h-x diagram (psychrometric chart) Determination of physical and thermodynamic properties of gas-vapour mixtures Department for Building Service and Process Engineering Balázs Bokor, PhD student Building D, Room 124 a Tel: 463-2535; e-mail: bokor@epgep.bme.hu
INTRODUCTION BUDAPEST TIHANY PÉCS Source: www.index.hu ESZTERGOM Source: balaton.network.hu Source: www.panoramio.com 2 Source: www.panoramio.com
Source: www.egykisfoldrajz.freeiz.com 3
INTRODUCTION Source: www.myallergo.de Source: www.teachingengineering.org Source: www.bontott-tetoablak.hu 4 Source: www.szelloztetes.hu
DEFINITIONS Atmospheric air consists of: Gaseous components Water vapour Contaminants (e.g. smoke, pollen and gaseous pollutants) Source: www.britannica.com 5
DEFINITIONS Dry air Oxygen 21% other gases 1% All water vapour and contaminants removed Its composition is relatively constant Moist air A two-component-mixture of dry air and water vapour Nitrogen 78% The components of dry air The amount of water vapour in moist air can vary from 0 (dry air) to a maximum value (saturation) Saturation depends on temperature and pressure 6
HUMIDITY PARAMETERS Absolute humidity (x) The absolute humidity of a given moist air sample is the ratio of the mass of water vapour to the mass of dry air in the sample wv: water vapour da: dry air x = m wv m da Assuming ideal gas behaviour kg wv kg da 7
HUMIDITY PARAMETERS Specific enthalpy The specific enthalpy of a humid air sample (h 1+x ) containing 1 kg dry air and x kg water vapour at a temperature of t equals the enthalpy of the dry air and the enthalpy of x kg water vapour. The specific enthalpy of dry air: h da = c p,da t c p,da : specific heat capacity of dry air kj kg K The specific enthalpy of x kg water vapour: h wv = x r o + c p,wv t r o : enthalpy of the water s vaporisation kj kg c p,wv : specific heat capacity of water vapour kj kg K h 1+x = c p,da t + x(r 0 + c p,wv t) sensible heat + latent heat 8
HUMIDITY PARAMETERS With exact values t = 0 C h 1+x = 0 kj kg The specific heat capacity of dry air: c p,da = 1 kj kg K The specific heat capacity of water vapour: c p,wv = 1.86 kj The enthalpy of the water s vaporisation: r 0 = 2501 kj kg kg K h 1+x = t + x(2501 + 1. 86 t) 9
STRUCTURE OF THE h-x DIAGRAM h 1+x = t + x(2501 + 1. 86 t) Lines of constant temperature in h 1 x x diagram Rise of lines: h 1+x x t=const. = 2501 + 1.86 t Lines of constant temperature diverge with rising temperature Source: Bihari: Termodinamika 10
Source: en.wikipedia.org STRUCTURE OF THE h-x DIAGRAM h 1+x = t + x(2501 + 1. 86 t) r 0 c p,wv divergence of lines is minimal Rise of line t = 0 C: 2501 Rise of line t = 100 C: 2687 Problem with readibility Richard Mollier (1863-1935) German professor of Applied Physics Transformation of coordinates Rotation of axis x by α axis x α h=const. lines axis x α 11
STRUCTURE OF THE h-x DIAGRAM Transformation of coordinates Rotation of axis x by α axis x α h=const. lines axis x α Still no information about condensation Source: Bihari: Termodinamika 12
To see the connection between pressure, humidity and partial vapour pressure, let s see the fraction of the ideal gas laws of both components: V k p da V k p wv = R m da T M da R m wv T M wv p wv p da = m wv m da M da M vw = x 29 18 = 1.61 x Knowing that: p 1+x = p da + p wv we can express p wv as follows: p wv = p 1+x x 0.622 + x x ; p wv What s the maximum value of x at a certain temperature? 13
At a certain temperature p wv, max = p s x s x s = 0.622 p s p 1+x p s From this point humidity mixed into the compound can be only in liquid state of matter. Liquid water droplets suspended in the air are commonly known as fog. The specific enthalpy of foggy air is: h 1+x = c p,da t + x s r 0 + c p,wv t + x x s c p,w t Substituting c p,w = 4.17 DRY AIR WATER VAPOUR FOG kj kg K temperature lines when x > x s : we determine the rise of constant h 1+x x t=const = 4.17 t 14
h-x DIAGRAM OF HUMID AIR Source: Bihari: Termodinamika With rising x until saturation curve constant temperature lines are slightly steeper than horizontal; reaching the saturation curve, the rise falls Curve connecting breaking points is called saturation curve (φ=1 or 100%) Position of the saturation curve depends on the p total If p total x s saturation curve 15
h-x DIAGRAM OF HUMID AIR Source: Bihari: Termodinamika Relative humidity (φ) is the ratio of the partial pressure of water vapour (p wv ) in a given moist air sample to the partial pressure of water vapour in an air sample saturated at the same temperature and pressure (p s (T)) φ = p wv p s (T) % or 16
Source: www.amazon.com RELATIVE HUMIDITY (ϕ) IN DAILY LIFE Everyday devices Breath becomes visible Weather forecast Source: www.memo.hu Source: www.saratoga.com 17
RELATIVE HUMIDITY (ϕ) IN DAILY LIFE Source: www.ezilon.com Source: www.kempinski.com Finnish sauna: t in = 90-95 C; φ = 10% 18
Source: www.fabian-plasztika.hu Source: www.erdekedvilag.hu THE IMPORTANCE OF RELATIVE HUMIDITY (ϕ) Medicine Operation theatres Relative humidity (φ) must be kept on an exact value If too low, wounds would dry out If too high, patient and personnel would sweat Rehabilitation treatment Lake cave in Tapolca Used for curing respiratory diseases t = 20 C; φ = ~100% High Ca content 19
THE IMPORTANCE OF RELATIVE HUMIDITY (ϕ) Pipe organs 20 Source: mupa.hu, seenandheard-international.com, organforum.com
THE IMPORTANCE OF RELATIVE HUMIDITY (ϕ) Pipe organs 21 Source: en.wikipedia.org
THE IMPORTANCE OF RELATIVE HUMIDITY (ϕ) Pipe organs Empty hall Full hall Increased human heat and moisture load 22 Source: www.bpg.hu, budapest.varosom.hu
THE IMPORTANCE OF RELATIVE HUMIDITY (ϕ) Pipe organs 23 Source: www.mupa.hu
Source: enfo.agt.bme.hu Source: www.provitamin.hu THE IMPORTANCE OF RELATIVE HUMIDITY (ϕ) Drying technologies Extremely complex air conditioning needed Relative humidity (φ) defines the intensity drying process If drying too intensive, product gets crusty If drying too weak, product gets mouldy 24
Source: www.boeing.com Source: en.wikipedia.org Source: Bihari: Termodinamika THE IMPORTANCE OF RELATIVE HUMIDITY (ϕ) Flight altitude: up to 12,000 m t outside = -50 C Thin outside air gets pressurised (gets very hot) and cooled Mixing with cabin air (50-50%) 25
ADIABATIC HUMIDIFICATION What happens when humid air contacts a large surface of water adiabatically? Source: Bihari: Termodinamika x air ; t air ; φ air t water because of evaporation If τ= t water = t air = t wb wet bulb temperature h 1 = h 2 t 1 > t 2 and φ 1 < φ 2 Q air water = Q evaporation Outgoing air is saturated (φ=100%) 26
Source: Bihari:Termodinamika Source: www.weldingcode.com ADIABATIC HUMIDIFICATION Dry bulb temperature is the temperature of the air-water vapour mixture measured in the normal way with a thermometer. t db [ C] Wet bulb temperature is the temperature shown by a thermometer with a wetted bulb exposed to a current of air to cause evaporation of its moisture. t wb [ C] 27
Source: www.bgrg.hu Source: webaruhaz.abako.hu HUMIDITY MEASUREMENT DEVICES The elastic modulus of certain organic (hair or sheep gut) materials can depend on their humidity content. Stressed with constant force their length can change depending on the humidity of the surrounding air. 28
MIXING PROCESSES IN h-x DIAGRAM Mixing two different qualities of humid air Accounting equations m 1 h 1 + m 2 h 2 = m m h m m 1 x 1 + m 2 x 2 = m m x m m 1 + m 2 = m m h m = m 1 h 1 + m 2 h 2 m 1 + m 2 x m = m 1 x 1 + m 2 x 2 m 1 + m 2 29
MIXING PROCESSES IN h-x DIAGRAM Mixing two different qualities of humid air Source: Bihari: Termodinamika Mixing two different qualities of humid air the condition of the mixture is to be found on the line connecting the two initial conditions. The position is to be defined by the law of the lever. 30
Source: www.clh.hu Source: Bihari: Termodinamika MIXING PROCESSES IN h-x DIAGRAM Mixing humid air with water If water is added to air without any heat supply, the air condition changes adiabatically along a constant enthalpy line. φ 2 =95% (complete saturation cannot be reached) 31
MIXING PROCESSES IN h-x DIAGRAM Mixing humid air with water Accounting equations m air h 1 + m w h w = m air h 2 m air x 1 + m w = m air x 2 h 2 = m air h 1 + m w h w m air x 2 = m air x 1 + m air m w Source: Bihari: Termodinamika 32
Source: Bihari: Termodinamika MIXING PROCESSES IN h-x DIAGRAM Mixing humid air with water Adiabatic humidification (along h=constant line) t air ; t water ; x air ; φ air Water hygiene extremely important 33
Source: www.randrwaterhygieneservices.co.uk MIXING PROCESSES IN h-x DIAGRAM Mixing humid air with water: WATER HYGENE EXTREMELY IMPORTANT Legionella bacteria present in water Legionellosis Legionellosis is transmitted by the inhalation of aerosolised water contaminated with the bacteria. Prevention: THERMAL DESINFECTATION 34
MIXING PROCESSES IN h-x DIAGRAM Mixing humid air with steam h x = h steam = r 0 + c p,steam t Source: Bihari: Termodinamika Accounting equations m air h 1 + m s h s = m air h 2 m air x 1 + m s = m air x 2 h 2 = m air h 1 + m s h s m air x 2 = m air x 1 + m air m s 35
Source: Bihari: Termodinamika COOLING AND HUMIDITY LOAD IN CLOSED SPACES Cooling load People Lighting Machinery Hot surfaces Surfaces of water Instationer cooling load (summer) Heat loss (winter) Humidity load People Surfaces of water Gradient scale h x = Q m w 36
Source: Bihari: Termodinamika HEATING PROCESSES IN h-x DIAGRAM When heating moist air Specific moisture (x) remains constant Relative humidity (φ) decreases Design parameter of outdoor air in Hungary (winter) t out = 15 C φ out = 90% 37
COOLING AND DEHUMIDIFYING Design parameter of outdoor air in Hungary (summer) t out = 30 C φ out = 45% Fall of temperature: x=const. Source: Bihari: Termodinamika Dew-point (t dew ) is the temperature at which an air-water vapour mixture will become saturated and begin to yield drops of condensed water. Cooling humid air from t 1 to t 2 results in Δx amount of condensate. 38
AVOIDING CONDENSATION Source: www.epitesimegoldasok.hu Source: www.construdeia.com Insulating heating pipelines Foil-laminated mineral rock wool insulation Air among fasers Economical solution Insulating cooling pipelines A built in vapour barrier prevents condensation For cold water services, chilled water lines, air conditioning ductwork and refrigerated pipework 39
Source: www.desiccantpacks.net Source: www.armygasmasks.com Source: en.wikipedia.org/wiki/silica_gel DRYING AGENT SILICA GEL Granular, porous form of silicon dioxide made synthetically from sodium silicate. High surface area: ~800 m 2 /g It has a strong affinity for water molecules (desiccant or drying agent). In WW1 used for the adsorption of vapours and gases in gas mask canisters. In WW2 used for keeping penicillin dry and protecting military equipment from moisture damage. Humidity indicator: changes colour. Source: en.wikipedia.org/wiki/silica_gel 40
Source: www.epitinfo.hu AIR HANDLING UNITS (AHU) Air heating Mixing two different qualities of humid air Adiabatic humidifying Air cooling 41
Source: www.gopixpic.com Source: www.fao.org FROM h-x DIAGRAM TO PSYCHROMETRIC CHART 42
THANK YOU FOR YOUR ATTENTION Department for Building Service and Process Engineering Balázs Bokor, PhD student Building D, Room 124 a Tel: 463-2535; e-mail: bokor@epgep.bme.hu 43