In the design of HVAC systems, the question arises as to what conditions the ambient air needs for a person to feel comfortable in it. To answer this question, the concepts of thermal comfort, PVM and PPD are defined. In other words, an attempt has been made to find out what percentage of people feel satisfied by checking the different parameters of the ambient air created by HVAC. In this article, we will review PVM and PPD and tell how to calculate each one.

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## What is Thermal Comfort?

Thermal comfort refers to the conditions in which a person is comfortable with the thermal conditions of the environment. Thermal comfort depends on various parameters such as physical activity of the person, humidity and air temperature. This feeling is measured by different statistical methods. One of these methods is PMV. The concept of thermal comfort is used to design different HVAC systems.

## What is The Predicted Mean Vote (PMV)?

In various conditions in terms of air conditioning, **people’s opinions** were asked about the feeling of comfort, and with the statistical results obtained, the PMV index was created, which represents a number from -3 to +3, as in the following table:

Table 1. The PMV scale range

PMV index | Thermal sensation |

+3 | Hot |

+2 | Warm |

+1 | Slightly warm |

0 | Neutral |

-1 | Slightly cool |

-2 | Cool |

-3 | Cold |

Many standards are used to describe and calculate PMV. One of the most famous of them is **ASHRAE Standard 55**. ASHRAE is the abbreviation of the American Society of Heating, Refrigerating, and Air Conditioning Engineers. In this standard, **the comfort zone or acceptable PMV range** is defined as **-0.5<PMV<+0.5**. This means that most people feel comfortable in the mentioned range.

In the PMV index, -3 indicates a very cold environment and +3 indicates a very hot environment, and 100% of people feel uncomfortable in these two environments.

## What is The Predicted Percentage of Dissatisfied (PPD)?

PPD describes how many percent of people feel thermally dissatisfied with each PMV. For example, at PMV=0, 5% of people feel uncomfortable. The equation between PPD and PMV is as follows:

The result of the above equation is shown in the plot below. It is clear that the thermal conditions of the environment can never be such that 100% of people feel satisfied.

The relationship between PMV and PPD is shown in this plot. The more we move away from PMV=0, the more dissatisfied people are with the thermal conditions of the environment.

## Calculation of PMV and PPD

Calculating PMV and PPD requires various data and is complex. It is better to use a PMV Calculator. Here, we describe the method of calculating PMV and PDD based on **ASHRAE 55**. First, we introduce the parameters needed to solve the problem.

**Calculate Clothing Area Factor (FCL): **This factor can be calculated using the following equations and Table 2. Note that clo is a unit of measurement used to express the thermal insulation provided by garments and clothing ensembles and 1 clo is equal to 0.155 m²·K/W.

Table 2. Clothing insulation (*I _{cl}*) values for typical ensembles, adopted from ASHRAE 55

Clothing Description |
Garments Included |
I_{cl} [clo] |

Trousers |
Trousers ,short -sleeve shirt | 0.57 |

Trousers ,long -sleeve shirt | 0.61 | |

#2plus suit jacket | 0.96 | |

#2plus suit jacket ,vest ,T -shirt | 1.14 | |

#2plus long -sleeve sweater ,T -shirt | 1.01 | |

#5plus suit jacket ,long underwear bottoms | 1.30 | |

Skirts /Dresses |
Knee -length skirt ,short -sleeve shirt (sandals ) | 0.54 |

Knee -length skirt ,long -sleeve shirt ,full slip | 0.67 | |

Knee -length skirt ,long -sleeve shirt ,half slip ,long -sleeve sweater | 1.10 | |

Knee -length skirt ,long -sleeve shirt ,half slip ,suit jacket | 1.04 | |

Ankle -length skirt ,long -sleeve shirt ,suit jacket | 1.10 | |

Shorts |
Walking shorts ,short -sleeve shirt | 0.36 |

Overalls /Coveralls |
Long -sleeve coveralls ,T -shirt | 0.72 |

Overalls ,long -sleeve shirt ,T -shirt | 0.89 | |

Insulated coveralls ,long -sleeve thermal underwear tops and bottoms | 1.37 | |

Athletic |
Sweat pants ,long -sleeve sweatshirt | 0.74 |

Sleepwear |
Long -sleeve pajama tops ,long pajama trousers ,short 3/4length robe (slippers ,no socks ) | 0.96 |

**Metabolic Rate (M):**It represents the rate of body heat production per unit of time. Use Table 3 to calculate the metabolic rate.

Table 3. Metabolic Rates for Typical Tasks, adopted from ASHRAE 55

Resting |
Met Units |
W/m² |
Btu/h.ft² |

Sleeping |
0.7 | 40 | 13 |

Reclining |
0.8 | 45 | 15 |

Seated, quiet |
1 | 60 | 18 |

Standing, relaxed |
1.2 | 70 | 22 |

Walking (on level surface) |
|||

0.9 m/s, 3.2 km/h, 2.0 mph |
2 | 115 | 37 |

1.2 m/s, 4.3 km/h, 2.7 mph |
2.6 | 150 | 48 |

1.8 m/s, 6.8 km/h, 4.2 mph |
3.8 | 220 | 70 |

Office Activities |
|||

Reading, seated |
1 | 55 | 18 |

Writing |
1 | 60 | 18 |

Typing |
1.1 | 65 | 20 |

Filing, seated |
1.2 | 70 | 22 |

Filing, standing |
1.4 | 80 | 26 |

Walking about |
1.7 | 100 | 31 |

Lifting/packing |
2.1 | 120 | 39 |

Driving/Flying |
|||

Automobile |
1.0-2.0 | 60-115 | 18-37 |

Aircraft, routine |
1.2 | 70 | 22 |

Aircraft, instrument landing |
1.8 | 105 | 33 |

Aircraft, combat |
2.4 | 140 | 44 |

Heavy vehicle |
3.2 | 185 | 59 |

Miscellaneous Occupational Activities |
|||

Cooking |
1.6-2.0 | 95-115 | 29-37 |

House cleaning |
2.0-3.4 | 115-200 | 37-63 |

Seated, heavy limb movement |
2.2 | 130 | 41 |

Machine work |
|||

sawing (table saw) |
1.8 | 105 | 33 |

light (electrical industry) |
2.0-2.4 | 115-140 | 37-44 |

heavy |
4 | 235 | 74 |

Handling 50 kg (100 lb) bags |
4 | 235 | 74 |

Pick and shovel work |
4.0-4.8 | 235-280 | 74-88 |

Miscellaneous Leisure Activities |
|||

Dancing, social |
2.4-4.4 | 140-255 | 44-81 |

Calisthenics/exercise |
3.0-4.0 | 175-235 | 55-74 |

Tennis, single |
3.6-4.0 | 210-270 | 66-74 |

Basketball |
5.0-7.6 | 290-440 | 90-140 |

Wrestling, competitive |
7.0-8.7 | 410-505 | 130-160 |

**Air Temperature (TAA):**Ambient air temperature is required in Kelvin.**Mean Radiant Temperature (TRA):**is defined as the uniform temperature of an imaginary black enclosure in which an occupant would exchange the same amount of heat by radiation as in the actual non-uniform environment. it can be measured using instruments such as a globe thermometer. Its unit should be Kelvin in our calculation.**Relative Air Velocity (VEL):**It is the relative velocity of air compared to the velocity of people.**External Work (W):**It is called the work done by a person that results in the release of mechanical energy.It is usually zero.**Relative Humidity (RH):**This parameter indicates the ratio of air humidity to the maximum humidity it can have.**Water Vapor Pressure (PA):**The partial pressure exerted by water vapor in the air. Note that:

So far, all the parameters needed to solve the problem have been introduced. Next is the internal heat production in the human body:

In the next step, **calculate surface temperature of clothing by iteration**, first guess for surface temperature of clothing is:

Then do the following calculations:

Heat transfer coefficient by natural convection is:

Choose a stop criteria in iteration and if ABS(XN-XF) is more than that, repeat all the calculations from the following equations:

If ABS(XN-XF) is less than the stop criteria in iteration then:

In the next step, **heat loss components** will be calculated. Heat loss diffusion through skin is:

Heat loss by sweating is:

Latent respiration heat loss is:

Dry respiration heat loss is:

Heat loss by radiation is:

Heat loss by convection is:

In the next step, we will do the final calculations related to **PMV and PDD**. Thermal sensation transfer coefficient is:

**The predicted mean vote** is:

**The predicted percentage of dissatisfied **is:

## Calculation of PMV and PPD in ANSYS Fluent

One of the most accurate methods for calculating ambient air parameters and evaluating HVAC performance is using CFD simulations by ANSYS Fluent. Using simulation results, PMV and PPD can be calculated in different environments in different HVAC functions. 3 methods are possible to calculate PMV and PPD in Fluent.

### User-Defined Functions (UDF)

In this method, problem parameters such as air temperature are obtained by simulation, and the user calculates PMV and PPD by writing functions in the form of UDF using these parameters and the equations in this article. It should be noted that writing UDF is a complex task and requires expertise. UDF functions are written in the C programming language and provide full access to Fluent’s internal data structures.

The window in ANSYS Fluent software for writing UDF.

### Custom Field Function

In this method, unlike UDF, the definition of functions is much simpler, but it is limited to the use of simple functions and more suitable for post-processing. This method is also used to calculate PMV and PPD in a simpler way than the equations of this article.

Custom field function window in ANSYS Fluent

### Expression

Expressions allow defining simple mathematical relationships between existing variables. This method is the easiest way to define calculations and does not require programming knowledge.

Expression window in ANSYS Fluent

## Conclusion

We have seen that with the help of PMV and PPD, the conditions that the HVAC system needs to provide can be calculated. As seen in the PMV calculations, many parameters are effective in the pleasantness of the thermal conditions of the environment.

HVAC System In Sociocultural Building CFD Simulation

After you have calculated the desired PMV and PPD for the environment and obtained each parameter, then you need to see if your HVAC is capable of providing those conditions and how it provides those conditions. A convenient method for HVAC evaluation is to use **CFD simulations with ANSYS Fluent**.

With these simulations, air temperature, air flow, and humidity levels in the entire environment can be predicted, defects are found, and then actions can be taken to fix them. Such projects have been carried out so far by CFDLAND experts, Like the project in the picture above or the projects in CFD Project. You can order HVAC CFD simulation projects with ANSYS Fluent to CFDLAND. Be sure of the quality and speed of our work.