08e3 - 1,14e3 m/s
Mechanical loss coefficient (tan delta) *0,1 - 0,2
Critical materials risk
Contains >5wt% critical elements? No
Absorption permeability
Water absorption @ 24 hrs 0,8 - 1 %
Durability
Water (fresh) Excellent Water (salt) Excellent Weak acids Excellent Strong acids Excellent Weak alkalis Excellent Strong alkalis Excellent Organic solvents Limited use Oxidation at 500C Unacceptable UV radiation (sunlight) Good Flammability Self-extinguishing
Primary production energy, CO2 and water
Embodied energy, primary production) 68,6 - 75,6 MJ/kg CO2 footprint, primary production *2,94 - 3,24 kg/kg Water usage *591 - 653 l/kg
Processing energy, CO2 footprint water
Polymer extrusion energy *7,38 - 8,14 MJ/kg Polymer extrusion CO2 *0,591 - 0,651 kg/kg Polymer extrusion water *5,47 - 8,21 l/kg Polymer molding energy *19 - 21 MJ/kg Polymer molding CO2 *1,52 - 1,68 kg/kg Polymer molding water *12,7 - 19,1 l/kg
Coarse machining energy (per unit wt removed) *0,596 - 0,659 MJ/kg Coarse machining CO2 (per unit wt removed) *0,0447 - 0,0494 kg/kg Fine machining energy (per unit wt removed) *1,69 - 1,87 MJ/kg
Fine machining CO2 (per unit wt removed) *0,127 - 0,14 kg/kg Grinding energy (per unit wt removed) *2,9 - 3,21 MJ/kg Grinding CO2 (per unit wt removed) *0,218 - 0,241 kg/kg
Recycling and end of life
Recycle False
Recycle fraction in current supply 0,1 % Downcycle True
Combust for energy recovery True
Heat of combustion (net) *17,5 - 18,3 MJ/kg Combustion CO2 *1,37 - 1,44 kg/kg
Landfill True Biodegrade False
Notes
Other notes Can be welded and thermomolded. Values marked * are estimates. No warranty is given for the accuracy of this data.
A.1.2 End-grain balsa (0.095)
General information
Designation End-grain balsa, 0.095 specific gravity Tradenames Balsalite, Baltek, ContourKore, ProBalsa
Typical uses Sustainable core material for lightweight sandwich panels and structures. Boat hulls, decks, bulkheads, superstructures, interiors, tooling. Automotive / train floors, walls, roof panels, body panels, interiors, side skirts. Wind turbine blades, spinners, nacelle covers, generator housings. Aircraft floor panels, galley carts, interior partitions, cargo pallets, containers. Industrial fascia panels, skis and snowboards.
Composition overview
Compositional summary Balsa wood bonded with thermoset adhesive Material family Natural
Base material Wood (tropical) Renewable content 100 %
Composition detail (polymers and natural materials)
Wood 100 %
Price
Price *63,2 - 85,3 SEK/kg
Price per unit volume *5,62e3 - 9,26e3 SEK/m3
Physical properties
Density 88,9 - 109 kg/m3
Relative density 0,299 - 0,45 Cell type Closed-cell Cells/volume *2 - 20 /mm3 Anisotropy ratio *1
Mechanical properties
Young’s modulus 0,0591 - 0,0789 GPa Specific stiffness 0,584 - 0,825 MN.m/kg Yield strength(elastic limit) 0,341 - 0,428 MPa Tensile strength 0,539 - 0,659 MPa
Specific strength 3,35 - 4,5 kN.m/kg Compressive modulus 1,84 - 2,25 GPa Compressive strength *5,4 - 6,76 MPa Flexural modulus 0,0591 - 0,0789 GPa
Flexural strength (modulus of rupture) 3,46 - 4,23 MPa Shear modulus 0,0918 - 0,112 GPa
Shear strength 1,55 - 1,9 MPa Poisson’s ratio 0,3 - 0,333 Shape factor 4,91
Elastic stored energy (springs) 0,831 - 1,37 kJ/m3
Thermal properties
Glass temperature 77 - 102 °C
Maximum service temperature 147 - 179 °C Minimum service temperature -233 - -191 °C Thermal conductivity 0,0555 - 0,0678 W/m.°C Specific heat capacity 1,52e3 - 1,85e3 J/kg.°C Thermal expansion coefficient 20,4 - 29,4 µstrain/°C Thermal shock resistance 178 - 293 °C
Thermal distortion resistance *0,00204 - 0,00307 MW/m
Electrical properties
Electrical resistivity 6e13 - 2e14 µohm.cm
Electrical conductivity 8,62e-13 - 2,87e-12 %IACS Dielectric constant (relative permittivity) 1,68 - 2,05 Dissipation factor(dielectric loss tangent) 0,0106 - 0,013 Dielectric strength (dielectric breakdown) 4,3 - 5,25 MV/m
Magnetic properties
Magnetic type Non-magnetic
Optical, aesthetic and acoustic properties
Transparency Opaque
Acoustic velocity 762 - 912 m/s
Critical materials risk
Contains >5wt% critical elements? No
Absorption permeability
Water absorption @ 24 hrs 180 - 220 %
Durability
Water (fresh) Limited use Water (salt) Limited use Weak acids Limited use Strong acids Unacceptable Weak alkalis Limited use Strong alkalis Unacceptable Organic solvents Acceptable Oxidation at 500C Unacceptable UV radiation (sunlight) Good Flammability Highly flammable
Primary production energy, CO2 and water
Embodied energy, primary production) *11,6 - 12,8 MJ/kg CO2 footprint, primary production *0,574 - 0,633 kg/kg Water usage *665 - 735 l/kg
Processing energy, CO2 footprint water
Coarse machining energy (per unit wt removed) *1,06 - 1,17 MJ/kg Coarse machining CO2 (per unit wt removed) *0,0794 - 0,0877 kg/kg Fine machining energy (per unit wt removed) *6,31 - 6,97 MJ/kg Fine machining CO2 (per unit wt removed) *0,473 - 0,523 kg/kg Grinding energy (per unit wt removed) *12,1 - 13,4 MJ/kg Grinding CO2 (per unit wt removed) *0,91 - 1,01 kg/kg
Recycling and end of life
Recycle False
Recycle fraction in current supply 0,1 % Downcycle True
Combust for energy recovery True
Heat of combustion (net) 18,5 - 22,6 MJ/kg
Combustion CO2 1,56 - 1,91 kg/kg Landfill True
Biodegrade False
NotesValues marked * are estimates. No warranty is given for the accuracy of this data
