Page 18 - Kỷ yếu hội thảo quốc tế: Ứng dụng công nghệ mới trong công trình xanh - lần thứ 9 (ATiGB 2024)
P. 18

th
               HỘI THẢO QUỐC TẾ ATiGB LẦN THỨ CHÍN - The 9  ATiGB 2024                                   9

                             Q +  Q                                         P
                            Q =  h  c   , W                   (6)   f =      c                                            (13)
                                                                             2 L
                                2                                    c  1   .V .
                  According  to  heat  transfer  theory,  ratio  between   2  c  c  D
               actual  and  maximum  achievable  heat  transfer  rates   Here,  ΔPc is pressure drop of the cold fluid flow
               represents effectiveness, which is calculated as:   (Pa),  Vc  is  fluid  velocity  at  inlet of  the  annulus  side

                          Q                                   (m/s)  and  ρc  is  fluid  density  of  the  cold  fluid  flow
                        =                                   (7)   (kg/m ).
                                                                   3
                         Q max
                                                                 Reynolds  numbers  of  the  hot  fluid  flow  and  the
                  Here,  Q  =  (m.C  ) (T  −  T  )            cold fluid flow are defined as
                         max     p  min  h,in  c,in
                                                                            .V .d
                  in  which  (mCp)min  indicates  the  smaller  value   Re =  h  h  3                                      (14)
               between mcCp,c and mhCp,h.                              h     h
                  And, mean convective heat transfer coefficients of        .V .D
               the  hot  fluid  flow  and  the  cold  fluid  flow  can  be   Re =  c  c                                       (15)
                                                                       c
               obtained as                                                   c
                                                                 Here,  μh  and  μc  are  dynamic  viscosity  of  the  hot
                                 q
                       =         w         , W/m .K           (8)   fluid flow and the cold fluid flow (kg/m.s).
                                                 2
                       h
                                       −
                          0,5 (T h,in  +  T h,out ) T w          C. Boundary conditions
                                 q                               Hot  fluid  enters  the  inner  pipe  at  constant
                       =         w         , W/m .K         (9)
                                                 2
                       c                                      temperature of 333K and velocity of
                          T −  0,5 (T  +  T  )
                           w      c,in  c,out                            Re .
                  Here,  T  is  mean  temperature  of  the  inner  pipe   V =  h  h  , m/s                                        (16)
                                                                      h
                        w                                                  h .d 3
               wall  (K),  and  q  is  mean  thermal  flux  on  the  inner   Cold  fluid  enters  the  annulus  with  constant  flow
                            w
                            2
               pipe wall (W/m ).                              rate  of  0.1  kg/s  and  temperature  of  293K  in  the
                  Thus, mean Nusselt numbers of the hot fluid flow   opposite direction.
               and the cold fluid flow are                       Static  pressure  is  assumed  to  be  atmospheric  at
                             .d                              both  outlets.  Moreover,  mass  balance  is  used.  Same
                     Nu =   h  3                                         (10)   turbulent intensity and hydraulic diameter as those at
                        h    h                               the  inlets  were  used  as  turbulence  conditions  at  the
                             .D                              outlets.
                     Nu =   c                             (11)   Non-slip condition for the fluid flow applies to all
                            
                        c
                             c
                                                              walls  of  the  heat  exchanger.  Moreover,  thermal
                  Here,  d3  is  inner  diameter  of  the  inner  pipe  (m),   insulation was assumed for the outer pipe of the heat
                D is  hydraulic  diameter  of  the  annulus  (m);  λh,  λc  is   exchanger.
               thermal conductivity of the hot fluid flow and the cold   D. Computational Mesh
               fluid flow (W/m.K).
                                                                 Structured  finite  volume  meshs  with  a  high
                  Friction  coefficient  is  evaluated  using  pressure   resolution of case 1, 2 and 3 are created.
               difference at the inlet and outlet on each side. Friction   A  mesh  sensitivity  study  is  conducted  both
               coefficient of the hot fluid flow is obtained as
                                                              quantitatively  and  qualitatively.  Fig.  3  shows  the
                             P                               variation in Th, Tc with different mesh resolutions. As
                     f =  1   h 2 L                                (12)   can  be  seen,  with  the  resolution  larger  than  792600,
                      h
                              h
                         2  h .V . d                         766320, 825995 elements (corresponding to cases 1, 2,
                                 3
                                                              3), the temperature at outlet of the hot fluid flow and
                  Here,  ΔPh  is  pressure  drop  of  the  hot  fluid  flow   the cold fluid flow is unchanged. This mesh resolution
               (Pa),  Vh  is  fluid  velocity  at  inlet  of  the  inner  pipe   is  considered  the  most  optimal  and  hence  employed
               (m/s), L is pipe length (m) and ρh is fluid density of   for our simulations.
                                  3
               the hot fluid flow (kg/m ).
                  Similarly, friction coefficient of the cold fluid flow
               is obtained as


                                                                                   ISBN: 978-604-80-9779-0
   13   14   15   16   17   18   19   20   21   22   23