Numerical analysis of heat transfer characteristics for deposit by rma97348


528 of Scientific & Industrial Research         J SCI IND RES VOL 66 JULY 2007
Vol. 66, July 2007, pp. 528-535

          Numerical analysis of heat transfer characteristics for deposit formation
                              shapes around single cylinder
                                                 Ahmet Fertelli and Ertan Buyruk*

                       University of Cumhuriyet, Department of Mechanical Engineering, 58140, Sivas / Turkey

                           Received 01 August 2006; revised 19 February 2007; accepted 22 February 2007

                 Fouling effect on heat transfer around a cylinder in cross-flow was investigated numerically by ANSYS software
      programme using finite element method. Calculations were made with variable local heat transfer coefficients, constant free-
      stream temperature and constant clean tube surface temperature. Heat transfer rates were presented for different cases with
      temperature field. Deposit thickness formed around the cylinder was fixed as follows: i) Non-uniform thickness of fouling
      shape was calculated with homogenous condition; ii) Non-uniform and non-homogenous fouling shape was considered; and
      iii) Effect of eccentricity was calculated for non-uniform and non-homogeneous cases. Numerical predictions were made as
      temperature contours through thickness of fouling and Qfoul / Qclean was plotted against the position of fouling.

      Keywords: ANSYS, Cross-flow, Deposit formation, Heat exchanger, Numerical analysis
      IPC Code: F28D1/00

Introduction                                                          that it is thicker at the rear stagnation point than at the
         Designing a heat exchanger involves factors such             forward and it may also built up different angle of the
as heat transfer rate, fouling, power consumption, etc. in            tube. In practice, deposit will not be perfectly circular
power generation industry. One of the major categories of             but this geometry enables the situation to be explored
heat exchanger fouling involves the suspended particulate             theoretically and the general trends observed will hold
matter that is encountered in many industrial fluid steams            regardless of the actual cross-sectional profile of the
and accumulation on the surface of particles from a fluid             deposit. The tube is assumed to be thin and to have a
stream on heat exchanger surface. A large number of                   constant inside surface temperature. The variations of
investigations, which assessed effect of fouling on heat              heat transfer rate and temperature contours are obtained
exchanger performance, include particle concentration,                for different shape of fouling and for varying thermal
size of particle, velocity1-3, thermal conductivity of ash4,          conductivity within the non-uniform fouling over the
different tube geometries of tube bank5, and theoretical              entire cylinder by using ANSYS software program that
approach of fouling6-10. Buyruk11 carried out a study to              uses finite element method (FEM).
measure the effects of fouling on heat transfer
characteristics of tubular heat exchanger.                            Finite Element Method (FEM)
         Present study focuses on non-uniform thickness                        FEM formulations for heat flow equations and
geometry, with special reference to fouling on a plain                matrices under steady state and/or transient heat transfer
tube in cross-flow. Since complete heat transfer involves             in a three dimensional solid Ω bounded by a surface Γ
conjugated convection and conduction, the geometry of                 have been derived as
fouling must also provide for a convective boundary
condition.                                                               ∂q  ∂q y ∂q z           ∂T
                                                                       − x +
                                                                         ∂x      +      + Q = ρC
                                                                                                                                    ...(1)
Materials and Methods                                                         ∂y   ∂z            ∂t
        It is shown that the deposit having built up on
the leading edge; it may also be build up in such a way                       If solution domain Ω is divided into M elements
*Author for correspondence                                            of r nodes each, finite element formulation for linear
E-mail:                                      steady state problem is identified12 as
                                      FERTELLI & BUYRUK: FOULING EFFECT ON HEAT TRANSFER AROUND A CYLINDER                             529

              [[K c ] + [K h ]]⋅ {T } = {RQ }+ {Rq }+ {Rh }           ...(2)                             df   
                                                                                                hf = h c 
                                                                                                          c   
                     [Kc] and [Kh] are element conductance matrices
             and relate to conduction and convection, respectively.
                                                                                        This relationship8 provides a systematic change
             {R }{R }, {R }
                Q        q        h   are heat load vectors arising from       in HTC on the external boundary as diameter increases
             internal heat generation, specified surface heating, and          due to fouling. HTC on the external surface is dependent
                                                                               on the diameter, df, irrespective of the disposition of the
             surface convection, respectively. {T } is the vector of
                                                                               foulant over the surface of clean tube.
             element nodal temperatures.
                                                                               Fouling Shapes
              [K c ] = ∫ [B] ⋅ [k ]⋅ [B ]⋅ dΩ
                                                                                        Buyruk11 carried out a study to measure the
                         Ω                                                     effects of fouling on heat transfer characteristics of
                                                                               tubular heat exchanger. In the present study, shape of
                                                                               first row fouling distribution was modelled for a single
             [K c ] = ∫ h ⋅ {N }⋅ [N ]⋅ dΓ                          ...(3)     cylinder. Therefore, eccentric annulus was chosen for
                                                                               requirement. External surface is circular and will be
                                                                               unchanged even when eccentricity and hence thickness
             where [B] is temperature gradient interpolation matrix            geometry is altered. Centre, bottom and upper tube of
             and [N] is temperature interpolation matrix. Heat load            first row were taken into consideration for possible
             vectors are:                                                      formation shape of deposit. Nature of fouling on the
                                                                               surface is not smooth and thickness of deposition does
                                                                               not have the same geometrical features. But as useful
              RQ = ∫ Q ⋅ {N }⋅ dΩ           Rq = ∫ q s ⋅ {N }⋅ dΓ              indication for engineering use, a theoretical model has
                     Ω                            S                            been considered using the finite element analysis.
hf d f           U ∞d f                                                               Tube diameters were as follows: clean tube,
         = 0.174        
  k                      
              Rq= νh ⋅ Te ⋅ {N }⋅ dΓ
                   ∫                                              ...(4)
                                                                               dc = 0.016 m (dclean); and fouled tube, df = 0.022 m (dfoul).
                    S        0.618
                                                                               Clean tube thickness was assumed to be thin. If
hc d c          U ∞ dc                                                       temperature drop across the wall is less than 1 % of
       = 0.174 Transfer Coefficient (HTC)
            Heat ν
  k                                                                          external temperature drop than Biot number must be
                     In present study, Reynolds number was fixed as            less than 0.01. Clean tube surface temperature was fixed
            the value of Re= 4400 based on the clean tube diameter             and chosen as Ts= 283 K and free-stream temperature
            (Re from Owen8). For a given fluid and stream velocity,            of air was chosen Ta= 373 K. Typical values4 of deposit
            local external HTC on a cylinder in cross-flow is                  material thermal conductivity (k 1 = 0.2 W/mK,
            dependent only upon angular position θ and external                k2= 2 W/mK) were used for calculation. In non-uniform
            diameter df. For Reynolds number (4000-40000), average             thickness, homogenous and non-homogeneous fouling
            Nusselt number reported13 for airflow across the cylinder          shapes (Fig. 1), non-uniform thickness and homogenous
            is given as                                                        fouling shapes (Fig. 1a) had thermal conductivity of
                 Nu =0.174×Re0.618                                   ...(5)    deposition as 0.2 W/mK. In this fouling shape,
                                                                               disposition of deposit was changed. First deposit
                     Since the distribution of local HTC is well               formation was modelled, as it is thinner on front
             defined in this range, HTC on the surface of foulant hf,          stagnation point than the rear stagnation point of the
             can be related to HTC on the clean tube h c as                    cylinder (centre tube of first row). Thinner section of
                                                                               deposit was moved (0-270°) gradually (possible
                                                                               formation of deposit of bottom and upper tube of tube
                                                                               bundle first row).
                                                                    ...(6)              Secondly, deposit thermal conductivity variation
                                                                               is through the thickness of deposit. For this, two different
                                                                               deposit materials were formed as radially (Fig. 1b) and
530                                          J SCI IND RES VOL 66 JULY 2007

                                       TS = 283 K
                                                                                Deposition on tube

                                 Flow                   dclean =16 mm      k1
                                 Ta=373 K

                                                      a) Homogeneous fouling
                                                    Fouling Area 1
                                                    Fouling Area 2

           Flow                          k1 k2                    Flow           k1                   k2

                  b) Radial non-homogeneous fouling (k1= 0,2            c) Circumferential non-homogeneous fouling
                             W/mK, k2= 2 W/mK)                                 (k1= 0,2 W/mK, k2= 2 W/mK)

                                   Fig. 1 — Fouling shapes and boundary conditions

circumferentially (Fig. 1c) around the cylinder. Fouling
shapes were created by dividing the whole fouling cross
section into sub-domain with different thermal
conductivities. Radial variation effect of thermal
conductivity was calculated. Small k material on the
clean tube was located adjacent tube with a large k
material replaced on it. Adjacent tube origin was moved
from left to right and temperature contours and heat
transfer rates were obtained. Circumferential variation
effect of thermal conductivity is considered by dividing
the foulant cross-sectional area. A region of small k was
located front stagnation point of the cylinder and this
area was increased. Selected geometries were
investigated and heat transfer rates and temperature
contours were predicated for different cases.
         Thirdly, non-uniform and non-homogeneous
cases (radial and circumferential) considered obtaining
effect of eccentricity with fixing the area of small k
material on the clean tube.
         HTC was matched on the grid point using
ANSYS software program. Modelled grids (Fig. 2) used
2500 as number of element for the calculation.                                    Fig. 2 — Grids for fouling shapes

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