HP 8 HEAT PROCESSES Heat transfer phase changes

HP 8 HEAT PROCESSES Heat transfer phase changes, evaporators Heat transfer at phase changes (boiling and condensation). Evaporation and evaporators. Powerpoint presentation of evaporators (falling, climbing film, multiple effects, vapour recompression). Mass and enthalpy balances. Boiling point temperature and its elevation. Design of thermal vapour recompression (Laval nozzle and Ts Rudolf Žitný, Ústav procesní a diagram). techniky Vacuum zpracovatelské ČVUT FS cooling. 2010

HP 8 HEAT transfer condensation Dropwise condensation Film condensation Duchamp

HEAT transfer film condensation HP 8 Film condensation (Nusselt) The following analysis holds only for laminar films (Re<1800). It is usually sufficient, because majority of practical cases are laminar. Transversal parabolic velocity profile and balance of forces gravity Viscous force at wall Transversal linear temperature profile, heat and mass fluxes dx x Tw Mass flow rate of condensed steam Ts=Tw+ T Thickness of film determines the heat transfer coefficient Gravity acting in the flow direction increases

HP 8 HEAT transfer film condensation Enthalpy balancing of a condenser requires mean value of heat transfer The coefficient c is theoretically c=2/3 2=0. 94 but experiments indicate that the actual value should be about 20% higher, therefore c=1. 13 The increased film thickness decreases heat transfer c=0. 725 Inclined wall Horizontal pipe N-rows of horizontal pipes See also M. N. Ozisik: Heat transfer, a basic approach, Mc. Graw Hill, 1985

HP 8 HEAT transfer dropwise condensation Dropwise condensation (Schmidt) yields much higher heat transfer coefficients than the film condensation, however special smooth or hydrophobic coatings (large contact angle and very low surface energy of wall) of heat transfer surfaces must be provided. = liquid- solid Gold plated surface Schmidt, E. , Schurig, W. and Sellschop, W. , Versuche uber die kondensation von wasserdampf und film und tropfenform. Tech. Mech. Thermodynamiks, Berlin, 1930, 1, 53 -63. Kakac S. : Boilers, evaporators, and condensers, Wiley 1991 D. W. Tanner, C. J. Potter, D. Pope, D. West: Heat transfer in dropwise condensation—Part I The effects of heat flux, steam velocity and non-condensable gas concentration International Journal of Heat and Mass Transfer, Volume 8, Issue 3, March 1965, Pages 419 -420, IN 5, 421 -426 M. ABU-ORABI: Modeling of heat transfer in dropwise condensation. Int. J. Heat Mass Transfer. Vol. 41, No. 1, pp. 81 -87, 1998

HP 8 HEAT transfer dropwise condensation H. M. Steinhagen: Smart surfaces for improved heat exchangers. Institute for Thermodynamics and thermal engineering, University of Stuttgart (presentation)

HP 8 HEAT transfer boiling Pool boiling Flow boiling Tanguy

HP 8 HEAT transfer pool boiling Nukyama curve (q- TSAT) see A. Bejan, A. Kraus: Heat transfer handbook. Willey 2003 Boiling crisis of the first kind

HP 8 HEAT transfer pool boiling Nucleate (pool) boiling Rohsenow (1952) All parameters are related to liquid L u. L - velocity of liquid surface Rohsenow W. M. , Trans. ASME, Vol. 74, pp. 969 -975 (1952) Exponent m is 0, 7 for all liquids with the exception of water (m=0). The coefficient CLS depends upon the combination surface-liquid (tables see Özisik (1985)) and for the most common combination steel-water CLS=0, 013. Db is the Laplace constant characterizing diameter of bubble Interpretation of Db follows from the equilibrium of surface stress and buoyancy forces

HP 8 HEAT transfer boiling onset The nucleate boiling (bubble boiling) regime is optimal for boilers or evaporators. How to specify its onset (or the level of superheating necessary for bubble formation on the heat transfer surface)? Balance of forces: overpressure – surface tension pb corresponds to saturated steam temperature at Tw=TSAT+ TSAT -surface tension Db diam. of a microcavity on heat transfer surface p corresponds to saturated steam temperature TSAT Pressure difference pb –p can be calculated from the temperature difference using Clausius Clapeyron equation Substituting into the balance of forces gives the final result

HP 8 HEAT transfer boiling crisis Bubble flow regime ends at such a high intensity of evaporation that a more or less continuous layer of vapor is formed and creates a thermal barrier between the heat transfer surface and liquid. Critical heat flux Theoretical solution Zuber (1958) predicts coefficient c=0, 131 , experimental data suggest little bit greater value c=0, 18 , Rohsenow (1973). The relation for critical heat flux shows that the boiling crisis can be delayed by increasing pressure (and therefore density G) or by acceleration pressing liquid layer towards the heat transfer surface (this is utilised in centrifugal evaporators). Theoretical prediction of boiling crisis is based upon stability analysis of a liquid layer (thickness H 2) sitting above the light layer of vapor (H 1). A small disturbance of initially planar interface increases area of interface (and therefore potential energy of surface tension W ) but at the same time decreases gravitational potential energy Wg. At the stability limit (neutral stability) the differential of the total potential energy is zero, This condition determines wavelength of disturbance causing disruption of continuous layer, and location of steam jets breaking through the liquid layer (it can be shown that the distance of these parallel jets is a multiple of the Laplace constant Db). Following stability analysis of these steam jets, based upon variation of potential energy of surface tension and kinetic energy, yields the previous expression for the critical heat flux.

HP 8 HEAT transfer flow boiling Flow boiling in vertical pipes is characterized by gradual changes of flow regime and the vapor quality x increase along the pipe Annular flow (rising film) Slug flow Enthalpy of liquid at saturation temperature Vapor quality x<0 means subcooled liquid, vapor quality x=0 liquid at the beginning of evaporation, x=1 state when all liquid is evaporated and x>1 superheated steam. Vapor quality is related to the Martinelli’s parameter (ratio of pressure drops corresponding to liquid and vapor) Nucleate boiling (bubbles), e. g. Rohsenow correlation Heat transfer by forced convection (e. g. Dittus Boelter) Vapor quality and Martinelli’s parameter are used in most correlations for convective boiling heat transfer.

HP 8 HEAT transfer flow boiling The previous slide introduced two basic characteristics of two phase liquid- vapor flows: vapor quality x and the Martinelli’s parameter X. Their relationship follows from the following reasoning: Gradient of pressure dp/dz for one phase flow is proportional to (see d. Arcy Weisbach equation) Exponent m=0. 25 for low Re (Blasius), m=0. 2 for high Reynolds numbers therefore and you can see that the corresponding exponent of Reynolds number in the correlation for pressure drop is m=0. 2. It is obvious that the Martinelli’s parameter is a decreasing function of vapor quality (its value is infinity for liquid).

HP 8 HEAT transfer flow boiling Chen (1966) calculates the flow boiling heat transfer coefficient as the weighted sum of nucleate boiling b and the convective heat transfer in liquid film c Forster Zuber correlation for nucleate boiling (Chen’s concept was later modified by different correlations for nucleate regime, for example by Rohsenow correlation for pool boiling) Dittus Boelter correlation for convective heat transfer Chen J. C. : A correlation for boiling heat transfer to saturated fluids in convective flows. Industrial and Engineering Chemistry, Process design and development, Vol. 5, no. 3, (1966), pp. 322 -329

HP 8 HEAT transfer flow boiling Chen’s method is probably the most frequently used, but it seems that his correlation overpredicts the effect of nucleation and many modifications were therefore suggested. These modifications replace the Forster Zuber pool boiling correlation by Rohsenow’s correlation and the suppression factor S and the convective enhancement factor F were correlated with other system variables Kandlikar S. G. : A general correlation for saturated two phase flow boiling heat transfer inside horizontal and vertical tubes. Journal of Heat Transfer, Vol. 112, pp. 219 -228 (1990) Bennett D. L. , Chen J. C. : Forced convective boiling in vertical tubes for saturated pure components and binary mixtures. AICh. E J. , Vol. 26, pp. 454 -461 (1980) Shah (1976) introduced correlations based upon boiling number Bo, convection number Co (that replaces the Martinelli’s parameter) and Froude number Fr G is the mass flux, kg/m 2 s Viscosity ratio (see Martinelli’s parameter) seems to be unimportant Shah M. M. : A new correlation for heat transfer during boiling through pipes. ASHRAE Transactions, Vol. 82, Part. II, pp. 66 -86 (1976)

HP 8 HEAT transfer flow boiling Heat transfer correlations for the film condensation (Nusselt) and the flow boiling (Chen) are used in the following Excel program designed for modeling of a climbed film evaporator (Kestner). Procedure: Tube is divided to short sections z. At each section (starting from bottom, feed input) are calculated: heat transfer coefficient at outer surface, heat flux, wall temperature, enthalpy change h, steam quality x, Martinelli’s parameter, and heat transfer coefficient using Chen’s method. Temperature dependence of all thermophysical properties is considered.

HP 8 Evaporators Hopper

HP 8 Evaporators Vapours (brüden) Saturated steam Evaporation of water (pool or flow boiling) Condenstation of saturated steam feed concentrate condensate Minton P. E. : Handbook of evaporation technology. Noyes Publ. , New Jersey, 1986

HP 8 Evaporators Nomenclature What to do with vapor: 1. It can be condensed in a direct (spray), shell and tube or plate condensers 2. It can be used for heating the following evaporator unit (multiple effects evaporators) 3. It can be recompressed (by mechanical or thermo-compressor) and used for heating Overall mass flow rate Mass balances mass flow rate of dissolved solid Enthalpy balance =cc(Tc-T 0) dissolution heat

HP 8 Evaporators External heater Natural circulation in short pipes vacuum POOL boiling prevails Long residence times condensate Climbed film condensate Falling film Wiegand Short residence times Only for low viscosities Kestner Suppressed boiling Vogelbusch (flash evaporation) High velocity in HElow fouling steam basket steam Robert’s condensate Circulation pump Wiped film Centrifugal forces promote dropwise condensation and increase critical heat flux Müller Viscous liquids Centritherm condensate Very small T Forced circulation

HP 8 Evaporators Multistage evaporators Number of effects 1 2 3 4 5 (latent heat of vapor is used for the next effect heating) kg steam/kg of evaporated water 1, 1 0, 6 0, 4 0, 3 0, 25 T 1 T 2 Counter current Low viscosity feed flows to the second stage at lower temperature (advantageous from point of view of heat transfer). T 1>T 2 therefore p 1>p 2 and it is necessary to use a pump T 1 T 2 Co current High viscosity concentrate flows to the second stage at lower temperature (suitable for heat sensitive products).

HP 8 Evaporators Number of effects is limited by range of temperatures (feed – condensate) T 1 > T 2 > T 3 T 2 T 1 -T 2 = THE + Tpch + T p Temperature difference on heat transfer surface (rising film >100 C, falling film >40 C) Temperature drop corresponding to pressure drop (frictional losses). Usually small ~ 10 C Physico chemical elevation of boiling point temperature (solution boils at elevated temperature). Can be large, depends on concentration Tpch Sugar 0. 5~3 Na. Cl 10 Na. OH 16

HP 8 Evaporators Optimisation of a two effects evaporator WI WII What is given (it is assumed that the temperature T II is determined by condenser and is the same as the temperature of boiling solution in the second effect and the temperature of product): Tf mf f – temperature, mass flowrate, mass fraction of feed D, TS TI Tf, mf, f k. ISI TII c – temperature and mass fraction of product TS – temperature of steam TII k. IISII What is to be calculated (9 variables): D, WII – mass flowrates of steam and vapours m 1, mc – mass flowrates of solution from the 1 st and 2 nd effect mc, c m 1, 1 Mass balances 1 - mass fraction of solution after 1 st stage TI –temperature of boiling solution in the 1 st effect k. ISI, k. IISII- heat transfer surfaces in both effects Enthalpy balances 1 st stage 2 nd stage There exist only 8 equations for 9 parameters – one of them can be selected (for example boiling temperature in the first stage TI). This degree of freedom can be used for optimisation (for minimisation of the heat transfer surface or consumption of steam).

HP 8 Evaporators Design of a two effect co-current evaporator can be implemented in Excel program Specify temperature of steam and feed Select temperature in the first effect TI Select substance and boiling point elevation CALC starts calculation Heat transfer surface will be result

Evaporators MVR HP 8 MVR Mechanical Vapor Recompression Root’s blower A C D Condensate injection It would not be a good idea to use superheated steam for heating, because will be too small. Saturated steam and condensation is achieved by water injection BTU=1. 054 k. J psi=6. 9 k. Pa F=1. 8 C+32

HP 8 Evaporators TVR Thermal Vapor Recompression 2 1 5 Thermocompressor Entrainment ratio fe (mass flowrate of entrained vaports to the mass florate of motive steam) follows from the momentum balance Power R. : Steam jet ejectors for the process industries. Mac Graw Hill, New York, 1994 The most important equation is the momentum balance (mixing chamber)

HP 8 Evaporators TVR Design diagram for TVR Motive steam presure Discharge pressure Suction pressure Power R. : Steam jet ejectors for the process industries. Mac Graw Hill, New York, 1994

HP 8 Evaporators TVR Thermal Vapor Recompression 2 1 5 Thermocompressor Previous analysis determined only the entrainment ratio. To complete the TVR design it is necessary to calculate the mass flowrate of motive steam through the Laval nozzle (given inlet pressure). Laval nozzle is characterised by converging and diverging section and the mass flowrate depends only upon the cross section of throat (the smallest cross section S*) where the speed of sound is achieved. To determine the flow rate m 1 as a function of S* and the inlet pressure p 1 it is necessary to solve the complete velocity and pressure profiles along the Laval nozzle.

HP 8 Evaporators TVR Thermocompressor and Laval nozzle Unknown profiles along the Laval nozzle: p(x), v(x)-or density, T(x), u(x)-velocity, and h(x), together 5 unknowns Available equations: pv=RT - state equation pv =p 1 v 1 - isoentropic flow (without friction) dh=-du 2/2 - Bernoulli equation dh=cpd. T By selecting any of the parameters, for example the pressure p, it is possible to calculate all other variables, for example the velocity u Mixing chamber Motive steam Ideal gas! Laval nozzle Diffuser v and dv is to be eliminated (expressed in terms of p) Suction Speed of sound By integration we obtain St. Venant Wanzel equation

HP 8 Evaporators TVR Mass flowrate is independent of axial coordinate Introducing dimension pressure P*=p(z)/p 1 the throat geometrical constraint (minimum cross section S) is S* Solution of this (algebraic) equation is and corresponding mass flowrate z

HP 8 H 2 O molecule riding inside a Laval nozzle S* z

HP 8 H 2 O molecule riding inside a Laval nozzle Slow, nice, eliptic ride, clear view Approaching speed of sound, view is misty Collision with different pressure at outlet of Laval nozzle (wrong design, of course not by our students) Speed of sound and still accelerating, Molecule is blind, nothing is seen (only the rear mirror view is clear) S* z

HP 8 Evaporators St Venant Wanzel equation is quite useful and not only for the Laval’s nozzle design. It is applied for example for estimation of an evaporator or a condenser leakage p 1 p Evaporator chamber operating at underpressure Mass flowrate through a gap with cross section S at subsonic flow Leakage at sonic flow (choking). Mass flowrate is independent of vacuum level p.

HP 8 Vacuum cooling LIQUIDS Evaporation is also used for rapid cooling of food materials. Material containing water (liquid solutions, but also porous solids like flowers, vegetables, meat) can be cooled down by evaporation of water at a decreased pressure. Assuming uniform temperature Tf(t) of the cooled material the enthalpy balance can be written as Foam separator Condenser cooker Mass flow rate of evaporated water M. Dostal, K. Petera: Vacuum cooling of liquids: mathematical model. Journal of Food Engineering 61 (2004) 533– 539 Heating jacket Condensate pump Vacuum pump There still exist controversial opinions concerning interpretation of thermal and mass transfer resistances at surface conduction Convection (n is mass flux) Area of liquid surface

HP 8 Vacuum cooling WATER Technical realization is similar to vacuum evaporators, only without heating of evaporated liquid. Jet pumps (steam ejectors) are usually used. Example: GEA Wiegand Gmb. H, 2 -stage steam jet cooling plant of compact design, cooling 44 m 3/hr of water from 30 to 10 °C.

HP 8 Spray cooling WATER Cooling ponds JETE

HP 8 Vacuum cooling MEAT Relatively new vacuum cooling technology is applied also to porous solids, for example meat. The visualised cross-section of the cooked meat L. Wang, D. -W. Sun / International Journal of Refrigeration 25 (2002) 862– 871 Mathematical modelling is usually based upon FK equation for heat transfer Heat flux Mass transport of vapour is expressed in terms of pressure P Mass flux Evaporation rate D. -W. Sun, L. Wang / Journal of Food Engineering 77 (2006) 379– 385 There exists doubt about this approach. It was objected that this model doesn’t recognize moving front between the boiling and diffusive regions. T. X. Jin, L. Xu / Energy Conversion and Management 47 (2006) 1830– 1842

HP 8 Evaporators papers Bosch

HP 8 Evaporators papers K. R. Morison, Q. A. G. Worth, N. P. O’dea Minimum Wetting and Distribution Rates in Falling Film Evaporators Food and Bioproducts Processing, Volume 84, Issue 4, December 2006, Pages 302 -310 Falling film evaporators are used extensively in the food industry for their ability to process heat sensitive liquids. A coherent liquid film is required to maintain heat transfer efficiency and minimize fouling. It is likely that most evaporator fouling occurs after film breakdown as the substance within the evaporator dries out. The minimum flow rate required to maintain a film is known as the minimum wetting rate which is defined as the minimum mass flow rate per unit circumference. In this work, minimum wetting rates were determined in a 1 m long, 48 mm internal diameter, vertical, stainless steel tube. Water and aqueous solutions of glycerol, alcohol and calcium chloride were used. These substances were chosen so as to give a wide range of properties such as viscosity (0. 5– 39 m. Pa s), density (950– 1410 kg m-3), surface tension (35– 90 m. N m-1) and contact angle (64– 980). In a separate set of experiments, the minimum flow rate required to distribute liquid and completely wet the top of industrial evaporator tubes was measured using a range of sucrose solutions. The tube wetting results obtained fitted a dimensionless power law relationship well. Surface tension and contact angle had a strong influence on the wetting rate but viscosity and density were found to have very little effect. The minimum flow rates for distribution were found to nearly always exceed the minimum wetting rates showing that more attention needs to be given to distributor design. Almost the same result can be derived from the Weber number limit Nii S. et al: Membrane evaporators. Journal of membrane science, 201 (2002), 149 -159

HP 8 Evaporators papers Susumu Nii, R. Selwyn Jebson, E. L. Cussler Membrane evaporators Journal of Membrane Science, Volume 201, Issues 1 -2, 31 May 2002, Pages 149 -159 We have built and tested a flat-sheet membrane evaporator for removing water from dilute feed streams likemilk and orange juice. The energy for the water’s evaporation comes from steam channels next to the feed channels, so that the operation differs sharply from other forms of “membrane distillation”. The membrane evaporator retains flavors effectively. Because it has an overall vapor phase mass transfer coefficient of about 1 cm/s, it is only 68% efficient: only about 0. 68 kg water is evaporated per kg steam condensed. This efficiency should be over 95% for a membrane which is 10 times more permeable.

HP 8 Evaporators papers S. Sharma, G. P. Rangaiah, K. S. Cheah Multi-objective optimization using MS Excel with an application to design of a falling-film evaporator system Food and Bioproducts Processing, Available online 9 February 2011 An Excel-based MOO (EMOO) program is developed based on the elitist non-dominated sorting genetic algorithm (NSGA-II) and tested on benchmark problems. It is then applied for MOO of design of a falling-film evaporator system, consisting of a pre-heater, evaporator, vapor condenser and steam jet ejector, for milk concentration. The EMOO program gave well-distributed Pareto-optimal solutions for the MOO problems tested. Design equations and results for two bi-objective optimization problems are presented and discussed.

HP 8 Evaporators papers Tarif Ali Adib, Bertrand Heyd, Jean Vasseur: Experimental results and modeling of boiling heat transfer coefficients in falling film evaporator usable for evaporator design Chemical Engineering and Processing: Process Intensification, Volume 48, Issue 4, April 2009, Pages 961 -968 The aim of this paper is to describe the variation laws of the boiling heat transfer coefficient (h) versus the main process parameters, using a pilot scale falling film evaporator as found in many food industries. Sugar solutions at different concentrations are used as a model of Newtonian liquid food. The studied parameters affecting boiling heat transfer coefficient (h) in the falling film evaporator are: the dry matter concentration XDM (or Brix for sugar solution), the evaporating temperature (L) or pressure (P) taking into account the boiling point elevation (BPE), the heat flux or the temperature difference between the heated surface and boiling liquid temperature () and the specific mass flow rate per unit of perimeter length ( ). The nature of heated surface is kept constant (stainless steel) and the effect of the emitted vapor velocity is not taken into account in our study. The variations of h with or , are given for pure water and sugar solutions at different concentrations (10%, 30%, 50% and 70%), and interpreted in relation with the two boiling regimes (non-nucleate and nucleate). The transition between non-nucleate regime and nucleate regime has also been visually observed. The critical specific mass flow ( cri) for water and sugar solution at dry matter concentration 50% has been studied. Variation of h as a function of temperature difference at P = 1010 mbar and = 0. 56 kg s− 1 m− 1 for pure water and sugar solution X = 10%, 30%, 50% and 70% DM.

HP 8 Evaporators papers Xianchang Li, Ting Wang, Benjamin Day: Numerical analysis of the performance of a thermal ejector in a steam evaporator Applied Thermal Engineering, Volume 30, Issues 17 -18, December 2010, Pages 2708 -2717 Ejectors have been widely used in many applications such as water desalination, steam turbine, refrigeration systems, and chemical plants. The advantage of an ejector system lies in its extremely reliable operation due to the complete absence of moving parts. However, the performance depends on a number of factors, among which the flow channel configuration/arrangement is critical. To improve the performance of an existing thermal compressor in a steam evaporator, a comprehensive study was conducted in this paper with a main focus on the sensitivity of performance to the geometric arrangement. Numerical simulation was employed to investigate thermal-flow behavior. The performance is measured by the entrainment ratio, i. e. , the secondary (suction) flow rate from a vapor plenum over the primary steam jet flow. It is observed that any downstream resistance will seriously impede the suction flow rate. In addition, the entrainment ratio is sensitive to the location of the jet exit, and there is an optimum location where the primary flow should be issued. A well-contoured diffuser can increase the entrainment ratio significantly. However, the size of suction opening to the plenum is less important, and a contoured annular passage to guide the entrained flow shows little effect on the overall performance. Based on the numerical results the steam entrainment rate of the best case in the confinement of the current study is approximately 430% of the jet flow rate, while some cases with mediocre design can only produce an entrainment of 24% of the primary jet flow. Fluent

HP 8

HP 8 EXAM Phase changes Evaporators Thermocompressors

What is important (at least for exam) HP 8 Nusselt correlation for film condensation dx x T w Mass flow rate of condensed steam Ts=Tw+ T Rohsenow correlation for pool boiling Laplace constant Db is used as a characteristic dimension in Nu and Re

HP 8 What is important (at least for exam) Vapours (brüden) Saturated steam Evaporation of water (pool or flow boiling). Use Rohsenow or Chen correlations Condensation of saturated steam (Nusselt correlation) feed concentrate Overall mass balance condensate Mass balance of solid Enthalpy balance

What is important (at least for exam) HP 8 Recompression of vapours by thermo-compressor (that is driven by Laval nozzle) 2 1 5 Thermocompressor Laval nozzle Supersonic flow for pressure ratio Mixing chamber Motive steam Laval nozzle Diffuser Sucti on Mass flowrate is independent of outlet pressure at supersonic flow Speed of sound