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Posted: December 6th, 2024

Smooth Rough Contact Formulation for Crack Planes

Table of Contents

Declaration

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Acknowledgements

Table of Contents

Table of Figures

List of Tables

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Abstract

1 Introduction

1.1 Rationale for this thesis

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1.2 Hypothesis

1.3 Structure of thesis

2 State of The Art Analysis

2.1 Thermal Comfort

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2.1.1 Air Temperature

2.1.2 Radiant Temperature

2.1.3 Relative Humidity

2.1.4 Air Velocity

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2.1.5 Activity (Metabolic Rate)

2.1.6 Clothing

2.2 Indoor Air Quality (IAQ)

2.2.1 Contributing Pollutants to IAQ

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2.3 Fluid Dynamics

2.3.1 Governing Equations

2.3.2 Analytical Fluid Dynamics

2.3.3 Computational Fluid Dynamics

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2.3.4 Stages of CDF

2.3.5 Computational Fluid Dynamics Software

2.3.6 Autodesk CFD

3 Software Architecture

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3.1 Software Flow Diagram

3.2 Proposed software description

4 Methodology Approach

4.1

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4.2

4.3

5 Case Study – ERI Building

5.1 Experimental Plan

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5.2

5.3

6 Discussions & Results

6.1

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6.2

6.3

7 Findings & Conclusion

8 Appendix

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9 Bibliography

Table of Figures

Figure 3 Material Nonlinearity

List of Tables

Table 1 Concrete Material Properties

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Table 2 Reinforcement Properties

Abstract

Although many consistent models have been created to accurately model the linear behaviour of concrete, the same cannot be said for the non-linear behaviour of concrete.  The complex nature of the softening behaviour of concrete cracking under loading and the contact that occurs between rough crack surfaces when they are closed or subjected to shear loading makes the development of such a model a truly difficult task.  One model, which aims to achieve this goal is a multi-crack model called the Craft Model developed by A.D.Jefferson. This model which is defined as a plastic-contact-model uses planes of degradation that can undergo damage and separation but can also regain contact.  Recent updates to the model introduce smooth rough contact formulation for crack planes to simulate closing under both normal and shear loading.

1       Introduction

1.1      Rationale for this thesis

Humans spend on average 90,000 hours at work over their lifetime with much of this time spent in the office, so it is imperative that the quality of air in these office spaces should be delivered at an optimal standard to enhance productivity and comfort conditions for the occupants in their work environment.

With the world leaning towards energy savings, it’s not just as simple as fitting out the premises with a top of the range air conditioning system, as the carbon foot print left behind for the next generation would be catastrophic. The need to correctly implement design features during the design phase of the structure should be met with open mind, such to limit unnecessary energy wastage.

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A picture containing thing

Description generated with high confidenceNatural ventilation, mechanical ventilation, and full air conditioning are some of a few methods of maintaining a building in relation to thermal comfort, but which design to implement is the burning question as the flow of air, be it via natural ventilation or otherwise is difficult to predict.

Figure 1 – Natural Ventilation in Buildings http://amienvironmental.com/natural-ventilation-section-2/

The need for accurate prediction of air movement in occupied spaces is essential, as copious quantities of air supplied to a space need to be evenly distributed. Without adequate air distribution, unwarranted air movement (drafts) may occur in some zones, whilst stagnant air may occur in other zones of the same area. Poor air distribution can affect the indoor climate and degrade the air quality leading to unsatisfied occupants [1].

Computational Fluid Dynamics (CFD) is now being applied to provide in-depth analysis of intricate fluid flows, including detailed flow features like velocity, turbulence, pressure and temperature for internal and external flows. By incorporating CFD into initial design procedures, the engineer tasked with designing the   ventilation system can limit if not eliminate the unwanted event of dissatisfaction amongst occupants arising [2].

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However, implementing CFD properly is time consuming, with a good knowledge of fluid dynamics a necessity. CFD output is only as good as human input.

1.2      Hypothesis

The need to provide computational fluid dynamics analysis during the design stage of a project is a costly measure due to high user knowledge input and the time allocated to running simulations as the speed at which the simulation runs varies in relation to the process power of the machine being used. This study aims to provide future designers the knowledge of what are the maximum and minimum requirements for implementation of a CFD analysis, the ratio of window apertures to room volume necessary to maintain a high standard when specifying natural ventilation to the design based on building layout, orientation and design parameters set out by governing bodies.

1.3      Structure of thesis

Chapter 2 – In the state of the art analysis the author begins with a literature review of the basic requirements set out; what defines thermal comfort and the ventilation requirements associated with indoor air quality. A further analysis looks at the requirements of computational fluid dynamics, drilling down to the categories of ventilation modelling.

Chapter 3 –    Discusses the software environment associated with computational fluid dynamics and their ability to perform analysis based on indoor air quality, thermal comfort, risk of overheating and essentially the ability to mimic the room air flow effectively enough so that it appears to resemble the real thing. Based on this software analysis the author defines the chosen software most suitable for the impending study

Chapter 4 –  This chapter discusses the methodology approach, specifying standards used, ventilation types, software implemented, reference material available, governing equations associated with air flow movement and all assumptions made during this study.

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Chapter 5 –  Chapter 4 looks at the case study based on the Environmental Research Institute (ERI) building. This study will provide sufficient information to determine the ventilation method acceptable within the defined space/zone whilst keeping to standards laid down by governing bodies.

Chapter 6 – This chapter discusses the granularity of the simulation results, indicating the estimated data processing time and input parameters required to produce adequate simulations for design discussion. Further discussions involve detailed analysis on improvements that could be made to improve the IAQ of similar building based on the various ventilation methods.

Chapter 7 – Findings & Conclusions

Appendices

Bibliography

2       State of The Art Analysis

The following chapter looks at the importance of thermal comfort within an occupied space, the required air quality necessary to meet the thermal comfort criteria and the methods used during the design stage to implement these findings based on computational analysis. The ability to analyse the level of thermal comfort and the state of the indoor air quality is of the utmost importance to maintaining a good working environment where occupants can avoid thermal stress.

2.1      Thermal Comfort

Thermal comfort is defined as “that condition of mind which expresses satisfaction with the thermal environment and is assessed by subjective evaluation” [3].

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The main influencing parameters for thermal comfort are as follows;

  • Temperature (Air, Surface, Asymmetry)
  • Air Speed/turbulance
  • Radiant Temperature
  • Activity (metabolic rate)
  • Relative Humidity
  • Clothing (clo-value)

Thermal comfort is essentially the way in which people interact with their thermal environment. When a person’s states that they are too hot or too cold, what is really happening is they are responding to the heat transfer from their body to the surrounding environment [4].Cf

The human body operates at a core temperature around 37oC for the internal organs to function properly. Any fluctuations in this temperature requires the body to self-regulate. Slight increases or decreases in this temperature can cause implications – a sudden drop can cause hypothermia whilst a sudden rise can result in hyperthermia [5].

Predicted Mean Vote (PMV) is a thermal sensation scale employed by Ashrae that incorporates a formula developed by Fanger to achieve thermal comfort amongst the majority of people in the occupied space. Although Fanger’s method is the most common method of calculating PMV, certain points should be noted:

  • Fanger’s study were based exclusively from climate chambers where conditions were kept at a constant, resulting in a steady state environment. This does not take for the everyday patterns of a building where door openings and closing takes place several times a day.
  • Clothing insulation [5] studies were determined in an experiment which used heated manikins
  • Humidity, air movements air temperatures and radiant temperatures have to be estimated when using Fanger’s equation.
  • Metabolic rates used in the equation are assumed, not really knowing what activity is actually taking place within the specified space. In addition to this, many spaces will have multiple activities.

Figure 2 – Ashrae and Bedford Comfort Descriptors [TM52: 2013]

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The following formula for PMV as expressed by P.O. Fanger

Where:

PMV = Predicted Mean Vote Index
M = Metabolic rate
L = Thermal load – defined as the difference between the internal heat production and the heat loss to the actual

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Description generated with very high confidenceThe term Percentage persons dissatisfied (PPD) is a representation of the way a group of occupants would judge their level of comfort.

Figure 4 – Sample Software Calculation of PMV / PPD (Course Notes)

2.1.1      Air Temperature

What temperatures are comfortable? CIBSE Guides proposes a temperature of 20oC to 22oC is ok for some sedentary situations, but where activities are taking place, it is proposed a lower temperature is necessary, but these levels of activities may vary depending on the level of work taking place. A prime example of this is where one office space may consist of sedentary work and require say 21oC, whereas another office space might have a high level physical work requiring a lower air supply temperature. The following table indicates responses to various temperatures.

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Temperature (oC) Response
18 Physically inactive people begin to shiver. Active people are comfortable.
21 Optimum for performance of metal work.
22 Most comfortable year-round indoor temperature for sedentary people.
24 People feel warm, lethargic and sleepy. Optimal for unclothed people
25 Optimal for bathing, showering. Sleep is disturbed.

1 – Typical Response to Various Temperatures [CIBSE Guide A]

2.1.2      Radiant Temperature

With ever office space there will be office furniture which produce heat, be it computers, printers, radiators, lights and even humans. The heat emitted from these objects radiates to the surrounding air. This radiant head in turn heats the surrounding air to produce a radiant temperature. To manually calculate this temperature would be a time-consuming process. With the development of advanced computer software, it is now possible to feed information into this software and receive the output data which can be critical to the future design of a structure.

2.1.3      Relative Humidity

When relative humidity is kept around 50%, occupants tend to have fewer respiratory problems. Higher humidity levels tend to make the occupied area stuffy whilst increasing the chances of bacterial and fungal growth. Humidity levels with fall below 50% tend to cause discomfort among occupants in the form of drying out skin causing skin rashes.  CIBSE Guide A recommends that relative humidity within the range 40-70% RH are generally accepted[6]

Figure 5 – The effect of humidity on environmental factors that affect occupants comfort and health

[ASHRAE Systems 2008; chapter 22, figure 1]

2.1.4      Air Velocity

Large air movement in occupied spaces can cause considerable discomfort especially during the winter period if the air is cold. For the human body, the two most susceptible parts are the neck and the ankles, cooler air tends to travel at floor level which may cause discomfort around the ankles. During design stages, air diffusion within the occupied space should be carefully considered as high-level supply can cause considerable discomfort on the back of the neck for people working at desks, while low level supply as stated earlier can cause stress around the ankles. CIBSE recommend the following air velocities during seasonal periods; Winter 0.1(m/s), Summer 0.3(m/s)

2.1.5      Activity (Metabolic Rate)

Metabolic heat production is largely dependent on the occupant’s activity. In simple terms, the more physical work undertaken by the occupant, the more heat they produce. Adding to this, the more heat produced, the greater the need to lose heat to prevent the body from overheating.

When incorporating the metabolic rate into our thermal comfort equations, certain characteristics of the human study need to be noted;

  • Size
  • Weight
  • Age
  • Sex

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Description generated with high confidenceAll these factors have an impact on the persons perception of thermal comfort and should not be omitted from design factors. The following table taken from Ashrae 55-2010 gives typical metabolic rates and heat generation per unit area of body surface for office activities.

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Figure 6 – Typical metabolic rates and heat generation

Activity Metabolic Rate/Met Heat Generation / W.m-2

2.1.6      Clothing

Clothing worn by the occupant alters accordingly to the time of year. During summer months, typical clothing may consist of a light form of dress, blouse, pants and even short sleeve shirt. Over compensating in clothing during warm months could result in the occupant overcoming to heat stress.

During winter, people tend to wear thicker, heavier and even more layers. If  the level of clothing does not provide enough insulation, the occupant is at risk of causing themselves injuries, even hypothermia.

The insulation effect of clothes is measured in the unit “CLO”. The following table are typical values for various items of clothing [ sample values taken from www.engineeringtoolbox.com ]

Clothing Insulation
Clo m2K/W
Nude 0 0
Trousers Shorts 0.06 0.009
Walking shorts 0.11 0.017
Light trousers 0.20 0.031
Normal trousers 0.25 0.039
Flannel trousers 0.28 0.043
Overalls 0.28 0.043
Skirts, dresses Light skirt 15 cm. above knee 0.01 0.016
Light skirt 15 cm. below knee 0.18 0.028
Heavy skirt knee-length 0.25 0.039
Light dress sleeveless 0.25 0.039
Winter dress long sleeves 0.40 0.062

Table 2 – Thermal Insulation Values for typical Clothing

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2.2      Indoor Air Quality (IAQ)

Indoor Air Quality (IAQ) refers to the air quality within a building. The need for indoor air quality must be addressed to meet the needs and requirements of the buildings occupants. Maintaining a good IAQ leads to a more happier and productive workforce, and a happier workforce reduces the work time which is lost due to unsatisfied occupants. Neglecting the standard of IAQ in a building can lead to high repair costs of the mechanical systems if adjustments must be made. The following table is an extract from CIBSE KS17 – Indoor Air Quality and Ventilation

Table 3 – Approximate thermal comfort variables and their affect on IAQ

By incorporating good practice of IAQ during the design stage of a project will result in a building that is more successful in meeting its design goals and achieving the desired levels of performance throughout its occupied life[7].

The ventilation of an occupied space is necessary to maintain good IAQ levels. Ventilation is needed for many reasons;

  • Providing fresh air to occupants to enhance their sense of thermal comfort.
  • The removal of contaminants and pollutants such as carbon dioxide, volatile organic compounds (VOC’s), odours and particulates which can lead to medical problems further down the line.

2.2.1      Contributing Pollutants to IAQ

Understanding and having the ability to control indoor air pollutants can help reduce the risk of indoor health concerns.

The following is a list of common pollutants that may exist in your current surroundings.

2.2.1.1     Carbon Dioxide (CO2)

Carbon dioxide is the most common pollutant

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Critical Outcome: High concentrations can cause irritation to the eyes and throat. Elevated levels can have an adverse effect on the levels of concentration sustained by occupants.

Source: Carbon Dioxide is exhaled as part of the metabolic process and is also emitted from everyday appliances such as boilers and cookers.

The following table indicates concentrations associated with air quality classifications [8]

Classification Indoor Air Quality Standard Fresh Air Ventilation Range Fresh Air Default Value (L/s/p) Approximate indoor CO2 Concentration (ppm)
IDA 1 High >15 20 700 to 750
IDA2 Medium 10-15 12.5 850 to 900
IDA3 Moderate 6-10 8 1,150 to 1,200
IDA4 Low <6 5 1,500 to 1,600

Table 4 – Indoor Air Quality Classification in BS EN 13779

2.2.1.2     Carbon Monoxide (CO)

Critical Outcome: Acute exposure-related reduction of exercise, with an increase in symptoms of heart disease.

Source: Carbon monoxide is produced both indoors and outdoors by combustion sources such as poorly installed heating systems, poorly ventilated cooking areas and is a product of petrol and diesel vehicles.

2.2.1.3     Benzene (C6H6)

Critical Outcome: Acute myeloid leukaemia and genotoxicity.

Source: Benzene can originate in building materials, furniture and other such artefacts. The presence of combustion sources and other human activities will be the main determinant of the concentration of benzene indoors.

2.2.1.4     Formaldehyde (CH20)

Critical Outcome: Sensory Irritation

Source: The source of formaldehyde in the indoor environment are; furniture and wooden products containing formaldehyde based resins (plywood, insulation). Other sources include man made products such as paint, glue and varnish.

2.2.1.5     Nitrogen Dioxide (NO2)

Critical Outcome: Respiratory symptoms, airway inflammation and a decrease in immune system.

Source: Indoor sources include smoking and the burning of natural resources (coal, gas and wood) in stoves where inadequate ventilation is applied.

2.2.1.6     Radon (Rn)

Critical Outcome: Lung cancer and has association with other forms of cancer such as leukaemia.

Source: From the earth beneath the structure, the higher the uranium content of the soil the greater the levels of radon possess a risk to the indoor air quality.

2.3      Fluid Dynamics

Fluid Dynamics is the process used to model the behaviour of fluids. In building’s it is typically used to model the flow of air within an occupied space. This can be invaluable to the designer, allowing them to predict internal conditions ever before the building is built, allowing them to simulate options and select the most applicable to the design.

Fluid dynamics can be subdivided into two initial topics, analytical and computational. Both topics require the use of three governing equations, the conservation of mass, conservation of momentum and the conservation of energy.

2.3.1      Governing Equations

The three governing equations used within CFD, are written as seen below in partial differential format[9].

Conservation of Mass:

The equation is derived by considering a fixed volume in a space and that the flow of air entering the space is equal to that which is exiting it. This air flow is expressed as the mass per unit volume per second. (kg/m3/s)

δρδt+δδxj ρuj=0

Equation 1 – Conservation of mass

In short, this equation states that the change of mass within the volume is equal to the overall flow of mass across the boundaries of the fixed volume.

Conservation of Momentum:

This equation is derived from Newton’s second law; force = mass x acceleration. The following equation gathers all the force elements to the right-hand side.

δδtρui+ δδxiρuiuj= μδτijδj- ϱδpijδxj+Bi

Equation 2 – Conservation of Momentum

Broken down from left to right as follows;

1 The change in momentum over time
2 Mass x acceleration
3 Force due to shear stress
4 Force due to pressure gradient in the fluid
5 Generic term representing all other body forces.

Conservation of Energy:

Is also known as the first law of thermodynamics, states that the rate of change of internal energy of a volume of air is equal to that of the heat supplies to the air less the work done by the volume of air on its surroundings. It is expressed using enthalpy as an indicator of energy.

δhδt+ δδxiρuih- δδxiλCpδhδxj=0

Equation 3 – Conservation of Energy

Broken down from left to right as follows;

1 Represents Enthalpy. (heat)
2 Change in enthalpy due to air movement.
3 Change in enthalpy caused on the air outside the volume being considered

2.3.2      Analytical Fluid Dynamics

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Description generated with high confidenceUsing long-hand calculation to predict the air flow within a defined space can become tedious, as the equations to be implemented (stated above) can be intricate and most time consuming. The zone in question would need to be broken up into c complex mesh, the more complex the mesh the greater the prediction on the aerodynamic flow within the space. Below is a simple 2-D mesh (Figure 7) with some typical terminology.

Figure 7 – A Simple 2-D Mesh

To establish a detailed picture of the flow patterns within the occupied space the user should consider using a 3-dimensional grid (Figure 8), this method increases the workload of the user as it becomes painstakingly tiresome to formulate hundreds if not thousands of equations.

Figure 8 – A Simple 3-D Mesh

Establishing a grid size is of the utmost importance when simulating the air stream flow in a space, a grid with large cells will output little useful data, but will be less time consuming, whereas implementing a 3-dimensional grid with small cell sizes will produce vast amounts of useful data for the user to study, such complex grids would result in days of complex calculations. It is with these unwanted constraints, engineers have moved away from the analytical form of fluid dynamics and moved towards the ever-advancing process of Computational Fluid Dynamics, where simulations can be tested and verified to suit the needs of the client.

Analytical Fluid Dynamics (AFD) cannot be independently verified and is very difficult for complex flows[1].

 

2.3.3      Computational Fluid Dynamics

With the evolving progress in computer technology in recent years, computational fluid dynamics has advanced to a level where intricate flows can be simulated using numerous variables which can hypothetically overcome the difficulties in predicting vital flow structures such as thermal stratification in natural ventilation.

CFD is arguably the most intricate air-flow modelling technique in use today and probably the least well understood. With the evolution of modern computers and full-bodied numerical algorithms, a division between the user and the governing equations being solved have left several users detached with limited knowledge on how the software established the results, this in turn leaves the user unable to diagnose problems in the event of unexpected or non-compliant results being returned by the software.

With a background knowledge in fluid dynamics CFD can be a powerful tool to any user with benefits that include;

  • Creating scenarios, with the model already build the user will only need to change the settings (variables) in order to create a “what if” analysis.
  • With advances in cloud computing, models can be generated in 1:1 scale which the unnecessary implication of scaling results to suit scaled down models.
  • CFD models are limitless as to the number of measurement sensors required during analysis.
  • Process time of analysis is only limited by the process power of the computer being used and is far more efficient than that of an analytical process.

2.3.4      Stages of CDF

Pre-Processing Stage

  • Defining the model geometry.
    • Import initial model into CFD software, unless model was created using the same software for modelling as for analysis.
  • Define the computational domain.
    • Select the space(s) within the model to be analysed.
  • Define the boundary and initial conditions.
    • Define flow rates to be used for study purpose
    • Specify design temperature, both internal and external
    • Create profiles for building occupancy, night-time cooling modes and heating/cooling set points
  • Define grid / mesh.
    • The space being analysed is subdivided into small blocks (the smaller the blocks the more defining results will be returned, note: the smaller the blocks, the more time consuming the process will be.) these blocks are to which the computational equations are applied.
  • Define all the necessary solver parameters.
    • This is dependent upon the computational models that are required based on the expected conditions of the flow.

Processing Stage

  • Inspect the progress of the run.
    • On completion of step 1, the model will be put forward for simulation to the solver. It is during this time the user should track and take note of the progress during the simulation run. Inconsistencies such as ambiguous temperatures (spikes) should be dealt with accordingly. It is at the user’s discretion to proceed or not with simulation runs if runs are deemed unrealistic.
    •  If simulation runs are stopped, the user may adjust the solver criteria and re-run the simulation to achieve convergence. It may be of benefit to return to step one and redefine the setup parameters, making changes in relation to the observations. Simulations are repeated until such time as the user deems results satisfactory.

Evaluation Stage

  • Upon completion of simulation where the user deems the results to be satisfactory, the user will analyse and generate a report based on the findings. Should the design criteria not me met, the user has the option of adjusting the initial model and progressing again with step one.

2.3.5      Computational Fluid Dynamics Software

With the increasing interest of airflow within occupied spaces during the building design, whole building CFD simulation programs are increasingly employed in the design process to help both engineers and architects determine fundamental design criteria to satisfy the occupants need for thermal comfort and in turn reducing the cost of additional plant where natural ventilation is acceptable within the building framework. The following are three simulation software packages on the market which can aid the designer to provide first-rate working conditions for its occupants.

2.3.5.1     EnergyPlus

EnergyPlus is an open source software and is defined as a whole building energy simulation program, used to model energy consumption in heating, cooling, lighting and ventilation. Some of the prominent features and facilities of EnergyPlus are:

  • Integrated, simultaneous solution of thermal zone conditions and HVAC system response that does not assume that the HVAC system can meet zone loads and can simulate un-conditioned and under-conditioned spaces.
  • Heat balance-based solution of radiant and convective effects that produce surface temperatures thermal comfort and condensation calculations.
  • Sub-hourly, user-definable time steps for interaction between thermal zones and the environment; with automatically varied time steps for interactions between thermal zones and HVAC systems. These allow EnergyPlus to model systems with fast dynamics while also trading off simulation speed for precision.
  • Combined heat and mass transfer model that accounts for air movement between zones.
  • Advanced fenestration models including actuated window blinds, electrochromic glazings, and layer-by-layer heat balances that calculate solar energy absorbed by window panes.
  • Illuminance and glare calculations for reporting visual comfort and driving lighting controls.
  • Component-based HVAC that supports both standard and novel system configurations.
  • A large number of built-in HVAC and lighting control strategies and an extensible runtime scripting system for user-defined control.
  • Functional Mockup Interface import and export for co-simulation with other engines.
  • Standard summary and detailed output reports as well as user definable reports with selectable time-resolution from annual to sub-hourly, all with energy source multipliers. [10]

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Description generated with high confidence

EnergyPlus is free, open-source, and cross-platform, latest release – v8.7.0 and is compatible with the following platforms;

Windows 7&8   32 and 64-bit versions

Mac OSX 10.9  64-bit version

Linux  (Ubuntu 14.04) 64 bit version

Item Description
Userface Complex
User Manual Difficult to follow for new users to CFD
Coverage of CFD Consists of only a small documented area within the user manual and is dependant of prior knowledge of fluid dynamics.
Cost EnergyPlus is an open source software (zero cost to user)
CPU requirements Standard amongst other CFD softwares
Plugins with Revit Yes
Cloud option Yes
Customer Support Slow response

Table 5 – EnergyPlus Software Capabilities

2.3.5.2     IES VE (MicroFlo)

MicroFlo is a vender specific software used to simulate air flow and heat transfer, both internally and externally. MicroFlo has the ability to define boundary conditions such as internal energy sources, environmental conditions and HVAC systems. It can be used to predict occupancy thermal comfort prior to construction, investigate in detail natural and mixed mode ventilation strategies.

System Requirements [11]

 
Supported Environments:
 

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