Zone and surface energy balances in Models

As with other simulation tools ESP-r resolves the energy balance within the model at each timestep of an assessment. Various subsystems such as radiant exchanges are evaluated in order to establish the energy balance.

Energy balances are maintained at the air volume of each thermal zone as well as at the room-face of each surface and the other-face of each surface and at nodes within system components.

Zone energy balance

The energy balance at each thermal zone air node usually resolves to a fraction of a Watt/hr over the assessment period and includes the following heat flux paths (and ):

Infiltration (air exchange with outside) via scheduled flows or flow networks.

Ventilation (air exchange with other thermal zones) via scheduled flows or flow networks.

Casual gains (sensible convective gains) reported for each defined casual gain type.

Thermal bridges (currently via length * psi value(s) * delta T) if linear thermal bridges defined in a zone.

Heat storage @ air (accounting for difference in starting and finishing air temperature).

Convection at surfaces separately reported for opaque and transparent surfaces facing the outside as well as opaque and transparent surfaces not facing the outside. Convection evaluated at each timestep for each surface based on current heat transfer regime directives.

Convection portion of plant (if defined for the zone)

Surface energy balance

The energy balance at each surface is illustrated by the following two reports. The first is for a partition between two thermal zones and the second is at glazing at the facade. The abbreviations are decoded after the listings.


 Causal energy breakdown (Whrs) for pt_general ( 1) in manager ( 1)
 Surface is opaque MLC, area= 13.50m^2 & connects to surface  2 in zone  2
                                Facing manager
                               Gain       Loss
 Conductive flux             7194.88    -6531.31
 Convective flux             3561.02   -17378.07
 Longwave rad inside         1537.74    -9407.29
 Longwave rad buildings          --         --
 Longwave rad sky                --         --
 Longwave rad ground             --         --
 Shortwave radiation        15373.45        0.00
 Casual Occupt               2542.15        0.00
 Casual Lights               1961.09        0.00
 Casual Equipt               1210.56        0.00
 Casual --                      0.00        0.00
 Controled casual gn            0.00        0.00
 Heat stored                 3012.29    -3076.54
 Plant                          0.00        0.00
 Totals                     36393.17   -36393.21

 Causal energy breakdown (Whrs) for glazing (10) in manager ( 1)
 Surface is trnsp. MLC, area=  5.32m^2 & connects to the outside
                                Facing manager           Facing outside
                               Gain       Loss          Gain       Loss
 Conductive flux              848.39  -124195.24   218313.86       -4.19
 Convective flux            32780.88    -3645.09       53.60  -132355.03
 Longwave rad inside        80672.84     -952.77         --          --
 Longwave rad buildings          --         --       2598.65    -5448.58
 Longwave rad sky                --         --          0.00  -103063.62
 Longwave rad ground             --         --       6328.35    -5220.84
 Shortwave radiation        12494.46        0.00    18886.98        0.00
 Casual Occupt                913.73        0.00         --          --
 Casual Lights                704.88        0.00         --          --
 Casual Equipt                435.11        0.00         --          --
 Casual --                      0.00        0.00         --          --
 Controled casual gn            0.00        0.00         --          --
 Heat stored                 2455.38    -2512.53     2770.65    -2860.02
 Plant                          0.00        0.00        0.00        0.00
 Totals                    131305.70  -131305.62   248952.09  -248952.30

The flux paths at surfaces include the following:

Convection at each face of the surface based on the current heat transfer regime.

Conduction at a point half-way between the surface node and the first node of the outer and inner layers.

Depending on the boundary condition the longwave radiant exchange at the face and if outside separated by longwave to other building faces, the sky and the ground.

Shortwave radiation absorbed at each face includes both direct and diffuse components.

The radiant portion of zone casual gains is tracked by the type of gain.

Heat storage takes into account the change in temperature at the start and end.

The radiant portion of plant systems is reported if defined.

Air movement contributions

During the solution process the sensible energy impact of air movement is appraised from the mass flows between the zones and ambient conditions as well as the temperature differences (using the last known temperature). If a flow network has been defined it might have iterated to determine the mass flows (which might be dependent on the zone temperatures). If scheduled the flows are imposed.

Solar energy contributions

During the solution process the energy impact of solar radiation is separately resolved. At the outside face of the surface it is based on the current weather data and pre-computed shading patterns (if they exist). At the zone face any pre-computed insolation patterns are imposed on the direct solar radiation prior to iterations of diffuse bounces taking into account the current optical properties of each glazing. Bookkeepping keeps track of solar radiation leaving zones for possible use in adjacent zones at the next timestep.

Sky and ground interactions

Facade interactions with the sky are based on a set of overall view-factors to the ground, sky and other buildings. The current sky temperature is derived from weather data and the radiation exchange is included in the energy balance.

Surfaces in ground contact have a high heat transfer coefficient set by default. Typically the user selects from a list of monthly ground temperature profiles or creates a named profile.

Longwave radiation contributions

During the solution process radiation between surfaces is established via a grey-body approach. If calculated view-factors are available these are used, otherwise an area-emissivity approach is used.

Surface convection contributions

During the solution process convection at surfaces is established via coefficients or correlations directives included in the model description and based on the current temperatures as well as the topology of the surface.

Internal mass contributions

During the solution process internal mass surfaces are treated in exactly the same way as other surfaces associated with the zone. They fully participate in convective, short-wave and long-wave exchanges and the temperature of the layers in these surfaces is resolved in the same way as all other surfaces.

Interactions with environmental controls

During the solution process the energy impact of environmental controls is delivered in the form of an extraction or addition of flux to a specific location. This might be at the air node, a mix of air nodes and surface nodes or to a specific layer within a specific surfaces.

Temperatures derived from the energy balances

After the solution has converged the following temperatures are available for use in other calculation or for recording and user exploration:

Zone dry bulb temperature, operative temperature, resultant temperature, mean radiant temperature (at the zone air node or at specific MRT sensors).

At the inside face and outside face and at intermediate nodes within surfaces in the model.

System components also include energy balances and depending on the descritization of the plant components this many include temperatures of interest to users.